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http://clumath343s15s2.wikidot.com/clu-linear-algebra-ch-1-s1-examples | Clu Linear Algebra Ch 1 S1 Examples
## Example Question
Solve each system by using elementary row operations on the equations or on the augmented matrix
(1)
\begin{matrix} x_1+5(x_2)=7 \end{matrix}
(2)
\begin{matrix} -2(x_1)-7(x_2)=-5 \end{matrix}
The matrix
(3)
\begin{matrix} 1 & 5 & | & 7 \\ -2 & -7 & | & -5 \\ \end{matrix}
The matrix row reduced to
(4)
\begin{matrix} 1 & 0 & | & -8 \\ 0 & 1 & | & 3 \\ \end{matrix}
(5)
\begin{matrix} x_1+0(x_2)=-8\\ x_1 =-8 \end{matrix}
(6)
\begin{matrix} 0(x_1)+1(x_2)=3\\ (x_2)=3 \end{matrix}
The Solution is ($x_1$,$x_2$)=($-8$,$3$)
page revision: 0, last edited: 10 Feb 2015 06:51
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License | 2019-02-20T13:49:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.999970555305481, "perplexity": 2201.6212822903635}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247495001.53/warc/CC-MAIN-20190220125916-20190220151916-00374.warc.gz"} |
https://lammps.sandia.gov/doc/fix_filter_corotate.html | # fix filter/corotate command
## Syntax
fix ID group-ID filter/corotate keyword value ...
• ID, group-ID are documented in fix command
• one or more constraint/value pairs are appended
• constraint = b or a or t or m
b values = one or more bond types
a values = one or more angle types
t values = one or more atom types
m value = one or more mass values
## Examples
timestep 8
run_style respa 3 2 8 bond 1 pair 2 kspace 3
fix cor all filter/corotate m 1.0
fix cor all filter/corotate b 4 19 a 3 5 2
## Description
This fix implements a corotational filter for a mollified impulse method. In biomolecular simulations, it allows the usage of larger timesteps for long-range electrostatic interactions. For details, see (Fath).
When using run_style respa for a biomolecular simulation with high-frequency covalent bonds, the outer time-step is restricted to below ~ 4fs due to resonance problems. This fix filters the outer stage of the respa and thus a larger (outer) time-step can be used. Since in large biomolecular simulations the computation of the long-range electrostatic contributions poses a major bottleneck, this can significantly accelerate the simulation.
The filter computes a cluster decomposition of the molecular structure following the criteria indicated by the options a, b, t and m. This process is similar to the approach in fix shake, however, the clusters are not kept constrained. Instead, the position is slightly modified only for the computation of long-range forces. A good cluster decomposition constitutes in building clusters which contain the fastest covalent bonds inside clusters.
If the clusters are chosen suitably, the run_style respa is stable for outer time-steps of at least 8fs.
Restart, fix_modify, output, run start/stop, minimize info:
No information about these fixes is written to binary restart files. None of the fix_modify options are relevant to these fixes. No global or per-atom quantities are stored by these fixes for access by various output commands. No parameter of these fixes can be used with the start/stop keywords of the run command. These fixes are not invoked during energy minimization.
## Restrictions
This fix is part of the USER-MISC package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
Currently, it does not support molecule templates. | 2019-06-27T04:16:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.622175395488739, "perplexity": 5484.382515006534}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000613.45/warc/CC-MAIN-20190627035307-20190627061307-00521.warc.gz"} |
https://datasciencecampus.ons.gov.uk/projects/green-spaces-in-residential-gardens/ | # Green spaces in residential gardens
A United Nations report showed that in 2014 approximately 54% of the population were living in towns and cities, with this figure projected to increase to 70% by the middle of the next century.
Identifying and understanding the features of urban green spaces (such as residential gardens) is therefore becoming of greater importance, given their environmental and emotional benefit.
Current approaches often assume residential gardens are almost exclusively covered by natural vegetation and do not take in to account urban areas such as steps, patios and paths.
We collaborated with Ordnance Survey (OS) to improve the current approach to identifying the proportion of vegetation for urban residential gardens in Great Britain. We used remote sensing and machine learning techniques with high-quality aerial and satellite imagery to test approaches. From the results, a tool able to classify the contents of an image with accuracy – a neural network classifier – was developed.
The initial results obtained using this approach estimate that 62% of garden space in Great Britain is vegetation. Data sampled from Cardiff and Bristol suggest that residential gardens in these areas contain approximately 54% and 45% vegetation respectively.
The methods and results presented in this report are from early research and are provided to assess the performance of the approaches tested. They are not official estimates and should not be interpreted in this way.
## 1. Introduction
In 2014 approximately 54% of the population were living in towns and cities, this figure is projected to increase to 70% by the middle of the next century (United Nations, 2014). Consequently, urban green spaces such as residential gardens are of great environmental and emotional benefit to a population. A recent study has shown that access to green space has a positive impact upon mental health (White and others, 2013). Green spaces absorb more carbon than they return to the atmosphere (Nowak and others, 2002) and reduce air pollution (Nowak, and others, 2006). Impermeable materials that are increasingly used to replace green spaces such as garden paths or patios increase rain water runoff and the likelihood of flooding (Ellis, 2002). Residential gardens also act as wildlife corridors that help animals, birds and insects move between larger green areas supporting diversity and promoting the pollinator populations such as bees and butterflies (Rouquette, 2013 and Baldcock and others, 2015).
With this in mind, it is no surprise that measuring the proportion of vegetation in Great Britain’s residential gardens and tracking changes over time is a vital area of interest to the Office for National Statistics (ONS) and Ordnance Survey (OS). Ordnance Survey, Britain’s National Mapping Agency maintains Private Garden extents across Great Britain as part of its OS MasterMap suite of geospatial data assets. Although useful to define the extent of private gardens – when utilised as a green space or vegetation asset they often lead to an assumption of complete natural surface coverage. This contributes towards a key disadvantage in that it is almost always an overestimate of natural capital as residential gardens will have some urban areas (steps, patios, paths etc.). Ordnance Survey’s Geospatial Content Improvement Programme (GCIP) has the objective to capture or update physical features that reflects construction, demolition or other alterations in the real world. When revised and updated content is available these in-garden structures are accounted for within the private garden geometry. However, additional urban surfaces such as patios, decking and artificial turf remain fully encompassed in the polygon extent.
With the recent advent of readily available and high-quality aerial and satellite imagery much activity has focussed upon identifying features such as water, crops and soil erosion using remote sensing. This report details the work undertaken at the Data Science Campus in collaboration with Ordnance Survey (OS) to use remote sensing and machine learning techniques to improve upon the current approach used within the ONS to identify the proportion of green space for urban residential gardens in Great Britain.
Several “off the shelf” and bespoke techniques developed by both the Campus and OS are used to detect the presence of vegetation. They are assessed both qualitatively on a library of 10 representative gardens and quantitatively on 100 manually labelled gardens selected randomly from Cardiff and Bristol. The sensitivity of these algorithms to shadows within the imagery is discussed and techniques applied to reduce its impact. Finally, a neural network is trained on the manually labelled library, this network classifies areas within a residential garden to one of following categories:
• vegetation
Results are encouraging and suggest that the neural network can accurately classify areas of vegetation and is less susceptible to the effects of shadows when compared with the other test algorithms.
## 2. Data
The data used during this project is split into two groups
• garden parcel polygons
• aerial imagery
### Garden parcel polygons
Private residential garden parcels have been derived through the geospatial analyses of multiple Ordnance Survey (OS) datasets licensed through the Public Sector Mapping Agreement (PSMA). This analyses involved using PSMA data to derive inferred property extents. These extents were used to collect and aggregate garden geometries together on a property-by-property basis within built-up-areas to form an indicative, functional garden extent. These extents do not define legal property ownership nor act as registered title extents. Datasets used included OS AddressBase Plus and OS MasterMap Topography Layer.
OS AddressBase Plus is a vector address point dataset for Great Britain that contains current properties and addresses sourced from local authorities identified using a Unique Property Reference Number (UPRN), matched to a series of third-party datasets including:
OS MasterMap Topography Layer is a vector dataset providing individual real-world topographic features in Great Britain represented by point, linestring, and polygon geometries, captured at 1:1250, 1:2500 and 1:10 000 scales in urban, rural and mountain or moorland areas respectively.
#### Figure 1: Polygon defining a garden boundary
Garden polygons for both Cardiff and Bristol were supplied in GeoJSON format, where each garden has a unique Topographic Identifier (TOID). The polygon was defined by a series of longitude and latitude co-ordinates as shown in Figure 1. 79,643 polygons were provided for Cardiff urban residential gardens and 209,205 were provided for Bristol.
### Aerial Imagery
JPEG format aerial imagery was provided by Bluesky International Ltd and Getmapping Plc via the Public-Sector Mapping Agreement (PSMA). RGB images were provided at 12.5, 25 and 50 centimetre (cm) resolution and colour infra-red provided at 50 cm resolution. The geographical coverage of the images is shown in Figure 2.
#### Figure 2: Image coverage, colour scale represents time period from 2006 (red) to 2017 (blue)
The 12.5 cm RGB images covered October 2005 to September 2017. 133,768 images (23.4 terabytes) were provided each covering a 1 kilometre x 1 kilometre (km) window. Each image consisted of 8,000 by 8,000 pixels. An example 12.5 cm RGB image is given in Figure 3.
The 25 cm RGB images covered April 2006 to October 2017. 244,712 images (10.6 terabytes) were provided each covering a 1 km x 1 km window. Each image consisted of 4,000 by 4,000 pixels.
The 50 cm Colour-infrared (CIR) images covered April 2006 to October 2017. 244,738 images (2.7 terabytes) were provided each covering a 1 km x 1 km window. Each image consisted of 2,000 by 2,000 pixels. An example CIR image is given in Figure 4.
#### Figure 4: Example 50 cm CIR image
A standard RGB spectral representation is used, with the infrared channel mapped to red, the red channel mapped to green and the green channel mapped to blue
File size prohibited storing the imagery as a single file, instead imagery was stored as 1 km x 1 km fixed resolution images based on the OSGB36 datum (an ellipsoid used to approximate the curvature of the earth around GB, with a grid overlaid upon it). For ease of access the images are stored in a hierarchy, for example the 1 km x 1 km cell covering Trafalgar Square (TQ 299 804) is stored as TQ/TQ28/TQ2980.jpg. The least significant digits of the grid point are then used to determine the exact fraction across the image (east, then north). This allows the tiles relating to individual gardens to be quickly and simply retrieved without adding additional platform load.
### Data Issues
Apart from the obvious challenges associated with storing and processing over 600,000 images relating to nearly 37 terabytes, several other issues were encountered with the data during the course of the project. Visual inspection of the labelled test dataset showed that three of the one hundred images were corrupted or inaccurate to some degree. Figure 5 shows an instance where the garden polygon spans two adjacent gardens belonging to separate properties.
#### Figure 5: Garden polygon spanning several gardens
First image shows two adjacent properties, the second image highlights the area within the garden polygon, this area clearly spans two gardens.
In another image (Figure 6), the garden polygon does not align correctly with the image with sections of the property being included within the polygon and areas of the garden excluded. One image (Figure 7) was found to be corrupted, where image tiles appear to have been incorrectly merged together. In all these cases, the images were removed from the training data and replacement images randomly selected.
#### Figure 7: Corrupted image tile
Although not data issues in the strictest sense, there were features within the images that increased the complexity of the classification task. The RGB and CIR images did not cover consistent resolutions, in this case the IR images were upsampled from 50 cm to 12.5 cm. As aerial imagery was captured between April and October, different ground conditions caused discrepancies between areas when the colour profile was cast to CIR. This rendered approaches that require the colour profile to be compared against the infrared channel more sensitive to temporal changes and therefore unfeasible. Finally, as the imagery was taken by aircraft rather than satellites, complete coverage of an area may take several years hence images are likely to be taken at different times of the day and year, they are also subject to the effect of seasonality and changing weather conditions. For instance, images taken late afternoon on a sunny day were more likely to contain shadow, whilst vegetation in gardens suffering from drought conditions are far less likely to be lush green in colour.
## 3. Vegetation detection
There are many approaches that may be used to detect vegetation in aerial and satellite imagery. These include:
• Red, Green and Blue (RGB) indices including Visual Normalised Difference Vegetation Index (vNDVI)
Green Leaf Index (GLI) and Visual Atmospheric Resistance Index (VARI)
• Transformed colour spaces such as Hue, Saturation, Value (HSV) and CEILAB
• Spectral methods such as Normalized Difference Vegetation Index (NDVI)
A comprehensive discussion may be found in Vina and others, 2011 and Xue and others, 2017. The following sections introduce the RGB indices and transformed colour space methods that were investigated in this project.
### Visual Normalised Difference Vegetation Index (vNDVI)
The vDVI algorithm is based upon the Normalised Green Red Difference Index (Rouse and others, 1974). It uses pixels expressed using the RGB spectral channels as shown in Figure 8.
#### Figure 8: RGB colour palette
The red (R) and green (G) channels of an image are used to calculate an index value, using the following equation,
$$vNDVI=\frac{(G-R)}{(G+R)}\$$
The numerator differentiates between plants and soil whilst the denominator normalises for light intensity variations between images. The index ranges from -1 to 1. Individual pixels with values greater than 0 are classified as representing vegetation. vNDVI is a robust and efficient algorithm as it considers only two of the spectral channels however it is sensitive to atmospheric effects, specifically cloud cover.
### Green Leaf Index (GLI)
As with vNDVI the GLI algorithm is based upon the RGB colour system, it attempts to distinguish living plants from soil and other matter be identifying the green colour of a healthy plant (Louhaichi, 2001). However, unlike vNDVI, GLI also uses the blue (B) channel,
$$GLI=\frac{(2 ×G-R-B)}{(2 ×G+R+B)}$$
As with vNDVI, the GLI index ranges from -1 to 1, with negative values representing soil or non-living material and positive values represent living plant material. The green leaf index is less susceptible to atmospheric effects, however as it uses all three spectral channels it is less efficient when compared to vNDVI.
### Visual Atmospheric Resistance Index (VARI)
The VARI algorithm again uses the RGB colour system to estimate the fraction of vegetation. Due to its insensitivity to atmospheric effects, it is particularly suited to satellite imagery (Gitelson and others, 2002). It is calculated using the following equation:
$$VARI=\frac{(G-R)}{(G+R-B)}$$
As with the other two RGB based approaches, VARI ranges from -1 to 1. With positive values indicating vegetation.
### Hue, Saturation, Value (HSV)
Unlike the RGB spectral channels where red, green and blue are mixed in an additive way to form a final colour, in HSV colours of each hue (H) are arranged in a radial slice, around a central axis of neutral colours, ranging from black at the bottom to white at the top (see Figure 9). Saturation (S) represents the amount of grey in the colour, with large proportions of grey producing a faded effect. Value (V) works with saturation and controls the brightness of the colour.
#### Figure 9: HSV colour palette
The main benefit of HSV compared to RGB spectral channels is that the colour information for a given pixel is separated from the image intensity, whereas in RGB, colour and intensity are specified by the red, green and blue values. For the purposes of this study a pixel was classified as being vegetation if its hue fell in the range between 30 and 80. Both saturation and value may assume any value in their respective ranges.
### CIELAB (Lab)
The CEILAB colour space expresses colour as three numerical values L represents lightness whilst a* and b* represent the green to red and blue to yellow colour components respectively (see Figure 10). Lab was designed to be perceptually similar to human colour vision where the same amount of numerical change in the L, a* and b* channels correspond to approximately the same amount of visually perceived change.
#### Figure 10: Lab colour palette
This study applies the threshold values determined in previous work at the Data Science Campus. In this work, the labelled images in the Mapillary Vistas dataset were converted to the Lab colour system. The a* and b* thresholds were then optimised using Bayesian parameter optimisation to maximise the classification of vegetation and urban pixels. The optimal parameters were found to be:
a* channel optimised Lab(a*)
$$-31 ≤a* ≤-11$$
a* and b* channels optimised Lab(a*b*)
$$-31 ≤a* ≤-6$$
$$5 ≤b* ≤57$$
## 4. Unlabelled test image library
There is a sizeable amount of literature relating to labelled datasets within street-level imagery, including Cityscapes (Cordts and others, 2016), ADEK20K (Zhou and others, 2017) and Mapilary Vistas (Scharr, 2016). There are also many databases containing general labelled imagery, such as the 15 million high resolution images of ImageNet. Unfortunately, far less work has focussed upon generating databases of labelled aerial imagery identifying areas of vegetation, soil, water and so on. This makes it particularly challenging to identify a comprehensive library of aerial images that can be used to quantitatively assess the performance of the approaches identified in the preceding section.
As an initial step, a more qualitative approach was taken. A library of 10 test images were used to empirically investigate the relative performance of each test algorithm. The test library is shown in Figure 11, each image was selected to capture the broad spectrum of garden designs and the seasons upon which the aerial imagery may have been taken, this included:
• garden type (traditional / patio)
• features (ponds, paths, flower beds, trees)
• formality (structured / wild)
• seasonality
#### Figure 11: The unlabelled test image library
Each test algorithm was applied to the 10 unlabelled test images. In each case the proportion of vegetation identified by each approach was compared against the corresponding test image to give a qualitative view of algorithm performance. A review of all the results is given in the appendix of this report. A selection of the more noteworthy cases is discussed in the next paragraph.
Test image one (Figure 12) explored the ability to identify vegetation in an image of a more traditional garden. All approaches perform well and can accurately identify areas of vegetation. All three of the RGB based algorithms along with the HSV approach are in broad agreement with vegetation coverage ranging from 84-88%. Both Lab approaches have lower values of 73% and 79% for the Lab(a*) and Lab(a*b*) respectively. On closer inspection of the Lab approaches it is evident that Lab(a*) misclassifies some areas of grass at the bottom and top left regions of the image.
#### Figure 12: Test image 1 results
Pixels identified as vegetation are coloured green
As test image three (Figure 13) contains very limited amounts of vegetation, it can be used to investigate false positive classifications. The RGB algorithms all perform particularly poorly in this instance with the GLI algorithm indicating that the image consists of almost 64% vegetation, this is a clear overestimate. Although not as poor as the RGB algorithms, misclassification is evident in the HSV result, particularly in the lower centre of the image. Conversely both Lab based algorithms perform well suggesting that the image contains only 2.5% and 3.3% vegetation for Lab(a*) and Lab(a*b*) respectively, these figures more accurately reflect the true reality of the image.
#### Figure 13: Test image 3 results
Pixels identified as vegetation are coloured green
Test image eight (Figure 14) shows a parched garden in which the green grass has turned to predominantly yellow and browner shades. The GLI approach performs particularly poorly here classifying 92% of the image as being vegetation. The performance of all the remaining algorithms are broadly comparable giving vegetation coverage of between 14% to 16%, however Lab(a*) struggles to identify the tree foliage at the lower right and centre of the image.
#### Figure 14: Test image 8 results
Pixels identified as vegetation are coloured green
Although not definitive, this study illustrates that no single approach performs well across all images in the unlabelled test library. Some approaches perform poorly in images containing patios whilst others struggle to differentiate between areas of water and vegetation.
Although by no means perfect, the performance of Lab(a*b*) and HSV appear to be less sensitive across the range of test images. It is interesting to note that both Lab(a*b*) and HSV apply thresholds to the raw colour channels of the image, rather than thresholding an index calculated from the colour channels as is the case with the remaining approaches.
## 5. Application to Bristol and Cardiff
The HSV threshold was applied to a selection of real-world images. It appears to perform well, identifying most regions covered in vegetation in Figure 15 – a wider view over Bristol.
#### Figure 15: Application of HSV approach to Bristol
Figure 16 shows a larger scale view of three randomly selected gardens in both Bristol and Cardiff. Although the HSV approach distinguishes between vegetation and urban areas, the performance does not appear to be as impressive as that observed in the higher-level image. There are notable areas of misclassification in all three images; sections of the driveway and the shed are misclassified as being vegetation in the first and second images respectively whilst large areas of vegetation in shadow are missed in the third image. It is suggested that these inaccuracies may be compounded by the lower resolution of the aerial imagery when compared to the images contained within the unlabelled test image library.
An obvious and significant drawback of the images investigated so far is the lack of labelling. Without this ground truth it is impossible to accurately compare performance across approaches or to recommend a preferred approach with any degree of confidence.
This limitation is addressed in the following section.
## 6. Labelled test image library
Up to this point the test algorithms have been assessed qualitatively on unlabelled test images. Although this approach has increased understanding of algorithm performance its does not allow an objective decision to be made regarding which algorithm gives the optimal performance. To address this a test library of labelled images was created.
100, 12.5 centimetre resolution aerial images covering gardens in Bristol and Cardiff were randomly sampled and independently reviewed by four individuals. Everyone was randomly assigned 75 images in such a way that each image was reviewed by three people. Each pixel was manually classified into one of the following four categories:
• green – vegetation
• blue – vegetation in shade
• red – urban in shade
• unclassified – urban
Two shaded categories were introduced to explore the relationship between shadow and predictive power and to facilitate the development of supervised learning techniques (see Vegetation detection using supervised machine learning).
To increase accuracy, voting logic was applied, with the overall classification of each pixel taken as the most common classification from the individual reviews (ties were randomly assigned a classification). In this way erroneous classifications were more likely to be “out-voted” by the other two reviews. An agreement matrix was used to illustrate the agreement rate between reviewers and therefore the confidence in the final classifications. If the agreement rate dropped below 80% for any image arbitration was applied and the image was reviewed by a fourth person and the voting logic reapplied. To overcome temporal errors the order of the images was randomised for each reviewer.
The results of the manual review for two images taken from the labelled test image library are given below. For the first image, the agreement matrix indicates very strong alignment across reviewers, with agreement in classification in at least 84% of all pixels within the image. This removed the need for arbitration in this instance (see Table 1). This result is impressive when one considers the complexity of the image being reviewed and demonstrates the power of this approach.
#### Table 1: Agreement matrix for test image 1
Review 1 3 4 1 85% 84% 3 85% 87% 4 84% 87%
Figure 17 shows the results of the individual reviews and the resulting classified image after voting logic has been applied. The complexity of the classification task is self-evident in the final image. Note that this image has not been reviewed by the second reviewer.
#### Figure 17: Results of manual review for test image 1
Turning to the second image, the values within the agreement matrix are lower than those in the preceding example (see Table 2). The result is interesting when one considers the more uniform nature of the image.
#### Table 2: Agreement matrix for test image 2
Review 1 2 3 4 1 84% 56% 82% 2 84% 57% 86% 3 56% 57% 54% 4 82% 86% 54%
As the values in the agreement matrix dropped below 75% the image went through arbitration and was reviewed by the fourth person. The results of this and the final post voting logic classification are given in Figure 18. On closer inspection of the final image, a checker board effect is noted in the top right area of the image. This is caused by classification ties and a random choice being made. It is believed that this effect could be reduced by applying a suitable smoothing filter, however as its prominence is slight this was deemed unnecessary.
#### Application of test approaches to labelled test image library
All six test algorithms were applied to the labelled test image library. In each case the classification error was calculated as:
$$\small classification \space error = |labelled \space vegetation \space proportion \space – \space observed \space vegetation \space proportion| \$$
Where “labelled vegetation proportion” is the proportion of vegetation in the labelled dataset and “observed vegetation proportion” is the proportion of vegetation identified by the test algorithm.
A pixel is deemed vegetation if it is either obscured by shadow (coloured blue) or not (coloured green). The results are shown in Table 3, Lab(a*b*) provides the best approach with an average classification error of 16.3% with HSV in second place with an error of 20.7%.
The comparable high performance in both HSV and Lab(a*b*) approaches are in general agreement with those of the qualitative assessment on the 10-image unlabelled test library.
#### Table 3: Classification error across all 100 labelled images, sorted in ascending classification error
Average StdDev Lab(a*b*) 16.3% 14.8% HSV 20.7% 18.4% vNDVI 23.2% 17.7% VARI 23.2% 17.7% Lab(a*) 31.3% 19.2% GLI 39.5% 27.9% Naive 60.2% 24.0%
The Naïve approach assumes all areas falling within the residential garden polygon are vegetation.
An interesting finding is noted if the results are broken down by region. Lab(a*b*) performs relatively poorly when applied to Bristol urban residential gardens (coming fifth out of the six approaches) whilst performing exceptionally well in Cardiff urban residential gardens. The HSV algorithm performs broadly well across both regions.
#### Table 4: Classification error across all 100 labelled images, broken down by Bristol and Cardiff, sorted in ascending classification error
##### Bristol
Average StdDev HSV 13.5% 14.6% vNDVI 15.4% 12.6% VARI 15.4% 12.6% GLI 19.1% 13.5% Lab(a*b*) 22.4% 16.7% Lab(a*) 34.2% 19.9% Naive 57.9% 24.6%
##### Cardiff
Average StdDev Lab(a*b*) 10.1% 9.4% HSV 28.0% 19.2% Lab(a*) 28.5% 18.1% vNDVI 30.9% 18.8% VARI 30.9% 18.8% GLI 59.8% 23.4% Naive 62.5% 23.4%
The Naïve approach assumes all area falling within the garden polygon is vegetation
This difference in performance of Lab(a*b*) across both regions may be caused by a sensitivity to shadow. Across the labelled test images the average proportion of vegetation covered by shadow was 15% in Bristol and 7% in Cardiff. The images where Lab(a*b*) performs poorly are those images that are subject to the highest proportion of shadow. Figure 19 and Figure 20 show the relationship between classification error and proportion of shadow (pixels classified as either red or blue) for HSV and Lab(a*b*) for all images in the training and test datasets. For Bristol gardens where shadow is more evident, the R-squared values are 0.84 and 0.89 for HSV and Lab(a*b*) respectively. Turning to Cardiff, classification again increases with increasing shadow for Lab(a*b*) with an R-squared of 0.51, however error decreases for HSV with an R-squared of -0.22.
In both cases Lab(a*b*) seems to be more sensitive to shadow, this may be explained by the fact that the Lab approaches were calibrated using street level imagery where the shadows would be less prominent when compared to the aerial imagery used in this study.
## 7. Vegetation detection using infra-red spectral bands
Light from the sun in the form of electromagnetic radiation includes wavelengths that are both visible (red, green and blue spectral channels) and invisible (ultra-violet and infrared channels). As well as visible light, aerial imagery can detect invisible light from the infrared part of the spectrum with the shortest wavelengths, termed the Near Infrared (NIR). When Near Infra-Red (NIR) light (Figure 21) hits organic matter containing chlorophyll the red part of the colour spectrum is absorbed and the NIR part is reflected. Hence the relationship between the red and NIR channels can be used to determine if a pixel corresponds to organic matter (Rouse and others, 1974).
#### Figure 21: Electromagnetic spectrum highlighting the visible and Near infra-red regions
The NIR imagery used for this project was provided as 50 centimetre resolution colour infra-red images consisting of NIR, red and green channels. Each image tile covered the same geographic area as the 12.5 cm resolution RGB images. The NIR channel was extracted and interpolated to 12.5 cm resolution and combined with the RGB images to produce 12.5 cm resolution four channel NIR, R, G, B images.
#### NDVI
The Normalised Difference Vegetation Index (NDVI) calculates the normalised difference between the red and infrared bands for quantitative and standardised measurement of vegetation presence and health (Deering and others, 1975). Healthy vegetation has a high reflectance of Near-Infrared wavelengths and greater absorption of red wavelengths due to a greater chlorophyll composition (see Figure 22).
The Near-Infrared (NIR) and red (R) spectral channels of an image are used to calculate an index value, using the following equation,
$$NDVI=\frac{(NIR-R)}{(NIR+R)}$$
The index ranges from -1 to 1. In this study, individual pixels with a value greater than 0 are classified as vegetation due to their higher reflectance of Near-Infrared. The closer to 1 the healthier the vegetation and greatest density of green leaves. vNDVI, in a similar manner to NDVI, is also sensitive to atmospheric effects, specifically cloud cover and should be atmospherically corrected when used in studies analysing change over time.
#### Figure 22: Reflection and absorption of wavelengths in healthy/unhealthy vegetation
The results of applying NDVI to the 100 labelled images are compared against Lab(a*b*) and HSV in Table 5. The use of the infra-red band in the NDVI approach appears to offer slight improvement over the dual threshold Lab approach (classification error of 15.6% compared to 16.3%), however this comes with a reduction in robustness indicated by the standard deviation of classification error.
#### Table 5: Classification error across all 100 labelled images for NDVI, Lab(a*b*) and HSV, sorted in ascending classification error
Average StdDev NDVI 15.6% 15.5% Lab(a*b*) 16.3% 14.8% HSV 20.7% 18.4%
If the results are broken down by region (Table 6), NDVI performs exceptionally well in Cardiff (where only 7% of the images are covered in shadow, but relatively poorly in Bristol with its greater proportion of shadow (15%).
#### Table 6: Classification error across all 100 labelled images for NDVI, Lab(a*b*) and HSV, broken down by Bristol and Cardiff and sorted in ascending classification error
##### Bristol
Average StdDev HSV 13.5% 14.6% Lab(a*b*) 22.4% 16.7% NDVI 24.5% 16.8%
##### Cardiff
Average StdDev NDVI 6.8% 6.6% Lab(a*b*) 10.1% 9.4% HSV 28.0% 19.2%
Further evidence of the sensitivity of NDVI to shadow can be seen in Figure 23. Here it can be seen that classification error increases with increasing proportion of shadow in the labelled images for both Bristol and Cardiff.
#### Figure 23: Relationship between classification error and shadow for NDVI (Bristol and Cardiff gardens).
This result and similar results with HSV (Figure 19) and Lab(a*b*) (Figure 20) illustrate the sensitivity of the solutions investigated so far to the effects of shadows. It is clearly unavoidable that aerial imagery will be subject to differing amounts of shadow as images may be taken at different times of the year, times of the day or on days where the weather conditions vary considerably. It follows that any approach used to extract information directly from such images should be as insensitive as possible to the effect of shadow. An approach to achieve this using supervised machine learning is discussed in the following section.
## 8. Vegetation detection using supervised machine learning
The use of machine learning to classify remote imagery is an ongoing area of interest. Generally, approaches focus upon either unsupervised learning where algorithms such as autoencoders are used to learn a set of representation directly from the data (Vincent and others, 2008, Firat and others, 2014) or by applying pre-trained supervised learning techniques such as Convolutional Neural Networks (CNN) to classify each image into a unique category such as buildings, tennis courts, harbours and so on (Marmanis and others, 2016).
Armed with a labelled image library, a supervised machine learning classifier was trained to specifically classify each pixel into one of the three labelled classes. The core inputs to the classifier included the standard RGB spectral channel values that describe the pixels. These inputs were further supplemented by firstly, a number of principal component-based features that specifically reduce the presence of shadows and secondly, an infra-red feature that can be used to identify the presence of chlorophyll. An additional classifier that uses the near infra-red spectral channel is also discussed.
### Principal component-based features
Principal component analysis (PCA), is an established technique for reducing the dimensionality of multiple spectral channels (JARS, 1993). More recently PCA has been used to remove shadows from surveillance images (Shin and others, 2000). Its application here is best explained by example. The image in Figure 24 shows a garden represented by the standard RGB colour channels. The building in the centre of the image projects a large shadow from its northern edge. If PCA is used to reduce the three channels to a single channel the resulting image may be shown monochromatically (second image of Figure 24), however the shadow is still present as it has been captured by the single principal component. However, if the three channels are reduced to two principal components, the first component will correspond to the strongest source of contrast within the image, which although not guaranteed, is most likely to relate to shadow. The stronger component can then be discarded, and the second weaker component represented as a monochromatic image (third image of Figure 24). In this instance is can be seen that the intensity of the shadow has diminished significantly.
#### Figure 24: Principal component analysis used to reduce an RGB image to a single monochromatic channel
This technique is developed further by taking comparable channels from the RGB, HSV and Lab spectral channels, extracting the first four principal components to remove the linear relationships between similar spectral channels and discarding the first component that contains shadow elements.
Figure 25 shows this approach applied to a sample garden. In the second image the channels that relate to image brightness are used, specifically the three channels from RGB, the value (V) channel from HSV and the lightness (L) channel from Lab. In the third image the colour related channels are used, the three channels from RGB, the hue (H) channel from HSV and the a and b channels from Lab. In both cases the first four principal components are extracted, and the first component discarded. The three remaining principal components can be visualised by mapping to a standard RGB representation. This mapping is arbitrary, however, it does give a general feel for the difference between the brightness and colour based principal components.
The shadow reducing principal components approach discussed here shares a similarity to the feature maps generated by CNNs (LeCun and others, 1998), where each map captures different characterises inherent within the image.
#### Figure 25: Principal component analysis used to reduce an RGB image to a brightness and colour channels
PC2 mapped to the red channel, PC3 mapped to the green channel and PC4 mapped to the blue channel
### Neural network classifier
In general, image-based classifiers work by using the spectral characteristics of a pixel, such as the Red, Green and Blue channel values to assign a classification to one or more known land cover classes. The challenge arises in determining a similarity measure that can be used to determine the most appropriate class.
Approaches range from simple Euclidean distance (Richards and Jia, 2006) to the more involved spectral angle mapping (Kruse and others, 1993) and parallelpiped (Richards and Jia, 2006) approaches. The approach presented here uses an Artificial Neural Network (ANN) to classify pixels into one of the following four categories:
• vegetation
• urban
The labelled image library was randomly sampled into training and test datasets in an 80:20 ratio, the samples were stratified to ensure equal representation from Bristol and Cardiff urban residential gardens (Table 7). Although the training data consisted of only 80 images; the pixels were treated independently so the training dataset contained over 880,000 records.
#### Table 7: Train and test dataset sizes
Train Test Images Pixels Images Pixels Bristol 40 514,531 10 136,948 Cardiff 40 368,670 10 104,995 80 883,201 20 241,943
The neural network contained four outputs (each relating to one of the classes) and the following eleven inputs:
• the three RGB spectral channels
• the single monochromatic principal component with first component (assumed to be shadow) removed
• the three brightness principal components with first component (assumed to be shadow) removed
• the three colour principal components with first component (assumed to be shadow) removed
• the single NIR spectral channel
All inputs were scaled to consistent distributions. A 20% validation dataset was used to terminate search before overtraining occurred. Various network architectures were explored using a randomised grid search, with a three layer 12:8:4 network giving the optimal performance. Standard rectified linear (ReLU) activation units were used in all but the output layer, where a softmax function was used to ensure all outputs summated to 1. Learning terminated with training and validation errors of 0.819 and 0.792 respectively.
The resulting network was used to classify the 20 images of the test dataset. The manual and predicted labels for three images taken from the test dataset are shown in Figure 26. Here it can be seen that the neural network performs well and matches the manual classification in many areas. However, there are areas where the network fails to correctly classify pixels, specifically in the first image significant areas in the lower region are classified as red (urban in shade), where the assumed correct label is blue (vegetation in shade), further instances of these are evident in the two remaining images of Figure 26.
There also appears to be areas where the network struggles to differentiate between vegetation and vegetation in shade, the lower region of the third test image is a notable example of this. In this instance the mismatch between the predicted and actual labels appear to be exasperated by the presence of the tree canopy resulting in a patch work of small regions of vegetation in and out of shade.
#### Figure 26: Manual and predicted labels for three images from the test dataset
A further drawback of the neural classifier is that it treats pixels in isolation and does not consider neighbouring pixels. Where a human observer would make the logical assumption that if all the pixels surrounding a given pixel relate to vegetation, then it is likely that the pixel itself will also be vegetation. The classifier will not detect this, instead it will make the classification based entirely upon the characteristics of that pixel. This drawback is particularly evident in areas with a dominant classification. The diagonal red area in the second row and the top left green area of the third row in Figure 26 are examples of this.
The performance of the neural network is compared with the other test algorithms in Table 8 and broken down for Bristol and Cardiff in Table 9. The first point of note is that the values differ from the results in Table 3 and Table 4, this is caused by the different test dataset sizes with the previous assessment being made across all 100 images in the test library and assessment here being made upon the 20 image test dataset.
#### Table 8: Classification error across all 20 labelled test images (sorted in ascending classification error)
Average StdDev ANN 7.7% 7.2% NDVI 17.2% 16.8% Lab(a*b*) 18.6% 21.4% HSV 19.7% 21.7% vNDVI 21.0% 14.7% VARI 21.0% 14.7% Lab(a*) 36.7% 19.8% GLI 37.1% 22.3% Naive 51.3% 22.2%
The neural network classifier outperforms the NDVI, Lab(a*b*) and HSV approaches, with classification errors being reduced by factors of 2.2, 2.4 and 2.6 respectively. The standard deviation is also significantly reduced, reflecting the increased robustness of the machine learning approach.
#### Table 9: Classification error across all 20 labelled test images, broken down by Bristol and Cardiff (sorted in ascending classification error)
##### Bristol
Average StdDev ANN 6.3% 7.0% vNDVI 16.0% 8.1% VARI 16.0% 8.1% HSV 17.6% 26.0% GLI 24.5% 15.6% Lab(a*b*) 28.6% 26.3% NDVI 28.9% 16.8% Lab(a*) 41.3% 23.3% Naive 49.4% 22.8%
##### Cardiff
Average StdDev NDVI 5.5% 2.9% Lab(a*b*) 8.6% 7.4% ANN 9.0% 7.6% HSV 21.7% 17.6% vNDVI 26.0% 18.3% VARI 26.0% 18.3% Lab(a*) 32.0% 15.4% GLI 49.7% 21.3% Naive 53.1% 22.6%
If the results are further broken down by region its can be seen that in the Cardiff images where shadows were less evident, the performance of the neural network classifier is:
• weaker than NDVI,
• on a par with Lab(a*b*)
• significantly better than all other approaches
Considering the results for Bristol (with greater proportions of shadow), the performance of both NDVI and Lab(a*b*) are significantly poorer and outperformed by the majority of the remaining test approaches.
The neural network significantly out performs all other test approaches as it is better able to cope with the difference in the imagery of both Bristol and Cardiff. As the deployed algorithm is to be applied to imagery taken from different regions and at different times of the day and year, it is concluded that the neural network offers the best compromise between performance and the robustness to classify vegetation under changing local conditions.
## 9. Deployment
Considerable effort was placed on developing a robust, efficient and scalable pipeline to deploy the investigated algorithms to large volumes images, the approach developed is discussed below.
The source code is available in a public GitHub repository.
### Configuration
A JSON file is used to store available image loaders and vegetation classification approaches. Each image loader defines the spectral channels for a given image (for instance R, G, B or Ir, R, G), the location of the data, the dataset name and the python class responsible for loading the data. This enables new image loaders to be added without changing existing code, with specific image loaders having additional parameters as required. For instance, Ordnance Survey (OS) national grid datasets have a specific number of pixels per 1 kilometre (km) square (determined by image resolution, for example 12.5 centimetre (cm) imagery is 8,000 pixels wide). This enables a resolution independent Ir, R, G, B data reader to be created that internally combines the CIR and RGB datasets to generate the required imagery on demand.
The data sources are intentionally independent of the vegetation indices. Additionally, the same data reader can be used with different physical datasets. For example, 25 cm OSGB data can be read using the same reader as 12.5 cm OSGB data, with a minor configuration change needed specifying the location of data and number of pixels per image. As the data readers are python classes with the same methods, the code that uses a reader does not need to know if it is consuming OSGB data or Web Mercator, it simply uses the returned results which are in a common form and hence source agnostic.
The vegetation indices are defined in the JSON file to enable the end user to add new metrics and change their thresholds without altering Python source code. Metrics may be from a different codebase entirely rather than restricted to be part of the project source code. Vegetation indices and image loaders are defined in terms of class name and created using Python’s importlib functionality to create class instances directly from names stored as text strings at run time. Geometries are passed as a command line argument (using argparse) for processing, along with the dataset to use and the index to be calculated (both named in the JSON configuration).
The standard JSON reader is used to read the GeoJSON data, and the garden polygons are extracted (see Figure 27).
### Polygon extraction and projection
Polygons are held within a dictionary. A standard loop iterates over the data file and extracts data stored against the specific geometry key. The image loader is a python class that can convert a polygon defined in terms of latitude and longitude into its local coordinate system. The transforms are stored as separate functions in a coordinate transforms library where they can be reused by different image loaders. The transformations use the pyproj library (a Python wrapper for the proj.4 library) to convert between standard geospatial coordinate systems.
### Image extraction
The bounding box containing the projected polygon is calculated and the footprint of the polygon is used to calculate what image tiles need to be loaded. The image loaders import the required tiles (using the raster library) and merge the tiles together to form a large, continuous image that is then cropped to only contain the bounding box.
A mask image is then generated that is the same size as the cropped image, but the projected polygon is drawn on the mask image such that pixels within the polygon are set to ‘true’ otherwise ‘false’ (using the shapely library). This indicates which pixels in the cropped image are to be analysed later by the index calculation code.
A major overhead in processing is downloading and decompressing the image files. To improve efficiency and reduced processing time, image tiles that are loaded are cached for reuse (via the method decorators in the cachetools package).
### Vegetation Indices
All vegetation indices are defined as python classes that extract their configuration directly from the JSON configuration file, enabling unique configuration options for each class. All classes implement an index method that accept the related cropped image bitmap, enabling the main codebase to use index classes interchangeably. The codebase has no dependency upon implementation. The index method iterates over pixels in the cropped image bitmap, using OpenCV and NumPy to import images and speed up processing respectively. A bitmap is returned where 1 indicates that a pixel represents vegetation and 0 otherwise.
The cropped image is processed in its entirety to simplify implementation of the index method and to utilise the vector processing support enabled by NumPy. The main code base combines the mask bitmap with the resulting vegetation bitmap to calculate the vegetation coverage for the given garden polygon.
### Process timings
To produce the final statistics for Cardiff and Bristol, the Neural Network classifier was used with the 12.5 centimetre RGB data combined with 50 cm IR to generate 12.5 cm RGBIr data. The Cardiff data (79,643 polygons) was processed with a two-core virtual machine hosted on a Xeon E5-2650 @ 2.20 GHz; 4 Gigabytes of memory was allocated for caching which resulted in 99.6% cache hit rate to analyse the gardens in 12 hours and 45 minutes. The Bristol data (209,035 polygons) was run on a two-core virtual machine hosted on a Xeon Gold 6126 @ 2.60GHz; 28 Gb of memory was allocated for caching which resulted in 70% cache hit rate but had taken 31 hours to process less than 50% of the data. This was too slow to be of use, so the Bristol run was aborted.
To reduce the problem of cache misses, pre-sorting code introduced where each polygon was projected onto the aerial imagery and its related image tile calculated. Polygons are then processed in order of image tile, to maximum image reuse. This has resulted in a cache hit rate of 99.9% with the Bristol gardens and final execution reduced to 29 hours and 38 minutes. Approximately 11 Gb of memory was used for caching out of 28 Gb made available.
### Testing
The code is tested using PyTest, verifying that the image transformation, image loaders and vegetation indices operate as expected. Further, Travis-CI integrated with GitHub is used to ensure that the tests are run as continuous integration to ensure the stability of the code.
### Codebase reuse
The existing codebase has no dependency on the concept of gardens or vegetation; it simply processes polygons and runs metrics over projected polygons. The code is therefore not restricted to vegetation coverage in gardens and could be applied to property polygons and metrics to calculate roof types, or farmland polygons with metrics to calculate crop types, hence the code is not restricted to vegetation coverage in gardens.
## 10. Final Results
Applying the trained neural network to urban residential gardens in Cardiff, Bristol and then for the whole of Great Britain, the total garden area and vegetation coverage is shown in table 10.
#### Table 10: Total urban garden area and percentage of vegetation
Area Total garden area (km2) Vegetation coverage Cardiff 13.4 53.9% Bristol 41.9 45.0% Great Britain 61.6%
## 11. Practical applications
The neural network classifier detailed in this report will be used by both the natural capital team at the Office for National Statistics (ONS) and Ordnance Survey (OS).
### ONS Natural capital team
Natural capital is the term encompassing all the UK’s natural assets that form the environment in which we live. The Natural Capital team at the ONS aims to measure the environment and its relationship with the economy. The team covers measurement in three main areas:
• Environmental flows – the flows of natural inputs, products and residuals between the environment and the economy, and within the economy, both in physical and monetary terms.
• Stocks of environmental assets – the stocks of individual assets, such as water or energy assets, and how they change over an accounting period due to economic activity and natural processes, both in physical and monetary terms.
• Economic activity related to the environment – monetary flows associated with economic activities related to the environment, including spending on environmental protection and resource management, and the production of “environmental goods and services”.
Uses for vegetation classifier include:
• Estimate the benefits of sustainable urban drainage (SUDS) such as vegetation. This would involve discussion with The Environment Agency and devolved equivalents about their own flood risk mapping and how these data might alter risk.
• Improving the calculation of Urban heat by including vegetation coverage and identifying areas where encouraging greener gardens may improve lives.
• Models are currently being developed to predict house prices, the current source of giving green spaces coverage is less accurate and may be replaced.
• Granular carbon sequestration – differentiate between trees and grass and understand how this may impact the carbon footprint at an individual household level.
### Ordnance Survey
The degree of surface naturalness is increasingly in demand among Green Infrastructure studies as intelligence beyond the vector garden boundary is lacking. Although an asset often belonging to a singular residence, these high-quality natural spaces are a key deliverable of the 25-year environment plan to increase engagement with the natural environment.
In a previous piece of work in accessing the Greater Manchester Combined Authority’s accessible natural greenspace, residential garden greenspace was used in its naïve entirety which contributed towards an overestimation of natural land cover when analysing land use across larger geographies. This refined insight is intended to provide robust statistics that can therefore improve estimations of greenspace coverage.
The Welsh Government also rely upon quality green infrastructure data to implement multiple policies and schemes – such as the Physical Environment domain within the Welsh Index of Multiple deprivations (WIMD) and the Understanding Welsh Places study.
In its infancy in 2019, the natural green space sub-domain will seek to acknowledge these data refinements into future iterations of WIMD to produce the most accurate account of accessible and ambient greenspace as possible. Beyond the core remit of this project it is hoped that the transferable methodologies from this work can continue to help support and underpin policies surrounding accessibility and quality of natural capital such as the Play Policy to increase Welsh Governments alignment to the United Nations Convention on Rights of the Child.
## 12. Summary
This report details the work undertaken at the ONS Data Science Campus, in collaboration with Ordnance Survey (OS) to use remote sensing and machine learning techniques to improve upon the current approach used within the ONS to identify the proportion of vegetation for urban residential gardens in Great Britain.
Data was provided in the form of garden parcel polygons covering Cardiff and Bristol, and aerial imagery at 12.5, 25 and 50 centimetre resolution using the RGB and near infra-red spectral channels.
Several “off the shelf” and bespoke techniques developed by both the Campus are used to detect the presence of vegetation. They were assessed qualitatively on a library of 10 garden images, selected to reflect the spectrum of garden designs and changing conditions. It was found that no single approach performed well over all the unlabelled test images. Some approaches performed poorly in images containing patios whilst others struggled to differentiate between areas of water and vegetation. Although by no means perfect, the performance of two approaches Lab (a*b*) and more notably HSV appear to be less sensitive across the range of test images.
Although the 10 images of the unlabelled library allowed a subjective assessment across the algorithms to be made, it did not provide enough quantitative evidence to make a definitive decision.
To overcome this, a second test library of labelled images was created by taking 100 images randomly sampled from Bristol and Cardiff. These were independently labelled by a team of four individuals from the Campus and Welsh Government to provide ground truth.
Application of the test algorithms to the labelled data shows the sensitivity of the test algorithms to shadows, with HSV performing well in images with more shadow whilst Lab(a*b*) performed poorly. Conversely in images subject to less shadows Lab(a*b*) was the clear winner.
A neural network was developed to assign pixels into one of the four classes, the inputs to the network were the standard RGB spectral channels, a NIR channel and a number of monochrome, brightness and colour based principal components with the first component (most likely to be shadow) removed. The performance of the neural network was compared to the test algorithms on a 20-image labelled test library. Results support the conclusion that a neural network classifier can accurately classify vegetation and less susceptible to the effect of shadows when compared with the other test algorithms.
Finally, a robust, efficient and scalable pipeline to deploy the investigated algorithms to any number of images.
## 13. Future work
There are many areas where the work discussed in this report may be developed or improved.
Firstly, the size of the labelled training dataset should be increased. In the machine learning approach deployed in this report, where pixels were treated in isolation there were enough training examples (over 800k) to train a classifier. However, if more complex networks are explored (such as convolutional networks) where pixels are not treated in isolation a training set of 100 images will be totally inadequate.
In the neural network approach described above, each pixel is treated in isolation, this was found to have a significant drawback. It is clear that if all the pixels surrounding a pixel are vegetation, then it is likely that the pixel itself will also be vegetation. The classifier will not detect this, instead it will make the classification based entirely upon the characteristics of the pixel. Features relating to the neighbouring pixels as potential network inputs should be investigated.
Within all the test algorithms the threshold that determines if a pixel is classified as being vegetation was set at an initial value and not changed. With the availability of labelled data, the thresholds should be recalibrated, to optimally classify the ground truth labels and provide a fairer test against the developed neural network classifier.
Finally, the detrimental effect of shadow upon performance has been shown in this report. The degree of shadow is dependent upon the prevailing weather conditions, the time of the day and the month of year in which the aerial imagery was captured. Given sufficient training data, these additional features may allow the neural network to determine the degree of shadow in the image and therefore automatically correct for this whilst making its prediction.
## 14. Acknowledgments
Authors: Christopher Bonham, Sonia Williams, Ian Grimstead (ONS Data Science Campus) and Matt Ricketts (Ordnance Survey).
The participants of this project would like to thank the Geography & Technology Team within the Welsh Government for providing resource that contributed towards the aerial imagery labelling aspect of this project, and the Geography team at the ONS for facilitating the provision of the data. The invaluable input and direction from the Natural Capital team at the Office of National Statistics was also greatly appreciated.
## 15. Appendix: Application of the test algorithms to the unlabelled test image library
The second test image explores the ability of the detection algorithms to distinguish between water, grass and shade (Figure 28). Regarding identified vegetation, the Red, Green and Blue (RGB) and Hue, Saturation, Value (HSV) algorithms are in close agreement, however all of these approaches misclassify both the garden pond at the centre of the image and regions of shade at the right of the image as vegetation, with the Green Leaf Index (GLI) algorithm being particularly poor. The Lab algorithms identify far less vegetation with both Lab(a*) and more notably Lab(a*b*) being able to distinguish between water and the green plants floating upon it. The Lab approaches are also more successful in discriminating between areas of vegetation and shade.
#### Figure 28: Test image 2 results
Pixels identified as vegetation are coloured green
As with the previous image, test image 4 (Figure 29) contains very limited vegetation. This being caused by snow which covers large areas of grass but leaves shrubs and tree foliage unaffected. This test image produces extreme results. For two of the three RGB based algorithms, significant portions of snow are incorrectly classified as vegetation with values of 60%. Conversely the two Lab approaches identify almost no vegetation (less than 1% in both cases). HSV offers an improvement upon this but this is only marginal. The remaining RGB algorithm, GLI, offers the best performance by far discriminating successfully between areas of snow and vegetation.
#### Figure 29: Test image 4 results
Pixels identified as vegetation are coloured green
Test image 5 (Figure 30) represents a flower bed garden with a mixture of grass, bedding plants and top soil. All the techniques perform well. However, the GLI approach appears better able to identify the both the semi-circular grass border at the bottom of the image and the bedding plants. Conversely, Lab(a*) struggles to identify large portions of the same border.
#### Figure 30: Test image 5 results
Pixels identified as vegetation are coloured green
Test image 6 (Figure 31) is an ornamental garden with formal flower beds and geometric walkways. The results here are similar to those observed for test image 5, however in this case both Lab instances perform less well with both failing to identify areas of grass most notably in the top right-hand corner of the image.
#### Figure 31: Test image 6 results
Pixels identified as vegetation are coloured green
Test image 7 (Figure 32) tests for the ability to classify vegetation in the form of tree foliage. All three RGB based algorithms and the HSV algorithm achieve this however they misclassify the roof at the centre of the image as also being vegetation. HSV identifies the tree canopy but also can correctly distinguish between the trees and the building roof. Both Lab approaches and more notably Lab(a*) struggle to accurately classify all the tree canopy as green, struggling with the lighter green shades.
#### Figure 32: Test image 7 results
Pixels identified as vegetation are coloured green
In test image 9 (Figure 33), Visual Normalised Difference Vegetation Index (vNDVI), Visual Atmospheric Resistance Index (VARI) and HSV all perform well and are able to classify the grass in the centre of the image and the tree canopy on the left of the image (struggling only with the more autumnal shades or orange and yellow). GLI also performs well however it does misclassify the path as being vegetation in several areas. Both Lab algorithms struggle to correctly classify large areas in the upper part of the image.
#### Figure 33: Test image 9 results
Pixels identified as vegetation are coloured green
The final test image is dominated by a large light-coloured shingle path, bordered by grass verges and surrounded by flower beds (Figure 34). Both Lab algorithms misclassify areas of the grass border in the lower portion of the image, however this is minimal. The GLI algorithm classifies 79% of the image as vegetation including a significant proportion of the shingle path on the right-hand side of the image. vNDVI, VARI and HSV all perform comparatively well.
To aggregate the results of each image into a single measure of performance, points we awarded on an image by image basis, with a point being awarded to each approach deemed a strong performer and a point deducted for every weak performing classification. The results are given below.
#### Figure 34: Test image 10 results
Pixels identified as vegetation are coloured green
Referring to Table 11, it can be seen that HSV gives the best overall performance when applied across the 10 test images. Surprisingly the optimised Lab approaches perform less well. Focussing on the case of Lab (a*b*) in particular, it either performs well (images 2, 3, 8 and 10) or poorly (images 4, 6 and 7). These swings in performance may be attributable to the fact that the Lab thresholds were optimised on street level images, taken form the Mapillary Vistas library but assessed on aerial imagery when the illumination conditions and resolution are very likely to be different.
#### Table 11: Individual results unlabelled test images library
Test Image vNDVI GLI VARI HSV Lab (a*) Lab (a*b*) 1 1 1 1 1 2 -1 -1 -1 -1 1 3 -1 -1 -1 -1 1 1 4 -1 1 -1 -1 5 1 -1 6 1 1 1 1 -1 -1 7 1 -1 -1 8 1 -1 1 1 1 9 1 1 1 10 1 1 1 1 1 Total 2 1 3 4 -2 1
###### 1 approach performs relatively well, -1 approach performs relatively poorly
To address these drawbacks, the lower bound of the a* threshold of both Lab(a*) and Lab(a*b*) were relaxed to cover the entire spectrum of vegetation. This increased performance in only 2 of the 10 test images, specifically 6 and 7. These results are given in Table 12, in both cases it can be seen the performance improves to a point where it was comparable with the other approaches. If these results are applied to the summary results table, although the overall performance of both Lab approaches improve the HSV approach is still the strongest.
#### Table 12: Summary results unlabelled test images library
Test Image vNDVI GLI VARI HSV Lab (a*) Lab (a*b*) Total 2 1 3 4 1 3
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Zhou B., Zhao H., Puig X., Fidler S. and Barriuso A. 2017. Scene Parsing through ADE20K Dataset, B. Zhou, H. Zhao, X. Puig Torralba. Computer Vision and Pattern Recognition (CVPR). 2017. | 2022-01-23T17:25:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45873168110847473, "perplexity": 2572.448300496544}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304309.5/warc/CC-MAIN-20220123172206-20220123202206-00247.warc.gz"} |
https://docs.dea.ga.gov.au/notebooks/Real_world_examples/Surface_area_duration.html | # Surface area duration plots from DEA Waterbodies data ¶
• Sign up to the DEA Sandbox to run this notebook interactively from a browser
• Compatibility: Notebook currently compatible with both the NCI and DEA Sandbox environments
• Products used: DEA Waterbodies time series data (available online)
## Background¶
A “surface area duration” (SAD) curve depicts the cumulative percentage of time that a waterbody had a larger extent than a given percentage of its maximum extent—in other words, the total amount of time that a waterbody was at least a certain amount full. These are similar to flow duration curves, and describe the long-term behaviour of a waterbody. SAD curves may be useful for identifying different types of waterbodies, which helps us to understand how water is used throughout Australia.
### Digital Earth Australia use case¶
The DEA Waterbodies product uses Geoscience Australia’s archive of over 30 years of Landsat satellite imagery to identify where almost 300,000 waterbodies are in the Australian landscape and tells us how the wet surface area within those waterbodies changes over time. These data can be analysed to obtain insights into the duration and temporal dynamics of inundation for any mapped waterbody in Australia.
## Description¶
This notebook plots “surface area duration” (SAD) curves, which show for how long a waterbody is filled at a given surface area. Such a curve can be generated for any DEA Waterbody. We also generate a time-dependent version of this plot called a “short-time surface area duration” (STSAD) curve, which shows how the surface area duration curve varies over time.
This analysis should work for any time series stored in a similar format.
## Getting started¶
Run the first cell, which loads all modules needed for this notebook. Then edit the configuration to match what you want the notebook to output.
[1]:
%matplotlib inline
import numpy as np
import pandas as pd
import scipy.signal
from pathlib import Path
from matplotlib import pyplot as plt
import sys
sys.path.insert(1, '../Tools/')
### Configuration¶
To generate a plot for a waterbody with a given geohash, specify the geohash here:
[2]:
geohash = "r3f225n9h" # Weereewa/Lake George
Also specify the window for the STSAD plot. Use ‘hann’ if you have no opinions on this, or ‘boxcar’ if you want a window that is easy to think about. You can see a list of possible windows here. Hann is fairly standard for short-time transforms like this and will give a smooth STSAD:
Boxcar is a sliding window:
[3]:
window = "hann"
Finally, specify the path to the waterbodies CSVs:
[4]:
waterbody_csv_path = "https://data.dea.ga.gov.au/projects/WaterBodies/timeseries"
The DEA Waterbodies time series are stored as CSV files. Each waterbody is labelled by a geohash, e.g. Weereewa is r3f225n9h. They are stored online (on Amazon S3) in a folder named after the first four characters of the geohash, and the filename is the geohash, e.g. Weereewa is at https://data.dea.ga.gov.au/projects/WaterBodies/timeseries/r3f2/r3f225n9h.csv. Each CSV has three columns: Observation Date, Wet pixel percentage, Wet pixel count (n = ?) where ? is the total number of observations. An example is:
Observation Date,Wet pixel percentage,Wet pixel count (n = 230894)
1987-05-29T23:14:29Z,,
1987-07-16T23:15:29Z,,
1987-09-02T23:16:50Z,,
1987-09-18T23:17:13Z,19.9,45926
First we will read the CSV containing the surface area vs time observations data directly from the URL path using pandas. We will rename the Observation Date, Wet pixel percentage, Wet pixel count (n = ?) columns to more consistent and easier to access names:
date, pc_wet, px_wet
We also ensure that the ‘date’ column is parsed as a datetime, and convert the data percentages to decimals:
[5]:
# Set path to the CSV file
csv_path = f"{waterbody_csv_path}/{geohash[:4]}/{geohash}.csv"
# Load the data using pandas:
names=["date", "pc_wet", "px_wet"],
parse_dates=["date"],
index_col="date",
)
# Convert percentages into a float between 0 and 1.
time_series.pc_wet /= 100
We can now inspect the first few rows of the data:
[6]:
time_series.head()
[6]:
pc_wet px_wet
date
1987-05-29 23:14:29+00:00 NaN NaN
1987-07-16 23:15:29+00:00 NaN NaN
1987-09-02 23:16:50+00:00 NaN NaN
1987-09-18 23:17:13+00:00 0.199 45926.0
1987-10-04 23:17:34+00:00 NaN NaN
## Interpolate data to daily values¶
DEA Waterbodies data is stored with one row per satellite observation. To make our data easier to analyse by time, we can use interpolation the data to estimate the percentage coverage of water for every individual day in our time series.
[7]:
# Round dates in the time series dataset to the nearest whole day
time_series.index = time_series.index.round(freq="d")
# Create a new datetime index with one value for every individual day
# between the first and last DEA Waterbodies observation
dt_index = pd.date_range(start=time_series.index[0],
end=time_series.index[-1], freq="d")
# Use this new index to modify the original time series so that it
# has a row for every individual day
time_series = time_series.reindex(dt_index)
assert len(time_series) == len(dt_index)
Then interpolate (linearly, since it’s the least-information thing other than constant).
[8]:
# Replace NaNs with a linear interpolation of the time series.
time_series.pc_wet.interpolate(inplace=True, limit_direction="both")
If we inspect the first rows in the dataset again, we can see that we now have one row for every day (e.g. 1987-05-30, 1987-05-31) instead of a row for each satellite observation:
[9]:
time_series.head()
[9]:
pc_wet px_wet
1987-05-30 00:00:00+00:00 0.199 NaN
1987-05-31 00:00:00+00:00 0.199 NaN
1987-06-01 00:00:00+00:00 0.199 NaN
1987-06-02 00:00:00+00:00 0.199 NaN
1987-06-03 00:00:00+00:00 0.199 NaN
For each rolling time step, calculate the SADs.
[10]:
sad_y, sad_x, sads = calculate_stsad(
time_series.pc_wet, window_size=365 * 2, window=window, step=10
)
Convert the time axis into integers for calculating tick locations.
[11]:
year_starts = (time_series.index.month == 1) & (time_series.index.day == 1)
year_start_days = (time_series.index - time_series.index[0])[year_starts].days
year_start_years = time_series.index.year[year_starts]
[12]:
sad = calculate_sad(time_series.pc_wet)
Calculate the SAD for the Millenium drought.
[13]:
# Select observations between the start and end of the Millenium drought.
millenium_drought_start = pd.to_datetime('2001-01-01', utc=True)
millenium_drought_end = pd.to_datetime('2009-12-12', utc=True)
millenium_drought = (time_series.index > millenium_drought_start) & (time_series.index < millenium_drought_end)
We can then plot the SAD.
[14]:
plt.figure(figsize=(8, 6))
plt.xlabel("Percentage of time")
plt.ylabel("Surface area (% maximum extent)")
plt.legend();
From this plot of the SAD for Weereewa/Lake George, we can tell that the lake was at least partly-inundated for 25 of the last 33 years. The lake was rarely full. The slope of the curve indicates how the lake varied over time, but is hard to interpret without comparison to another SAD curve.
Comparing the all-time curve to the SAD during the Millenium drought shows that the lake was significantly drier during the drought, never exceeding 50% capacity. The very sharp drop at the beginning of the SAD curve indicates rapid drying when the lake was near its peak, suggesting either that the lake bed is not steep at the point where it is 50% full, or that the only significant influx of water into the lake was during a period of rapid drying.
[15]:
plt.figure(figsize=(10, 10))
plt.xlabel("Days in two-year period")
plt.yticks(year_start_days[::2], year_start_years[::2])
plt.ylabel("Date")
plt.colorbar(label="Surface area (% maximum extent)")
plt.title("Short-time surface area duration");
The STSAD plot helps visualise the change in Weereewa/Lake George over time. Here, the Millenium drought is clearly visible between 2000 and 2009 as a period of very little wet extent. The lake was mostly full during the 1990s, and it filled and dried fairly consistently over time, indicating that it is unregulated. It was stably partly-filled for significant parts of 1988, during the 2010–12 La Niña, and 2016–17.
Contact: If you need assistance, please post a question on the Open Data Cube Slack channel or on the GIS Stack Exchange using the open-data-cube tag (you can view previously asked questions here). If you would like to report an issue with this notebook, you can file one on Github. | 2022-01-16T21:17:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37103620171546936, "perplexity": 4525.457553861767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300244.42/warc/CC-MAIN-20220116210734-20220117000734-00652.warc.gz"} |
https://drupal.star.bnl.gov/STAR/presentations/dnp-2020/identified-particle-v1-and-v2-sqrtsnn-3-gev-auau-collisions-star-0 | # Identified particle $v_{1}$ and $v_{2}$ in $\sqrt{s_{NN}}$ = 3 GeV Au+Au Collisions at STAR
Under:
Author : Shaowei Lan Meeting : 2020 Fall Meeting of the Division of Nuclear Physics of the American Physical Society - New Orleans , LA, Oct. 29 - Nov. 1, 2020 Format : abstract File(s) : PDF | 2021-03-02T08:54:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6424811482429504, "perplexity": 7038.17303428922}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178363782.40/warc/CC-MAIN-20210302065019-20210302095019-00445.warc.gz"} |
https://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Opposite_category | # Opposite category
In category theory, a branch of mathematics, the opposite category or dual category Cop of a given category C is formed by reversing the morphisms, i.e. interchanging the source and target of each morphism. Doing the reversal twice yields the original category, so the opposite of an opposite category is the original category itself. In symbols, ${\displaystyle (C^{\text{op}})^{\text{op}}=C}$ .
## Examples
• An example comes from reversing the direction of inequalities in a partial order. So if X is a set and ≤ a partial order relation, we can define a new partial order relation ≤op by
xop y if and only if yx.
The new order is commonly called dual order of ≤, and is mostly denoted by symbols such as ≥. Therefore, duality plays an important role in order theory and every purely order theoretic concept has a dual. For example, there are opposite pairs child/parent, descendant/ancestor, infimum/supremum, down-set/up-set, ideal/filter etc. This order theoretic duality is in turn a special case of the construction of opposite categories as every ordered set can be understood as a category.
## Properties
Opposite preserves products:
${\displaystyle (C\times D)^{\text{op}}\cong C^{\text{op}}\times D^{\text{op}}}$ (see product category)
Opposite preserves functors:
${\displaystyle (\mathrm {Funct} (C,D))^{\text{op}}\cong \mathrm {Funct} (C^{\text{op}},D^{\text{op}})}$ [2][3] (see functor category, opposite functor)
Opposite preserves slices:
${\displaystyle (F\downarrow G)^{\text{op}}\cong (G^{\text{op}}\downarrow F^{\text{op}})}$ (see comma category)
## References
1. "Is there an introduction to probability theory from a structuralist/categorical perspective?". MathOverflow. Retrieved 25 October 2010.
2. H. Herrlich, G. E. Strecker, Category Theory, 3rd Edition, Heldermann Verlag, ISBN 978-3-88538-001-6, p. 99.
3. O. Wyler, Lecture Notes on Topoi and Quasitopoi, World Scientific, 1991, p. 8.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files. | 2021-09-17T10:59:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 4, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9241557121276855, "perplexity": 1412.5981534919788}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780055632.65/warc/CC-MAIN-20210917090202-20210917120202-00607.warc.gz"} |
https://www.usgs.gov/center-news/volcano-watch-rockfalls-alter-size-and-shape-halemaumau-crater | Volcano Watch — Rockfalls alter size and shape of Halemaumau Crater
Release Date:
For the past 10 years, most of the evident changes on Kīlauea Volcano have occurred down the east rift zone near and downslope from the Puu Oo and Kupaianaha vents. Last Sunday, a sequence of rockfalls occurred within the summit caldera that modestly changed the size and shape of Halemaumau Crater.
For the past 10 years, most of the evident changes on Kīlauea Volcano have occurred down the east rift zone near and downslope from the Puu Oo and Kupaianaha vents. Last Sunday, a sequence of rockfalls occurred within the summit caldera that modestly changed the size and shape of Halemaumau Crater. Most changes at Kīlauea are caused either directly or indirectly by movement of magma within the volcano; however, the rockfalls on November 29 were caused by the heavy rainfall over Kīlauea's summit, as well as over most of the island.
Between 11:00 a.m. and midnight, 70 discrete rockfalls, detected by our nearby seismometer occurred inside Halemaumau. The number per hour peaked between 1:00 and 2:00 p.m. but was most intense from noon to 4:00 p.m. These rockfalls enlarged the diameter of the crater and filled in the floor somewhat. Compared to changes occurring within Halemaumau that are related to eruptions or magma movement down the rift zones from the summit, these rockfalls are small in scale.
The caldera at the summit of Kīlauea and Halemaumau Crater with it have changed dramatically in the geologically recent past. Today, the caldera looks much as it appears in this photograph (view towards the northwest). But it has not always looked like this. Much of the 3.25 by 4.75-kilometer caldera formed shortly before the catastrophic eruption of 1790, which produced the Keanakakoi Ash. Since then, the history of the caldera has been one of rapid filling by new lava flows, interrupted by intervals of renewed collapse. Upward growth of the caldera floor during the 19th century was rapid, mainly due to sustained lava lake overflows. In 1823, when viewed by the Rev. William Ellis, the caldera floor was over twice as deep as it is today.
In 1868, the magnitude-8.0 earthquake that accompanied a southwest rift eruption of Mauna Loa Volcano also disrupted the summit of Kīlauea, and the floor of the caldera again collapsed. Approximately two thirds of the caldera floor sank from 100-300 feet during this event. By 1871, the new, deeper caldera was again being refilled by overflows from new lava lakes in the area where Halemaumau is now located. Over the next five years, a large, gently sloping lava shield, with Halemaumau at its summit, grew rapidly over the entire caldera floor. In July 1894, the summit of the shield collapsed, and lava lake activity ceased until 1905.
From 1905 to 1924, Halemaumau Crater contained an almost continuously active lava lake as much as 400 meters across. Occasionally, this lake would overflow onto the surrounding caldera floor, but most of the time, the lake was confined within levees on the crater floor. At its highest level, the lava lake reached an elevation equal to that of the Volcano House Hotel.
In 1924, the lava lake drained away. A series of steam explosions followed that doubled the diameter of Halemaumau to about its present size. Since 1924, a series of 18 eruptions, ranging from less than one day to eight months in duration has partially refilled the 400-meter-deep crater that existed in 1924. This slow build-up of lavas has been interrupted by four episodes of collapse triggered by sudden draining of the underlying magma chamber. Today, the floor of the Halemaumau is about 85 meters below its rim. Thus, Halemaumau has existed since 1871 but has been close to its present size and depth only since 1974.
Most of the lava making up the floor of Halemaumau was erupted in September 1974. This lava is now partly covered by talus from last Sunday's rockfalls near the base of the crater walls. Other rockfalls have occurred since 1974, but most were triggered by earthquakes rather than by heavy rains.
The summit of Kīlauea has been slowly deflating during most of the 10 years of east-rift-zone eruptive activity. A future rapid draining of additional magma from beneath the summit could trigger renewed collapse in Halemaumau. Such rapid magma withdrawal is usually associated with fissure eruptions along the rift zones. These fissure eruptions are likely occurrences before the ten-year-long eruption finally quits. In fact, the fissure eruptions of episodes 49 (November 1991) and 50 (February 1992) each began with moderately rapid withdrawal of magma from beneath the summit, but the volumes were too small to cause summit collapse. | 2020-09-23T22:39:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4366784989833832, "perplexity": 4942.836384277314}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400212959.12/warc/CC-MAIN-20200923211300-20200924001300-00328.warc.gz"} |
https://par.nsf.gov/biblio/10388089-clustered-formation-massive-stars-within-ionized-rotating-disk | Clustered Formation of Massive Stars within an Ionized Rotating Disk
Abstract
We present Atacama Large Millimeter/submillimeter Array observations with a 800 au resolution and radiative-transfer modeling of the inner part (r≈ 6000 au) of the ionized accretion flow around a compact star cluster in formation at the center of the luminous ultracompact Hiiregion G10.6-0.4. We modeled the flow with an ionized Keplerian disk with and without radial motions in its outer part, or with an external Ulrich envelope. The Markov Chain Monte Carlo fits to the data give total stellar massesMfrom 120 to 200M, with much smaller ionized-gas massesMion-gas= 0.2–0.25M. The stellar mass is distributed within the gravitational radiusRg≈ 1000 to 1500 au, where the ionized gas is bound. The viewing inclination angle from the face-on orientation isi= 49°–56°. Radial motions at radiir>Rgconverge tovr,0≈ 8.7 km s−1, or about the speed of sound of ionized gas, indicating that this gas is marginally unbound at most. From additional constraints on the ionizing-photon rate and far-IR luminosity of the region, we conclude that the stellar cluster consists of a few massive stars withMstar= 32–60M, or one star in this range of masses accompanied by a population of lower-mass stars. Any active accretion of ionized gas onto the massive (proto)stars is residual. The more »
Authors:
; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10388089
Journal Name:
The Astrophysical Journal Letters
Volume:
942
Issue:
1
Page Range or eLocation-ID:
Article No. L7
ISSN:
2041-8205
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
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1. Abstract
We present a high-resolution view of bubbles within the Phantom Galaxy (NGC 628), a nearby (∼10 Mpc), star-forming (∼2Myr−1), face-on (i∼ 9°) grand-design spiral galaxy. With new data obtained as part of the Physics at High Angular resolution in Nearby GalaxieS (PHANGS)-JWST treasury program, we perform a detailed case study of two regions of interest, one of which contains the largest and most prominent bubble in the galaxy (the Phantom Void, over 1 kpc in diameter), and the other being a smaller region that may be the precursor to such a large bubble (the Precursor Phantom Void). When comparing to matched-resolution Hαobservations from the Hubble Space Telescope, we see that the ionized gas is brightest in the shells of both bubbles, and is coincident with the youngest (∼1 Myr) and most massive (∼105M) stellar associations. We also find an older generation (∼20 Myr) of stellar associations is present within the bubble of the Phantom Void. From our kinematic analysis of the HI, H2(CO), and Hiigas across the Phantom Void, we infer a high expansion speed of around 15 to 50 km s−1. The large size and high expansion speed of the Phantom Void suggest that the driving mechanism ismore »
2. Aims. Thanks to the high angular resolution, sensitivity, image fidelity, and frequency coverage of ALMA, we aim to improve our understanding of star formation. One of the breakthroughs expected from ALMA, which is the basis of our Cycle 5 ALMA-IMF Large Program, is the question of the origin of the initial mass function (IMF) of stars. Here we present the ALMA-IMF protocluster selection, first results, and scientific prospects. Methods. ALMA-IMF imaged a total noncontiguous area of ~53 pc 2 , covering extreme, nearby protoclusters of the Milky Way. We observed 15 massive (2.5 −33 × 10 3 M ⊙ ), nearby (2−5.5 kpc) protoclusters that were selected to span relevant early protocluster evolutionary stages. Our 1.3 and 3 mm observations provide continuum images that are homogeneously sensitive to point-like cores with masses of ~0.2 M ⊙ and ~0.6 M ⊙ , respectively, with a matched spatial resolution of ~2000 au across the sample at both wavelengths. Moreover, with the broad spectral coverage provided by ALMA, we detect lines that probe the ionized and molecular gas, as well as complex molecules. Taken together, these data probe the protocluster structure, kinematics, chemistry, and feedback over scales from clouds to filaments to cores.more »
3. Context. Stellar evolution models are highly dependent on accurate mass estimates, especially for highly massive stars in the early stages of stellar evolution. The most direct method for obtaining model-independent stellar masses is derivation from the orbit of close binaries. Aims. Our aim was to derive the first astrometric plus radial velocity orbit solution for the single-lined spectroscopic binary star MWC 166 A, based on near-infrared interferometry over multiple epochs and ∼100 archival radial velocity measurements, and to derive fundamental stellar parameters from this orbit. A supplementary aim was to model the circumstellar activity in the system from K band spectral lines. Methods. The data used include interferometric observations from the VLTI instruments GRAVITY and PIONIER, as well as the MIRC-X instrument at the CHARA Array. We geometrically modelled the dust continuum to derive relative astrometry at 13 epochs, determine the orbital elements, and constrain individual stellar parameters at five different age estimates. We used the continuum models as a base to examine differential phases, visibilities, and closure phases over the Br γ and He I emission lines in order to characterise the nature of the circumstellar emission. Results. Our orbit solution suggests a period of P = 367.7 ± 0.1 d, approximatelymore »
4. Abstract
We measure the molecular-to-atomic gas ratio,Rmol, and the star formation rate (SFR) per unit molecular gas mass, SFEmol, in 38 nearby galaxies selected from the Virgo Environment Traced in CO (VERTICO) survey. We stack ALMA12CO (J= 2−1) spectra coherently using Hivelocities from the VIVA survey to detect faint CO emission out to galactocentric radiirgal∼ 1.2r25. We determine the scale lengths for the molecular and stellar components, finding a ∼3:5 relation compared to ∼1:1 in field galaxies, indicating that the CO emission is more centrally concentrated than the stars. We computeRmolas a function of different physical quantities. While the spatially resolvedRmolon average decreases with increasing radius, we find that the mean molecular-to-atomic gas ratio within the stellar effective radiusRe,Rmol(r<Re), shows a systematic increase with the level of Hi, truncation and/or asymmetry (HIperturbation). Analysis of the molecular- and the atomic-to-stellar mass ratios withinRe,$R⋆mol(rand$R⋆atom(r, shows that VERTICO galaxies have increasingly lower$R⋆atom(rfor larger levels of HIperturbation (compared to field galaxies matched in stellar mass), but no significant change in$R⋆mol(r. We also measure a clear systematic decrease of the SFEmolwithinRe, SFEmol(r<Re),more »
5. ABSTRACT
Young massive clusters (YMCs) are compact (≲1 pc), high-mass (>104 M⊙) stellar systems of significant scientific interest. Due to their rarity and rapid formation, we have very few examples of YMC progenitor gas clouds before star formation has begun. As a result, the initial conditions required for YMC formation are uncertain. We present high resolution (0.13 arcsec, ∼1000 au) ALMA observations and Mopra single-dish data, showing that Galactic Centre dust ridge ‘Cloud d’ (G0.412 + 0.052, mass = 7.6 × 104 M⊙, radius = 3.2 pc) has the potential to become an Arches-like YMC (104 M⊙, r ∼ 1 pc), but is not yet forming stars. This would mean it is the youngest known pre-star-forming massive cluster and therefore could be an ideal laboratory for studying the initial conditions of YMC formation. We find 96 sources in the dust continuum, with masses ≲3 M⊙ and radii of ∼103 au. The source masses and separations are more consistent with thermal rather than turbulent fragmentation. It is not possible to unambiguously determine the dynamical state of most of the sources, as the uncertainty on virial parameter estimates is large. We find evidence for large-scale (∼1 pc) converging gas flows, which could cause the cloud to grow rapidly, gaining 104 M⊙ within 105 yr. The highest density gas is found atmore » | 2023-03-22T09:27:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6944057941436768, "perplexity": 3700.753783575863}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943809.22/warc/CC-MAIN-20230322082826-20230322112826-00355.warc.gz"} |
https://fermi.gsfc.nasa.gov/ssc/data/analysis/gbm/gbm_data_tools/gdt-docs/notebooks/PhaExport.html | # Analysis Workflow: Reduction and Export¶
GBM was designed with high temporal and spectral resolution primarily to study GRB spectra and spectral evolution throughout a GRB. So, ideally we would like to reduce the data and model the background so that we can get at the thing we’re really interested in: the source spectrum. The following workflow will show you how you can do this and export the relevant data so that it can be used with XSPEC to fit the source spectrum.
To start, we need to be able to read in some data. Let’s use TTE. Because we’re using TTE, we’ll need a binning algorithm. And we need some response files. Luckily these are already generated for us if it’s a GRB that was triggered onboard GBM.
[1]:
from gbm import test_data_dir
from gbm.data import TTE
from gbm.binning.unbinned import bin_by_time
# open a TTE file
tte = TTE.open(test_data_dir+'/glg_tte_n9_bn090131090_v00.fit')
# bin to 1.024 s resolution, reference time is trigger time
phaii = tte.to_phaii(bin_by_time, 1.024, time_ref=0.0)
Of course we’ll want to visualize what we’re doing, so we need some classes from the gbm.plot module. Also, what we’re going to do here is set the energy range we’re interested in. Generally, for the NaIs, you don’t want to go below 8 keV. Yes, GBM data goes below that, but the response is poorly calibrated below 8 keV. And you don’t want to include the overflow channel, so going up to ~900 keV should be sufficient.
[2]:
%matplotlib inline
from gbm.plot import Lightcurve, Spectrum
erange = (8.0, 900.0)
lc_data = phaii.to_lightcurve(energy_range=erange)
lcplot = Lightcurve(data=lc_data)
Nice looking lightcurve! Next, we’ll want to define regions outside the obvious source region to identify as background. The TTE data early in the mission unfortunately didn’t have very much pre-trigger background, but we’ll try our best. We haven’t actually talked about background modeling yet, but I’ll walk you through it; it’s not very hard.
[3]:
# we want two background intervals, one before and one after the source.
# by eye, let's try:
bkgd_times = [(-20.0, -5.0), (75.0, 200.0)]
The background module is in gbm.background, and similar to the binning algorithms, background modeling algorithms can be divded between binned and unbinned data. Now TTE data is temporally unbinned, but for simplicitly let’s use an algorithm for pre-binned data. In fact we’ll use the same polynomial background algorithm that RMfit uses.
[4]:
# the background fitter interface
from gbm.background import BackgroundFitter
# our fitting algorithm
from gbm.background.binned import Polynomial
# we initialize our background fitter with the phaii object, the algorithm, and the time ranges to fit.
# if we were using an unbinned algorithm, we'd call .from_tte() and give it tte instead of phaii
backfitter = BackgroundFitter.from_phaii(phaii, Polynomial, time_ranges=bkgd_times)
# and once initialized, we can run the fit with the fitting parameters appropriate for our algorithm.
# here, we'll do a 1st order polynomial
backfitter.fit(order=1)
Ok, the fit is done, but how do we know if it is a good fit? You can return the fit statistic and degrees-of-freedom (DoF) for each energy channel fit, and try to figure out if it’s a good fit based on that (Note: not always the best way to go).
[5]:
backfitter.statistic/backfitter.dof
[5]:
array([1.05253464, 0.97225381, 0.91227241, 0.98050048, 0.84681665,
1.0109339 , 0.83987198, 0.99393676, 0.93546538, 0.97676709,
1.06159651, 1.13014594, 1.02241299, 0.87300405, 0.93111584,
0.77749972, 0.88585415, 1.24709709, 1.00078239, 1.18972735,
1.08504497, 0.86004 , 1.09627527, 1.26029689, 1.02805267,
1.09511262, 1.09453753, 0.84877554, 1.03829697, 1.18797705,
1.17876657, 1.0435771 , 0.87277942, 1.1235214 , 0.75154049,
1.16525405, 0.96174605, 0.86952962, 1.05345248, 1.06671789,
0.98715977, 0.87106808, 0.81729816, 1.01830519, 0.96619755,
0.96130275, 1.26006097, 1.10956129, 0.7465444 , 1.14112326,
1.17921618, 0.99306683, 0.94085532, 0.75801103, 0.93522882,
0.93297998, 1.34048725, 0.97457337, 0.92851687, 1.13544663,
1.03582596, 0.86974828, 0.95736557, 0.90115499, 0.97121474,
0.99067311, 1.03314964, 1.05197093, 0.67085108, 0.86989996,
1.13958071, 0.79637932, 0.83125611, 0.96961894, 0.70648981,
1.28318981, 0.96054971, 0.95883523, 0.98814164, 0.79250393,
0.98667504, 0.85922942, 1.07602863, 0.89644774, 1.04385212,
0.74181608, 0.88999557, 0.89085185, 0.85543955, 0.74622679,
0.84810177, 1.00566535, 0.7757027 , 0.77445155, 0.83288842,
0.81179572, 1.03735701, 0.78808631, 0.77720697, 0.68643965,
0.76911826, 0.82697149, 0.94950339, 0.69566148, 0.84312887,
0.83848112, 0.72023423, 0.64302101, 0.87508165, 0.95623795,
0.90862106, 0.74499819, 0.85851114, 0.82726985, 1.10998919,
1.16072684, 0.85533812, 1.0301769 , 0.55424838, 0.6925533 ,
0.73817561, 0.71850524, 0.86838555, 0.62815818, 0.869434 ,
0.91485833, 0.93208495, 1.21406148])
You can also plot it. If you want to plot the background model, it’s a good idea to plot it not just during the background segments you fit, but also during the source interval. This is important because you want to see how well the background is modeled during the source interval. This means that the model needs to be interpolated over the source interval. For simplicity, and to make the background look smooth, we’ll go ahead and interpolate across every time bin in the lightcurve:
[6]:
bkgd = backfitter.interpolate_bins(phaii.data.tstart, phaii.data.tstop)
type(bkgd)
[6]:
gbm.background.background.BackgroundRates
So what is bkgd? It’s similar to the same data structure that contains the PHAII data: a 2D Time-Energy histogram, but instead of containing observed counts, it contains the modeled background rates for each time bin and energy channel. So if we want to plot the background model on our lightcurve, we need to integrate over energy. Reminder: we don’t want to integrate over all energy channels, only the ones we set in erange.
[7]:
lc_bkgd = bkgd.integrate_energy(*erange)
lcplot = Lightcurve(data=lc_data, background=lc_bkgd)
And look at that! The red line shows our background model interpolated at each lightcurve bin. If you find your fit to be unacceptable, you can try refitting with a different polynomial order like this:
backfitter.fit(order=2)
Or you can try adjusting the background selection ranges.
Now, we are currently viewing the full time-extent of the data in the file, but if we want to identify a particular time interval for analysis, it’s kind of hard when we’re zoomed out so far. So you should zoom in appropriately:
[8]:
lcplot = Lightcurve(data=lc_data, background=lc_bkgd)
# zoom in to 5 seconds before to 20 s after the trigger time
view_range = (-5.0, 20.0)
lcplot.xlim = view_range
Now, we need to define a time interval of interest. It could be a single bin, or it could be multiple bins. Let’s select the brightest two bins in this view.
[9]:
# our lightcurve source selection
src_time = (7.0, 8.0)
src_lc = phaii.to_lightcurve(time_range=src_time, energy_range=erange)
lcplot = Lightcurve(data=lc_data, background=lc_bkgd)
lcplot.xlim = view_range
The orange shading indicates the time bins you’ve selected as source signal. You can also make a plot of the count spectrum during the selection to see what the background model looks like in comparison to the data:
[10]:
# the observed count spectrum during the source selection
spec_data = phaii.to_spectrum(time_range=src_time)
# the background model integrated over the source selection time
spec_bkgd = bkgd.integrate_time(*src_time)
# and the energy range selection that was made
spec_selection = phaii.to_spectrum(time_range=src_time, energy_range=erange)
specplot = Spectrum(data=spec_data, background=spec_bkgd)
And there you have it! The background model, integrated over the source window, as a function of energy is red, while the orange shaded region indicates the part of the spectrum you’re interested in.
If we are satisifed with everything we’ve done, it’s now time to export our selections. XSPEC uses PHA and BAK files containing a single observed count spectrum and the background model during the exposure of the spectrum, respectively. To get from where we are to where we need to be, it is really just two function calls:
[11]:
# the single-spectrum PHA object over our source time interval and energy range
pha = phaii.to_pha(time_ranges=src_time, energy_range=erange)
# the background spectrum
bak = bkgd.to_bak(time_range=src_time)
type(pha), type(bak)
[11]:
(gbm.data.pha.PHA, gbm.data.pha.BAK)
So now you have a PHA and BAK object which can be written as fully-formed FITS files using the .write() methods:
bak.write('./', filename='my_first_custom.bak')
pha.write('./', filename='my_first_custom.pha', backfile='my_first_custom.bak')
You can omit the filename keywords if the default naming convention is good enough for you (although beware of naming conflicts if you are writing multiple files from one event). The backfile keyword is necessary if you want to use the PHA and BAK files in XSPEC.
Now there is one thing missing; we forgot about the response file! You can’t do any spectral fitting without the response.
[12]:
from gbm.data import RSP
rsp = RSP.open(test_data_dir+'/glg_cspec_n9_bn090131090_v00.rsp2')
This is an RSP2 file, meaning that it is a time sequence of DRMs. We want to choose the DRM that is most appropriate for our time selection. We have a couple of options: we could simply return the DRM that is closest to our interval of interest, or we can interpolate the time series of DRMs to provide a response at the time of our interval (more specifically at the center of our time interval).
[13]:
# the DRM that is nearest to our time of interest
nearest_drm = rsp.extract_drm(atime=pha.tcent)
# the interpolated DRM
interp_drm = rsp.interpolate(pha.tcent)
Choose one, and you can write it to a file just like the PHA and BAK:
interp_drm.write('./', filename='my_first_custom.rsp')
We’re done! You have successfully exported your source selection, background model, and an appropriate detector response. Looking back, it may seem like we’ve done a lot, but most of the commands we issued were for the sake of plotting! Once you’re more familiar with the workflow, you don’t have to make quite so many plots along the way.
In any case, you can now XSPEC to your heart’s content!
Of course, maybe XSPEC isn’t your thing. That’s alright, too. In fact, the GBM Data Tools have the functionality to perform maximum likelihood fits of the spectra, and if you are interested, continue on! | 2023-03-23T14:31:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3033253252506256, "perplexity": 1962.4053937243343}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945168.36/warc/CC-MAIN-20230323132026-20230323162026-00068.warc.gz"} |
https://finalfantasy.fandom.com/wiki/Nail_Bat_(Final_Fantasy_VII) | ## FANDOM
38,269 Pages
The Nail Bat is a joke weapon for Cloud in Final Fantasy VII, which can first be found in the Temple of the Ancients. The weapon has a very high Attack stat for when it is acquired, but no Materia, locking Cloud into the role of physical attacks. The player can equip it to Cloud, or throw it.
## ObtainedEdit
The Nail Bat can first be found in the Temple of the Ancients. In the room with the clock, if Cloud is knocked off by the hands and wins a battle, the Nail Bat is obtained by opening a chest.
Later, it can be purchased from Junon for 2,800 gil after the Highwind is obtained.
## StatsEdit
Attack 70 100 0 None Element: Cut Critical% +4
As the Nail Bat has a base Attack stat bonus of 70, the base damage for physical attacks when it is equipped is the following formula:
$\text{Base Damage} = \text{(70 + Strength)} + \frac{\text{(70 + Strength)} + \text{Level}}{32} \times \frac{\text{(70 + Strength)} \times \text{Level}}{32}$
where "Level" is Cloud's current level and "Strength" is his Strength stat. The Nail Bat also has an Attack% (Accuracy) of 100%. It grants no bonus to Cloud's Magic stat.
## UseEdit
The Nail Bat has a very high Attack stat for when it is acquired, but no Materia slots, and no boost to Cloud's Magic stat. If equipped, it provides a great boost to Cloud's physical attacks and Limits, but hinders his ability to cast spells. This also means that Cloud relies on armor for Materia slots.
Cloud has both high Strength and Magic stats, meaning he can be built towards either physical damage or magical damage. Though the Nail Bat will allow Cloud to deal a significant amount of physical damage with attacks and Limits, it will waste his potential to deal strong magic damage. It also removes Cloud's ability to link his attacks with Elemental or Added Effect, and severely limits how many Command Materia he can equip. The player should be careful when equipping this weapon, and may opt to use a more well-rounded weapon for Cloud instead.
Nail Bat later on is outclassed by more powerful weapons, such as Crystal Sword and Heaven's Cloud, which have comparably high stats, without sacrificing Cloud's spellcasting ability.
## EtymologyEdit
A baseball bat is a smooth wooden or metal club used in baseball to hit the ball after it is thrown by the pitcher. Due to its bludgeoning nature, a baseball bat may be used as a club-like weapon. A nail bat is a modified baseball bat with sharp objects, typically nails, protruding from the broad end. Within the modern world, they are found on street gangs as a makeshift weapon, specifically on bikers and punks in western civilization; its inclusion as a part of the "Force of the Resolute" combination in Dissidia emphasizes this.
Community content is available under CC-BY-SA unless otherwise noted. | 2020-07-09T16:15:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41301050782203674, "perplexity": 5509.159922529737}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655900335.76/warc/CC-MAIN-20200709131554-20200709161554-00354.warc.gz"} |
http://dlmf.nist.gov/1.15 | # §1.15 Summability Methods
1.15.1
1.15.2
if
1.15.3
1.15.4
if
1.15.5
For ,
1.15.6
if
## §1.15(ii) Regularity
Methods of summation are regular if they are consistent with conventional summation. All of the methods described in §1.15(i) are regular. For example if
1.15.10
then
1.15.11
## §1.15(iii) Summability of Fourier Series
### ¶ Poisson Kernel
1.15.13
As
1.15.14
uniformly for . (Here and elsewhere in this subsection is a constant such that .)
For ,
1.15.15
As
1.15.17
uniformly for .
### ¶ Abel Means
1.15.18
where
is a harmonic function in polar coordinates ((1.9.27)), and
Let
1.15.21
, where
Then
### ¶ Convergence
If is periodic and integrable on , then as the Abel means and the (C,1) means converge to
1.15.24
at every point where both limits exist. If is also continuous, then the convergence is uniform for all .
For real-valued , if
is the Fourier series of , then the series
can be extended to the interior of the unit circle as an analytic function
Here is the Abel (or Poisson) sum of , and has the series representation
compare §1.15(v).
## §1.15(iv) Definitions for Integrals
### ¶ Abel Summability
is Abel summable to , or
1.15.29
when
### ¶ Cesàro Summability
is (C,1) summable to , or
1.15.31
when
1.15.32
If converges and equals , then the integral is Abel and Cesàro summable to .
## §1.15(v) Summability of Fourier Integrals
### ¶ Poisson Kernel
1.15.33, .
For each ,
1.15.35as .
Let
where is the Fourier transform of 1.14(i)). Then
is the Poisson integral of .
If is integrable on , then
1.15.38
Suppose now is real-valued and integrable on . Let
where and . Then is an analytic function in the upper half-plane and its real part is the Poisson integral ; compare (1.9.34). The imaginary part
is the conjugate Poisson integral of . Moreover, is the Hilbert transform of 1.14(v)).
### ¶ Fejér Kernel
1.15.41
For each ,
1.15.43as .
If is integrable on , then
1.15.46
## §1.15(vi) Fractional Integrals
For and , the fractional integral operator of order is defined by
1.15.47
For see §5.2, and compare (1.4.31) in the case when is a positive integer.
1.15.48, .
For extensions of (1.15.48) see Love (1972b).
If
1.15.49
then
## §1.15(vii) Fractional Derivatives
For , an integer, and ,
1.15.51
When none of , , and is an integer
1.15.53
## §1.15(viii) Tauberian Theorems
If
1.15.54
,, ,
then
1.15.55
If
1.15.56
and either or , then
1.15.57 | 2013-06-19T02:06:12 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9792616367340088, "perplexity": 4848.693085312808}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368707439689/warc/CC-MAIN-20130516123039-00044-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://www.anl.gov/argonne-scientific-publications/pub/164048 | Publication
# Manifold Sampling for Optimizing Nonsmooth Nonconvex Compositions
### Authors
Larson, Jeffrey; Menickelly, Matt; Zhou, Baoyu
### Abstract
We propose a manifold sampling algorithm for minimizing a nonsmooth composition $f= h\circ F$, where we assume $h$ is nonsmooth and may be inexpensively computed in closed form and $F$ is smooth but its Jacobian may not be available. We additionally assume that the composition $h\circ F$ defines a continuous selection. Manifold sampling algorithms can be classified as model-based derivative-free methods, in that models of $F$ are combined with particularly sampled information about $h$ to yield local models for use within a trust-region framework. We demonstrate that cluster points of the sequence of iterates generated by the manifold sampling algorithm are Clarke stationary. We consider the tractability of three particular subproblems generated by the manifold sampling algorithm and the extent to which inexact solutions to these subproblems may be tolerated. Numerical results demonstrate that manifold sampling as a derivative-free algorithm is competitive with state-of-the-art algorithms for nonsmooth optimization that utilize first-order information about $f$. | 2022-10-03T10:56:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6889029741287231, "perplexity": 708.3134036387229}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337415.12/warc/CC-MAIN-20221003101805-20221003131805-00595.warc.gz"} |
https://www.anl.gov/organizations/high-energy-physics-division | High Energy Physics Division
Below is a comprehensive list of articles, events, projects, references and research related content that is specific to the organization described above. Use the filter to narrow the results further or please visit High Energy Physics Division for more information.
Filter Results
• Factorization theorem for an exclusive QCD process with endpoint singularities
HEP Theory Seminar
• Functional prescription for STrEAMlined EFT matching
HEP Theory Seminar
• The Muon g-2 Experiment at Fermilab and Search for CPT and Lorentz Violation Effects
HEP Special Seminar
• The energy-energy correlator and transverse-energy-energy correlator
HEP Theory Seminar
HEP Seminar
• Search for the Rare Decay of the Kaon
HEP Special Seminar
HEP Seminar
HEP Seminar
• Steps Toward Differentiable and Scalable Physics Analyses at the Large Hadron Collider
HEP Lunch Seminar
• High Gradient and rf Breakdown Testing of a 110 GHz Accelerating Structure
HEP Lunch Seminar | 2021-02-27T07:44:46 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8320818543434143, "perplexity": 10795.573228722638}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178358203.43/warc/CC-MAIN-20210227054852-20210227084852-00019.warc.gz"} |
https://math.wikia.org/wiki/Integration_by_substitution | ## FANDOM
1,168 Pages
In calculus, integration by substitution — popularly called u-substituion or simply the substitution method — is a technique of integration whereby a complicated looking integrand is rewritten into a simpler form by using a change of variables:
$\int f\bigl(g(x)\bigr)g'(x)dx=\int f(u)du$ , where $u=g(x)$ .
In the case of a definite integral,
$\int\limits_a^b f\bigl(g(x)\bigr)g'(x)dx=\int\limits_c^d f(u)du$ , where $u=g(x)$ , $c=g(a),\ d=g(b)$ .
Integration by u-substitution is the inverse operation of the chain rule from differential calculus. It is also the two-dimensional version of using a Jacobian matrix to transform coordinates.
## Example
Consider the integral:
$\int x(x+3)^7dx$
By letting $u=x+3$ , thus $du=dx$ (since $\frac{du}{dx}=1$), and observing that $x=u-3$ , the integral simplifies to
$\int x(x+3)^7dx=\int(u-3)u^7du=\int(u^8-3u^7)du$
which is easily integrated to obtain:
$\frac{u^9}{9}-\frac{3u^8}{8}+C=\frac{(x+3)^9}{9}-\frac{3(x+3)^8}{8}+C$
Note that this integral can also be done using integration by parts, although the final answer may look different because of the different steps involved.
Community content is available under CC-BY-SA unless otherwise noted. | 2019-12-14T21:00:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9934984445571899, "perplexity": 355.9979937261809}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541294513.54/warc/CC-MAIN-20191214202754-20191214230754-00153.warc.gz"} |
https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2017.11.002 | • •
### 资产流动性、融资约束与经济波动
• 出版日期:2017-11-15 发布日期:2017-11-25
### Asset liquidity, Financial Constraint and Economic Fluctuations
Liu Hongzhong & Fu Jiafan
• Online:2017-11-15 Published:2017-11-25
Abstract: With the development of asset securitization and the increased proportion of direct financing, liquidity constraints that agents faced will be relaxed. However, there is little relevant literature about the effect of shocks on the Chinese macroeconomic fluctuations from the perspective of asset liquidity. This paper builds a NK-DSGE model which incorporates collateral and liquidity constraint, in order to explore the dynamic effects and the mechanism of asset liquidity constraints on Chinese economic fluctuations, and make use of 2003Q1~2016Q3 quarterly data of the cash flow statement of non-financial companies, to construct the model and do the calibration. We conclude that: (1) positive productivity and asset price shock cause growth of output, consumption and investment, and this effect will be strengthened by higher asset liquidity level at steady state; (2) a negative asset liquidity shock will trigger negative effect on output, consumption and investment; (3) About 21% of the variance of output and 89% of the variance of investment can be explained by financial shocks, and its negative effect will be diminished with the improvement of asset liquidity. Therefore we conclude that asset securitization would revitalize the stock of assets and enhance the liquidity of operational assets, which could contribute to solve enterprises’ problem of financing difficulties and high leverage. | 2022-08-17T07:38:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2976672649383545, "perplexity": 3875.3926437962123}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572870.85/warc/CC-MAIN-20220817062258-20220817092258-00498.warc.gz"} |
https://pos.sissa.it/301/494/ | Volume 301 - 35th International Cosmic Ray Conference (ICRC2017) - Session Cosmic-Ray Indirect. CRI-properties of CRs at high energies (anisotropy, energy, mass)
Cross correlation of UHECRs and local matter distribution taking into account the energy attenuation due to interaction with the cosmic background radiation
R. de Almeida,* C. Pinto, V. Braga, J. de Mello Neto
*corresponding author
Full text: pdf
Pre-published on: April 17, 2018
Published on: August 03, 2018
Abstract
The arrival direction distribution of ultra-high energy cosmic rays (UHECRs) is a key element to understand their sources and composition as well the galactic and
extragalactic magnetic fields. The particles that arrive on Earth with energies above $\sim 50$ EeV must be originated in sources nearby us as a
result of the GZK effect. Furthermore, if these particle are protons and the magnetic fields along their propagations until Earth are not too
large, we expect that their arrival directions are correlated with their sources. The cross-correlation used in cosmology is a good tool for
studying such anisotropies in the cosmic ray data. In this work, assuming a proton composition, we modify the Landy-Szalay cross-correlation estimator in order to take into account the energy losses in the cosmic ray propagation due to its interaction with the background radiation. Using Monte Carlo simulations, we have compared its efficiency with relation to the original estimator, testing the correlation of
the simulated events arrival directions with sources from the 2MRS catalog. We show that even in case of absence of significant signal, the modified estimator has the capability to constrain the proton fraction of the experimental data provided that the detection efficiency of the astrophysical scenario under consideration is maximal.
DOI: https://doi.org/10.22323/1.301.0494
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-ShareAlike. | 2020-11-30T02:31:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4411848783493042, "perplexity": 1850.7360342879094}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141204453.65/warc/CC-MAIN-20201130004748-20201130034748-00050.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/proc.2013.2013.95 | Article Contents
Article Contents
# Bifurcation to positive solutions in BVPs of logistic type with nonlinear indefinite mixed boundary conditions
• In this paper a nonlinear boundary value problem of logistic type is considered, with nonlinear mixed boundary conditions, and with spatial heterogeneities of arbitrary sign in the differential equation and on the boundary conditions. The main goal of this paper is analyzing the structure of the continuum of positive solutions emanating from the trivial state at a unique bifurcation value, depending on the size and sign of the different potentials and parameters of the problem. The results in this paper extend the previous ones obtained by R. Gómez-Reñasco and J. López-Gómez [5, Proposition 2.1], for a superlinear indefinite problem of logistic type under Dirichlet boundary conditions, to a wide class of superlinear indefinite problems with nonlinear indefinite mixed boundary conditions.
Mathematics Subject Classification: Primary: 35J66, 35J65, 35J60; Secondary: 35J25.
Citation:
• [1] H. Amann, Nonlinear elliptic equations with nonlinear boundary conditions, in "New Developments in Differential Equations" (ed. W. Eckhaus), Math Studies, 21, North-Holland, Amsterdam (1976), 43-63. [2] H. Amann, Dual semigroups second order linear elliptic boundary value problems, Israel Journal of Mathematics, 45 (1983), 225-254. [3] M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Func. Analysis, 8 (1971), 321-340. [4] J. García-Melián, C. Morales-Rodrigo, J. D. Rossi and A. Suárez, Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary, Ann. Mat. Pura Appl. (4) , 187 (2008), 459-486. [5] R. Gómez-Reñasco and J. López-Gómez, The effect of varying coefficients on the dynamics of a class of superlinear indefinite reaction-diffucion equations, Journal of Differential Equations , 167 (2000), 36-72. [6] E. M. Stein, "Singular Integrals and Differentiability Properties of Functions", Princeton Mathematical Series, No. 30. Princeton Univ. Press, Princeton, NJ, 1970.
Open Access Under a Creative Commons license | 2023-02-08T04:57:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.5414603352546692, "perplexity": 742.7406651182226}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500671.13/warc/CC-MAIN-20230208024856-20230208054856-00672.warc.gz"} |
https://asphalt.fandom.com/wiki/Lamborghini_Centenario_R%26D_Mini_Kit_Box | ## FANDOM
4,148 Pages
SOURCE EDITOR ONLY!This page uses LaTeX markup to display mathematical formulas. Editing the page with the VisualEditor or Classic rich-text editor disrupts the layout.Do not even switch to one of these editors while editing the page!For help with mathematical symbols, see Mathematical symbols and expressions.
R&D Mini Kit Box
(discontinued)
"Grants 3 cards for the R&D Lamborghini Centenario!"
Official info
Last checked Jan 15, 2020 Description ✔ Correct Sample space ? Incomplete Drop rates ? Incomplete
Price 300 ( 100 per trial)
Drop rates Rare: 50.13 %
Legendary: 49.87 %
Availability Research & Development
(only during the Lamborghini Centenario R&D)
Statistics
Period Dec 22, 2018 – Jan 15, 2020
Sample size 18 trials (6 boxes)
Critical: Sample size < 200
Common 0 0.00 % Rare 8 44.44 % Legendary 10 55.56 %
Blueprints 0 0.00 % Engines 6 33.33 % Tech 5 27.78 % Parts 7 38.89 %
Dispersion per box
min–max Mean
0
Range
3
Common 0–0 0.00
Rare 0–2 1.33
Legendary 1–3 1.67
Blueprints 0–0 0.00
Engines 0–2 1.00
Tech 0–2 0.83
Parts 0–2 1.17
6 Engine cards by name
Four-Stroke 0 0.00 %
i3 0 0.00 %
i4 0 0.00 %
i5 0 0.00 %
V6 0 0.00 %
V8 0 0.00 %
V-Twin 0 0.00 %
Electric 0 0.00 %
Forced Four-Str. 0 0.00 %
Hot Wheels 0 0.00 %
Hybrid 0 0.00 %
Serial Racing 0 0.00 %
Custom Racing 0 0.00 %
Exceptional 0 0.00 %
F12 0 0.00 %
F6 0 0.00 %
Forced-Ind. V8 0 0.00 %
i6 0 0.00 %
Legendary Electr. 0 0.00 %
Rotary 0 0.00 %
V10 0 0.00 %
V12 0 0.00 %
V12 MPI 6 33.33 %
V16 0 0.00 %
W16 0 0.00 %
5 Tech cards by name
Early Tech 0 0.00 %
Initial Tech 0 0.00 %
Mid-Tech 1 5.56 %
Common Tech 0 0.00 %
Rare Tech 0 0.00 %
Pro Tech 0 0.00 %
7 Part cards by type
Tires 3 16.67 %
Suspension 2 11.11 %
Drivetrain 0 0.00 %
Exhaust 2 11.11 %
7 Part cards by class
Class D 0 0.00 %
Class C 0 0.00 %
Class B 0 0.00 %
Class A 0 0.00 %
Class S 7 38.89 %
7 Part cards by vehicle type
Car 7 38.89 %
Bike 0 0.00 %
The Lamborghini Centenario R&D Mini Kit Box is a Pro Kit Box in Asphalt 8: Airborne. It has taken over the concept of event Mini Boxes from the McLaren Championships and is available exclusively during the Lamborghini Centennario R&D event.
Unlike the 2018 McLaren X2 Championship Mini Box which grants almost no engine card at all, this box seems to grant at least 1 V12 MPI Engine in (almost!) every box.
## Availabilty
The box was not offered again in the January 2020 rerun of the event. Therefore it has to be considered as discontinued as there are no other ways to obtain it.
## Analysis
The drop rate of legendary cards in this box was increased from 45 % to 49.87 % around June 2019. It is unclear whether this means a higher drop rate of V12 MPI Engines. The last box of the sample in the infobox to the right was opened in January 2020 when the box was already discontinued. It contained 1 V12 MPI Engine and 2 Advanced Tech cards and is not listed in the table below.
### Probabilities
If it was assumed that
1. the probabilities of Advanced Tech and V12 MPI Engines (both legendary) were equal and
2. there could be only 1 V12 MPI Engine per Mini Box,
the chance of getting a V12 MPI Engine from a box would be
$45 % : 2 = 22.5 %.$
If a player bought 5 Mini Boxes, the chance of getting at least 1 V12 MPI Engine would be
\begin{align} &\sum_{k = 1}^{5} 0.225^k \cdot \left (1 - 0.225 \right )^{5-k} \cdot \binom{5}{k}\\ \\ \\ &= 72.04 %. \end{align}
The amount $n$ of boxes needed to get at least 1 V12 MPI Engine with a probability of 90 % would be
$n \geq \frac{\ln(1 - 0.9)}{\ln(1 - 0.225)} = 9.03 > 9.$
### Statistics
Opening 5 Mini boxes delivered the following results:
V12 MPI
Mid-Tech
Tires
Suspension
Drivetrain
Exhaust
1 1 1
1 1 1
2 1
1 1 1
1 1 1
As some players obtained more than 1 engine from a box and nearly every opened box contained at least 1 engine, both of the above assumptions were false which leads to the following conclusions:
• While the official drop rate of 45 % for legendary items is correct, the probabilites for V12 MPI Eninges and Advanced Tech are not equal.
• The probability of getting at least 1 V12 MPI Engine seems to be around 90 %.
The statistical data on this page is part of WikiProject Statistics.It contains original research which may be incomplete, incorrect or biased.
Community content is available under CC-BY-SA unless otherwise noted. | 2020-06-04T04:23:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5112283825874329, "perplexity": 5784.988570390577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347439019.86/warc/CC-MAIN-20200604032435-20200604062435-00121.warc.gz"} |
https://detailedpedia.com/wiki-Administration_of_federal_assistance_in_the_United_States | Administration of federal assistance in the United States
In the United States, federal assistance, also known as federal aid, federal benefits, or federal funds, is defined as any federal program, project, service, or activity provided by the federal government that directly assists domestic governments, organizations, or individuals in the areas of education, health, public safety, public welfare, and public works, among others.
Recipients
A recipient of federal awards or funds is defined as any non-federal entity that receives federal assistance and is part of, or located within, the United States and its territories and possessions. Recipients are grouped into six main categories, as established by the GSA:[8]
Every program is designed with a specific recipient in mind. Certain programs have restrictions on who may receive the assistance because of the nature of its activity or service.[8] Examples include infrastructure programs and grants, which are usually restricted to States, local governments, and U.S. territories—because these are usually the only entities that administer public roads, bridges, etc. Another example is health-related research grants, which individuals are eligible for as long as they satisfy certain criteria, such as that they have a professional or scientific degree, three years of research experience, and are a citizen of the United States.[9]
Pass-through entities and sub-recipients
The federal government allows certain entities mentioned above to act as a Pass-through entity that provides the federal assistance to another recipient. The Pass-through entity is still considered a recipient, but the assistance assigned to it may be "passed on" or "passed-through it" to another recipient. The entity that receives the assistance from a pass-through entity is a sub-recipient.[10][11] This is allowed because certain federal programs may not have the organizational structure to provide assistance directly to the final recipient and requires support from other entities.
For example, crime-prevention federal programs may be assigned to a State Attorney General's Office (AGO) (considered a State government). This State office may decide to assign part of its federal grant through sub-grants (also known as sub-awards)[10] to cities and counties within the State (considered local governments) for crime-prevention activities such as neighborhood watch programs or supplying new equipment to police forces. The original recipient, the AGO, has become a Pass-through entity and the cities and counties have become "sub-recipients", all the while the assistance is still serving the federal program's purpose to prevent crime.
Sub-recipients may in turn pass on the assistance to another sub-recipient to serve the purpose required by the federal program, for example if the cities mentioned above pass on part of their assistance to nonprofit organizations dedicated to patrolling neighborhoods at night. Therefore, a recipient may be considered a pass-through entity and a sub-recipient at the same time.[citation needed]
Certain programs may require the original recipient to pass on the assistance to sub-recipients (i.e., the federal program requires that the assistance be provided to nonprofit neighborhood watch organizations, and the assistance passes recipient through recipient until it reaches them), while others may require that the recipient not pass on the assistance (i.e., State must use the assistance entirely on its own). Some programs award assistance to a pass-through entity who is neither the direct applicant nor the ultimate beneficiary, such as the Pell Grant program where students apply and receive the aid but it is the university's responsibility to receive and administer the applications and disburse the aid.[9]
Pass-through entities and sub-recipients are equally responsible for the management of federal aid received. The federal government monitors the federal aid provided to any recipient and requires all pass-through entities to monitor the aid they pass on. Noncompliance of a federal regulation on the part of the sub-recipient may also be attributed to the pass-through entity because it is still responsible for the funds it passed on.[citation needed]
Catalog of Federal Domestic Assistance
The Catalog of Federal Domestic Assistance (CFDA) logo.
The task of organizing and categorizing federal assistance programs into a uniform and standardized system has been assigned to the U.S. General Services Administration (GSA) since 1984.[12] There were precursor catalogs to this one, focusing on particular topics and maintained by other groups, such as the US office of education https://archive.org/details/ERIC_ED067776/page/n17/mode/2up pub. 1972 pg. iii . The GSA achieves these tasks by maintaining the Federal assistance information database, which incorporates all federal agency programs that provide grants and awards to recipients. The Office of Management and Budget assists the GSA in maintaining the database by serving as an intermediary agent between the Federal agencies and GSA.[citation needed]
In addition to these tasks, the Federal Program Information Act requires the GSA to provide federal assistance information to the general public through the Catalog of Federal Domestic Assistance (CFDA), a free register, which incorporates both federal agency and federal program information. This register acts both as a directory and as a dictionary, facilitating both recipients and the general public in finding information of a specific program.
Currently, programs in the Catalog are being classified by the GSA into 15 types of assistance, which are then sub-classified into seven financial types of assistance and eight non-financial types of assistance:[8]
Financial type assistance
• Formula Grants (A) – Includes allocations of money to States or their subdivisions in accordance with distribution formulas prescribed by law or administrative regulation, for activities of a continuing nature not confined to a specific project. Examples of this type of assistance include transportation and infrastructure grants designated by Congress, such as the Community Development Block Grant (CDBG).[8]
• Project Grants (B) – Includes funding of specific projects for fixed or known periods. Project grants can include fellowships, scholarships, research grants, training grants, traineeships, experimental and demonstration grants, evaluation grants, planning grants, technical assistance grants, survey grants, and construction grants.[8]
• Direct Payments for Specified Use (C) – Includes financial assistance from the Federal government provided directly to individuals, private firms, and other private institutions to encourage or subsidize a particular activity by conditioning the receipt of the assistance on a particular performance by the recipient. One example of this type of assistance is the Section 8 Housing Choice Voucher program.[8]
• Direct Payments with Unrestricted Use (D) – Includes financial assistance from the Federal government provided directly to beneficiaries who satisfy Federal eligibility requirements with no restrictions being imposed on the recipient as to how the money is spent. Included are payments under retirement, pension, and compensatory programs.[8]
• Direct Loans (E) – Includes financial assistance provided through the lending of Federal monies for a specific period of time, with a reasonable expectation of repayment, of which may or may not require the payment of interest.[8]
• Guaranteed/Insured Loans (F) – Includes programs in which the Federal government makes an arrangement to indemnify a lender against part or all of any defaults by those responsible for repayment of loans.[8]
• Insurance (G)– Includes financial assistance provided to assure reimbursement for losses sustained under specified conditions. Coverage may be provided directly by the Federal government or through private companies, and may or may not involve the payment of premiums.[8]
Non-financial type assistance
• Sale, Exchange, or Donation of Property and Goods (H) – Includes programs that provide for the sale, exchange, or donation of Federal real property, personal property, commodities, and other goods including land, buildings, equipment, food and drugs.[8]
• Use of Property, Facilities, and Equipment (I) – Includes programs that provide for the loan of, use of, or access to Federal facilities or property wherein the federally owned facilities or property do not remain in the possession of the recipient of the assistance.[8]
• Provision of Specialized Services (J) – Includes programs that provide Federal personnel directly to perform certain tasks for the benefit of communities or individuals. These services may be performed in conjunction with non-federal personnel, but they involve more than consultation, advice, or counseling. Examples include the legal representation provided by the "Protection of Voting Rights" and the 'Civil Rights of Institutionalized Persons" programs.[8]
• Advisory Services and Counseling (K) – Includes programs that provide Federal specialists to consult, advise, or counsel communities or individuals to include conferences, workshops, or personal contacts.[8]
• Dissemination of Technical Information (L) – Includes programs that provide for the publication and distribution of information or data of a specialized or technical nature frequently through clearinghouses or libraries.[8]
• Training (M)– Includes programs that provide instructional activities conducted directly by a Federal agency for individuals not employed by the Federal government.[8]
• Investigation of Complaints (N) – Includes federal administrative agency activities that are initiated in response to requests to examine or investigate violations of Federal statutes, policies, or procedures.[8]
• Federal Employment (O) – Includes programs that reflect the Government-wide responsibilities of the Office of Personnel Management in the recruitment and hiring of Federal civilian agency personnel.[8]
CFDA number
To help potential recipients locate a federal program, the General Services Administration assigns a two-digit number unique to each federal agency authorized to provide assistance, and a three digit number to each federal assistance program within that agency. With these designations, a federal assistance program is identified by the combination of both numbers, which in turn creates a five digit number divided by a dot (55.555).[3] The two digit numbers assigned to federal agencies are:
Monitoring activities
Due to the extensive amount of assistance the federal government provides, federal agencies rely on numerous monitoring activities performed by themselves, pass-through entities, and external sources. The most common monitoring procedure is the Single Audit. This is an annual examination of a recipient's operations and records that determines whether or not the recipient complied with laws and regulations applicable to the assistance they received. Additionally, Federal agencies routinely visit recipients and inspect their records and statements to check for situations of noncompliance with laws and regulations, and require periodic financial and performance reports that detail recipient operations. Federal agencies also require pass-through entities to perform similar procedures to their sub-recipients, since they are responsible for the assistance they pass on.[13][14][15]
Notes
1. ^ United States Office of Management and Budget; Office of Federal Financial Management, The Single Audit Archived 2007-06-21 at the Wayback Machine
2. ^ a b c 2006 CFDA Archived November 18, 2016, at the Wayback Machine; "Introduction And How To Use This Catalog"; pg. I, par. 6-8
3. ^ a b c 2006 CFDA Archived November 18, 2016, at the Wayback Machine; "Introduction And How To Use This Catalog: Organization of this Catalog"; pg. VIII, par. 7; "Program Title, Number and Popular Name"
4. ^ OMB A-133: Compliance Supplement Archived 2009-06-21 at the Wayback Machine, Part 4, pg. 4-14.182-1: "Supportive Housing for the Elderly (Sec. 202)" (CFDA 14.157), pg. 4-14.157-1 & "Section 8 Housing Assistance Payments Program-Special Allocations (CFDA 14.195)
5. ^ OMB A-133: Compliance Supplement Archived 2009-06-21 at the Wayback Machine; Part III, pg. 3-H-1, Period of Availability of Federal Funds, par. 1
6. ^ OMB A-133: Compliance Supplement Archived 2009-06-21 at the Wayback Machine; Part I, pg. 1-6, par. 5
7. ^ Jonathan Weisman (March 27, 2006). "Proposals Call For Disclosure of Ties to Lobbyists". Washington Post. Retrieved April 23, 2010.
8. 2006 CFDA Archived November 18, 2016, at the Wayback Machine; "Introduction And How To Use This Catalog"; pg. III; Types of Assistance
9. ^ a b 2006 CFDA Archived November 18, 2016, at the Wayback Machine; "Introduction And How To Use This Catalog: Organization of this Catalog"; pg. IX; "Eligibility Requirements: Applicant Eligibility"
10. ^ a b U.S. State Department Grant Terminology Archived 2007-04-23 at the Wayback Machine
11. ^ U.S. DOJ Glossary of Terms Archived 2006-12-12 at the Wayback Machine
12. ^ 2006 CFDA; "Introduction And How To Use This Catalog"; pg. I, par. 2
13. ^ Understanding Single Audits
14. ^ OMB A-133: Compliance Supplement Archived 2009-06-21 at the Wayback Machine; Part III, pg. 3-M-1: Sub-recipient Monitoring
15. ^ The Single Audit Act: Audits of States, Local Governments and Non-Profit Organizations; AICPA Audit Committee Toolkit: Non-profit Organizations; American Institute of Certified Public Accountants
References
Secondary sources
• Rhett D. Harrell (May 4, 2006), Local Government and Single Audits 2006, CCH (Wolters Kluwer), ISBN 0-8080-9023-2
OMB Circulars
The following is a list of circular letters issued by the U.S. Office of Management and Budget that provide significant information and guidance for Federal agencies, recipients, auditors, and the general public over the use and management of federal funds, operations of federal assistance programs, and agencies' and recipients' compliance with laws and regulations imposed by the federal government:
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https://zbmath.org/authors/?q=ai%3Afulton.william | # zbMATH — the first resource for mathematics
## Fulton, William
Compute Distance To:
Author ID: fulton.william Published as: Fulton, W.; Fulton, William External Links: MGP · Wikidata · GND
Documents Indexed: 78 Publications since 1969, including 21 Books Biographic References: 1 Publication
all top 5
#### Co-Authors
35 single-authored 13 MacPherson, Robert Duncan 5 Baum, Paul Frank 5 Lazarsfeld, Robert Kendall 2 Anderson, Dave Edward 2 Harris, Joseph Daniel 2 Kleiman, Steven Lawrence 2 Laksov, Dan 2 Quart, George 2 Sturmfels, Bernd 1 Bertram, Aaron 1 Bloch, Spencer J. 1 Skovsted Buch, Anders 1 Ciocan-Fontanine, Ionuţ 1 Collino, Alberto 1 Diaconis, Persi Warren 1 Dolgachev, Igor’ Vladimirovich 1 Ellingsrud, Geir 1 Fomin, Sergey Vladimirovich 1 Gillet, Henri A. 1 Hansen, Johan P. 1 Johnson, Kent W. 1 Lang, Serge 1 Lascoux, Alain 1 Li, Chi-Kwong 1 Olsson, Martin C. 1 Pandharipande, Rahul 1 Piene, Ragni 1 Poon, Yiu-Tung 1 Pragacz, Piotr 1 Sottile, Frank 1 Tai, Hsin-Sheng 1 Vistoli, Angelo 1 Woodward, Christopher T.
all top 5
#### Serials
6 Annals of Mathematics. Second Series 4 Acta Mathematica 3 American Journal of Mathematics 3 Duke Mathematical Journal 3 Inventiones Mathematicae 2 Bulletin de la Société Mathématique de France 2 Compositio Mathematica 2 Publications Mathématiques 2 Journal of Algebraic Geometry 2 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge 2 Graduate Texts in Mathematics 2 Lecture Notes in Mathematics 1 Journal of Algebra 1 Journal of Differential Geometry 1 Manuscripta Mathematica 1 Mathematica Scandinavica 1 Memoirs of the American Mathematical Society 1 Proceedings of the American Mathematical Society 1 Topology 1 Rendiconti del Seminario Matematico 1 Linear Algebra and its Applications 1 Bulletin of the American Mathematical Society. New Series 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Bulletin of the American Mathematical Society 1 Annals of Mathematics Studies 1 Grundlehren der Mathematischen Wissenschaften 1 London Mathematical Society Student Texts 1 Regional Conference Series in Mathematics 1 Algebra & Number Theory 1 Trends in Mathematics 1 Algebraic Combinatorics
all top 5
#### Fields
70 Algebraic geometry (14-XX) 8 Combinatorics (05-XX) 8 Algebraic topology (55-XX) 8 Manifolds and cell complexes (57-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Group theory and generalizations (20-XX) 4 Topological groups, Lie groups (22-XX) 3 Commutative algebra (13-XX) 2 General and overarching topics; collections (00-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Operator theory (47-XX) 1 Nonassociative rings and algebras (17-XX) 1 Geometry (51-XX) 1 Probability theory and stochastic processes (60-XX) 1 Quantum theory (81-XX) 1 Biology and other natural sciences (92-XX)
#### Citations contained in zbMATH
68 Publications have been cited 6,757 times in 5,782 Documents Cited by Year
Representation theory. A first course. Zbl 0744.22001
Fulton, William; Harris, Joe
1991
Intersection theory. Zbl 0541.14005
Fulton, William
1984
Introduction to toric varieties. The 1989 William H. Roever lectures in geometry. Zbl 0813.14039
Fulton, William
1993
Intersection theory. 2nd ed. Zbl 0885.14002
Fulton, William
1998
Young tableaux. With applications to representation theory and geometry. Zbl 0878.14034
Fulton, William
1997
Algebraic curves. Zbl 0181.23901
Fulton, W.
1969
Notes on stable maps and quantum cohomology. Zbl 0898.14018
Fulton, W.; Pandharipande, R.
1997
Eigenvalues, invariant factors, highest weights, and Schubert calculus. Zbl 0994.15021
Fulton, William
2000
A compactification of configuration spaces. Zbl 0820.14037
Fulton, William; MacPherson, Robert
1994
Riemann-Roch for singular varieties. Zbl 0332.14003
Baum, Paul; Fulton, William; MacPherson, Robert
1975
Flags, Schubert polynomials, degeneracy loci, and determinantal formulas. Zbl 0788.14044
Fulton, William
1992
Hurwitz schemes and irreducibility of moduli of algebraic curves. Zbl 0194.21901
Fulton, W.
1969
Connectivity and its applications in algebraic geometry. Zbl 0484.14005
Fulton, William; Lazarsfeld, Robert
1981
Algebraic curves. An introduction to algebraic geometry. Notes written with collab. of R. Weiss. new ed. Zbl 0681.14011
Fulton, William
1989
On the connectedness of degeneracy loci and special divisors. Zbl 0469.14018
Fulton, W.; Lazarsfeld, R.
1981
Schubert varieties and degeneracy loci. Zbl 0913.14016
Fulton, William; Pragacz, Piotr
1998
Intersection theory on toric varieties. Zbl 0885.14025
Fulton, William; Sturmfels, Bernd
1997
Categorical framework for the study of singular spaces. Zbl 0467.55005
Fulton, William; MacPherson, Robert
1981
Riemann-Roch algebra. Zbl 0579.14011
Fulton, William; Lang, Serge
1985
Algebraic topology. A first course. Zbl 0852.55001
Fulton, William
1995
Rational equivalence on singular varieties. Zbl 0332.14002
Fulton, William
1975
A growth model, a game, an algebra, Lagrange inversion, and characteristic classes. Zbl 0776.60128
Diaconis, P.; Fulton, W.
1991
On the quantum product of Schubert classes. Zbl 1081.14076
Fulton, W.; Woodward, C.
2004
Intersection theory on spherical varieties. Zbl 0819.14019
Fulton, William; MacPherson, Robert; Sottile, F.; Sturmfels, Bernd
1995
Riemann-Roch and topological K-theory for singular varieties. Zbl 0474.14004
Baum, Paul; Fulton, William; MacPherson, Robert
1979
Quantum multiplication of Schur polynomials. Zbl 0936.05086
Bertram, Aaron; Ciocan-Fontanine, Ionuţ; Fulton, William
1999
Positive polynomials for ample vector bundles. Zbl 0537.14009
Fulton, William; Lazarsfeld, Robert
1983
A connectedness theorem for projective varieties, with applications to intersections and singularities of mappings. Zbl 0389.14002
Fulton, William; Hansen, Johan
1979
A Pieri formula in the Grothendieck ring of a flag bundle. Zbl 0840.14007
Fulton, William; Lascoux, Alain
1994
Chern class formulas for quiver varieties. Zbl 0942.14027
Skovsted Buch, Anders; Fulton, William
1999
On the quantum cohomology of homogeneous varieties. Zbl 1083.14065
Fulton, W.
2004
Lefschetz-Riemann-Roch for singular varieties. Zbl 0454.14009
Baum, Paul; Fulton, William; Quart, George
1979
Eigenvalues, singular values, and Littlewood-Richardson coefficients. Zbl 1072.15010
Fomin, Sergey; Fulton, William; Li, Chi-Kwong; Poon, Yiu-Tung
2005
Determinantal formulas for orthogonal and symplectic degeneracy loci. Zbl 0911.14001
Fulton, William
1996
Eigenvalues of majorized Hermitian matrices and Littlewood-Richardson coefficients. Zbl 0968.15010
Fulton, William
2000
Excess linear series on an algebraic curve. Zbl 0549.14004
Fulton, William; Harris, Joe; Lazarsfeld, Robert
1984
On the fundamental group of the complement of a node curve. Zbl 0406.14008
Fulton, William
1980
A note on weakly complete algebras. Zbl 0205.34303
Fulton, W.
1969
Canonical classes on singular varieties. Zbl 0451.14001
Fulton, William; Johnson, Kent
1980
Intersecting cycles on an algebraic variety. Zbl 0385.14002
Fulton, William; MacPherson, Robert
1977
Universal Schubert polynomials. Zbl 0981.14022
Fulton, William
1999
Eigenvalues of sums of Hermitian matrices [after A. Klyachko]. Zbl 0929.15006
Fulton, William
1998
Characteristic classes of direct image bundles for covering maps. Zbl 0628.55010
Fulton, William; MacPherson, Robert
1987
Schubert varieties in flag bundles for the classical groups. Zbl 0862.14032
Fulton, William
1996
Chern class formulas for classical-type degeneracy loci. Zbl 1412.14034
Anderson, David; Fulton, William
2018
Intersection rings of spaces of triangles. Zbl 0726.14006
Collino, Alberto; Fulton, William
1989
Riemann-Roch for general algebraic varieties. Zbl 0579.14013
Fulton, William; Gillet, Henri
1983
Ample vector bundles, Chern classes, and numerical criteria. Zbl 0341.14004
Fulton, William
1976
Positivity and excess intersection. Zbl 0501.14003
Fulton, William; Lazarsfeld, Robert
1982
Introduction to intersection theory in algebraic geometry. Expository lectures from the CBMS regional conference, George Mason University, Fairfax, VA, USA, June 27–July 1, 1983. 3rd printing with corrections. Zbl 0913.14001
Fulton, William
1996
Defining algebraic intersections. Zbl 0405.14003
Fulton, William; MacPherson, Robert
1978
The Picard group of $$\mathcal M_{1,1}$$. Zbl 1198.14010
Fulton, William; Olsson, Martin
2010
Adjoints and Max Noether’s Fundamentalsatz. Zbl 1092.14035
Fulton, William
2003
On the topology of algebraic varieties. Zbl 0703.14012
Fulton, William
1987
About the enumeration of contacts. Zbl 0529.14030
Fulton, William; Kleiman, Steven; MacPherson, Robert
1983
Residual intersections and the double point formula. Zbl 0388.14005
Fulton, William; Laksov, Dan
1977
Some intrinsic and extrinsic characterizations of the projective space. Zbl 0581.14037
Fulton, W.; Kleiman, S.; Piene, R.; Tai, H.
1985
A note on residual intersections and the double point formula. Zbl 0388.14004
Fulton, William
1978
A Hirzebruch-Riemann-Roch formula for analytic spaces and non-projective algebraic varieties. Zbl 0367.14008
Fulton, William
1977
Some aspects of positivity in algebraic geometry. Zbl 0611.14012
Fulton, William
1984
On nodal curves. Zbl 0514.14012
Fulton, William
1983
On the irreducibility of the moduli space of curves. Appendix to the paper of Harris and Mumford. Zbl 0506.14017
Fulton, William
1982
A note on the arithmetic genus. Zbl 0497.14002
Fulton, William
1979
A fixed point formula for varieties over finite fields. Zbl 0417.14006
Fulton, William
1978
Lefschetz-Riemann-Roch for singular varieties. Zbl 0357.14004
Baum, Paul; Fulton, William; Quart, George
1977
Recent progress in intersection theory. Based on the international conference on intersection theory, Bologna, Italy, December 1997. Zbl 0935.00036
Ellingsrud, Geir (ed.); Fulton, William (ed.); Vistoli, Angelo (ed.)
2000
Algebraic geometry. Proceedings of the US-USSR symposium, held in Chicago, IL, USA, June 20-July 14, 1989. Zbl 0742.00065
Bloch, S. (ed.); Dolgachev, I. (ed.); Fulton, W. (ed.)
1991
Riemann-Roch for singular varieties. Zbl 0306.14005
Fulton, William
1975
Chern class formulas for classical-type degeneracy loci. Zbl 1412.14034
Anderson, David; Fulton, William
2018
The Picard group of $$\mathcal M_{1,1}$$. Zbl 1198.14010
Fulton, William; Olsson, Martin
2010
Eigenvalues, singular values, and Littlewood-Richardson coefficients. Zbl 1072.15010
Fomin, Sergey; Fulton, William; Li, Chi-Kwong; Poon, Yiu-Tung
2005
On the quantum product of Schubert classes. Zbl 1081.14076
Fulton, W.; Woodward, C.
2004
On the quantum cohomology of homogeneous varieties. Zbl 1083.14065
Fulton, W.
2004
Adjoints and Max Noether’s Fundamentalsatz. Zbl 1092.14035
Fulton, William
2003
Eigenvalues, invariant factors, highest weights, and Schubert calculus. Zbl 0994.15021
Fulton, William
2000
Eigenvalues of majorized Hermitian matrices and Littlewood-Richardson coefficients. Zbl 0968.15010
Fulton, William
2000
Recent progress in intersection theory. Based on the international conference on intersection theory, Bologna, Italy, December 1997. Zbl 0935.00036
Ellingsrud, Geir (ed.); Fulton, William (ed.); Vistoli, Angelo (ed.)
2000
Quantum multiplication of Schur polynomials. Zbl 0936.05086
Bertram, Aaron; Ciocan-Fontanine, Ionuţ; Fulton, William
1999
Chern class formulas for quiver varieties. Zbl 0942.14027
Skovsted Buch, Anders; Fulton, William
1999
Universal Schubert polynomials. Zbl 0981.14022
Fulton, William
1999
Intersection theory. 2nd ed. Zbl 0885.14002
Fulton, William
1998
Schubert varieties and degeneracy loci. Zbl 0913.14016
Fulton, William; Pragacz, Piotr
1998
Eigenvalues of sums of Hermitian matrices [after A. Klyachko]. Zbl 0929.15006
Fulton, William
1998
Young tableaux. With applications to representation theory and geometry. Zbl 0878.14034
Fulton, William
1997
Notes on stable maps and quantum cohomology. Zbl 0898.14018
Fulton, W.; Pandharipande, R.
1997
Intersection theory on toric varieties. Zbl 0885.14025
Fulton, William; Sturmfels, Bernd
1997
Determinantal formulas for orthogonal and symplectic degeneracy loci. Zbl 0911.14001
Fulton, William
1996
Schubert varieties in flag bundles for the classical groups. Zbl 0862.14032
Fulton, William
1996
Introduction to intersection theory in algebraic geometry. Expository lectures from the CBMS regional conference, George Mason University, Fairfax, VA, USA, June 27–July 1, 1983. 3rd printing with corrections. Zbl 0913.14001
Fulton, William
1996
Algebraic topology. A first course. Zbl 0852.55001
Fulton, William
1995
Intersection theory on spherical varieties. Zbl 0819.14019
Fulton, William; MacPherson, Robert; Sottile, F.; Sturmfels, Bernd
1995
A compactification of configuration spaces. Zbl 0820.14037
Fulton, William; MacPherson, Robert
1994
A Pieri formula in the Grothendieck ring of a flag bundle. Zbl 0840.14007
Fulton, William; Lascoux, Alain
1994
Introduction to toric varieties. The 1989 William H. Roever lectures in geometry. Zbl 0813.14039
Fulton, William
1993
Flags, Schubert polynomials, degeneracy loci, and determinantal formulas. Zbl 0788.14044
Fulton, William
1992
Representation theory. A first course. Zbl 0744.22001
Fulton, William; Harris, Joe
1991
A growth model, a game, an algebra, Lagrange inversion, and characteristic classes. Zbl 0776.60128
Diaconis, P.; Fulton, W.
1991
Algebraic geometry. Proceedings of the US-USSR symposium, held in Chicago, IL, USA, June 20-July 14, 1989. Zbl 0742.00065
Bloch, S. (ed.); Dolgachev, I. (ed.); Fulton, W. (ed.)
1991
Algebraic curves. An introduction to algebraic geometry. Notes written with collab. of R. Weiss. new ed. Zbl 0681.14011
Fulton, William
1989
Intersection rings of spaces of triangles. Zbl 0726.14006
Collino, Alberto; Fulton, William
1989
Characteristic classes of direct image bundles for covering maps. Zbl 0628.55010
Fulton, William; MacPherson, Robert
1987
On the topology of algebraic varieties. Zbl 0703.14012
Fulton, William
1987
Riemann-Roch algebra. Zbl 0579.14011
Fulton, William; Lang, Serge
1985
Some intrinsic and extrinsic characterizations of the projective space. Zbl 0581.14037
Fulton, W.; Kleiman, S.; Piene, R.; Tai, H.
1985
Intersection theory. Zbl 0541.14005
Fulton, William
1984
Excess linear series on an algebraic curve. Zbl 0549.14004
Fulton, William; Harris, Joe; Lazarsfeld, Robert
1984
Some aspects of positivity in algebraic geometry. Zbl 0611.14012
Fulton, William
1984
Positive polynomials for ample vector bundles. Zbl 0537.14009
Fulton, William; Lazarsfeld, Robert
1983
Riemann-Roch for general algebraic varieties. Zbl 0579.14013
Fulton, William; Gillet, Henri
1983
About the enumeration of contacts. Zbl 0529.14030
Fulton, William; Kleiman, Steven; MacPherson, Robert
1983
On nodal curves. Zbl 0514.14012
Fulton, William
1983
Positivity and excess intersection. Zbl 0501.14003
Fulton, William; Lazarsfeld, Robert
1982
On the irreducibility of the moduli space of curves. Appendix to the paper of Harris and Mumford. Zbl 0506.14017
Fulton, William
1982
Connectivity and its applications in algebraic geometry. Zbl 0484.14005
Fulton, William; Lazarsfeld, Robert
1981
On the connectedness of degeneracy loci and special divisors. Zbl 0469.14018
Fulton, W.; Lazarsfeld, R.
1981
Categorical framework for the study of singular spaces. Zbl 0467.55005
Fulton, William; MacPherson, Robert
1981
On the fundamental group of the complement of a node curve. Zbl 0406.14008
Fulton, William
1980
Canonical classes on singular varieties. Zbl 0451.14001
Fulton, William; Johnson, Kent
1980
Riemann-Roch and topological K-theory for singular varieties. Zbl 0474.14004
Baum, Paul; Fulton, William; MacPherson, Robert
1979
A connectedness theorem for projective varieties, with applications to intersections and singularities of mappings. Zbl 0389.14002
Fulton, William; Hansen, Johan
1979
Lefschetz-Riemann-Roch for singular varieties. Zbl 0454.14009
Baum, Paul; Fulton, William; Quart, George
1979
A note on the arithmetic genus. Zbl 0497.14002
Fulton, William
1979
Defining algebraic intersections. Zbl 0405.14003
Fulton, William; MacPherson, Robert
1978
A note on residual intersections and the double point formula. Zbl 0388.14004
Fulton, William
1978
A fixed point formula for varieties over finite fields. Zbl 0417.14006
Fulton, William
1978
Intersecting cycles on an algebraic variety. Zbl 0385.14002
Fulton, William; MacPherson, Robert
1977
Residual intersections and the double point formula. Zbl 0388.14005
Fulton, William; Laksov, Dan
1977
A Hirzebruch-Riemann-Roch formula for analytic spaces and non-projective algebraic varieties. Zbl 0367.14008
Fulton, William
1977
Lefschetz-Riemann-Roch for singular varieties. Zbl 0357.14004
Baum, Paul; Fulton, William; Quart, George
1977
Ample vector bundles, Chern classes, and numerical criteria. Zbl 0341.14004
Fulton, William
1976
Riemann-Roch for singular varieties. Zbl 0332.14003
Baum, Paul; Fulton, William; MacPherson, Robert
1975
Rational equivalence on singular varieties. Zbl 0332.14002
Fulton, William
1975
Riemann-Roch for singular varieties. Zbl 0306.14005
Fulton, William
1975
Algebraic curves. Zbl 0181.23901
Fulton, W.
1969
Hurwitz schemes and irreducibility of moduli of algebraic curves. Zbl 0194.21901
Fulton, W.
1969
A note on weakly complete algebras. Zbl 0205.34303
Fulton, W.
1969
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#### Cited by 5,433 Authors
31 Sottile, Frank 29 Yokura, Shoji 28 Laterveer, Robert 27 Aluffi, Paolo 27 Ballico, Edoardo 23 Skovsted Buch, Anders 22 Fulton, William 21 Biswas, Indranil 21 Harris, Joseph Daniel 20 Sturmfels, Bernd 20 Yong, Alexander 19 Kwon, Jae-Hoon 18 Kucharz, Wojciech 18 Schürmann, Jörg 17 Pandharipande, Rahul 17 Sommese, Andrew John 17 Vainsencher, Israel 16 Eisenbud, David 16 Maxim, Laurentiu G. 16 Michałek, Mateusz 15 Anderson, Dave Edward 15 Gillet, Henri A. 15 Lenart, Cristian 14 Knutson, Allen 14 Kollár, János 14 Levine, Lionel 14 Perrin, Nicolas 14 Tamvakis, Harry 14 Weyman, Jerzy M. 13 Belkale, Prakash 13 Brion, Michel 13 Ciliberto, Ciro 13 Kresch, Andrew 13 Kumar, Shrawan 13 Llibre, Jaume 13 Schlomiuk, Dana I. 12 Edidin, Dan 12 Eelbode, David 12 Ikenmeyer, Christian 12 Karpenko, Nikita Aleksandrovich 12 Kurano, Kazuhiko 12 Matera, Guillermo 12 Morrison, David R. 12 Mustaţă, Mircea 12 Ottaviani, Giorgio Maria 12 Pirola, Gian Pietro 12 Ramgoolam, Sanjaye 12 Rietsch, Konstanze 12 Rimányi, Richárd 12 Schoen, Chad 11 Heintz, Joos 11 Hulek, Klaus 11 Lam, Thomas F. 11 Pragacz, Piotr 11 Ran, Ziv 11 Reiner, Victor 11 Saito, Takeshi 11 Sam, Steven V. 11 Shimozono, Mark 11 Srinivas, Vasudevan 11 Totaro, Burt 11 Walker, Mark E. 11 Woodward, Christopher T. 10 Billey, Sara C. 10 Ciocan-Fontanine, Ionuţ 10 Coskun, Izzet 10 Fujino, Osamu 10 Hausen, Jürgen 10 Katz, Sheldon 10 Kim, Sangjib 10 Levine, Marc Noel 10 Li, Chi-Kwong 10 Manivel, Laurent 10 Masuda, Mikiya 10 Mihalcea, Leonardo Constantin 10 Mironov, Andrei D. 10 Sato, Hiroshi 10 Soulé, Christophe 10 Stapledon, Alan 10 Stošić, Marko 10 Van Willigenburg, Stephanie J. 10 Vistoli, Angelo 9 Abramovich, Dan 9 Brasselet, Jean-Paul 9 Chipalkatti, Jaydeep V. 9 Di Gennaro, Vincenzo 9 Diaz, Steven P. 9 Farkas, Gavril 9 Feigin, Evgeny 9 Franco, Davide 9 Giusti, Marc 9 Gross, Mark 9 Ilten, Nathan Owen 9 Jonsson, Mattias 9 Karu, Kalle 9 Katz, Eric 9 Klemm, Albrecht 9 Miller, Ezra 9 Pardo, Luis Miguel 9 Payne, Sam ...and 5,333 more Authors
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#### Cited in 411 Serials
348 Journal of Algebra 309 Advances in Mathematics 217 Transactions of the American Mathematical Society 208 Duke Mathematical Journal 182 Journal of Pure and Applied Algebra 149 Mathematische Annalen 133 Mathematische Zeitschrift 128 Inventiones Mathematicae 114 Journal of High Energy Physics 112 Annales de l’Institut Fourier 112 Proceedings of the American Mathematical Society 109 Journal of Algebraic Combinatorics 104 Manuscripta Mathematica 95 Communications in Algebra 93 Communications in Mathematical Physics 93 Compositio Mathematica 93 Linear Algebra and its Applications 93 Journal of Algebraic Geometry 80 Nuclear Physics. B 76 Journal of Combinatorial Theory. Series A 74 Journal of the American Mathematical Society 65 Journal of Geometry and Physics 63 Journal of Symbolic Computation 57 Transformation Groups 56 Geometriae Dedicata 52 Tohoku Mathematical Journal. Second Series 48 Journal of Mathematical Physics 48 International Journal of Mathematics 47 Michigan Mathematical Journal 42 Israel Journal of Mathematics 41 Journal für die Reine und Angewandte Mathematik 40 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 38 Annals of Mathematics. Second Series 37 Comptes Rendus. Mathématique. Académie des Sciences, Paris 36 Journal of Number Theory 35 Bulletin of the American Mathematical Society. New Series 35 Selecta Mathematica. New Series 34 Algebraic & Geometric Topology 30 Acta Mathematica 29 Advances in Applied Mathematics 29 Algebras and Representation Theory 28 European Journal of Combinatorics 28 Finite Fields and their Applications 27 Discrete Mathematics 26 Topology and its Applications 26 Geometry & Topology 25 Publications of the Research Institute for Mathematical Sciences, Kyoto University 25 Journal of the European Mathematical Society (JEMS) 24 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 22 Archiv der Mathematik 22 Bulletin de la Société Mathématique de France 22 Journal of Functional Analysis 22 Indagationes Mathematicae. New Series 22 Documenta Mathematica 21 Discrete & Computational Geometry 21 Journal of Mathematical Sciences (New York) 21 Representation Theory 20 Mathematics of Computation 20 Nagoya Mathematical Journal 20 Séminaire Lotharingien de Combinatoire 20 Central European Journal of Mathematics 19 European Journal of Mathematics 18 Publications Mathématiques 18 The Journal of Geometric Analysis 17 Annali di Matematica Pura ed Applicata. Serie Quarta 17 Osaka Journal of Mathematics 17 Rendiconti del Seminario Matematico della Università di Padova 17 Journal of Complexity 17 Advances in Geometry 17 Journal of the Institute of Mathematics of Jussieu 16 Collectanea Mathematica 16 Journal de Mathématiques Pures et Appliquées. Neuvième Série 16 Bulletin des Sciences Mathématiques 16 Annals of Combinatorics 15 Rocky Mountain Journal of Mathematics 15 Mathematische Nachrichten 15 Memoirs of the American Mathematical Society 15 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 15 Proceedings of the Steklov Institute of Mathematics 14 Letters in Mathematical Physics 14 Mathematical Notes 14 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 14 Journal of Differential Equations 14 Journal of the Mathematical Society of Japan 14 Proceedings of the Japan Academy. Series A 14 Rendiconti del Circolo Matemàtico di Palermo. Serie II 14 Computer Aided Geometric Design 14 Journal of Commutative Algebra 14 Algebraic Combinatorics 13 Beiträge zur Algebra und Geometrie 13 Communications in Contemporary Mathematics 12 Journal of Statistical Physics 12 Functional Analysis and its Applications 12 $$K$$-Theory 12 Geometric and Functional Analysis. GAFA 12 Expositiones Mathematicae 12 Journal de Théorie des Nombres de Bordeaux 12 The Electronic Journal of Combinatorics 12 Forum of Mathematics, Sigma 11 Mathematical Proceedings of the Cambridge Philosophical Society ...and 311 more Serials
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#### Cited in 60 Fields
3,660 Algebraic geometry (14-XX) 734 Combinatorics (05-XX) 623 Group theory and generalizations (20-XX) 514 Several complex variables and analytic spaces (32-XX) 512 Commutative algebra (13-XX) 449 Number theory (11-XX) 415 Quantum theory (81-XX) 371 Nonassociative rings and algebras (17-XX) 357 Differential geometry (53-XX) 323 Manifolds and cell complexes (57-XX) 229 Linear and multilinear algebra; matrix theory (15-XX) 229 Convex and discrete geometry (52-XX) 222 Algebraic topology (55-XX) 219 Associative rings and algebras (16-XX) 218 Topological groups, Lie groups (22-XX) 199 $$K$$-theory (19-XX) 152 Category theory; homological algebra (18-XX) 150 Global analysis, analysis on manifolds (58-XX) 133 Dynamical systems and ergodic theory (37-XX) 124 Computer science (68-XX) 114 Probability theory and stochastic processes (60-XX) 99 Field theory and polynomials (12-XX) 96 Numerical analysis (65-XX) 90 Statistical mechanics, structure of matter (82-XX) 87 Relativity and gravitational theory (83-XX) 83 Ordinary differential equations (34-XX) 70 Functions of a complex variable (30-XX) 65 Special functions (33-XX) 62 Geometry (51-XX) 54 Operator theory (47-XX) 51 Partial differential equations (35-XX) 51 Information and communication theory, circuits (94-XX) 43 Functional analysis (46-XX) 42 Order, lattices, ordered algebraic structures (06-XX) 30 Abstract harmonic analysis (43-XX) 28 Statistics (62-XX) 23 Mathematical logic and foundations (03-XX) 22 Operations research, mathematical programming (90-XX) 21 Harmonic analysis on Euclidean spaces (42-XX) 17 Mechanics of particles and systems (70-XX) 16 Systems theory; control (93-XX) 15 History and biography (01-XX) 15 Difference and functional equations (39-XX) 15 Biology and other natural sciences (92-XX) 14 Real functions (26-XX) 13 General topology (54-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 General and overarching topics; collections (00-XX) 8 Measure and integration (28-XX) 8 Approximations and expansions (41-XX) 7 Potential theory (31-XX) 7 Integral transforms, operational calculus (44-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 3 General algebraic systems (08-XX) 3 Mechanics of deformable solids (74-XX) 3 Fluid mechanics (76-XX) 3 Mathematics education (97-XX) 2 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX)
#### Wikidata Timeline
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https://zbmath.org/authors/?q=ai%3Abhatia.rajendra | zbMATH — the first resource for mathematics
Bhatia, Rajendra
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Author ID: bhatia.rajendra Published as: Bhatia, R.; Bhatia, Rajendra External Links: MGP · Wikidata · dblp · GND
Documents Indexed: 159 Publications since 1978, including 21 Books Biographic References: 2 Publications
all top 5
Co-Authors
46 single-authored 16 Kittaneh, Fuad 15 Jain, Tanvi 13 Davis, Chandler 11 Elsner, Ludwig F. 7 Holbrook, John A. R. 6 Šemrl, Peter 5 Li, Rencang 4 Lim, Yongdo 4 Pal, Arup Kumar 4 Rangarajan, Gita 4 Sinha, Kalyan B. 4 Srinivas, Vasudevan 4 Vanninathan, Muthusamy 3 Bhattacharyya, Tirthankar 3 Mukherjea, Kalyan K. 3 Sharma, Rajesh 2 Choi, Man-Duen 2 Drissi, Driss 2 Friedland, Shmuel 2 Gaubert, Stéphane 2 Grover, Priyanka 2 Kirkland, Steve J. 2 Krause, Gerd M. 2 Parthasarathy, Kalyanapuram Rangachari 2 Perdigão Dias da Silva, José António 2 Rosenthal, Peter 2 Sano, Takashi 2 Zhan, Xingzhi 1 Ando, T. jun. 1 Bhatt, Abhay G. 1 Bunse-Gerstner, Angelika 1 Congedo, Marco 1 Guralnick, Robert Michael 1 Horn, Roger Alan 1 Kahan, William Morton 1 Karandikar, Rajeeva L. 1 Koosis, Paul 1 Kosaki, Hideki 1 Li, Chi-Kwong 1 McIntosh, Alan 1 Mehrmann, Volker 1 Nielsen, Frank 1 Okube, K. 1 Olesky, D. Dale 1 Omladič, Matjaž 1 Poithasarathy, K. R. 1 Prasad, K. Manjunatha 1 Puntanen, Simo 1 Rajan, Conjeeveram S. 1 Singh, Ajit Iqbal 1 Singh, Dinesh Chandra 1 Sourour, Ahmed Ramzi 1 Tsatsoneros, M. J. 1 Uchiyama, Mitsuru 1 Wolkowicz, Henry 1 Yamazaki, Takeaki
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Serials
43 Linear Algebra and its Applications 7 American Mathematical Monthly 7 Linear and Multilinear Algebra 6 SIAM Journal on Matrix Analysis and Applications 6 Texts and Readings in Mathematics 4 Letters in Mathematical Physics 4 The Mathematical Intelligencer 4 Mathematische Annalen 4 Proceedings of the American Mathematical Society 3 Communications in Mathematical Physics 3 Studia Mathematica 3 Bulletin of the London Mathematical Society 3 Indiana University Mathematics Journal 3 Journal of Operator Theory 3 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 3 Positivity 2 Indian Journal of Pure & Applied Mathematics 2 Journal of Mathematical Physics 2 Archiv der Mathematik 2 The Mathematics Student 2 Aequationes Mathematicae 2 Expositiones Mathematicae 2 ELA. The Electronic Journal of Linear Algebra 1 Mathematics of Computation 1 Reviews in Mathematical Physics 1 Acta Scientiarum Mathematicarum 1 BIT 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Journal of Functional Analysis 1 The Journal of the Indian Mathematical Society. New Series 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Transactions of the American Mathematical Society 1 Journal of the Ramanujan Mathematical Society 1 International Journal of Mathematics 1 Indagationes Mathematicae. New Series 1 Classics in Applied Mathematics 1 Graduate Texts in Mathematics 1 Operators and Matrices 1 Communications on Stochastic Analysis 1 Annals of Functional Analysis 1 Journal of Spectral Theory 1 Mathematics Newsletter 1 Princeton Series in Applied Mathematics 1 Classroom Resource Materials
all top 5
Fields
106 Linear and multilinear algebra; matrix theory (15-XX) 67 Operator theory (47-XX) 15 Functional analysis (46-XX) 13 General and overarching topics; collections (00-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 11 Numerical analysis (65-XX) 9 Real functions (26-XX) 8 History and biography (01-XX) 8 Differential geometry (53-XX) 7 Quantum theory (81-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Information and communication theory, circuits (94-XX) 3 Geometry (51-XX) 3 Probability theory and stochastic processes (60-XX) 2 Number theory (11-XX) 2 Functions of a complex variable (30-XX) 2 Statistics (62-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Systems theory; control (93-XX)
Citations contained in zbMATH
133 Publications have been cited 3,079 times in 1,989 Documents Cited by Year
Matrix analysis. Zbl 0863.15001
Bhatia, Rajendra
1996
Positive definite matrices. Zbl 1133.15017
Bhatia, Rajendra
2007
Positive definite matrices. Zbl 1125.15300
Bhatia, Rajendra
2007
Riemannian geometry and matrix geometric means. Zbl 1088.15022
Bhatia, Rajendra; Holbrook, John
2006
How and why to solve the operator equation $$AX-XB=Y$$. Zbl 0909.47011
Bhatia, Rajendra; Rosenthal, Peter
1997
More matrix forms of the arithmetic-geometric mean inequality. Zbl 0767.15012
Bhatia, Rajendra; Davis, Chandler
1993
On the singular values of a product of operators. Zbl 0704.47014
1990
Perturbation of spectral subspaces and solution of linear operator equations. Zbl 0518.47013
Bhatia, Rajendra; Davis, Chandler; McIntosh, Alan
1983
Perturbation bounds for matrix eigenvalues. Zbl 0696.15013
Bhatia, Rajendra
1987
Notes on matrix arithmetic-geometric mean inequalities. Zbl 0974.15016
2000
Orthogonality of matrices and some distance problems. Zbl 0937.15023
Bhatia, Rajendra; Šemrl, Peter
1999
Monotonicity of the matrix geometric mean. Zbl 1253.15047
Bhatia, Rajendra; Karandikar, Rajeeva L.
2012
On the exponential metric increasing property. Zbl 1052.15013
Bhatia, Rajendra
2003
Positive definite functions and operator inequalities. Zbl 1037.15021
Bhatia, Rajendra; Parthasarathy, K. R.
2000
Norm inequalities for partitioned operators and an application. Zbl 0688.47005
1990
Interpolating the arithmetic–geometric mean inequality and its operator version. Zbl 1092.15018
Bhatia, Rajendra
2006
A better bound on the variance. Zbl 1009.15009
Bhatia, Rajendra; Davis, Chandler
2000
A Cauchy-Schwarz inequality for operators with applications. Zbl 0824.47006
Bhatia, Rajendra; Davis, Chandler
1995
Mean matrices and infinite divisibility. Zbl 1124.15015
Bhatia, Rajendra; Kosaki, Hideki
2007
Infinitely divisible matrices. Zbl 1132.15019
Bhatia, Rajendra
2006
Maps on matrices that preserve the spectral radius distance. Zbl 0927.15006
Bhatia, Rajendra; Šemrl, Peter; Sourour, A. R.
1999
The matrix arithmetic-geometric mean inequality revisited. Zbl 1148.15014
2008
Perturbation bounds for matrix eigenvalues. Reprint of the 1987 original. Zbl 1139.15303
Bhatia, Rajendra
2007
Norm inequalities related to the matrix geometric mean. Zbl 1252.15023
Bhatia, Rajendra; Grover, Priyanka
2012
An extremal problem in Fourier analysis with applications to operator theory. Zbl 0674.42002
Bhatia, Rajendra; Davis, Chandler; Koosis, Paul
1989
Matrix factorizations and their perturbations. Zbl 0794.15006
Bhatia, Rajendra
1994
Clarkson inequalities with several operators. Zbl 1071.47011
2004
A bound for the spectral variation of a unitary operator. Zbl 0539.15010
Bhatia, Rajendra; Davis, Chandler
1984
Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix. Zbl 0713.15005
Bhatia, R.; Elsner, L.; Krause, G.
1990
Some inequalities for norm ideals. Zbl 0632.47005
Bhatia, Rajendra
1987
Norm inequalities for positive operators. Zbl 0912.47005
1998
Analysis of spectral variation and some inequalities. Zbl 0488.15010
Bhatia, Rajendra
1982
Eigenvalue inequalities associated with the Cartesian decomposition. Zbl 0641.15007
Ando, T.; Bhatia, R.
1987
On the Bures-Wasserstein distance between positive definite matrices. Zbl 1437.15044
Bhatia, Rajendra; Jain, Tanvi; Lim, Yongdo
2019
Some inequalities for positive linear maps. Zbl 1252.15024
Bhatia, Rajendra; Sharma, Rajesh
2012
Variation of Grassmann powers and spectra. Zbl 0469.15004
Bhatia, Rajendra; Friedland, Shmuel
1981
Loewner matrices and operator convexity. Zbl 1172.15010
Bhatia, Rajendra; Sano, Takashi
2009
On the Clarkson-McCarthy inequalities. Zbl 0618.47008
Bhatia, Rajendra; Holbrook, John A. R.
1988
More operator versions of the Schwarz inequality. Zbl 0984.46040
Bhatia, Rajendra; Davis, Chandler
2000
Cartesian decompositions and Schatten norms. Zbl 0981.47008
2000
On the rate of change of spectra of operators. Zbl 0421.15019
Bhatia, Rajendra; Mukherjea, Kalyan K.
1979
Pinching, trimming, truncating, and averaging of matrices. Zbl 0984.15024
Bhatia, Rajendra
2000
Approximate isometries on Euclidean spaces. Zbl 0901.46016
Bhatia, Rajendra; Šemrl, Peter
1997
First and second order perturbation bounds for the operator absolute value. Zbl 0815.47006
Bhatia, Rajendra
1994
Perturbation inequalities for the absolute value map in norm ideals of operators. Zbl 0698.47029
Bhatia, Rajendra
1988
Some norm inequalities for matrix means. Zbl 1334.15052
Bhatia, Rajendra; Lim, Yongdo; Yamazaki, Takeaki
2016
Compact operators whose real and imaginary parts are positive. Zbl 0965.47013
Bhatia, Rajendra; Zhan, Xingzhi
2001
The Hoffman-Wielandt inequality in infinite dimensions. Zbl 0805.47017
Bhatia, Rajendra; Elsner, Ludwig
1994
Some inequalities for commutators and an application to spectral variation. Zbl 0752.47005
Bhatia, Rajendra; Davis, Chandler; Kittaneh, Fuad
1991
Short normal paths and spectral variation. Zbl 0568.15012
Bhatia, Rajendra; Holbrook, John A. R.
1985
The Riemannian mean of positive matrices. Zbl 1271.15019
Bhatia, Rajendra
2013
Linear algebra to quantum cohomology: The story of Alfred Horn’s inequalities. Zbl 1016.15014
Bhatia, Rajendra
2001
Variation of real powers of positive operators. Zbl 0836.47011
Bhatia, Rajendra; Sinha, Kalyan B.
1994
Variation of the unitary part of a matrix. Zbl 0805.15006
Bhatia, Rajendra; Mukherjea, Kalyan
1994
On symplectic eigenvalues of positive definite matrices. Zbl 1329.15048
Bhatia, Rajendra; Jain, Tanvi
2015
Positive definite matrices. Reprint of the 2007 hardback edition. Zbl 1321.15003
Bhatia, Rajendra
2015
Trace inequalities for products of positive definite matrices. Zbl 1288.15022
Bhatia, Rajendra
2014
Higher order derivatives and perturbation bounds for determinants. Zbl 1177.15006
Bhatia, Rajendra; Jain, Tanvi
2009
The singular values of $$A+B$$ and $$A+iB$$. Zbl 1172.47011
2009
The operator equation $$\sum _{i=0}^n A^{n-i}XB^i=Y$$. Zbl 1167.15010
Bhatia, Rajendra; Uchiyama, Mitsuru
2009
Commutators, pinchings, and spectral variation. Zbl 1147.15019
2008
Generalized Lyapunov equations and positive definite functions. Zbl 1097.15015
Bhatia, Rajendra; Drissi, Driss
2005
Differentiation of operator functions and perturbation bounds. Zbl 0918.47017
Bhatia, Rajendra; Singh, Dinesh; Sinha, Kalyan B.
1998
Some inequalities for norms of commutators. Zbl 0877.15023
1997
On perturbations of matrix pencils with real spectra. II. Zbl 0852.15008
Bhatia, Rajendra; Li, Ren-Cang
1996
Unitary invariance and spectral variation. Zbl 0657.15019
Bhatia, Rajendra; Holbrook, John A. R.
1987
Positive linear maps and spreads of matrices. Zbl 1320.15015
Bhatia, Rajendra; Sharma, Rajesh
2014
Matrix information geometry. Selected papers based on the presentations at the Indo-French workshop on matrix information geometries (MIG): Applications in sensor and cognitive systems engineering, Palaiseau, France, February 23–25, 2011. Zbl 1252.94003
Nielsen, Frank (ed.); Bhatia, Rajendra (ed.)
2013
Noncommutative geometric means. Zbl 1091.26022
Bhatia, Rajendra; Holbrook, John
2006
Norm inequalities for operators with positive real part. Zbl 1043.47011
Bhatia, Rajendra; Zhan, Xingzhi
2003
Inertia of the matrix $$[(p_i+p_j)^r]$$. Zbl 1321.15017
Bhatia, Rajendra; Jain, Tanvi
2015
Positivity preserving Hadamard matrix functions. Zbl 1130.15011
Bhatia, Rajendra; Elsner, Ludwig
2007
Partial traces and entropy inequalities. Zbl 1027.15007
Bhatia, Rajendra
2003
Fréchet derivatives of the power function. Zbl 0988.47011
Bhatia, Rajendra; Holbrook, John A.
2000
A note on the Lyapunov equation. Zbl 0881.15016
Bhatia, Rajendra
1997
Perturbation bounds for the operator absolute value. Zbl 0835.47009
Bhatia, Rajendra
1995
A generalization of the Hoffman-Wielandt theorem. Zbl 0774.15011
Bhatia, Rajendra; Bhattacharyya, Tirthankar
1993
Min matrices and mean matrices. Zbl 1247.15029
Bhatia, Rajendra
2011
Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
1997
Comparing a matrix to its off-diagonal part. Zbl 0674.15018
Bhatia, Rajendra; Choi, Man-Duen; Davis, Chandler
1989
On some perturbation inequalities for operators. Zbl 0659.47016
1988
Variation of symmetric tensor powers and permanents. Zbl 0552.15014
Bhatia, Rajendra
1984
Positive linear maps and spreads of matrices. II. Zbl 1391.15075
Bhatia, Rajendra; Sharma, Rajesh
2016
Notes on functional analysis. Zbl 1175.46001
Bhatia, Rajendra
2009
Pinchings and norms of scaled triangular matrices. Zbl 1004.15020
Bhatia, Rajendra; Kahan, William; Li, Ren-Cang
2002
Letter to the editor. Zbl 0780.51017
Bhatia, Rajendra
1991
On the rate of change of spectra of operators. II. Zbl 0479.15009
Bhatia, Rajendra
1981
Lectures on functional analysis. Part I: Perturbation by bounded operators. Zbl 0451.47020
Bhatia, Rajendra; Parthasarathy, K. R.
1978
Matrix versions of the Hellinger distance. Zbl 1420.15016
Bhatia, Rajendra; Gaubert, Stephane; Jain, Tanvi
2019
Inequalities for the Wasserstein mean of positive definite matrices. Zbl 1418.15017
Bhatia, Rajendra; Jain, Tanvi; Lim, Yongdo
2019
Strong convexity of sandwiched entropies and related optimization problems. Zbl 1402.49036
Bhatia, Rajendra; Jain, Tanvi; Lim, Yongdo
2018
On some positive definite functions. Zbl 1331.42009
Bhatia, Rajendra; Jain, Tanvi
2015
Modulus of continuity of the matrix absolute value. Zbl 1226.47010
Bhatia, Rajendra
2010
Corners of normal matrices. Zbl 1119.15026
Bhatia, Rajendra; Choi, Man-Duen
2006
Fourier series. Zbl 1060.42001
Bhatia, Rajendra
2005
Higher order logarithmic derivatives of matrices in the spectral norm. Zbl 1062.15015
Bhatia, Rajendra; Elsner, Ludwig
2003
Variation of induced linear operators. Zbl 1151.47301
Bhatia, Rajendra; Dias da Silva, J. A.
2002
Derivations, derivatives and chain rules. Zbl 0951.47012
Bhatia, Rajendra; Sinha, Kalyan B.
1999
Distance between commuting tuples of normal operators. Zbl 0931.47001
Bhatia, Rajendra; Elsner, Ludwig; Šemrl, Peter
1998
A softer, stronger Lidskii theorem. Zbl 0675.15001
Bhatia, Rajendra; Holbrook, John A. R.
1989
A Schur-Horn theorem for symplectic eigenvalues. Zbl 1451.15012
Bhatia, Rajendra; Jain, Tanvi
2020
On the Bures-Wasserstein distance between positive definite matrices. Zbl 1437.15044
Bhatia, Rajendra; Jain, Tanvi; Lim, Yongdo
2019
Matrix versions of the Hellinger distance. Zbl 1420.15016
Bhatia, Rajendra; Gaubert, Stephane; Jain, Tanvi
2019
Inequalities for the Wasserstein mean of positive definite matrices. Zbl 1418.15017
Bhatia, Rajendra; Jain, Tanvi; Lim, Yongdo
2019
Correction to: “Matrix versions of the Hellinger distance”. Zbl 1435.15018
Bhatia, Rajendra; Gaubert, Stephane; Jain, Tanvi
2019
Procrustes problems in Riemannian manifolds of positive definite matrices. Zbl 1404.15025
Bhatia, Rajendra; Congedo, Marco
2019
Strong convexity of sandwiched entropies and related optimization problems. Zbl 1402.49036
Bhatia, Rajendra; Jain, Tanvi; Lim, Yongdo
2018
Some norm inequalities for matrix means. Zbl 1334.15052
Bhatia, Rajendra; Lim, Yongdo; Yamazaki, Takeaki
2016
Positive linear maps and spreads of matrices. II. Zbl 1391.15075
Bhatia, Rajendra; Sharma, Rajesh
2016
Inertia of Loewner matrices. Zbl 1354.15005
Bhatia, Rajendra; Friedland, Shmuel; Jain, Tanvi
2016
On symplectic eigenvalues of positive definite matrices. Zbl 1329.15048
Bhatia, Rajendra; Jain, Tanvi
2015
Positive definite matrices. Reprint of the 2007 hardback edition. Zbl 1321.15003
Bhatia, Rajendra
2015
Inertia of the matrix $$[(p_i+p_j)^r]$$. Zbl 1321.15017
Bhatia, Rajendra; Jain, Tanvi
2015
On some positive definite functions. Zbl 1331.42009
Bhatia, Rajendra; Jain, Tanvi
2015
The geometric mean of exponentials of Pauli matrices. Zbl 1425.15035
Bhatia, Rajendra; Jain, Tanvi
2015
Trace inequalities for products of positive definite matrices. Zbl 1288.15022
Bhatia, Rajendra
2014
Positive linear maps and spreads of matrices. Zbl 1320.15015
Bhatia, Rajendra; Sharma, Rajesh
2014
Positivity properties of the matrix $${\left[(i+j)^{i+j}\right]}$$. Zbl 1305.15072
Bhatia, Rajendra; Jain, Tanvi
2014
The Riemannian mean of positive matrices. Zbl 1271.15019
Bhatia, Rajendra
2013
Matrix information geometry. Selected papers based on the presentations at the Indo-French workshop on matrix information geometries (MIG): Applications in sensor and cognitive systems engineering, Palaiseau, France, February 23–25, 2011. Zbl 1252.94003
Nielsen, Frank (ed.); Bhatia, Rajendra (ed.)
2013
Derivatives of tensor powers and their norms. Zbl 1283.15073
Bhatia, Rajendra; Grover, Priyanka; Jain, Tanvi
2013
The bipolar decomposition. Zbl 1283.15039
Bhatia, Rajendra
2013
Monotonicity of the matrix geometric mean. Zbl 1253.15047
Bhatia, Rajendra; Karandikar, Rajeeva L.
2012
Norm inequalities related to the matrix geometric mean. Zbl 1252.15023
Bhatia, Rajendra; Grover, Priyanka
2012
Some inequalities for positive linear maps. Zbl 1252.15024
Bhatia, Rajendra; Sharma, Rajesh
2012
An interpolating family of means. Zbl 1331.26053
Bhatia, Rajendra; Li, Ren-Cang
2012
Min matrices and mean matrices. Zbl 1247.15029
Bhatia, Rajendra
2011
Modulus of continuity of the matrix absolute value. Zbl 1226.47010
Bhatia, Rajendra
2010
Positivity and conditional positivity of Loewner matrices. Zbl 1204.15039
Bhatia, Rajendra; Sano, Takashi
2010
Loewner matrices and operator convexity. Zbl 1172.15010
Bhatia, Rajendra; Sano, Takashi
2009
Higher order derivatives and perturbation bounds for determinants. Zbl 1177.15006
Bhatia, Rajendra; Jain, Tanvi
2009
The singular values of $$A+B$$ and $$A+iB$$. Zbl 1172.47011
2009
The operator equation $$\sum _{i=0}^n A^{n-i}XB^i=Y$$. Zbl 1167.15010
Bhatia, Rajendra; Uchiyama, Mitsuru
2009
Notes on functional analysis. Zbl 1175.46001
Bhatia, Rajendra
2009
The matrix arithmetic-geometric mean inequality revisited. Zbl 1148.15014
2008
Commutators, pinchings, and spectral variation. Zbl 1147.15019
2008
Infinite divisibility of GCD matrices. Zbl 1169.15301
Bhatia, Rajendra; Dias da Silva, J. A.
2008
Positive definite matrices. Zbl 1133.15017
Bhatia, Rajendra
2007
Positive definite matrices. Zbl 1125.15300
Bhatia, Rajendra
2007
Mean matrices and infinite divisibility. Zbl 1124.15015
Bhatia, Rajendra; Kosaki, Hideki
2007
Perturbation bounds for matrix eigenvalues. Reprint of the 1987 original. Zbl 1139.15303
Bhatia, Rajendra
2007
Positivity preserving Hadamard matrix functions. Zbl 1130.15011
Bhatia, Rajendra; Elsner, Ludwig
2007
Riemannian geometry and matrix geometric means. Zbl 1088.15022
Bhatia, Rajendra; Holbrook, John
2006
Interpolating the arithmetic–geometric mean inequality and its operator version. Zbl 1092.15018
Bhatia, Rajendra
2006
Infinitely divisible matrices. Zbl 1132.15019
Bhatia, Rajendra
2006
Noncommutative geometric means. Zbl 1091.26022
Bhatia, Rajendra; Holbrook, John
2006
Corners of normal matrices. Zbl 1119.15026
Bhatia, Rajendra; Choi, Man-Duen
2006
Generalized Lyapunov equations and positive definite functions. Zbl 1097.15015
Bhatia, Rajendra; Drissi, Driss
2005
Fourier series. Zbl 1060.42001
Bhatia, Rajendra
2005
Clarkson inequalities with several operators. Zbl 1071.47011
2004
On the exponential metric increasing property. Zbl 1052.15013
Bhatia, Rajendra
2003
Norm inequalities for operators with positive real part. Zbl 1043.47011
Bhatia, Rajendra; Zhan, Xingzhi
2003
Partial traces and entropy inequalities. Zbl 1027.15007
Bhatia, Rajendra
2003
Higher order logarithmic derivatives of matrices in the spectral norm. Zbl 1062.15015
Bhatia, Rajendra; Elsner, Ludwig
2003
Pinchings and norms of scaled triangular matrices. Zbl 1004.15020
Bhatia, Rajendra; Kahan, William; Li, Ren-Cang
2002
Variation of induced linear operators. Zbl 1151.47301
Bhatia, Rajendra; Dias da Silva, J. A.
2002
Positive linear maps and the Lyapunov equation. Zbl 1018.15003
Bhatia, Rajendra; Elsner, Ludwig
2002
Compact operators whose real and imaginary parts are positive. Zbl 0965.47013
Bhatia, Rajendra; Zhan, Xingzhi
2001
Linear algebra to quantum cohomology: The story of Alfred Horn’s inequalities. Zbl 1016.15014
Bhatia, Rajendra
2001
A key inequality for functions of matrices. Zbl 0978.15016
Bhatia, Rajendra; Davis, Chandler
2001
Notes on matrix arithmetic-geometric mean inequalities. Zbl 0974.15016
2000
Positive definite functions and operator inequalities. Zbl 1037.15021
Bhatia, Rajendra; Parthasarathy, K. R.
2000
A better bound on the variance. Zbl 1009.15009
Bhatia, Rajendra; Davis, Chandler
2000
More operator versions of the Schwarz inequality. Zbl 0984.46040
Bhatia, Rajendra; Davis, Chandler
2000
Cartesian decompositions and Schatten norms. Zbl 0981.47008
2000
Pinching, trimming, truncating, and averaging of matrices. Zbl 0984.15024
Bhatia, Rajendra
2000
Fréchet derivatives of the power function. Zbl 0988.47011
Bhatia, Rajendra; Holbrook, John A.
2000
Orthogonality of matrices and some distance problems. Zbl 0937.15023
Bhatia, Rajendra; Šemrl, Peter
1999
Maps on matrices that preserve the spectral radius distance. Zbl 0927.15006
Bhatia, Rajendra; Šemrl, Peter; Sourour, A. R.
1999
Derivations, derivatives and chain rules. Zbl 0951.47012
Bhatia, Rajendra; Sinha, Kalyan B.
1999
Perturbation of extended enumerations of eigenvalues. Zbl 0933.47015
Bhatia, Rajendra; Davis, Chandler
1999
Perturbation theorems for Hermitian elements in Banach algebras. Zbl 0940.46026
Bhatia, Rajendra; Drissi, Driss
1999
Norm inequalities for positive operators. Zbl 0912.47005
1998
Differentiation of operator functions and perturbation bounds. Zbl 0918.47017
Bhatia, Rajendra; Singh, Dinesh; Sinha, Kalyan B.
1998
Distance between commuting tuples of normal operators. Zbl 0931.47001
Bhatia, Rajendra; Elsner, Ludwig; Šemrl, Peter
1998
Eigenvalues of symmetrizable matrices. Zbl 0898.15015
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
1998
How and why to solve the operator equation $$AX-XB=Y$$. Zbl 0909.47011
Bhatia, Rajendra; Rosenthal, Peter
1997
Approximate isometries on Euclidean spaces. Zbl 0901.46016
Bhatia, Rajendra; Šemrl, Peter
1997
Some inequalities for norms of commutators. Zbl 0877.15023
1997
A note on the Lyapunov equation. Zbl 0881.15016
Bhatia, Rajendra
1997
Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
1997
Spectral variation bounds for diagonalisable matrices. Zbl 0897.15007
Bhatia, Rajendra; Elsner, Ludwig; Krause, Gerd M.
1997
Matrix analysis. Zbl 0863.15001
Bhatia, Rajendra
1996
On perturbations of matrix pencils with real spectra. II. Zbl 0852.15008
Bhatia, Rajendra; Li, Ren-Cang
1996
Distance between Hermitian operators in Schatten classes. Zbl 0857.47013
Bhatia, Rajendra; Šemrl, Peter
1996
On joint eigenvalues of commuting matrices. Zbl 0870.15003
Bhatia, R.; Elsner, L.
1996
A Cauchy-Schwarz inequality for operators with applications. Zbl 0824.47006
Bhatia, Rajendra; Davis, Chandler
1995
Perturbation bounds for the operator absolute value. Zbl 0835.47009
Bhatia, Rajendra
1995
On the joint spectral radius of commuting matrices. Zbl 0830.47002
Bhatia, Rajendra; Bhattacharyya, Tirthankar
1995
Matrix factorizations and their perturbations. Zbl 0794.15006
Bhatia, Rajendra
1994
First and second order perturbation bounds for the operator absolute value. Zbl 0815.47006
Bhatia, Rajendra
1994
The Hoffman-Wielandt inequality in infinite dimensions. Zbl 0805.47017
Bhatia, Rajendra; Elsner, Ludwig
1994
Variation of real powers of positive operators. Zbl 0836.47011
Bhatia, Rajendra; Sinha, Kalyan B.
1994
Variation of the unitary part of a matrix. Zbl 0805.15006
Bhatia, Rajendra; Mukherjea, Kalyan
1994
Relations of linking and duality between symmetric gauge functions. Zbl 0808.15016
Bhatia, Rajendra; Davis, Chandler
1994
A simple proof of an operator inequality of Jocić and Kittaneh. Zbl 0851.47012
Bhatia, Rajendra
1994
More matrix forms of the arithmetic-geometric mean inequality. Zbl 0767.15012
Bhatia, Rajendra; Davis, Chandler
1993
A generalization of the Hoffman-Wielandt theorem. Zbl 0774.15011
Bhatia, Rajendra; Bhattacharyya, Tirthankar
1993
Fourier series. Zbl 0940.42001
Bhatia, Rajendra
1993
A Henrici theorem for joint spectra of commuting matrices. Zbl 0790.15015
Bhatia, Rajendra; Bhattacharyya, Tirthankar
1993
...and 33 more Documents
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Cited by 2,222 Authors
79 Bhatia, Rajendra 72 Kittaneh, Fuad 52 Lim, Yongdo 40 Serra-Capizzano, Stefano 36 Hiai, Fumio 31 Moslehian, Mohammad Sal 22 Li, Rencang 21 Bourin, Jean-Christophe 21 Uchiyama, Mitsuru 19 Hirzallah, Omar 18 Garoni, Carlo 18 Kim, Sejong 18 Massey, Pedro G. 17 Stojanoff, Demetrio 16 Lee, Hosoo 16 Li, Chi-Kwong 16 Niezgoda, Marek 16 Seo, Yuki 15 Audenaert, Koenraad M. R. 15 Jain, Tanvi 15 Sababheh, Mohamad Suboh 14 Dragomir, Sever Silvestru 14 Elsner, Ludwig F. 14 Lin, Minghua 14 Moradi, Hamid Reza 14 Tam, Tin-Yau 13 Sain, Debmalya 12 Aujla, Jaspal Singh 11 Conde, Cristian M. 11 Holbrook, John A. R. 11 Pálfia, Miklós 11 Petz, Dénes 11 Sesana, Debora 11 Singh, Mandeep 10 Dinh Trung Hoa 10 Gil’, Michael Iosif 10 Kian, Mohsen 10 Lawson, Jimmie Don 10 Rastegin, Alexey E. 10 Sra, Suvrit 10 Zou, Limin 9 Antezana, Jorge 9 Furuichi, Shigeru 9 Furuta, Takayuki 9 Kosaki, Hideki 9 Lee, Eun-Young 9 Li, Wen 9 Paul, Kallol 9 Ruiz, Mariano A. 9 Sendov, Hristo S. 9 Zhan, Xingzhi 8 Bourhim, Abdellatif 8 Drury, Stephen William 8 Fujii, Jun Ichi 8 Jocić, Danko R. 8 Krnić, Mario 8 Larotonda, Gabriel 8 Molnár, Lajos 8 Sano, Takashi 8 Zhang, Fuzhen 7 Arambašić, Ljiljana 7 Davis, Chandler 7 Dumitru, Raluca 7 Guillot, Dominique 7 Hayajneh, Mostafa 7 Khare, Apoorva 7 Rajić, Rajna 7 Rodman, Leiba X. 7 Saito, Kichisuke 7 Šemrl, Peter 7 Sharma, Rajesh 7 Tanaka, Ryotaro 7 Wada, Shuhei 7 Zamani, Ali 6 Bakherad, Mojtaba 6 Ding, Chao 6 Franco, Jose A. 6 Friedland, Shmuel 6 Fu, Xiaohui 6 Grover, Priyanka 6 Gumus, Ibrahim Halil 6 Haukkanen, Pentti 6 Hayajneh, Saja 6 Horn, Roger Alan 6 Huhtanen, Marko 6 Iannazzo, Bruno 6 Kapil, Yogesh 6 Kum, Sangho 6 Kuzma, Bojan 6 Li, Hanyu 6 Najafi, Hamed 6 Nechita, Ion 6 Omidvar, Mohsen Erfanian 6 O’Reilly, Małgorzata M. 6 Pečarić, Josip 6 Rajaratnam, Bala 6 Sun, Defeng 6 Taghavi Jelodar, Ali 6 Tropp, Joel A. 6 Wójcik, Paweł ...and 2,122 more Authors
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Cited in 351 Serials
531 Linear Algebra and its Applications 82 Linear and Multilinear Algebra 68 Journal of Mathematical Analysis and Applications 42 Proceedings of the American Mathematical Society 41 Journal of Mathematical Physics 39 Journal of Functional Analysis 30 The Annals of Statistics 26 Communications in Mathematical Physics 25 Integral Equations and Operator Theory 23 SIAM Journal on Matrix Analysis and Applications 21 Journal of Inequalities and Applications 19 Mathematical Inequalities & Applications 18 ELA. The Electronic Journal of Linear Algebra 18 Positivity 17 Letters in Mathematical Physics 16 Journal of Statistical Physics 16 Advances in Operator Theory 15 Applied Mathematics and Computation 15 Transactions of the American Mathematical Society 15 Complex Analysis and Operator Theory 15 Journal of Mathematical Inequalities 14 Mathematics of Computation 14 Banach Journal of Mathematical Analysis 13 Quantum Information Processing 12 Journal of Computational and Applied Mathematics 12 Numerische Mathematik 11 Mathematical Programming. Series A. Series B 10 Physics Letters. A 10 Operators and Matrices 10 Annals of Functional Analysis 9 Probability Theory and Related Fields 9 International Journal of Mathematics 8 Reviews in Mathematical Physics 8 Results in Mathematics 8 Bulletin of the Iranian Mathematical Society 8 The Journal of Fourier Analysis and Applications 8 Special Matrices 7 Computers & Mathematics with Applications 7 Advances in Mathematics 7 Numerical Functional Analysis and Optimization 7 Aequationes Mathematicae 7 Numerical Linear Algebra with Applications 7 Advances in Computational Mathematics 7 Foundations of Computational Mathematics 7 Mediterranean Journal of Mathematics 6 Bulletin of the Australian Mathematical Society 6 Discrete Applied Mathematics 6 Reports on Mathematical Physics 6 The Annals of Probability 6 Automatica 6 BIT 6 Calcolo 6 Journal of Multivariate Analysis 6 Journal of Optimization Theory and Applications 6 Mathematische Annalen 6 Statistics & Probability Letters 6 Stochastic Processes and their Applications 6 SIAM Journal on Scientific Computing 6 Applied and Computational Harmonic Analysis 6 Abstract and Applied Analysis 6 Journal of High Energy Physics 6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 6 Journal of Machine Learning Research (JMLR) 6 Electronic Journal of Statistics 5 Indian Journal of Pure & Applied Mathematics 5 Journal of the Franklin Institute 5 Journal of Approximation Theory 5 Journal of Econometrics 5 Numerical Algorithms 5 Annals of Physics 5 Expositiones Mathematicae 5 Bernoulli 5 Journal of the Australian Mathematical Society 5 Physical Review A, Third Series 5 Journal of Spectral Theory 4 Communications in Algebra 4 Mathematical Notes 4 Rocky Mountain Journal of Mathematics 4 The Mathematical Intelligencer 4 Mathematische Zeitschrift 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University 4 Journal of Theoretical Probability 4 Journal of Elasticity 4 SIAM Review 4 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 4 Indagationes Mathematicae. New Series 4 SIAM Journal on Optimization 4 Journal of Mathematical Sciences (New York) 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Acta Mathematica Sinica. English Series 4 Physical Review Letters 4 Journal of Applied Mathematics 4 Journal of Physics A: Mathematical and Theoretical 4 Science China. Mathematics 3 Archive for Rational Mechanics and Analysis 3 Discrete Mathematics 3 International Journal of Theoretical Physics 3 Israel Journal of Mathematics 3 Journal of Computational Physics 3 Lithuanian Mathematical Journal ...and 251 more Serials
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Cited in 60 Fields
929 Linear and multilinear algebra; matrix theory (15-XX) 731 Operator theory (47-XX) 251 Numerical analysis (65-XX) 228 Functional analysis (46-XX) 183 Quantum theory (81-XX) 141 Statistics (62-XX) 132 Probability theory and stochastic processes (60-XX) 123 Real functions (26-XX) 112 Information and communication theory, circuits (94-XX) 67 Operations research, mathematical programming (90-XX) 57 Differential geometry (53-XX) 50 Combinatorics (05-XX) 47 Partial differential equations (35-XX) 47 Harmonic analysis on Euclidean spaces (42-XX) 45 Computer science (68-XX) 44 Statistical mechanics, structure of matter (82-XX) 35 Systems theory; control (93-XX) 34 Calculus of variations and optimal control; optimization (49-XX) 34 Global analysis, analysis on manifolds (58-XX) 30 Functions of a complex variable (30-XX) 30 Dynamical systems and ergodic theory (37-XX) 26 Convex and discrete geometry (52-XX) 24 Topological groups, Lie groups (22-XX) 24 Ordinary differential equations (34-XX) 24 Difference and functional equations (39-XX) 19 Geometry (51-XX) 17 Group theory and generalizations (20-XX) 17 Approximations and expansions (41-XX) 15 Measure and integration (28-XX) 14 Number theory (11-XX) 14 Biology and other natural sciences (92-XX) 13 Order, lattices, ordered algebraic structures (06-XX) 13 General topology (54-XX) 12 Mechanics of deformable solids (74-XX) 11 Special functions (33-XX) 10 Nonassociative rings and algebras (17-XX) 10 Several complex variables and analytic spaces (32-XX) 10 Relativity and gravitational theory (83-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Abstract harmonic analysis (43-XX) 8 Integral equations (45-XX) 7 Fluid mechanics (76-XX) 6 Field theory and polynomials (12-XX) 6 Algebraic geometry (14-XX) 5 History and biography (01-XX) 4 Integral transforms, operational calculus (44-XX) 4 Optics, electromagnetic theory (78-XX) 3 Associative rings and algebras (16-XX) 3 $$K$$-theory (19-XX) 3 Sequences, series, summability (40-XX) 3 Manifolds and cell complexes (57-XX) 3 Mechanics of particles and systems (70-XX) 2 Mathematical logic and foundations (03-XX) 2 Category theory; homological algebra (18-XX) 2 Potential theory (31-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Commutative algebra (13-XX) 1 Algebraic topology (55-XX) 1 Geophysics (86-XX) 1 Mathematics education (97-XX)
Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-04-14T08:47:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5638599395751953, "perplexity": 6868.353346829644}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038077336.28/warc/CC-MAIN-20210414064832-20210414094832-00524.warc.gz"} |
http://dlmf.nist.gov/3.12 | # §3.12 Mathematical Constants
The fundamental constant
3.12.1 $\pi=3.14159\;26535\;89793\;23846\;\ldots$ Defines: $\pi$: the ratio of the circumference of a circle to its diameter Notes: For more digits see OEIS Sequence A000796; see also Sloane (2003). Permalink: http://dlmf.nist.gov/3.12.E1 Encodings: TeX, pMML, png See also: Annotations for 3.12
can be defined analytically in numerous ways, for example,
3.12.2 $\pi=4\int_{0}^{1}\frac{\mathrm{d}t}{1+t^{2}}.$
Other constants that appear in the DLMF include the base $e$ of natural logarithms
3.12.3 $e=2.71828\;18284\;59045\;23536\;\ldots\,,$ Symbols: $\mathrm{e}$: base of exponential function Notes: For more digits see OEIS Sequence A001113; see also Sloane (2003). Permalink: http://dlmf.nist.gov/3.12.E3 Encodings: TeX, pMML, png See also: Annotations for 3.12
see §4.2(ii), and Euler’s constant $\gamma$
3.12.4 $\gamma=0.57721\;56649\;01532\;86060\;\ldots,$ Symbols: $\gamma$: Euler’s constant Notes: For more digits see OEIS Sequence A001620; see also Sloane (2003). Permalink: http://dlmf.nist.gov/3.12.E4 Encodings: TeX, pMML, png See also: Annotations for 3.12
see §5.2(ii).
For access to online high-precision numerical values of mathematical constants see Sloane (2003). For historical and other information see Finch (2003). | 2017-01-22T05:49:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 13, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9828252196311951, "perplexity": 8868.6115199854}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281353.56/warc/CC-MAIN-20170116095121-00577-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://zbmath.org/authors/macmahon.percy-alexander | ## MacMahon, Percy Alexander
Compute Distance To:
Author ID: macmahon.percy-alexander Published as: MacMahon, P. A.; MacMahon, Percy Alexander; MacMahon, Percy A.; MacMahon; MacMahon, P. A. (Major).; Macmahon, P. A. more...less External Links: MacTutor · Wikidata · GND · IdRef
Documents Indexed: 135 Publications since 1880, including 10 Books Biographic References: 3 Publications Co-Authors: 48 Co-Authors with 6 Joint Publications 479 Co-Co-Authors
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### Co-Authors
126 single-authored 2 Andrews, George F. 2 Easton, B. S. 2 Knowles, R. L. 2 Mathews, George Ballard 2 Rota, Gian-Carlo 2 Scott, Robert Forsyth 2 Simmons, T. C. 2 Tucker, Robert 1 Ayrton, Herta 1 Barisien, E.-N. 1 Barton, W. J. 1 Beyens, J. 1 Brocard, Henri 1 Busk, E. 1 Chakrvarti, B. 1 Chambeau, A. 1 Curtis 1 Curtis, A. Hill. 1 Darling, H. B. C. 1 Davis, R. F. 1 Gohierre de Longchamps, Gaston Albert 1 Eastwood, D. 1 Galliers, T. 1 Garcia, Paul 1 Greenstreet, William John 1 Hammond, James 1 Hudson, William Henry Hoar 1 Jenkins, J. S. 1 Johnston, J. P. 1 MacFarlane, Alexander 1 MacMahon, W. P. D. 1 Malet, John C. 1 Martin, Artemas 1 McClelland, William J. 1 Mee, W. M. 1 Miller, William John Clarke 1 Mukhopadhyay, Ashutosh 1 Neuberg, Joseph 1 Nilkanta 1 O’Regan, J. 1 Perrin, E. 1 Rau, B. H. 1 Reeves, J. M. 1 Roberts, Samuel 1 Rutter, E. 1 Scott, Charlotte Angas 1 Symons, E. W. 1 Theodosius, A. F. 1 Townsend, Robert 1 Voyson, W. 1 Young, J. R.
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### Serials
15 Proceedings of the London Mathematical Society. Second Series 13 American Journal of Mathematics 13 The Quarterly Journal of Pure and Applied Mathematics 12 Proceedings of the London Mathematical Society 10 Philosophical Transactions of the Royal Society of London, Series A 9 Proceedings of the Cambridge Philosophical Society 5 Nature, London 4 Proceedings of the Royal Society of London. Series A 3 Philosophical Transactions of the Royal Society of London, A 2 Journal of the London Mathematical Society 2 Mathematicians of Our Time 1 Discrete Applied Mathematics 1 Bulletin de la Société Mathématique de France 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 1 The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, V. Series
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### Fields
27 Combinatorics (05-XX) 22 Number theory (11-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 History and biography (01-XX) 3 Special functions (33-XX) 3 Ordinary differential equations (34-XX) 2 Differential geometry (53-XX) 2 Probability theory and stochastic processes (60-XX) 1 General and overarching topics; collections (00-XX) 1 Geometry (51-XX) 1 Mechanics of particles and systems (70-XX) 1 Information and communication theory, circuits (94-XX)
### Citations contained in zbMATH Open
49 Publications have been cited 771 times in 702 Documents Cited by Year
Combinatory analysis. Vol. 2. JFM 46.0118.07
MacMahon, P. A.
1916
Combinatory analysis. Vol. I, II. Zbl 0101.25102
MacMahon, Percy A.
1960
Combinatory analysis. Vol. 1. JFM 45.1271.01
MacMahon, P. A.
1915
The indices of permutations and the derivation therefrom of functions of a single associated with the permutations of any assemblage of objects. JFM 44.0076.02
MacMahon, P. A.
1913
Two applications of general theorems in combinatory analysis: (1) To the theory of inversions of permutations; (2) To the ascertainment of the numbers of terms in the development of a determinant which has amongst its elements an arbitrary number of zero. JFM 46.0107.04
MacMahon, P. A.
1916
Combinatorial analysis. JFM 31.0219.01
MacMahon, P. A.
1900
Divisors of numbers and their continuations in the theory of partitions. JFM 47.0117.01
MacMahon, P. A.
1920
Memoir on the theory of the compositions of numbers. (Memoir on the theory of the eompositions of numbers.) JFM 25.0258.01
MacMahon, P. A.
1893
Combinatory analysis. Vols. I, II (bound in one volume). Reprint of An introduction to combinatory analysis (1920) and Combinatory analysis. Vol. I, II (1915, 1916). Zbl 1144.05300
MacMahon, Percy A.
2004
Memoir on the theory of the partitions of numbers. Part V. Partitions in two-dimensional space. JFM 42.0236.21
MacMahon, P. A.
1911
Second memoir on the composition of numbers. JFM 39.0241.01
MacMahon, P. A.
1908
Small contribution to combinatory analysis. JFM 46.0108.01
MacMahon, P. A.
1918
Collected papers. Volume I: Combinatorics. Ed. and with a preface by George F. Andrews. With an introduction by Gian-Carlo Rota. Zbl 0557.01015
MacMahon, Percy Alexander
1978
Dirichlet series and the theory of partitions. JFM 50.0083.02
MacMahon, P. A.
1924
Memoir on the theory of the partitions of numbers. Part VI. Partitions in two-dimesional space, to which is added an adumbration of the theory of the partitions in three-dimensional space. JFM 42.0237.01
MacMahon, P. A.
1911
Memoir on the theory of the partition of numbers. – Part IV: On the probability that the successful candidate at an election by ballot may never at any time have fewer votes than the one who is insucessful; on a generalisation of this question, and on its connexion with other questions of partition, permutation, and combination. JFM 40.0281.04
Macmahon, P. A.
1909
Partitions of numbers whose graphs possess symmetry. (Partitions of numbers whose graphs possess symmetry.) JFM 30.0201.04
MacMahon, P. A.
1899
Note on the parity of the number which enumerates the partitions of a number. JFM 48.1160.01
MacMahon, P. A.
1921
Application of a theory of permutations in circular precession to the theory of numbers. JFM 24.0181.01
MacMahon, P. A.
1892
The divisors of numbers. JFM 47.0107.02
MacMahon, P. A.
1920
Memoir on the symmetric functions of the roots of equations. JFM 22.0187.02
MacMahon, P. A.
1890
Memoir on the theory of the partition of numbers. Part I. JFM 27.0134.04
MacMahon, P. A.
1896
Combinatory analysis: a review of the present state of knowledge. JFM 28.0103.01
MacMahon, P. A.
1897
New mathematical pastimes. JFM 48.0075.06
MacMahon, P. A.
1921
Note on the parity of the number which enumerates the partitions of a number. JFM 48.0153.01
MacMahon, P. A.
1921
The theory of modular partitions. JFM 48.1161.01
MacMahon, P. A.
1922
Combinations derived from $$m$$ identical sets of $$n$$ different letters and their connexion with general magic squares. JFM 46.0108.02
MacMahon, P. A.
1917
Seventh memoir on the partition of numbers. JFM 46.0205.03
MacMahon, P. A.
1918
A new method in combinatory analysis, with application to latin squares and associated questions. JFM 30.0227.11
MacMahon, P. A.
1898
Yoke-chains and multipartite compositions in connexion with the analytical forms called trees. JFM 23.0565.02
MacMahon, P. A.
1891
The structure of a determinant. (Lecture on the Rouse Ball Foundation, University of Cambridge, 7. 6. 27.). JFM 53.0074.05
MacMahon, P. A.
1927
Researches in the theory of determinants. JFM 50.0069.01
MacMahon, P. A.
1924
An introduction to combinatory analysis. JFM 47.0066.07
MacMahon, P. A.
1920
Second memoir on the compositions of numbers. JFM 38.0225.01
MacMahon, P. A.
1907
Yoke-chains and multipartite compositions in connexion with the analytical forms called “trees”. JFM 23.0132.02
MacMahon, P. A.
1891
A second paper on perpetuants. JFM 17.0082.03
MacMahon, P. A.
1885
The combinations of resistances. Zbl 1053.94585
MacMahon, P. A.
1994
The parity of $$p(n)$$, the number of partitions of $$n$$, when $$n\leqq \, 1000$$. JFM 52.0167.01
MacMahon, P. A.
1926
The theory of modular partitions. JFM 48.0154.01
MacMahon, P. A.
1922
The superior and inferior indices of permutations. JFM 45.1264.01
MacMahon, P. A.
1915
The sums of powers of the binomial coefficients. JFM 33.0285.05
MacMahon, P. A.
1902
Memoir on the theory of the partitions of numbers. Part. II. (Memoir on the theory of the partitions of numbers. Part. II.) JFM 30.0171.11
MacMahon, P. A.
1899
James Joseph Sylvester. JFM 28.0030.03
MacMahon, P. A.
1896
The perpetuant invariants of binary quantics. JFM 26.0141.01
MacMahon, P. A.
1895
A certain class of generating functions in the theory of numbers. (A certain class of generating functions in the theory of numbers.) JFM 25.0258.02
MacMahon, P. A.
1893
Weighing by a series of weights. (Weighing by a series of weights.) JFM 23.0186.03
MacMahon, P. A.
1890
A new theorem in symmetric functions. JFM 17.0113.03
MacMahon
1885
Certain special partitions of numbers. (Certain special partitions of numbers.) JFM 18.0138.04
MacMahon, P. A.
1886
Seminvariants and symmetric functions. JFM 15.0127.01
MacMahon, P. A.
1883
Combinatory analysis. Vols. I, II (bound in one volume). Reprint of An introduction to combinatory analysis (1920) and Combinatory analysis. Vol. I, II (1915, 1916). Zbl 1144.05300
MacMahon, Percy A.
2004
The combinations of resistances. Zbl 1053.94585
MacMahon, P. A.
1994
Collected papers. Volume I: Combinatorics. Ed. and with a preface by George F. Andrews. With an introduction by Gian-Carlo Rota. Zbl 0557.01015
MacMahon, Percy Alexander
1978
Combinatory analysis. Vol. I, II. Zbl 0101.25102
MacMahon, Percy A.
1960
The structure of a determinant. (Lecture on the Rouse Ball Foundation, University of Cambridge, 7. 6. 27.). JFM 53.0074.05
MacMahon, P. A.
1927
The parity of $$p(n)$$, the number of partitions of $$n$$, when $$n\leqq \, 1000$$. JFM 52.0167.01
MacMahon, P. A.
1926
Dirichlet series and the theory of partitions. JFM 50.0083.02
MacMahon, P. A.
1924
Researches in the theory of determinants. JFM 50.0069.01
MacMahon, P. A.
1924
The theory of modular partitions. JFM 48.1161.01
MacMahon, P. A.
1922
The theory of modular partitions. JFM 48.0154.01
MacMahon, P. A.
1922
Note on the parity of the number which enumerates the partitions of a number. JFM 48.1160.01
MacMahon, P. A.
1921
New mathematical pastimes. JFM 48.0075.06
MacMahon, P. A.
1921
Note on the parity of the number which enumerates the partitions of a number. JFM 48.0153.01
MacMahon, P. A.
1921
Divisors of numbers and their continuations in the theory of partitions. JFM 47.0117.01
MacMahon, P. A.
1920
The divisors of numbers. JFM 47.0107.02
MacMahon, P. A.
1920
An introduction to combinatory analysis. JFM 47.0066.07
MacMahon, P. A.
1920
Small contribution to combinatory analysis. JFM 46.0108.01
MacMahon, P. A.
1918
Seventh memoir on the partition of numbers. JFM 46.0205.03
MacMahon, P. A.
1918
Combinations derived from $$m$$ identical sets of $$n$$ different letters and their connexion with general magic squares. JFM 46.0108.02
MacMahon, P. A.
1917
Combinatory analysis. Vol. 2. JFM 46.0118.07
MacMahon, P. A.
1916
Two applications of general theorems in combinatory analysis: (1) To the theory of inversions of permutations; (2) To the ascertainment of the numbers of terms in the development of a determinant which has amongst its elements an arbitrary number of zero. JFM 46.0107.04
MacMahon, P. A.
1916
Combinatory analysis. Vol. 1. JFM 45.1271.01
MacMahon, P. A.
1915
The superior and inferior indices of permutations. JFM 45.1264.01
MacMahon, P. A.
1915
The indices of permutations and the derivation therefrom of functions of a single associated with the permutations of any assemblage of objects. JFM 44.0076.02
MacMahon, P. A.
1913
Memoir on the theory of the partitions of numbers. Part V. Partitions in two-dimensional space. JFM 42.0236.21
MacMahon, P. A.
1911
Memoir on the theory of the partitions of numbers. Part VI. Partitions in two-dimesional space, to which is added an adumbration of the theory of the partitions in three-dimensional space. JFM 42.0237.01
MacMahon, P. A.
1911
Memoir on the theory of the partition of numbers. – Part IV: On the probability that the successful candidate at an election by ballot may never at any time have fewer votes than the one who is insucessful; on a generalisation of this question, and on its connexion with other questions of partition, permutation, and combination. JFM 40.0281.04
Macmahon, P. A.
1909
Second memoir on the composition of numbers. JFM 39.0241.01
MacMahon, P. A.
1908
Second memoir on the compositions of numbers. JFM 38.0225.01
MacMahon, P. A.
1907
The sums of powers of the binomial coefficients. JFM 33.0285.05
MacMahon, P. A.
1902
Combinatorial analysis. JFM 31.0219.01
MacMahon, P. A.
1900
Partitions of numbers whose graphs possess symmetry. (Partitions of numbers whose graphs possess symmetry.) JFM 30.0201.04
MacMahon, P. A.
1899
Memoir on the theory of the partitions of numbers. Part. II. (Memoir on the theory of the partitions of numbers. Part. II.) JFM 30.0171.11
MacMahon, P. A.
1899
A new method in combinatory analysis, with application to latin squares and associated questions. JFM 30.0227.11
MacMahon, P. A.
1898
Combinatory analysis: a review of the present state of knowledge. JFM 28.0103.01
MacMahon, P. A.
1897
Memoir on the theory of the partition of numbers. Part I. JFM 27.0134.04
MacMahon, P. A.
1896
James Joseph Sylvester. JFM 28.0030.03
MacMahon, P. A.
1896
The perpetuant invariants of binary quantics. JFM 26.0141.01
MacMahon, P. A.
1895
Memoir on the theory of the compositions of numbers. (Memoir on the theory of the eompositions of numbers.) JFM 25.0258.01
MacMahon, P. A.
1893
A certain class of generating functions in the theory of numbers. (A certain class of generating functions in the theory of numbers.) JFM 25.0258.02
MacMahon, P. A.
1893
Application of a theory of permutations in circular precession to the theory of numbers. JFM 24.0181.01
MacMahon, P. A.
1892
Yoke-chains and multipartite compositions in connexion with the analytical forms called trees. JFM 23.0565.02
MacMahon, P. A.
1891
Yoke-chains and multipartite compositions in connexion with the analytical forms called “trees”. JFM 23.0132.02
MacMahon, P. A.
1891
Memoir on the symmetric functions of the roots of equations. JFM 22.0187.02
MacMahon, P. A.
1890
Weighing by a series of weights. (Weighing by a series of weights.) JFM 23.0186.03
MacMahon, P. A.
1890
Certain special partitions of numbers. (Certain special partitions of numbers.) JFM 18.0138.04
MacMahon, P. A.
1886
A second paper on perpetuants. JFM 17.0082.03
MacMahon, P. A.
1885
A new theorem in symmetric functions. JFM 17.0113.03
MacMahon
1885
Seminvariants and symmetric functions. JFM 15.0127.01
MacMahon, P. A.
1883
all top 5
### Cited by 783 Authors
19 Lai, Tri 17 Krattenthaler, Christian Friedrich 16 Andrews, George Eyre 16 Ciucu, Mihai 14 Foata, Dominique C. 14 Merca, Mircea 11 Ehrenborg, Richard 11 Sills, Andrew V. 10 Rawlings, Don 9 Chen, William Yong-Chuan 8 Han, Guo-Niu 8 Zeilberger, Doron 7 Jackson, David M. 7 Konvalinka, Matjaž 7 Mansour, Toufik 7 Munagi, Augustine O. 6 Biagioli, Riccardo 6 Carlitz, Leonard 6 Caselli, Fabrizio 6 Drensky, Vesselin 6 Gessel, Ira Martin 6 Goulden, Ian P. 6 Rohatgi, Ranjan 6 Savage, Carla D. 6 Stanley, Richard Peter 6 Swanson, Joshua P. 6 Wachs, Michelle Lynn 5 Remmel, Jeffrey Brian 5 Roichman, Yuval 5 Sagan, Bruce Eli 5 Warnaar, S. Ole 5 Zeng, Jiang 4 Brenti, Francesco 4 Clarke, Robert J. 4 Eisenkölbl, Theresia 4 Fischer, Ilse 4 Hopkins, Samuel Francis 4 Mutafchiev, Lyuben R. 4 Pak, Igor 4 Readdy, Margaret A. 4 Rosas, Mercedes Helena 4 Steingrímsson, Einar 4 Tewari, Vasu V. 4 Viennot, Xavier Gérard 3 Adin, Ron M. 3 Beck, Matthias 3 Billey, Sara C. 3 Borodin, Alexei 3 Cerasoli, Mauro 3 Chu, Wenchang 3 Corteel, Sylvie 3 Dousse, Jehanne 3 Eu, Sen-Peng 3 Fındık, Şehmus 3 Fu, Shishuo 3 Gilmore, Tomack 3 Good, Irving John (Jack) 3 Haglund, James 3 Hernane, Mohand-Ouamar 3 Ji, Kathy Qing 3 Knopfmacher, Arnold 3 Lin, Zhicong 3 Nicolas, Jean-Louis 3 Ono, Ken 3 Park, SeungKyung 3 Poznanović, Svetlana 3 Rhoades, Brendon 3 Riordan, John F. 3 Vallejo, Ernesto 3 Yan, Catherine Huafei 2 Abramson, Morton 2 Adler, Mark 2 Ahlbach, Connor 2 Armstrong, Drew 2 Assaf, Sami H. 2 Bayad, Abdelmejid 2 Bell, Eric Temple 2 Berkove, Ethan J. 2 Berkovich, Alexander 2 Björner, Anders 2 Braun, Benjamin 2 Canfield, E. Rodney 2 Choliy, Yuriy 2 Colmenarejo, Laura 2 Conflitti, Alessandro 2 Conger, Mark A. 2 Crilly, Tony 2 Dangovski, Rumen 2 Désarménien, Jacques 2 Destainville, Nicolas 2 Domokos, Mátyás 2 Elizalde, Sergi 2 Ewell, John A. 2 Feltrin, Guglielmo 2 Foulkes, H. O. 2 Fox, N. Bradley 2 Fu, James C. 2 Fulmek, Markus 2 Galovich, Jennifer 2 Gamburd, Alexander ...and 683 more Authors
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### Cited in 168 Serials
81 Journal of Combinatorial Theory. Series A 69 Discrete Mathematics 53 Advances in Applied Mathematics 35 European Journal of Combinatorics 24 Annals of Combinatorics 22 Advances in Mathematics 21 The Ramanujan Journal 20 The Electronic Journal of Combinatorics 19 Proceedings of the American Mathematical Society 15 Journal of Number Theory 15 Transactions of the American Mathematical Society 15 Linear Algebra and its Applications 12 Journal of Algebraic Combinatorics 10 Journal of Algebra 9 International Journal of Number Theory 8 Journal of Integer Sequences 7 Discrete Applied Mathematics 7 Séminaire Lotharingien de Combinatoire 6 Journal of Mathematical Analysis and Applications 6 Mathematics of Computation 6 Journal of Statistical Planning and Inference 6 Theoretical Computer Science 6 Integers 5 Journal of Mathematical Physics 5 Nuclear Physics. B 4 Journal of Statistical Physics 4 Mathematische Annalen 4 Studies in Applied Mathematics 4 Journal of Symbolic Computation 4 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) 3 Israel Journal of Mathematics 3 Journal of Geometry and Physics 3 The Mathematical Intelligencer 3 Journal of Computational and Applied Mathematics 3 Statistics & Probability Letters 3 SIAM Journal on Discrete Mathematics 3 Aequationes Mathematicae 3 Historia Mathematica 3 Journal of Mathematical Sciences (New York) 3 Algebraic Combinatorics 2 International Journal of Modern Physics B 2 Computers & Mathematics with Applications 2 Communications in Mathematical Physics 2 Physica A 2 Rocky Mountain Journal of Mathematics 2 Biometrical Journal 2 Duke Mathematical Journal 2 Inventiones Mathematicae 2 Manuscripta Mathematica 2 Mathematische Nachrichten 2 Memoirs of the American Mathematical Society 2 Quaestiones Mathematicae 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Discrete & Computational Geometry 2 Journal of the Ramanujan Mathematical Society 2 Bulletin of the American Mathematical Society. New Series 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Indagationes Mathematicae. New Series 2 The Australasian Journal of Combinatorics 2 Experimental Mathematics 2 Journal de Théorie des Nombres de Bordeaux 2 Combinatorics, Probability and Computing 2 Journal of Algebra and its Applications 2 Mediterranean Journal of Mathematics 2 Bulletin of the American Mathematical Society 2 Contributions to Discrete Mathematics 2 Forum of Mathematics, Sigma 2 Combinatorial Theory 1 American Mathematical Monthly 1 Analysis Mathematica 1 Applicable Analysis 1 Bulletin of the Australian Mathematical Society 1 Communications in Algebra 1 Indian Journal of Pure & Applied Mathematics 1 Lithuanian Mathematical Journal 1 Linear and Multilinear Algebra 1 The Mathematical Gazette 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Periodica Mathematica Hungarica 1 Theoretical and Mathematical Physics 1 Ukrainian Mathematical Journal 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Arithmetica 1 Algebra Universalis 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Probability 1 The Annals of Statistics 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 1 Archiv der Mathematik 1 Functiones et Approximatio. Commentarii Mathematici 1 Functional Analysis and its Applications 1 Fuzzy Sets and Systems 1 Integral Equations and Operator Theory 1 Journal of Applied Probability 1 Journal of Combinatorial Theory. Series B 1 Journal of Differential Equations 1 The Journal of the Indian Mathematical Society. New Series 1 Journal of Multivariate Analysis 1 Journal of Pure and Applied Algebra ...and 68 more Serials
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### Cited in 48 Fields
549 Combinatorics (05-XX) 213 Number theory (11-XX) 53 Group theory and generalizations (20-XX) 43 Special functions (33-XX) 38 Convex and discrete geometry (52-XX) 37 Linear and multilinear algebra; matrix theory (15-XX) 33 Probability theory and stochastic processes (60-XX) 30 Order, lattices, ordered algebraic structures (06-XX) 23 Commutative algebra (13-XX) 21 Algebraic geometry (14-XX) 21 Computer science (68-XX) 20 Statistical mechanics, structure of matter (82-XX) 18 Quantum theory (81-XX) 17 Associative rings and algebras (16-XX) 15 Nonassociative rings and algebras (17-XX) 12 History and biography (01-XX) 12 Functions of a complex variable (30-XX) 8 Statistics (62-XX) 5 Real functions (26-XX) 5 Ordinary differential equations (34-XX) 5 Difference and functional equations (39-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 General and overarching topics; collections (00-XX) 4 Functional analysis (46-XX) 4 Numerical analysis (65-XX) 3 Field theory and polynomials (12-XX) 3 Topological groups, Lie groups (22-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Operator theory (47-XX) 3 Manifolds and cell complexes (57-XX) 3 Biology and other natural sciences (92-XX) 2 Mathematical logic and foundations (03-XX) 2 Operations research, mathematical programming (90-XX) 2 Information and communication theory, circuits (94-XX) 1 Category theory; homological algebra (18-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Systems theory; control (93-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2023-03-27T13:29:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4490553140640259, "perplexity": 5514.368291482432}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948632.20/warc/CC-MAIN-20230327123514-20230327153514-00546.warc.gz"} |
https://finalfantasy.fandom.com/wiki/Holy_(Final_Fantasy_VIII) | ## FANDOM
37,127 Pages
Holy magic damage/one enemy
Description
Holy is an attack magic spell in Final Fantasy VIII. It is the only Holy-elemental spell, and can deal significant damage when cast as a spell. It provides among the highest boost to Strength and Magic when junctioned, as can also be junctioned to absorb or deal Holy damage.
## ObtainedEdit
Holy is difficult to acquire, as it can only be drawn from challenging or high-level enemies. It can be acquired from a few draw points, including the Island Closest to Heaven and the Island Closest to Hell. It can also be refined using the Guardian Force Siren's ability L Mag-RF, from Holy Stones and Moon Stones; the Krysta card modifies into 10 Holy Stones, but is not overly common in card games.
## UseEdit
Holy has a spell power of 48 when cast, meaning its damage is calculated as:
$Damage = AttackerMag + 48$[1]
$Damage = Damage * (265 - TargetSpr) / 4$
$Damage = Damage * Power / 256$
It can deal heavy Holy-elemental damage to a single target when cast as a spell. It is cast as a spell in the Magic command, Selphie's Slot Limit Break, or Rinoa's Angel Wing if she has it in her inventory.
Casting Holy in battle increases compatibility with Alexander by 2, with Carbuncle and Leviathan by 1, with Eden by 0.4 and with Bahamut by 0.2, but lowers compatibility with Doomtrain by 2.
Due to its rarity and its very strong bonuses when junctioned, it is better to stock Holy spells and not cast with the Magic command. However, it can deal significant damage when cast with Rinoa's Angel Wing, while not expending a spell.
Holy provides among the highest boosts to HP, Strength, or Magic of any spell. It can also resist a variety of status effects, and provides decent boosts to all stats. Additionally, it can be junctioned to either deal or resist Holy-elemental damage, though this is a niche use. Ultimately, Holy is best used defending against status effects, as it is outclassed by spells such as Ultima in providing a boost to HP and Strength; in the absence of more powerful spells, however, Holy is very potent in providing such boosts.
Holy is used against the player by Adel, Elnoyle, Imp (used as a final attack), Torama, and all forms of the final boss. The spell can be reflected back at the caster.
## ReferencesEdit
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http://plataformadeaprendizaje.iom.int/blog/index.php?entryid=797 | ## Blog entry by Dave Moore
Anyone in the world
Revolutionary speakers stimulate Linaeum Corp
. In the early 1980s, while constructing speaker closets in his daddy's garage in McMinnville, Paul Paddock created a euphonious concept. He envisioned an audio speaker efficient in cranking out a crisper Chopin, a much more sweet-sounding Mozart. Currently, greater than one decade later on, his desire has actually appeared in the type of an innovative audio speaker vehicle driver that a New York Times audio movie critic identifies as a "genuine breakthrough in an environment of gimmickry.".
Basically, Paddock's curious-looking motorists utilize incredibly flexible materials to basically get rid of distortion at higher regularities.
To produce the audio speakers, Paddock as well as Steve Haessler formed Linaeum Corp. in 1983. Haessler, a Stanford MBA and former small-business owner, gave the financial expertise, and also Paddock, that researched the trombone at Linfield Neighborhood University, provided the inventive ideas. "Paul just has a way of checking out points," claims Linaeum Executive Vice Head of state Ben Stutz enthusiastically. "It's impressive he generated this suggestion while qualified specialists missed it.".
Since Linaeum launched its first model three years back, the motorist has been obtaining go crazy reviews from audiophiles as well as trade publications all over the globe, such as England's Hi Fi News and also Record Review, U.S.-based Favorable Responses and also Germany's Sound. "Linaeum is creating audio that companies are going to have to bust their butt to meet," claims Joe Webber, manager of Northwest Portland's Corner Sound, which lugs Linaeum's audio speakers.
And Michael Johnson, supervisor of regional radio station KBOO (90.7 FM), claims, "It's such a neat idea I can not find out why no one thought of this prior to.".
Paddock coordinated this brand-new audio by taking a soft strategy to an age-old sound issue. Besides Linaeum's, there are generally 3 approaches for audio speaker vehicle drivers to provide songs-- electrostatic, ribbon, and also cone. Although the techniques vary, all have vehicle drivers having an inflexible cone or dome that pushes out air in a piston movement, which reaches our ears as noise. Rigidity of the cone is vital because any type of surface area bending or flexing misshapes sound. But some amount of distortion is unavoidable at regularities where the dome is compelled to shake backward and forward as lots of as 10,000 times per secondly. "It's like trying to keep a notepad from bending while holding it with two hands as well as pushing it back and also fourth" states Steve Geist, a former Tektronix designer who signed up with Linaeum in 1987.
To solve this trouble, Linaeum rather utilizes a flexible material to create noise. Right here is just how it functions: On each driver, 2 pliable plastic membrane layers are wrapped around rectangle-shaped really felt pads to create side-by-side half cylinders. In between the cyndrical tubes exists a coil suspended in position with magnets. When the coil obtains signals from the amplifier it oscillates, triggering the adaptable cyndrical tubes to wiggle in a style straight mimicking the sound wave it is producing.
RELATED ARTICLE: Best car speakers for sound quality
Linaeum claims that distortion with the chauffeur really lowers with greater frequencies due to the fact that much less cyndrical tube area is required to reproduce much shorter waves.
Although pleasing to the ear, the speakers might appear cacophonous to your pocketbook. One of the most prominent design, the LFX Standard, will set you back $600 a pair. If you can get a$13,500 trade-in on your existing set of scratchy speakers, you could acquire a set of the 7-foot Design 9Bs.
Steve Nelson, vice president of sales, contends that the speakers are really reasonably valued. "You would have to pay $2,900 for a pair of Martin Logans if you wanted the very same audio high quality," states Nelson of Linaeum's LS-1000 design, priced at$900. "At this degree, however, people are usually concerned with noise as opposed to cost.".
Although Stutz would not specify concerning sales numbers, he did say the business experienced a seven-fold increase contrasted to in 2014. Linaeum hopes this trend proceeds as more people tune into their audio speakers.
To power these sales, Linaeum Head of state Haessler intends to proceed expanding his network of dealers. After starting with two suppliers in Oregon 3 years back, Linaeum currently boasts over 80 dealers worldwide.
Perhaps much more eruptive in terms of growth for Linaeum than audio dealerships are prospective licensing arrangements.
Licensing offers are pending with General Motors Inc., Boston Acoustics and electronic devices large Phillips Inc., says Haessler.
" I checked out some executives from GM recently and also they informed us we've obtained additionally than a lot of in the discussing procedure," claims Stutz. Of specific rate of interest to GM, he states, is the electric coil in Linaeum's vehicle driver. All coils in GM (ideal vehicle speaker for sound top quality Carspeakersland) https://carspeakerland.com/the-best-car-speakers-reviews-on-the-market are merely slim copper cable twisted around a cardboard hoop. Linaeum's patented coil, nevertheless, is a versatile plastic strip containing engraved circuitry.
Linaeum manufactures its motorists in 9,000 square feet of warehouse space near Northwest 13th and also Glisan and also has 12 workers.
The name Linaeum, Latin for "line," was picked, states Haessler, because the audio speakers deliver audio in "line source," indicating audio emits from the driver like light from a nude bulb. Additionally Haessler assumed the name would work well worldwide.
Although sales have been quick as well as product passion has actually been high, the speaker producer has yet to turn a web profit. Haessler, that says his firm has always handled to cover its operating costs, expects to damage the profit obstacle in the coming year. License costs as well as research and development costs represent most of the costs, says Haessler.
With innovation as its discerning function, Linaeum will certainly continue upgrading its drivers. One slated enhancement requires the enhancement of a compound called Ferro-fluid, a magnetic liquid created to improve the coil's capability to send information to the adaptable diaphram. | 2019-07-17T21:38:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20852962136268616, "perplexity": 9808.60367121682}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525402.30/warc/CC-MAIN-20190717201828-20190717223828-00196.warc.gz"} |
https://www.ftc.gov/policy/public-comments/comment-543809-00048 | # 16 CFR Part 425: "Rule Concerning the Use of Prenotification Negative Option Plans" #543809-00048
Submission Number:
543809-00048
Commenter:
Gibbons
State:
CO
Initiative Name:
16 CFR Part 425: "Rule Concerning the Use of Prenotification Negative Option Plans"
This type of advertising should be outlawed as it is absolutely taking advantage of the public. I was stupid enough to believe it once but never again as the "Handling & Shipping" charges were exorbitant and the product could not produce the results advertised. All these so-called businesses are scams & frauds. | 2022-01-17T18:55:27 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8574336767196655, "perplexity": 8616.902541394036}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300616.11/warc/CC-MAIN-20220117182124-20220117212124-00309.warc.gz"} |
https://kelvins.esa.int/proba-v-super-resolution/data/ | #### Timeline
The competition is over.
## Origin of the data
We collected satellite data from the PROBA-V mission of the European Space Agency from 74 hand-selected regions around the globe at different points in time. The data is composed of radiometrically and geometrically corrected Top-Of-Atmosphere (TOA) reflectances for the RED and NIR spectral bands at 300m and 100m resolution in Plate Carrée projection. The 300m resolution data is delivered as 128x128 grey-scale pixel images, the 100m resolution data as 384x384 grey-scale pixel images. The bit-depth of the images is 14, but they are saved in a 16-bit .png-format (which makes them look relatively dark if opened in typical image viewers).
Each image comes with a quality map, indicating which pixels in the image are concealed (i.e. clouds, cloud shadows, ice, water, missing, etc) and which should be considered clear. For an image to be included in the dataset, at least 75% of its pixels have to be clear for 100m resolution images, and 60% for 300m resolution images. Each data-point consists of exactly one 100m resolution image and several 300m resolution images from the same scene. In total, the dataset contains 1450 scenes, which are split into 1160 scenes for training and 290 scenes for testing. On average, each scene comes with 19 different low resolution images and always with at least 9. We expect you to submit a 384x384 image for each of the 290 test-scenes, for which we will not provide a high resolution image.
### Changes in landscape
The images have been recorded within a time window of 30 days. As such, the scenes are not always permanent but can change marginally.
### Image registration
The images are delivered as recorded by PROBA-V and have not been modified to align with each other. While the mean geolocation accuracy of PROBA-V is about 61m, (sub)-pixelshifts in the content occur and are - in a sense - necessary to perform super-resolution. Thus, the dataset itself is not corrected for these shifts and none of the images are registered to each other. The scoring will take pixel-shifts of the high resolution image into account, as registration cannot be computed by the participant for the test-set.
The data for this competition can be downloaded as a compressed zip file (675MB).
## Contents
The zip file is organized as follows:
• train/NIR images from the NIR channel of PROBA-V for training
• train/RED images from the RED channel of PROBA-V for training
• test/NIR images from the NIR channel of PROBA-V to produce the submission
• test/RED images from the RED channel of PROBA-V to produce the submission
• norm.csv $$cPSNR$$ of a baseline solution which is used to normalize the submissions (see scoring)
Each scene is saved in a separate folder, named imgsetxxxx, where xxxx is a running number from 0000 to 1449. Each scene in the training folders contains the following file:
• HR.png: high resolution image (ground truth for super-resolution)
• SM.png: status map of HR.png, indicating clear pixels by a value of 1
• LRXXX.png: low resolution image
• QMXXX.png: status map of LRXXX.png, indicating clear pixels by a value of 1
The scenes in the test folders are structured the same, but do not include HR.png as your task is to reconstruct it! They include however SM.png, so you know which pixels do count. | 2019-10-20T11:01:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32312172651290894, "perplexity": 2761.4839503770404}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986707990.49/warc/CC-MAIN-20191020105426-20191020132926-00539.warc.gz"} |
https://dlmf.nist.gov/13.6 | §13.6 Relations to Other Functions
§13.6(i) Elementary Functions
13.6.1 $\displaystyle M\left(a,a,z\right)$ $\displaystyle=e^{z},$ ⓘ Symbols: $M\left(\NVar{a},\NVar{b},\NVar{z}\right)$: $={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$ Kummer confluent hypergeometric function, $\mathrm{e}$: base of natural logarithm and $z$: complex variable A&S Ref: 13.6.12 Referenced by: §13.10(v) Permalink: http://dlmf.nist.gov/13.6.E1 Encodings: TeX, pMML, png See also: Annotations for 13.6(i), 13.6 and 13 13.6.2 $\displaystyle M\left(1,2,2z\right)$ $\displaystyle=\frac{e^{z}}{z}\sinh z,$ 13.6.3 $\displaystyle M\left(0,b,z\right)$ $\displaystyle=U\left(0,b,z\right)=1,$ 13.6.4 $\displaystyle U\left(a,a+1,z\right)$ $\displaystyle=z^{-a}.$ ⓘ Symbols: $U\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Kummer confluent hypergeometric function and $z$: complex variable Permalink: http://dlmf.nist.gov/13.6.E4 Encodings: TeX, pMML, png See also: Annotations for 13.6(i), 13.6 and 13
§13.6(ii) Incomplete Gamma Functions
For the notation see §§6.2(i), 7.2(i), 8.2(i), and 8.19(i). When $a-b$ is an integer or $a$ is a positive integer the Kummer functions can be expressed as incomplete gamma functions (or generalized exponential integrals). For example,
13.6.5 $M\left(a,a+1,-z\right)=e^{-z}M\left(1,a+1,z\right)=az^{-a}\gamma\left(a,z% \right),$
13.6.6 $U\left(a,a,z\right)=z^{1-a}U\left(1,2-a,z\right)=z^{1-a}e^{z}E_{a}\left(z% \right)=e^{z}\Gamma\left(1-a,z\right).$
Special cases are the error functions
13.6.7 $M\left(\tfrac{1}{2},\tfrac{3}{2},-z^{2}\right)=\frac{\sqrt{\pi}}{2z}% \operatorname{erf}\left(z\right),$
13.6.8 $U\left(\tfrac{1}{2},\tfrac{1}{2},z^{2}\right)=\sqrt{\pi}e^{z^{2}}\operatorname% {erfc}\left(z\right).$
§13.6(iii) Modified Bessel Functions
When $b=2a$ the Kummer functions can be expressed as modified Bessel functions. For the notation see §§10.25(ii) and 9.2(i).
13.6.9 $\displaystyle M\left(\nu+\tfrac{1}{2},2\nu+1,2z\right)$ $\displaystyle=\Gamma\left(1+\nu\right)e^{z}\left(\ifrac{z}{2}\right)^{-\nu}I_{% \nu}\left(z\right),$ 13.6.10 $\displaystyle U\left(\nu+\tfrac{1}{2},2\nu+1,2z\right)$ $\displaystyle=\frac{1}{\sqrt{\pi}}e^{z}\left(2z\right)^{-\nu}K_{\nu}\left(z% \right),$ 13.6.11 $\displaystyle U\left(\tfrac{5}{6},\tfrac{5}{3},\tfrac{4}{3}z^{3/2}\right)$ $\displaystyle=\sqrt{\pi}\frac{3^{5/6}\exp\left(\tfrac{2}{3}z^{3/2}\right)}{2^{% 2/3}z}\mathrm{Ai}\left(z\right).$
§13.6(iv) Parabolic Cylinder Functions
For the notation see §12.2.
13.6.12 $U\left(\tfrac{1}{2}a+\tfrac{1}{4},\tfrac{1}{2},\tfrac{1}{2}z^{2}\right)=2^{% \frac{1}{2}a+\frac{1}{4}}e^{\frac{1}{4}z^{2}}U\left(a,z\right),$
13.6.13 $U\left(\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},\tfrac{1}{2}z^{2}\right)=2^{% \frac{1}{2}a+\frac{3}{4}}\frac{e^{\frac{1}{4}z^{2}}}{z}U\left(a,z\right).$
13.6.14 $M\left(\tfrac{1}{2}a+\tfrac{1}{4},\tfrac{1}{2},\tfrac{1}{2}z^{2}\right)=\frac{% 2^{\frac{1}{2}a-\frac{3}{4}}\Gamma\left(\tfrac{1}{2}a+\tfrac{3}{4}\right)e^{% \frac{1}{4}z^{2}}}{\sqrt{\pi}}\*\left(U\left(a,z\right)+U\left(a,-z\right)% \right),$
13.6.15 $M\left(\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},\tfrac{1}{2}z^{2}\right)=\frac{% 2^{\frac{1}{2}a-\frac{5}{4}}\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{4}\right)e^{% \frac{1}{4}z^{2}}}{z\sqrt{\pi}}\*\left(U\left(a,-z\right)-U\left(a,z\right)% \right).$
§13.6(v) Orthogonal Polynomials
Special cases of §13.6(iv) are as follows. For the notation see §§18.3, 18.19.
Hermite Polynomials
13.6.16 $\displaystyle M\left(-n,\tfrac{1}{2},z^{2}\right)$ $\displaystyle=(-1)^{n}\frac{n!}{(2n)!}H_{2n}\left(z\right),$ 13.6.17 $\displaystyle M\left(-n,\tfrac{3}{2},z^{2}\right)$ $\displaystyle=(-1)^{n}\frac{n!}{(2n+1)!2z}H_{2n+1}\left(z\right),$ 13.6.18 $\displaystyle U\left(\tfrac{1}{2}-\tfrac{1}{2}n,\tfrac{3}{2},z^{2}\right)$ $\displaystyle=2^{-n}z^{-1}H_{n}\left(z\right).$ ⓘ Symbols: $H_{\NVar{n}}\left(\NVar{x}\right)$: Hermite polynomial, $U\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Kummer confluent hypergeometric function, $n$: nonnegative integer and $z$: complex variable A&S Ref: 13.6.38 (as corrected in later editions) Referenced by: §13.6(v) Permalink: http://dlmf.nist.gov/13.6.E18 Encodings: TeX, pMML, png See also: Annotations for 13.6(v), 13.6(v), 13.6 and 13
Laguerre Polynomials
13.6.19 $U\left(-n,\alpha+1,z\right)=(-1)^{n}{\left(\alpha+1\right)_{n}}M\left(-n,% \alpha+1,z\right)=(-1)^{n}n!L^{(\alpha)}_{n}\left(z\right).$
Charlier Polynomials
13.6.20 $U\left(-n,z-n+1,a\right)={\left(-z\right)_{n}}M\left(-n,z-n+1,a\right)=a^{n}C_% {n}\left(z;a\right).$
§13.6(vi) Generalized Hypergeometric Functions
13.6.21 $U\left(a,b,z\right)=z^{-a}{{}_{2}F_{0}}\left(a,a-b+1;-;-z^{-1}\right).$
For the definition of ${{}_{2}F_{0}}\left(a,a-b+1;-;-z^{-1}\right)$ when neither $a$ nor $a-b+1$ is a nonpositive integer see §16.5.
§13.6(vii) Coulomb Functions
For representations of Coulomb functions in terms of Kummer functions see (33.2.4), (33.2.8) and (33.14.5). | 2018-04-27T04:37:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 161, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9894238710403442, "perplexity": 9665.529503211814}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125949036.99/warc/CC-MAIN-20180427041028-20180427061028-00608.warc.gz"} |
https://www.usgs.gov/centers/chesapeake-bay-activities/usgs-chesapeake-bay-watershed-accomplishments-fiscal-year-2018-0 | # USGS Chesapeake Bay Watershed Accomplishments for Fiscal Year 2018
The USGS has the critical role of providing scientific information to improve the understanding and management of the Nation’s largest estuary -- the Chesapeake Bay ecosystem. The USGS works with Federal, State, and academic science partners to provide monitoring, research, and communication of results to enhance ecosystem management for both the Chesapeake and other critical ecosystems.
The U.S. Department of the Interior (DOI), through the USGS, the U.S. Fish and Wildlife Service (USFWS), and the National Park Service (NPS), is providing leadership, expertise, and resources to carry out the Chesapeake Watershed Agreement (2014--2025), which was signed by the Chesapeake Bay Program (CBP), and includes the Federal Government, six states and the District of Columbia. The DOI has a leadership role for carrying out 7 of the 10 goals described in the Agreement. Major USGS Chesapeake Bay accomplishments for 2018 are described below. The efforts are supported by multiple USGS Mission Areas (MAs) and partners.
#### New Directions for USGS Chesapeake Science Activities
The USGS has revised its Chesapeake science themes for 2019 and beyond. The revised science themes align strongly with new DOI and USGS priorities, the directions of USGS Mission Areas and Programs, and address important goals of the Chesapeake Watershed Agreement. Overall, the revised science themes focus USGS science to inform the management of recreational fish, waterbird species, and their habitats, as well as the lands important for the 18 million people across the watershed. The science themes are:
• Theme 1: Provide an integrated understanding of the factors affecting fish habitat, fish health, and landscape conditions.
• Theme 2: Assess the risks to coastal habitats, DOI lands, and migratory waterbirds.
• Theme 3: Characterize land use and change to assess the vulnerability and resiliency of vital lands and healthy watersheds.
• Theme 4: Integrate science and inform stakeholders.
#### Highlights include:
1. Fish habitat and fish health: habitat and introduced species affecting brook trout; effects of unconventional Oil and Gas on forests and brook trout; improved understand of stream health; and factors affecting health of fisheries
2. Water quality and landscape conditions affecting fish habitat: explaining trends to inform nutrient and sediment reductions; new tools to understand water-quality change; sediment sources and transport; watershed impacts on estuary conditions; effects of 2018 flow-flow events and a new research strategy for toxic contaminants
3. Coastal habitats and water birds: increasing habitat for water birds
4. Land change and forecasting: improving land classification; incorporating projected growth into water- quality targets
#### 1. Fish Habitat and Fish Health
##### Restoring native recreational species by understanding competition with introduced species
Native fish conservation is a high priority for natural resource managers in the Chesapeake Bay watershed, and new research by USGS is assisting conservation planning for trust species. The USGS has been working with National Park Service (NPS) and the Maryland Department of Natural Resources to enhance a declining Brook Trout population in Maryland (Big Hunting Creek) by removing introduced Brown Trout. This on-the-ground management work stemmed from USGS, which demonstrated strong effects of Brown Trout competition for food resources with increasing stream temperatures. On-going USGS research in Shenandoah National Park is also contributing to a national research initiative on stream flow and drought to improve conservation planning.
Supported by the USGS Ecosystems and Water MAs
##### The effects of unconventional oil and gas development on brook trout and forests
The USGS, in collaboration with researchers from West Virginia University completed a study of unconventional oil and gas (UOG) impacts on eastern brook trout occupancy in the upper Susquehanna River watershed. Modeling results predicted a 4% loss of brook trout in streams impacted by existing UOG and occurred most often in streams with intermediate levels of non-UOG stress (i.e., agriculture, residential and commercial development, and historic mining). Additionally, USGS researchers found that a large volume of forest canopy was removed by UOG activities in the study area, particularly caused by pipeline right of ways, and the impacts were more dispersed than other types of land conversion such as timber harvesting.
Supported by the USGS Ecosystems MA.
##### Developing new approaches to assess fish habitat and stream conditions.
Understanding the multiple factors that affect fish habitat is critical to restore commercial and recreational species in the Bay and its watershed. The USGS, in collaboration with NOAA, led efforts for a STAC workshop, which brought together fishery managers and scientists, to develop new approaches to assess fish habitat. Based on data inventory, the participants identified key factors for a fish habitat assessment could further inform restoration activities for inter-related CBP goals for fisheries, habitat, and water quality. Additionally, the USGS, in collaboration with Interstate Commission on the Potomac River Basin, completed a study that predicted stream biological condition using the Chesapeake Basin-wide Index of Biotic Integrity (Chessie BIBI) for all small streams throughout the watershed. Results will help improve the tracking progress toward improving stream conditions.
Supported by USGS Ecosystems MA
Recreational fishing has an important economic impact within the Chesapeake Bay watershed, and the annual economic impact of smallmouth bass fishing alone is estimated to exceed $150 million. The USGS, together with state agencies, completed important field work and analysis looking at the effects of endocrine-disrupting compounds and other factors degrading fish health in the watershed. Risk factors, including pathogens (bacteria, largemouth bass virus, myxozoans, cestode and trematode parasites) and tissue contaminants (legacy and current-use pesticides, PCB, and others), associated with smallmouth bass young of year mortality were identified. Agricultural land-use had a probability of being positively correlated with prevalence of specific parasites and coinfections. Models were developed for quantifying temporal trends in smallmouth bass abundance, as well as population-level effects of water temperature, flow and chemical-induced reproductive depression. Long-term spatial and temporal monitoring of water contaminant concentrations (pesticides, hormones, phytoestrogens) along with in-depth fish health assessments is continuing and will provide important exposure information during key developmental periods. The findings will be summarized in 2019 and used to inform integrated water-quality and habitat management approaches to improve the health of fisheries in the watershed. Supported by USGS Environmental Health and Ecosystems MAs #### 2. Water quality and landscape conditions affecting fish habitat ##### Explaining water-quality patterns and trends to inform nutrient and sediment management To inform the CBP Midpoint Assessment of the Bay TMDL, the USGS completed several water-quality syntheses to explain patterns in water quality and inform watershed management. The synthesis topics included: • Factors affecting yields and trends of nitrogen and phosphorus throughout the Chesapeake watershed. • Long-term changes in nutrient and sediment inputs to Chesapeake Bay. • Understanding sediment sources, transport, and delivery processes relevant to Chesapeake restoration efforts (see next accomplishment topic regarding sediment). • Influence of Susquehanna Reservoirs on loads and water quality in the Bay and management implications under the Total Maximum Daily Load (TMDL). New methods were developed to better explain the amount, and causes, of nutrient changes over the several decades in areas across the watershed. Two innovative methods, both extensions of the well-respected USGS SPAtially Referenced Regressions On Watershed attributes (SPARROW) model, were used to help explain change. Results from the Decadal SPARROW model and Spatiotemporal Watershed Accumulation of Net effects (SWAN) were used for the synthesis efforts and to improve the CBP watershed model. The results from the synthesis are being used by jurisdictions and EPA to develop new approaches to reduce nutrients and sediment, that will be in the Phase III Watershed Implementation Plans, that will be released in 2019. Some initial examples of how the results are being applied include: • Pennsylvania has decided to have a tiered approach for restoration, based on USGS finding showing areas with the greatest nutrient loads. • The finding for the Conowingo Reservoirs revealed increases in nutrients and sediment, which resulted in EPA and states deciding to have a dedicated restoration plan to address Conowingo reservoirs. • MD is using results to inform the targeting for their$50M Chesapeake Bay Restoration Fund.
Supported by the USGS Water and Ecosystems MAs.
##### Sediment sources, transport, and fate in priority watersheds
Sediment causes most stream impairments and degrades conditions for fisheries. New studies by the USGS have documented the importance of streambanks and floodplains to the sources and trapping of sediment in Chesapeake watersheds. In a suburban watershed (Difficult Run, VA), studies found:
• Over 90% of the suspended sediment load in the headwaters is due to erosion of streambanks
• Erosion in the headwaters can be nearly matched by floodplain deposition of sediment in the lower watershed; the value of floodplain trapping in this small watershed was estimated at \$727,000/yr.
In an agricultural watershed (Smith Creek, VA):
• Streambanks contribute more than 70% of the suspended sediment in the watershed.
• Floodplain deposition exceeded streambank erosion throughout the larger streams
Together with long-term USGS monitoring of suspended sediment loads, these studies highlight the importance of streambank erosion in headwaters as a dominant source of suspended sediment, much of which can be trapped by floodplains along larger streams. This information is critical to efficiently target management actions that can reduce downstream sediment loading.
Supported by the Water and Ecosystems MAs
##### USGS coordinates researchers on syntheses of estuarine conditions
Documenting estuary changes are critical for assessing progress in water-quality conditions and understanding the response to nutrient and sediment reduction efforts. Teams of researchers including Federal, State, and academic partners were formed under USGS leadership, with support from USEPA, to address these key topics:
• Developing and applying new techniques to evaluate trends in tidal waters.
• Estuarine water quality and dissolved oxygen responses to changes in nutrient inputs.
• Developing an integrated understanding of drivers of changes in water clarity in different settings.
• Factors controlling the distribution and abundance of submerged aquatic vegetation (SAV).
• Linking watershed and estuarine changes in the Potomac River.
The results are part of the information being used by the jurisdictions to prepare their Phase III Watershed Implementation Plans.
Supported by the USGS Water and Ecosystems MAs.
##### Summer 2018 high river flows, and effects, on the Chesapeake Bay
Every year a team of scientists from NOAA, University of MD, and USGS utilize the most recent streamflow and nutrient monitoring data from the Susquehanna and Potomac Rivers to predict the Bay’s hypoxic (low-oxygen) and anoxic (oxygen-free) zones. These conditions occur in during the summer, and are largely driven by nutrients delivered from the watershed in the winter and spring. However, beginning in May 2018, the river flows to the Bay were above average and set records for the months of August and September. USGS monitoring programs were able to document the high flows and worked with partners to begin to predict the effects including:
• Higher nutrient and sediment loads contributing to low dissolved oxygen
• Potential reduction of submerged aquatic vegetation
• Probable morality of oysters due to fresh water delivery to the Bay
• Shifts in habitats being occupied by crabs and other recreational fisheries
The forecasts, and subsequent monitoring, provide resource managers valuable information for fisheries management decisions and serve as a clear public reminder that conditions in the Bay are driven by pollution in the watershed.
Supported by the USGS Water and Ecosystems MAs.
##### USGS leads update on strategy for toxic contaminants research
The Chesapeake Bay Agreement has a goal to ensure that the Bay and its rivers are free of effects of toxic contaminants on living resources and human health. The two associated outcomes are (1) research and (2) policy and prevention. The strategy for the research outcome will improve information about the occurrence, concentrations, sources and effects of toxic contaminants on fish and wildlife. The findings will be used by the CBP Toxic Contaminant Workgroup (TCW) and Water-Quality Goal Implementation Team to consider policy and prevention approaches to reduce the effects of contaminants on living resources in the Bay watershed and make them safer for human consumption. The USGS led the effort the research strategy, which will focus on:
• Supply information to make fish and shellfish safer for human consumption;
• Understand the influence of contaminants degrading the health, and contributing to mortality, of fish and wildlife;
• Document the sources, occurrence, and transport contaminants in different landscape settings.
• Provide science to help mitigate contaminants, and emphasize the co-benefits with nutrients and sediment reductions.
• Gather information on issues of emerging concern
#### 3. Coastal habitats and water birds
##### Increasing habitat for migratory waterbirds
The Chesapeake provides critical habitat for migratory waterfowl in the Atlantic Flyway. The USGS completed models of how the availability of quality habitat for wintering black ducks in the refuges changes due to development and sea-level rise pressures. The USGS also continued data collection and began analysis of detailed light and water levels and vegetation surveys across key locations to better understand how marshes migrate in response to sea-level rise. Finally results of impacts of coastal land use and shoreline armoring along the Chesapeake Bay coast on the waterbird community integrity were published; our results show shoreline hardening and invasive Phragmites each have negative effects on the waterbird community. All of findings are being considered by USFWS and state agencies to consider approaches to protect and restore coastal wetlands.
Supported by the USGS Ecosystems and Land Resources MAs.
#### 4. Land change and forecasting to assess the vulnerability and resiliency
##### USGS improves land cover and use information needed to understand ecosystem conditions
Agencies and resource managers are working together to collect higher resolution land-cover information to focus restoration practices. The USGS supported the Chesapeake Conservancy to develop more current, higher-resolution information for the Bay watershed. Several areas were identified that needed light detection and ranging (LIDAR) to better define elevation changes that affect the movement of nutrients and sediment. The USGS partnered with Natural Resources Conservation Service (NRCS), through the National Map: 3-D Elevation Program (3DEP), to collect over 6,500 square miles of Quality Level 2 LIDAR data for 13 counties in the Susquehanna basin. The information will help inform NRCS to implement conservation practices and enhance the Chesapeake Conservancy effort to improve stream network information.
Supported by the USGS Core Science Systems and Land Resources MAs.
##### Future growth in the Chesapeake watershed will increase nutrient loads so partners needed forecasts of development to inform water-quality management plans.
The USGS, working with CBP partners, used the USGS’ Chesapeake Bay Land Change Model in several ways:
• Contributed forecasts for newly developed Chesapeake Conservation Atlas, which will help the NPS and the Chesapeake Conservation Partnership focus land conservation efforts.
• Simulated future land-use scenarios out to 2025 to evaluate potential nutrient and sediment pollution to the Chesapeake Bay resulting from land conservation and land use planning actions. Four States and the District of Columbia are using USGS’ model to develop custom future scenarios reflective of ongoing land-use policies and conservation programs. These scenarios will be incorporated into the jurisdictions Phase III WIPs to comply with Total Maximum Daily Load (TMDL) pollution limits.
• Using growth projections so partners could enable the formal crediting of land-use planning and land conservation practices towards avoiding future increases in pollution to meet the TMDL.
• Finally, the development scenarios are being utilized by the CBP Healthy Watershed Goal Implementation Team and other CBP groups to identify high quality natural resource areas that may be vulnerable to development.
The USGS also updated the protected lands data for the entire watershed to track progress toward the goal of conserving 2M acres.
Supported by the USGS Ecosystems MA and USEPA. | 2023-02-05T07:33:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1775899976491928, "perplexity": 13162.298422334874}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500250.51/warc/CC-MAIN-20230205063441-20230205093441-00468.warc.gz"} |
http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/trigamma.htm | Dataplot Vol 2 Vol 1
# TRIGAMMA
Name:
TRIGAMMA (LET)
Type:
Library Function
Purpose:
Compute the trigamma function.
Description:
The digamma function is the logarithmic derivative of the gamma function and is defined as:
$\psi(x) = \frac{\Gamma'(x)} {\Gamma(x)}$
where $$\Gamma$$ is the gamma function and $$\Gamma'$$ is the derivative of the gamma function.
The trigamma function is the derivative of the digamma function and is defined as
$\begin{array}{lcl} \psi_{1}(x) & = & \psi'(x) \\ & = & \frac{d^2}{dx^2} \ln (\Gamma(x)) \\ & = & \sum_{n=0}^{\infty}{\frac{1}{(x+n)^{2}}} \end{array}$
This function is defined for positive numbers.
Syntax:
LET <y> = TRIGAMMA(<x>) <SUBSET/EXCEPT/FOR qualification>
where <x> is a number, variable or a parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed trigamma values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = TRIGAMMA(1)
LET X2 = TRIGAMMA(X1)
LET X2 = TRIGAMMA(X1-4)
Note:
Dataplot uses the routine DPSIFN from the SLATEC Common Mathematical Library to compute this function. SLATEC is a large set of high quality, portable, public domain Fortran routines for various mathematical capabilities maintained by seven federal laboratories.
Default:
None
Synonyms:
None
Related Commands:
GAMMA = Compute the gamma function. DIGAMMA = Compute the digamma function. LOGGAMMA = Compute the log (to base e) gamma function.
Reference:
D. E. Amos (1983), "A portable Fortran subroutine for derivatives of the Psi function", Algorithm 610, ACM Transactions on Mathematical Software 9, 4, pp. 494-502.
Abramowitz and Stegun, "Handbook of Mathematical Functions, Applied Mathematics Series, Vol. 55", National Bureau of Standards, 1964 (chapter 6).
Applications:
Special Functions
Implementation Date:
2014/12
Program:
TITLE CASE ASIS
TITLE Trigamma Function
PLOT TRIGAMMA(X) FOR X = 0.01 0.01 10
NIST is an agency of the U.S. Commerce Department.
Date created: 01/31/2015
Last updated: 01/31/2015 | 2017-10-24T11:26:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8152863383293152, "perplexity": 4362.942912098659}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187828411.81/warc/CC-MAIN-20171024105736-20171024125736-00389.warc.gz"} |
https://docs.nersc.gov/programming/performance-debugging-tools/performancereports/ | Arm Performance Reports¶
Introduction¶
Arm Performance Reports is a low-overhead tool that produces one-page text and HTML reports summarizing and characterizing both scalar and MPI application performance. The report intends to answer a range of vital questions:
• Is this application optimized for the system it is running on?
• Does it benefit from running at this scale?
• Are there I/O or networking bottlenecks affecting performance?
• Which hardware, software or configuration changes can be made to improve performance further?
The tool is based on MAP's low-overhead adaptive sampling technology that keeps data volumes collected and application overhead low.
Compiling Code to Run with Arm Performance Reports¶
To collect performance data, Arm Performance Reports uses the same sampling libraries that MAP uses: MAP sampler (map-sampler) and MPI wrapper (map-sampler-pmpi) libraries. The same build and link rules as with MAP apply here. For info, please read the User Guide or the MAP web page.
Just as with MAP, your program must be compiled with the -g option to keep debugging symbols, together with optimization flags that you would normally use. If you use the Cray compiler on the Cray machines, we recommend the -G2 option.
Below we show build instructions using a Fortran case, but the C or C++ usage is the same.
On Cray Machines¶
Building an executable for MAP is more complicated on Cray machines. First, you need to explicitly build the MAP sampler and MPI wrapper libraries using make-profiler-libraries, and link your executable against them.
To build a statically-linked executable, follow this procedure. It creates a plain text file allinea-profiler.ld which contains suggested options for linking the map libraries. You only need to use -Wl,@/your/directory/allinea-profiler.ld flag with this file in your link command in order to use the options contained in the file.
nersc$make-profiler-libraries --lib-type=static Creating Cray static libraries in /your/directory Created the libraries: libmap-sampler.a libmap-sampler-pmpi.a To instrument a program, add these compiler options: compilation for use with MAP - not required for Performance Reports: -g (or '-G2' for native Cray Fortran) (and -O3 etc.) linking (both MAP and Performance Reports): -Wl,@/your/directory/allinea-profiler.ld ... EXISTING_MPI_LIBRARIES If your link line specifies EXISTING_MPI_LIBRARIES (e.g. -lmpi), then these must appear *after* the Allinea sampler and MPI wrapper libraries in the link line. There's a comprehensive description of the link ordering requirements in the 'Preparing a Program for Profiling' section of either userguide-forge.pdf or userguide-reports.pdf, located in /global/common/sw/cray/cnl6/haswell/allinea-reports/19.1/doc/. nersc$ ftn -g -c jacobi_mpi.f90 # Use -G2 instead of -g for the Cray compiler
nersc$ftn -o jacobi_mpi jacobi_mpi.o -Wl,@/your/directory/allinea-profiler.ld You can provide an optional argument to make-profiler-libraries to build the libraries in a directory other than the current working directory. To build a dynamically-linked executable, you don't have to build the MAP libraries. You build your executable as you would normally do, but with the -g compile flag: nersc$ ftn -c -g jacobi_mpi.f90
nersc$ftn -dynamic -o jacobi_mpi jacobi_mpi.o -Wl,--eh-frame-hdr Starting a Job with Arm Performance Reports¶ In order to use this tool, you do not have to run your application in an interactive batch job session. Just make sure that the module is still loaded in the batch session (that is, in your batch job script if you use the tool in a non-interactie batch job): module load allinea-reports Add a command that launches the tool: perf-report srun <usual srun flags> ./jacobi_mpi where ./jacobi_mpi is the name of a program to profile. Note The above perf-report srun ... command with version 19.1 dumps a core file, and the vendor will release a fixed version. Note that the tool still generates performance summary results. Profiling Results¶ After completing the run, Arm Performance Reports prepares performance summary results in two files, one plain-text file and a HTML file: executablename_#p_#n_yyyy-mm-dd_HH-MM.txt and executablename_#p_#n_yyyy-mm-dd_HH-MM.html where # before the letter p is for the process count, # before the letter n is for the node count, and yyyy-mm-dd_HH-MM is the time stamp. For example: $ ls -lrt jacobi_mpi*
...
-rw-r--r-- 1 xxxxx xxxxx 476702 Jun 28 08:40 jacobi_mpi_8p_2n_2019-06-28_08-39.html
-rw-r--r-- 1 xxxxx xxxxx 3092 Jun 28 08:40 jacobi_mpi_8p_2n_2019-06-28_08-39.txt
The performance results in both files are basically the same. If you want to use a web browser for a better display, download the HTML file to your local workstation and view it with your favorite browser.
The top portion of the report shows the command that was run and info about the compute nodes, followed by a performance characterization of the application run - whether it is a compute, MPI-communication or I/O bound:
The triangular radar chart in the top-right corner of the report reflects the values of the three key measurement.
Then, the report shows more detailed info in each category, by breaking down relevant performance metrics into subcategories. For example, The 'CPU' component shows how much time was spent on scalar numeric operations, vector onumeric operations and memory access. Simlar breakdowns are done for MPI, I/O, threading, etc.
Summarizing an existing MAP file¶
If you have performance data collected with MAP before, you can get a performance summary report from the MAP file, too. To get a report, simply run the perf-report command on the MAP file:
nersc$ls -l ... -rw-r--r-- 1 xxxxx xxxxx 475005 Jun 21 17:16 jacobi_mpi_8p_2n_2019-06-21_17-16.map ... nersc$ perf-report jacobi_mpi_8p_2n_2019-06-28_08-49.map
nersc\$ ls -l
...
-rw-r--r-- 1 xxxxx xxxxx 476414 Jun 28 08:52 jacobi_mpi_8p_2n_2019-06-21_17-16.html
-rw-r--r-- 1 xxxxx xxxxx 3078 Jun 28 08:52 jacobi_mpi_8p_2n_2019-06-21_17-16.txt
... | 2019-07-16T02:08:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30121588706970215, "perplexity": 4673.44401280602}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524475.48/warc/CC-MAIN-20190716015213-20190716041213-00163.warc.gz"} |
https://lammps.sandia.gov/doc/fix_client_md.html | fix client/md command
Syntax
fix ID group-ID client/md
• ID, group-ID are documented in fix command
• client/md = style name of this fix command
Examples
fix 1 all client/md
Description
This fix style enables LAMMPS to run as a “client” code and communicate each timestep with a separate “server” code to perform an MD simulation together.
The Howto client/server doc page gives an overview of client/server coupling of LAMMPS with another code where one code is the “client” and sends request messages to a “server” code. The server responds to each request with a reply message. This enables the two codes to work in tandem to perform a simulation.
When using this fix, LAMMPS (as the client code) passes the current coordinates of all particles to the server code each timestep, which computes their interaction, and returns the energy, forces, and virial for the interacting particles to LAMMPS, so it can complete the timestep.
Note that the server code can be a quantum code, or another classical MD code which encodes a force field (pair_style in LAMMPS lingo) which LAMMPS does not have. In the quantum case, this fix is a mechanism for running ab initio MD with quantum forces.
The group associated with this fix is ignored.
The protocol and units for message format and content that LAMMPS exchanges with the server code is defined on the server md doc page.
Note that when using LAMMPS as an MD client, your LAMMPS input script should not normally contain force field commands, like a pair_style, bond_style, or kspace_style command. However it is possible for a server code to only compute a portion of the full force-field, while LAMMPS computes the remaining part. Your LAMMPS script can also specify boundary conditions or force constraints in the usual way, which will be added to the per-atom forces returned by the server code.
See the examples/message directory for example scripts where LAMMPS is both the “client” and/or “server” code for this kind of client/server MD simulation. The examples/message/README file explains how to launch LAMMPS and another code in tandem to perform a coupled simulation.
Restart, fix_modify, output, run start/stop, minimize info
The fix_modify energy option is supported by this fix to add the potential energy computed by the server application to the system’s potential energy as part of thermodynamic output.
The fix_modify virial option is supported by this fix to add the server application’s contribution to the system’s virial as part of thermodynamic output. The default is virial yes
This fix computes a global scalar which can be accessed by various output commands. The scalar is the potential energy discussed above. The scalar value calculated by this fix is “extensive”.
No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.
Restrictions
This fix is part of the MESSAGE package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
A script that uses this command must also use the message command to setup and shut down the messaging protocol with the server code.
none | 2020-10-21T13:51:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5086677074432373, "perplexity": 3265.241338638118}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107876500.43/warc/CC-MAIN-20201021122208-20201021152208-00204.warc.gz"} |
https://dlmf.nist.gov/2.5#E35 | # §2.5 Mellin Transform Methods
## §2.5(i) Introduction
Let $f(t)$ be a locally integrable function on $(0,\infty)$, that is, $\int_{\rho}^{T}f(t)\mathrm{d}t$ exists for all $\rho$ and $T$ satisfying $0<\rho. The Mellin transform of $f(t)$ is defined by
2.5.1 $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)=\int_{0}^{\infty}t^{z-1}f% (t)\mathrm{d}t,$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\mathrm{d}\NVar{x}$: differential, $\int$: integral and $f(x)$: locally integrable function Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.5.E1 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(i), §2.5 and Ch.2
when this integral converges. The domain of analyticity of $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ is usually an infinite strip $a<\Re z parallel to the imaginary axis. The inversion formula is given by
2.5.2 $f(t)=\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}t^{-z}\mathscr{M}\mskip-3.0mu% f\mskip 3.0mu \left(z\right)\mathrm{d}z,$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential, $\mathrm{i}$: imaginary unit, $\int$: integral, $f(x)$: locally integrable function and $c$: point Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.5.E2 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(i), §2.5 and Ch.2
with $a.
One of the two convolution integrals associated with the Mellin transform is of the form
2.5.3 $I(x)=\int_{0}^{\infty}f(t)\,h(xt)\mathrm{d}t,$ $x>0$, ⓘ Symbols: $\mathrm{d}\NVar{x}$: differential, $\int$: integral, $f(x)$: locally integrable function, $I(x)$: convolution integral and $h(x)$: function Referenced by: §2.5(ii), §2.5(ii) Permalink: http://dlmf.nist.gov/2.5.E3 Encodings: TeX, pMML, png See also: Annotations for §2.5(i), §2.5 and Ch.2
and
2.5.4 $\mathscr{M}\mskip-3.0mu I\mskip 3.0mu \left(z\right)=\mathscr{M}\mskip-3.0mu f% \mskip 3.0mu \left(1-z\right)\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z% \right).$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $f(x)$: locally integrable function, $I(x)$: convolution integral and $h(x)$: function Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.5.E4 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(i), §2.5 and Ch.2
If $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)$ and $\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)$ have a common strip of analyticity $a<\Re z, then
2.5.5 $I(x)=\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}x^{-z}\mathscr{M}\mskip-3.0mu% f\mskip 3.0mu \left(1-z\right)\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z% \right)\mathrm{d}z,$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential, $\mathrm{i}$: imaginary unit, $\int$: integral, $f(x)$: locally integrable function, $c$: point, $I(x)$: convolution integral and $h(x)$: function Keywords: Mellin transform Referenced by: §2.5(i), §2.5(ii), §2.5(iii) Permalink: http://dlmf.nist.gov/2.5.E5 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(i), §2.5 and Ch.2
where $a. When $x=1$, this identity is a Parseval-type formula; compare §1.14(iv).
If $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)$ and $\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)$ can be continued analytically to meromorphic functions in a left half-plane, and if the contour $\Re z=c$ can be translated to $\Re z=d$ with $d, then
2.5.6 $I(x)=\sum\limits_{d<\Re z ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\Re$: real part, $\Residue$: residue, $f(x)$: locally integrable function, $c$: point, $I(x)$: convolution integral, $h(x)$: function, $d$: point and $E(x)$: function Keywords: Mellin transform Referenced by: §2.5(i), §2.5(i) Permalink: http://dlmf.nist.gov/2.5.E6 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(i), §2.5 and Ch.2
where
2.5.7 $E(x)=\frac{1}{2\pi i}\int_{d-i\infty}^{d+i\infty}x^{-z}\mathscr{M}\mskip-3.0mu% f\mskip 3.0mu \left(1-z\right)\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z% \right)\mathrm{d}z.$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential, $\mathrm{i}$: imaginary unit, $\int$: integral, $f(x)$: locally integrable function, $h(x)$: function, $d$: point and $E(x)$: function Keywords: Mellin transform Referenced by: §2.5(i) Permalink: http://dlmf.nist.gov/2.5.E7 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(i), §2.5 and Ch.2
The sum in (2.5.6) is taken over all poles of $x^{-z}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)\mathscr{M}\mskip-% 3.0mu h\mskip 3.0mu \left(z\right)$ in the strip $d<\Re z, and it provides the asymptotic expansion of $I(x)$ for small values of $x$. Similarly, if $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)$ and $\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)$ can be continued analytically to meromorphic functions in a right half-plane, and if the vertical line of integration can be translated to the right, then we obtain an asymptotic expansion for $I(x)$ for large values of $x$.
### Example
2.5.8 $I(x)=\int_{0}^{\infty}\frac{{J_{\nu}}^{2}\left(xt\right)}{1+t}\mathrm{d}t,$ $\nu>-\tfrac{1}{2}$,
where $J_{\nu}$ denotes the Bessel function (§10.2(ii)), and $x$ is a large positive parameter. Let $h(t)={J_{\nu}}^{2}\left(t\right)$ and $f(t)=1/(1+t)$. Then from Table 1.14.5 and Watson (1944, p. 403)
2.5.9 $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)=\frac{\pi}{\sin\left(% \pi z\right)},$ $0<\Re z<1$, ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\pi$: the ratio of the circumference of a circle to its diameter, $\Re$: real part, $\sin\NVar{z}$: sine function and $f(t)=1/(1+t)$: function Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.5.E9 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(i), §2.5(i), §2.5 and Ch.2
2.5.10 $\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)=\frac{2^{z-1}\Gamma\left(% \nu+\frac{1}{2}z\right)}{{\Gamma}^{2}\left(1-\frac{1}{2}z\right)\Gamma\left(1+% \nu-\frac{1}{2}z\right)\Gamma\left(z\right)}\frac{\pi}{\sin\left(\pi z\right)},$ $-2\nu<\Re z<1$. ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\pi$: the ratio of the circumference of a circle to its diameter, $\Re$: real part, $\sin\NVar{z}$: sine function, $h(t)={J_{\nu}}^{2}\left(t\right)$: function and $f(t)=1/(1+t)$: function Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.5.E10 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(i), §2.5(i), §2.5 and Ch.2
In the half-plane $\Re z>\max(0,-2\nu)$, the product $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)\mathscr{M}\mskip-3.0mu % h\mskip 3.0mu \left(z\right)$ has a pole of order two at each positive integer, and
2.5.11 $\Residue_{z=n}\left[x^{-z}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z% \right)\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)\right]=(a_{n}\ln x% +b_{n})x^{-n},$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\ln\NVar{z}$: principal branch of logarithm function, $\Residue$: residue, $h(t)={J_{\nu}}^{2}\left(t\right)$: function, $a_{n}$: coefficients, $b_{n}$: coefficients and $f(t)=1/(1+t)$: function Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.5.E11 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(i), §2.5(i), §2.5 and Ch.2
where
2.5.12 $\displaystyle a_{n}$ $\displaystyle=\frac{2^{n-1}\Gamma\left(\nu+\tfrac{1}{2}n\right)}{{\Gamma}^{2}% \left(1-\tfrac{1}{2}n\right)\Gamma\left(1+\nu-\tfrac{1}{2}n\right)\Gamma\left(% n\right)},$ ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function and $a_{n}$: coefficients Referenced by: §2.5(i) Permalink: http://dlmf.nist.gov/2.5.E12 Encodings: TeX, pMML, png See also: Annotations for §2.5(i), §2.5(i), §2.5 and Ch.2 2.5.13 $\displaystyle b_{n}$ $\displaystyle=-a_{n}\left(\ln 2+\tfrac{1}{2}\psi\left(\nu+\tfrac{1}{2}n\right)% +\psi\left(1-\tfrac{1}{2}n\right)+\tfrac{1}{2}\psi\left(1+\nu-\tfrac{1}{2}n% \right)-\psi\left(n\right)\right),$ ⓘ Symbols: $\psi\left(\NVar{z}\right)$: psi (or digamma) function, $\ln\NVar{z}$: principal branch of logarithm function, $a_{n}$: coefficients and $b_{n}$: coefficients Referenced by: §2.5(i) Permalink: http://dlmf.nist.gov/2.5.E13 Encodings: TeX, pMML, png See also: Annotations for §2.5(i), §2.5(i), §2.5 and Ch.2
and $\psi$ is the logarithmic derivative of the gamma function (§5.2(i)).
We now apply (2.5.5) with $\max(0,-2\nu), and then translate the integration contour to the right. This is allowable in view of the asymptotic formula
2.5.14 $|\Gamma\left(x+iy\right)|=\sqrt{2\pi}e^{-\pi|y|/2}|y|^{x-(1/2)}\left(1+o\left(% 1\right)\right),$
as $y\to\pm\infty$, uniformly for bounded $|x|$; see (5.11.9). Then as in (2.5.6) and (2.5.7), with $d=2n+1-\epsilon$ $(0<\epsilon<1)$, we obtain
2.5.15 $I(x)=-\sum_{s=0}^{2n}(a_{s}\ln x+b_{s})x^{-s}+O\left(x^{-2n-1+\epsilon}\right),$ $n=0,1,2,\dots$.
From (2.5.12) and (2.5.13), it is seen that $a_{s}=b_{s}=0$ when $s$ is even. Hence
2.5.16 $I(x)=\sum_{s=0}^{n-1}(c_{s}\ln x+d_{s})x^{-2s-1}+O\left(x^{-2n-1+\epsilon}% \right),$
where $c_{s}=-a_{2s+1}$, $d_{s}=-b_{2s+1}$.
## §2.5(ii) Extensions
Let $f(t)$ and $h(t)$ be locally integrable on $(0,\infty)$ and
2.5.17 $f(t)\sim\sum_{s=0}^{\infty}a_{s}t^{\alpha_{s}},$ $t\to 0+$, ⓘ Symbols: $\sim$: Poincaré asymptotic expansion, $f(x)$: locally integrable function and $a_{s}$: coefficients Referenced by: §2.5(ii) Permalink: http://dlmf.nist.gov/2.5.E17 Encodings: TeX, pMML, png See also: Annotations for §2.5(ii), §2.5 and Ch.2
where $\Re\alpha_{s}>\Re\alpha_{s^{\prime}}$ for $s>s^{\prime}$, and $\Re\alpha_{s}\to+\infty$ as $s\to\infty$. Also, let
2.5.18 $h(t)\sim\exp\left(i\kappa t^{p}\right)\sum_{s=0}^{\infty}b_{s}t^{-\beta_{s}},$ $t\to+\infty$,
where $\kappa$ is real, $p>0$, $\Re\beta_{s}>\Re\beta_{s^{\prime}}$ for $s>s^{\prime}$, and $\Re\beta_{s}\to+\infty$ as $s\to\infty$. To ensure that the integral (2.5.3) converges we assume that
2.5.19 $f(t)=O\left(t^{-b}\right),$ $t\to+\infty$, ⓘ Symbols: $O\left(\NVar{x}\right)$: order not exceeding, $f(x)$: locally integrable function and $b$: right endpoint Referenced by: §2.5(ii) Permalink: http://dlmf.nist.gov/2.5.E19 Encodings: TeX, pMML, png See also: Annotations for §2.5(ii), §2.5 and Ch.2
with $b+\Re\beta_{0}>1$, and
2.5.20 $h(t)=O\left(t^{c}\right),$ $t\to 0+$, ⓘ Symbols: $O\left(\NVar{x}\right)$: order not exceeding, $h(x)$: locally integrable function and $c$: point Referenced by: §2.5(iii), §2.5(ii), §2.5(ii), §2.5(iii), §2.5(iii) Permalink: http://dlmf.nist.gov/2.5.E20 Encodings: TeX, pMML, png See also: Annotations for §2.5(ii), §2.5 and Ch.2
with $c+\Re\alpha_{0}>-1$. To apply the Mellin transform method outlined in §2.5(i), we require the transforms $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)$ and $\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)$ to have a common strip of analyticity. This, in turn, requires $-b<\Re\alpha_{0}$, $-c<\Re\beta_{0}$, and either $-c<\Re\alpha_{0}+1$ or $1-b<\Re\beta_{0}$. Following Handelsman and Lew (1970, 1971) we now give an extension of this method in which none of these conditions is required.
First, we introduce the truncated functions $f_{1}(t)$ and $f_{2}(t)$ defined by
2.5.21 $\displaystyle f_{1}(t)$ $\displaystyle=\begin{cases}f(t),&0 ⓘ Symbols: $f(x)$: locally integrable function and $f_{j}(t)$: truncated functions Permalink: http://dlmf.nist.gov/2.5.E21 Encodings: TeX, pMML, png See also: Annotations for §2.5(ii), §2.5 and Ch.2 2.5.22 $\displaystyle f_{2}(t)$ $\displaystyle=f(t)-f_{1}(t).$ ⓘ Symbols: $f(x)$: locally integrable function and $f_{j}(t)$: truncated functions Permalink: http://dlmf.nist.gov/2.5.E22 Encodings: TeX, pMML, png See also: Annotations for §2.5(ii), §2.5 and Ch.2
Similarly,
2.5.23 $\displaystyle h_{1}(t)$ $\displaystyle=\begin{cases}h(t),&0 ⓘ Symbols: $h(x)$: locally integrable function Referenced by: §2.5(iii) Permalink: http://dlmf.nist.gov/2.5.E23 Encodings: TeX, pMML, png See also: Annotations for §2.5(ii), §2.5 and Ch.2 2.5.24 $\displaystyle h_{2}(t)$ $\displaystyle=h(t)-h_{1}(t).$ ⓘ Symbols: $h(x)$: locally integrable function Referenced by: §2.5(iii) Permalink: http://dlmf.nist.gov/2.5.E24 Encodings: TeX, pMML, png See also: Annotations for §2.5(ii), §2.5 and Ch.2
With these definitions and the conditions (2.5.17)–(2.5.20) the Mellin transforms converge absolutely and define analytic functions in the half-planes shown in Table 2.5.1.
Furthermore, $\mathscr{M}\mskip-3.0mu f_{1}\mskip 3.0mu \left(z\right)$ can be continued analytically to a meromorphic function on the entire $z$-plane, whose singularities are simple poles at $-\alpha_{s}$, $s=0,1,2,\dots$, with principal part
2.5.25 $a_{s}/\left(z+\alpha_{s}\right).$ ⓘ Symbols: $a_{s}$: coefficients Permalink: http://dlmf.nist.gov/2.5.E25 Encodings: TeX, pMML, png See also: Annotations for §2.5(ii), §2.5 and Ch.2
By Table 2.5.1, $\mathscr{M}\mskip-3.0mu f_{2}\mskip 3.0mu \left(z\right)$ is an analytic function in the half-plane $\Re z. Hence we can extend the definition of the Mellin transform of $f$ by setting
2.5.26 $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)=\mathscr{M}\mskip-3.0mu f% _{1}\mskip 3.0mu \left(z\right)+\mathscr{M}\mskip-3.0mu f_{2}\mskip 3.0mu % \left(z\right)$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $f(x)$: locally integrable function and $f_{j}(t)$: truncated functions Keywords: Mellin transform Referenced by: §2.5(ii) Permalink: http://dlmf.nist.gov/2.5.E26 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(ii), §2.5 and Ch.2
for $\Re z. The extended transform $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ has the same properties as $\mathscr{M}\mskip-3.0mu f_{1}\mskip 3.0mu \left(z\right)$ in the half-plane $\Re z.
Similarly, if $\kappa=0$ in (2.5.18), then $\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)$ can be continued analytically to a meromorphic function on the entire $z$-plane with simple poles at $\beta_{s}$, $s=0,1,2,\dots$, with principal part
2.5.27 $-b_{s}/\left(z-\beta_{s}\right).$ ⓘ Symbols: $b$: right endpoint Permalink: http://dlmf.nist.gov/2.5.E27 Encodings: TeX, pMML, png See also: Annotations for §2.5(ii), §2.5 and Ch.2
Alternatively, if $\kappa\neq 0$ in (2.5.18), then $\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)$ can be continued analytically to an entire function.
Since $\mathscr{M}\mskip-3.0mu h_{1}\mskip 3.0mu \left(z\right)$ is analytic for $\Re z>-c$ by Table 2.5.1, the analytically-continued $\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)$ allows us to extend the Mellin transform of $h$ via
2.5.28 $\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)=\mathscr{M}\mskip-3.0mu h% _{1}\mskip 3.0mu \left(z\right)+\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu % \left(z\right)$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $f(x)$: locally integrable function and $h(x)$: locally integrable function Referenced by: §2.5(iii), §2.5(ii) Permalink: http://dlmf.nist.gov/2.5.E28 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(ii), §2.5 and Ch.2
in the same half-plane. From (2.5.26) and (2.5.28), it follows that both $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)$ and $\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)$ are defined in the half-plane $\Re z>\max(1-b,-c)$.
We are now ready to derive the asymptotic expansion of the integral $I(x)$ in (2.5.3) as $x\to\infty$. First we note that
2.5.29 $I(x)=\sum\limits_{j,k=1}^{2}I_{jk}(x),$ ⓘ Symbols: $I(x)$: convolution integral Referenced by: §2.5(ii) Permalink: http://dlmf.nist.gov/2.5.E29 Encodings: TeX, pMML, png See also: Annotations for §2.5(ii), §2.5 and Ch.2
where
2.5.30 $I_{jk}(x)=\int_{0}^{\infty}f_{j}(t)h_{k}(xt)\mathrm{d}t.$
By direct computation
2.5.31 $I_{21}(x)=0,$ for $x\geq 1$. ⓘ Symbols: $I(x)$: convolution integral Permalink: http://dlmf.nist.gov/2.5.E31 Encodings: TeX, pMML, png See also: Annotations for §2.5(ii), §2.5 and Ch.2
Next from Table 2.5.1 we observe that the integrals for the transform pair $\mathscr{M}\mskip-3.0mu f_{j}\mskip 3.0mu \left(1-z\right)$ and $\mathscr{M}\mskip-3.0mu h_{k}\mskip 3.0mu \left(z\right)$ are absolutely convergent in the domain $D_{jk}$ specified in Table 2.5.2, and these domains are nonempty as a consequence of (2.5.19) and (2.5.20).
For simplicity, write
2.5.32 $G_{jk}(z)=\mathscr{M}\mskip-3.0mu f_{j}\mskip 3.0mu \left(1-z\right)\mathscr{M% }\mskip-3.0mu h_{k}\mskip 3.0mu \left(z\right).$ ⓘ Symbols: $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $f(x)$: locally integrable function, $h(x)$: locally integrable function, $f_{j}(t)$: truncated functions and $G_{jk}(z)$: function Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.5.E32 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(ii), §2.5 and Ch.2
From Table 2.5.2, we see that each $G_{jk}(z)$ is analytic in the domain $D_{jk}$. Furthermore, each $G_{jk}(z)$ has an analytic or meromorphic extension to a half-plane containing $D_{jk}$. Now suppose that there is a real number $p_{jk}$ in $D_{jk}$ such that the Parseval formula (2.5.5) applies and
2.5.33 $I_{jk}(x)=\frac{1}{2\pi i}\int_{p_{jk}-i\infty}^{p_{jk}+i\infty}x^{-z}G_{jk}(z% )\mathrm{d}z.$
If, in addition, there exists a number $q_{jk}>p_{jk}$ such that
2.5.34 $\sup_{p_{jk}\leq x\leq q_{jk}}\left|G_{jk}(x+iy)\right|\to 0,$ $y\to\pm\infty$,
then
2.5.35 $I_{jk}(x)=\sum_{p_{jk}<\Re z
where
2.5.36 $E_{jk}(x)=\frac{1}{2\pi i}\int_{q_{jk}-i\infty}^{q_{jk}+i\infty}x^{-z}G_{jk}(z% )\mathrm{d}z=o\left(x^{-q_{jk}}\right)$
as $x\to+\infty$. (The last order estimate follows from the Riemann–Lebesgue lemma, §1.8(i).) The asymptotic expansion of $I(x)$ is then obtained from (2.5.29).
For further discussion of this method and examples, see Wong (1989, Chapter 3), Paris and Kaminski (2001, Chapter 5), and Bleistein and Handelsman (1975, Chapters 4 and 6). The first reference also contains explicit expressions for the error terms, as do Soni (1980) and Carlson and Gustafson (1985).
The Mellin transform method can also be extended to derive asymptotic expansions of multidimensional integrals having algebraic or logarithmic singularities, or both; see Wong (1989, Chapter 3), Paris and Kaminski (2001, Chapter 7), and McClure and Wong (1987). See also Brüning (1984) for a different approach.
## §2.5(iii) Laplace Transforms with Small Parameters
Let $h(t)$ satisfy (2.5.18) and (2.5.20) with $c>-1$, and consider the Laplace transform
2.5.37 $\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta\right)=\int_{0}^{\infty}h(t)% e^{-\zeta t}\mathrm{d}t.$ ⓘ Symbols: $\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Laplace transform, $\mathrm{d}\NVar{x}$: differential, $\mathrm{e}$: base of natural logarithm, $\int$: integral and $h(x)$: locally integrable function Keywords: Laplace transform Permalink: http://dlmf.nist.gov/2.5.E37 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Laplace transform was changed to $\mathscr{L}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{L}(f;z)$. See also: Annotations for §2.5(iii), §2.5 and Ch.2
Put $x=1/\zeta$ and break the integration range at $t=1$, as in (2.5.23) and (2.5.24). Then
2.5.38 $\zeta\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta\right)=I_{1}(x)+I_{2}(x),$ ⓘ Symbols: $\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Laplace transform, $h(x)$: locally integrable function and $I_{j}(x)$: integral Keywords: Laplace transform Referenced by: §2.5(iii) Permalink: http://dlmf.nist.gov/2.5.E38 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Laplace transform was changed to $\mathscr{L}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{L}(f;z)$. See also: Annotations for §2.5(iii), §2.5 and Ch.2
where
2.5.39 $I_{j}(x)=\int_{0}^{\infty}e^{-t}h_{j}(xt)\mathrm{d}t,$ $j=1,2$.
Since $\mathscr{M}\mskip-3.0mu e^{-t}\mskip 3.0mu \left(z\right)=\Gamma\left(z\right)$, by the Parseval formula (2.5.5), there are real numbers $p_{1}$ and $p_{2}$ such that $-c, $p_{2}<\min(1,\Re\beta_{0})$, and
2.5.40 $I_{j}(x)=\frac{1}{2\pi i}\int_{p_{j}-i\infty}^{p_{j}+i\infty}x^{-z}\Gamma\left% (1-z\right)\mathscr{M}\mskip-3.0mu h_{j}\mskip 3.0mu \left(z\right)\mathrm{d}z,$ $j=1,2$. ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential, $\mathrm{i}$: imaginary unit, $\int$: integral, $h(x)$: locally integrable function, $I_{j}(x)$: integral and $p_{j}$: real numbers Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.5.E40 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(iii), §2.5 and Ch.2
Since $\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)$ is analytic for $\Re z>-c$, by (2.5.14),
2.5.41 $I_{1}(x)=\mathscr{M}\mskip-3.0mu h_{1}\mskip 3.0mu \left(1\right)x^{-1}+\frac{% 1}{2\pi i}\int_{\rho-i\infty}^{\rho+i\infty}x^{-z}\Gamma\left(1-z\right)% \mathscr{M}\mskip-3.0mu h_{1}\mskip 3.0mu \left(z\right)\mathrm{d}z,$ ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential, $\mathrm{i}$: imaginary unit, $\int$: integral, $h(x)$: locally integrable function, $I_{j}(x)$: integral and $\rho$: parameter Keywords: Mellin transform Referenced by: §2.5(iii) Permalink: http://dlmf.nist.gov/2.5.E41 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(iii), §2.5 and Ch.2
for any $\rho$ satisfying $1<\rho<2$. Similarly, since $\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)$ can be continued analytically to a meromorphic function (when $\kappa=0$) or to an entire function (when $\kappa\neq 0$), we can choose $\rho$ so that $\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)$ has no poles in $1<\Re z\leq\rho<2$. Thus
2.5.42 $I_{2}(x)=\sum_{\Re\beta_{0}\leq\Re z\leq 1}\Residue\left[-x^{-z}\Gamma\left(1-% z\right)\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)\right]+\frac{% 1}{2\pi i}\int_{\rho-i\infty}^{\rho+i\infty}x^{-z}\Gamma\left(1-z\right)% \mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)\mathrm{d}z.$ ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential, $\mathrm{i}$: imaginary unit, $\int$: integral, $\Re$: real part, $\Residue$: residue, $h(x)$: locally integrable function, $I_{j}(x)$: integral and $\rho$: parameter Keywords: Mellin transform Referenced by: §2.5(iii) Permalink: http://dlmf.nist.gov/2.5.E42 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(iii), §2.5 and Ch.2
On substituting (2.5.41) and (2.5.42) into (2.5.38), we obtain
2.5.43 $\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta\right)=\mathscr{M}\mskip-3.0% mu h_{1}\mskip 3.0mu \left(1\right)+\sum_{\Re\beta_{0}\leq\Re z\leq 1}\Residue% \left[-\zeta^{z-1}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.% 0mu \left(z\right)\right]+\sum\limits_{1<\Re z ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Laplace transform, $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential, $\mathrm{i}$: imaginary unit, $\int$: integral, $\Re$: real part, $\Residue$: residue, $h(x)$: locally integrable function and $\delta$: arbitrary small positive constant Keywords: Laplace transform, Mellin transform Referenced by: §2.5(iii), §2.5(iii) Permalink: http://dlmf.nist.gov/2.5.E43 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Laplace transform was changed to $\mathscr{L}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{L}(f;z)$. In addition, the notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(iii), §2.5 and Ch.2
where $l$ ($\geq 2$) is an arbitrary integer and $\delta$ is an arbitrary small positive constant. The last term is clearly $O\left(\zeta^{l-\delta-1}\right)$ as $\zeta\to 0+$.
If $\kappa=0$ in (2.5.18) and $c>-1$ in (2.5.20), and if none of the exponents in (2.5.18) are positive integers, then the expansion (2.5.43) gives the following useful result:
2.5.44 $\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta\right)\sim\sum_{n=0}^{\infty% }b_{n}\Gamma\left(1-\beta_{n}\right)\zeta^{\beta_{n}-1}+\sum\limits_{n=0}^{% \infty}\frac{(-\zeta)^{n}}{n!}\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(n+1% \right),$ $\zeta\to 0+$. ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Laplace transform, $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\sim$: Poincaré asymptotic expansion, $!$: factorial (as in $n!$), $h(x)$: locally integrable function and $b$: right endpoint Keywords: Laplace transform, Mellin transform Permalink: http://dlmf.nist.gov/2.5.E44 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Laplace transform was changed to $\mathscr{L}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{L}(f;z)$. In addition, the notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(iii), §2.5 and Ch.2
### Example
2.5.45 $\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta\right)=\int_{0}^{\infty}% \frac{e^{-\zeta t}}{1+t}\mathrm{d}t,$ $\Re\zeta>0$. ⓘ Symbols: $\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Laplace transform, $\mathrm{d}\NVar{x}$: differential, $\mathrm{e}$: base of natural logarithm, $\int$: integral, $\Re$: real part and $h(x)$: locally integrable function Keywords: Laplace transform Permalink: http://dlmf.nist.gov/2.5.E45 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Laplace transform was changed to $\mathscr{L}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{L}(f;z)$. See also: Annotations for §2.5(iii), §2.5(iii), §2.5 and Ch.2
With $h(t)=1/(1+t)$, we have $\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)=\pi\csc\left(\pi z\right)$ for $0<\Re z<1$. In the notation of (2.5.18) and (2.5.20), $\kappa=0$, $\beta_{s}=s+1$, and $c=0$. Straightforward calculation gives
2.5.46 $\Residue_{z=k}\left[-\zeta^{z-1}\Gamma\left(1-z\right)\pi\csc\left(\pi z\right% )\right]=\left(-\ln\zeta+\psi\left(k\right)\right)\dfrac{\zeta^{k-1}}{(k-1)!},$
where $\psi\left(z\right)=\Gamma'\left(z\right)/\Gamma\left(z\right)$. From (2.5.28)
2.5.47 $\Residue_{z=1}\left[-\zeta^{z-1}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu % h_{2}\mskip 3.0mu \left(z\right)\right]=\left(-\ln\zeta-\gamma\right)-\mathscr% {M}\mskip-3.0mu h_{1}\mskip 3.0mu \left(1\right),$ ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\gamma$: Euler’s constant, $\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform, $\ln\NVar{z}$: principal branch of logarithm function, $\Residue$: residue and $h(x)$: locally integrable function Keywords: Mellin transform Permalink: http://dlmf.nist.gov/2.5.E47 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Mellin transform was changed to $\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{M}(f;z)$. See also: Annotations for §2.5(iii), §2.5(iii), §2.5 and Ch.2
where $\gamma$ is Euler’s constant (§5.2(ii)). Insertion of these results into (2.5.43) yields
2.5.48 $\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta\right)\sim(-\ln\zeta)\sum_{k% =0}^{\infty}\frac{\zeta^{k}}{k!}+\sum_{k=0}^{\infty}\psi\left(k+1\right)\frac{% \zeta^{k}}{k!},$ $\zeta\to 0+$. ⓘ Symbols: $\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Laplace transform, $\sim$: Poincaré asymptotic expansion, $\psi\left(\NVar{z}\right)$: psi (or digamma) function, $!$: factorial (as in $n!$), $\ln\NVar{z}$: principal branch of logarithm function and $h(x)$: locally integrable function Keywords: Laplace transform Referenced by: §2.5(iii) Permalink: http://dlmf.nist.gov/2.5.E48 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Laplace transform was changed to $\mathscr{L}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{L}(f;z)$. See also: Annotations for §2.5(iii), §2.5(iii), §2.5 and Ch.2
To verify (2.5.48) we may use
2.5.49 $\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta\right)=e^{\zeta}E_{1}\left(% \zeta\right);$ ⓘ Symbols: $\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Laplace transform, $\mathrm{e}$: base of natural logarithm, $E_{1}\left(\NVar{z}\right)$: exponential integral and $h(x)$: locally integrable function Keywords: Laplace transform Permalink: http://dlmf.nist.gov/2.5.E49 Encodings: TeX, pMML, png Notational Change (effective with 1.0.15): The notation for the Laplace transform was changed to $\mathscr{L}\mskip-3.0mu f\mskip 3.0mu \left(z\right)$ from $\mathscr{L}(f;z)$. See also: Annotations for §2.5(iii), §2.5(iii), §2.5 and Ch.2
compare (6.2.2) and (6.6.3).
For examples in which the integral defining the Mellin transform $\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)$ does not exist for any value of $z$, see Wong (1989, Chapter 3), Bleistein and Handelsman (1975, Chapter 4), and Handelsman and Lew (1970). | 2021-10-22T18:43:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 553, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.976414680480957, "perplexity": 8511.670624406599}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585518.54/warc/CC-MAIN-20211022181017-20211022211017-00375.warc.gz"} |
http://dergipark.gov.tr/hujms/issue/7748/101281 | | | | |
## entrNew Integral Inequalities Via (α,m)-Convexity and Quasi-ConvexityNew Integral Inequalities Via (α,m)-Convexity and Quasi-Convexity
#### Wenjun Liu [1]
##### 212 545
In this paper, we establish some new integral inequalities involvingBeta function via (α, m)-convexity and quasi-convexity, respectively.Our results in special cases recapture known results.
Hermite’s inequality, Euler Beta function, H¨older’s inequality, (α, m)convexity, quasi-convexity2000 AMS Classification:26D15, 33B15, 26A51, 39B62.
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Primary Language tr Mathematics Author: Wenjun Liu
Bibtex @ { hujms101281, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe University}, year = {2013}, volume = {42}, pages = {289 - 297}, doi = {}, title = {New Integral Inequalities Via (\α,m)-Convexity and Quasi-Convexity}, key = {cite}, author = {Liu, Wenjun} } APA Liu, W . (2013). New Integral Inequalities Via (α,m)-Convexity and Quasi-Convexity. Hacettepe Journal of Mathematics and Statistics, 42 (3), 289-297. Retrieved from http://dergipark.gov.tr/hujms/issue/7748/101281 MLA Liu, W . "New Integral Inequalities Via (α,m)-Convexity and Quasi-Convexity". Hacettepe Journal of Mathematics and Statistics 42 (2013): 289-297 Chicago Liu, W . "New Integral Inequalities Via (α,m)-Convexity and Quasi-Convexity". Hacettepe Journal of Mathematics and Statistics 42 (2013): 289-297 RIS TY - JOUR T1 - New Integral Inequalities Via (α,m)-Convexity and Quasi-Convexity AU - Wenjun Liu Y1 - 2013 PY - 2013 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 289 EP - 297 VL - 42 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics New Integral Inequalities Via (α,m)-Convexity and Quasi-Convexity %A Wenjun Liu %T New Integral Inequalities Via (α,m)-Convexity and Quasi-Convexity %D 2013 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 42 %N 3 %R %U ISNAD Liu, Wenjun . "New Integral Inequalities Via (α,m)-Convexity and Quasi-Convexity". Hacettepe Journal of Mathematics and Statistics 42 / 3 (March 2013): 289-297. | 2019-04-18T18:34:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2738732695579529, "perplexity": 7838.312754924622}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578526228.27/warc/CC-MAIN-20190418181435-20190418203435-00403.warc.gz"} |
http://pdglive.lbl.gov/Particle.action?node=M173&init=0&home=MXXX040 | CHARMED, STRANGE MESONS($\boldsymbol C$ = $\boldsymbol S$ = $\pm1$) ${{\mathit D}_{{s}}^{+}}$ = ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit s}}}$, ${{\mathit D}_{{s}}^{-}}$ = ${\mathit {\overline{\mathit c}}}$ ${\mathit {\mathit s}}$, similarly for ${{\mathit D}_{{s}}^{*}}$'s INSPIRE search
# ${{\boldsymbol D}_{{s1}}{(2460)}^{\pm}}$ $I(J^P)$ = $0(1^{+})$
${{\mathit D}_{{s1}}{(2460)}^{\pm}}$ MASS $2459.5 \pm0.6$ MeV (S = 1.1)
${\mathit m}_{{{\mathit D}_{{s1}}{(2460)}^{\pm}}}–{\mathit m}_{{{\mathit D}_{{s}}^{*\pm}}}$ $347.3 \pm0.7$ MeV (S = 1.2)
${\mathit m}_{{{\mathit D}_{{s1}}{(2460)}^{\pm}}}–{\mathit m}_{{{\mathit D}_{{s+-}}}}$ $491.2 \pm0.6$ MeV (S = 1.1)
${{\mathit D}_{{s1}}{(2460)}^{\pm}}$ WIDTH $<3.5$ MeV CL=95.0%
${{\mathit D}_{{s1}}{(2460)}^{-}}$ modes are charge conjugates of the modes below.
constrained fit information | 2019-12-09T06:07:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9925048351287842, "perplexity": 1988.7578888639673}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540517557.43/warc/CC-MAIN-20191209041847-20191209065847-00081.warc.gz"} |
https://gea.esac.esa.int/archive/documentation/GDR3/Data_analysis/chap_cu8par/sec_cu8par_apsis/ssec_cu8par_apsis_gspspec.html | 11.3.4 General Stellar Parametrizer from Spectroscopy (GSP-Spec)
Author(s): Alejandra Recio-Blanco, Marco A. Álvarez
Goal
GSP-Spec (Recio-Blanco and et al. 2022) estimates the stellar atmospheric parameters, individual chemical abundances and Diffuse Interstellar Band (DIB) parameters from combined RVS spectra of single stars. No additional information (astrometric, photometric or BP/RP data) is considered, allowing a purely spectroscopic treatment. Two different algorithms described in Recio-Blanco et al. (2016), MatisseGauguin and ANN, are applied for atmospheric-parameter estimation. Individual abundances and DIB parameters are only estimated from the MatisseGauguin atmospheric parameters, using the Gauguin algorithm (Recio-Blanco et al. 2006) and Gaussian fitting methods (Zhao et al. 2021), respectively. Uncertainties are estimated from 50 Monte Carlo realisations considering the spectral flux uncertainties per pixel provided by CU6. For each realisation, a new complete parameterisation, from atmospheric parameters to related chemical abundances and DIB parameters, is performed. Upper and lower confidence values are provided from quantiles 84th and 16th, respectively.
Inputs
GSP-Spec uses as input combined RVS spectra and their flux uncertainties per pixel. The spectra are continuum normalised from CU6 pipelines, however, GSP-Spec reviews the continuum placement during the spectra parameterisation procedure. In addition, the spectra are rebinned from 2400 pixels to 800 pixels (without reducing the spectral resolution thanks to the RVS oversampling), allowing to increase their signal-to-noise (SNR) ratio. The RVS spectra analysed by GSPspec during DR3 operations were selected to have SNR$>$20 before resampling.
Further input data are model grids of synthetic RVS spectra. The spectra have been derived from MARCS atmospheric models of FGKM-type stars (Gustafsson et al. 2008), using the TURBOSPECTRUM spectral synthesis code (Plez 2012). The associated line lists are those of Contursi et al. (2021). These models are used for the stellar atmospheric parameters ($T_{\rm eff}$, $\log g$, $[\rm M/H]$ and [$\alpha$/Fe]), but also for the individual abundances estimate, for which a fifth dimension is added on [X/Fe], with X being the considered chemical element. We used an empirical law for the microturbulence parameter. This parametrized relation is a function of $T_{\rm eff}$, $\log g$ and $[\rm M/H]$, and has been derived from $V_{\rm micro}$ literature values for the Gaia-ESO Survey (Bergemann et al., in preparation).
Methods
Two main procedures are implemented in GSP-Spec: MatisseGauguin (results published in the table astrophysical_parameters) and ANN (published in the astrophysical_parameters_supp table). Please refer to Recio-Blanco and et al. (2022) for a detailed description of the methodology.
The MatisseGauguin parameterisation procedure, producing the GSP-Spec atmospheric parameters, individual chemical abundances and DIB parameters included in the astrophysical_parameters table, is as follows:
1. 1.
Stellar parameters initialization with DEGAS: Once the RVS spectra are rebinned to 800 pixels, the DEGAS decision tree method (Kordopatis et al. 2011), considering the entire parameter space of the grid (FGKM-type stars), is used to derive a first guess in $T_{\rm eff}$, $\log g$, $[\rm M/H]$ and [$\alpha$/Fe].
2. 2.
Matisse algorithm application: The MATISSE algorithm (Recio-Blanco et al. 2006) is applied following an iterative procedure in the parameter estimation to overcome non-linearity problems. MATISSE is a projection method in the sense that the full input spectra are projected into a set of vectors derived during a learning phase, based on the noise-free reference grids. The noise optimization is taken into account thanks to a Landweber algorithm during the covariance matrix inversion and it is adapted to each application. These vectors are a linear combination of reference spectra and could be viewed roughly as the derivatives of these spectra with respect to the different stellar parameters. MATISSE is, thus, a local multi-linear regression method. The MATISSE projection is first applied around the DEGAS solution in a local environment of $\pm$500 K in $T_{\rm eff}$, $\pm$0.5 dex in $\log g$, $\pm$0.25 dex in $[\rm M/H]$ and $\pm$0.20 dex in [$\alpha$/Fe]. This produces a second solution around which MATISSE is applied again. This iterative procedure is repeated until convergence, within a maximum of 10 iterations.
3. 3.
Refinement of parameters with GAUGUIN: The GAUGUIN algorithm is applied around the final MATISSE solution of the previous step, considering a local environment of $\pm$250 K in $T_{\rm eff}$, $\pm$0.5 dex in $\log g$, $\pm$0.25 dex in $[\rm M/H]$ and $\pm$0.20 dex in [$\alpha$/Fe]. GAUGUIN (Bijaoui et al. 2012; Recio-Blanco et al. 2016) is a classical, local optimization method implementing a Gauss-Newton algorithm. It is based on a local linearization around a given set of parameters that are associated with a reference synthetic spectrum (via linear interpolation of the derivatives). Its goal is to find the direction in the parameter space that has the highest negative gradient as a function of the distance. Once this direction is found, the method proceeds in an iterative way, by modifying the initial guess of the studied parameter and re-calculating the gradient again, until convergence of the parameter solution. A few iterations are carried out through linearization around the new solutions, until the algorithm converges towards the minimum distance. In practice, and to avoid trapping into secondary minima, GAUGUIN is initialized by parameters independently determined by other algorithms such as MATISSE. The final MATISSE+GAUGUIN solution in $T_{\rm eff}$, $\log g$, $[\rm M/H]$ and [$\alpha$/Fe] is considered in the following.
4. 4.
Continuum placement and spectra normalization: The parameters solution of the previous step is used to re-estimate the continuum placement. This step is particularly important in the case of cool stars, having pseudo-continuum flux values lower than one. The continuum placement and normalization procedure is described in detail in Santos-Peral et al. (2020). In this step, the spectrum flux is normalised over the entire RVS wavelength domain. To this purpose, the observed spectrum (O) is compared to an interpolated synthetic one (S) with the same atmospheric parameters. First, the most appropriate pixels of the residual (R = S/O) are selected using an iterative procedure implementing a linear fit to R followed by a $\sigma-$clipping. Then, the residual trend is fitted with a low degree polynomial. Finally, the normalised spectrum is obtained after dividing the observed spectrum by a linear function resulting by the fit of the residual.
5. 5.
Iteration in the atmospheric parameters solution following the continuum refinement: The module comes back to step 1, to re-estimate the atmospheric parameters using the new spectra normalization. This loop is performed five times, iterating on the parameters and the continuum placement. The final parameters solution in $T_{\rm eff}$, $\log g$, $[\rm M/H]$ and [$\alpha$/Fe] is saved in the memory, as well as the final normalized spectrum. A goodness-of-fit (g.o.f.) between the observed and the synthetic spectrum interpolated to the final atmospheric parameters is derived and saved. This g.o.f. is reported in the final table only for the original observed spectra, not including Monte Carlo variations of the flux (see step 8).
6. 6.
Chemical abundances per spectral line using GAUGUIN: Considering the final atmospheric parameters solution and normalized spectrum, selected spectral lines are considered for individual chemical abundance estimates. For each line identified in the list, a specific reference synthetic spectra grid is interpolated at the input atmospheric parameters in order to measure the abundance from the related chemical element responsible for the line absorption. This grid now includes a large range in the element abundance dimension (AX). First of all, a local normalization around the line is performed (Santos-Peral et al. 2020). A minimum quadratic distance is then calculated between the reference grid and the observed spectrum, providing a first guess of the abundance estimate (A0). This first guess is optimised via the GAUGUIN algorithm, carrying out iterations through linearisation around the new solutions. The algorithm stops when the relative difference between two consecutive iterations is less than a given value (typically one hundredth of the grid abundance step).
7. 7.
Diffuse Interstellar Band parameters: After a specific local normalisation around the DIB feature at 862 nm, the DIB parameters are extracted (Zhao et al. 2021). More particularly, the DIB characteristics are derived from the spectra of late-type stars by subtracting the corresponding synthetic spectra. For early-type stars we applied a specific model based on the Gaussian process that needs no prior knowledge of the stellar parameters.
8. 8.
CN over/under abundance proxy: a cyanogen line is analysed subtracting the corresponding synthetic spectra and estimated the equivalent width of the remaining feature (the value is positive for a CN over-abundance or negative for a CN under-abundance with respect to the standard value of [CN/Fe]=0.0 dex. To this purpose, the same Gaussian fitting procedure employed for DIB parameters of late-type stars is used, although allowing negative equivalent width values for CN under abundances.
9. 9.
Monte Carlo iterations using flux uncertainties: flux uncertainties provided by CU6 are used to estimate the uncertainties in the GSP-Spec output parameters. To this purpose, 50 Monte Carlo realizations of the spectral flux are implemented. Variations of the spectral flux per pixel are generated, following a Gaussian distribution whose standard deviation is equal to the input flux uncertainties. For each realisation, a new complete parameterisation is performed, starting from step 1. This allows final set of 50 values for each atmospheric parameter, each spectral-line abundance and each DIB fitting parameter. Thanks to this, median, upper and lower confidence values are provided from quantiles 50th, 84th and 16th, respectively.
10. 10.
Individual chemical abundances per element: The final chemical abundances per element are derived by combining the independent abundance estimates of all the lines of the same element. To this purpose, a weighted mean is calculated, using the inverse of the line-abundance uncertainty (defined as the upper minus lower abundance value of all the MC realisations of that line abundance) as a weight.
The Artificial Neural Network (ANN) parameterisation procedure is responsible for the GSP-Spec atmospheric parameters published on the astrophysical_parameters_supp table. The architecture used for ANN is feed-forward with three fully connected layers, see Figure 11.22. The input layer has as many neurons as predictor variables and the output layer has as many neurons as variables to be predicted. In this case, the input layer corresponds to the pixels in the spectrum (800) and the output layer to the four APs. The hidden layer connect both input and output layers and the number of neurons has been determined empirically between 50 and 100 for nets trained with low to high SNR spectra, respectively. The ANN analysis procedure is as follows:
1. 1.
ANN selection: ANN behaves well in the presence of noise (Manteiga et al. 2010), proving that it is a robust method when performing the estimation of APs. However, the error in the estimates depends on the signal to noise ratio (SNR) so, in order to reduce the error in the estimation, we decided to discriminate between five SNR ranges, see Table 11.21, training a network for each range. For each spectrum we use the SNR value, given by CU6, to select which net performs the parameter estimation.
2. 2.
Check boundaries: Some RVS spectra have NaN values at the beginning or at the end of the spectrum, caused by radial velocity corrections, that could lead to a heavy variation in flux. This can be interpreted as an important characteristic by the ANN, and to avoid this behaviour, we truncate these zero values to the mean of the spectrum.
3. 3.
Normalisation: A min-max normalisation procedure is applied to the RVS spectra (800 pixels) to avoid geometric biases, and to ensure that all dimensions of the spectrum are in the same range to have the same importance in training.
4. 4.
Parameter estimation: Once the net has been selected, it is fed with the normalised spectrum deriving the estimations of $T_{\rm eff}$, $\log g$, $[\rm M/H]$ and [$\alpha$/Fe]. These parameters are also normalised so, a de-normalisation procedure is applied to return the correct values.
5. 5.
Monte Carlo iterations using flux uncertainties: The same procedure used for MatisseGauguin (see item 9 above) is also applied for ANN, obtaining the median, upper and lower confidence values from quantiles 50th, 84th and 16th, respectively.
The activation function used for input and output layers is lineal, but for the hidden layer the logistic function is the chosen one.
The learning function used to train ANNs is the back-propagation algorithm, that can be interpreted as a problem of minimization of the error existing between the obtained and desired outputs.
In order to select the ANN that best generalizes avoiding the overtraining, we use the early stopping procedure, obtaining the net that minimize the error by stopping the training at the point when performance starts to degrade. We also initialize weights in the range [-0.2,0.2].
The learning rate, used to determine the speed and quality of learning, has been determined empirically in the range [0.001, 0.2].
Due to the fact that the effectiveness of the ANN depends on the input ordering, we perform ten trains with different initializations, selecting the one with minimum error. Each train has a limit of one thousand iterations because we observed that beyond that number, the training process does not improve but the computational cost increases.
To train ANNs we use the grid of synthetic spectra mentioned before (Section 11.3.4), since there is no noise model of Gaia RVS, we empirically determined the relation between the noise given by CU6 and the Gaussian noise that we have to use to train the nets, as it is shown in Table 11.21
To guarantee that all inputs are in a comparable range, all spectra used to train ANNs must be normalized with the same procedure. Desired parameters ($T_{\rm eff}$, $\log g$, $[\rm M/H]$ and [$\alpha$/Fe]) are also normalized in order to have the same importance in the training process. In this case, the normalization is performed using the maximum and minimum values of the grid.
As a result, we obtained five trained nets to estimate the atmospheric parameters according to these SNR ranges. Each network estimates the parameters of a given spectrum according to the signal to noise ratio provided by CU6.
Output
MatisseGauguin results provide 23 independent APs in the astrophysical_parameters table. This includes: $T_{\rm eff}$, log g, $[\rm M/H]$, [$\alpha$/Fe], goodness-of-fit over the entire spectral range, individual chemical abundances of [N/Fe], [Mg/Fe], [Si/Fe], [S/Fe], [Ca/Fe], [Ti/Fe], [Cr/Fe], [Fe/M], [FeII/M], [Ni/Fe], [Zr/Fe], [Ce/Fe], [Nd/Fe], CN equivalent width and its fitting parameters, DIB equivalent width and its fitting parameters. In addition, for each atmospheric parameter, chemical abundance and equivalent width, upper and lower confidence values are provided. For each chemical element abundance, the number of used spectral lines, as well as the line-to-line scatter are presented.
ANN results provide 4 APs in the astrophysical_parameters_supp table. This includes: $T_{\rm eff}$, $\log g$, $[\rm M/H]$, [$\alpha$/Fe] and their upper and lower confidence values and a goodness-of-fit over the entire spectral range.
Finally, following the results of the internal GSPspec validation, a GSPspec catalogue flag has been implemented during the post-processing and published in both the astrophysical_parameters and the astrophysical_parameters_supp tables. The GSPspec catalogue flag is a chain of 41 characters including all the adopted failure criteria and uncertainty sources considered during the post-processing. In this chain, value “0” is the best, and “9” is the worse, generally implying the parameter masking. The order of the individual flags is listed in Table 11.22, including the possible adopted values for each of them. Please refer to Recio-Blanco and et al. (2022) for a detailed description of the GSPspec catalogue flags.
Scope
All results are provided for stars with SNR$>$20 (for an estimate of the RVS signal-to-noise see the expected$\_$sig$\_$to$\_$noise field). During the post-processing, dubious results were filtered out based on processing flags. In particular, results out of the validity range of the reference synthetic spectra grids (essentially FGK-type stars) are flagged thanks to the extrapolation character of the GSP-Spec catalogue flag chain.
Results
A detailed description of GSP-Spec results, including an in depth analysis of methodological biases and comparison with literature parameters can be found in Recio-Blanco and et al. (2022). Gaia self-consistent calibrations are proposed for the observed biases. It is important to underline the fact that the use of GSP-Spec catalogue flags is crucial for any scientific use of the GSP-Spec results.
Notes on ANN observed biases
ANN shows no important internal bias as inferred from tests with synthetic spectra, see Table 11.23. However, compared to the literature, ANN results present important biases that have to be taken into account, see Table 11.24.
In Figure 11.23 the parameterisation for all stars (5 524 387) is shown, considering all possible flag values.
Plots in Figure 11.24 and Figure 11.25 show that the stars with vbroad values greater than 20 km/s, or radial velocity errors greater than 2 km/s, occupy specific regions of the parameter space, mostly coincident for both.
In Figure 11.26 only the best quality parameterisations are shown (1 307 443), this means stars with no bias induced by vbroad nor radial velocity, also stars with noise uncertainties flag equals to 0 and parameters without extrapolations. | 2022-07-01T13:45:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 126, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7296328544616699, "perplexity": 1457.2841551522292}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103941562.52/warc/CC-MAIN-20220701125452-20220701155452-00717.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=S029IAA | #### Invisible ${{\mathit A}^{0}}$ (Axion) MASS LIMITS from Astrophysics and Cosmology
$\mathit v_{1}$ = $\mathit v_{2}$ is usually assumed ($\mathit v_{\mathit i}$ = vacuum expectation values). For a review of these limits, see RAFFELT 1991 and TURNER 1990 . In the comment lines below, D and K refer to DFSZ and KSVZ axion types, discussed in the above minireview.
VALUE (eV) CL% DOCUMENT ID TECN COMMENT
• • We do not use the following data for averages, fits, limits, etc. • •
$>1.4 \times 10^{-21}$ 95 1
2021
ASTR Fuzzy DM
$<1.9 \times 10^{4}$ 2
2021
COSM warm dark matter
3
2021
ASTR SN 1987A, axion-muon coupling
4
2021
ASTR Microlensing
5
2021
ASTR SN 1987A, ${{\mathit \Lambda}}$ decay
$\text{none } 1.3 - 2.7 \times 10^{-13}$ 6
2021
$>2 \times 10^{-20}$ 95 7
2021
COSM Lyman-$\alpha$
$\text{none } 0.8 - 6.5 \times 10^{-13}$ 95 8
2021
$>2 \times 10^{-17}$ 9
2020
COSM Isocurvature fluctuations
10
2020
ASTR Compact binary systems
$>2.1 \times 10^{-21}$ 11
2020
COSM Fuzzy DM
$\text{none } 6.4 - 8.0 \times 10^{-13}$ 95 12
2020
$\text{none } 2.9 - 4.6 \times 10^{-21}$ 13
2019
$\text{none } 10^{-21} - 6 \times 10^{-20}$ 14
2019
ASTR Fuzzy DM
$\text{none } 1.1 - 4 \times 10^{-13}$ 95 15
2019
$<0.06$ 16
2018
ASTR K, SN 1987A
$<0.67$ 95 17
2013 A
COSM K, hot dark matter
$\text{none } 0.7 - 3 \times 10^{5}$ 18
2011
COSM ${}^{}\mathrm {D}$ abundance
$<105$ 90 19
2011 A
CNTR D, solar axion
20
2010
CAST K, solar axions
$<0.72$ 95 21
2010
COSM K, hot dark matter
22
2009
CAST K, solar axions
$<191$ 90 23
2009 A
CNTR K, solar axions
$<334$ 95 24
2009
HPGE K, solar axions
$<1.02$ 95 25
2008
COSM K, hot dark matter
$<1.2$ 95 26
2007
COSM K, hot dark matter
$<0.42$ 95 27
2007 A
COSM K, hot dark matter
$<1.05$ 95 28
2005 A
COSM K, hot dark matter
$3\text{ to }20$ 29
1998
COSM K, hot dark matter
$<0.007$ 30
1997
ASTR D, neutron star
$<4$ 31
1997
ASTR D, neutron star cooling
$<(0.5 - 6){\times }\text{ 10}$$^{-3} 32 1997 ASTR SN 1987A <0.018 33 1995 ASTR D, red giant <0.010 34 1994 ASTR D, red giants, white dwarfs 35 1993 ASTR K, SN 1987A <0.01 1992 ASTR D, white dwarf <0.03 1992 C ASTR D, C-O burning \text{none 3 - 8} 36 1991 ASTR D, K, intergalactic light <10 37 1991 C COSM D, K, mass density of the universe, supersymmetry 38 1991 B ASTR D,K, SN 1987A <1 \times 10^{-3} 39 1991 ASTR K, intergalactic light \text{none } 10^{-3} - 3 1990 ASTR D,K, SN 1987A 40 1990 ASTR D,K, SN 1987A <0.02 41 1990 D ASTR D, red giant <1 \times 10^{-3} 42 1989 ASTR D,K, SN 1987A <(1.4 - 10){\times }\text{ 10}$$^{-3}$ 43
1989
ASTR D,K, SN 1987A
$<3.6 \times 10^{-4}$ 44
1989
ASTR D,K, SN 1987A
$<12$
1988
ASTR D, Sun
$<1 \times 10^{-3}$
1988
ASTR D,K, SN 1987A
45
1988 B
ASTR red giant
$<0.07$
1987
ASTR D, red giant
$<0.7$ 46
1987
ASTR K, red giant
$\text{< 2-5}$
1987
COSM K, thermal production
$<0.01$ 47
1986
ASTR D, red giant
$<0.06$
1986
ASTR D, red giant
$<0.7$ 48
1986
ASTR K, red giant
$<0.03$
1986 B
ASTR D, white dwarf
$<1$ 49
1985
ASTR K, red giant
$\text{<0.003 - 0.02}$
1984
ASTR D, K, neutron star
$>1 \times 10^{-5}$
1983
COSM D,K, mass density of the universe
$>1 \times 10^{-5}$
1983
COSM D,K, mass density of the universe
$<0.04$
1983 B
ASTR D, red giant
$>1 \times 10^{-5}$
1983
COSM D,K, mass density of the universe
$<0.1$
1982
ASTR D, red giant
$<1$ 50
1982
ASTR D, stellar cooling
$<0.07$
1982 B
ASTR D, red giant
1 BANIK 2021 use the subhalo mass function inferred from the analyses of the GD-1 and Pal 5 stellar streams. The limit is strengthened to $2.2 \times 10^{-21}$ eV when adding dwarf satellite counts.
2 BAUMHOLZER 2021 study the freeze-in production of axion dark matter through couplings to photons, and set the limit using Lyman-$\alpha$ forest data and the observed number of Milky Way subhalos.
3 CROON 2021 study the supernova cooling effect of the axion-muon coupling, taking account of semi-Compton scattering and muon-proton bremsstrahlung, as well as the loop-induced axion-photon coupling, and exclude the range of $\mathit g_{ {{\mathit A}} {{\mathit \mu}} {{\mathit \mu}} }$ $\simeq{}$ $7 \times 10^{-3} - 2 \times 10^{-10}$ for ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $0.5$ GeV. See their Fig. 8 for mass-dependent limits.
4 FUJIKURA 2021 use the EROS-2 survey and the Subaru HSC observation to set limits on spherically symmetric axion clumps, taking account of the finite lens and source size effects. $\mathit f_{{{\mathit A}^{0}} }{ {}\gtrsim{} }$ $10^{12}$ GeV can be constrained depending on the fraction of the axion dark matter collapsed into clumps, and the clump densities. See their Figs. $7 - 10$ for the limits.
5 MARTINCAMALICH 2021 considered axion emission from a supernova core through the ${{\mathit \Lambda}}$ hyperon decay, and set the limit on B( ${{\mathit \Lambda}}$ $\rightarrow$ ${{\mathit n}}{{\mathit A}^{0}}$ ) ${ {}\lesssim{} }$ $8 \times 10^{-9}$, or equivalently, $\mathit f_{{{\mathit A}^{0}} }/C_{sd}{ {}\gtrsim{} }$ $2.6 \times 10^{9}$ GeV in terms of the flavor-violating axion coupling to the down and strange quarks.
6 NG 2021 use the binary black holes reported by LIGO and Virgo to determine the black hole spin distribution at formation and the scalar boson mass simultaneously, neglecting the boson self-interaction.
7 ROGERS 2021 set the limit by using a framework involving Bayesian emulator optimization to accurately forward-model the Lyman-$\alpha$ flux power spectrum, and comparing this with small-scale data to constrain the predicted suppression of cosmic structure growth.
8 TSUKADA 2021 look for a stochastic GW background produced by extragalactic BH-hidden photon cloud systems through the superradiant instability. They assume a uniform spin distribution at birth of isolated BHs from 0 to 1.
9 IRSIC 2020 used the Lyman-$\alpha$ forest constraint on small-scale isocurvature perturbation to derive limits on the axion mass and decay constant, assuming that the axion makes up all dark matter in the post-inflationary scenario. See their Fig. 1 for other astrophysical limits as well as the limits on the case of the temperature-dependent axion mass.
10 PODDAR 2020 used the observed decay in orbital period of four compact binary systems to derive a limit on the emission of axions with ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $1 \times 10^{-19}$ eV, assuming they couple to nucleons and the strong $\mathit CP$ phase vanishes at the potential minimum. They exclude $\mathit f_{{{\mathit A}^{0}} }{ {}\lesssim{} }$ $10^{11}$ GeV for such axions.
11 SCHUTZ 2020 set a limit on fuzzy dark matter based on the existing limits for warm dark matter derived from the inferred subhalo mass function.
12 SUN 2020 look for quasimonochromatic gravitational waves emitted from boson clouds around the Cygnus X-1 black hole. The quoted limit assume the black hole age of $5 \times 10^{6}$ years. A mass range of $9.6 - 15.5 \times 10^{-13}$ eV is disfavored when repeated induction of bosenova for string axions with decay constant $\mathit f_{{{\mathit A}^{0}} }$ $\simeq{}$ $10^{15}$ GeV prevents the superradiance from being saturated.
13 DAVOUDIASL 2019 used the observed data of M87* by the Event Horizon Telescope to set the limit. A mass range of $0.85 - 4.6 \times 10^{-21}$ eV is disfavored for a spin-1 boson.
14 MARSH 2019 considered heating of star clusters due to the stochastic oscillations of the core and granular quasiparticles in the outer halo. The limit was derived by requiring the survival of the old star cluster in Eridanus II, where the lower end is set by the validity of diffusion approximation. The effect of tidal stripping is also discussed for lower masses.
15 PALOMBA 2019 used the LIGO O2 dataset to derive limits on nearly monochromatic gravitational waves emitted by boson clouds formed around a stellar-mass black hole. They exclude boson masses in a range of $1.1 \times 10^{-13}$ and $4 \times 10^{-13}$ eV for high initial black hole spin, and $1.2 \times 10^{-13}$ and $1.8 \times 10^{-13}$ eV for moderate spin. See their Figs. 2 and 3 for limits based on various values of black hole initial spin, boson cloud age, and distance.
16 CHANG 2018 update axion bremsstrahlung emission rates in nucleon-nucleon collisions, shifting the excluded mass range to higher values. They rule out the hadronic axion with mass up to a few hundred eV, closing the hadronic axion window. See their Fig. 11 for results based on several different choices of the temperature and density profile of the proto-neutron star.
17 ARCHIDIACONO 2013A is analogous to HANNESTAD 2005A. The limit is based on the CMB temperature power spectrum of the Planck data, the CMB polarization from the WMAP 9-yr data, the matter power spectrum from SDSS-DR7, and the local Hubble parameter measurement by the Carnegie Hubble program.
18 CADAMURO 2011 use the deuterium abundance to show that the ${\mathit m}_{{{\mathit A}^{0}}}$ range 0.7$~$eV -- 300$~$keV is excluded for axions, complementing HANNESTAD 2010 .
19 DERBIN 2011A look for solar axions produced by Compton and bremsstrahlung processes, in the resonant excitation of ${}^{169}\mathrm {Tm}$, constraining the axion-electron ${\times }$ axion nucleon couplings.
20 ANDRIAMONJE 2010 search for solar axions produced from ${}^{7}\mathrm {Li}$ (478 keV) and ${}^{}\mathrm {D}({{\mathit p}}$ ,${{\mathit \gamma}}$ )${}^{3}\mathrm {He}$ (5.5 MeV) nuclear transitions. They show limits on the axion-photon coupling for two reference values of the axion-nucleon coupling for ${\mathit m}_{{{\mathit A}}}<$ 100 eV.
21 This is an update of HANNESTAD 2008 including 7 years of WMAP data.
22 ANDRIAMONJE 2009 look for solar axions produced from the thermally excited 14.4 keV level of ${}^{57}\mathrm {Fe}$. They show limits on the axion-nucleon ${\times }$ axion-photon coupling assuming ${\mathit m}_{{{\mathit A}}}<$ 0.03 eV.
23 DERBIN 2009A look for Primakoff-produced solar axions in the resonant excitation of ${}^{169}\mathrm {Tm}$, constraining the axion-photon ${\times }$ axion-nucleon couplings.
24 KEKEZ 2009 look at axio-electric effect of solar axions in HPGe detectors. The one-loop axion-electron coupling for hadronic axions is used.
25 This is an update of HANNESTAD 2007 including 5 years of WMAP data.
26 This is an update of HANNESTAD 2005A with new cosmological data, notably WMAP (3 years) and baryon acoustic oscillations (BAO). Lyman-$\alpha$ data are left out, in contrast to HANNESTAD 2005A and MELCHIORRI 2007A, because it is argued that systematic errors are large. It uses Bayesian statistics and marginalizes over a possible neutrino hot dark matter component.
27 MELCHIORRI 2007A is analogous to HANNESTAD 2005A, with updated cosmological data, notably WMAP (3 years). Uses Bayesian statistics and marginalizes over a possible neutrino hot dark matter component. Leaving out Lyman-$\alpha$ data, a conservative limit is 1.4 eV.
28 HANNESTAD 2005A puts an upper limit on the mass of hadronic axion because in this mass range it would have been thermalized and contribute to the hot dark matter component of the universe. The limit is based on the CMB anisotropy from WMAP, SDSS large scale structure, Lyman $\alpha$, and the prior Hubble parameter from HST Key Project. A ${{\mathit \chi}^{2}}$ statistic is used. Neutrinos are assumed not to contribute to hot dark matter.
29 MOROI 1998 points out that a KSVZ axion of this mass range (see CHANG 1993 ) can be a viable hot dark matter of Universe, as long as the model-dependent $\mathit g_{ {{\mathit A}} {{\mathit \gamma}} }$ is accidentally small enough as originally emphasized by KAPLAN 1985 ; see Fig.$~$1.
30 BORISOV 1997 bound is on the axion-electron coupling $\mathit g_{\mathit ae}<1 \times 10^{-13}$ from the photo-production of axions off of magnetic fields in the outer layers of neutron stars.
31 KACHELRIESS 1997 bound is on the axion-electron coupling $\mathit g_{\mathit ae}<1 \times 10^{-10}$ from the production of axions in strongly magnetized neutron stars. The authors also quote a stronger limit, $\mathit g_{\mathit ae}<9 \times 10^{-13}$ which is strongly dependent on the strength of the magnetic field in white dwarfs.
32 KEIL 1997 uses new measurements of the axial-vector coupling strength of nucleons, as well as a reanalysis of many-body effects and pion-emission processes in the core of the neutron star, to update limits on the invisible-axion mass.
33 RAFFELT 1995 reexamined the constraints on axion emission from red giants due to the axion-electron coupling. They improve on DEARBORN 1986 by taking into proper account degeneracy effects in the bremsstrahlung rate. The limit comes from requiring the red giant core mass at helium ignition not to exceed its standard value by more than 5$\%$ ($0.025$ solar masses).
34 ALTHERR 1994 bound is on the axion-electron coupling $\mathit g_{\mathit ae}<1.5 \times 10^{-13}$, from energy loss via axion emission.
35 CHANG 1993 updates ENGEL 1990 bound with the Kaplan-Manohar ambiguity in $\mathit z={\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit d}}}$ (see the Note on the Quark Masses in the Quark Particle Listings). It leaves the window $\mathit f_{\mathit A}=3 \times 10^{5}-3 \times 10^{6}$ GeV open. The constraint from Big-Bang Nucleosynthesis is satisfied in this window as well.
36 BERSHADY 1991 searched for a line at wave length from $3100 - 8300$ $Å$ expected from 2${{\mathit \gamma}}$ decays of relic thermal axions in intergalactic light of three rich clusters of galaxies.
37 KIM 1991C argues that the bound from the mass density of the universe will change drastically for the supersymmetric models due to the entropy production of saxion (scalar component in the axionic chiral multiplet) decay. Note that it is an $\mathit upperbound$ rather than a lowerbound.
38 RAFFELT 1991B argue that previous SN$~$1987A bounds must be relaxed due to corrections to nucleon bremsstrahlung processes.
39 RESSELL 1991 uses absence of any intracluster line emission to set limit.
40 ENGEL 1990 rule out $10^{-10}~{ {}\lesssim{} }$ $\mathit g_{\mathit AN}{ {}\lesssim{} }~10^{-3}$, which for a hadronic axion with EMC motivated axion-nucleon couplings corresponds to $2.5 \times 10^{-3}~$eV ${ {}\lesssim{} }{\mathit m}_{{{\mathit A}^{0}}}{ {}\lesssim{} }$ $2.5 \times 10^{4}~$eV. The constraint is loose in the middle of the range, i.e. for ${\mathit g}_{\mathit AN}$ $\sim{}~10^{-6}$.
41 RAFFELT 1990D is a re-analysis of DEARBORN 1986 .
42 The region ${\mathit m}_{{{\mathit A}^{0}}}{ {}\gtrsim{} }$ 2 eV is also allowed.
43 ERICSON 1989 considered various nuclear corrections to axion emission in a supernova core, and found a reduction of the previous limit (MAYLE 1988 ) by a large factor.
44 MAYLE 1989 limit based on naive quark model couplings of axion to nucleons. Limit based on couplings motivated by EMC measurements is 2$-$4 times weaker. The limit from axion-electron coupling is weak: see HATSUDA 1988B.
45 RAFFELT 1988B derives a limit for the energy generation rate by exotic processes in helium-burning stars $\epsilon$ $<$ 100 erg g${}^{−1}$ s${}^{-1}$, which gives a firmer basis for the axion limits based on red giant cooling.
46 RAFFELT 1987 also gives a limit ${\mathit g}_{\mathit A{{\mathit \gamma}} }$ $<$ $1 \times 10^{-10}$ GeV${}^{-1}$.
47 DEARBORN 1986 also gives a limit ${\mathit g}_{\mathit A{{\mathit \gamma}} }$ $<$ $1.4 \times 10^{-11}$ GeV${}^{-1}$.
48 RAFFELT 1986 gives a limit ${\mathit g}_{\mathit A{{\mathit \gamma}} }$ $<$ $1.1 \times 10^{-10}$ GeV${}^{-1}$ from red giants and $<2.4 \times 10^{-9}$ GeV${}^{-1}$ from the sun.
49 KAPLAN 1985 says ${\mathit m}_{{{\mathit A}^{0}} }$ $<$ 23 eV is allowed for a special choice of model parameters.
50 FUKUGITA 1982 gives a limit ${\mathit g}_{\mathit A{{\mathit \gamma}} }$ $<$ $2.3 \times 10^{-10}$ GeV${}^{-1}$.
References:
BANIK 2021
JCAP 2110 043
BAUMHOLZER 2021
JCAP 2105 004 Structure Formation Limits on Axion-Like Dark Matter
CROON 2021
JHEP 2101 107 Supernova Muons: New Constraints on $Z$? Bosons, Axions and ALPs
FUJIKURA 2021
PR D104 123012
MARTINCAMALICH 2021
PR D103 L121301 Supernova Constraints on Dark Flavored Sectors
NG 2021
PRL 126 151102 Constraints on Ultralight Scalar Bosons within Black Hole Spin Measurements from the LIGO-Virgo GWTC-2
ROGERS 2021
PRL 126 071302 Strong Bound on Canonical Ultralight Axion Dark Matter from the Lyman-Alpha Forest
PR D103 083005 Modeling and searching for a stochastic gravitational-wave background from ultralight vector bosons
IRSIC 2020
PR D101 123518 Early structure formation constraints on the ultralight axion in the postinflation scenario
PODDAR 2020
PR D101 083007 Constraints on ultralight axions from compact binary systems
SCHUTZ 2020
PR D101 123026 Subhalo mass function and ultralight bosonic dark matter
SUN 2020
PR D101 063020 Search for ultralight bosons in Cygnus X-1 with Advanced LIGO
DAVOUDIASL 2019
PRL 123 021102 Ultralight Boson Dark Matter and Event Horizon Telescope Observations of M87*
MARSH 2019
PRL 123 051103 Strong Constraints on Fuzzy Dark Matter from Ultrafaint Dwarf Galaxy Eridanus II
PALOMBA 2019
PRL 123 171101 Direct constraints on ultra-light boson mass from searches for continuous gravitational waves
CHANG 2018
JHEP 1809 051 Supernova 1987A Constraints on Sub-GeV Dark Sectors, Millicharged Particles, the QCD Axion, and an Axion-like Particle
ARCHIDIACONO 2013A
JCAP 1310 020 Axion Hot Dark Matter Bounds after Planck
JCAP 1102 003 Cosmological Bounds on sub-MeV Mass Axions
DERBIN 2011A
PR D83 023505 Constraints on the Axion-Electron Coupling for Solar Axions Produced by a Compton Process and Bremsstrahlung
ANDRIAMONJE 2010
JCAP 1003 032 Search for Solar Axion Emission from ${}^{7}\mathrm {Li}$ and ${{\mathit D}}$ (${{\mathit p}}$ ,${{\mathit \gamma}}$ )${}^{3}\mathrm {He}$ Nuclear Decays with the CAST ${{\mathit \gamma}}$ -ray Calorimeter
JCAP 1008 001 Neutrino and Axion Hot Dark Matter Bounds after WMAP-7
ANDRIAMONJE 2009
JCAP 0912 002 Search for 14.4 keV Solar Axions Emitted in the M1-Transition of ${}^{57}\mathrm {Fe}$ Nuclei with CAST
DERBIN 2009A
PL B678 181 Search for Solar Axions Produced by Primakoff Conversion using Resonant Absorption by Nuclei
KEKEZ 2009
PL B671 345 Search for Solar Hadronic Axions Produced by a Bremsstrahlung-like Process
JCAP 0804 019 Cosmological Constraints on Neutrino plus Axion Hot Dark Matter: Update after WMAP-5
JCAP 0708 015 Cosmological Constraints on Neutrino plus Axion Hot Dark Matter
MELCHIORRI 2007A
PR D76 041303 Improved Cosmological Bound on the Thermal Axion Mass
JCAP 0507 002 A New Cosmological Mass Limit on Thermal Relic Axions
MOROI 1998
PL B440 69 Axionic Hot Dark Matter in the Hadronic Axion Window
BORISOV 1997
JETP 83 868 Compton Production of Axions on Electrons in a Constant External Field
KACHELRIESS 1997
PR D56 1313 Axion Cyclotron Emissivity of Magnetized White Dwarfs and Neutron Stars
KEIL 1997
PR D56 2419 Fresh Look at Axions and SN1987a
RAFFELT 1995
PR D51 1495 Red Giant Bound on the Axion $−$ Electron Coupling Revisited
ALTHERR 1994
ASP 2 175 Axion Emission from Red Giants and White Dwarfs
CHANG 1993
PL B316 51 Hadronic Axion Window and the Big Bang Nucleosynthesis
WANG 1992
MPL A7 1497 Constraints of Axions from White Dwarf Cooling
WANG 1992C
PL B291 97 Constraints on Mass of the DFSZ Axions from the Carbon$−$Oxygen Burning Stage of Stars
PRL 66 1398 Telescope Search for Multi-eV Axions
KIM 1991C
PRL 67 3465 Effects of Decay of Scalar Partner of Axion on Cosmological Bounds of Axion Supermultiplet Properties
RAFFELT 1991B
PRL 67 2605 Multiple Scattering Suppression of the Bremsstrahlung Emission of Neutrinos and Axions in Supernovae
RESSELL 1991
PR D44 3001 Limits to the Radiative Decay of the Axion
BURROWS 1990
PR D42 3297 Axions and SN1987a: Axion Trapping
ENGEL 1990
PRL 65 960 Emission and Detectability of Hadronic Axions from SN1987a
RAFFELT 1990D
PR D41 1324 Axion Bremsstrahlung in Red Giants
BURROWS 1989
PR D39 1020 Axions and SN1987a
Also
PRL 60 1797 Axions from SN1987a
ERICSON 1989
PL B219 507 Axion Emission from SN1987a: Nuclear Physics Constraints
MAYLE 1989
PL B219 515 Updated Constraints on Axions from SN1987a
Also
PL B203 188 Constraints on Axions from SN1987a
CHANDA 1988
PR D37 2714 Astrophysical Constraints on Axion and Majoron Couplings
RAFFELT 1988B
PR D37 549 Bounds on Weakly Interacting Particles from Observational Lifetimes of Helium Burning Stars
RAFFELT 1988
PRL 60 1793 Boundson ExoticParticle Interactions from SN1987a
FRIEMAN 1987
PR D36 2201 Axions and Stars
RAFFELT 1987
PR D36 2211 Bounds on Hadronic Axions from Stellar Evolution
TURNER 1987
PRL 59 2489 Thermal Production of not so Invisible Axions in the Early Universe
DEARBORN 1986
PRL 56 26 Astrophysical Constraints on the Couplings of Axions Majorons and Familons
RAFFELT 1986B
PL 166B 402 Axion Constraints from White Dwarf Cooling Times
RAFFELT 1986
PR D33 897 Astrophysical Axion Bounds Diminished by Screening Effects
KAPLAN 1985
NP B260 215 Opening the Axion Window
IWAMOTO 1984
PRL 53 1198 Axion Emission from Neutron Stars
ABBOTT 1983
PL 120B 133 A Cosmological Bound on the Invisible Axion
DINE 1983
PL 120B 137 The not so Harmless Axion
ELLIS 1983B
NP B223 252 Constraints on Light Particles from Stellar Evolution
PRESKILL 1983
PL 120B 127 Cosmology of the Invisible Axion
BARROSO 1982
PL 116B 247 Constraints on Light Axions
FUKUGITA 1982B
PR D26 1840 Astrophysical Constraints on a New Light Axion and other Weakly Interacting Particles
FUKUGITA 1982
PRL 48 1522 Light Pseudoscalar Particle and Stellar Energy Loss | 2023-03-25T04:16:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7324008345603943, "perplexity": 8154.065630834584}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945315.31/warc/CC-MAIN-20230325033306-20230325063306-00176.warc.gz"} |
https://www.usgs.gov/center-news/volcano-watch-magma-magma-whos-got-magma | # Volcano Watch — Magma, magma, who's got the magma?
Release Date:
Last week's Volcano Watch described HVO's most recent and exciting challenge: to figure out what might happen next with Kīlauea's marked change in eruptive activity.
View of Pu‘u ‘Ō‘ō.
(Public domain.)
It is often through change that we learn and grow in our understanding of life. The same idea is certainly true for the study of volcanic processes. Eruptive changes provide some of the best opportunities to better understand how volcanoes "live."
Philosophy aside, HVO staff members are pretty jazzed right now about what's happening at Kīlauea. One of this week's big questions is a twofold one: Where is the magma going and how might it re-emerge?
To briefly recap the event, Kīlauea's 24-year-old ongoing eruption was disrupted early on Father's Day by a swarm of earthquakes in the upper east rift zone, indicating that magma was intruding in a new area near Kane Nui o Hamo, just east of Mauna Ulu. Within several days, the rift zone in the intrusive area spread apart nearly a meter (3 feet).
Lava broke the surface, forming two small flows that covered an area of about 0.8 hectares (2 acres) before stopping abruptly. The intrusion and extrusion processes drained a substantial amount of magma from Kīlauea's summit reservoir and appeared to have also nearly stopped the supply to Puu Oo. The cone's crater floor collapsed, leaving a gaping maw at least 100 meters (330 feet) deep. Its lava tubes have drained, and flows are no longer entering the ocean.
Overall, gas emissions from the volcano have declined as well. Sulfur dioxide, the gas principally responsible for the nearly ubiquitous vog in Kau and Kona, has dropped by about 75 percent, and HVO has begun receiving phone calls of appreciation for the improved air quality in these districts.
One mystery right now, though, is the disparity between how much magma we believe is still entering the volcano from the mantle, and the fact that no new lava and very little gas has been erupted at the surface for over a week.
Several studies of Kīlauea's long-term behavior conclude that magma is supplied to the volcano at a fairly consistent rate of between 0.1 and 0.2 cubic kilometers (0.024 to 0.48 cubic miles) per year. This amount, as erupted lava, could fill between 100 and 200 Olympic-sized swimming pools (OSP) each day. For the past 24 years, Kīlauea has eschewed the Olympic pools, but instead, has favored resurfacing nearly 120 square kilometers (46 square miles) of the island, and has added an additional 202 hectares (500 acres) to Hawaii.
So if magma is still being supplied at a rate of 100 OSPs per day, where is it going, and what might happen next? The short answer is that the intrusion and eruption of lava on the upper east rift rapidly depleted Kīlauea's summit reservoir of the volume of magma required to produce the intrusion and the small associated surface flow. Because of this geologically "momentary" depletion, the reservoir will take some time to refill.
We don't know yet precisely how much magma is tied up in the new intrusion. Ground-based and space-base measurements and modeling will help refine estimates of this quantity. However, studying past events like this one indicates that Kīlauea has already recovered roughly 25 percent of the deflation that occurred in the summit area during the event.
Still, the science of eruptive processes is not always straightforward. Magma supply rate and lava eruption rate are often not quite equal. And while volcanologists studying Kīlauea, mostly agree that magma supply to the volcano has been steady in the long term (tens to hundreds to thousands of years), shorter term variations do occur.
Within the past several years, for example, Kīlauea showed signs—increased expansion and gas release—that a short term magma supply increase had occurred. With such supply rate perturbations comes the interplay between getting magma into the volcanic edifice and having it affect eruptive processes. Time will tell what the very immediate subsurface changes will actually bring in terms of surface expression.
The eruptive changes occurring now at Kīlauea are unmistakably helping HVO scientists better understand and appreciate the wonders of this young volcano's life. In that same spirit, we at HVO would like wish two of our younger staff members, Sara Abraham and Kevan Kamibayashi, our best wishes for growth as they experience a change in their lives together this week by becoming newlyweds. Aloha Nui Loa, Sara and Kevan!
————————————————————————————————————————————————————————————————
### Volcano Activity Update
Puu Oo is no longer erupting, and there are no active surface flows anywhere on the flow field or at the coast. This is the first eruptive pause since December 15, 2000. A small pad of lava that was erupted on the northeast flank of Kane Nui o Hamo shield early on June 19 was only active for a few hours. There has been no continuation or resumption of activity in this area. The output of steam and fume from ground cracks near this new flow, and from cracks west of the base of Kane Nui o Hamo shield, has decreased and is now barely visible.
Only one earthquake beneath Hawai`i Island was reported felt within the past week. A magnitude-2.9 earthquake occurred at 6:15 p.m. H.s.t. on Wednesday, June 27, and was located 15 km (9 miles) west northwest of Kawaihae at a depth of 16 km (10 miles). Mauna Loa is not erupting. Two earthquakes were located beneath the summit area in the past week. Extension between locations spanning the summit, indicating inflation, continues at steady, slow rates which have slowed further since May 2007. | 2021-01-17T12:54:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3204942047595978, "perplexity": 2604.1488050642524}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703512342.19/warc/CC-MAIN-20210117112618-20210117142618-00661.warc.gz"} |
https://www.anl.gov/awa/highgradient-and-high-efficiency-acceleration | Skip to main content
# Argonne National Laboratory .st0{fill:none;} .st1{fill:#007934;} .st2{fill:#0082CA;} .st3{fill:#101E8E;} .st4{fill:#FFFFFF;} .st5{fill:#A22A2E;} .st6{fill:#D9272E;} .st7{fill:#82BC00;} Argonne National Laboratory
Argonne Wakefield Accelerator Facility
# High-Gradient and High Efficiency-Acceleration
A comprehensive program to develop the next generation of high-gradient and high-efficiency acceleration is being carried out at the AWA facility.
Applications for this technology includes future HEP and other advanced accelerator such as radiation generation. The method developed at the AWA, electron beam driven wakefield acceleration, takes places in both structures and plasmas. The accelerator development moves from the conceptual stage, through design and fabrication, and all the way to demonstration at high power. The AWA program develops both dielectric and metallic accelerating structures, high power radiation generation, and high-gradient acceleration. | 2019-06-26T15:48:43 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8052711486816406, "perplexity": 9513.573221348863}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000367.74/warc/CC-MAIN-20190626154459-20190626180459-00223.warc.gz"} |
https://par.nsf.gov/biblio/10127175-plasmoid-mediated-reconnection-solar-uv-bursts | Plasmoid-mediated reconnection in solar UV bursts
Context . Ultraviolet bursts are transients in the solar atmosphere with an increased impulsive emission in the extreme UV lasting for one to several tens of minutes. They often show spectral profiles indicative of a bi-directional outflow in response to magnetic reconnection. Aims . To understand UV bursts, we study how motions of magnetic elements at the surface can drive the self-consistent formation of a current sheet resulting in plasmoid-mediated reconnection. In particular, we want to study the role of the height of the reconnection in the atmosphere. Methods . We conducted numerical experiments solving the 2D magnetohydrodynamic equations from the solar surface to the upper atmosphere. Motivated by observations, we drove a small magnetic patch embedded in a larger system of magnetic field of opposite polarity. This type of configuration creates an X-type neutral point in the initial potential field. The models are characterized by the (average) plasma- β at the height of this X point. Results . The driving at the surface stretches the X-point into a thin current sheet, where plasmoids appear, accelerating the reconnection, and a bi-directional jet forms. This is consistent with what is expected for UV bursts or explosive events, and we provide a more »
Authors:
; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10127175
Journal Name:
Astronomy & Astrophysics
Volume:
628
Page Range or eLocation-ID:
A8
ISSN:
0004-6361
4. Quasi-periodic plasmoid formation at the tip of magnetic streamer structures is observed to occur in experiments on the Big Red Ball as well as in simulations of these experiments performed with the extended magnetohydrodynamics code, NIMROD. This plasmoid formation is found to occur on a characteristic time scale dependent on pressure gradients and magnetic curvature in both experiment and simulation. Single mode, or laminar, plasmoids exist when the pressure gradient is modest, but give way to turbulent plasmoid ejection when the system drive is higher, which produces plasmoids of many sizes. However, a critical pressure gradient is also observed, below which plasmoids are never formed. A simple heuristic model of this plasmoid formation process is presented and suggested to be a consequence of a dynamic loss of equilibrium in the high- $\beta$ region of the helmet streamer. This model is capable of explaining the periodicity of plasmoids observed in the experiment and simulations, and produces plasmoid periods of 90 minutes when applied to two-dimensional models of solar streamers with a height of $3R_\odot$ . This is consistent with the location and frequency at which periodic plasma blobs have been observed to form by Large Angle and Spectrometric Coronograph and Sunmore » | 2023-03-26T09:25:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5822771191596985, "perplexity": 1591.0977615365}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945440.67/warc/CC-MAIN-20230326075911-20230326105911-00283.warc.gz"} |
https://pages.nist.gov/feasst/plugin/flat_histogram/doc/Window.html | Window¶
class Window
Macrostate ranges are often broken into separate windows for parallelization. The relative size of these windows can be optimized depending upon the system.
A segment is a countinuous, theoretical formula for analytically spacing macrostate ranges. This line segment includes both the minimum, maximum, and intermediate values. Thus, a 4 window segment would contain 5 values.
Boundaries are integer macrostate minimums and maximums utilized by each window. Thus, 4 window boundaries would contain 4 min and max values. Boundaries use the given line segment, either from formula or user input, and then account for rounding and extra overlap between windows.
For example, 4 windows with segments given by [0, 100.00, 141.42, 173.21, 200] with 5 overlap and rounding would result in the following boundaries: [[0, 100], [96, 141], [137, 173], [169, 200]] where each of the 4 window is expressed as a [min, max] pair.
In order to recover the free energy over all of the windows, it is possible to splice either (1) the probability distribution or (2) the collection matrix elements.
For (1) probability distribution splicing, each window must share atleast one macrostate (overlap) with its neighbors.
For (2) collection matrix splicing, windows cannot share any macrostates but the boundaries must be adjacent and all trial moves of the windows must be exactly the same.
Subclassed by feasst::WindowCustom, feasst::WindowExponential
Public Functions
Window(argtype args = argtype())
args:
• minimum: minimum in macrostate range (default: 0).
• maximum: maximum in macrostate range (default: -1).
• num: number of windows (default: -1).
• num_from_omp: obtain num from OMP threads (default: false).
• overlap: number of macrostate overlaps between windows (default: 1).
• min_size: minimum size of each window (default: 1).
virtual int minimum() const
Return the minimum.
virtual int maximum() const
Return the maximum.
virtual int num() const
Return the number of windows.
int overlap() const
Return the overlap.
virtual std::vector<double> segment() const = 0
Return the continuous, segmented boundaries of the range. This should be return num + 1 boundaries, to include global min and max.
std::vector<std::vector<int>> boundaries() const
Return the boundaries as a vector of vectors. | 2022-10-06T04:46:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2701975107192993, "perplexity": 5945.682075513034}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337723.23/warc/CC-MAIN-20221006025949-20221006055949-00537.warc.gz"} |
https://alldimensions.fandom.com/wiki/Plane | FANDOM
2,801 Pages
The plane has length and width. The plane also refers to a hypothetical two-dimensional space of infinite extent; this use is used, for example, when describing tilings of the plane. Points on the plane can be shown using two coordinates, written as
$(x,y)$ . In analogue with Space.
Objects on the Plane
• Henagon
• Digon
• Triangle
• Square
• Pentagram
• Pentagon
• Hexagon
• heptagon
• octagon
• nonagon
• decagon
• henceagon
• dodecagon
• tridecagon
• icosagon
• tricosagon
• tetracosagon
• pentacosagon
• hexacosagon
• heptacosagon
• octacosagon
• enneacosagon
• hectoton
• chilliagon
• megagon
• gigagon
• teragon
• petagon
• exagon
• zettagon
• yottagon
• Apeirogon
Flexagons
Polygon has 3 or more faces called flexagon
Polyominoes
Polyominoes are two-dimensional figures consisting of multiple squares fixed edge-to-edge. There are an infinite number of polyominoes, and the number of polyominoes increases with the amount of squares allowed.
Coordinates on the Plane
There are two coordinate systems that can be used to define points on the plane - Cartesian coordinates, and polar coordinates.
Cartesian coordinates consist of two distances - the left-right distance from the origin, and the up-down distance from the origin. This is written as
$(x,y)$ . Cartesian coordinates where either x or y are fixed trace out an infinite line. Cartesian coordinates where both are fixed trace out a point, and where none are fixed trace out a plane. Polar coordinates consist of a distance and an angle - the overall distance from the origin, and the angle of the point from horizontal. This is written as
$(x,\theta )$ . Polar coordinates where x is fixed trace out a circle; polar coordinates where θ is fixed trace out an infinite line. Polar coordinates where both are fixed trace out a point, and where none are fixed trace out a plane. When converting from polar to Cartesian coordinates, the equations
$x\cos { \theta } =x$ and
$x\sin{\theta } =y$ can be used. When converting from Cartesian to polar coordinates, the equations
$\sqrt { { x }^{ 2 }+{ y }^{ 2 } } =x$ and
$\tan ^{ -1 }{ (\frac { y }{ x } ) } =\theta$ can be used.
Dimension
Name: Polygon
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Community content is available under CC-BY-SA unless otherwise noted. | 2019-11-19T01:22:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9699544310569763, "perplexity": 1519.9746249742607}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669868.3/warc/CC-MAIN-20191118232526-20191119020526-00250.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Akullback.solomon | # zbMATH — the first resource for mathematics
## Kullback, Solomon
Compute Distance To:
Author ID: kullback.solomon Published as: Kullback, S.; Kullback, Solomon External Links: MGP · Wikidata · dblp · GND
Documents Indexed: 72 Publications since 1933, including 5 Books Biographic References: 1 Publication
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#### Co-Authors
49 single-authored 6 Ku, Harry H. 3 Gokhale, D. V. 3 Keegel, John C. 2 Frankel, A. 2 Kupperman, Morton 1 Borpujari, Aroona S. 1 Fisher, Michael W. 1 Ireland, C. T. 1 Khairat, M. A. 1 Kullback, J. H. 1 Leibler, R. A. 1 Melnick, Edward L. 1 Reeves, P. N. 1 Rosenblatt, H. M. 1 Thall, Peter F. 1 Varner, R. N.
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#### Serials
27 Annals of Mathematical Statistics 14 Bulletin of the American Mathematical Society 3 Biometrische Zeitschrift 2 Biometrika 2 Journal of the American Statistical Association 2 Journal of Combinatorics, Information & System Sciences 2 Metron 2 Communications in Statistics. Theory and Methods 2 SIAM Journal on Control 2 Journal of Research of the National Bureau of Standards 1 The American Statistician 1 IEEE Transactions on Information Theory 1 Journal of Applied Probability 1 Technometrics 1 Computational Statistics and Data Analysis 1 Lecture Notes in Statistics 1 Statistics: Textbooks and Monographs
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#### Fields
18 Statistics (62-XX) 4 Information and communication theory, circuits (94-XX) 1 Measure and integration (28-XX) 1 Probability theory and stochastic processes (60-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)
#### Citations contained in zbMATH
32 Publications have been cited 2,694 times in 2,107 Documents Cited by Year
On information and sufficiency. Zbl 0042.38403
Kullback, S.; Leibler, R. A.
1951
Information theory and statistics. Zbl 0088.10406
Kullback, Solomon
1959
Information theory and statistics. Zbl 0149.37901
Kullback, S.
1967
Interaction in multidimensional contingency tables: an information theoretic approach. Zbl 0274.62036
Ku, H. H.; Kullback, S.
1968
The information in contingency tables. Zbl 0405.62002
Gokhale, D. V.; Kullback, Solomon
1978
Information theory and statistics. Reprint of the 2nd ed. ’68. Zbl 0897.62003
Kullback, Solomon
1997
Contingency tables with given marginals. Zbl 0155.26701
Ireland, C. T.; Kullback, S.
1968
Probability densities with given marginals. Zbl 0165.20303
Kullback, S.
1968
Approximating discrete probability distributions. Zbl 0174.23202
Ku, Harry H.; Kullback, Solomon
1969
Marginal homogeneity of multidimensional contingency tables. Zbl 0215.54305
Kullback, S.
1971
On the analysis of multiple regression in $$k$$ categories. Zbl 0082.35201
Kullback, S.; Rosenblatt, H. M.
1957
Certain inequalities in information theory and the Cramer-Rao inequality. Zbl 0057.35402
Kullback, S.
1954
Information analysis of linear interactions in contingency tables. Zbl 0382.62044
Kullback, S.; Gokhale, D. V.
1978
Topics in statistical information theory. Zbl 0632.62003
Kullback, S.; Keegel, J. C.; Kullback, J. H.
1987
A note on minimum discrimination information. Zbl 0143.20904
Kullback, S.; Khairat, M. A.
1966
An application of information theory to multivariate analysis. Zbl 0047.13503
Kullback, S.
1952
An application of information theory to the analysis of contingency tables, with a table of $$2n \ln n$$, $$n = 1(1) 10,000$$. Zbl 0107.13601
Kullback, Solomon; Kupperman, M.; Ku, Harry H.
1962
The minimum discrimination information approach in analyzing categorical data. Zbl 0385.62037
Gokhale, D. V.; Kullback, S.
1978
An information-theoretic derivation of certain limit relations for a stationary Markov chain. Zbl 0199.21301
Kullback, S.
1966
An information theoretic proof of the integral representation theorem. Zbl 0405.94004
Kullback, S.; Thall, Peter F.
1977
Tests for contingency tables and Markov chains. Zbl 0133.12004
Kullback, Solomon; Kupperman, M.; Ku, Harry H.
1962
An application of information theory to multivariate analysis. II. Zbl 0075.29204
Kullback, S.
1956
An application of characteristic functions to the distribution problem of statistics. JFM 60.1169.01
Kullback, S.
1934
Categorical data problems using information theoretic approach. Zbl 0597.62055
Kullback, S.; Keegel, J. C.
1984
An extension of an information-theoretic derivation of certain limit relations for a Markov chain. Zbl 0183.20001
Kullback, S.
1967
On the Charlier type $$B$$ series. Zbl 0030.03801
Kullback, S.
1947
Loglinear models in contingency table analysis. Zbl 0317.62036
Ku, Harry H.; Kullback, Solomon
1974
A bound for the variation of Gaussian densities. Zbl 0187.15002
Kullback, S.
1969
On certain distributions derived from the multinomial distribution. Zbl 0018.03305
Kullback, Solomon
1937
On certain distributions derived from the multinomial distribution. JFM 63.1087.02
Kullback, S.
1937
The distribution laws of the difference and quotient of variables independently distributed in Pearson type III laws. Zbl 0014.07302
Kullback, Solomon
1936
A note on Sheppard’s corrections. Zbl 0012.17502
Kullback, Solomon
1935
Information theory and statistics. Reprint of the 2nd ed. ’68. Zbl 0897.62003
Kullback, Solomon
1997
Topics in statistical information theory. Zbl 0632.62003
Kullback, S.; Keegel, J. C.; Kullback, J. H.
1987
Categorical data problems using information theoretic approach. Zbl 0597.62055
Kullback, S.; Keegel, J. C.
1984
The information in contingency tables. Zbl 0405.62002
Gokhale, D. V.; Kullback, Solomon
1978
Information analysis of linear interactions in contingency tables. Zbl 0382.62044
Kullback, S.; Gokhale, D. V.
1978
The minimum discrimination information approach in analyzing categorical data. Zbl 0385.62037
Gokhale, D. V.; Kullback, S.
1978
An information theoretic proof of the integral representation theorem. Zbl 0405.94004
Kullback, S.; Thall, Peter F.
1977
Loglinear models in contingency table analysis. Zbl 0317.62036
Ku, Harry H.; Kullback, Solomon
1974
Marginal homogeneity of multidimensional contingency tables. Zbl 0215.54305
Kullback, S.
1971
Approximating discrete probability distributions. Zbl 0174.23202
Ku, Harry H.; Kullback, Solomon
1969
A bound for the variation of Gaussian densities. Zbl 0187.15002
Kullback, S.
1969
Interaction in multidimensional contingency tables: an information theoretic approach. Zbl 0274.62036
Ku, H. H.; Kullback, S.
1968
Contingency tables with given marginals. Zbl 0155.26701
Ireland, C. T.; Kullback, S.
1968
Probability densities with given marginals. Zbl 0165.20303
Kullback, S.
1968
Information theory and statistics. Zbl 0149.37901
Kullback, S.
1967
An extension of an information-theoretic derivation of certain limit relations for a Markov chain. Zbl 0183.20001
Kullback, S.
1967
A note on minimum discrimination information. Zbl 0143.20904
Kullback, S.; Khairat, M. A.
1966
An information-theoretic derivation of certain limit relations for a stationary Markov chain. Zbl 0199.21301
Kullback, S.
1966
An application of information theory to the analysis of contingency tables, with a table of $$2n \ln n$$, $$n = 1(1) 10,000$$. Zbl 0107.13601
Kullback, Solomon; Kupperman, M.; Ku, Harry H.
1962
Tests for contingency tables and Markov chains. Zbl 0133.12004
Kullback, Solomon; Kupperman, M.; Ku, Harry H.
1962
Information theory and statistics. Zbl 0088.10406
Kullback, Solomon
1959
On the analysis of multiple regression in $$k$$ categories. Zbl 0082.35201
Kullback, S.; Rosenblatt, H. M.
1957
An application of information theory to multivariate analysis. II. Zbl 0075.29204
Kullback, S.
1956
Certain inequalities in information theory and the Cramer-Rao inequality. Zbl 0057.35402
Kullback, S.
1954
An application of information theory to multivariate analysis. Zbl 0047.13503
Kullback, S.
1952
On information and sufficiency. Zbl 0042.38403
Kullback, S.; Leibler, R. A.
1951
On the Charlier type $$B$$ series. Zbl 0030.03801
Kullback, S.
1947
On certain distributions derived from the multinomial distribution. Zbl 0018.03305
Kullback, Solomon
1937
On certain distributions derived from the multinomial distribution. JFM 63.1087.02
Kullback, S.
1937
The distribution laws of the difference and quotient of variables independently distributed in Pearson type III laws. Zbl 0014.07302
Kullback, Solomon
1936
A note on Sheppard’s corrections. Zbl 0012.17502
Kullback, Solomon
1935
An application of characteristic functions to the distribution problem of statistics. JFM 60.1169.01
Kullback, S.
1934
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#### Cited by 3,297 Authors
21 Nalewajski, Roman F. 21 Pardo, Leandro 20 Soofi, Ehsan S. 19 Kárný, Miroslav 19 Sugiyama, Masashi 16 Taneja, Inder Jeet 14 Dragomir, Sever Silvestru 14 Ebrahimi, Nader D. 14 Morales, Domingo 12 Cavanaugh, Joseph E. 12 Pečarić, Josip 12 Taneja, Harish Chander 11 Bozdogan, Hamparsum 11 Gzyl, Henryk 11 Menéndez, María Luisa 11 Pečaric, Đilda 10 Guiasu, Silviu 10 Majda, Andrew J. 10 Moral, Serafín 10 Vajda, Igor 10 Yanagihara, Hirokazu 10 Zografos, Konstantinos G. 9 Golan, Amos 9 Karagrigoriou, Alex , Skiadas, Christos H. 9 Salmerón, Antonio 8 Cano, Andrés 8 Judge, George G. 8 Konishi, Sadanori 8 Niven, Robert K. 8 Suzuki, Taiji 8 Tagliani, Aldo 7 Gokhale, D. V. 7 Kanamori, Takafumi 7 Pardo, Julio Angel 7 Pardo Llorente, María del Carmen 7 Park, Sangun 7 Petz, Dénes 7 Salicrú, Miquel 7 Walker, Stephen Grahm 6 Balakrishnan, Narayanaswamy 6 Brockett, Patrick L. 6 Drovandi, Christopher C. 6 Gil, María Angeles 6 Kannappan, Pl. 6 Malvestuto, Francesco Mario 6 Mattheou, Kyriacos 6 Nath, Pran 6 Pavon, Michele 6 Rathie, Pushpa Narayan 6 Toscani, Giuseppe 6 Villa, Cristiano 5 Ay, Nihat 5 Choi, Hwan-sik 5 Devarajan, Karthik 5 Fang, Shu-Cherng 5 Fang, Weiwu 5 Frank, Till Daniel 5 Friston, Karl J. 5 Ghanem, Roger G. 5 Girardin, Valerie 5 Guy, Tatiana Valentine 5 Jumarie, Guy M. 5 Kundu, Chanchal 5 Li, Tze Fen 5 McGree, James M. 5 Nagy, Ivan 5 Plastino, Angel Luis 5 Savchenko, Andrey V. 5 Sayyareh, Abdolreza 5 Sharma, Bhu Dev 5 Sukumar, Natarajan 5 Yamada, Makoto 5 Yanagimoto, Takemi 4 Abellán, Joaquín 4 Akaike, Hirotugu 4 Ando, Tomohiro 4 Arizono, Ikuo 4 Asadi, Majid 4 Bar-Hen, Avner 4 Basu, Ayanendranath 4 Ben-Tal, Aharon 4 Bernardo, Jose-Miguel 4 Bhattacharjee, S. K. 4 Bhattacharya, Bhaskar 4 Chang, Shui-Ching 4 Chen, Nan 4 Commenges, Daniel 4 de Campos, Luis Miguel 4 Dunsmore, Ian R. 4 Ferentinos, Kosmas 4 Georgiou, Tryphon T. 4 Gomez Villegas, Miguel Angel 4 Grim, Jiří 4 Ikeda, Sadao 4 Kamps, Udo 4 Kikianty, Eder 4 Kirmani, Syed N. U. A. 4 Klafszky, Emil 4 Kulhavý, Rudolf 4 Kumar, Satish ...and 3,197 more Authors
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#### Cited in 426 Serials
88 Communications in Statistics. Theory and Methods 62 Information Sciences 60 Journal of Statistical Planning and Inference 54 Computational Statistics and Data Analysis 47 Journal of Econometrics 42 Annals of the Institute of Statistical Mathematics 41 Journal of Multivariate Analysis 39 International Journal of Approximate Reasoning 33 Kybernetika 32 Statistics & Probability Letters 29 Journal of Statistical Computation and Simulation 28 Communications in Statistics. Simulation and Computation 26 Metrika 26 Neural Computation 24 Journal of Mathematical Chemistry 24 Entropy 23 Pattern Recognition 20 Applied Mathematics and Computation 19 Psychometrika 19 Statistics 19 European Journal of Operational Research 19 Journal of Applied Statistics 18 Linear Algebra and its Applications 17 Journal of Statistical Physics 17 Physics Letters. A 17 Automatica 15 Journal of Computational Physics 15 Journal of Mathematical Physics 15 Journal of Computational and Applied Mathematics 15 Journal of Mathematical Psychology 14 Computer Methods in Applied Mechanics and Engineering 14 The Annals of Statistics 14 Neural Networks 14 Electronic Journal of Statistics 14 Statistics and Computing 14 Journal of Theoretical Biology 13 Computers & Mathematics with Applications 13 Biometrical Journal 13 Chaos 11 International Journal of General Systems 11 Physica A 11 Reports on Mathematical Physics 11 Biometrics 11 Physica D 11 Machine Learning 11 Test 10 International Journal of Systems Science 10 Journal of Mathematical Analysis and Applications 10 Theoretical Computer Science 9 Artificial Intelligence 9 Communications in Mathematical Physics 9 Bulletin of Mathematical Biology 9 Fuzzy Sets and Systems 9 Kybernetes 9 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 9 Insurance Mathematics & Economics 9 International Journal of Adaptive Control and Signal Processing 9 Computational Statistics 9 Statistical Papers 8 Journal of Information & Optimization Sciences 8 Annals of Operations Research 8 Open Systems & Information Dynamics 8 Journal of Inequalities and Applications 8 Methodology and Computing in Applied Probability 8 Statistical Methodology 8 Kodai Mathematical Seminar Reports 8 SIAM/ASA Journal on Uncertainty Quantification 7 Synthese 7 Stochastic Processes and their Applications 7 Mathematical Problems in Engineering 6 Biological Cybernetics 6 International Journal of Theoretical Physics 6 Inverse Problems 6 Information Processing Letters 6 Journal of the Franklin Institute 6 Chaos, Solitons and Fractals 6 Journal of Optimization Theory and Applications 6 Theoretical Population Biology 6 Trabajos de Estadistica y de Investigacion Operativa 6 Systems & Control Letters 6 Journal of Economic Dynamics & Control 6 Economics Letters 6 Applications of Mathematics 6 Applied Mathematical Modelling 6 Journal of Nonparametric Statistics 6 Data Mining and Knowledge Discovery 6 Journal of Statistical Mechanics: Theory and Experiment 6 Bayesian Analysis 5 Physics Reports 5 Scandinavian Journal of Statistics 5 Cybernetics and Systems 5 Optimization 5 Statistical Science 5 Econometric Reviews 5 Computers & Operations Research 5 Annals of Physics 5 Automation and Remote Control 5 Journal of Mathematical Imaging and Vision 5 Bernoulli 5 Mathematical Inequalities & Applications ...and 326 more Serials
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#### Cited in 54 Fields
1,164 Statistics (62-XX) 423 Information and communication theory, circuits (94-XX) 281 Computer science (68-XX) 221 Probability theory and stochastic processes (60-XX) 207 Numerical analysis (65-XX) 162 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 131 Biology and other natural sciences (92-XX) 121 Operations research, mathematical programming (90-XX) 98 Statistical mechanics, structure of matter (82-XX) 83 Systems theory; control (93-XX) 70 Quantum theory (81-XX) 48 Real functions (26-XX) 39 Dynamical systems and ergodic theory (37-XX) 32 Partial differential equations (35-XX) 31 Functional analysis (46-XX) 26 Combinatorics (05-XX) 26 Operator theory (47-XX) 24 Fluid mechanics (76-XX) 23 Linear and multilinear algebra; matrix theory (15-XX) 22 Measure and integration (28-XX) 22 Difference and functional equations (39-XX) 19 Geophysics (86-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 17 Mathematical logic and foundations (03-XX) 17 Mechanics of deformable solids (74-XX) 16 Differential geometry (53-XX) 13 Ordinary differential equations (34-XX) 9 Integral transforms, operational calculus (44-XX) 9 Convex and discrete geometry (52-XX) 8 Optics, electromagnetic theory (78-XX) 7 General and overarching topics; collections (00-XX) 7 Classical thermodynamics, heat transfer (80-XX) 7 Relativity and gravitational theory (83-XX) 5 Astronomy and astrophysics (85-XX) 4 Integral equations (45-XX) 3 History and biography (01-XX) 3 Number theory (11-XX) 3 Functions of a complex variable (30-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Special functions (33-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Algebraic geometry (14-XX) 2 Approximations and expansions (41-XX) 2 Geometry (51-XX) 2 Algebraic topology (55-XX) 2 Mechanics of particles and systems (70-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-04-11T02:16:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4512688219547272, "perplexity": 7622.3282515368455}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038060603.10/warc/CC-MAIN-20210411000036-20210411030036-00432.warc.gz"} |
https://indico.fnal.gov/event/19348/contributions/186553/ | Indico search will be reestablished in the next version upgrade of the software: https://getindico.io/roadmap/
# Neutrino 2020
June 22, 2020 to July 2, 2020
US/Central timezone
## Neutral Pion Production on CH at $<E_{\nu}> \sim 6$ GeV.
Not scheduled
10m
Poster
### Speaker
Ms Barbara Yaeggy (Universidad Tecnica Federico Santa Maria)
### Description
Quasi-elastic scattering is generally used to measure oscillation due to being the channel where final state interactions and energy reconstruction are best understood. However, the most important background comes from the pion resonances, in which the pion might not be observed due to final state interactions. This is particularly true for CC neutral pion production from the Delta resonance. In this work we study a sample of charged current $(\pi^{0})$ production in the scattering channel $\nu_{\mu} + CH \longrightarrow \mu^{-} + \pi^{0} + X (nucleons)$ on a hydrocarbon target using the medium energy NuMI beam (peak energy of ∼ 6 GeV). We encounter the scenario where neutral pions are misidentified. Event when improvements in traditional methods were introduced, these were not efficient enough to distinguish between charged pions and neutral pions. To overcome this issue we determined to use a machine learning (ML) approach via semantic segmentation method. This is the process of partitioning a digital image into multiple segments, linking each pixel in an image to a class label (particles). We present here traditional reconstruction techniques employed for neutral pion and a comparison with ML for the final selection.
### Mini-abstract
Pion FS interactions of $\nu_{\mu} + CH \longrightarrow \mu^{-} + \pi^{0} + X (nucleons)$ in MINERvA
### Primary author
Ms Barbara Yaeggy (Universidad Tecnica Federico Santa Maria) | 2021-11-30T09:20:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5212851166725159, "perplexity": 2289.8478380955808}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358966.62/warc/CC-MAIN-20211130080511-20211130110511-00598.warc.gz"} |
https://par.nsf.gov/biblio/10381306-demographics-quasars-black-hole-massluminosity-plane | This content will become publicly available on October 18, 2023
Demographics of z ∼ 6 quasars in the black hole mass–luminosity plane
ABSTRACT We study the demographics of z ∼ 6 broad-line quasars in the black hole (BH) mass–luminosity plane using a sample of more than 100 quasars at 5.7 < z < 6.5. These quasars have well-quantified selection functions and nearly one-third of them also have virial BH masses estimated from near-IR spectroscopy. We use forward modelling of parametrized intrinsic distributions of BH masses and Eddington ratios, and account for the sample flux limits and measurement uncertainties of the BH masses and luminosities. We find significant differences between the intrinsic and observed distributions of the quantities due to measurement uncertainties and sample flux limits. There is also marginal evidence that the virial BH masses are susceptible to a positive luminosity-dependent bias (BH mass is overestimated when luminosity is above the average), and that the mean Eddington ratio increases with BH mass. Our models provide reliable constraints on the z ∼ 6 BH mass function at $M_{\rm BH}\gt 10^{8.5}\, M_\odot$, with a median 1σ uncertainty of ∼0.5 dex in abundance. The intrinsic Eddington ratio distribution of $M_{\rm BH}\gt 10^{8.5}\, M_\odot$ quasars can be approximated by a mass-dependent Schechter model, with a broad peak around log (Lbol/LEdd) ∼ −0.9. We also find that, at more »
Authors:
; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10381306
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
517
Issue:
2
Page Range or eLocation-ID:
2659 to 2676
ISSN:
0035-8711
National Science Foundation
##### More Like this
1. ABSTRACT
Direct collapse black holes (BHs) are promising candidates for producing massive z ≳ 6 quasars, but their formation requires fine-tuned conditions. In this work, we use cosmological zoom simulations to study systematically the impact of requiring: (1) low gas angular momentum (spin), and (2) a minimum incident Lyman–Werner (LW) flux in order to form BH seeds. We probe the formation of seeds (with initial masses of $M_{\rm seed} \sim 10^4\!-\!10^6\, \mathrm{M}_{\odot }\, h^{-1})$ in haloes with a total mass >3000 × Mseed and a dense, metal-poor gas mass >5 × Mseed. Within this framework, we find that the seed-forming haloes have a prior history of star formation and metal enrichment, but they also contain pockets of dense, metal-poor gas. When seeding is further restricted to haloes with low gas spins, the number of seeds formed is suppressed by factors of ∼6 compared to the baseline model, regardless of the seed mass. Seed formation is much more strongly impacted if the dense, metal-poor gas is required to have a critical LW flux (Jcrit). Even for Jcrit values as low as 50J21, no $8\times 10^{5}~\mathrm{M}_{\odot }\, h^{-1}$ seeds are formed. While lower mass ($1.25\times 10^{4},1\times 10^{5}~\mathrm{M}_{\odot }\, h^{-1}$) seeds do form, they are strongly suppressed (by factors of ∼10–100) comparedmore »
2. Abstract
We present ALMA [C ii] line and far-infrared (FIR) continuum observations of three $z \gt 6$ low-luminosity quasars ($M_{\rm 1450} \gt -25$ mag) discovered by our Subaru Hyper Suprime-Cam (HSC) survey. The [C ii] line was detected in all three targets with luminosities of $(2.4\mbox{--}9.5) \times 10^8\, L_{\odot }$, about one order of magnitude smaller than optically luminous ($M_{\rm 1450} \lesssim -25$ mag) quasars. The FIR continuum luminosities range from $\lt 9 \times 10^{10}\, L_{\odot }$ (3 $\sigma$ limit) to ${\sim } 2 \times 10^{12}\, L_{\odot }$, indicating a wide range in star formation rates in these galaxies. Most of the HSC quasars studied thus far show [C ii]/ FIR luminosity ratios similar to local star-forming galaxies. Using the [C ii]-based dynamical mass ($M_{\rm dyn}$) as a surrogate for bulge stellar mass ($M_{\rm\, bulge}$), we find that a significant fraction of low-luminosity quasars are located on or even below the local $M_{\rm\, BH}$–$M_{\rm\, bulge}$ relation, particularly at the massive end of the galaxy mass distribution. In contrast, previous studies of optically luminous quasars have found that black holes are overmassive relative to the local relation. Given the low luminosities of our targets, we are exploring the nature of the early co-evolution of supermassive black holes andmore »
3. ABSTRACT
We explore implications of a range of black hole (BH) seeding prescriptions on the formation of the brightest $z$ ≳ 6 quasars in cosmological hydrodynamic simulations. The underlying galaxy formation model is the same as in the IllustrisTNG simulations. Using constrained initial conditions, we study the growth of BHs in rare overdense regions (forming $\gtrsim 10^{12}\, {\rm M}_{\odot }\,h^{-1}$ haloes by $z$ = 7) using a (9 Mpc h−1)3 simulated volume. BH growth is maximal within haloes that are compact and have a low tidal field. For these haloes, we consider an array of gas-based seeding prescriptions wherein $M_{\mathrm{seed}}=10^4\!-\!10^6\, {\rm M}_{\odot }\,h^{-1}$ seeds are inserted in haloes above critical thresholds for halo mass and dense, metal-poor gas mass (defined as $\tilde{M}_{\mathrm{h}}$ and $\tilde{M}_{\mathrm{sf,mp}}$, respectively, in units of Mseed). We find that a seed model with $\tilde{M}_{\mathrm{sf,mp}}=5$ and $\tilde{M}_{\mathrm{h}}=3000$ successfully produces a $z$ ∼ 6 quasar with $\sim 10^9\, {\rm M}_{\odot }$ mass and ∼1047 erg s−1 luminosity. BH mergers play a crucial role at $z$ ≳ 9, causing an early boost in BH mass at a time when accretion-driven BH growth is negligible. With more stringent seeding conditions (e.g. $\tilde{M}_{\mathrm{sf,mp}}=1000$), the relative paucity of BH seeds results in a much lower merger rate. In this case, $z$more »
4. ABSTRACT
The elemental abundances in the broad-line regions of high-redshift quasars trace the chemical evolution in the nuclear regions of massive galaxies in the early Universe. In this work, we study metallicity-sensitive broad emission-line flux ratios in rest-frame UV spectra of 25 high-redshift (5.8 < z < 7.5) quasars observed with the VLT/X-shooter and Gemini/GNIRS instruments, ranging over $\log \left({{M}_{\rm {BH}}/\rm {M}_{\odot }}\right) = 8.4-9.8$ in black hole mass and $\log \left(\rm {L}_{\rm {bol}}/\rm {erg \, s}^{-1}\right) = 46.7-47.7$ in bolometric luminosity. We fit individual spectra and composites generated by binning across quasar properties: bolometric luminosity, black hole mass, and blueshift of the C iv line, finding no redshift evolution in the emission-line ratios by comparing our high-redshift quasars to lower redshift (2.0 < z < 5.0) results presented in the literature. Using cloudy-based locally optimally emitting cloud photoionization model relations between metallicity and emission-line flux ratios, we find the observable properties of the broad emission lines to be consistent with emission from gas clouds with metallicity that are at least 2–4 times solar. Our high-redshift measurements also confirm that the blueshift of the C iv emission line is correlated with its equivalent width, which influences line ratios normalized against C iv. When accountingmore »
5. ABSTRACT
We present 10 main-sequence ALPINE galaxies (log (M/M⊙) = 9.2−11.1 and ${\rm SFR}=23-190\, {\rm M_{\odot }\, yr^{-1}}$) at z ∼ 4.5 with optical [O ii] measurements from Keck/MOSFIRE spectroscopy and Subaru/MOIRCS narrow-band imaging. This is the largest such multiwavelength sample at these redshifts, combining various measurements in the ultraviolet, optical, and far-infrared including [C ii]158 $\mu$m line emission and dust continuum from ALMA and H α emission from Spitzer photometry. For the first time, this unique sample allows us to analyse the relation between [O ii] and total star-formation rate (SFR) and the interstellar medium (ISM) properties via [O ii]/[C ii] and [O ii]/H α luminosity ratios at z ∼ 4.5. The [O ii]−SFR relation at z ∼ 4.5 cannot be described using standard local descriptions, but is consistent with a metal-dependent relation assuming metallicities around $50{{\ \rm per\ cent}}$ solar. To explain the measured dust-corrected luminosity ratios of $\log (L_{\rm [OII]}/L_{\rm [CII]}) \sim 0.98^{+0.21}_{-0.22}$ and $\log (L_{\rm [OII]}/L_{\rm H\alpha }) \sim -0.22^{+0.13}_{-0.15}$ for our sample, ionization parameters log (U) < −2 and electron densities $\log (\rm n_e / {\rm [cm^{-3}]}) \sim 2.5-3$ are required. The former is consistent with galaxies at z ∼ 2−3, however lower than at z > 6. The latter may be slightly higher than expected given the galaxies’ specific SFR. Themore » | 2023-03-25T23:59:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6667670011520386, "perplexity": 2942.622407798581}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945376.29/warc/CC-MAIN-20230325222822-20230326012822-00727.warc.gz"} |
https://mooseframework.inl.gov/source/userobjects/CrystalPlasticityStateVariable.html | # CrystalPlasticityStateVariable
## Description
CrystalPlasticityStateVariable represents a state variable, such as dislocation density in crystal plasticity system. The initial values of this state variable are either provided in the input file readInitialValueFromInline() or read from the file readInitialValueFromFile(). The state variable evolves as is the state variable evolution rate. The can have multiple components, such as where "" are the scale_factor and are the individual rate components.
## Input Parameters
• variable_sizeThe userobject's variable size.
C++ Type:unsigned int
Options:
Description:The userobject's variable size.
### Required Parameters
• group_valuesThe initial values correspoinding to each group, i.e. '0.0 1.0 2.0' means 0-4 = 0.0, 4-8 = 1.0 and 8-12 = 2.0
C++ Type:std::vector
Options:
Description:The initial values correspoinding to each group, i.e. '0.0 1.0 2.0' means 0-4 = 0.0, 4-8 = 1.0 and 8-12 = 2.0
• state_variable_file_nameName of the file containing the initial values of slip system resistances
C++ Type:FileName
Options:
Description:Name of the file containing the initial values of slip system resistances
• scale_factorScale factor of individual component.
C++ Type:std::vector
Options:
Description:Scale factor of individual component.
• zero0Numerical zero for interval variable
Default:0
C++ Type:double
Options:
Description:Numerical zero for interval variable
• groupsTo group the initial values on different slip systems 'format: [start end)', i.e.'0 4 8 11' groups 0-3, 4-7 and 8-11
C++ Type:std::vector
Options:
Description:To group the initial values on different slip systems 'format: [start end)', i.e.'0 4 8 11' groups 0-3, 4-7 and 8-11
• uo_state_var_evol_rate_comp_nameName of state variable evolution rate component property: Same as state variable evolution rate component user object specified in input file.
C++ Type:std::vector
Options:
Description:Name of state variable evolution rate component property: Same as state variable evolution rate component user object specified in input file.
• intvar_read_typeinline_inputRead from options for initial value of internal variables: Default from .i file
Default:inline_input
C++ Type:MooseEnum
Options:file_input inline_input user_input
Description:Read from options for initial value of internal variables: Default from .i file
• blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
### Optional Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
• allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Options:
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
• seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
• implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form | 2019-04-23T13:57:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21506381034851074, "perplexity": 6673.356842193037}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578605510.53/warc/CC-MAIN-20190423134850-20190423160850-00365.warc.gz"} |
http://www.scstatehouse.gov/sess120_2013-2014/SJ14/20140408.htm | South Carolina General Assembly
120th Session, 2013-2014
Journal of the Senate
Tuesday, April 8, 2014
(Statewide Session)
Indicates Matter Stricken
Indicates New Matter
The Senate assembled at 12:00 Noon, the hour to which it stood adjourned, and was called to order by the PRESIDENT.
A quorum being present, the proceedings were opened with a devotion by the Chaplain as follows:
The prophet Micah writes:
"Do not rejoice over me, O my enemy; when I fall, I shall rise; when I sit in darkness, the Lord will be a light to me."
(Micah 7:8)
Bow with me in prayer, please:
Holy God, inevitably there come those moments when these servants of our State truly feel themselves overwhelmed by the enormity of their responsibilities. And when those pressures befall the Senators and aides who serve in this place, may each person feel the same confidence that consumed the prophet: the clear knowledge that You are with them, just as You were there strengthening and leading Micah so long ago. Inspire each leader here as You alone can, O God, and bring about a sense of bold hopefulness to each one. This we pray in Your loving name, dear Lord. Amen.
The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers.
MESSAGE FROM THE GOVERNOR
The following appointments were transmitted by the Honorable Nikki Randhawa Haley:
Statewide Appointments
Initial Appointment, South Carolina Crime Victim's Ombudsman, with term coterminous with Governor
Director:
Veronica Swain Kunz, 14 Southpine Court, Columbia, SC 29212 VICE Deborah D. Curtis
Referred to the Committee on Judiciary.
Initial Appointment, South Carolina State Board of Cosmetology, with the term to commence March 20, 2014, and to expire March 20, 2018
Cosmetologist:
Eddie L. Jones, 7 Hilltopper Court, Blythewood, SC 29016 VICE Ms. Ruth Settles
Referred to the Committee on Labor, Commerce and Industry.
Initial Appointment, South Carolina State Board of Cosmetology, with the term to commence March 31, 2008, and to expire March 31, 2012
Cosmetologist:
Patricia Walters, 809 Michaelmas Ave., Cayce, SC 29033 VICE Ms. Katherine Webb
Referred to the Committee on Labor, Commerce and Industry.
The following was received and referred to the appropriate committee for consideration:
Document No. 4350
Agency: South Carolina Criminal Justice Academy
Chapter: 37
Statutory Authority: 1976 Code Sections 23-23-10 et seq. and 23-47-20(C)(15)
SUBJECT: Law Enforcement Officer and E-911 Officer Training and Certification
Received by Lieutenant Governor April 8, 2014
Referred to Judiciary Committee
Legislative Review Expiration March 15, 2015
REGULATIONS RESUBMITTED
Document No. 4369
Agency: South Carolina Criminal Justice Academy
Chapter: 37
Statutory Authority: 1976 Code Section 23-47-20(C)(15)
SUBJECT: Allow E-911 Operators One Year to Attend Training at the Academy
Received by Lieutenant Governor May 1, 2013
Referred to Judiciary Committee
Legislative Review Expiration April 7, 2014
04/04/2014 Resubmitted
Document No. 4370
Agency: South Carolina Criminal Justice Academy
Chapter: 37
Statutory Authority: 1976 Code Section 23-47-20(C)(15)
SUBJECT: Requirement of Good Character (E-911 Operators)
Received by Lieutenant Governor May 1, 2013
Referred to Judiciary Committee
Legislative Review Expiration April 7, 2014
04/04/2014 Resubmitted
Document No. 4374
Agency: South Carolina Criminal Justice Academy
Chapter: 37
Statutory Authority: 1976 Code Section 23-47-20(C)(15)
SUBJECT: Application for Issuance or Re-issuance of Certification
Received by Lieutenant Governor May 1, 2013
Referred to Judiciary Committee
Legislative Review Expiration April 7, 2014
04/04/2014 Resubmitted
REGULATION WITHDRAWN
Document No. 4436
Agency: Board of Registration for Foresters
Chapter: 53
Statutory Authority: 1976 Code Sections 40-1-70 and 48-27-80
SUBJECT: Board of Registration for Foresters
Received by Lieutenant Governor January 23, 2014
Referred to Fish, Game and Forestry Committee
Legislative Review Expiration: Permanently Withdrawn
04/03/2014 Permanently Withdrawn
REGULATIONS WITHDRAWN AND RESUBMITTED
Document No. 4445
Agency: Department of Labor, Licensing and Regulation - Office of State Fire Marshal
Chapter: 71
Statutory Authority: 1976 Code Sections 23-9-40, 23-9-60, 23-9-550, 23-35-45, and 23-36-80
SUBJECT: Office of State Fire Marshal
Received by Lieutenant Governor February 4, 2014
Referred to Labor, Commerce and Industry Committee
Legislative Review Expiration June 4, 2014
04/03/2014 Withdrawn and Resubmitted
Document No. 4446
Agency: Department of Labor, Licensing and Regulation - Office of Occupational Safety and Health
Chapter: 71
Statutory Authority: 1976 Code Sections 41-3-40 and 41-15-210
SUBJECT: Enforcement of Violations
Received by Lieutenant Governor February 4, 2014
Referred to Labor, Commerce and Industry Committee
Legislative Review Expiration June 4, 2014
04/03/2014 Withdrawn and Resubmitted
Leave of Absence
On motion of Senator PEELER, at 12:05 P.M., Senators CLEARY and MASSEY were granted a leave of absence for today.
Expression of Personal Interest
Senator SHANE MARTIN rose for an Expression of Personal Interest.
S. 204 (Word version) Sens. Shane Martin, Grooms
S. 1100 (Word version) Sen. Setzler
S. 139 (Word version) Sen. Rankin
INTRODUCTION OF BILLS AND RESOLUTIONS
The following were introduced:
S. 1203 (Word version) -- Senator Alexander: A SENATE RESOLUTION TO DECLARE FRIDAY, JUNE 13, 2014, AS "CATHERINE DEVOE FISHER DAY" AND TO RECOGNIZE CATHERINE "CATIE" DEVOE FISHER ON HER MANY MUSICAL ACCOMPLISHMENTS.
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The Senate Resolution was introduced and referred to the Committee on Invitations.
S. 1204 (Word version) -- Senator Bryant: A CONCURRENT RESOLUTION TO DECLARE THE "GAIN MOMENTUM: BUSINESS EXPO AND SHRIMP & GRITS COOK-OFF" EVENT, HOSTED BY THE ANDERSON AREA CHAMBER OF COMMERCE, AS THE OFFICIAL STATE SHRIMP & GRITS COOK-OFF.
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The Concurrent Resolution was introduced and referred to the Committee on Agriculture and Natural Resources.
S. 1205 (Word version) -- Senators Matthews and Hutto: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR THE COURAGE AND SACRIFICE OF THE ELLOREE 21 IN ORANGEBURG COUNTY, A GROUP OF TEACHERS IN ELLOREE WHO CHANGED THE COURSE OF HISTORY OF THE CIVIL RIGHTS MOVEMENT IN SOUTH CAROLINA, AND TO COMMEND THEIR ROLE IN SECURING EQUALITY FOR AFRICAN-AMERICAN CITIZENS OF OUR STATE.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 1206 (Word version) -- Senator Alexander: A BILL TO AMEND SECTION 12-54-122, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO TAX LIENS, SO AS TO ALLOW THE DEPARTMENT OF REVENUE TO FILE TAX LIENS VALIDLY BY IMPLEMENTING AN INTERNET ACCESSIBLE NOTICE SYSTEM.
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Read the first time and referred to the Committee on Finance.
S. 1207 (Word version) -- Medical Affairs Committee: A BILL TO AMEND SECTION 24-21-440, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PERIODS OF PROBATION, SO AS TO TOLL THE PERIOD DURING PERIODS OF CIVIL COMMITMENT; TO AMEND SECTION 24-21-560, AS AMENDED, RELATING TO COMMUNITY SUPERVISION PROGRAMS, SO AS TO TOLL THE COMMUNITY SUPERVISION PERIOD DURING PERIODS OF CIVIL COMMITMENT; AND TO AMEND SECTION 24-21-670, RELATING TO PERIODS OF PAROLE, SO AS TO TOLL THE PAROLE PERIOD DURING PERIODS OF CIVIL COMMITMENT.
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Read the first time and ordered placed on the Calendar without reference.
S. 1208 (Word version) -- Senator Matthews: A SENATE RESOLUTION TO HONOR MARGARET BERRY BAYLOR OF ORANGEBURG COUNTY FOR HER MANY YEARS OF DEDICATED COMMUNITY AND PUBLIC SERVICE AND TO WISH HER MUCH SUCCESS AND FULFILLMENT IN ALL HER FUTURE ENDEAVORS.
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S. 1209 (Word version) -- Senators Courson, Peeler, Setzler and Jackson: A CONCURRENT RESOLUTION TO HONOR DR. DONALD L. FOWLER FOR HIS DISTINGUISHED CAREER IN PUBLIC SERVICE AND TO CONGRATULATE HIM ON A HALF CENTURY OF TEACHING AT THE UNIVERSITY OF SOUTH CAROLINA.
l:\council\bills\rm\1564htc14.docx
The Concurrent Resolution was adopted, ordered sent to the House.
S. 1210 (Word version) -- Senator McGill: A SENATE RESOLUTION TO CONGRATULATE THE WILLIAMSBURG ACADEMY "STALLIONS" FOOTBALL TEAM ON CAPTURING THE 2013 SOUTH CAROLINA INDEPENDENT SCHOOLS ASSOCIATION 1A STATE FOOTBALL CHAMPIONSHIP TITLE AND TO ALSO CONGRATULATE THEM ON AN OUTSTANDING FOOTBALL SEASON.
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S. 1211 (Word version) -- Senators Thurmond, McElveen, Hembree and Setzler: A SENATE RESOLUTION TO RECOGNIZE THAT CHILDHOOD OBESITY HAS A PROFOUND IMPACT AND IS A SERIOUS HEALTH RISK FOR YOUTH IN THE STATE OF SOUTH CAROLINA AND TO ENCOURAGE ALL CITIZENS OF THIS GREAT STATE TO PARTICIPATE IN ACTIVITIES THAT PROMOTE HEALTHY EATING AND PHYSICAL ACTIVITY.
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H. 4499 (Word version) -- Reps. Cole, Spires, Sottile, D. C. Moss, Tallon, Allison, Rivers, Finlay, M. S. McLeod, Hardee, Norrell, Brannon, Atwater, Bowen, Weeks, V. S. Moss, Neal, Whipper, Nanney, Gilliard, Anderson, Bales, G. A. Brown, R. L. Brown, Forrester, Hamilton, Mack, Wells, Willis and Wood: A BILL TO AMEND SECTION 56-1-140, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ISSUANCE OF A DRIVER'S LICENSE, SO AS TO REMOVE THE ONE DOLLAR FEE CHARGED BY THE DEPARTMENT OF MOTOR VEHICLES FOR THE PLACEMENT OF A VETERAN DESIGNATION ON A DRIVER'S LICENSE.
Read the first time and referred to the Committee on Transportation.
H. 4650 (Word version) -- Reps. Bannister, Bedingfield, Simrill, Burns and Henderson: A BILL TO AMEND SECTION 59-5-65, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO POWERS AND RESPONSIBILITIES OF THE STATE BOARD OF EDUCATION, SO AS TO PROVIDE THE BOARD SHALL ESTABLISH BEFORE AUGUST 1, 2014, A PROFICIENCY-BASED SYSTEM AS AN ALTERNATIVE TO TRADITIONAL SEAT-TIME REQUIREMENTS FOR CHILDREN NOT EXEMPT FROM COMPULSORY SCHOOL ATTENDANCE REQUIREMENTS, TO PROVIDE THE SYSTEM MUST BE OPTIONAL FOR SCHOOL DISTRICTS, AND TO DEFINE NECESSARY TERMS; AND TO AMEND SECTION 59-65-90, RELATING TO RULES AND REGULATIONS CONCERNING STUDENT ATTENDANCE REQUIREMENTS, SO AS TO MAKE A CONFORMING CHANGE.
Read the first time and referred to the Committee on Education.
H. 4802 (Word version) -- Reps. Burns, Loftis, G. R. Smith and Willis: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION ERECT INDIVIDUAL SIGNS AT TWO MILE INTERVALS ALONG INTERSTATE HIGHWAY 385 FROM MILE MARKER 22 TO MILE MARKER 34 THAT CONTAIN THE WORDS "WORLD WAR I 1917-1918", "WORLD WAR II 1941-1945", "THE KOREAN WAR 1950-1953", "THE VIETNAM WAR 1956-1975", "SECOND PERSIAN GULF WAR 'OPERATION DESERT STORM' 1991", "AFGHANISTAN WAR OCTOBER 7, 2001 TO PRESENT", AND "THIRD PERSIAN GULF WAR MARCH 19, 2003 TO PRESENT".
The Concurrent Resolution was introduced and referred to the Committee on Transportation.
H. 4900 (Word version) -- Reps. Gilliard, Whipper, Mack, Kennedy, Stavrinakis, Murphy, Willis, Harrell and Williams: A JOINT RESOLUTION TO DIRECT THE DEPARTMENT OF TRANSPORTATION TO CONDUCT A COST-BENEFIT STUDY TO DETERMINE THE FEASIBILITY OF ERECTING A PEDESTRIAN OVERPASS AT THE INTERSECTION OF THE SEPTIMA P. CLARK PARKWAY AND COMING STREET IN THE CITY OF CHARLESTON.
Read the first time and referred to the Committee on Transportation.
H. 4945 (Word version) -- Rep. Goldfinch: A BILL TO AMEND SECTION 50-5-1705, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO CATCH LIMITS IMPOSED ON THE TAKING OF CERTAIN FISH, SO AS TO IMPOSE CATCH LIMITS FOR TAKING OR POSSESSING IN ANY ONE DAY A COMBINATION OF SPOT, WHITING, AND ATLANTIC CROAKER.
Read the first time and referred to the Committee on Fish, Game and Forestry.
H. 5042 (Word version) -- Reps. Horne, Alexander, Allison, Anderson, Anthony, Atwater, Bales, Ballentine, Bannister, Barfield, Bedingfield, Bernstein, Bingham, Bowen, Bowers, Branham, Brannon, G. A. Brown, R. L. Brown, Burns, Chumley, Clemmons, Clyburn, Cobb-Hunter, Cole, H. A. Crawford, K. R. Crawford, Crosby, Daning, Delleney, Dillard, Douglas, Edge, Erickson, Felder, Finlay, Forrester, Funderburk, Gagnon, Gambrell, George, Gilliard, Goldfinch, Govan, Hamilton, Hardee, Hardwick, Harrell, Hart, Hayes, Henderson, Herbkersman, Hiott, Hixon, Hodges, Hosey, Howard, Huggins, Jefferson, Kennedy, King, Knight, Limehouse, Loftis, Long, Lowe, Lucas, Mack, McCoy, McEachern, M. S. McLeod, W. J. McLeod, Merrill, Mitchell, D. C. Moss, V. S. Moss, Munnerlyn, Murphy, Nanney, Neal, Newton, Norman, Norrell, R. L. Ott, Owens, Parks, Patrick, Pitts, Pope, Putnam, Quinn, Ridgeway, Riley, Rivers, Robinson-Simpson, Rutherford, Ryhal, Sabb, Sandifer, Sellers, Simrill, Skelton, G. M. Smith, G. R. Smith, J. E. Smith, J. R. Smith, Sottile, Southard, Spires, Stavrinakis, Stringer, Tallon, Taylor, Thayer, Toole, Vick, Weeks, Wells, Whipper, White, Whitmire, Williams, Willis and Wood: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR THE OUTSTANDING HEALTH CARE THAT NURSE PRACTITIONERS AND CERTIFIED NURSE MIDWIVES PROVIDE IN OUR STATE AND TO DECLARE THURSDAY, APRIL 3, 2014, THE COALITION FOR ACCESS TO HEALTH CARE'S ANNUAL "NURSE PRACTITIONER AND CERTIFIED NURSE MIDWIFE DAY" IN SOUTH CAROLINA.
The Concurrent Resolution was adopted, ordered returned to the House.
H. 5069 (Word version) -- Rep. Hodges: A CONCURRENT RESOLUTION TO HONOR MARIAN WRIGHT EDELMAN, FOUNDER AND PRESIDENT OF THE CHILDREN'S DEFENSE FUND, ON HER LIFETIME OF SERVING AS AN AMBASSADOR FOR DISADVANTAGED AMERICANS AND TO CONGRATULATE HER ON BEING INDUCTED INTO THE SOUTH CAROLINA HALL OF FAME.
The Concurrent Resolution was adopted, ordered returned to the House.
HOUSE CONCURRENCE
S. 1153 (Word version) -- Senator Courson: A CONCURRENT RESOLUTION TO AUTHORIZE PALMETTO GIRLS STATE TO USE THE CHAMBERS OF THE SENATE AND THE HOUSE OF REPRESENTATIVES ON FRIDAY, JUNE 13, 2014.
Returned with concurrence.
THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR.
CARRIED OVER
S. 459 (Word version) -- Senators Sheheen and Rankin: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 56-1-55, SO AS TO PROVIDE THAT IT IS UNLAWFUL FOR A PERSON WHO HOLDS A BEGINNER'S PERMIT OR A RESTRICTED DRIVER'S LICENSE TO DRIVE A MOTOR VEHICLE WHILE USING A CELLULAR TELEPHONE OR TEXT MESSAGING DEVICE; AND TO PROVIDE THAT IT IS UNLAWFUL FOR A PERSON TO DRIVE A MOTOR VEHICLE THROUGH A SCHOOL ZONE WHILE USING A CELLULAR TELEPHONE OR TEXT MESSAGING DEVICE WHEN THE SCHOOL ZONE'S WARNING LIGHTS HAVE BEEN ACTIVATED.
On motion of Senator MALLOY, the Bill was carried over.
S. 862 (Word version) -- Senators Shealy and Turner: A BILL TO AMEND SECTION 40-59-260 OF THE 1976 CODE, RELATING TO THE EXCEPTION FOR PROJECTS BY A PROPERTY OWNER FOR PERSONAL USE, TO PROVIDE THAT AN OWNER OF RESIDENTIAL PROPERTY WHO IMPROVES THE PROPERTY OR WHO BUILDS OR IMPROVES THE STRUCTURES OR APPURTENANCES ON THE PROPERTY AT A COST OF MORE THAN TWO THOUSAND FIVE HUNDRED DOLLARS SHALL NOT WITHIN TWO YEARS AFTER COMPLETION OR ISSUANCE OF A CERTIFICATE OFFER THE STRUCTURE FOR SALE OR RENT, AND CONSTRUCTION OR IMPROVEMENTS TO THE STRUCTURE, GROUP OF STRUCTURES, OR APPURTENANCES THAT COST THE OWNER-BUILDER LESS THAN TWO THOUSAND FIVE HUNDRED DOLLARS ARE NOT EVIDENCE OF "SALE" OR "RENT" FOR THE PURPOSES OF THIS SECTION.
On motion of Senator ALEXANDER, the Bill was carried over.
On motion of Senator MALLOY, the Bill was carried over.
S. 375 (Word version) -- Senators Hutto, L. Martin, Johnson and Rankin: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 38 TO TITLE 6 SO AS TO ENACT THE "DILAPIDATED BUILDINGS ACT", TO PROVIDE DEFINITIONS, TO PROVIDE THAT A MUNICIPALITY MAY BRING A CAUSE OF ACTION AGAINST THE OWNER OF PROPERTY NOT IN SUBSTANTIAL COMPLIANCE WITH CERTAIN MUNICIPAL ORDINANCES, TO IDENTIFY WHO MAY SERVE AS A COURT-APPOINTED RECEIVER FOR PROPERTY SUBJECT TO THIS CAUSE OF ACTION, TO DESIGNATE THE POWERS OF A COURT-APPOINTED RECEIVER, TO ESTABLISH REPORTING REQUIREMENTS OF THE MUNICIPALITY CONCERNING A VIOLATION AGAINST WHICH THE MUNICIPALITY MAY BRING A CAUSE OF ACTION UNDER THIS ACT, AND TO PROVIDE CERTAIN REMEDIES AND PROCEDURES.
On motion of Senator SHANE MARTIN, the Bill was carried over.
H. 3124 (Word version) -- Reps. Bingham, Taylor, Long and M.S. McLeod: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 63-7-315 SO AS TO PROHIBIT AN EMPLOYER FROM DISMISSING, DEMOTING, SUSPENDING, OR DISCIPLINING AN EMPLOYEE WHO REPORTS CHILD ABUSE OR NEGLECT, WHETHER REQUIRED OR PERMITTED TO REPORT; AND TO CREATE A CAUSE OF ACTION FOR REINSTATEMENT AND BACK PAY WHICH AN EMPLOYEE MAY BRING AGAINST AN EMPLOYER WHO VIOLATES THIS PROHIBITION.
On motion of Senator YOUNG, the Bill was carried over.
H. 3191 (Word version) -- Reps. Cole and Tallon: A BILL TO AMEND SECTIONS 56-5-130 AND 56-5-140, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEFINITION OF THE TERMS "MOTOR VEHICLE" AND "MOTORCYCLE", SO AS TO PROVIDE THAT MOPEDS ARE MOTOR VEHICLES AND NOT MOTORCYCLES.
On motion of Senator HUTTO, the Bill was carried over.
H. 4259 (Word version) -- Reps. Goldfinch and Clemmons: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 16-17-760 SO AS TO ENACT THE "SOUTH CAROLINA MILITARY SERVICE INTEGRITY AND PRESERVATION ACT", TO PROVIDE THAT A PERSON WHO, WITH THE INTENT OF SECURING A TANGIBLE BENEFIT, KNOWINGLY AND FALSELY REPRESENTS HIMSELF TO HAVE SERVED IN THE ARMED FORCES OF THE UNITED STATES OR TO HAVE BEEN AWARDED A DECORATION, MEDAL, RIBBON, OR OTHER DEVICE AUTHORIZED BY CONGRESS OR PURSUANT TO FEDERAL LAW FOR THE ARMED FORCES OF THE UNITED STATES, IS GUILTY OF A MISDEMEANOR.
On motion of Senator SCOTT, the Bill was carried over.
H. 3631 (Word version) -- Reps. Daning, Crosby, Sottile, Atwater, Sabb, Erickson, Newton and Herbkersman: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 56-3-115 SO AS TO PROVIDE FOR THE ISSUANCE OF GOLF CART PERMITS, TO REGULATE THE OPERATION OF GOLF CARTS, AND TO PROVIDE A PENALTY; AND TO REPEAL SECTION 56-2-105 RELATING TO THE ISSUANCE OF GOLF CART PERMITS AND THE OPERATION OF GOLF CARTS.
On motion of Senator SCOTT, the Bill was carried over.
S. 894 (Word version) -- Senators Massey and Alexander: A BILL TO AMEND CHAPTER 1, TITLE 14 OF THE 1976 CODE, RELATING TO GENERAL PROVISIONS APPLICABLE TO COURTS, BY ADDING SECTION 14-1-240, TO PROVIDE THAT A FIVE DOLLAR SURCHARGE TO FUND TRAINING AT THE SOUTH CAROLINA CRIMINAL JUSTICE ACADEMY SHALL BE LEVIED ON ALL FINES, FORFEITURES, ESCHEATMENTS, OR OTHER MONETARY PENALTIES IMPOSED IN THE GENERAL SESSIONS COURT OR IN MAGISTRATES OR MUNICIPAL COURT FOR MISDEMEANOR TRAFFIC OFFENSES OR FOR NONTRAFFIC VIOLATIONS.
On motion of Senator BRIGHT, the Bill was carried over.
S. 1187 (Word version) -- Labor, Commerce and Industry Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE MANUFACTURED HOUSING BOARD, RELATING TO FINANCIAL RESPONSIBILITY, DESIGNATED AS REGULATION DOCUMENT NUMBER 4438, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
On motion of Senator ALEXANDER, the Joint Resolution was carried over.
S. 1188 (Word version) -- Labor, Commerce and Industry Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE CONTRACTORS LICENSING BOARD, RELATING TO REGULATIONS ADMINISTERING FIRE PROTECTION SPRINKLER SYSTEMS ACT, DESIGNATED AS REGULATION DOCUMENT NUMBER 4418, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
On motion of Senator ALEXANDER, the Joint Resolution was carried over.
S. 919 (Word version) -- Senator L. Martin: A BILL TO AMEND SECTION 43-7-60, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO FALSE CLAIMS, STATEMENTS, AND REPRESENTATIONS FOR PURPOSES OF QUALIFYING FOR AND RECEIVING PAYMENT FOR AND REIMBURSEMENT OF MEDICAID CLAIMS AND BENEFITS, SO AS TO PROHIBIT ANY PERSON FROM ENGAGING IN THE PROHIBITED CONDUCT AND TO EXPAND OFFENSES AND PENALTIES FOR VIOLATING THE PROVISIONS OF THE ARTICLE; AND TO AMEND SECTION 43-7-90, RELATING TO ENFORCEMENT OF THE ARTICLE, SO AS TO PROVIDE THE ATTORNEY GENERAL, OR A DESIGNEE, ADDITIONAL POWERS.
Senator HUTTO explained the Bill.
On motion of Senator MALLOY, the Bill was carried over.
The following Bills were read the third time and ordered sent to the House of Representatives:
S. 1032 (Word version) -- Senators Campsen, Verdin and Reese: A BILL TO AMEND SECTION 48-39-130 OF THE 1976 CODE, RELATING TO PERMITS REQUIRED FOR COASTAL ZONE CRITICAL AREAS, TO INCLUDE TEMPORARY QUALIFIED WAVE DISSIPATION DEVICES AS A TECHNIQUE TO BE USED IN THE BEACH/DUNE CRITICAL AREA TO PROTECT THE PUBLIC HEALTH AND SAFETY; TO AMEND SECTION 48-39-270, RELATING TO TERMS PERTAINING TO COASTAL TIDELANDS AND WETLANDS, TO DEFINE QUALIFIED WAVE DISSIPATION DEVICE; AND TO AMEND SECTION 48-39-290, RELATING TO CONSTRUCTION RESTRICTIONS SEAWARD OF THE BASELINE, TO PROVIDE AN EXCEPTION FOR QUALIFIED WAVE DISSIPATION DEVICES.
S. 1036 (Word version) -- Senator Cleary: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 3 TO CHAPTER 15, TITLE 40 SO AS TO ENACT THE "DENTAL SEDATION ACT", TO PROVIDE REQUIREMENTS CONCERNING THE PROVISION OF VARYING LEVELS OF SEDATION TO DENTAL PATIENTS; TO AMEND SECTION 40-15-85, RELATING TO DEFINITIONS IN THE DENTISTRY PRACTICE ACT, SO AS TO ADD NECESSARY DEFINITIONS; AND TO DESIGNATE THE EXISTING SECTIONS OF CHAPTER 15, TITLE 40 AS ARTICLE 1 "GENERAL PROVISIONS".
S. 1085 (Word version) -- Senators Campbell, Grooms, Matthews, McGill, O'Dell and Bennett: A BILL TO AMEND SECTION 4-37-30, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, RELATING TO THE USE OF LOCAL SALES AND USE TAX OR TOLL REVENUES TO FINANCE TRANSPORTATION INFRASTRUCTURE IN A COUNTY, SO AS TO PROVIDE A PROCEDURE FOR THE GOVERNING BODY OF A COUNTY IN WHICH THE TRANSPORTATION INFRASTRUCTURE LOCAL SALES AND USE TAX IS CURRENTLY IMPOSED FOR LESS THAN THE TWENTY-FIVE YEAR MAXIMUM IMPOSITION PERIOD, UPON REFERENDUM APPROVAL, MAY EXTEND WITHOUT INTERRUPTION THE INITIAL IMPOSITION FOR AN IMPOSITION PERIOD IN THE AGGREGATE NOT TO EXCEED TWENTY-FIVE YEARS, TO PROVIDE WHAT QUESTIONS MUST APPEAR ON THE REFERENDUM BALLOT, TO PROVIDE THAT A REFERENDUM FOR OTHER THAN THE INITIAL IMPOSITION OF THE TAX MAY BE HELD AT THE TIME OF EITHER A GENERAL OR SPECIAL ELECTION IN THE COUNTY, AS THE GOVERNING BODY OF THE COUNTY MAY DETERMINE, AND TO PROVIDE THAT THE GOVERNING BODY OF A COUNTY IN WHICH THE TRANSPORTATION INFRASTRUCTURE LOCAL SALES AND USE TAX IS CURRENTLY IMPOSED, WITHIN TWO YEARS OF THE TERMINATION OF THE TAX OR THE ANTICIPATED TERMINATION OF THE TAX AND UPON REFERENDUM APPROVAL, MAY RENEW WITHOUT INTERRUPTION THE IMPOSITION OF THE TAX AND PROVIDE THAT NO MORE THAN ONE REFERENDUM RELATING TO THIS TAX BE HELD IN A CALENDAR YEAR.
S. 1085--Recorded Vote
Senators BRYANT, SHANE MARTIN and BRIGHT desired to be recorded as voting against the third reading of the Bill.
S. 1099 (Word version) -- Senators Sheheen and Bryant: A BILL TO AMEND SECTION 41-27-260 OF THE 1976 CODE, RELATING TO EXEMPTIONS FROM THE DEFINITION OF EMPLOYMENT FOR UNEMPLOYMENT BENEFIT PURPOSES, TO PROVIDE AN EXEMPTION FOR MOTOR CARRIERS THAT UTILIZE INDEPENDENT CONTRACTORS.
S. 1100 (Word version) -- Senators Bryant, Sheheen, Young and Setzler: A BILL TO AMEND ARTICLE 3, CHAPTER 27, TITLE 41 OF THE 1976 CODE, RELATING TO DEFINITIONS CONCERNING UNEMPLOYMENT BENEFITS AND CLAIMS, BY ADDING SECTION 41-27-265, TO PROVIDE THAT CORPORATE OFFICERS ARE EXEMPT FROM UNEMPLOYMENT BENEFITS UNLESS THE EMPLOYER ELECTS COVERAGE, AND TO PROVIDE FOR THE PROCESS OF ELECTING COVERAGE, AND TO PROVIDE FOR FEDERALLY REQUIRED EXEMPTIONS FROM THE PROVISIONS OF THIS SECTION FOR INDIVIDUALS EMPLOYED BY AN INDIAN TRIBE AND RELIGIOUS, CHARITABLE, EDUCATIONAL, OR OTHER FEDERALLY DEFINED ORGANIZATIONS.
CARRIED OVER
S. 1178 (Word version) -- Senators Hembree and Campsen: A BILL TO AMEND ARTICLE 10, CHAPTER 11, TITLE 50 OF THE 1976 CODE, RELATING TO WILDLIFE MANAGEMENT AREAS, TO PROVIDE THAT A HUNTER'S PRIVILEGE TO PARTICIPATE IN LOTTERY HUNTS MAY BE REVOKED IF A DEPARTMENT OF NATURAL RESOURCES ENFORCEMENT OFFICER WITNESSES, OR HAS PROBABLE CAUSE TO BELIEVE THAT, A VIOLATION OF THE ARTICLE HAS OCCURRED; AND TO PROVIDE FOR REMEDIES IF THE HUNTER IS NOT CONVICTED OF VIOLATIONS OF THIS ARTICLE ARISING FROM THE LOTTERY HUNT.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Fish, Game and Forestry.
The Committee on Fish, Game and Forestry proposed the following amendment (1178R001.GEC), which was adopted:
Amend the bill, as and if amended, page 1, by striking line 36 and inserting:
/ arising from the occurrence precipitating the revocation of his /
Renumber sections to conform.
Amend title to conform.
Senator HEMBREE explained the committee amendment.
The question then was second reading of the Bill.
On motion of Senator HEMBREE, the Bill was carried over.
COMMITTED
S. 1186 (Word version) -- Labor, Commerce and Industry Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF LABOR, LICENSING AND REGULATION - OFFICE OF OCCUPATIONAL SAFETY AND HEALTH, RELATING TO ENFORCEMENT OF VIOLATIONS, DESIGNATED AS REGULATION DOCUMENT NUMBER 4446, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
Senator ALEXANDER moved to commit the Joint Resolution to the Committee on Labor, Commerce and Industry.
The Joint Resolution was committed to the Committee on Labor, Commerce and Industry.
H. 4644 (Word version) -- Rep. Sandifer: A BILL TO AMEND SECTION 40-60-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, AND SECTIONS 40-60-31, 40-60-33, 40-60-34, 40-60-35, AS AMENDED, 40-60-36, 40-60-37, 40-60-38, 40-60-80, AND 40-60-220, ALL RELATING TO THE SOUTH CAROLINA REAL ESTATE APPRAISERS LICENSE AND CERTIFICATION ACT, SO AS TO CONFORM THE PROVISIONS TO CERTAIN REVISED NATIONAL UNIFORM STANDARDS FOR LICENSING, CERTIFYING, AND RECERTIFYING REAL ESTATE APPRAISERS.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the previously proposed amendment as follows.
Senator HUTTO proposed the following amendment (4644MW1), which was adopted:
Amend the bill, as and if amended, page 4, by striking Section 40-60-31(2)(C) and inserting:
/ (c) a bachelor's degree or its equivalent as promulgated by the board through regulation to become a state-certified residential appraiser or state-certified general appraiser; /
Further amend the bill, as and if amended, page 5, by striking Section 40-60-33(2) and inserting:
/ (2) To qualify as a state-licensed appraiser, an applicant shall: /
Further amend the bill, as and if amended, page 6, by striking Section 40-60-33(3) and inserting:
/ (3) To qualify as a state-certified residential appraiser, an applicant shall: /
Further amend the bill, as and if amended, page 6, by striking Section 40-60-33(4) and inserting:
/ (4) To qualify as a state-certified general appraiser an applicant shall: /
Further amend the bill, as and if amended, by striking Section 40-60-33(5) and inserting:
/ (5) To qualify as a licensed mass appraiser, state-certified residential mass appraiser, or state-certified general mass appraiser, the applicant shall satisfy the requirements enumerated in this section, and any other applicable provisions of this chapter to qualify, respectively, as a licensed appraiser, state-certified residential appraiser, and state-certified general appraiser, with the exception that one hundred percent of the required experience hours for the mass appraiser designations may be in the area of mass appraisals." /
Further amend the bill, as and if amended, page 12, by striking Section 40-60-220 and inserting:
/ "Section 40-60-220. A person who is licensed as a licensed appraiser, licensed mass appraiser, state-certified residential appraiser, state-certified residential mass appraiser, state-certified general appraiser, or state-certified general mass appraiser on December 31, 2007 2014, may continue licensure in that category without meeting the requirements of Section 40-60-31 and Section 40-60-33, so long as the person is otherwise authorized to hold such the license." /
Renumber sections to conform.
Amend title to conform.
Senator HUTTO explained the amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 36; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Corbin Courson
Cromer Davis Fair
Grooms Hayes Hembree
Hutto Jackson Johnson
Kimpson Leatherman Malloy
Martin, Larry Martin, Shane Matthews
McElveen McGill Nicholson
O'Dell Peeler Scott
Setzler Sheheen Thurmond
Turner Verdin Young
Total--36
NAYS
Total--0
There being no further amendments, the Bill was read the second time and ordered placed on the Third Reading Calendar.
S. 356 (Word version) -- Senators Alexander and Reese: A BILL TO AMEND CHAPTER 1, TITLE 26, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO NOTARIES PUBLIC, SO AS TO DEFINE TERMS, TO MAKE GRAMMATICAL CORRECTIONS, TO PROVIDE THAT TO BE QUALIFIED FOR A NOTARIAL COMMISSION, A PERSON MUST BE REGISTERED TO VOTE AND READ AND WRITE IN THE ENGLISH LANGUAGE, TO AUTHORIZE AND PROHIBIT CERTAIN ACTS OF A NOTARY PUBLIC, TO PROVIDE MAXIMUM FEE A NOTARY MAY CHARGE, TO PROVIDE THE PROCESS FOR GIVING A NOTARIAL CERTIFICATE, TO SPECIFY CHANGES FOR WHICH A NOTARY MUST NOTIFY THE SECRETARY OF STATE, TO PROVIDE THE ELEMENTS AND PENALTIES OF CERTAIN CRIMES RELATING TO NOTARIAL ACTS, AND TO PROVIDE THE FORM FOR A NOTARIZED DOCUMENT SENT TO ANOTHER STATE, AMONG OTHER THINGS.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
The Committee on Judiciary proposed the following amendment (JUD0356.003), which was adopted:
Amend the bill, as and if amended, by striking Section 26-1-160, beginning on line 8 on page 14 and inserting:
/ Section 26-1-160. (A) Except as otherwise permitted by law, a person who commits one of the following acts is guilty of a misdemeanor:
(1) holding one's self out to the public as a notary if the person does not have a commission;
(2) performing a notarial act if the person's commission has expired or been suspended or restricted; or
(3) performing a notarial act before the person had taken the oath of office.
(B) A notary is guilty of a misdemeanor if the notary takes:
(1) an acknowledgment or administers an oath or affirmation without the principal appearing in person before the notary;
(2) a verification or proof without the subscribing witness appearing in person before the notary;
(3) an acknowledgment or administers an oath or affirmation without personal knowledge or satisfactory evidence of the identity of the principal;
(4) a verification or proof without personal knowledge or satisfactory evidence of the identity of the subscribing witness; or
(5) an acknowledgment or a verification or proof or administers an oath or affirmation if the notary knows it is false or fraudulent.
C) It is a misdemeanor for a person to perform notarial acts in this State with the knowledge that he is not commissioned pursuant to this chapter.
(D) A person who without authority obtains, uses, conceals, defaces, or destroys the seal or notarial records of a notary is guilty of a misdemeanor.
(E) A person who knowingly solicits, coerces, or in a material way influences a notary to commit official misconduct is guilty of aiding and abetting and is subject to the same level of punishment as the notary.
(F) The sanctions and remedies of this chapter supplement other sanctions and remedies provided by law.
(G) A notary public convicted under the provisions of this section must forfeit his commission and must not be issued another commission. The court in which the notary public is convicted shall notify the Secretary of State within ten days after conviction.
(H) A person who violates the provisions of subsections (A), (B), (C), (D), or (E) is guilty of a misdemeanor and, upon conviction, must be fined not more than five hundred dollars or imprisoned for not more than thirty days. /
To further amend the bill, as and if amended, by striking Section 26-1-230(B), beginning on line 38 on page 16 and inserting:
/ (B) The Secretary shall not issue a certificate of authority or an Apostille if:
(1) a seal or signature cannot be authenticated by either the Secretary or another official;
(2) the seal or signature is of a foreign official; or
(3) the document is a facsimile, photocopy, photographic, or other reproduction of a signature or seal. /
To further amend the bill, as and if amended, by striking SECTION 2, line 13 on page 17 and inserting:
/ SECTION 2. The provisions of this act are severable. If any section, subsection, paragraph, subparagraph, item, subitem, sentence, clause, phrase, or word of this act is for any reason held to be unconstitutional or invalid, such holding shall not affect the constitutionality or validity of the remaining portions of the act, the General Assembly hereby declaring that it would have passed each and every section, subsection, paragraph, subparagraph, item, subitem, sentence, clause, phrase, and word thereof, irrespective of the fact that any one or more other sections, subsections, paragraphs, subparagraphs, items, subitems, sentences, clauses, phrases, or words hereof may be declared to be unconstitutional, invalid, or otherwise ineffective.
SECTION 3. This act takes effect upon approval by the Governor./ Renumber sections to conform.
Amend title to conform.
Senator LARRY MARTIN explained the committee amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 38; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Corbin Courson
Cromer Davis Fair
Grooms Hayes Hembree
Hutto Jackson Kimpson
Leatherman Lourie Malloy
Martin, Larry Martin, Shane McElveen
McGill Nicholson O'Dell
Peeler Pinckney Rankin
Reese Scott Setzler
Sheheen Thurmond Turner
Verdin Young
Total--38
NAYS
Total--0
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
H. 4604 (Word version) -- Reps. Sandifer, Mack and Toole: A BILL TO AMEND SECTION 40-22-280, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO EXEMPTIONS FROM THE LICENSURE REQUIREMENT TO PRACTICE ENGINEERING, SO AS TO PROVIDE AN EXEMPTION FOR CERTAIN ACTIVITIES PERFORMED BY FULL-TIME EMPLOYEES OR OTHER PERSONNEL OF A MANUFACTURING COMPANY, AND TO DEFINE NECESSARY TERMS.
The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill.
Senator O'DELL explained the Bill.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 39; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Corbin Courson
Cromer Davis Fair
Grooms Hayes Hembree
Hutto Johnson Kimpson
Leatherman Lourie Malloy
Martin, Larry Martin, Shane Matthews
McElveen McGill Nicholson
O'Dell Peeler Pinckney
Rankin Reese Scott
Setzler Sheheen Thurmond
Turner Verdin Young
Total--39
NAYS
Total--0
The Bill was read the second time and ordered placed on the Third Reading Calendar.
S. 779 (Word version) -- Senator Davis: A BILL TO AMEND CHAPTER 19, TITLE 16 OF THE 1976 CODE, RELATING TO GAMBLING AND LOTTERIES, BY ADDING SECTION 16-19-60, TO PROVIDE THAT CERTAIN SOCIAL CARD AND DICE GAMES ARE NOT UNLAWFUL.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
The Committee on Judiciary proposed the following amendment (JUD0779.004), which was adopted:
Amend the bill, as and if amended, by striking all after the enacting words and inserting the following:
/ SECTION 1. Chapter 19, Title 16 of the 1976 Code is amended by adding:
"Section 16-19-60. Notwithstanding any other provision of law to the contrary, it is not unlawful for persons who are members of a club or other social organization to gather for the purpose of engaging in games of tiles, cards, or dice, including, but not limited to, canasta, mahjong, and bridge, where the games are played among members in a private residence, home, or community clubhouse or similar structure; no mechanical or electronic devices or machines of any kind, slot machines, pull tabs, punch boards, pull boards, or video games, devices, or machines of any kind are used or incorporated in any way; no person or entity of any kind receives any direct or indirect economic, financial, or monetary benefit of any kind; the host of the game or owner or lessee of the location in which the games are played does not receive any direct or indirect economic, financial, or monetary benefit of any kind; there is no betting, wagering, or gambling of any kind; a bona fide social relationship among the participants exists; and, except for the advantage of skill or luck, the risks of losing or winning are the same for all parties."
SECTION 2. This act takes effect upon approval by the Governor./
Renumber sections to conform.
Amend title to conform.
Senator DAVIS explained the committee amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 39; Nays 0; Present 1
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Coleman Corbin
Courson Cromer Davis
Fair Grooms Hembree
Hutto Jackson Johnson
Kimpson Leatherman Lourie
Malloy Martin, Larry Martin, Shane
McElveen McGill Nicholson
O'Dell Peeler Pinckney
Rankin Reese Scott
Setzler Sheheen Thurmond
Turner Verdin Young
Total--39
NAYS
Total--0
PRESENT
Hayes
Total--1
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
S. 813 (Word version) -- Senators Hayes, Peeler, O'Dell, Alexander, McElveen, McGill, Pinckney, Johnson, Williams and Verdin: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 16-11-625 SO AS TO PROVIDE A PERSON WHO, WITHOUT LEGAL CAUSE OR GOOD EXCUSE, ENTERS A PUBLIC LIBRARY AFTER HAVING BEEN WARNED BY AN EMPLOYEE, AGENT, OR REPRESENTATIVE OF THE LIBRARY NOT TO DO SO OR WITHOUT HAVING BEEN WARNED FAILS AND REFUSES, WITHOUT GOOD CAUSE OR GOOD EXCUSE, TO LEAVE IMMEDIATELY UPON BEING ORDERED OR REQUESTED TO DO SO IS GUILTY OF A MISDEMEANOR TRIABLE IN A MUNICIPAL OR MAGISTRATES COURT, AND TO PROVIDE THE PROVISIONS OF THIS SECTION MUST BE CONSTRUED AS IN ADDITION TO, AND NOT AS SUPERSEDING, ANOTHER STATUTE RELATING TO TRESPASS OR UNLAWFUL ENTRY ON LANDS OF ANOTHER.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
The Committee on Judiciary proposed the following amendment (JUD0813.001), which was adopted:
Amend the bill, as and if amended, by striking SECTION 1 and inserting:
/ SECTION 1. Article 7, Chapter 11, Title 16 of the 1976 Code is amended by adding:
"Section 16-11-625. (A)(1) A person who enters a public library, without legal cause or good excuse, after having been warned not to do so by the library director, the branch manager, or the acting branch manager of the library in consultation with the library director is guilty of a misdemeanor and, upon conviction, must be fined not more than two hundred dollars or be imprisoned not more than thirty days.
(2) A copy of the warning provided for by subsection (A)(1) must be given to the person in writing, in the presence of a law enforcement officer, and must state:
(a) the alleged criminal law violation or the alleged violation of the library's code of conduct promulgated by the library's board of trustees under the authority provided by Section 4-9-37(b);
(b) the duration of the prohibition to return; and
(c) the procedure by which the person may appeal the warning to the library board of trustees.
(B) A person who fails and refuses to leave the library immediately, without good cause or good excuse, upon being ordered or requested to do so by law enforcement, the library director, the branch manager, or the acting branch manager of the library in consultation with the library director is guilty of a misdemeanor and, upon conviction, must be fined not more than two hundred dollars or be imprisoned not more than thirty days. A previous written warning is not required to enforce the provisions of this subsection.
(C) A violation of the provisions of this section is triable in the appropriate municipal or magistrates court with jurisdiction over the offense. Any law enforcement officer of this State or a subdivision of this State may enforce the provisions of this section within their respective jurisdictions.
(D) The provisions of this section must be construed as in addition to, and not as superseding, another statute relating to trespass or unlawful entry on lands of another." /
Renumber sections to conform.
Amend title to conform.
Senator LARRY MARTIN explained the committee amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 32; Nays 6
AYES
Alexander Allen Campbell
Coleman Courson Cromer
Davis Fair Gregory
Grooms Hayes Hutto
Johnson Kimpson Leatherman
Lourie Malloy Martin, Larry
Martin, Shane McElveen McGill
Nicholson O'Dell Peeler
Pinckney Reese Scott
Setzler Sheheen Thurmond
Turner Young
Total--32
NAYS
Bennett Bright Bryant
Corbin Hembree Verdin
Total--6
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
S. 1084 (Word version) -- Senators Nicholson, Scott, Williams, Hutto, Cromer, Campbell, O'Dell, Reese, Lourie, Coleman, Kimpson and Sheheen: A BILL TO AMEND SECTIONS 44-29-150 AND 44-29-160, CODE OF LAWS OF SOUTH CAROLINA, 1976, BOTH RELATING TO PERSONS APPLYING FOR EMPLOYMENT IN SCHOOLS, KINDERGARTENS, NURSERY, OR DAYCARE CENTERS TO BE TESTED FOR AND FREE FROM ACTIVE TUBERCULOSIS AND PROVIDING THAT RETESTING OF CONSECUTIVELY RETURNING EMPLOYEES IS NOT REQUIRED, SO AS TO REQUIRE INDIVIDUALS RETURNING TO EMPLOYMENT IN CONSECUTIVE YEARS IN THESE SETTINGS TO BE TESTED AND FREE FROM TUBERCULOSIS IN AN ACTIVE STAGE.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Medical Affairs.
Senator HUTTO proposed the following amendment (S-1084 AMENDMENT1), which was adopted:
Amend the committee amendment, as and if amended, page [1084-2] by striking lines 9-20 and inserting:
/ SECTION 2. This act takes effect upon approval by the Governor, and beginning with the 2014-2015 school year applies to individuals applying for employment. Provided that all existing employees, and employees returning to employment in consecutive years in public or private schools, kindergartens, nurseries, or childcare facilities for infants and children of the State have until the beginning of the 2015-2016 school year to be appropriately evaluated for tuberculosis. And further provided that all existing employees and employees returning to employment in consecutive years who possess a health certificate dated within five years prior to the effective date of this act from a licensed physician certifying that such person does not have tuberculosis in an active state are exempt from the requirement to be tested prior to the 2014-2015 school year. /
Renumber sections to conform.
Amend title to conform.
Senator NICHOLSON explained the amendment.
The Committee on Medical Affairs proposed the following amendment (S-1083), which was adopted:
Amend the bill, as and if amended, by striking all after the enacting words and inserting:
/ SECTION 1. Sections 44-29-150 and 44-29-160 of the 1976 Code are amended to read:
"Section 44-29-150. No person will be An individual must not be initially hired or enter into a full time contract to work in any public or private school, kindergarten, nursery, or day care center childcare facility for infants and children until appropriately evaluated for tuberculosis according to guidelines approved by the Board of Health and Environmental Control. Re-evaluation will not be required for employment in consecutive years unless otherwise indicated by such guidelines. Public or private schools, kindergartens, nurseries, or childcare facilities shall require employees or full time contracted workers to be reevaluated for tuberculosis every five years. These evaluations shall be kept on file with the custodian of records. As a condition of continued employment, any employee or contracted worker testing positive for tuberculosis, shall secure a health certificate from a licensed physician certifying that such person does not have tuberculosis in an active stage.
Section 44-29-160. Any person An individual applying for a position in any of the public or private schools, kindergartens, nurseries, or day care centers childcare facilities for infants and children of the State shall, as a prerequisite to employment, secure a health certificate from a licensed physician certifying that such person does not have tuberculosis in an active stage."
SECTION 2. This act takes effect upon approval by the Governor, and beginning with the 2014-2015 school year, applies to individuals applying for employment, to all existing employees, and to employees returning to employment in consecutive years in public or private schools, kindergartens, nurseries, or childcare facilities for infants and children of the State. Provided that all existing employees and employees returning to employment in consecutive years who possess a health certificate dated within five years prior to the effective date of this act from a licensed physician certifying that such person does not have tuberculosis in an active state are exempt from the requirement to be tested prior to the 2014-2015 school year. /
Renumber sections to conform.
Amend title to conform.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 37; Nays 0
AYES
Allen Bennett Bright
Bryant Campbell Campsen
Coleman Corbin Courson
Cromer Davis Fair
Gregory Grooms Hayes
Hutto Jackson Johnson
Kimpson Leatherman Lourie
Malloy Martin, Larry Martin, Shane
McElveen McGill Nicholson
Peeler Rankin Reese
Scott Setzler Sheheen
Thurmond Turner Verdin
Young
Total--37
NAYS
Total--0
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
S. 1096 (Word version) -- Senators Campsen and Cromer: A BILL TO AMEND SECTION 50-5-1705 OF THE 1976 CODE, RELATING TO CATCH LIMITS IMPOSED ON THE TAKING OF CERTAIN FISH, TO IMPOSE CATCH LIMITS FOR TAKING OR POSSESSING IN ANY ONE DAY A COMBINATION OF SPOT, WHITING, AND ATLANTIC CROAKER.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Fish, Game and Forestry.
The Committee on Fish, Game and Forestry proposed the following amendment (1096R001.GEC), which was adopted:
Amend the bill, as and if amended, page 2, by striking lines 4-7 and inserting:
/ (J) It is unlawful for a person to take or possess in any one day more than forty-five of a combination of the following: spot (Leiostomus xanthurus), whiting (Menticirrhus spp.), and Atlantic croaker (Micropogonias undulatus) taken by hook and line. /
Renumber sections to conform.
Amend title to conform.
Senator CAMPSEN explained the committee amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 36; Nays 1
AYES
Alexander Allen Bennett
Bryant Campbell Campsen
Coleman Corbin Cromer
Davis Fair Gregory
Grooms Hayes Hembree
Hutto Jackson Johnson
Kimpson Leatherman Lourie
Malloy Martin, Larry Martin, Shane
McElveen McGill Nicholson
Peeler Rankin Reese
Scott Setzler Thurmond
Turner Verdin Young
Total--36
NAYS
Bright
Total--1
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
S. 1198 (Word version) -- Medical Affairs Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL, RELATING TO WATER POLLUTION CONTROL PERMITS, DESIGNATED AS REGULATION DOCUMENT NUMBER 4444, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
The Senate proceeded to a consideration of the Joint Resolution, the question being the second reading of the Joint Resolution.
Senator HUTTO explained the Joint Resolution.
The question then was second reading of the Joint Resolution.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 38; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Coleman Corbin
Courson Cromer Davis
Fair Gregory Grooms
Hayes Hutto Johnson
Kimpson Leatherman Lourie
Malloy Martin, Larry Martin, Shane
McElveen McGill Nicholson
Peeler Pinckney Rankin
Reese Scott Setzler
Sheheen Thurmond Turner
Verdin Young
Total--38
NAYS
Total--0
The Joint Resolution was read the second time and ordered placed on the Third Reading Calendar.
H. 3968 (Word version) -- Reps. Hamilton, Alexander, Allison, Anderson, Anthony, Atwater, Bales, Ballentine, Bannister, Barfield, Bedingfield, Bernstein, Bingham, Bowen, Bowers, Branham, Brannon, G.A. Brown, R.L. Brown, Burns, Chumley, Clemmons, Clyburn, Cobb-Hunter, Cole, H.A. Crawford, K.R. Crawford, Crosby, Daning, Delleney, Dillard, Douglas, Edge, Erickson, Felder, Finlay, Forrester, Funderburk, Gagnon, Gambrell, George, Gilliard, Goldfinch, Govan, Hardee, Hardwick, Harrell, Hart, Hayes, Henderson, Herbkersman, Hiott, Hixon, Hodges, Horne, Hosey, Howard, Huggins, Jefferson, Kennedy, King, Knight, Limehouse, Loftis, Long, Lowe, Lucas, Mack, McCoy, McEachern, M.S. McLeod, W.J. McLeod, Merrill, Mitchell, D.C. Moss, V.S. Moss, Munnerlyn, Murphy, Nanney, Neal, Newton, Norman, H.L. Ott, Owens, Parks, Patrick, Pitts, Pope, Powers Norrell, Putnam, Quinn, Ridgeway, Riley, Rivers, Robinson-Simpson, Rutherford, Ryhal, Sabb, Sandifer, Sellers, Simrill, Skelton, G.M. Smith, G.R. Smith, J.E. Smith, J.R. Smith, Sottile, Southard, Spires, Stavrinakis, Stringer, Tallon, Taylor, Thayer, Toole, Vick, Weeks, Wells, Whipper, White, Whitmire, Williams, Willis and Wood: A CONCURRENT RESOLUTION TO PROCLAIM MAY 16, 2013, AS SENIOR HUNGER AWARENESS DAY IN SOUTH CAROLINA, TO ENCOURAGE ALL SOUTH CAROLINIANS TO LEARN MORE ABOUT THE IMPACT OF HUNGER AND MALNUTRITION ON THE HEALTH OF OUR CITIZENS AND ON THE PROGRESS OF OUR STATE, AND TO WORK TOGETHER FOR A HUNGER-FREE SOUTH CAROLINA.
The Senate proceeded to a consideration of the Concurrent Resolution, the question being the adoption of the Resolution.
The Committee on Medical Affairs proposed the following amendment (NBD\3968C002.NBD.AC14), which was adopted:
Amend the concurrent resolution, as and if amended, page 2, line 19 by deleting / May 16, 2013 / and inserting / May 9, 2014 /.
Amend the concurrent resolution further, by deleting the title on page 1, lines 11-17 and inserting:
/ TO PROCLAIM MAY 9, 2014, AS SENIOR HUNGER AWARENESS DAY IN SOUTH CAROLINA, TO ENCOURAGE ALL SOUTH CAROLINIANS TO LEARN MORE ABOUT THE IMPACT OF HUNGER AND MALNUTRITION ON THE HEALTH OF OUR CITIZENS AND ON THE PROGRESS OF OUR STATE, AND TO WORK TOGETHER FOR A HUNGER-FREE SOUTH CAROLINA. /
Renumber sections to conform.
Amend title to conform.
Senator HUTTO explained the committee amendment.
There being no further amendments, the Concurrent Resolution was adopted and ordered returned to the House with amendments.
Privilege of the Chamber
On motion of Senator BRYANT, on behalf of Senator MATTHEWS, with unanimous consent, the Privilege of the Chamber, to that area behind the rail, was extended to Dr. and Mrs. Henry Tisdale of Claflin University on the occasion of being named People of the Year by the Times and Democrat Newspaper.
Expression of Personal Interest
Senator BRIGHT rose for an Expression of Personal Interest.
THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD.
At 1:48 P.M., on motion of Senator PEELER, the Senate agreed to dispense with the balance of the Motion Period.
HAVING DISPENSED WITH THE MOTION PERIOD, THE SENATE PROCEEDED TO A CONSIDERATION OF BILLS AND RESOLUTIONS RETURNED FROM THE HOUSE.
AMENDMENT PROPOSED, CARRIED OVER
S. 137 (Word version) -- Senators Lourie, L. Martin, Hayes, Fair, Davis, Ford, Cromer, Grooms and Alexander: A BILL TO AMEND SECTION 56-1-286, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE SUSPENSION OF A DRIVER'S LICENSE OF A PERSON UNDER THE AGE OF TWENTY-ONE FOR HAVING AN UNLAWFUL ALCOHOL CONCENTRATION, SO AS TO REVISE THE PENALTIES TO INCLUDE REQUIRING AN OFFENDER WHO OPERATES A VEHICLE TO HAVE AN IGNITION INTERLOCK DEVICE INSTALLED ON THE VEHICLE; TO AMEND SECTION 56-1-400, AS AMENDED, RELATING TO THE SUSPENSION OF A LICENSE, A LICENSE RENEWAL OR ITS RETURN, AND ISSUANCE OF A LICENSE THAT RESTRICTS THE DRIVER TO ONLY OPERATING A VEHICLE WITH AN IGNITION INTERLOCK DEVICE INSTALLED.
The Senate proceeded to a consideration of the Bill, the question being concurrence in the House amendments.
Amendment No. RFH-1
Senator MALLOY proposed the following amendment (JUD0137.025):
Amend the bill, as and if amended, by striking all after the enacting words and inserting:
/ SECTION 1. This act may be cited as "Emma's Law".
SECTION 2. Section 56-1-286 of the 1976 Code is amended to read:
"Section 56-1-286. (A) The Department of Motor Vehicles must shall suspend the driver's license, permit, or nonresident operating privilege of, or deny the issuance of a license or permit to a person under the age of twenty-one who drives a motor vehicle and has an alcohol concentration of two one-hundredths of one percent or more. In cases in which a law enforcement officer initiates suspension proceedings for a violation of this section, the officer has elected to pursue a violation of this section and is subsequently prohibited from prosecuting the person for a violation of Section 63-19-2440, 63-19-2450, 56-5-2930, or 56-5-2933, arising from the same incident.
(B) A person under the age of twenty-one who drives a motor vehicle in this State is considered to have given consent to chemical tests of his the person's breath or blood for the purpose of determining the presence of alcohol.
(C) A law enforcement officer who has arrested a person under the age of twenty-one for a violation of Chapter 5 of this title (Uniform Act Regulating Traffic on Highways), or any other traffic offense established by a political subdivision of this State, and has reasonable suspicion that the person under the age of twenty-one has consumed alcoholic beverages and driven a motor vehicle may order the testing of the person arrested to determine the person's alcohol concentration.
A law enforcement officer may detain and order the testing of a person to determine the person's alcohol concentration if the officer has reasonable suspicion that a motor vehicle is being driven by a person under the age of twenty-one who has consumed alcoholic beverages.
The person tested or giving samples for testing may have a qualified person of his the person's choice conduct additional tests at the person's expense and must be notified in writing of that right. A person's request or failure to request additional blood tests is not admissible against the person in any proceeding. The person's failure or inability of the person tested to obtain additional tests does not preclude the admission of evidence relating to the tests or samples taken at the officer's direction of the officer. The officer must shall provide affirmative assistance to the person to contact a qualified person to conduct and obtain additional tests. Affirmative assistance shall, at a minimum, include providing transportation for the person to the nearest medical facility which provides blood tests to determine a person's alcohol concentration. If the medical facility obtains the blood sample but refuses or fails to test the blood to determine the person's alcohol concentration, SLED must the State Law Enforcement Division shall test the blood and provide the result to the person and to the officer. Failure to provide affirmative assistance upon request to obtain additional tests bars the admissibility of the breath test result in any a judicial or administrative proceeding.
(E) A qualified person and his the person's employer who obtain samples or administer the tests or assist in obtaining samples or administering of tests at the direction of the primary investigating officer officer's direction are immune from civil and criminal liability unless the obtaining of samples or the administering of tests is performed in a negligent, reckless, or fraudulent manner. A person may not be required by the officer ordering the tests to obtain or take any sample of blood or urine.
(F) If Except as provided in subsection (H), if a person refuses upon the request of the primary investigating officer officer's request to submit to chemical tests as provided in subsection (C), the department must shall suspend his the person's license, permit, or any nonresident operating privilege, or deny the issuance of a license or permit to him the person for:
(1) six months; or
(2) one year, if the person, within the five three years preceding the violation of this section, has been previously convicted of violating Section 56-5-2930, 56-5-2933, or 56-5-2945, or any other a law of this State or another state that prohibits a person from driving a motor vehicle while under the influence of alcohol or another drug other drugs, or the person has had a previous suspension imposed pursuant to Section 56-1-286, 56-5-2950, or 56-5-2951, or 56-5-2990.
(G) If Except as provided in subsection (H), if a person submits to a chemical test and the test result indicates an alcohol concentration of two one-hundredths of one percent or more, the department must shall suspend his the person's license, permit, or any nonresident operating privilege, or deny the issuance of a license or permit to him the person for:
(1) three months; or
(2) six months, if the person, within the five three years preceding the violation of this section, has been previously convicted of violating Section 56-5-2930, 56-5-2933, or 56-5-2945, or any other a law of this State or another state that prohibits a person from driving a motor vehicle while under the influence of alcohol or another drug other drugs, or the person has had a previous suspension imposed pursuant to Section 56-1-286, 56-5-2950, or 56-5-2951, or 56-5-2990.
(H) In lieu of serving the remainder of a suspension or denial of the issuance of a license or permit, a person may enroll in the Ignition Interlock Device Program pursuant to Section 56-5-2941, end the suspension or denial of the issuance of a license or permit, and obtain an ignition interlock restricted license pursuant to Section 56-1-400. The ignition interlock device is required to be affixed to the motor vehicle equal to the length of time remaining on the person's suspension or denial of the issuance of a license or permit. If the length of time remaining is less than three months, the ignition interlock device is required to be affixed to the motor vehicle for three months. Once a person has enrolled in the Ignition Interlock Device Program and obtained an ignition interlock restricted license, the person is subject to Section 56-5-2941 and cannot subsequently choose to serve the suspension.
(H)(I) A person's driver's license, permit, or nonresident operating privilege must be restored when the person's period of suspension under pursuant to subsection (F) or (G), or ignition interlock restricted license requirement pursuant to subsection (H), has concluded, even if the person has not yet completed the Alcohol and Drug Safety Action Program in which he the person is enrolled. After the person's driving privilege is restored, he must the person shall continue to participate in the Alcohol and Drug Safety Action Program in which he the person is enrolled. If the person withdraws from or in any way stops making satisfactory progress toward the completion of the Alcohol and Drug Safety Action Program, the person's license must be suspended until he the person completes the Alcohol and Drug Safety Action Program. A person must shall be attending or have completed an Alcohol and Drug Safety Action Program pursuant to Section 56-5-2990 before his the person's driving privilege can may be restored at the conclusion of the suspension period or ignition interlock restricted license requirement.
(I)(J) A test may not be administered or samples taken unless, upon activation of the video recording equipment and prior to the commencement of the testing procedure, the person has been given a written copy of and verbally informed that:
(1) he the person does not have to take the test or give the samples but that his the person's privilege to drive must be suspended or denied for at least six months with the option of ending the suspension or denial if the person enrolls in the Ignition Interlock Device Program, if he the person refuses to submit to the tests, and that his the person's refusal may be used against him the person in court;
(2) his the person's privilege to drive must be suspended for at least three months with the option of ending the suspension if the person enrolls in the Ignition Interlock Device Program, if he the person takes the test or gives the samples and has an alcohol concentration of two one-hundredths of one percent or more;
(3) he the person has the right to have a qualified person of his the person's own choosing conduct additional independent tests at his the person's expense;
(4) he the person has the right to request an administrative a contested case hearing within thirty days of the issuance of the notice of suspension; and
(5) he must the person shall enroll in an Alcohol and Drug Safety Action Program within thirty days of the issuance of the notice of suspension if he the person does not request an administrative a contested case hearing or within thirty days of the issuance of notice that the suspension has been upheld at the administrative contested case hearing.
The primary investigating officer must notify promptly shall promptly notify the department of the a person's refusal of a person to submit to a test requested pursuant to this section as well as the test result of any a person who submits to a test pursuant to this section and registers an alcohol concentration of two one-hundredths of one percent or more. The notification must be in a manner prescribed by the department.
(J)(K) If the test registers an alcohol concentration of two one-hundredths of one percent or more or if the person refuses to be tested, the primary investigating officer must shall issue a notice of suspension, and the suspension is effective beginning on the date of the alleged violation of this section. The person, within thirty days of the issuance of the notice of suspension, must shall enroll in an Alcohol and Drug Safety Action Program pursuant to Section 56-5-2990 if he the person does not request an administrative hearing. If the person does not request an administrative hearing and does not enroll in an Alcohol and Drug Safety Action Program within thirty days, the suspension remains in effect, and a temporary alcohol license must not be issued. If the person drives a motor vehicle during the period of suspension without a temporary alcohol license, the person must be penalized for driving while his the person's license is suspended pursuant to Section 56-1-460.
(K)(L) Within thirty days of the issuance of the notice of suspension the person may:
(1) obtain a temporary alcohol license by filing with the Department of Motor Vehicles a form for this purpose. A one-hundred-dollar fee must be assessed for obtaining a temporary alcohol license. Twenty-five dollars of the fee collected by the Department of Motor Vehicles must be distributed to the Department of Public Safety for supplying and maintaining all necessary vehicle videotaping equipment. The remaining seventy-five dollars must be placed by the Comptroller General into a special restricted account to be used by the Department of Motor Vehicles to defray its the Department of Motor Vehicle's expenses. The temporary alcohol license allows the person to drive a motor vehicle without any restrictive conditions pending the outcome of the contested case hearing provided for in this section or the final decision or disposition of the matter; and
(2) request a contested case hearing before the Office of Motor Vehicle Hearings pursuant to its rules of procedure.
At the contested case hearing if:
(a) the suspension is upheld, the person must shall enroll in an Alcohol and Drug Safety Action Program and his the person's driver's license, permit, or nonresident operating privilege must be suspended or the person must be denied the issuance of a license or permit for the remainder of the suspension periods provided for in subsections (F) and (G); or
(b) the suspension is overturned, the person must have his person's driver's license, permit, or nonresident operating privilege must be reinstated.
(L)(M) The periods of suspension provided for in subsections (F) and (G) begin on the day the notice of suspension is issued, or at the expiration of any other suspensions, and continue until the person applies for a temporary alcohol license and requests an administrative hearing.
(M)(N) If a person does not request a contested case hearing, he shall have the person has waived his the person's right to the hearing and his the person's suspension must not be stayed but shall continue for the periods provided for in subsections (F) and (G).
(N)(O) The notice of suspension must advise the person of the requirement to enroll in an Alcohol and Drug Safety Action Program and of his the person's right to obtain a temporary alcohol license and to request a contested case hearing. The notice of suspension also must advise the person that, if he the person does not request a contested case hearing within thirty days of the issuance of the notice of suspension, he must the person shall enroll in an Alcohol and Drug Safety Action Program, and he the person waives his the person's right to the contested case hearing, and the suspension continues for the periods provided for in subsections (F) and (G).
(O)(P) A contested case hearing must be held after the request for the hearing is received by the Office of Motor Vehicle Hearings. The scope of the hearing is limited to whether the person:
(1) was lawfully arrested or detained;
(2) was given a written copy of and verbally informed of the rights enumerated in subsection (I)(J);
(3) refused to submit to a test pursuant to this section; or
(4) consented to taking a test pursuant to this section, and the:
(a) reported alcohol concentration at the time of testing was two one-hundredths of one percent or more;
(b) individual who administered the test or took samples was qualified pursuant to this section;
(c) test administered and samples taken were conducted pursuant to this section; and
(d) the machine was operating properly.
Nothing in this section prohibits the introduction of evidence at the contested case hearing on the issue of the accuracy of the breath test result.
The Department of Motor Vehicles and the arresting officer shall have the burden of proof in contested case hearings conducted pursuant to this section. If neither the Department of Motor Vehicles nor the arresting officer appears at the contested case hearing, the hearing officer shall rescind the suspension of the person's license, permit, or nonresident's operating privilege regardless of whether the person requesting the contested case hearing or the person's attorney appears at the contested case hearing.
A written order must be issued to all parties either reversing or upholding the suspension of the person's license, permit, or nonresident's operating privilege, or denying the issuance of a license or permit. If the suspension is upheld, the person must receive credit for the number of days his the person's license was suspended before he the person received a temporary alcohol license and requested the contested case hearing.
(P)(Q) A contested case hearing is a contested proceeding under the Administrative Procedures Act, and a person has a right to appeal the decision of the hearing officer pursuant to that act to the Administrative Law Court in accordance with its appellate rules. The filing of an appeal shall stay the suspension until a final decision is issued.
(Q)(R) A person who is unconscious or otherwise in a condition rendering him incapable of refusal is considered to be informed and not to have withdrawn the consent provided for in subsection (B) of this section.
(R)(S) When a nonresident's privilege to drive a motor vehicle in this State has been suspended under the procedures of this section, the department shall give written notice of the action taken to the motor vehicle administrator of the state of the person's residence and of any state in which he has a license or permit.
(S)(T) A person required to submit to a test must be provided with a written report including the time of arrest, the time of the tests, and the results of the tests before any proceeding in which the results of the tests are used as evidence. A person who obtains additional tests shall furnish a copy of the time, method, and results of any additional tests to the officer before any trial, hearing, or other proceeding in which the person attempts to use the results of the additional tests as evidence.
(T)(U) A person whose driver's license or permit is suspended under this section is not required to file proof of financial responsibility.
(U)(V) The department shall administer the provisions of this section, not including subsection (D), and shall promulgate regulations necessary to carry out its provisions.
(V)(W) Notwithstanding any other provision of law, no suspension imposed pursuant to this section is counted as a demerit or result in any insurance penalty for automobile insurance purposes if at the time he the person was stopped, the person whose license is suspended had an alcohol concentration that was less than eight one-hundredths of one percent."
SECTION 3. Section 56-1-400 of the 1976 Code is amended to read:
(B)(1) A person who does not own a vehicle, as shown in the Department of Motor Vehicles' records, and who certifies that he the person:
(a) cannot obtain a vehicle owner's permission to have an ignition interlock device installed on a vehicle;
(b) will not be driving any a vehicle other than the one a vehicle owned by his the person's employer; and
(c) that he will not own a vehicle during the interlock period, may petition the Department of Motor Vehicles department, on a form provided by it the department, for issuance of a an ignition interlock restricted license containing an ignition interlock device restriction, that permits the person to operate a vehicle specified by the employee according to the employer's needs as contained in the employer's statement during the days and hours specified in the employer's statement without having to show that an ignition interlock device has been installed.
(2) The form must contain:
(a) identifying information about the employer's noncommercial vehicles that the person will be operating;
(b) a statement that explains the circumstances in which the person will be operating the employer's vehicles; and (c) the notarized signature of the person's employer.
(3) This subsection does not apply to a person who is self-employed or to a person who is employed by a business owned in whole or in part by the person or a member of the person's household or immediate family unless during the defense of a criminal charge, the court finds that the vehicle's ownership by the business serves a legitimate business purpose and that titling and registration of the vehicle by the business was not done to circumvent the intent of this section.
(4) Whenever the person operates the employer's vehicle pursuant to this subsection, the person shall have with the person a copy of the form specified by this subsection.
(5) The determination of eligibility for this the waiver is subject to periodic review at the discretion of the Department of Motor Vehicles department. The Department of Motor Vehicles must department shall revoke a license waiver issued pursuant to this exemption if it the department determines that the person has been driving a vehicle other than the one vehicle owned by his the person's employer or has been operating the person's employer's vehicle outside the locations, days, or hours specified by the employer in the department's records. The person may seek relief from the Department of Motor Vehicle's department's determination by filing a request for a contested case hearing with the Office of Motor Vehicle Hearings pursuant to the Administrative Procedures Act and the rules of procedure for the Office of Motor Vehicle Hearings. However, the filing of a request for a contested case hearing will not stay the revocation of the waiver pending the hearing.
(C) Any A person whose license has been suspended or revoked for an offense within the jurisdiction of the court of general sessions shall provide the Department of Motor Vehicles department with proof that the fine owed by the person has been paid before the Department of Motor Vehicles department may return or issue the person a license. Proof that the fine has been paid may be a receipt from the clerk of court of the county in which the conviction occurred stating that the fine has been paid in full."
SECTION 4. Section 56-1-460 of the 1976 Code is amended to read:
"Section 56-1-460. (A)(1) Except as provided in item (2), a person who drives a motor vehicle on any a public highway of this State when his the person's license to drive is canceled, suspended, or revoked must, upon conviction, be punished as follows:
(a) for a first offense, fined three hundred dollars or imprisoned for up to thirty days, or both;
(b) for a second offense, fined six hundred dollars or imprisoned for up to sixty consecutive days, or both; and
(c) for a third and or subsequent offense, fined one thousand dollars, and imprisoned for up to ninety days or confined to a person's place of residence pursuant to the Home Detention Act for not less than up to ninety days nor more than six months. No portion of a term of imprisonment or confinement under home detention may be suspended by the trial judge except when the court is suspending a term of imprisonment upon successful completion of the terms and conditions of confinement under home detention. For purposes of this item, a person sentenced to confinement pursuant to the Home Detention Act is required to pay for the cost of such confinement.
(d) Notwithstanding the provisions of Sections 22-3-540, 22-3-545, 22-3-550, and 14-25-65, an offense punishable under this item may be tried in magistrates or municipal court.
(e)(i) A person convicted of a first or second offense of this item, as determined by the records of the department, and who is employed or enrolled in a college or university at any time while his the person's driver's license is suspended pursuant to this item, may apply for a route restricted driver's license permitting him the person to drive only to and from work or his the person's place of education and in the course of his the person's employment or education during the period of suspension. The department may issue the route restricted driver's license only upon a showing by the person that he the person is employed or enrolled in a college or university and that he the person lives further than one mile from his the person's place of employment or place of education.
(ii) When the department issues a route restricted driver's license, it shall designate reasonable restrictions on the times during which and routes on which the person may operate a motor vehicle. A person holding a route restricted driver's license pursuant to this item must shall report to the department immediately any change in his the person's employment hours, place of employment, status as a student, or residence.
(iii) The fee for a route restricted driver's license issued pursuant to this item is one hundred dollars, but no additional fee is due when changes occur in the place and hours of employment, education, or residence. Of this fee, eighty dollars must be placed by the Comptroller General into a special restricted account to be used by the Department of Motor Vehicles to defray its the Department of Motor Vehicle's expenses. The remainder of the fees collected pursuant to this item must be credited to the Department of Transportation State Non-Federal Aid Highway Fund.
(iv) The operation of a motor vehicle outside the time limits and route imposed by a route restricted license by the person issued that license is a violation of subsection (A)(1).
(2) A person who drives a motor vehicle on any a public highway of this State when his the person's license has been suspended or revoked pursuant to the provisions of Section 56-5-2990 or 56-5-2945 must, upon conviction, be punished as follows:
(a) for a first offense, fined three hundred dollars or imprisoned for not less than ten nor more than thirty days;
(b) for a second offense, fined six hundred dollars or imprisoned for not less than sixty days nor more than six months;
(c) for a third and or subsequent offense, fined one thousand dollars and imprisoned for not less than six months nor more than three years;
(d) noNo portion of the minimum sentence imposed under pursuant to this item may be suspended.
(C) One hundred dollars of each fine imposed pursuant to this section must be placed by the Comptroller General into a special restricted account to be used by the Department of Public Safety for the Highway Patrol."
SECTION 5. Section 56-1-748 of the 1976 Code is amended to read:
"Section 56-1-748. (A) No person issued a restricted driver's license under the provisions of Section 56-1-170(B) 56-1-170, Section 56-1-320(A) 56-1-320, Section 56-1-740(B) 56-1-740, 56-1-745, Section 56-1-746 (D) 56-1-746, Section 56-5-750(G) 56-5-750, Section 56-9-430(B) 56-9-430, Section 56-10-260(B) 56-10-260, Section 56-10-270(C) 56-10-270, or Section 56-5-2951(H) 56-5-2951 shall subsequently be eligible for issuance of a restricted driver's license under these provisions.
(B) A person who obtains a route restricted driver's license and who is required to attend an Alcohol and Drug Safety Action Program or a court ordered drug program as a condition of reinstatement of the person's driving privileges may use the route restricted driver's license to attend the Alcohol and Drug Safety Action Program classes or court ordered drug program in addition to the other permitted uses of the route restricted driver's license."
SECTION 6. Section 56-1-1310 of the 1976 Code is repealed.
SECTION 7. Section 56-1-1320 of the 1976 Code is amended to read:
(B) Ninety-five dollars of the collected fee must be credited to the State's General Fund of the State for use of the Department of Public Safety in the hiring, training, and equipping of members of the South Carolina Highway Patrol and Transportation Police and in the operations of the South Carolina Highway Patrol and Transportation Police."
SECTION 8. Section 56-1-1350 of the 1976 Code is repealed.
SECTION 9. Section 56-5-2941 of the 1976 Code is amended to read:
"Section 56-5-2941. (A) Except as otherwise provided in this section, in addition to the penalties required and authorized to be imposed against a person violating the provisions of Section 56-5-2930, 56-5-2933, or 56-5-2945, or violating the provisions of another law of any other another state that prohibits a person from driving a motor vehicle while under the influence of alcohol or other drugs the The Department of Motor Vehicles must shall require the a person, if he is a subsequent offender and who is a resident of this State, and who has violated the provisions of Section 56-5-2930, 56-5-2933, 56-5-2945, 56-5-2947, or a law of another state that prohibits a person from driving a motor vehicle while under the influence of alcohol or other drugs, to have installed on any motor vehicle the person drives an ignition interlock device designed to prevent driving of the motor vehicle if the person has consumed alcoholic beverages. This section does not apply to a person convicted of a first offense violation of Section 56-5-2930 or 56-5-2933, unless the person submitted to a breath test pursuant to Section 56-5-2950 and had an alcohol concentration of twelve one hundredths of one percent or more. The Department of Motor Vehicles department may waive the requirements of this section if it finds the department determines that the offender person has a medical condition that makes him the person incapable of properly operating the installed device. If the department grants a medical waiver, the department shall suspend the person's driver's license for the length of time that the person would have been required to hold an ignition interlock restricted license. The department may withdraw the waiver at any time that the department becomes aware that the person's medical condition has improved to the extent that the person has become capable of properly operating an installed device. The department also shall require a person who has enrolled in the Ignition Interlock Device Program in lieu of the remainder of a driver's license suspension or denial of the issuance of a driver's license or permit to have an ignition interlock device installed on any motor vehicle the person drives.
The length of time that an interlock a device is required to be affixed to a motor vehicle following the completion of a period of license suspension imposed on the offender person is two years for a second offense, three years for a third offense, and the remainder of the offender's person's life for a fourth or subsequent offense is set forth in Sections 56-1-286, 56-5-2945, 56-5-2947, 56-5-2951, and 56-5-2990.
(B) Notwithstanding the pleadings, for purposes of a second or a subsequent offense, the specified length of time that an interlock a device is required to be affixed to a motor vehicle is based on the Department of Motor Vehicle's records for offenses pursuant to Section 56-1-286, 56-5-2930, 56-5-2933, or 56-5-2945, 56-5-2947, 56-5-2950, or 56-5-2951.
(B)(C) If a person who is a subsequent offender and a resident of this State is convicted of violating the provisions of a law of any other another state that prohibits a person from driving a motor vehicle while under the influence of alcohol or other drugs, and, as a result of the conviction, the person is subject to an ignition interlock device requirement in the other state, the person is subject to the requirements of this section for the length of time that would have been required for an offense committed in South Carolina, or for the length of time that is required by the other state, whichever is longer.
(C)(D) If a person from another state becomes a resident of South Carolina while subject to an ignition interlock device requirement in another state, the person may only obtain a South Carolina driver's license if the person enrolls in the South Carolina ignition interlock device program Ignition Interlock Device Program pursuant to this section. The person is subject to the requirements of this section for the length of time that would have been required for an offense committed in South Carolina, or for the length of time that is required by the other state, whichever is longer.
(D)(E) The offender shall person must be subject to an Ignition Interlock Device Point System managed by the Department of Probation, Parole and Pardon Services. An offender receiving A person accumulating a total of:
(1) two points or more, but less than three points, will must have their the length of time that the interlock device is required extended by two months.;
(2) An offender receiving a total of three points or more, but less than four points, will must have their the length of time that the interlock device is required extended by four months, and must shall submit to a substance abuse assessment pursuant to Section 56-5-2990, and shall successfully complete the plan of education and treatment, or both, as recommended by the certified substance abuse program. Should the individual person not complete the recommended plan, or not make progress toward completing the plan, the Department of Motor Vehicles must shall suspend the individual's driver's person's ignition interlock restricted license until the plan is completed or progress is being made toward completing the plan.;
(3) An offender receiving a total of four points or more shall must have their the person's ignition interlock restricted license suspended for a period of one year six months, and shall submit to a substance abuse assessment pursuant to Section 56-5-2990, and shall successfully complete the plan of education and treatment, or both, as recommended by the certified substance abuse program. Completion of the plan is mandatory as a condition of reinstatement of the person's driving privileges Should the person not complete the recommended plan or not make progress toward completing the plan, the Department of Motor Vehicles shall leave the person's ignition interlock restricted license in suspended status, or, if the license has already been reinstated following the six-month suspension, shall resuspend the person's ignition interlock restricted license until the plan is completed or progress is being made toward completing the plan. The Department of Alcohol and Other Drug Abuse Services is responsible for notifying the Department of Motor Vehicles of an individual's a person's completion and compliance with education and treatment programs. Upon reinstatement of driving privileges following the six-month suspension, the Department of Probation, Parole and Pardon Services shall reset the person's point total to zero points, and the person shall complete the remaining period of time on the ignition interlock device.
(E)(F) The cost of the interlock device must be borne by the offender person. However, if the offender believes he person is indigent and cannot afford the cost of the ignition interlock device, the offender person may submit an affidavit of indigency to the Department of Probation, Parole and Pardon Services for a determination of indigency as it pertains to the cost of the ignition interlock device. The affidavit of indigency form must be made publicly accessible on the Department of Probation, Parole and Pardon Services' Internet web site. If the Department of Probation, Parole and Pardon Services determines that the offender person is indigent as it pertains to the ignition interlock device, it the Department of Probation, Parole and Pardon Services may authorize an interlock a device to be affixed to the motor vehicle and the cost of the initial installation and standard use of the ignition interlock device to be paid for by the Ignition Interlock Device Fund managed by the Department of Probation, Parole and Pardon Services. Funds remitted to the Department of Probation, Parole and Pardon Services for the Ignition Interlock Device Fund also may be used by the Department of Probation, Parole and Pardon Services to support the Ignition Interlock Device Program. For purposes of this section, a person is indigent if the person is financially unable to afford the cost of the ignition interlock device. In making a determination whether a person is indigent, all factors concerning the person's financial conditions should be considered including, but not limited to, income, debts, assets, number of dependants dependents claimed for tax purposes, living expenses, and family situation. A presumption that the person is indigent is created if the person's net family income is less than or equal to the poverty guidelines established and revised annually by the United States Department of Health and Human Services published in the Federal Register. 'Net income' means gross income minus deductions required by law. The determination of indigency is subject to periodic review at the discretion of the Department of Probation, Parole and Pardon Services.
(F)(G) The ignition interlock service provider must shall collect and remit monthly to the Ignition Interlock Device Fund a fee as determined by the Department of Probation, Parole and Pardon Services not to exceed three hundred sixty thirty dollars per year month for each year month the person is required to drive a vehicle with an ignition interlock a device. Any A ignition service provider failing who fails to properly remit funds to the Ignition Interlock Device Fund may be decertified as an ignition interlock a service provider by the Department of Probation, Parole and Pardon Services. If a service provider is decertified for failing to remit funds to the Ignition Interlock Device Fund, the cost for removal and replacement of an ignition interlock a device must be borne by the service provider.
(G)(H)(1) The offender must person shall have the interlock device inspected every sixty days to verify that the device is affixed to the motor vehicle and properly operating, and to allow for the preparation of an ignition interlock device inspection report by the service provider indicating the offender's person's alcohol content at each attempt to start and running re-test retest during each sixty-day period. Failure of the person to have the interlock device inspected every sixty days must result in one ignition interlock device point.
(2) Only a service provider authorized by the Department of Probation, Parole and Pardon Services to perform inspections on ignition interlock devices may conduct inspections. The service provider immediately must shall report any devices that fail inspection to the Department of Probation, Parole and Pardon Services. The report must contain the person's name of the offender, identify the vehicle upon which the failed device is installed, and the reason for the failed inspection, and.
(3) If the inspection report reflects that the person has failed to complete a running retest, the person must be assessed one ignition interlock device point.
(4) The inspection report must indicate the offender's person's alcohol content at each attempt to start and running re-test retest during each sixty-day period. Failure of the offender to have the interlock device inspected every sixty days will result in one ignition interlock device point. Upon review of the ignition interlock device inspection report, if the report reflects that the offender attempted to start the motor vehicle with an alcohol concentration of two one-hundredths of one percent or more, the offender is assessed one-half interlock device point. Upon review of the interlock device inspection report, if If the report reflects that the offender person violated a running re-test retest by having an alcohol concentration of:
(a) between two one-hundredths of one percent or more and but less than four one-hundredths of one percent, the offender is person must be assessed one-half ignition interlock device point.;
(b) Upon review of the interlock device inspection report, if the report reflects that the offender person violated a running re-test retest by having an alcohol concentration between four one-hundredths of one percent or more and but less than fifteen one-hundredths of one percent, the offender is person must be assessed one ignition interlock device point.; or
(c) Upon review of the interlock device inspection report, if the report reflects that the offender person violated a running re-test retest by having an alcohol concentration above fifteen one-hundredths of one percent or more, the offender is person must be assessed two ignition interlock device points.
(5) An individual A person may appeal any interlock device points received to an administrative hearing officer with the Department of Probation, Parole and Pardon Services through a process established by the Department of Probation, Parole and Pardon Services. The administrative hearing officer's decision on appeal shall be is final and no appeal from such decision shall be is allowed.
(H)(I) Ten Five years from the date of the person's last conviction driver's license reinstatement and every five years thereafter a fourth or subsequent offender whose license has been reinstated pursuant to Section 56-1-385 may apply to the Department of Probation, Parole and Pardon Services for removal of the ignition interlock device and the removal of the restriction from his the person's driver's license. The Department of Probation, Parole and Pardon Services may, for good cause shown, remove the device and remove the restriction notify the Department of Motor Vehicles that the person is eligible to have the restriction removed from the offender's person's license.
(I)(J)(1) Except as otherwise provided in this section, it is unlawful for a person issued a driver's license with an ignition interlock restriction who is subject to the provisions of this section to drive a motor vehicle that is not equipped with a properly operating, certified ignition interlock device. A person who violates this section must be punished in the manner provided by law subsection:
(a) for a first offense, is guilty of a misdemeanor, and, upon conviction, must be fined not less than one thousand dollars or imprisoned not more than one year. The person must have the length of time that the ignition interlock device is required extended by six months;
(b) for a second offense, is guilty of a misdemeanor, and, upon conviction, must be fined not less than five thousand dollars or imprisoned not more than three years. The person must have the length of time that the ignition interlock device is required extended by one year; and
(c) for a third or subsequent offense, is guilty of a felony, and, upon conviction, must be fined not less than ten thousand dollars or imprisoned not more than ten years. The person must have the length of time that the ignition interlock device is required extended by three years.
(2) No portion of the minimum sentence imposed pursuant to this subsection may be suspended.
(3) Notwithstanding any other provision of law, a first or second offense punishable pursuant to this subsection may be tried in summary court.
(J)(K)(1) An offender that A person who is required in the course and scope of his the person's employment to drive a motor vehicle owned by the offender's person's employer may drive his the employer's motor vehicle without installation of an ignition interlock device, provided that the offender's person's use of the employer's motor vehicle is solely for the employer's business purposes. This subsection does not apply to an offender a person who is self-employed or to an offender a person who is employed by a business owned in whole or in part by the offender person or a member of the offender's person's household or immediate family unless during the defense of a criminal charge, the court finds that the vehicle's ownership by the business serves a legitimate business purpose and that titling and registration of the vehicle by the business was not done to circumvent the intent of this section.
(2) Whenever the person operates the employer's vehicle pursuant to this subsection, the person shall have with the person a copy of the Department of Motor Vehicle's form specified by Section 56-1-400(B).
(3) This subsection will be construed in parallel with the requirements of subsection 56-1-400(B). A waiver issued pursuant to this subsection will be subject to the same review and revocation as described in subsection 56-1-400(B).
(K)(L) It is unlawful for a person to tamper with or disable, or attempt to tamper with or disable, an ignition interlock device installed on a motor vehicle pursuant to this section. Obstructing or obscuring the camera lens of an ignition interlock device constitutes tampering. A person who violates this subsection is guilty of a misdemeanor, and, upon conviction, must be fined not more than five hundred dollars or imprisoned not more than thirty days, or both.
(L)(M) It is unlawful for a person to knowingly rent, lease, or otherwise provide an offender a person who is subject to this section with a motor vehicle without a properly operating, certified ignition interlock device. This subsection does not apply if the person began the lease contract period for the motor vehicle prior to the person's arrest for a first offense violation of Section 56-5-2930 or Section 56-5-2933. A person who violates this subsection is guilty of a misdemeanor, and, upon conviction, must be fined not more than five hundred dollars or imprisoned not more than thirty days, or both.
(M)(N) It is unlawful for an offender a person who is subject to the provisions of this section to solicit or request another person, or for a person to solicit or request another person on behalf of an offender a person who is subject to the provisions of this section, to engage an ignition interlock device to start a motor vehicle with a device installed pursuant to this section. A person who violates this subsection is guilty of a misdemeanor, and, upon conviction, must be fined not more than five hundred dollars or imprisoned not more than thirty days, or both.
(N)(O) It is unlawful for another person to engage an ignition interlock device to start a motor vehicle with a device installed pursuant to this section. A person who violates this subsection is guilty of a misdemeanor, and, upon conviction, must be fined not more than five hundred dollars or imprisoned not more than thirty days, or both.
(O)(P) Only ignition interlock devices certified by the Department of Probation, Parole and Pardon Services may be used to fulfill the requirements of this section.
(1) The Department of Probation, Parole and Pardon Services must shall certify whether a device meets the accuracy requirements and specifications provided in guidelines or regulations adopted by the National Highway Traffic Safety Administration, as amended from time to time. All devices certified to be used in South Carolina must be set to prohibit the starting of a motor vehicle when an alcohol concentration of two one-hundredths of one percent or more is measured and all running re-tests retests must record violations of an alcohol concentration of two one-hundredths of one percent or more, and must capture a photographic image of the driver as the driver is operating the ignition interlock device. The photographic images recorded by the ignition interlock device may be used by the Department of Probation, Parole and Pardon Services to aid in the Department of Probation, Parole and Pardon Services' management of the Ignition Interlock Device Program; however, neither the Department of Probation, Parole and Pardon Services, the Department of Probation, Parole and Pardon Services' employees, nor any other political subdivision of this State may be held liable for any injury caused by a driver or other person who operates a motor vehicle after the use or attempted use of an ignition interlock device.
(2) The Department of Probation, Parole and Pardon Services shall maintain a current list of certified ignition interlock devices and their manufacturers. The list must be updated at least quarterly. If a particular certified device fails to continue to meet federal requirements, the device must be decertified, may not be used until it is compliant with federal requirements, and must be replaced with a device that meets federal requirements. The cost for removal and replacement must be borne by the manufacturer of the noncertified device.
(3) Only ignition interlock installers certified by the Department of Probation, Parole and Pardon Services may install and service ignition interlock devices required pursuant to this section. The Department of Probation, Parole and Pardon Services shall maintain a current list of vendors that are certified to install the devices.
(P)(Q) In addition to availability under the Freedom of Information Act, any Department of Probation, Parole and Pardon Services policy concerning ignition interlock devices must be made publicly accessible on the Department of Probation, Parole and Pardon Service's Services' Internet web site. Information obtained by the Department of Probation, Parole and Pardon Services and ignition interlock service providers regarding a person's participation in the Ignition Interlock Device Program is to be used for internal purposes only and is not subject to the Freedom of Information Act. A person participating in the Ignition Interlock Device Program or the person's family member may request that the Department of Probation, Parole and Pardon Services provide the person or family member with information obtained by the department and ignition interlock service providers. The Department of Probation, Parole and Pardon Services may release the information to the person or family member at the department's discretion. The Department of Probation, Parole and Pardon Services and ignition interlock service providers may retain information regarding a person's participation in the Ignition Interlock Device Program for a period not to exceed eighteen months from the date of the person's completion of the Ignition Interlock Device Program.
(Q)(R) The Department of Probation, Parole and Pardon Services shall develop policies including, but not limited to, the certification, use, maintenance, and operation of ignition interlock devices and the Ignition Interlock Device Fund."
SECTION 10. Section 56-5-2942 of the 1976 Code is amended to read:
"Section 56-5-2942. (A) A person who is convicted of or pleads guilty or nolo contendere to a second or subsequent violation of Section 56-5-2930, 56-5-2933, or 56-5-2945 must have all motor vehicles owned by or registered to him the person immobilized if the person is a resident of this State, unless the vehicle has been confiscated pursuant to Section 56-5-6240 or the person is a holder of a valid ignition interlock restricted license.
(B) For purposes of this section, 'immobilized' and 'immobilization' mean suspension and surrender of the registration and motor vehicle license plate.
(C) Upon receipt of a conviction by the department from the court for a second or subsequent violation of Section 56-5-2930, 56-5-2933, or 56-5-2945, the department must shall determine all vehicles registered to the convicted person, both solely and jointly, and suspend all vehicles registered to the person, unless the person is a holder of a valid ignition interlock restricted license.
(D) Upon notification by a court in this State or by any other another state of a conviction for a second or subsequent violation of Section 56-5-2930, 56-5-2933, or 56-5-2945, the department must shall require the person, unless the person is a holder of a valid ignition interlock restricted license, convicted to surrender all license plates and vehicle registrations subject to immobilization pursuant to this section. The immobilization is for a period of thirty days to take place during the driver's license suspension pursuant to a conviction for a second or subsequent violation of Section 56-5-2930, 56-5-2933, or 56-5-2945. The department must shall maintain a record of all vehicles immobilized pursuant to this section.
(E) An immobilized motor vehicle must be released to the holder of a bona fide lien on the motor vehicle when possession of the motor vehicle is requested, as provided by law, by the lienholder for the purpose of foreclosing on and satisfying the lien.
(F) An immobilized motor vehicle may be released by the department without legal or physical restraints to a person who has not been convicted of a second or subsequent violation of Section 56-5-2930, 56-5-2933, or 56-5-2945, if that person is a registered owner of the motor vehicle or a member of the household of a registered owner. The vehicle must be released if an affidavit is submitted by that person to the department stating that:
(1) he the person regularly drives the motor vehicle subject to immobilization;
(2) the immobilized motor vehicle is necessary to his the person's employment, transportation to an educational facility, or for the performance of essential household duties;
(3) no other motor vehicle is available for the person's use;
(4) the person will not authorize the use of the motor vehicle by any other person known by him the person to have been convicted of a second or subsequent violation of Section 56-5-2930, 56-5-2933, or 56-5-2945; or
(5) the person will report immediately to a local law enforcement agency any unauthorized use of the motor vehicle by a person known by him the person to have been convicted of a second or subsequent violation of Section 56-5-2930, 56-5-2933, or 56-5-2945.
(G) The department may issue a determination permitting or denying the release of the vehicle based on the affidavit submitted pursuant to subsection (F). A person may seek relief from a department determination immobilizing a motor vehicle or denying the release of the motor vehicle by filing a request for a contested case hearing with the Office of Motor Vehicle Hearings pursuant to the Administrative Procedures Act and the rules of procedure for the Office of Motor Vehicle Hearings.
(H) A person who drives an immobilized motor vehicle except as provided in subsections (E) and (F) is guilty of a misdemeanor, and, upon conviction, must be fined not more than five hundred dollars or imprisoned not more than thirty days.
(I) A person who fails to surrender registrations and license plates pursuant to this section is guilty of a misdemeanor, and, upon conviction, must be fined not more than five hundred dollars or imprisoned not more than thirty days.
(J) A fee of fifty dollars must be paid to the department for each motor vehicle that was suspended before any of the suspended registrations and license plates may be registered or before the motor vehicle may be released pursuant to subsection (F). This fee must be placed by the Comptroller General into a special restricted interest bearing account to be used by the Department of Motor Vehicles to defray its the Department of Motor Vehicle's expenses.
(K) For purposes of this article, a conviction of or plea of nolo contendere to Section 56-5-2933 is considered a prior offense of Section 56-5-2930."
SECTION 11. Section 56-5-2945 of the 1976 Code is amended to read:
"Section 56-5-2945. (A) A person who, while under the influence of alcohol, drugs, or the combination of alcohol and drugs, drives a motor vehicle and when driving a motor vehicle does any act forbidden by law or neglects any duty imposed by law in the driving of the motor vehicle, which act or neglect proximately causes great bodily injury or death to a another person other than himself, is guilty of the offense of felony driving under the influence, and, upon conviction, must be punished:
(1) by a mandatory fine of not less than five thousand one hundred dollars nor more than ten thousand one hundred dollars and mandatory imprisonment for not less than thirty days nor more than fifteen years when great bodily injury results;
(2) by a mandatory fine of not less than ten thousand one hundred dollars nor more than twenty-five thousand one hundred dollars and mandatory imprisonment for not less than one year nor more than twenty-five years when death results.
A part of the mandatory sentences required to be imposed by this section must not be suspended, and probation must not be granted for any portion.
(B) As used in this section, 'great bodily injury' means bodily injury which creates a substantial risk of death or which causes serious, permanent disfigurement, or protracted loss or impairment of the function of any bodily member or organ.
(C)(1) The Department of Motor Vehicles must shall suspend the driver's license of a person who is convicted or who receives sentence upon a plea of guilty or nolo contendere pursuant to this section for a period to include a period of incarceration plus three years for a conviction of Section 56-5-2945 when 'great bodily injury' occurs and five years when a death occurs. This period of incarceration shall must not include any portion of a suspended sentence such as probation, parole, supervised furlough, or community supervision. For suspension purposes of this section, convictions arising out of a single incident shall must run concurrently.
(2) After the person is released from prison, the person shall enroll in the Ignition Interlock Device Program pursuant to Section 56-5-2941, end the suspension, and obtain an ignition interlock restricted license pursuant to Section 56-1-400. The ignition interlock device is required to be affixed to the motor vehicle for three years when 'great bodily injury' results and five years when a death occurs.
(C)(D) One hundred dollars of each fine imposed pursuant to this section must be placed by the Comptroller General into a special restricted account to be used by the Department of Public Safety for the Highway Patrol."
SECTION 12. Section 56-5-2947 of the 1976 Code is amended to read:
"Section 56-5-2947. (A) A person eighteen years of age or over older is guilty of child endangerment when:
(1) the person is in violation of violates:
(a) Section 56-5-750;
(b) Section 56-5-2930;
(c) Section 56-5-2933; or
(d) Section 56-5-2945; and
(2) the person has one or more passengers under younger than sixteen years of age in the motor vehicle when the violation occurs.
If more than one passenger under younger than sixteen years of age is in the vehicle when a violation of subsection (A)(1) occurs, the person may be charged with only one violation of this section.
(B) Upon conviction, the person must be punished by:
(1) a fine of fined not more than one-half of the maximum fine allowed for committing the violation enumerated in subsection (A)(1), when the person is fined for that offense;
(2) a term of imprisonment of imprisoned not more than one-half of the maximum term of imprisonment allowed for committing the violation enumerated listed in subsection (A)(1), when the person is imprisoned for the offense; or
(3) both a fine and imprisonment fined and imprisoned as prescribed in items (1) and (2) when the person is fined and imprisoned for the offense.
(C) No portion of the penalty assessed under pursuant to subsection (B) may be suspended or revoked and probation may not be awarded.
(D)(1) In addition to imposing the penalties for offenses enumerated listed in subsection (A)(1) and the penalties contained in subsection (B), the Department of Motor Vehicles must shall suspend the person's driver's license for sixty days.
(2) The person shall enroll in the Ignition Interlock Device Program pursuant to Section 56-5-2941, end the suspension, and obtain an ignition interlock restricted license pursuant to Section 56-1-400. The ignition interlock device is required to be affixed to the motor vehicle for three months.
(3) Sections 56-1-1320 and 56-5-2990 as they relate to enrollment in an alcohol and drug safety action program and to the issuance of a provisional driver's license will not be effective until the sixty-day suspension ignition interlock restricted license period is completed.
(E) A person may be convicted under pursuant to this section for child endangerment in addition to being convicted for an offense enumerated listed in subsection (A)(1).
(F) The court that has jurisdiction over an offense enumerated listed in subsection (A)(1) has jurisdiction over the offense of child endangerment.
(G) A first offense charge for a violation of this section may not be used as the only evidence for taking a child into protective custody pursuant to Sections 63-7-620(A) and 63-7-660."
SECTION 13. Section 56-5-2950 of the 1976 Code is amended to read:
(B) No tests may be administered or samples obtained unless, upon activation of the video recording equipment and prior to the commencement of the testing procedure, the person has been given a written copy of and verbally informed that:
(1) he the person does not have to take the test or give the samples, but that his the person's privilege to drive must be suspended or denied for at least six months with the option of ending the suspension if the person enrolls in the Ignition Interlock Device Program, if he the person refuses to submit to the test, and that his the person's refusal may be used against him the person in court;
(2) his the person's privilege to drive must be suspended for at least one month with the option of ending the suspension if the person enrolls in the Ignition Interlock Device Program, if he the person takes the test or gives the samples and has an alcohol concentration of fifteen one-hundredths of one percent or more;
(3) he the person has the right to have a qualified person of his the person's own choosing conduct additional independent tests at his the person's expense;
(4) he the person has the right to request an administrative a contested case hearing within thirty days of the issuance of the notice of suspension; and
(5) if he the person does not request an administrative a contested case hearing or if his the person's suspension is upheld at the administrative contested case hearing, he must the person shall enroll in an Alcohol and Drug Safety Action Program.
(C) A hospital, physician, qualified technician, chemist, or registered nurse who obtains the samples or conducts the test or participates in the process of obtaining the samples or conducting the test in accordance with this section is not subject to a cause of action for assault, battery, or another cause alleging that the drawing of blood or taking samples at the request of the arrested person or a law enforcement officer was wrongful. This release from liability does not reduce the standard of medical care required of the person obtaining the samples or conducting the test. This qualified release also applies to the employer of the person who conducts the test or obtains the samples.
(D) The person tested or giving samples for testing may have a qualified person of his the person's own choosing conduct additional tests at his the person's expense and must be notified in writing of that right. A person's request or failure to request additional blood or urine tests is not admissible against the person in the criminal trial. The failure or inability of the person tested to obtain additional tests does not preclude the admission of evidence relating to the tests or samples obtained at the direction of the law enforcement officer.
(E) The arresting officer must shall provide affirmative assistance to the person to contact a qualified person to conduct and obtain additional tests. Affirmative assistance, at a minimum, includes providing transportation for the person to the nearest medical facility which performs blood tests to determine a person's alcohol concentration. If the medical facility obtains the blood sample but refuses or fails to test the blood sample to determine the person's alcohol concentration, SLED must shall test the blood sample and provide the result to the person and to the arresting officer. Failure to provide affirmative assistance upon request to obtain additional tests bars the admissibility of the breath test result in any a judicial or administrative proceeding.
SLED must shall administer the provisions of this subsection and must shall make regulations necessary to carry out its this subsection's provisions. The costs of the tests administered at the direction of the law enforcement officer must be paid from the State's general fund of the state. However, if the person is subsequently convicted of violating Section 56-5-2930, 56-5-2933, or 56-5-2945, then, upon conviction, the person must shall pay twenty-five dollars for the costs of the tests. The twenty-five dollars must be placed by the Comptroller General into a special restricted account to be used by the State Law Enforcement Division to offset the costs of administration of the breath testing devices, breath testing site video program, and toxicology laboratory.
(F) A qualified person who obtains samples or administers the tests or assists in obtaining samples or the administration of tests at the direction of a law enforcement officer is released from civil and criminal liability unless the obtaining of samples or tests is performed in a negligent, reckless, or fraudulent manner. No person may be required by the arresting officer, or by another law enforcement officer, to obtain or take any sample of blood or urine.
(G) In the criminal prosecution for a violation of Section 56-5-2930, 56-5-2933, or 56-5-2945 the alcohol concentration at the time of the test, as shown by chemical analysis of the person's breath or other body fluids, gives rise to the following:
(1) if the alcohol concentration was at that time five one-hundredths of one percent or less, it is conclusively presumed that the person was not under the influence of alcohol;
(2) if the alcohol concentration was at that time in excess of five one-hundredths of one percent but less than eight one-hundredths of one percent, this fact does not give rise to any inference that the person was or was not under the influence of alcohol, but this fact may be considered with other evidence in determining the guilt or innocence of the person; or
(3) if the alcohol concentration was at that time eight one-hundredths of one percent or more, it may be inferred that the person was under the influence of alcohol.
The provisions of this section must not be construed as limiting the introduction of any other evidence bearing upon the question of whether or not the person was under the influence of alcohol, drugs, or a combination of them alcohol and drugs.
(H) A person who is unconscious or otherwise in a condition rendering him the person incapable of refusal is considered to be informed and not to have withdrawn the consent provided by subsection (A) of this section.
(I) A person required to submit to tests by the arresting law enforcement officer must be provided with a written report including the time of arrest, the time of the tests, and the results of the tests before any trial or other proceeding in which the results of the tests are used as evidence. A person who obtains additional tests must shall furnish a copy of the time, method, and results of any tests such tests to the officer before any a trial, hearing, or other proceeding in which the person attempts to use the results of the additional tests as evidence.
(J) Policies, procedures, and regulations promulgated by SLED may be reviewed by the trial judge or hearing officer on motion of either party. The failure to follow any of these policies, procedures, and regulations, or the provisions of this section, shall result in the exclusion from evidence of any test results, if the trial judge or hearing officer finds that this failure materially affected the accuracy or reliability of the test results or the fairness of the testing procedure and the court trial judge or hearing officer rules specifically as to the manner in which the failure materially affected the accuracy or reliability of the test results or the fairness of the procedure.
(K) If a state employee charged with the maintenance of breath testing devices in this State and the administration of breath testing policy is required to testify at an administrative a contested case hearing or court proceeding, the entity employing the witness may charge a reasonable fee to the defendant for these such services."
SECTION 14. Section 56-5-2951 of the 1976 Code is amended to read:
"Section 56-5-2951. (A) The Department of Motor Vehicles must shall suspend the driver's license, permit, or nonresident operating privilege of, or deny the issuance of a license or permit to, a person who drives a motor vehicle and refuses to submit to a test provided for in Section 56-5-2950 or has an alcohol concentration of fifteen one-hundredths of one percent or more. The arresting officer must shall issue a notice of suspension which is effective beginning on the date of the alleged violation of Section 56-5-2930, 56-5-2933, or 56-5-2945.
(B) Within thirty days of the issuance of the notice of suspension, the person may:
(1) obtain a temporary alcohol license by filing with from the Department of Motor Vehicles a form for this purpose. A one hundred dollar fee must be assessed for obtaining a temporary alcohol license. Twenty-five dollars of the fee must be distributed by the Department of Motor Vehicles to the Department of Public Safety for supplying and maintaining all necessary vehicle videotaping equipment. The remaining seventy-five dollars must be placed by the Comptroller General into a special restricted account to be used by the Department of Motor Vehicles to defray its the Department of Motor Vehicle's expenses. The temporary alcohol license allows the person to drive without any restrictive conditions pending the outcome of the contested case hearing provided for in subsection (F) or the final decision or disposition of the matter. If the suspension is upheld at the contested case hearing, the temporary alcohol license remains in effect until the Office of Motor Vehicle Hearings issues the hearing officer's decision and the Department of Motor Vehicles sends notice to the person that he the person is eligible to receive a restricted license pursuant to subsection (H); and
(2) request a contested case hearing before the Office of Motor Vehicle Hearings in accordance with its the Office of Motor Vehicle Hearings' rules of procedure.
At the contested case hearing if:
(a) the suspension is upheld, the person's driver's license, permit, or nonresident operating privilege must be suspended or the person must be denied the issuance of a license or permit for the remainder of the suspension period provided for in subsection (I). Within thirty days of the issuance of the notice that the suspension has been upheld, the person must shall enroll in an Alcohol and Drug Safety Action Program pursuant to Section 56-5-2990;
(b) the suspension is overturned, the person must have his the person's driver's license, permit, or nonresident operating privilege reinstated.
The provisions of this subsection do not affect the trial for a violation of Section 56-5-2930, 56-5-2933, or 56-5-2945.
(C) The period of suspension provided for in subsection (I) begins on the day the notice of suspension is issued, or at the expiration of any other suspensions, and continues until the person applies for a temporary alcohol license and requests a contested case hearing.
(D) If a person does not request a contested case hearing, he the person waives his the person's right to the hearing, and his the person's suspension must not be stayed but continues for the period provided for in subsection (I).
(E) The notice of suspension must advise the person:
(1) of his the person's right to obtain a temporary alcohol driver's license and to request a contested case hearing before the Office of Motor Vehicle Hearings.;
(2) The notice of suspension also must advise the person that, if he the person does not request a contested case hearing within thirty days of the issuance of the notice of suspension, he the person waives his the person's right to the administrative contested case hearing, and the suspension continues for the period provided for in subsection (I).; and
(3) The notice of suspension also must advise the person that if the suspension is upheld at the contested case hearing or if he the person does not request a contested case hearing, he the person must shall enroll in an Alcohol and Drug Safety Action Program.
(F) A contested case hearing must be held after the request for the hearing is received by the Office of Motor Vehicle Hearings. The scope of the hearing is limited to whether the person:
(1) was lawfully arrested or detained;
(2) was given a written copy of and verbally informed of the rights enumerated in Section 56-5-2950;
(3) refused to submit to a test pursuant to Section 56-5-2950; or
(4) consented to taking a test pursuant to Section 56-5-2950, and the:
(a) reported alcohol concentration at the time of testing was fifteen one-hundredths of one percent or more;
(b) individual who administered the test or took samples was qualified pursuant to Section 56-5-2950;
(c) tests administered and samples obtained were conducted pursuant to Section 56-5-2950; and
(d) machine was working properly.
Nothing in this section prohibits the introduction of evidence at the contested case hearing on the issue of the accuracy of the breath test result.
A written order must be issued to all parties either reversing or upholding the suspension of the person's license, permit, or nonresident's operating privilege, or denying the issuance of a license or permit. If the suspension is upheld, the person must receive credit for the number of days his the person's license was suspended before he the person received a temporary alcohol license and requested the contested case hearing.
The Department of Motor Vehicles and the arresting officer shall have the burden of proof in contested case hearings conducted pursuant to this section. If neither the Department of Motor Vehicles nor the arresting officer appears at the contested case hearing, the hearing officer shall rescind the suspension of the person's license, permit, or nonresident's operating privilege regardless of whether the person requesting the contested case hearing or the person's attorney appears at the contested case hearing.
(G) A contested case hearing is governed by the Administrative Procedures Act, and a person has a right to appeal the decision of the hearing officer pursuant to that act to the Administrative Law Court in accordance with its the Administrative Law Court's appellate rules. The filing of an appeal stays the suspension until a final decision is issued on appeal.
(H)(1) If the person did not request a contested case hearing or the suspension is upheld at the administrative contested case hearing, the person must shall enroll in an Alcohol and Drug Safety Action Program pursuant to Section 56-5-2990, and may apply for a restricted license if he the person is employed or enrolled in a college or university. The restricted license permits him the person to drive only to and from work and his the person's place of education and in the course of his the person's employment or education during the period of suspension. The restricted license also permits him the person to drive to and from the Alcohol Drug Safety Action Program classes or to a court-ordered drug program. The department may issue the restricted license only upon showing by the individual person that he the person is employed or enrolled in a college or university, that he the person lives further than one mile from his the person's place of employment, place of education, or location of his the person's Alcohol and Drug Safety Action Program classes, or the location of his the person's court-ordered drug program, and that there is no adequate public transportation between his the person's residence and his the person's place of employment, his the person's place of education, the location of his the person's Alcohol and Drug Safety Action Program classes, or the location of his the person's court-ordered drug program.
(2) If the department issues a restricted license pursuant to this subsection, it must the department shall designate reasonable restrictions on the times during which and routes on which the individual person may drive a motor vehicle. A change in the employment hours, place of employment, status as a student, status of attendance of Alcohol and Drug Safety Action Program classes, status of attendance of his the person's court-ordered drug program, or residence must be reported immediately to the department by the licensee person.
(3) The fee for a restricted license is one hundred dollars, but no additional fee may be charged because of changes in the place and hours of employment, education, or residence. Twenty dollars of this fee must be deposited in the state state's general fund, and eighty dollars must be placed by the Comptroller General into a special restricted account to be used by the Department of Motor Vehicles to defray the expenses of the Department of Motor Vehicles Vehicle's expenses.
(4) Driving a motor vehicle outside the time limits and route imposed by a restricted license by the person issued that license is a violation of Section 56-1-460.
(I)(1) The Except as provided in subsection (I)(3), the period of a driver's license, permit, or nonresident operating privilege suspension for, or denial of issuance of a license or permit to, an arrested person who has no previous convictions for violating Section 56-5-2930, 56-5-2933, or 56-5-2945, or any other a law of this State or another state that prohibits a person from driving a motor vehicle while under the influence of alcohol or another drug other drugs within the ten years preceding a violation of this section, and who has had no previous suspension imposed pursuant to Section 56-5-2950 56-1-286, or 56-5-2951, or 56-5-2990, within the ten years preceding a violation of this section is:
(a) six months for a person who refuses to submit to a test pursuant to Section 56-5-2950; or
(b) one month for a person who takes a test pursuant to Section 56-5-2950 and has an alcohol concentration of fifteen one-hundredths of one percent or more.
(2) The period of a driver's license, permit, or nonresident operating privilege suspension for, or denial of issuance of a license or permit to, an arrested a person who has been convicted previously for violating Section 56-5-2930, 56-5-2933, or 56-5-2945, or any other another law of this State or another state that prohibits a person from driving a motor vehicle while under the influence of alcohol or another drug within the ten years preceding a violation of this section, or who has had a previous suspension imposed pursuant to Section 56-5-2950 56-1-286, or 56-5-2951, or 56-5-2990, within the ten years preceding a violation of this section is:
(a) for a second offense, nine months if he the person refuses to submit to a test pursuant to Section 56-5-2950, or two months if he the person takes a test pursuant to Section 56-5-2950 and has an alcohol concentration of fifteen one-hundredths of one percent or more;
(b) for a third offense, twelve months if he the person refuses to submit to a test pursuant to Section 56-5-2950, or three months if he the person takes a test pursuant to Section 56-5-2950 and has an alcohol concentration of fifteen one-hundredths of one percent or more; and
(c) for a fourth or subsequent offense, fifteen months if he the person refuses to submit to a test pursuant to Section 56-5-2950, or four months if he the person takes a test pursuant to Section 56-5-2950 and has an alcohol concentration of fifteen one-hundredths of one percent or more.
(3) In lieu of serving the remainder of a suspension or denial of the issuance of a license or permit, a person may enroll in the Ignition Interlock Device Program pursuant to Section 56-5-2941, end the suspension or denial of the issuance of a license or permit, and obtain an ignition interlock restricted license pursuant to Section 56-1-400. The ignition interlock device is required to be affixed to the motor vehicle equal to the length of time remaining on the person's suspension or denial of the issuance of a license or permit. If the length of time remaining is less than three months, the ignition interlock device is required to be affixed to the motor vehicle for three months. Once a person has enrolled in the Ignition Interlock Device Program and obtained an ignition interlock restricted license, the person is subject to Section 56-5-2941 and cannot subsequently choose to serve the suspension.
(J) A person's driver's license, permit, or nonresident operating privilege must be restored when the person's period of suspension or ignition interlock restricted license requirement under pursuant to subsection (I) has concluded, even if the person has not yet completed the Alcohol and Drug Safety Action Program in which he is enrolled. After the person's driving privilege is restored, he must the person shall continue the services of the Alcohol and Drug Safety Action Program in which he is enrolled. If the person withdraws from or in any way stops making satisfactory progress toward the completion of the Alcohol and Drug Safety Action Program, the person's license must be suspended until the completion of the Alcohol and Drug Safety Action Program. A person must shall be attending or have completed an Alcohol and Drug Safety Action Program pursuant to Section 56-5-2990 before his the person's driving privilege can be restored at the conclusion of the suspension period or ignition interlock restricted license requirement.
(K) When a nonresident's privilege to drive a motor vehicle in this State has been suspended under pursuant to the provisions of this section, the department must shall give written notice of the action taken to the motor vehicle administrator of the state of the person's residence and of any state in which he the person has a license or permit.
(L) The department must shall not suspend the privilege to drive of a person under the age of twenty-one pursuant to Section 56-1-286, if the person's privilege to drive has been suspended under pursuant to this section arising from the same incident.
(M) A person whose driver's license or permit is suspended pursuant to this section is not required to file proof of financial responsibility.
(N) An insurer may shall not increase premiums on, add surcharges to, or cancel the automobile insurance of a person charged with a violation of Section 56-1-286, 56-5-2930, 56-5-2933, or 56-5-2945, or another a law of this State another state that prohibits a person from driving a motor vehicle while under the influence of alcohol or another drug other drugs based solely on the violation unless he the person is convicted of the violation.
(O) The department must shall administer the provisions of this section and must promulgate regulations necessary to carry out its provisions.
(P) If a person does not request a contested case hearing within the thirty-day period as authorized pursuant to this section, the person may file with the department a form after enrolling in a certified Alcohol and Drug Safety Action Program to apply for a restricted license. The restricted license permits him to drive only to and from work and his place of education and in the course of his employment or education during the period of suspension. The restricted license also permits him to drive to and from Alcohol and Drug Safety Action Program classes or a court-ordered drug program. The department may issue the restricted license at any time following the suspension upon a showing by the individual that he is employed or enrolled in a college or university, that he lives further than one mile from his place of employment, place of education, the location of his Alcohol and Drug Safety Action Program classes, or the location of his court-ordered drug program, and that there is no adequate public transportation between his residence and his place of employment, his place of education, the location of his Alcohol and Drug Safety Action Program classes, or the location of his court-ordered drug program. The department must designate reasonable restrictions on the times during which and routes on which the individual may drive a motor vehicle. A change in the employment hours, place of employment, status as a student, status of attendance of Alcohol and Drug Safety Action Program classes, status of his court-ordered drug program, or residence must be reported immediately to the department by the licensee. The route restrictions, requirements, and fees imposed by the department for the issuance of the restricted license issued pursuant to this item are the same as those provided in this section had the person requested a contested case hearing. A restricted license is valid until the person successfully completes a certified Alcohol and Drug Safety Action Program, unless the person fails to complete or make satisfactory progress to complete the program."
SECTION 15. Section 56-5-2990 of the 1976 Code is amended to read:
"Section 56-5-2990. (A)(1) The Department of Motor Vehicles shall suspend the driver's license of a person who is convicted, receives sentence upon a plea of guilty or of nolo contendere, or forfeits bail posted for a violation of Section 56-5-2930, 56-5-2933, or for the violation of another law or ordinance of this State or of a municipality of this State a law of another state that prohibits a person from driving a motor vehicle while under the influence of intoxicating liquor, drugs, or narcotics for six months for the first conviction, plea of guilty or nolo contendre, or forfeiture of bail; one year for the a second conviction, plea of guilty or of nolo contendere, or forfeiture of bail; two years for the a third conviction, plea of guilty or of nolo contendere, or forfeiture of bail; and a permanent revocation of the driver's license for the a fourth or subsequent conviction, plea of guilty or of nolo contendere, or forfeiture of bail. Only those violations which occurred within ten years including and immediately preceding the date of the last violation shall constitute prior violations within the meaning of this section. However, if the third conviction occurs within five years from the date of the first offense, then the department shall suspend the driver's license for four years. A person whose license is revoked following conviction for a fourth offense as provided in this section is forever barred from being issued any license by the Department of Motor Vehicles to operate a motor vehicle except as provided in Section 56-1-385 alcohol or other drugs.
(2) For a first offense:
(a) If a person refused to submit to a breath test pursuant to Section 56-5-2950, the person's driver's license must be suspended six months. The person is not eligible for a provisional license pursuant to Article 7, Chapter 1, Title 56. In lieu of serving the remainder of the suspension, the person may enroll in the Ignition Interlock Device Program pursuant to Section 56-5-2941, end the suspension, and obtain an ignition interlock restricted license pursuant to Section 56-1-400. The ignition interlock device is required to be affixed to the motor vehicle equal to the length of time remaining on the person's suspension. If the length of time remaining is less than three months, the ignition interlock device is required to be affixed to the motor vehicle for three months. Once a person has enrolled in the Ignition Interlock Device Program and obtained an ignition interlock restricted license, the person is subject to Section 56-5-2941 and cannot subsequently choose to serve the suspension.
(b) If a person submitted to a breath test pursuant to Section 56-5-2950 and had an alcohol concentration of less than twelve one hundredths of one percent, the person's driver's license must be suspended six months. The person is eligible for a provisional license pursuant to Article 7, Chapter 1, Title 56. In lieu of serving the remainder of the suspension, the person may enroll in the Ignition Interlock Device Program pursuant to Section 56-5-2941, end the suspension, and obtain an ignition interlock restricted license pursuant to Section 56-1-400. The ignition interlock device is required to be affixed to the motor vehicle equal to the length of time remaining on the person's suspension. If the length of time remaining is less than three months, the ignition interlock device is required to be affixed to the motor vehicle for three months. Once a person has enrolled in the Ignition Interlock Device Program and obtained an ignition interlock restricted license, the person is subject to Section 56-5-2941 and cannot subsequently choose to serve the suspension.
(c) If a person submitted to a breath test pursuant to Section 56-5-2950 and had an alcohol concentration of twelve one hundredths of one percent or more, the person shall enroll in the Ignition Interlock Device Program pursuant to Section 56-5-2941, end the suspension, and obtain an ignition interlock restricted license pursuant to Section 56-1-400. The ignition interlock device is required to be affixed to the motor vehicle for six months. The person is not eligible for a provisional license pursuant to Article 7, Chapter 1, Title 56.
(3) For a second offense, a person shall enroll in the Ignition Interlock Device Program pursuant to Section 56-5-2941, end the suspension, and obtain an ignition interlock restricted license pursuant to Section 56-1-400. The ignition interlock device is required to be affixed to the motor vehicle for two years.
(4) For a third offense, a person shall enroll in the Ignition Interlock Device Program pursuant to Section 56-5-2941, end the suspension, and obtain an ignition interlock restricted license pursuant to Section 56-1-400. The ignition interlock device is required to be affixed to the motor vehicle for three years. If the third offense occurs within five years from the date of the first offense, the ignition interlock device is required to be affixed to the motor vehicle for four years.
(5) For a fourth or subsequent offense, a person shall enroll in the Ignition Interlock Device Program pursuant to Section 56-5-2941, end the suspension, and obtain an ignition interlock restricted license pursuant to Section 56-1-400. The ignition interlock device is required to be affixed to the motor vehicle for life.
(6) Except as provided in subsection (A)(4), only those offenses which occurred within ten years, including and immediately preceding the date of the last offense, shall constitute prior offenses within the meaning of this section.
(B) A person whose license is suspended under the provisions pursuant to this section, Section 56-1-286, Section 56-5-2945, or Section 56-5-2951 must be notified by the department of the suspension and of the requirement to enroll in and successfully complete an Alcohol and Drug Safety Action Program certified by the Department of Alcohol and Other Drug Abuse Services. A person who must complete an Alcohol and Drug Safety Action Program as a condition of reinstatement of his driving privileges or a court-ordered drug program may use the route restricted or special restricted driver's license to attend the Alcohol and Drug Safety Action Program classes or court-ordered drug program in addition to the other permitted uses of a route restricted driver's license or a special restricted driver's license. An assessment of the extent and nature of the alcohol and drug abuse problem, if any, of the applicant person must be prepared and a plan of education or treatment, or both, must be developed for the applicant person. Entry into and successful completion of the services, if the services are necessary, recommended in the plan of education or treatment, or both, developed for the applicant person is a mandatory requirement of the issuance of an ignition interlock restricted license and restoration of driving privileges to the applicant person whose license is suspended pursuant to this section. The Alcohol and Drug Safety Action Program shall determine if the applicant person has successfully completed the services. Alcohol and Drug Safety Action Programs shall meet at least once a month. The person whose license is suspended must shall attend the first Alcohol and Drug Safety Action Program available after the date of enrollment.
(C) The Department of Alcohol and Other Drug Abuse Services shall determine the cost of services provided by each certified Alcohol and Drug Safety Action Program. Each applicant person shall bear the cost of services recommended in the applicant's person's plan of education or treatment. The cost may not exceed five hundred dollars for education services, two thousand dollars for treatment services, and two thousand five hundred dollars in total for all services. No applicant person may be denied services due to an inability to pay. Inability to pay for services may not be used as a factor in determining if the applicant person has successfully completed services. An applicant A person who is unable to pay for services shall perform fifty hours of community service as arranged by the Alcohol and Drug Safety Action Program, which may use the completion of this community service as a factor in determining if the applicant person has successfully completed services. The Department of Alcohol and Other Drug Abuse Services will shall report annually to the House Ways and Means Committee and Senate Finance Committee on the number of first and multiple offenders completing the Alcohol and Drug Safety Action Program, the amount of fees collected and expenses incurred by each Alcohol and Drug Safety Action Program, and the number of community service hours performed in lieu of payment.
(D) If the applicant person has not successfully completed the services as directed by the Alcohol and Drug Safety Action Program within one year of enrollment, a hearing must be provided by the Alcohol and Drug Safety Action Program whose decision is appealable to the Department of Alcohol and Other Drug Abuse Services. If the applicant person is unsuccessful in the Alcohol and Drug Safety Action Program, the Department of Motor Vehicles may restore the privilege to drive a motor vehicle waive the successful completion of the program as a mandatory requirement of the issuance of an ignition interlock restricted license upon the recommendation of the Medical Advisory Board as utilized by the department Department of Motor Vehicles, if it the Medical Advisory Board determines public safety and welfare of the petitioner person may not be endangered.
(E) The Department of Motor Vehicles and the Department of Alcohol and Other Drug Abuse Services shall develop procedures necessary for the communication of information pertaining to relicensing, or otherwise. These procedures must be consistent with the confidentiality laws of the State and the United States. If the drivers a person's driver's license of any a person is suspended by authority of pursuant to this section, no an insurance company may shall not refuse to issue insurance to cover the remaining members of his the person's family, but the insurance company is not liable for any actions of the person whose license has been suspended or who has voluntarily turned his the person's license in to the Department of Motor Vehicles.
(F) Except as provided for in Section 56-1-365(D) and (E), the driver's license suspension periods under this section begin on the date the person is convicted, receives sentence upon a plea of guilty or of nolo contendere, or forfeits bail posted for the a violation of Section 56-5-2930, 56-5-2933, or for the violation of any other a law of this State or ordinance of a county or municipality of this State that prohibits a person from operating a motor vehicle while under the influence of intoxicating liquor, or narcotics; however, a person is not prohibited from filing a notice of appeal and receiving a certificate which entitles him to operate a motor vehicle for a period of sixty days after the conviction, plea of guilty or nolo contendere, or bail forfeiture pursuant to Section 56-1-365(F)."
SECTION 16. The repeal or amendment by this act of any law, whether temporary or permanent or civil or criminal, does not affect pending actions, rights, duties, or liabilities founded thereon, or alter, discharge, release or extinguish any penalty, forfeiture, or liability incurred under the repealed or amended law, unless the repealed or amended provision shall so expressly provide. After the effective date of this act, all laws repealed or amended by this act must be taken and treated as remaining in full force and effect for the purpose of sustaining any pending or vested right, civil action, special proceeding, criminal prosecution, or appeal existing as of the effective date of this act, and for the enforcement of rights, duties, penalties, forfeitures, and liabilities as they stood under the repealed or amended laws.
SECTION 17. This act takes effect on October 1, 2014. /
Renumber sections to conform.
Amend title to conform.
Senator HUTTO spoke on the Bill.
Senator LARRY MARTIN spoke on the Bill.
On motion of Senator MALLOY, the Bill was carried over.
Expression of Personal Interest
Senators BRYANT and LOURIE rose for an Expression of Personal Interest.
On motion of Senator COURSON, the Senate stood adjourned until 11:15 A.M. tomorrow to attend the Joint Assembly and at the conclusion of the Joint Assembly, the Senate would reconvene at 2:00 P.M.
On motion of Senator CAMPBELL, with unanimous consent, the Senate stood adjourned out of respect to the memory of Mr. Michael C. Macklen of Myrtle Beach, S.C. Mr. Macklen was the owner of Macklen Septic Tank Service and the brother-in-law of Senator CLEARY. Michael loved NASCAR racing and cooking. He lived everyday like it was his last. Michael was a loving husband and devoted father who will be dearly missed.
and
On motion of Senator HUTTO, with unanimous consent, the Senate stood adjourned out of respect to the memory of the Honorable Norman E. Fogle of Neeses, S.C. Norman was born in rural Orangeburg County, a son of the late Anthony and Lila Flake Fogle. He was a prominent local attorney and had served as First Circuit Solicitor until his medical retirement in 1983. Norman was a devoted church leader of Calvary Baptist Church and a faithful community servant. He also served in the U.S. Army and was an avid USC supporter. Norman was a loving husband to Emma Caughman Fogle. He was a devoted father and doting grandfather who will be dearly missed. | 2015-05-22T10:16:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3139272630214691, "perplexity": 6179.109808750802}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207924919.42/warc/CC-MAIN-20150521113204-00011-ip-10-180-206-219.ec2.internal.warc.gz"} |
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Call number: 9781420005813:ONLINE Show nearby items on shelf Title: AC power systems handbook Author(s): Jerry C. Whitaker Date: 2007 Edition: 3rd ed. Publisher: CRCnetBase Size: 1 online resource (428 p) Contents: Ch. 1. AC power systems -- ch. 2. Power-generation systems -- ch. 3. Power factor -- ch. 4. Power transformers -- ch. 5. Capacitors -- ch. 6. Semiconductors -- ch. 7. Rectifier and filter circuits -- ch. 8. Power electronics -- ch. 9. Origins of AC line disturbances -- ch. 10. Power disturbance characterization -- ch. 11. Power system protection methods -- ch. 12. Motor-generator set -- ch. 13. Uninterruptible power systems -- ch. 14. Power conditioning devices -- ch. 15. Transient-suppression devic es -- ch. 16. Facility wiring and transient protection -- ch. 17. Circuit-level transient suppression -- ch. 18. Grounding practices -- ch. 19. Grounding tower elements -- ch. 20. Facility ground-system design -- ch. 21. Standby power systems -- ch. 22. D esiging for fault-tolerance -- ch. 23. The efficient use of energy -- ch. 24. Safety and protection systems -- ch. 25. Reference data and tables -- ch. 26. Units conversion table. ISBN: 9780849340345 Series: eBooks Series: CRCnetBase Keywords: Electric power distribution , Electric power systems Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 1848210957:ONLINE Show nearby items on shelf Title: Electric Power for Automotive Drive Systems Author(s): Beretta Date: 2010 Publisher: Wiley-ISTE Size: 1 online resource (305 p.) ISBN: 9781848210950 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Electrical & Electronics Engineering Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 1848210086:ONLINE Show nearby items on shelf Title: Electric Power Systems Author(s): Crappe Date: 2008 Publisher: Wiley-ISTE Size: 1 online resource (449 p.) ISBN: 9781848210080 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Energy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 1118867092:ONLINE Show nearby items on shelf Title: Line Loss Analysis and Calculation of Electric Power Systems Author(s): Wu Date: 2016 Publisher: Wiley Size: 1 online resource (385 p.) ISBN: 9781118867099 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Electrical & Electronics Engineering Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 1118679695:ONLINE Show nearby items on shelf Title: Fundamentals of Electric Power Engineering: From Electromagnetics to Power Systems Author(s): Ceraolo Date: 2014 Publisher: Wiley-IEEE Press Size: 1 online resource (553 p.) ISBN: 9781118679692 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Energy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 0471453250:ONLINE Show nearby items on shelf Title: Communication and Control in Electric Power Systems - Application of Parallel and Distributed Processing Author(s): Shahidehpour Date: 2003 Publisher: Wiley-IEEE Press Size: 1 online resource (535 p.) ISBN: 9780471453253 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Energy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 0471446521:ONLINE Show nearby items on shelf Title: Understanding Electric Power Systems: An Overviewof the Technology and the Marketplace Author(s): Casazza Date: 2003 Publisher: Wiley-IEEE Press Size: 1 online resource (233 p.) ISBN: 9780471446521 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Energy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 0471443379:ONLINE Show nearby items on shelf Title: Market Operations in Electric Power Systems: Forecasting, Scheduling, and Risk Management Author(s): Shahidehpour Date: 2002 Publisher: Wiley-IEEE Press Size: 1 online resource (553 p.) ISBN: 9780471443377 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Energy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 0471280607:ONLINE Show nearby items on shelf Title: Renewable and Efficient Electric Power Systems Author(s): Masters Date: 2004 Publisher: Wiley-IEEE Press Size: 1 online resource (681 p.) ISBN: 9780471280606 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Energy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 0471234397:ONLINE Show nearby items on shelf Title: Electric Power Systems: Author(s): Saccomanno Date: 2003 Publisher: Wiley-IEEE Press Size: 1 online resource (745 p.) ISBN: 9780471234395 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Energy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 0471178594:ONLINE Show nearby items on shelf Title: Electric Power Systems: A Conceptual Introduction, Online Version Author(s): von Meier Date: 2006 Publisher: Wiley-IEEE Press Size: 1 online resource (329 p.) ISBN: 9780471178590 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Energy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 0470484403:ONLINE Show nearby items on shelf Title: Direct Methods for Stability Analysis of Electric Power Systems: Theoretical Foundation, BCU Methodologies and Applications Author(s): Chiang Date: 2010 Publisher: Wiley Size: 1 online resource (495 p.) ISBN: 9780470484401 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Energy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 0470484187:ONLINE Show nearby items on shelf Title: Understanding Electric Power Systems: An Overview Of Technology, the Marketplace, and Government Regulation, Second Edition Author(s): Casazza Date: 2010 Publisher: Wiley-IEEE Press Size: 1 online resource (345 p.) ISBN: 9780470484180 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Energy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 0470472081:ONLINE Show nearby items on shelf Title: Economic Market Design and Planning for Electric Power Systems Author(s): Momoh Date: 2009 Publisher: Wiley-IEEE Press Size: 1 online resource (293 p.) ISBN: 9780470472088 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Energy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 0470260645:ONLINE Show nearby items on shelf Title: Restructured Electric Power Systems: Analysis of Electricity Markets with Equilibrium Models Author(s): Zhang Date: 2010 Publisher: Wiley-IEEE Press Size: 1 online resource (331 p.) ISBN: 9780470260647 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Energy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 047018776X:ONLINE Show nearby items on shelf Title: Integration of Green and Renewable Energy in Electric Power Systems Author(s): Keyhani Date: 2009 Publisher: Wiley Size: 1 online resource (329 p.) ISBN: 9780470187760 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Electrical & Electronics Engineering Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: TK3227.I33::1982 Show nearby items on shelf Title: IEEE recommended practice for grounding of industrial and commercial power systems Author(s): Date: 1982 Edition: [4th ed.]. Publisher: Institute of Electrical and Electronics Engineers, New York Size: 136 ISBN: 0471895733 Keywords: Electric currents Grounding United States. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
Call number: TK3144.W334::2010 Show nearby items on shelf Title: High voltage engineering Author(s): C. L. Wadhwa Date: 2010 Edition: 3rd ed. Publisher: Tunbridge Wells, UK : New Age Science Size: 291 p ISBN: 9781906574727 Keywords: Electric insulators and insulation , Electric power distribution TOC = Electric stress estimation and control -- Brea Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: TK1005.G76::1986 Show nearby items on shelf Title: Power system analysis Author(s): Charles A. Gross Date: 1986 Edition: 2nd ed. Publisher: Wiley, New York Size: 593 ISBN: 0471862061 Keywords: Electric power systems. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
Call number: TK1001.F28::1997 Show nearby items on shelf Title: Electrical power systems technology Author(s): Stephen W. Fardo Dale R. Patrick Date: 1997 Edition: 2nd ed. Publisher: Newnes, Boston Size: 437 ISBN: 0750697229 Keywords: Electric power systems. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
Call number: SPRINGER-1994-9783709193525:ONLINE Show nearby items on shelf Title: Few-Body Problems in Physics ’93 Proceedings of the XIVth European Conference on Few-Body Problems in Physics, Amsterdam, The Netherlands, August 23–27, 1993 Author(s): Date: 1994 Size: 1 online resource (486 p.) Note: 10.1007/978-3-7091-9352-5 Contents: Session 1 -- Baryon-baryon interactions -- Precise measurements of spin observables in nucleon-nucleon scattering -- Session 2 -- Production of antihyperon-hyperon pairs at LEAR -- Antiproton-proton partial-wave analysis below 925 MeV/c -- Session 3 -- Spin observables and annihilation in antiproton-proton reactions -- The nucleon-nucleon interaction and violation of fundamental symmetries -- Status of the Virginia Tech Partial-Wave Analyses -- Session 4 -- Periodic orbits and recurrences: an introduction and review -- Nuclear aspects of few-baryon physics -- Session 5 -- Electromagnetic form factors of two-nucleon and three-nucleon bound states -- Electron scattering with polarized 3He targets -- Reactions of polarised electrons on D and 3He -- Session 6 -- Electron scattering from polarised deuterium at VEPP-3 -- Results of (e,e’x) studies on 4He -- Separation of electromagnetic response functions of few-body nuclei in (e,e’p) reactions -- Session 7 -- A Simultaneous measurement of the (?,n) and (?,p) reactions in 4He -- Electrodisintegration of the deuteron -- Exclusive electron scattering from deuterium at high Q2 -- Session 8 -- Recent advances in the quantum theory of chemical reaction rates 2 -- Proton-deuteron break-up including Coulomb effects -- Session 9 -- Structure and fragmentation of few-body atomic systems -- Recent developments on the four-nucleon frontier -- Photo-induced reactions on 4He -- Session 10 -- Nuclear transitions in muonic molecules -- Theory of formation and decay of metastable states of hadronic helium atoms -- Signature of a narrow ?NN-resonance in the energy dependence of the pionic double charge exchange -- Exotic dibaryons correlated with experiment -- Alpha-particle binding energies for realistic nucleon-nucleon interactions -- Session 11 -- Recent results from the nucleon-nucleon program at SATURNE II -- Measurement of the np?pp?- at 443 MeV -- A gauge invariant unitary theory for pion photoproduction -- The ?d??r0d and ?d?pn reactions in the ?-resonance region -- Final-state interaction effects in the coupled-channel NN-N? approach of the ?NN System -- Session 12 -- Cross section and analyzing power A y in the proton induced deuteron breakup reaction at 65 MeV -- Meson production near threshold via the reaction p+d?3He+X -- Influence of isobars on deuteron electric stucture function A(q2) -- Tensor and vector analyzing powers in the reaction 2H(e,e’p) -- Outgoing nucleon polarization in exclusive deuteron electrodisintegration -- Trinucleon threshold electrodisintegration -- Session 13 -- Solving Faddeev equations in the interaction domain -- Cluster-dynamical treatment of three-nucleon forces -- Variational calculations for scattering states in few-nucleon systems -- Relativistic meson spectroscopy in momentum space -- Relativistic two-body bound-state calculations beyond the ladder approximation -- A relativistic constituent quark model -- Session 14 -- Convolution approach to the ?NN system -- Pionic hydrogen and the low energy ?N-interaction -- The E2/M1 mixing ratio in the excitation of the ? from polarized photo-reactions -- Session 15 -- Pion photoproduction on the nucleon and light nuclei -- Pion absorption in tritium and helium -- Session 16 -- Monte Carlo studies of light nuclei: structure and response -- Numerical methods in configuration-space A=3,4 bound-state and scattering calculations -- Hyperspherical approach to ultra-precise nonvariational calculations in the few-body problem -- Session 17 -- The role of two-body interactions in the description of few and many-nucleon systems -- Stability of Hierarchical Triple Stars -- Session 18 -- Relativistic quasipotential approaches and electromagnetic form factors of the deuteron -- Relativistic effects in $$q\bar q$$ systems -- Charmonium spectroscopy with antiprotons -- Session 19 -- Quarks in few hadron systems -- Pions and neutrinos as probes of the nucleon and nuclear few-body systems -- Session 20 -- Spin-structure function of the neutron (3He): SLAC results -- The spin-dependent structure function of the deuteron -- Inclusive quasielastic and deep inelastic scattering of polarized electrons by polarized 3He ISBN: 9783709193525 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Few-Body Systems, Supplementum: 7 Keywords: Physics , Nuclear physics , Heavy ions , Hadrons , Elementary particles (Physics) , Quantum field theory , Nuclear fusion , Atoms , Physical measurements , Measurement , Physics , Elementary Particles, Quantum Field Theory , Nuclear Physics, Heavy Ions, Hadrons , Nuclear Fusion , Measurement Science and Instrumentation , Atomic, Molecular, Optical and Plasma Physics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1978-9783540357605:ONLINE Show nearby items on shelf Title: Few Body Systems and Nuclear Forces I 8. International Conference Held in Graz, August 24–30, 1978 Author(s): Date: 1978 Size: 1 online resource (442 p.) Note: 10.1007/3-540-08917-9 Contents: Neutron-proton charge exchange scattering between 200 and 600 MeV -- n-p Charge exchange scattering from 150 TO 800 MeV -- Nucleon-nucleon scattering in a non-Abelian gauge theory -- Coupled channel effects on nucleon-nucleon phase shifts and resonances -- Nucleon-nucleon potential from Regge-Pole theory in momentum space -- N-N potential from Regge-Pole theory -- On the potential reconciliation of the n-p 3S1-3D1 and 3D2 phase parameters and the quadrupole moment of the deuteron -- Role of non-iterative diagrams in nn-scattering -- Correlations between potentials and observables in the nn interaction -- Particle mixing and charge asymmetric an forces -- Treatment of divergent expansions in scattering theory -- Measurements on bound antinucleon-nucleon systems -- Nonperturbative calculation of nucleon-antinucleon annihilation diagrams in a simple model -- Investigation of the A.N interaction in the deuteron -- Investigation of the ?NN, ??N and ??? formfactor -- Light front field theory treatment of the 2n problem -- Unity of relativistic corrections and meson exchange currents -- Nucleon — Nucleon phase shifts calculated using the Blankenbecler — Sugar equation -- Quasi-elastic electron scattering and the momentum distribution of the deuteron -- Neutron-proton capture total cross section between 38 and 73 MeV -- The neutron electric form factor and quasi-elastic electron-deuteron scattering -- The electron-deuteron tensor polarization and the short range behaviour of the deuteron wave function -- Deuteron formfactor calculations with the Bethe-Salpeter equation -- Relativistic calculation of the photon circular polarization in np??d process -- Thermal n-p radiative capture -- Special coherent states for ?-n scattering -- On the field-theoretic approach to low-energy ?-N interaction -- S-wave pion-nucleon phase shifts in Padé approximation -- Some considerations of the nucleon as a bound triquark -- Multiquark dibaryon resonances -- High energy p-p elastic scattering and constituent multiple scattering model -- A new stable dibaryon -- Proton-proton bremsstrahlung -- Proton-proton bremsstrahlung with polarized protons -- Isobar excitation in proton-proton bremsstrahlung -- Criteria for the choice of p-p bremsstrahlung experiments -- The interference of initial and final state amplitudes in p-d bremsstrahlung near the break-up threshold -- Off-energy-shell continuation of the two-body T-matrix in the presence of resonances -- The coulomb contribution to proton-proton scattering phase shifts -- The Coulomb contribution to ?+-p phase shifts -- The one photon exchange potential in configuration space -- The Coulomb interference term in polarization analysis and the determination of the transition matrix -- Polarized proton-proton scattering at intermediate energies -- Polarization measurement in proton-proton scattering at 6.14 MeV -- Measurement of spin interactions in high Pt proton-proton elastic scattering -- Measurement of the component Ayy of the spin-correlation tensor for p-p elastic scattering at 10 MeV -- D,R,A and P for small angle p-p elastic scattering at 312,392 and 493 MeV -- NP triple scattering experiments and I=O NN phase shifts -- Status of n-p measurements and phase shift analyses near 50 MeV -- The production of pions by polarized protons incident on hydrogen and deuterium -- Quasi-elastic scattering of polarized protons -- The three-nucleon bound state computed with explicit ?(1236) components -- Solution of the bound trinucleon including the effects of the isobar ?(1236) -- Perturbation approach to the 3He bound state with the reid soft-core potential -- Three nucleon observables with meson theoretical interactions -- Charge-dependent three-body force with N*(1236) in the intermediate states -- The N-D and N-D* momentum distributions -- Electromagnetic structure of 3He and 4He at large momentum transfer -- S-matrix pole trajectories in the 3N-system -- Is there a three neutron resonance? -- Three-body reactions with charged particles -- Unexpected behavior of the cca transition operators under particle interchange -- Minimal relativistic dynamics of the 3? and ??N systems -- (n,d) elastic differential cross section at 2.48 and 3.28 MeV and related phase shift analyses -- Backward elastic nd-scattering in the energy range 350 – 550 MeV -- nd backward scattering from 200 to 800 MeV -- Quasi free scattering in the 2H(n, 2n)p reaction at En = 21. 5MeV -- A four-dimensional approach to the almost 4? H(d,2p)n data -- The D(p,2p)n reaction at 50 MeV -- What collinearity effect? -- A test on p1-n-p2 colinearity resonance of D(po,p1p2)n reaction at E0= 156 MeV -- Coulomb break-up of Deuteron by Muon and n-p off-energy-shell effects -- Detailed calculations of ?-d elastic scattering at medium energies -- Practical scheme for low energy ? - d scattering -- An important contribution to ?D scattering in the resonance region -- The NN? system--an effective 3-body problem with unusual disconnectedness structure -- Pion-deuteron optical potential -- Dibaryon resonances in ?NN and ??NN dynamics -- Elastic scattering differential cross-section of ?± on deuteron at 47 MeV -- Application of Faddeev equations to K? d??? Ap at low energy -- Exchange current effects in the reaction 3He(?,?+)3H -- Electromagnetic sum rules for light nuclei -- Practical calculations of P-D scattering -- Differential cross-sections for elastic p-d and n-d scattering at 10 MeV -- Investigation of the p-d elastic scattering with polarized protons and deuterons -- Measurement on T21 for proton-deuteron elastic scattering at ED 20 Mev -- On the asymptotic normalization of the deuteron D-state by p-d elastic scattering -- Proton-deuteron analyzing power at 14.1 MEV -- 1H( $$\vec n$$ ,n)1H and 2H( $$\vec n$$ ,n)2H at 14.2 MeV -- Analysing power measurements in deuteron-proton scattering from 5 to 13 MeV -- Backward angle p-d elastic scattering at 316 and 516 MeV -- Neutron analyzing power in the reaction $$\vec n$$ +d?n1+n2+p -- Vector analyzing power in final state interaction region for deuteron breakup reaction -- Solution of four-nucleon integral equations using the effective UPA -- The bound states of the two-, three- and four-nucleon systems and the nuclear force -- Energy-dependent pole approximations in the four-body equations -- Four-body calculation of 3He(p,p)3He and d(d,p)3H -- Four-body model of the four-nucleon system -- Study of few-nucleon systems by means of analytical continuation in core constant -- Analyzing power measurements for the 4-nucleon system below 6 MeV -- Comparison of the mirror reactions 2H(d,p)3H and 2H(d,n)3He -- Analyzing power for the elastic n-3He-scattering -- The low energy neutron scattering lengths of He3 and T and their relation to the four-body problem -- p+3He elastic scattering from 18 to 48 MeV -- Collinearity revisited in D(d,pd)n at 12.2 MeV -- The 2H(d,N) reaction: Measurement and theoretical analysis -- The 3He(p,pp)d*/3He(p,pp)d ratio at E = 136 MeV -- Photo-disintegration of the alpha particle -- The bound states of ? 4 He - ? 4 H -- Some phenomena near nuclear surface -- Exploration of a continuum ambiguity in the 3He(d,d)3He phase-shift analysis at 0.32 MeV -- The scattering of polarized deuterons on 3 He between 10 and 17 MeV -- The deuteron break-up induced by ?-particles -- Low-energy alpha-induced deuteron breakup studied with a six-detector system and a Faddeev analysis -- Investigation of resonances in d-? elastic scattering -- Three-body model of the deuteron breakup reaction by an ?-particle -- Three model approaches to the ?-d relative wave function in the 6Li nucleus -- ?+n+P??+n+P elastic scattering at very low energies -- 3He + 6Li elastic scattering at 27 MeV -- The 6Li(3He,3He)6Li and 6Li(3He,3H)6Be Reactions at 27 MeV -- Three trion breakup of 6Li + 3He at 132 MeV -- Three-alpha model calculations and the O2 + state of 12 C -- Three-body calculations for light nuclei using separable potentials -- A model three-particle system for studying limitations of the shell-model approach to nuclear reactions -- Effect of higher ordered terms in the cluster expansion of correlation function on the structure of light nuclei -- Nucleon spectral function in Li6 -- New-results in the search of high energy deuterons from the 3He + 3He reaction -- Interaction-time effects of quasifree processes -- Continuous particle spectra from ?-induced breakup of ?-particles at E? = 130 MeV -- Phase-space analysis of continuous spectra -- Four-body approach to ?(3He,3He)? and 6Li(p,p)6Li reactions -- Application of few-body methods to atomic and molecular structure -- Two Hilbert space scattering theory: Recent progress -- Relationships between different formulations of N-body scattering and origin of spurious solutions -- Spurious solutions in few-body equations -- Time delay in N-body scattering -- Derivation of an approximate three-body model of deuteron stripping from N-body scattering theory -- Time dependent approach to the collision of two charged composite particles -- Scattering amplitudes for two charged fragments -- On off-shell transformations and wave function formalisms in many-body scattering theories -- Hamiltonian formulation of N-body theories -- Quantal rules for non-Hermitian bound state formalisms based on N-body scattering theory -- Method of orthogonalized distorted waves in the many-body scattering theory -- Ghost states and pauli principle in many-body scattering -- The green function hierarchy and the three-body problem -- Examination of many-body resonances by means of analytical continuation of bound states -- Convergence of the distorted wave series -- On asymptotic completeness in scattering theory -- Multiparticle core in nuclei -- The two pion exchange three-nucleon potential and nuclear matter -- Charge asymmetry of nuclear forces and binding energies of heavy nuclei -- Solution of the inverse scattering problem in the finite-difference approximation ISBN: 9783540357605 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Lecture Notes in Physics: 82 Keywords: Physics , Physics , Physics, general Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. 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# Preparatory Joint Sessions on "Open questions and News Ideas"
7-8 July 2020
US/Eastern timezone
## Quantifying the effects of beam polarisation on charged triple gauge couplings
Not scheduled
20m
Short Talks
### Speaker
Jakob Beyer (DESY)
### Description
Charged triple gauge couplings (cTGCs) describe potential deviations from the Standard Model in the coupling of two $W$ bosons to a $Z$ boson or a photon. These couplings may interfere with the extraction of Higgs properties. Future $e^+e^-$ colliders need to measure these cTGCs with high precision to fully exploit the potential of their Higgs program.
Current proposals for $e^+e^-$ colliders vary in many aspects, most notably in their energy, luminosities and beam polarisations. Of those, the energy determines the relevant physics and the luminosity trivially scales the statistical precision.
Beam polarisation refers to the preferred direction of the spin in the beam particles. A dedicated magnet setup can flip the direction of a spin with non-zero polarisation.
Electroweak physics depends on the chirality and therefore the spin of the colliding particles. This flipping of the spin changes the allowed interactions. Both reducible and irreducible backgrounds can be suppressed by choosing the appropriate polarisation combination. The cTGC measurement is performed in the production of W bosons and highly sensitive to this effect.
While the physics changes when flipping the polarisations, the systematic effects remain the same. Beam polarisation may therefore provide a direct handle on systematic uncertainties in any measurement.
This study aims to quantify these effects of that a polarised beam may offer.
An extraction of cTGCs is performed together with a measurement of beam polarisations and 2-fermion parameters on generator level differential distributions. The fit is planned to be extended to include systematic effects that are correlated between the different processes.
A collider with polarised beams may achieve a qualitatively different measurement of cTGCs and other electroweak parameters. The extent to which polarisation may reduce systematics and provide access to electroweak physics needs to be clarified.
### Presentation Materials
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http://dlmf.nist.gov/31.11 | # §31.11(i) Introduction
The formulas in this section are given in Svartholm (1939) and Erdélyi (1942b, 1944).
The series of Type I (§31.11(iii)) are useful since they represent the functions in large domains. Series of Type II (§31.11(iv)) are expansions in orthogonal polynomials, which are useful in calculations of normalization integrals for Heun functions; see Erdélyi (1944) and §31.9(i).
For other expansions see §31.16(ii).
# §31.11(ii) General Form
Let $w(z)$ be any Fuchs–Frobenius solution of Heun’s equation. Expand
31.11.1 $w(z)=\sum_{j=0}^{\infty}c_{j}P_{j},$
where (§15.11(i))
31.11.2 $P_{j}=\mathop{P\/}\nolimits\!\begin{Bmatrix}0&1&\infty&\\ 0&0&\lambda+j&z\\ 1-\gamma&1-\delta&\mu-j&\end{Bmatrix},$
with
31.11.3 $\lambda+\mu=\gamma+\delta-1=\alpha+\beta-\epsilon.$ Symbols: $\gamma$: real or complex parameter, $\delta$: real or complex parameter, $\epsilon$: real or complex parameter, $\alpha$: real or complex parameter, $\beta$: real or complex parameter, $\lambda$ and $\mu$ Permalink: http://dlmf.nist.gov/31.11.E3 Encodings: TeX, pMML, png
The coefficients $c_{j}$ satisfy the equations
31.11.4 $L_{0}c_{0}+M_{0}c_{1}=0,$
31.11.5 $K_{j}c_{j-1}+L_{j}c_{j}+M_{j}c_{j+1}=0,$ $j=1,2,\dots$,
where
31.11.6 $\displaystyle K_{j}$ $\displaystyle=-\frac{(j+\alpha-\mu-1)(j+\beta-\mu-1)(j+\gamma-\mu-1)(j+\lambda% -1)}{(2j+\lambda-\mu-1)(2j+\lambda-\mu-2)},$ 31.11.7 $\displaystyle L_{j}$ $\displaystyle=a(\lambda+j)(\mu-j)-q+\frac{(j+\alpha-\mu)(j+\beta-\mu)(j+\gamma% -\mu)(j+\lambda)}{(2j+\lambda-\mu)(2j+\lambda-\mu+1)}+\frac{(j-\alpha+\lambda)% (j-\beta+\lambda)(j-\gamma+\lambda)(j-\mu)}{(2j+\lambda-\mu)(2j+\lambda-\mu-1)},$ 31.11.8 $\displaystyle M_{j}$ $\displaystyle=-\frac{(j-\alpha+\lambda+1)(j-\beta+\lambda+1)(j-\gamma+\lambda+% 1)(j-\mu+1)}{(2j+\lambda-\mu+1)(2j+\lambda-\mu+2)}.$
$\lambda$, $\mu$ must also satisfy the condition
31.11.9 $M_{-1}P_{-1}=0.$ Symbols: $P_{j}$ and $M_{j}$: coefficients Referenced by: §31.11(iii) Permalink: http://dlmf.nist.gov/31.11.E9 Encodings: TeX, pMML, png
# §31.11(iii) Type I
Here
31.11.10 $\displaystyle\lambda$ $\displaystyle=\alpha,$ $\displaystyle\mu$ $\displaystyle=\beta-\epsilon,$
or
31.11.11 $\displaystyle\lambda$ $\displaystyle=\beta,$ $\displaystyle\mu$ $\displaystyle=\alpha-\epsilon.$
Then condition (31.11.9) is satisfied.
Every Fuchs–Frobenius solution of Heun’s equation (31.2.1) can be represented by a series of Type I. For instance, choose (31.11.10). Then the Fuchs–Frobenius solution at $\infty$ belonging to the exponent $\alpha$ has the expansion (31.11.1) with
31.11.12 $P_{j}=\frac{\mathop{\Gamma\/}\nolimits\!\left(\alpha+j\right)\mathop{\Gamma\/}% \nolimits\!\left(1-\gamma+\alpha+j\right)}{\mathop{\Gamma\/}\nolimits\!\left(1% +\alpha-\beta+\epsilon+2j\right)}z^{-\alpha-j}\*\mathop{{{}_{2}F_{1}}\/}% \nolimits\!\left({\alpha+j,1-\gamma+\alpha+j\atop 1+\alpha-\beta+\epsilon+2j};% \frac{1}{z}\right),$
and (31.11.1) converges outside the ellipse $\mathcal{E}$ in the $z$-plane with foci at 0, 1, and passing through the third finite singularity at $z=a$.
Every Heun function (§31.4) can be represented by a series of Type I convergent in the whole plane cut along a line joining the two singularities of the Heun function.
For example, consider the Heun function which is analytic at $z=a$ and has exponent $\alpha$ at $\infty$. The expansion (31.11.1) with (31.11.12) is convergent in the plane cut along the line joining the two singularities $z=0$ and $z=1$. In this case the accessory parameter $q$ is a root of the continued-fraction equation
31.11.13 $\left(L_{0}/M_{0}\right)-\cfrac{K_{1}/M_{1}}{L_{1}/M_{1}-\cfrac{K_{2}/M_{2}}{L% _{2}/M_{2}-\cdots}}=0.$ Symbols: $K_{j}$: coefficients, $L_{j}$: coefficients and $M_{j}$: coefficients Referenced by: §31.18 Permalink: http://dlmf.nist.gov/31.11.E13 Encodings: TeX, pMML, png
The case $\alpha=-n$ for nonnegative integer $n$ corresponds to the Heun polynomial $\mathop{\mathit{Hp}_{n,m}\/}\nolimits\!\left(z\right)$.
The expansion (31.11.1) for a Heun function that is associated with any branch of (31.11.2)—other than a multiple of the right-hand side of (31.11.12)—is convergent inside the ellipse $\mathcal{E}$.
# §31.11(iv) Type II
Here one of the following four pairs of conditions is satisfied:
31.11.14 $\displaystyle\lambda$ $\displaystyle=\gamma+\delta-1,$ $\displaystyle\mu$ $\displaystyle=0,$ 31.11.15 $\displaystyle\lambda$ $\displaystyle=\gamma,$ $\displaystyle\mu$ $\displaystyle=\delta-1,$ 31.11.16 $\displaystyle\lambda$ $\displaystyle=\delta,$ $\displaystyle\mu$ $\displaystyle=\gamma-1,$ 31.11.17 $\displaystyle\lambda$ $\displaystyle=1,$ $\displaystyle\mu$ $\displaystyle=\gamma+\delta-2.$
In each case $P_{j}$ can be expressed in terms of a Jacobi polynomial (§18.3). Such series diverge for Fuchs–Frobenius solutions. For Heun functions they are convergent inside the ellipse $\mathcal{E}$. Every Heun function can be represented by a series of Type II.
# §31.11(v) Doubly-Infinite Series
Schmidt (1979) gives expansions of path-multiplicative solutions (§31.6) in terms of doubly-infinite series of hypergeometric functions. | 2014-10-31T13:38:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 151, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.937242329120636, "perplexity": 1690.9799533052474}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637899702.24/warc/CC-MAIN-20141030025819-00185-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://trove.nla.gov.au/work/126115?q&versionId=134161 | # English, Article edition: ON ASYNCHRONOUS CELLULAR AUTOMATA A. Ã…. HANSSON; H. S. MORTVEIT; C. M. REIDYS
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Physical Description
• article
Language
• English
### Edition details
Title
• ON ASYNCHRONOUS CELLULAR AUTOMATA
Author
• A. Ã…. HANSSON
• H. S. MORTVEIT
• C. M. REIDYS
Physical Description
• article
Notes
• We study asynchronous cellular automata (ACA) induced by symmetric Boolean functions [1]. These systems can be considered as sequential dynamical systems (SDS) over words, a class of dynamical systems that consists of (a) a finite, labeled graph Y with vertex set {v1,â¦,vn} and where each vertex vi has a state xvi in a finite field K, (b) a sequence of functions (Fvi,Y)i, and (c) a word w = (w1,â¦,wk), where each wi is a vertex in Y. The function Fvi,Y updates the state of vertex vi as a function of the state of vi and its Y-neighbors and maps all other vertex states identically. The SDS is the composed map $[\mathfrak{F}_Y,w]=\prod_{i=1}^{k} F_{w_{i}}: K^n\rightarrow K^n$. In the particular case of ACA, the graph is the circle graph on n vertices (Y = Circn), and all the maps Fvi are induced by a common Boolean function. Our main result is the identification of all w-independent ACA, that is, all ACA with periodic points that are independent of the word (update schedule) w. In general, for each w-independent SDS, there is a finite group whose structure contains information about for example SDS with specific phase space properties. We classify and enumerate the set of periodic points for all w-independent ACA, and we also compute their associated groups in the case of Y = Circ4. Finally, we analyze invertible ACA and offer an interpretation of S35 as the group of an SDS over the three-dimensional cube with local functions induced by nor3 + nand3.
• Sequential dynamical system, asynchronous cellular automaton, periodic point, phase space, update schedule invariance, invertibility
• RePEc:wsi:acsxxx:v:08:y:2005:i:04:p:521-538
Language
• English
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https://physics.fandom.com/wiki/Dot_product | ## FANDOM
162 Pages
The dot product is a vector operation, which, along with the cross product and scalar multiplication, comprise the three types of "multiplication" operations that can be performed on vectors. Vector division is not defined.
The fundamental definition of a dot product is the product of the scalar magnitudes (lengths) of each vector and the cosine of the angle in between them. $\vec{u} \cdot \vec{v} = |\vec{u}| |\vec{v}| \cos(\theta)$
This definition can be equivalently written as a scalar projection, or component, of vector u onto vector v, times the magnitude of vector v: $\vec{u} \cdot \vec{v} = |\vec{v}| \mathrm{comp}_{\vec{v}} \vec{u}$
By consequence of the definition, a dot product is the sum of the products of corresponding elements within the vector. This is often regarded as an alternative definition. Given the two (3-dimensional) vectors u and v:
• $\vec{u} = \langle u_1,u_2,u_3 \rangle = u_1 \mathbf{\hat{i}} + u_2 \mathbf{\hat{j}} + u_3 \mathbf{\hat{k}}$
• $\vec{v} = \langle v_1,v_2,v_3 \rangle = v_1 \mathbf{\hat{i}} + v_2 \mathbf{\hat{j}} + v_3 \mathbf{\hat{k}}$
The dot product is:
$\vec{u} \cdot \vec{v} = u_1 v_1 + u_2 v_2 + u_3 v_3$
Community content is available under CC-BY-SA unless otherwise noted. | 2020-07-13T22:12:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9260179996490479, "perplexity": 311.80748615067034}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657146845.98/warc/CC-MAIN-20200713194203-20200713224203-00336.warc.gz"} |
https://www.usgs.gov/center-news/volcano-watch-kulanaokuaiki-campground-a-whole-lot-shaking-going | # Volcano Watch — Kulanaokuaiki campground: a whole lot of shaking going on
Release Date:
On March 31, Hawaii Volcanoes National Park officially opened Kulanaokuaiki campground, a barrier-free facility along the Hilina Pali Road south of Kīlauea's caldera. The new campground replaces the Kipuka Nene picnic area, 2 km (1.2 miles) farther southwest, which is now closed to protect Hawaii's state bird.
On March 31, Hawaii Volcanoes National Park officially opened Kulanaokuaiki campground, a barrier-free facility along the Hilina Pali Road south of Kīlauea's caldera. The new campground replaces the Kipuka Nene picnic area, 2 km (1.2 miles) farther southwest, which is now closed to protect Hawaii's state bird. Kulanaokuaiki campground occupies a dynamic landscape controlled by Kīlauea's eruptive and faulting history.
The name tells a lot about the area. Kulanaokuaiki means "the shaking of a small spine [or sharp ridge]." The campground is just north of the 15-m-high (50-foot-high) pali that bears its name. This pali is an earthquake fault, formed by vertical ground movement during periods of intense shaking. Imagine people on top of the pali during an earthquake. Rocks would crash from the face of the pali to the ground below, and the pali would tremble from one shock after another during a swarm of earthquakes.
Such an earthquake swarm took place 35 years ago. On Christmas Eve and Day in 1965, strong shaking and faulting broke the Hilina Pali Road, where it crosses Kulanaokuaiki Pali near the new campground. The pavement was offset vertically 2.6 m (8.4 feet). The campground side of the fault went down 1.8 m (6 feet), and the other side (the south side) went up 0.8 m (2.4 feet). During the swarm, a truck from HVO carrying portable seismic equipment was parked near the broken road when it was nearly toppled by a large earthquake.
Hundreds of other faults and cracks north and northeast of Kulanaokuaiki Pali broke open and moved during the 1965 swarm. Similar, though smaller, episodes of ground breakage had occurred in 1960 and 1963, and another was to take place in 1975. In fact, this area, part of the Koae fault system, is one of the most active areas of faulting in the world. In the past 700 years or so, the Koae system has opened nearly 20 m (65 feet) in a north-south direction along a traverse that passes just west of the new campground. Along another traverse 2 km (1.2 miles) northeast of the first, the amount of opening is even greater, more than 30 m (100 feet).
The Koae fault system is part of the breakaway zone that, over long periods of time, separates Kīlauea's mobile south flank from the rest of the volcano. Swarms of earthquakes and ground ruptures will recur for thousands of years to come, and the name of the new campground will remain pertinent.
Lava flows as well as shaking and cracking have impacted the area. The campground is located in a small kipuka. The older flow in the kipuka is more than 1,300 years old, and the younger surrounding the kipuka is about 700 years old. Both flows were erupted from the summit of Kīlauea at times when lava flows could escape the caldera. The present caldera will have to fill up more before any lava erupted in it can reach the new campground, and there are several pali between that would have to be overtopped or run around. For those reasons, the campground seems rather safe from lava inundation for some time to come.
Between the two flows at the campground are several beds of volcanic ash and blocks. These layers were well exposed when the pit for the campground toilet was being dug. That is now off limits, but more layers can be seen by walking westward for 200 m (yards) or so to a place where little grass-covered mesas of ash stand above the older flow. Careful looking will find heavy gray rocks 3 cm (1 inch) or more in diameter lying on the surface of the older flow. These rocks rained from the sky during one or more powerful explosions before about A.D. 1000. Such explosions could happen again, though they are rarer events than lava flows.
Kulanaokuaiki campground is in a dynamic geologic setting. Enjoy!
### Volcano Activity Update
Eruptive activity of Kīlauea Volcano continued unabated during the past week. Lava is erupting from Puu Oo and flowing through a network of tubes toward the coast. Lava is visible at times on Pulama pali, and surface flows are active in the area between the Royal Gardens subdivision private access road and the sea coast. Lava is intermittently entering the ocean between Wahaula and Kamokuna. The public is reminded that the ocean-entry areas are extremely hazardous, with explosions accompanying sudden collapses of the new land. The active lava flows are hot and have places with very thin crust. The steam clouds are highly acidic and laced with glass particles.
Residents in all districts of the Big Island were shaken by a magnitude-5.0 earthquake at 8:18 p.m. on Saturday, April 1. The large temblor was located 10.0 km (6 miles) southeast of the summit of Kīlauea Volcano at a depth of 8.5 km (5.1 miles). The shaking did not affect the eruption at Puu Oo, and, except for falling items, there were no reports of damages or injuries resulting from the earthquake. | 2020-08-04T11:52:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23279863595962524, "perplexity": 5959.1512224877815}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735867.93/warc/CC-MAIN-20200804102630-20200804132630-00096.warc.gz"} |
https://www.usgs.gov/observatories/hvo/news/volcano-watch-volcanoes-source-artistic-inspiration | # Volcano Watch — Volcanoes-a source of artistic inspiration?
January 14, 2010
In celebration of Volcano Awareness Month (January 2010), we examine the influence of volcanoes on human society, beginning last week with religion. This week, we will explore the impact of volcanoes on art.
Too often, art and science are seen as mutually exclusive endeavors. A common misconception is that artists are creative and inspiring, while scientists are cold and logical, with little overlap between the two groups. In fact, there is a surprising amount of science in art, and art in science. Painters study color and light to better translate their visions into reality. Likewise, scientists must be creative in their study of complex problems. Historically, volcanoes have proven to be fertile ground for interactions between the artist and scientist, each drawn by inspiration and curiosity.
The earliest known visual representation of a volcano is from central Anatolia (present-day Turkey). Archeologists excavating an ancient city near Hasan Dagi volcano-which has been inactive for several thousand years-discovered a wall painting that depicts the mountain in eruption. The painting, sometimes referred to as the "first landscape" by art historians, provides evidence for an eruption of Hasan Dagi that occurred about 9,000 years ago, and corroborates geological studies of ancient eruptive activity.
Artistic interest in volcanoes continued into the Renaissance. Paintings of volcanoes from that period indicate that artists directly observed eruptions, and may have even understood the volcanic processes at work. For example, paintings of the 1631 eruption of Vesuvius show ground-hugging clouds now known to be pyroclastic surges-a phenomenon that was not recognized by volcanologists until the 20th century.
During the 18th and 19th centuries (before cameras were invented), artists were essential members of exploration parties who created visual records of new discoveries. Artist Robert Dampier visited Hawaii as part of a British expedition in 1825, while Titian Ramsay Peale (son of Charles Wilson Peale, who painted the famous portrait of George Washington) was part of an American expedition to Hawaii in 1840-1841. Their paintings, along with the drawings and illustrations of Reverend William Ellis, are the first visual record of Kīlauea and are invaluable today as evidence of the volcano's appearance in the 1800s.
Even after the invention of the camera, many artists continued to record realistic depictions of volcanic activity. The growth of Paricutin volcano, which started erupting in 1943 in Mexico, was extensively documented by Dr. Atl, a self-named and self-titled Mexican artist, philosopher, politician, and writer. Dr. Atl promoted the practice of painting outdoors, and volcanoes were among his favorite subjects. In fact, Dr. Atl's observations of volcanoes convinced him that the theory of continental drift (the forerunner to modern plate tectonic theory) was applicable to volcanic activity around the world"”something that was not recognized by geologists for another 20 years.
Of course, scientific observation is, at best, a secondary motivation behind most paintings of volcanoes. The primary purpose is that of capturing the inspiring and dramatic sight of primal creative forces at work in nature. The beautiful form of Vesuvius and its infamous eruptions are, perhaps, the reason that it is the most painted volcano in Western art. Similarly, the veneration that the Japanese feel for Mount Fuji explains its frequent depiction in Eastern art, perhaps most famously in Hokusai's series of woodblock prints, "Thirty-Six Views of Mount Fuji."
Looking at the impacts of eruptions, it is apparent that volcanoes have provided indirect artistic inspiration. The 1815 eruption of Tambora, Indonesia, ejected so much gas and ash into the atmosphere that the colors of sunsets and sunrises around the world were intensified for many years thereafter. These displays may have motivated the fiery skies of the English artist Joseph Turner. Similarly, the 1883 eruption of Krakatau, also in Indonesia, created worldwide spectacular atmospheric effects. The British painter William Ashcroft and the American painter Frederic Church painted and sketched the spectacular sunsets in the years that followed the eruption.
There can be no doubt that volcanoes are important elements in art-but this should be no surprise to Hawaii residents and visitors. The sight of snow-capped Mauna Kea, the experience of a sunrise from the summit of Haleakalā, and the spectacle of a Kīlauea lava flow are everyday artistic inspirations in Hawaii.
Next week, in the third part of out series on volcanoes and society, we will investigate the relation between volcanoes and literature.
————————————————————————————————————————————————————————————————
### Volcano Activity Update
This has been a quiet week on Kīlauea's east rift zone, with no sign of lava erupting from the TEB vent. Puu Oo had begun to re-inflate as of this writing (Thursday, January 14), and may result in new surface flows above the pali as portions of the lava tube become reoccupied.
At Kīlauea's summit, a prolonged deflation through the first half of the week was accompanied by a withdrawal of lava to a deeper level. As a result, night-time glow above the collapse pit inset within the floor of Halemauma`u Crater was relatively weak. The glow became brighter during the second half of the week, however, as the summit began to re-inflate and lava rose back up to a shallower level in the pit. After the lava rose back into view, the Webcam revealed a churning and spattering lava surface often with minor fluctuations in height. Volcanic gas emissions remain elevated, resulting in high concentrations of sulfur dioxide downwind.
One earthquake was felt this past week. A magnitude-3.1 earthquake occurred at 8:27 p.m., H.s.t., on Wednesday, January 13, 2010, and was located 27 km (17 miles) W of Kawaihae at a depth of 22 km (14 miles). | 2022-07-07T02:49:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18733295798301697, "perplexity": 3481.4986640487027}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104683020.92/warc/CC-MAIN-20220707002618-20220707032618-00657.warc.gz"} |
https://www.usgs.gov/center-news/volcano-watch-new-map-defines-lava-flow-hazard-zones-big-island | # Volcano Watch — New map defines lava flow hazard zones on the Big Island
Release Date:
The U.S Geological Survey has recently published a new, full-sized map which defines the boundaries of nine lava flow hazard zones on the island. This map is an updated version of the page-sized map included in the USGS booklet Volcanic and Seismic Hazards on the Island of Hawaii published in 1990.
New map defines lava flow hazard zones on the Big Island
(Public domain.)
The U.S Geological Survey has recently published a new, full-sized map which defines the boundaries of nine lava flow hazard zones on the island. This map is an updated version of the page-sized map included in the USGS booklet Volcanic and Seismic Hazards on the Island of Hawaii published in 1990. We have discussed the lava flow hazards on Kīlauea and Hualālai Volcanoes in previous "Volcano Watch" columns, and in the future, we will detail the lava flow hazards for the remaining volcanoes.
The updated, more detailed map was produced in cooperation with the Hawaii Office of State Planning, which digitized hazard zone boundaries to produce the nine-color map. The staff at HVO and the USGS Branch of Technical Reports added an underlay showing roads and towns. The map was published at a scale of 1:250,000, meaning that one inch on the map equals about four miles on the ground. It can be overlain on the USGS single-sheet topographic map of the Big Island, which was published at the same scale.
The designation of nine lava flow hazard zones, with number one used for the most hazardous areas, is based solely on geologic criteria, including frequency of past lava flows and coverage, distance from eruptive ventsand topography that currently protects certain areas from lava inundation. The areas designated as the most hazardous zones are the summits and rift zones of Kīlauea and Mauna Loa Volcanoes and the least hazardous zone is all of Kohala Volcano.
Boundaries between volcanoes are depicted with lines equivalent to a mile in width, to reflect the overlapping of flows from adjacent volcanoes along their common boundaries. Boundaries between hazard zones are drawn with a line equivalent to one-quarter to one-half mile in width to reflect uncertainties in the geological placement of boundaries. These boundaries are approximate and gradational and are not specific enough to determine the absolute degree of danger at any particular site.
The map was designed to be used for general planning purposes only, according to Thomas Wright, former Scientist-in-Charge at the Hawaiian Volcano Observatory and the map's first author. The lava flow hazard is one factor that should be considered in land-use decisions, but it is not the only factor. In order to use this map effectively in the development or preservation of any land parcel, a risk analysis should be made to balance positive economic and social benefits against risks posed by lava flows.
The new lava flow hazard map will be displayed at public libraries on the Big Island starting this week and at the Jaggar Museum in Hawaii Volcanoes National Park, at the summit of Kīlauea Volcano. Copies of the map can be purchased by mail from Map Sales, U.S. Geological Survey, Box 25286, Federal Center, Denver, CO 80225. The cost of the map is $2.75, plus$1.00 for shipping and handling. Orders must include the name of the map ("Map showing lava flow hazards zones, Island of Hawaii"), its order number (MF-2193), and a check or money order payable to the Department of the Interior. State and County offices and community groups may obtain a free copy by calling the Hawaiian Volcano Observatory at 967-7328.
The booklet Volcanic and Seismic Hazards on the Island of Hawaii contains the original lava flow hazards maps for each of the five volcanoes on the island, an earthquake hazards map, volcanic eruptions and damage resulting from them and from earthquakes. Lava flows are only one of the geologic hazards in Hawaii, which include earthquakes, explosive eruptions at the summit of Kīlauea, and ground cracking and subsidence along the rift zones and earthquake faults associated with the volcanoes. The booklet may be obtained at no cost from the map sales center in Denver at the address listed above. We distributed copies of the booklet and displayed the new map at the recent County Fair in Hilo. The Observatory maintains a small supply of the booklet for local distribution.
### Volcano Activity Update
The eruption on the East Rift Zone of Kīlauea Volcano continues at the episode 51 vents, located on the west side of the Puu Oo cone. Slowly advancing pahoehoe flows are heading toward the south and are slowly consuming the forest at about the 2,100-foot elevation. There were two earthquakes strong enough to be felt this past week. The first, which occurred September 19 at 7:56 a.m., was located beneath the south flank of Kīlauea Volcano and had a magnitude of 3.5. The second, which was recorded on September 22 at 4:23 a.m., was located northwest of Pahala and had a magnitude of 3.3. | 2021-04-23T12:00:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2769986689090729, "perplexity": 3707.233815298539}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039617701.99/warc/CC-MAIN-20210423101141-20210423131141-00515.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Aosgood.brad-g | Compute Distance To:
Author ID: osgood.brad-g Published as: Osgood, Brad; Osgood, B.; Osgood, Brad G.; Osgood, Brad O.; Osgood, B. G. more...less Homepage: http://ee.stanford.edu/~osgood/ External Links: MGP · Wikidata · ResearchGate
Documents Indexed: 54 Publications since 1979, including 7 Books 1 Contribution as Editor · 2 Further Contributions Co-Authors: 45 Co-Authors with 52 Joint Publications 695 Co-Co-Authors
all top 5
Co-Authors
4 single-authored 30 Chuaqui, Martin 17 Duren, Peter Larkin 6 Gleason, Andrew Mattei 6 Hughes-Hallett, Deborah 6 McCallum, William G. 6 Quinney, Douglas 6 Stowe, Dennis C. 6 Tecosky-Feldman, Jeff 6 Tucker, Thomas W. 5 Flath, Daniel Evans 4 Gordon, Sheldon P. 4 Lock, Patti Frazer 4 Mumford, David Bryant 4 Phillips, Ralph Saul 4 Sarnak, Peter Clive 4 Thrash, Joe B. 3 Lomen, David O. 3 Wu, William D. 2 Gehring, Frederick William 2 Kalayciôglu, Selin 2 Lahme, Brigitte 2 Lozano, Guadalupe I. 2 Pasquale, Andrew 2 Patterson, Cody L. 2 Pommerenke, Christian 2 Raskind, Wayne 2 Siripuram, Aditya 2 Spiegler, Adam H. 2 Thrash, Karen R. 1 Ahlfors, Lars Valerian 1 Brown Flinn, Barbara 1 Brown, Johnny E. 1 Connally, Eric 1 Ferguson, Tim 1 Heinonen, Juha 1 Khavinson, Dima 1 Krantz, Steven George 1 Ma, William 1 Martin, Gaven J. 1 Mejía, Diego Alejandro 1 Minda, David 1 Morris, Jerry 1 Palka, Bruce P. 1 Rhea, Karen 1 Rindler, Harald 1 Schuster, Alex 1 Weir, Rachel J.
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Serials
6 Journal d’Analyse Mathématique 4 Proceedings of the American Mathematical Society 2 IEEE Transactions on Information Theory 2 Commentarii Mathematici Helvetici 2 Indiana University Mathematics Journal 2 Journal of Functional Analysis 2 Results in Mathematics 2 Annales Academiae Scientiarum Fennicae. Mathematica 2 Computational Methods and Function Theory 1 Bulletin of the Australian Mathematical Society 1 Israel Journal of Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Annales Academiae Scientiarum Fennicae. Series A I. Mathematica 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 1 Bulletin of the London Mathematical Society 1 Duke Mathematical Journal 1 Illinois Journal of Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Monatshefte für Mathematik 1 Pacific Journal of Mathematics 1 Transactions of the American Mathematical Society 1 The Journal of Geometric Analysis 1 Proceedings of the National Academy of Sciences of the United States of America 1 Notices of the American Mathematical Society 1 Journal of Integer Sequences 1 Annals of Mathematics. Second Series 1 Complex Variables and Elliptic Equations 1 Pure and Applied Mathematics Quarterly 1 Pure and Applied Undergraduate Texts
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Fields
38 Functions of a complex variable (30-XX) 12 Differential geometry (53-XX) 9 Potential theory (31-XX) 8 General and overarching topics; collections (00-XX) 8 Real functions (26-XX) 5 Global analysis, analysis on manifolds (58-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Ordinary differential equations (34-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Combinatorics (05-XX) 2 Integral transforms, operational calculus (44-XX) 2 Numerical analysis (65-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Mathematics education (97-XX)
Citations contained in zbMATH Open
44 Publications have been cited 795 times in 583 Documents Cited by Year
Extremals of determinants of Laplacians. Zbl 0653.53022
Osgood, B.; Phillips, R.; Sarnak, P.
1988
Uniform domains and the quasi-hyperbolic metric. Zbl 0449.30012
Gehring, F. W.; Osgood, B. G.
1979
Compact isospectral sets of surfaces. Zbl 0653.53021
Osgood, B.; Phillips, R.; Sarnak, P.
1988
The Schwarzian derivative and conformal mapping of Riemannian manifolds. Zbl 0766.53034
1992
The Schwarzian derivative for harmonic mappings. Zbl 1054.31003
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2003
Curvature properties of planar harmonic mappings. Zbl 1051.30025
Chuaqui, Martin; Duren, Peter; Osgood, Brad O.
2004
The quasihyperbolic metric and associated estimates on the hyperbolic metric. Zbl 0621.30023
Martin, Gaven J.; Osgood, Brad G.
1986
Some properties of f”/f’ and the Poincaré metric. Zbl 0503.30014
1982
Sharp distortion theorems associated with the Schwarzian derivative. Zbl 0792.30013
Chuaqui, M.; Osgood, B.
1993
Moduli space, heights and isospectral sets of plane domains. Zbl 0677.58045
Osgood, B.; Phillips, R.; Sarnak, P.
1989
Univalence criteria for lifts of harmonic mappings to minimal surfaces. Zbl 1211.30011
Chuaqui, M.; Duren, P.; Osgood, B.
2007
Old and new on the Schwarzian derivative. Zbl 0894.30001
1998
Schwarzian derivative criteria for valence of analytic and harmonic mappings. Zbl 1134.30315
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2007
Ellipses, near ellipses, and harmonic Möbius transformations. Zbl 1068.30018
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2005
A generalization of Nehari’s univalence criterion. Zbl 0722.53029
1990
Conformal invariants. Topics in geometric function theory. With a new foreword by Peter Duren, F. W. Gehring, and Brad Osgood and an extensive errata. Reprint of 1973 original published by McGraw-Hill Company. Zbl 1211.30002
Ahlfors, Lars V.
2010
John domains, quasidisks, and the Nehari class. Zbl 0841.30018
Chuaqui, M.; Osgood, B.; Pommerenke, Ch.
1996
Injectivity criteria for holomorphic curves in $$\mathbb{C}^n$$. Zbl 1252.30003
Chuaqui, M.; Duren, P.; Osgood, B.
2011
Univalence criteria in multiply-connected domains. Zbl 0442.30012
1980
Ahlfors-Weill extensions of conformal mappings and critical points of the Poincaré metric. Zbl 0826.30013
Chuaqui, M.; Osgood, B.
1994
Schwarzian norms and two-point distortion. Zbl 1253.30031
Chuaqui, Martin; Duren, Peter; Ma, William; Mejía, Diego; Minda, David; Osgood, Brad
2011
Oscillation of solutions of linear differential equations. Zbl 1182.34046
Chuaqui, Martin; Duren, Peter; Osgood, Brad; Stowe, Dennis
2009
Schwarzian derivatives and uniform local univalence. Zbl 1156.30019
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2008
Compact isospectral of plane domains. Zbl 0674.30021
Osgood, B.; Phillips, R.; Sarnak, P.
1988
Finding complete conformal metrics to extend conformal mappings. Zbl 0937.30026
Chuaqui, M.; Osgood, B.
1998
General univalence criteria in the disk: Extensions and extremal function. Zbl 0910.30004
Chuaqui, M.; Osgood, B.
1998
Quasiconformal extensions to space of Weierstrass-Enneper lifts. Zbl 1410.30005
Chuaqui, M.; Duren, P.; Osgood, B.
2018
The Schwarzian derivative and conformally natural quasiconformal extensions from one to two to three dimensions. Zbl 0794.30016
1992
Schwarzian derivatives of convex mappings. Zbl 1239.30003
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2011
Two-point distortion theorems for harmonic mappings. Zbl 1207.30035
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2009
The Schwarzian derivative, conformal connections, and Möbius structures. Zbl 0992.53015
1998
Lectures on the Fourier transform and its applications. Zbl 1412.42003
2019
Concave conformal mappings and pre-vertices of Schwarz-Christoffel mappings. Zbl 1283.30048
Chuaqui, M.; Duren, P.; Osgood, B.
2012
Hyperbolic curvature and conformal mapping. Zbl 0594.30008
Brown Flinn, Barbara; Osgood, Brad G.
1986
Quasiconformal mappings and analysis. A collection of papers honoring Frederick W. Gehring to his 70th birthday. Proceedings of the international symposium, Ann Arbor, MI, USA, August 1995. Zbl 0883.00018
1998
On the coefficients of small univalent functions. Zbl 0894.30012
Chuaqui, M.; Osgood, B.; Pommerenke, Ch.
1998
Calculus. Single and multivariable. 2nd ed. Zbl 0913.26003
Hughes-Hallett, Deborah; Gleason, Andrew M.; McCallum, William G.; Flath, Daniel E.; Lock, Patti Frazer; Gordon, Sheldon P.; Lomen, David O.; Lovelock, David; Mumford, David; Osgood, Brad G.; Pasquale, Andrew; Quinney, Douglas; Tecosky-Feldman, Jeff; Thrash, Joe B.; Thrash, Karen R.; Tucker, Thomas W.
1998
Functions with prescribed quasisymmetry quotients. Zbl 0981.26010
Chuaqui, M.; Osgood, B.; Stowe, D.
1997
Multivariable calculus. Zbl 0892.26002
McCallum, William G.; Hughes-Hallett, Deborah; Gleason, Andrew M.; Flath, Daniel; Gordon, Sheldon P.; Mumford, David; Osgood, Brad G.; Quinney, Douglas; Raskind, Wayne; Tecosky-Feldman, Jeff; Thrash, Joe B.; Tucker, Thomas W.
1997
On a theorem of Haimo regarding concave mappings. Zbl 1243.30014
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2011
Falling factorials, generating functions, and conjoint ranking tables. Zbl 1215.05008
2009
An extension of a theorem of Gehring and Pommerenke. Zbl 0833.30011
Chuaqui, M.; Osgood, B.
1995
The Schwarzian distance between domains: A question of O. Lehto. Zbl 0642.30006
1987
Recent progress on the geometry of univalence criteria. Zbl 0938.30011
1999
Lectures on the Fourier transform and its applications. Zbl 1412.42003
2019
Quasiconformal extensions to space of Weierstrass-Enneper lifts. Zbl 1410.30005
Chuaqui, M.; Duren, P.; Osgood, B.
2018
Concave conformal mappings and pre-vertices of Schwarz-Christoffel mappings. Zbl 1283.30048
Chuaqui, M.; Duren, P.; Osgood, B.
2012
Injectivity criteria for holomorphic curves in $$\mathbb{C}^n$$. Zbl 1252.30003
Chuaqui, M.; Duren, P.; Osgood, B.
2011
Schwarzian norms and two-point distortion. Zbl 1253.30031
Chuaqui, Martin; Duren, Peter; Ma, William; Mejía, Diego; Minda, David; Osgood, Brad
2011
Schwarzian derivatives of convex mappings. Zbl 1239.30003
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2011
On a theorem of Haimo regarding concave mappings. Zbl 1243.30014
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2011
Conformal invariants. Topics in geometric function theory. With a new foreword by Peter Duren, F. W. Gehring, and Brad Osgood and an extensive errata. Reprint of 1973 original published by McGraw-Hill Company. Zbl 1211.30002
Ahlfors, Lars V.
2010
Oscillation of solutions of linear differential equations. Zbl 1182.34046
Chuaqui, Martin; Duren, Peter; Osgood, Brad; Stowe, Dennis
2009
Two-point distortion theorems for harmonic mappings. Zbl 1207.30035
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2009
Falling factorials, generating functions, and conjoint ranking tables. Zbl 1215.05008
2009
Schwarzian derivatives and uniform local univalence. Zbl 1156.30019
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2008
Univalence criteria for lifts of harmonic mappings to minimal surfaces. Zbl 1211.30011
Chuaqui, M.; Duren, P.; Osgood, B.
2007
Schwarzian derivative criteria for valence of analytic and harmonic mappings. Zbl 1134.30315
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2007
Ellipses, near ellipses, and harmonic Möbius transformations. Zbl 1068.30018
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2005
Curvature properties of planar harmonic mappings. Zbl 1051.30025
Chuaqui, Martin; Duren, Peter; Osgood, Brad O.
2004
The Schwarzian derivative for harmonic mappings. Zbl 1054.31003
Chuaqui, Martin; Duren, Peter; Osgood, Brad
2003
Recent progress on the geometry of univalence criteria. Zbl 0938.30011
1999
Old and new on the Schwarzian derivative. Zbl 0894.30001
1998
Finding complete conformal metrics to extend conformal mappings. Zbl 0937.30026
Chuaqui, M.; Osgood, B.
1998
General univalence criteria in the disk: Extensions and extremal function. Zbl 0910.30004
Chuaqui, M.; Osgood, B.
1998
The Schwarzian derivative, conformal connections, and Möbius structures. Zbl 0992.53015
1998
Quasiconformal mappings and analysis. A collection of papers honoring Frederick W. Gehring to his 70th birthday. Proceedings of the international symposium, Ann Arbor, MI, USA, August 1995. Zbl 0883.00018
1998
On the coefficients of small univalent functions. Zbl 0894.30012
Chuaqui, M.; Osgood, B.; Pommerenke, Ch.
1998
Calculus. Single and multivariable. 2nd ed. Zbl 0913.26003
Hughes-Hallett, Deborah; Gleason, Andrew M.; McCallum, William G.; Flath, Daniel E.; Lock, Patti Frazer; Gordon, Sheldon P.; Lomen, David O.; Lovelock, David; Mumford, David; Osgood, Brad G.; Pasquale, Andrew; Quinney, Douglas; Tecosky-Feldman, Jeff; Thrash, Joe B.; Thrash, Karen R.; Tucker, Thomas W.
1998
Functions with prescribed quasisymmetry quotients. Zbl 0981.26010
Chuaqui, M.; Osgood, B.; Stowe, D.
1997
Multivariable calculus. Zbl 0892.26002
McCallum, William G.; Hughes-Hallett, Deborah; Gleason, Andrew M.; Flath, Daniel; Gordon, Sheldon P.; Mumford, David; Osgood, Brad G.; Quinney, Douglas; Raskind, Wayne; Tecosky-Feldman, Jeff; Thrash, Joe B.; Tucker, Thomas W.
1997
John domains, quasidisks, and the Nehari class. Zbl 0841.30018
Chuaqui, M.; Osgood, B.; Pommerenke, Ch.
1996
An extension of a theorem of Gehring and Pommerenke. Zbl 0833.30011
Chuaqui, M.; Osgood, B.
1995
Ahlfors-Weill extensions of conformal mappings and critical points of the Poincaré metric. Zbl 0826.30013
Chuaqui, M.; Osgood, B.
1994
Sharp distortion theorems associated with the Schwarzian derivative. Zbl 0792.30013
Chuaqui, M.; Osgood, B.
1993
The Schwarzian derivative and conformal mapping of Riemannian manifolds. Zbl 0766.53034
1992
The Schwarzian derivative and conformally natural quasiconformal extensions from one to two to three dimensions. Zbl 0794.30016
1992
A generalization of Nehari’s univalence criterion. Zbl 0722.53029
1990
Moduli space, heights and isospectral sets of plane domains. Zbl 0677.58045
Osgood, B.; Phillips, R.; Sarnak, P.
1989
Extremals of determinants of Laplacians. Zbl 0653.53022
Osgood, B.; Phillips, R.; Sarnak, P.
1988
Compact isospectral sets of surfaces. Zbl 0653.53021
Osgood, B.; Phillips, R.; Sarnak, P.
1988
Compact isospectral of plane domains. Zbl 0674.30021
Osgood, B.; Phillips, R.; Sarnak, P.
1988
The Schwarzian distance between domains: A question of O. Lehto. Zbl 0642.30006
1987
The quasihyperbolic metric and associated estimates on the hyperbolic metric. Zbl 0621.30023
Martin, Gaven J.; Osgood, Brad G.
1986
Hyperbolic curvature and conformal mapping. Zbl 0594.30008
Brown Flinn, Barbara; Osgood, Brad G.
1986
Some properties of f”/f’ and the Poincaré metric. Zbl 0503.30014
1982
Univalence criteria in multiply-connected domains. Zbl 0442.30012
1980
Uniform domains and the quasi-hyperbolic metric. Zbl 0449.30012
Gehring, F. W.; Osgood, B. G.
1979
all top 5
Cited by 610 Authors
38 Ponnusamy, Saminathan 28 Chuaqui, Martin 24 Vuorinen, Matti Keijo Kustaa 21 Osgood, Brad G. 19 Wang, Xiantao 15 Li, Yaxiang 12 Zhou, Qingshan 10 Choi, Junesang 10 Duren, Peter Larkin 10 Huang, Manzi 10 Ibragimov, Zair 9 Hernández, Rodrigo 9 Herron, David A. 9 Sahoo, Swadesh Kumar 8 Branson, Thomas Patrick 8 Minda, David 8 Rasila, Antti 7 Chang, Sun-Yung Alice 7 Chen, Shaolin 7 Hästö, Peter A. 7 Martin, Gaven J. 7 Väisälä, Jussi 6 Awonusika, Richard Olu 6 Klén, Riku 6 Martín, María J. 6 Srivastava, Hari Mohan 6 Sugawa, Toshiyuki 5 Aldana, Clara L. 5 Bétermin, Laurent 5 Ding, Shusen 5 Guan, Tiantian 5 Gursky, Matthew J. 5 Hirata, Kentaro 5 Koskela, Pekka 5 Yang, Paul C. P. 4 Buckley, Stephen M. 4 Chen, Chaoping 4 Efraimidis, Iason 4 Faulhuber, Markus 4 Gilkey, Peter B. 4 Harmelin, Reuven 4 Kaliraj, Anbareeswaran Sairam 4 Morpurgo, Carlo 4 Nieminen, Tomi 4 Okikiolu, Kate 4 Ørsted, Bent 4 Perry, Peter A. 4 Stowe, Dennis C. 4 Taheri, Ali 4 Zhang, Xiaohui 3 Albin, Pierre 3 Arbeláez, Hugo 3 Astala, Kari 3 Avkhadiev, Farit Gabidinovich 3 Bonfert-Taylor, Petra 3 Brooks, Robert Wolfe 3 Case, Jeffrey S. 3 Dolbeault, Jean 3 Dubinin, Vladimir N. 3 Esteban, Maria J. 3 Gehring, Frederick William 3 Guo, Changyu 3 Hamada, Hidetaka 3 Jorgenson, Jay Alan 3 Kaloshin, Vadim Yu. 3 Kalvin, Victor 3 Kirsten, Klaus 3 Koh, Ngin-Tee 3 Kohr, Gabriela 3 Kokotov, Aleksey 3 Latfullin, T. G. 3 Liu, Pan 3 Maharana, Sudhananda 3 Martio, Olli 3 Mateljević, Miodrag S. 3 Mejía, Diego Alejandro 3 Mohapatra, Manas Ranjan 3 Moscovici, Henri 3 Nikolov, Nikolai Marinov 3 Petrache, Mircea 3 Pommerenke, Christian 3 Rochon, Frédéric 3 Sher, David A. 3 Wylie, William C. 3 Xu, Xingwang 2 Aharonov, Dov 2 Ahmed, Ahmed El-Sayed 2 Anderson, Glen Douglas 2 Andreev, Lyubomir 2 Azzam, Jonas 2 Bharanedhar, S. Vaidhyanathan 2 Borthwick, David 2 Chanillo, Sagun 2 Chen, Xingdi 2 Christodoulou, Dimitris M. 2 Chu, Yuming 2 Chua, Kok Seng 2 Dumas, David 2 El Soufi, Ahmad 2 Elias, Uri ...and 510 more Authors
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Cited in 161 Serials
30 The Journal of Geometric Analysis 26 Journal d’Analyse Mathématique 25 Journal of Mathematical Analysis and Applications 23 Proceedings of the American Mathematical Society 20 Duke Mathematical Journal 19 Transactions of the American Mathematical Society 16 Computational Methods and Function Theory 14 Complex Variables and Elliptic Equations 13 Communications in Mathematical Physics 13 Israel Journal of Mathematics 13 Journal of Functional Analysis 12 Results in Mathematics 11 Advances in Mathematics 11 Monatshefte für Mathematik 9 Mathematische Zeitschrift 7 Rocky Mountain Journal of Mathematics 7 Conformal Geometry and Dynamics 7 Complex Analysis and Operator Theory 6 Mathematische Annalen 6 Potential Analysis 5 Bulletin of the Australian Mathematical Society 5 Inventiones Mathematicae 5 Journal of Differential Equations 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Geometric and Functional Analysis. GAFA 5 The Journal of Analysis 5 Abstract and Applied Analysis 5 Annals of Mathematics. Second Series 5 Communications in Contemporary Mathematics 5 Journal of the Australian Mathematical Society 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Journal of Mathematical Physics 4 Annales de l’Institut Fourier 4 Applied Mathematics and Computation 4 Manuscripta Mathematica 4 Nagoya Mathematical Journal 4 Siberian Mathematical Journal 4 Chinese Annals of Mathematics. Series B 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Calculus of Variations and Partial Differential Equations 4 Journal of the European Mathematical Society (JEMS) 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Analysis and Mathematical Physics 4 Annales Fennici Mathematici 3 Archive for Rational Mechanics and Analysis 3 Journal of Statistical Physics 3 Letters in Mathematical Physics 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Journal of Geometry and Physics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Archiv der Mathematik 3 International Journal of Mathematics and Mathematical Sciences 3 Journal of Number Theory 3 Mathematische Nachrichten 3 Tohoku Mathematical Journal. Second Series 3 Differential Geometry and its Applications 3 Communications in Partial Differential Equations 3 Bulletin of the American Mathematical Society. New Series 3 Filomat 3 Annales Academiae Scientiarum Fennicae. Mathematica 3 International Journal of Geometric Methods in Modern Physics 3 Advances in Difference Equations 3 Complex Analysis and its Synergies 2 Computers & Mathematics with Applications 2 Mathematical Notes 2 Acta Mathematica 2 Illinois Journal of Mathematics 2 Publications Mathématiques 2 Journal of Computational and Applied Mathematics 2 Journal of the Mathematical Society of Japan 2 Kodai Mathematical Journal 2 Michigan Mathematical Journal 2 Proceedings of the Japan Academy. Series A 2 Annals of Global Analysis and Geometry 2 Constructive Approximation 2 Revista Matemática Iberoamericana 2 Applied Mathematics Letters 2 Journal of the American Mathematical Society 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 SIAM Journal on Mathematical Analysis 2 International Journal of Computer Vision 2 Advances in Applied Clifford Algebras 2 Bulletin des Sciences Mathématiques 2 Journal of Inequalities and Applications 2 Acta Mathematica Sinica. English Series 2 Lobachevskii Journal of Mathematics 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Applicable Analysis and Discrete Mathematics 2 Communications in Mathematics and Statistics 2 Journal of Function Spaces 1 Houston Journal of Mathematics 1 Indian Journal of Pure & Applied Mathematics 1 Nonlinearity 1 Studia Mathematica 1 Arkiv för Matematik 1 The Annals of Probability 1 Applied Mathematics and Optimization 1 Geometriae Dedicata 1 Journal of Approximation Theory 1 Journal of Combinatorial Theory. Series A ...and 61 more Serials
all top 5
Cited in 47 Fields
281 Functions of a complex variable (30-XX) 123 Global analysis, analysis on manifolds (58-XX) 114 Differential geometry (53-XX) 85 Partial differential equations (35-XX) 72 Potential theory (31-XX) 40 Functional analysis (46-XX) 35 Number theory (11-XX) 35 Special functions (33-XX) 31 Several complex variables and analytic spaces (32-XX) 25 Real functions (26-XX) 25 Geometry (51-XX) 18 Ordinary differential equations (34-XX) 16 Operator theory (47-XX) 15 Quantum theory (81-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 13 Algebraic geometry (14-XX) 10 Dynamical systems and ergodic theory (37-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Manifolds and cell complexes (57-XX) 9 Probability theory and stochastic processes (60-XX) 7 Measure and integration (28-XX) 7 Approximations and expansions (41-XX) 7 Convex and discrete geometry (52-XX) 6 Relativity and gravitational theory (83-XX) 5 Mechanics of deformable solids (74-XX) 5 Fluid mechanics (76-XX) 4 Group theory and generalizations (20-XX) 4 Abstract harmonic analysis (43-XX) 4 Numerical analysis (65-XX) 4 Mechanics of particles and systems (70-XX) 3 Topological groups, Lie groups (22-XX) 3 Difference and functional equations (39-XX) 3 Computer science (68-XX) 2 Combinatorics (05-XX) 2 Nonassociative rings and algebras (17-XX) 2 General topology (54-XX) 2 Statistics (62-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Algebraic topology (55-XX)
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The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2022-07-01T17:48:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5818588137626648, "perplexity": 9849.022114092766}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103943339.53/warc/CC-MAIN-20220701155803-20220701185803-00090.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=S041T&home=sumtabM | # ${{\boldsymbol B}^{\pm}}$ MEAN LIFE INSPIRE search
See ${{\mathit B}^{\pm}}/{{\mathit B}^{0}}/{{\mathit B}_{{s}}^{0}}/{{\mathit b}}$-baryon ADMIXTURE section for data on ${{\mathit B}}$-hadron mean life averaged over species of bottom particles. OUR EVALUATION'' is an average using rescaled values of the data listed below. The average and rescaling were performed by the Heavy Flavor Averaging Group (HFLAV) and are described at https://hflav.web.cern.ch/. The averaging/rescaling procedure takes into account correlations between the measurements and asymmetric lifetime errors.
VALUE ($10^{-12}$ s) EVTS DOCUMENT ID TECN COMMENT
$\bf{ 1.638 \pm0.004}$ OUR EVALUATION
$1.637$ $\pm0.004$ $\pm0.003$
2014 E
LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$1.639$ $\pm0.009$ $\pm0.009$ 1
2011
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV
$1.663$ $\pm0.023$ $\pm0.015$ 2
2011 B
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV
$1.635$ $\pm0.011$ $\pm0.011$ 3
2005 B
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$1.624$ $\pm0.014$ $\pm0.018$ 4
2004 E
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$1.636$ $\pm0.058$ $\pm0.025$ 5
2002 C
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.8 TeV
$1.673$ $\pm0.032$ $\pm0.023$ 6
2001 F
BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$1.648$ $\pm0.049$ $\pm0.035$ 7
2000 R
ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$1.643$ $\pm0.037$ $\pm0.025$ 8
1999 J
OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$1.637$ $\pm0.058$ ${}^{+0.045}_{-0.043}$ 7
1998 Q
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$1.66$ $\pm0.06$ $\pm0.03$ 8
1998 S
L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$1.66$ $\pm0.06$ $\pm0.05$ 8
1997 J
SLD ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$1.58$ ${}^{+0.21}_{-0.18}$ ${}^{+0.04}_{-0.03}$ 94 5
1996 J
ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$1.61$ $\pm0.16$ $\pm0.12$ 7, 9
1995 Q
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$1.72$ $\pm0.08$ $\pm0.06$ 10
1995
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$1.52$ $\pm0.14$ $\pm0.09$ 7
1995 T
OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$1.695$ $\pm0.026$ $\pm0.015$ 6
2002 H
BELL Repl. by ABE 2005B
$1.68$ $\pm0.07$ $\pm0.02$ 5
1998 B
CDF Repl. by ACOSTA 2002C
$1.56$ $\pm0.13$ $\pm0.06$ 7
1996 C
CDF Repl. by ABE 1998Q
$1.58$ $\pm0.09$ $\pm0.03$ 11
1996 J
ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$1.58$ $\pm0.09$ $\pm0.04$ 7
1996 J
ALEP Repl. by BARATE 2000R
$1.70$ $\pm0.09$ 12
1995
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$1.61$ $\pm0.16$ $\pm0.05$ 148 5
1994 D
CDF Repl. by ABE 1998B
$1.30$ ${}^{+0.33}_{-0.29}$ $\pm0.16$ 92 7
1993 D
DLPH Sup. by ABREU 1995Q
$1.56$ $\pm0.19$ $\pm0.13$ 134 10
1993 G
DLPH Sup. by ADAM 1995
$1.51$ ${}^{+0.30}_{-0.28}$ ${}^{+0.12}_{-0.14}$ 59 7
1993 C
OPAL Sup. by AKERS 1995T
$1.47$ ${}^{+0.22}_{-0.19}$ ${}^{+0.15}_{-0.14}$ 77 7
1993 D
ALEP Sup. by BUSKULIC 1996J
1 Measured mean life using fully reconstructed decays ( ${{\mathit J / \psi}}{{\mathit K}^{(*)}}$ ).
2 Measured using ${{\mathit B}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{-}}$ with ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ events that were selected using a silicon vertex trigger.
3 Measurement performed using a combined fit of $\mathit CP$-violation, mixing and lifetimes.
4 Measurement performed using an inclusive reconstruction and ${{\mathit B}}$ flavor identification technique.
5 Measured mean life using fully reconstructed decays.
6 Events are selected in which one ${{\mathit B}}$ meson is fully reconstructed while the second ${{\mathit B}}~$meson is reconstructed inclusively.
7 Data analyzed using ${{\mathit D}}$ / ${{\mathit D}^{*}}{{\mathit \ell}}$ X event vertices.
8 Data analyzed using charge of secondary vertex.
9 ABREU 1995Q assumes B( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{**-}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ ) = $3.2$ $\pm1.7\%$.
10 Data analyzed using vertex-charge technique to tag ${{\mathit B}}$ charge.
11 Combined result of ${{\mathit D}}$/ ${{\mathit D}^{*}}{{\mathit \ell}}$ X analysis and fully reconstructed ${{\mathit B}}$ analysis.
12 Combined ABREU 1995Q and ADAM 1995 result.
References:
AAIJ 2014E
JHEP 1404 114 Measurements of the ${{\mathit B}^{+}},{{\mathit B}^{0}},{{\mathit B}_{{s}}^{0}}$ Meson and ${{\mathit \Lambda}_{{b}}^{0}}$ Baryon Lifetimes
AALTONEN 2011B
PR D83 032008 Measurement of the ${{\mathit B}^{-}}$ Lifetime using a Simulation Free Approach for Trigger Bias Correction
AALTONEN 2011
PRL 106 121804 Measurement of ${\mathit {\mathit b}}$ Hadron Lifetimes in Exclusive Decays Containing a ${{\mathit J / \psi}}$ in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
ABE 2005B
PR D71 072003 Improved Measurement of $\mathit CP$ Violation Parameters sin2$\phi _{1}$ and $\vert {{\mathit \lambda}}\vert$, ${{\mathit B}}$ Meson Lifetimes, and ${{\mathit B}^{0}}−{{\overline{\mathit B}}^{0}}$ Mixing Parameter $\Delta {{\mathit m}_{{d}}}$
ABDALLAH 2004E
EPJ C33 307 A Precise Measurement of the ${{\mathit B}^{+}}$, ${{\mathit B}^{0}}$ and Mean b-hadron Lifetime with the DELPHI Detector at LEP I
ABE 2002H
PRL 88 171801 Precise Measurement of ${{\mathit B}}$ Meson Lifetimes with Hadronic Decay Final States
ACOSTA 2002C
PR D65 092009 Measurement of ${{\mathit B}}$ Meson Lifetimes using Fully Reconstructed ${{\mathit B}}$ Decays Produced in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.8 TeV
AUBERT 2001F
PRL 87 201803 Measurement of the ${{\mathit B}^{0}}$ and ${{\mathit B}^{+}}$ Meson Lifetimes with Fully Reconstructed Hadronic Final States
BARATE 2000R
PL B492 275 Measurement of the ${{\overline{\mathit B}}^{0}}$ and ${{\mathit B}^{-}}$ Meson Lifetimes
ABBIENDI 1999J
EPJ C12 609 Measurement of the ${{\mathit B}^{+}}$ and ${{\mathit B}^{0}}$ Lifetimes and Search for $\mathit CP(T)$ Violation using Reconstructed Secondary Vertices
ABE 1998B
PR D57 5382 Measurement of ${{\mathit B}}$ Hadron Lifetimes using ${{\mathit J / \psi}}$ Final States at CDF
ABE 1998Q
PR D58 092002 Improved Measurement of the ${{\mathit B}^{-}}$ and ${{\overline{\mathit B}}^{0}}$ Meson Lifetimes using Semileptonic Decays
ACCIARRI 1998S
PL B438 417 Upper Limit on the Lifetime Difference of Short- and Long-Lived ${{\mathit B}_{{s}}^{0}}$ Mesons
ABE 1997J
PRL 79 590 Measurement of the ${{\mathit B}^{+}}$ and ${{\mathit B}^{0}}$ Lifetimes using Topological Reconstruction of Inclusive and Semileptonic Decays
ABE 1996C
PRL 76 4462 Measurement of the ${{\mathit B}^{-}}$ and ${{\overline{\mathit B}}^{0}}$ Meson Lifetimes using Semileptonic Decays
BUSKULIC 1996J
ZPHY C71 31 Improved Measurement of the ${{\overline{\mathit B}}^{0}}$ and ${{\mathit B}^{-}}$ Meson Lifetimes
ABREU 1995Q
ZPHY C68 13 A Measurement of ${{\mathit B}^{+}}$ and ${{\mathit B}^{0}}$ Lifetimes using ${{\overline{\mathit D}}}{{\mathit \ell}^{+}}$ Events
ZPHY C68 363 Lifetimes of Charged and Neutral ${{\mathit B}}$ Hadrons using Event Topology
ZPHY C67 379 Improved Measurements of the ${{\mathit B}^{0}}$ and ${{\mathit B}^{+}}$ Meson Lifetimes
PRL 72 3456 Measurement of the ${{\mathit B}^{+}}$ and ${{\mathit B}^{0}}$ Meson Lifetimes
PL B312 253 A Measurement of the Mean Lifetimes of Charged and Neutral ${{\mathit B}}$ Hadrons
ZPHY C57 181 A Measurement of ${{\mathit B}}$ Meson Production and Lifetime using ${{\mathit D}}{{\mathit \ell}^{-}}$ Events in ${{\mathit Z}^{0}}$ Decays
PL B307 247 Measurement of the ${{\mathit B}^{0}}$ and ${{\mathit B}^{+}}$ Lifetime
PL B307 194 Measurement of the ${{\overline{\mathit B}}^{0}}$ and ${{\mathit B}^{-}}$ Meson Lifetime | 2021-05-12T04:42:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8484479188919067, "perplexity": 4944.59745011259}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991252.15/warc/CC-MAIN-20210512035557-20210512065557-00326.warc.gz"} |
http://dergipark.gov.tr/gujs/issue/37206/323742 | | | | |
## On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number
#### CAN KIZILATEŞ [1] , Naim TUGLU [2]
##### 67 140
In this paper, we study the spectral norms of the geometric circulant matrices and the symmetric geometric circulant matrices with the Tribonacci numbers and any complex numbers r.
Tribonacci numbers, Circulant matrix, Spectral norms
• [1] Solak, S., “On the norms of circulant matrices with the Fibonacci and Lucas numbers”, Applied Mathematics and Computation, 160: 125-132, (2005).
• [2] Kocer, EG, Mansour, T, Tuglu, N., “Norms of circulant and semicirculant matrices with Horadam's numbers”, Ars Combinatoria, 85: 353-359, (2007).
• [3] Shen, S.Q, Cen, J.M., “On the bounds for the norms of circulant matrices with Fibonacci and Lucas numbers”, Applied Mathematics and Computation, 216: 2891-2897, (2010).
• [4] Bahsi, M., “On the norms of circulant matrices with the hyperharmonic numbers”, Journal of Mathematical Inequalities, 10: (2), 445-458, (2016).
• [5] Bahsi, M. and Solak, S., “On the norms of circulant matrices with the hyper-Fibonacci and Lucas numbers”, Journal of Mathematical Inequalities,8: (4), 693-705, (2014).
• [6] Kızılateş, C. and Naim, T., “On the bounds for the spectral norms of geometric circulant matrices”, Journal of Inequalities and Applications, 2016:312 (2016).
• [7] Tuglu, N. and Kızılateş C., “On the norms of circulant and circulant matrices with the hyperharmonic Fibonacci numbers”, Journal of Inequalities and Applications, 2015: 253, (2015).
• [8] Tuglu, N, Kızılateş, C, Kesim, S., “On the harmonic and hyperharmonic Fibonacci numbers”, Advances Difference Equations, 2015: 297, (2015).
• [9] Tuglu, N. and Kızılateş, C., “On the norms of some special matrices with the harmonic Fibonacci numbers”, Gazi University Journal of Science 28: (3) 447-501, (2015).
• [10] Yazlik, Y, Taskara, N., “On the norms of an circulant matrix with the generalized Horadam numbers”, Journal of Inequalities and Applications, 2013: 394, (2013).
• [11] R.A. Horn, C.R. Johnson, “Matrix Analysis”, Cambridge University Press, Cambridge, UK, 1985.
• [12] R.A. Horn, C.R. Johnson, “Topics in Matrix Analysis”, Cambridge University Press, 1991, 259-260.
• [13] He, C, Ma, J, Zhang, K, Wang, Z., “The upper bound estimation on the spectral norm circulant matrices with the Fibonacci and Lucas numbers”, Journal of Inequalities and Applications, 2015: 72, (2015).
• [14] Bahsi, M., “On the norms of circulant matrices with the generalized Fibonacci and Lucas numbers”, TWWS Journal of Pure and Applied. Mathematics, 6: (1), 84-92, (2015).
• [15] Jiang, Z. and Zhou, J., “A note on spectral norms of even-order circulant matrices”, Applied Mathematics and Computation, 250: 368-371, (2015).
• [16] Sintunavarat, W., “The upper bound estimation for the spectral norm of circulant and symmetric circulant matrices with the Padovan sequence”, Journal of Nonlinear Science and its Applications, 9: 92-101, (2016).
• [17] Li, J, Jiang, Z, Lu, F., “Determinants, Norms and spread of circulant matrices with Tribonacci and generalized Lucas numbers”, Abstract Applied Analysis, 2014, Article ID 381829 (2014).
• [18] Rabinowitz, S., “Algorithmic manipulation of third-order linear recurrences”, The Fibonacci Quarterly, 34: (5), 34: 447-463, (1996).
• [19] Tascı, D., “On quadrapell numbers and quadrapell polynomials”, Hacettepe Journal of Mathematics and Statistics, 38: (3), 265-275, (2009).
Konular Mathematics Yazar: CAN KIZILATEŞÜlke: Turkey Yazar: Naim TUGLUÜlke: Turkey
Bibtex @araştırma makalesi { gujs323742, journal = {Gazi University Journal of Science}, issn = {}, eissn = {2147-1762}, address = {Gazi Üniversitesi}, year = {}, volume = {31}, pages = {555 - 567}, doi = {}, title = {On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number}, key = {cite}, author = {TUGLU, Naim and KIZILATEŞ, CAN} } APA KIZILATEŞ, C , TUGLU, N . (). On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number. Gazi University Journal of Science, 31 (2), 555-567. Retrieved from http://dergipark.gov.tr/gujs/issue/37206/323742 MLA KIZILATEŞ, C , TUGLU, N . "On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number". Gazi University Journal of Science 31 (): 555-567 Chicago KIZILATEŞ, C , TUGLU, N . "On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number". Gazi University Journal of Science 31 (): 555-567 RIS TY - JOUR T1 - On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number AU - CAN KIZILATEŞ , Naim TUGLU Y1 - 2018 PY - 2018 N1 - DO - T2 - Gazi University Journal of Science JF - Journal JO - JOR SP - 555 EP - 567 VL - 31 IS - 2 SN - -2147-1762 M3 - UR - Y2 - 2018 ER - EndNote %0 Gazi University Journal of Science On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number %A CAN KIZILATEŞ , Naim TUGLU %T On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number %D 2018 %J Gazi University Journal of Science %P -2147-1762 %V 31 %N 2 %R %U ISNAD KIZILATEŞ, CAN , TUGLU, Naim . "On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number". Gazi University Journal of Science 31 / 2 555-567. | 2018-12-12T04:53:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5200359225273132, "perplexity": 9838.598150156398}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823738.9/warc/CC-MAIN-20181212044022-20181212065522-00603.warc.gz"} |
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• Prove that $\sum_{n=-\infty}^{\infty}\frac{1}{(x+\pi n)^2}=\frac{1}{sin^2x}$
by Ozod on February 26, 2021 at 6:24 pm
$$\sum_{n=-\infty}^{\infty}\frac{1}{(x+\pi n)^2}=\frac{1}{sin^2x}$$ Marko Riedel Dec 30 '18 at 14:46 Show 5 more comments 1 Answer order by votes Up vote 3 Down vote Accepted With the quoted proof being unsatisfactory we try again. With the goal of evaluating $$\sum_{n=-\infty}^\infty \frac{1}{(u+n)^2}$$ where $u$ is not an integer we study the function $$f(z) = \frac{1}{(u+z)^2} \pi\cot(\pi z).$$ which has the property that with $S$ being our sum, $$S = \sum_n \mathrm{Res}_{z=n} f(z) = \sum_n \frac{1}{(u+n)^2}.$$ 😓😓😓😓 please help prove that
• Why isn't the determinant function zero?
by user9343456 on February 26, 2021 at 6:24 pm
Let $P_1,\ldots,P_n$ be $n$ dimensional column vectors. The determinant function $D(P_1,\ldots,P_n)$ is a multilinear, alternating real function of these vectors. Since it's alternating, if $P_1,\ldots,P_n$ are not linearly independent, then $D$ evaluates to zero. So far so good. Let $E_1,\ldots,E_n$ be the standard basis column vectors ($n$-dimensional). Let the $i$-th entry in $P_j$ be $p^i_j$. My question is: due to multilinearity can't I write $D(P_1,\ldots,P_n)$ as $$D(p^1_1E_1,\ldots,p^1_mE_1)+D(p^2_1E_2,\ldots,p^2_mE_2)+\ldots+D(p^m_1E_m,\ldots,p^m_mE_m)$$ and say that all terms are zero, since in each term, the arguments are not independent? So the entire thing must be zero? I'm not able to figure out where I'm going wrong.
• Question in Hatcher proposition 1.26 proof
by love_sodam on February 26, 2021 at 6:22 pm
(a) If $Y$ is obtained from $X$ by attaching 2-cells as described above, then the inclusion $X\hookrightarrow Y$ induces a surjection $\pi_1(X,x_0)\to\pi_1(Y,x_0)$ whose kernel is $N$.Rather than writing down the meaning 'describe above' and '$N$' in the statement, I think it's better to look p.49 of Hatcher's algebraic topology here.The question is I can't understand the red line in the image. I understand why they're trying to choose such $\delta_\alpha$, but why such an element exists in $\pi_1(A\cap B,z_0)$? The map $\pi_1(A\cap B)\to \pi_1(A)$ is not surjective. Could you explain this?
• Hi! I'm having a problem with the integral $\displaystyle\int_{n}^{n+1}x^2 dx$
by Algoak on February 26, 2021 at 6:22 pm
Basically, i noticed that when $n\subset \mathbb{N}$, $\displaystyle\int_{n}^{n+1}{x^2}dx$ gives a prime number divided by 3 or a multiplication of prime numbers. Here's a table i made.is this something already known or a "function that generates prime numbers"? I don't know much about math and I don't have a great academic background so I'm asking this here.
## Surrey Mathematics Research Blog The blog on research in mathematics at the University of Surrey
• Alessandro Torrielli gives virtual seminars to universities in Germany and Italy
by Tom Bridges on February 26, 2021 at 4:22 pm
Alessandro Torrielli has given two virtual seminars this month. The first, on 18 February, was a talk in the Emmy Noether Seminar at the Institute for Theoretical Physics at the University of Leipzig in Germany. The title of the talk was “Massless integrable scattering in the AdS/CFT correspondence” (link here). The second talk, on 24
• Paper of Bin Cheng and Thomas O’Neill on Monge-Ampère equation published in JFA
by Tom Bridges on February 26, 2021 at 9:52 am
The paper “Interior estimates for Monge-Ampère equation in terms of modulus of continuity” co-authored by Bin Cheng and Thomas O’Neill has been published in the Journal of Functional Analysis. The paper forms part of the PhD thesis of Thomas. The published version is available for download here and the final form arXiv version is available
• Paper of Juan Miguel Nieto García, Alessandro Torrielli, and Leander Wyss published in JGP
by Tom Bridges on February 25, 2021 at 6:18 pm
The paper “Boosts superalgebras based on centrally-extended su(1|1)^2” co-authored by Juan Miguel Nieto García, Alessandro Torrielli, and Leander Wyss has been accepted for publication in the Journal of Geometry and Physics. The final form arXiv version can be found here, and the screenshot below shows Figure 1 from the paper.
• Two grants awarded to the Data Group by the Surrey Institute for Advanced Studies
by Tom Bridges on February 24, 2021 at 9:03 am
An IAS Fellowship grant has been awarded to the Data Group. The co-investigators are Stefan Klus and Naratip Santitissadeekorn, with support from David Lloyd. The Fellowship grant funds a visit by Jason Bramburger (Seattle). An IAS Workshop grant has also been awarded with PI Payel Das (Physics, Surrey), with support from Masanori Hanada and David
• Two new papers published by Stefan Klus
by Tom Bridges on February 22, 2021 at 11:45 am
Stefan Klus has had two new papers published in the latter part of 2020. The paper “Kernel based approximation of the Koopman generator and Schrodinger operator“, co-authored with Feliks Nuske (Paderborn) and Boumediene Hamzi (Imperial College) was published in the journal Entropy, and chosen by the journal for a cover story (link here). The second
## Wolfram Blog » Mathematics News, views, and ideas from the front lines at Wolfram Research.
• 3D-Printed Jewelry Made with the Wolfram Language Showcases the Beauty of Mathematics
by Christopher Hanusa on February 15, 2021 at 8:09 pm
h2.bookpost{display:block;} img.bookpost{padding-top:20px} I enjoy turning mathematical concepts into wearable pieces of art. That’s the idea behind my business, Hanusa Design. I make unique products that feature striking designs inspired by the beauty and precision of mathematics. These pieces are created using the range of functionality in the Wolfram Language. Just in time for Valentine’s Day, we recently launched Spikey [...]
• Step-by-Step Math Tools in Wolfram|Alpha Help Your Chemistry Course Prep
by Becky Song on February 12, 2021 at 8:51 pm
Math is one of the main things that deters students from wanting to learn more about chemistry. Being a chemical engineering student, I understand this, especially for students who just have to get chemistry out of the way as a general education requirement. Essentially, step-by-step solutions are like your own on-demand math tutor: in addition [...]
• How We Navigated a Hybrid Remote Learning Environment Using Wolfram Technology
by Timothy Newlin on January 14, 2021 at 6:00 pm
The past year of learning ushered in a variety of new experiences for instructors and students alike, and the United States Military Academy at West Point was no exception. In addition to masks in the classroom, reduced class sizes to allow for social distancing, rigorous testing and tracing efforts, and precautionary remote video classes, we [...]
• New Wolfram Language Books on Wolfram|Alpha, Calculus, Applied Engineering and System Modeler
by Paige Bremner on October 29, 2020 at 3:24 pm
h2.bookpost{display:block;} img.bookpost{padding-top:20px} The pandemic has postponed or canceled a lot of things this year, but luckily learning isn’t one of them. Check out these picks for new Wolfram Language books that will help you explore new software, calculus, engineering and more from the comfort of home. Hands-on Start to Wolfram|Alpha Notebook Edition New from Wolfram [...]
• Learn Linear Algebra in Five Hours Today with the Wolfram Language!
by Devendra Kapadia on August 14, 2020 at 1:44 pm
Linear algebra is probably the easiest and the most useful branch of modern mathematics. Indeed, topics such as matrices and linear equations are often taught in middle or high school. On the other hand, concepts and techniques from linear algebra underlie cutting-edge disciplines such as data science and quantum computation. And in the field of [...]
• New Wolfram Books: Releases from Wolfram Media and Others Featuring the Wolfram Language
by Amy Simpson on July 2, 2020 at 6:11 pm
h2.bookpost{display:block;} img.bookpost{padding-top:20px} The first half of 2020 has brought with it another exciting batch of publications. Wolfram Media has released Conrad Wolfram’s The Math(s) Fix. Keep an eye out for the upcoming third edition of Hands-on Start to Wolfram Mathematica later in 2020. The Math(s) Fix The Math(s) Fix: An Education Blueprint for the AI [...]
• New 12.1 Dataset Interactive Controls and Formatting Options
by Christopher Carlson on June 23, 2020 at 2:08 pm
In his blog post announcing the launch of Mathematica Version 12.1, Stephen Wolfram mentioned the extensive updates to Dataset that we undertook to make it easier to explore, understand and present your data. Here is how the updated Dataset works and how you can use it to gain deeper insight into your data. New Interactive [...]
• Using Integer Optimization to Build and Solve Sudoku Games with the Wolfram Language
by Paritosh Mokhasi on June 2, 2020 at 1:40 pm
Sudoku is a popular game that pushes the player’s analytical, mathematical and mental abilities. Solving sudoku problems has long been discussed on Wolfram Community, and there has been some fantastic code presented to solve sudoku problems. To add to that discussion, I will demonstrate several features that are new to Mathematica Version 12.1, including how [...]
• From Sine to Heun: 5 New Functions for Mathematics and Physics in the Wolfram Language
by Tigran Ishkhanyan on May 6, 2020 at 5:02 pm
Mathematica was initially built to be a universal solver of different mathematical tasks for everything from school-level algebraic equations to complicated problems in real scientific projects. During the past 30 years of development, over 250 mathematical functions have been implemented in the system, and in the recent release of Version 12.1 of the Wolfram Language, [...]
• 非線形偏微分方程式への有限要素法の適用
by Koji Maruyama on April 29, 2020 at 9:19 pm
Mathematica 12 has powerful functionality for solving partial differential equations (PDEs) both symbolically and numerically. This article focuses on, among other things, the finite element method (FEM)–based solver for nonlinear PDEs that has been newly implemented in Version 12. After briefly reviewing basic syntax of the Wolfram Language for PDEs, including how to designate Dirichlet [...] | 2021-02-26T18:29:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34942057728767395, "perplexity": 1073.5815604351533}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178357935.29/warc/CC-MAIN-20210226175238-20210226205238-00620.warc.gz"} |
https://www.itl.nist.gov/div898/handbook/pri/section3/pri339.htm | 5. Process Improvement
5.3. Choosing an experimental design
5.3.3. How do you select an experimental design?
## Three-level full factorial designs
Three-level designs are useful for investigating quadratic effects The three-level design is written as a 3k factorial design. It means that k factors are considered, each at 3 levels. These are (usually) referred to as low, intermediate and high levels. These levels are numerically expressed as 0, 1, and 2. One could have considered the digits -1, 0, and +1, but this may be confusing with respect to the 2-level designs since 0 is reserved for center points. Therefore, we will use the 0, 1, 2 scheme. The reason that the three-level designs were proposed is to model possible curvature in the response function and to handle the case of nominal factors at 3 levels. A third level for a continuous factor facilitates investigation of a quadratic relationship between the response and each of the factors.
Three-level design may require prohibitive number of runs Unfortunately, the three-level design is prohibitive in terms of the number of runs, and thus in terms of cost and effort. For example a two-level design with center points is much less expensive while it still is a very good (and simple) way to establish the presence or absence of curvature.
The 32 design
The simplest 3-level design - with only 2 factors This is the simplest three-level design. It has two factors, each at three levels. The 9 treatment combinations for this type of design can be shown pictorially as follows:
FIGURE 3.23: A 32 Design Schematic
A notation such as "20" means that factor A is at its high level (2) and factor B is at its low level (0).
The 33 design
The model and treatment runs for a 3 factor, 3-level design This is a design that consists of three factors, each at three levels. It can be expressed as a 3 x 3 x 3 = 33 design. The model for such an experiment is
$$\begin{array}{lcl} Y_{ijk} & = & \mu + A_{i} + B_{j} + AB_{ij} + C_{k} + AC_{ik} + \\ & & BC_{jk} + ABC_{ijk} + \epsilon_{ijk} \end{array}$$
where each factor is included as a nominal factor rather than as a continuous variable. In such cases, main effects have 2 degrees of freedom, two-factor interactions have 22 = 4 degrees of freedom and k-factor interactions have 2k degrees of freedom. The model contains 2 + 2 + 2 + 4 + 4 + 4 + 8 = 26 degrees of freedom. Note that if there is no replication, the fit is exact and there is no error term (the epsilon term) in the model. In this no replication case, if one assumes that there are no three-factor interactions, then one can use these 8 degrees of freedom for error estimation.
In this model we see that i = 1, 2, 3, and similarly for j and k, making 27 treatments.
Table of treatments for the 33 design These treatments may be displayed as follows:
Factor A Factor B Factor C 0 0 0 000 100 200 0 1 001 101 201 0 2 002 102 202 1 0 010 110 210 1 1 011 111 211 1 2 012 112 212 2 0 020 120 220 2 1 021 121 221 2 2 022 122 222
Pictorial representation of the 33 design The design can be represented pictorially by
FIGURE 3.24 A 33 Design Schematic
Two types of 3k designs Two types of fractions of 3k designs are employed:
• Box-Behnken designs whose purpose is to estimate a second-order model for quantitative factors (discussed earlier in section 5.3.3.6.2)
• 3k-p orthogonal arrays. | 2018-05-27T09:25:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6977635025978088, "perplexity": 470.52324162278967}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794868239.93/warc/CC-MAIN-20180527091644-20180527111644-00273.warc.gz"} |
http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc433.htm | 6. Process or Product Monitoring and Control
6.4. Introduction to Time Series Analysis
6.4.3. What is Exponential Smoothing?
## Double Exponential Smoothing
Double exponential smoothing uses two constants and is better at handling trends As was previously observed, Single Smoothing does not excel in following the data when there is a trend. This situation can be improved by the introduction of a second equation with a second constant, $$\gamma$$, which must be chosen in conjunction with $$\alpha$$.
Here are the two equations associated with Double Exponential Smoothing. $$\begin{eqnarray} S_t & = & \alpha y_t + (1 - \alpha)(S_{t-1} + b_{t-1}) & & 0 \le \alpha \le 1 \\ & & \\ b_t & = & \gamma(S_t - S_{t-1}) + (1 - \gamma) b_{t-1} & & 0 \le \gamma \le 1 \end{eqnarray}$$ Note that the current value of the series is used to calculate its smoothed value replacement in double exponential smoothing.
Initial Values
Several methods to choose the initial values As in the case for single smoothing, there are a variety of schemes to set initial values for $$S_t$$ and $$b_t$$ in double smoothing.
$$S_1$$ is in general set to $$y_1$$. Here are three suggestions for $$b_1$$. $$\begin{eqnarray} b_1 & = & y_2 - y_1 \\ & & \\ b_1 & = & \frac{1}{3} \left[ (y_2 - y_1) + (y_3 - y_2) + (y_4 - y_3) \right] \\ & & \\ b_1 & = & \frac{y_n - y_1}{n-1} \end{eqnarray}$$
Meaning of the smoothing equations The first smoothing equation adjusts $$S_t$$ directly for the trend of the previous period, $$b_{t-1}$$, by adding it to the last smoothed value, $$S_{t-1}$$. This helps to eliminate the lag and brings $$S_t$$ to the appropriate base of the current value.
Non-linear optimization techniques can be used The values for $$\alpha$$ and $$\gamma$$ can be obtained via non-linear optimization techniques, such as the Marquardt Algorithm. | 2016-12-06T02:54:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.728257954120636, "perplexity": 415.2234518782317}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541876.62/warc/CC-MAIN-20161202170901-00364-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://code.ornl.gov/b1n/scale-manual/-/blame/b1fabfd431d57dbb9d6bb35346e1ab39ee20e106/_build/html/BONAMI.html | Batson Iii committed Nov 17, 2020 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
BONAMI: Resonance Self-Shielding by the Bondarenko Method
U. Mertyurek and M. L. Williams
ABSTRACT
BONAMI is a module of the SCALE code system that is used to perform Bondarenko calculations for resonance self-shielding. BONAMI obtains problem-independent cross sections and Bondarenko shielding factors from a multigroup (MG) AMPX master library, and it creates a MG AMPX working library of self-shielded, problem-dependent cross sections. Several options may be used to compute the background cross section values using the narrow resonance or intermediate resonance approximations, with and without Bondarenko iterations. A novel interpolation scheme is used that avoids many of the problems exhibited by other interpolation methods for the Bondarenko factors. BONAMI is most commonly used in automated SCALE sequences and is fully integrated within the SCALE cross section processing module, XSProc.
Acknowledgments
The authors express gratitude to B. T. Rearden and M. A. Jessee for their supervision of the SCALE project and review of the manuscript. The authors acknowledge N. M. Greene, formerly of ORNL, for his original development of and contributions to the BONAMI module and methodology. Finally, the authors wish to thank Sheila Walker for the completion and publication of this document.
Introduction
BONAMI (BONdarenko AMPX Interpolator) is a SCALE module that performs resonance self-shielding calculations based on the Bondarenko method [IlichB64]. It reads Bondarenko shielding factors (“f-factors”) and infinitely dilute microscopic cross sections from a problem-independent nuclear data library processed by the AMPX Batson Iii committed Jan 19, 2021 69 system [WWCD15], interpolates the tabulated shielding factors to appropriate Batson Iii committed Nov 17, 2020 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 temperatures and background cross sections for each nuclide in the system, and produces a self-shielded, problem-dependent data set.
The code performs self-shielding for an arbitrary number of mixtures using either the narrow resonance (NR) or intermediate resonance (IR) approximation [GC62]. The latter capability was introduced in SCALE 6.2. BONAMI has several options for computing background cross sections, which may include Bondarenko iterations to approximately account for the impact of resonance interference for multiple resonance absorbers. Heterogeneous effects are treated using equivalence theory based on an “escape cross section” for arrays of slabs, cylinders, or spheres. During the execution of a typical SCALE computational sequence using XSProc, Dancoff factors for uniform lattices of square- or triangular-pitched units are calculated automatically for BONAMI by numerical integration over the chord length distribution. However, for non-uniform lattices—such as those containing water holes, control rods, and so on—the SCALE module MCDancoff can be run to compute Dancoff factors using Monte Carlo for an arbitrary 3D configuration, and these values are then provided in the sequence input.
The major advantages of the Bondarenko approach are its simplicity and speed compared with SCALE’s more rigorous CENTRM/PMC self-shielding method, which performs a pointwise (PW) deterministic transport calculation “on the fly” to compute multigroup (MG) self-shielded cross sections. With the availability of IR theory in BONAMI, accurate results can be obtained for a variety of system types without the computation expense of CENTRM/PMC.
Bondarenko Self-Shielding Theory
In MG resonance self-shielding calculations, one is interested in calculating effective cross sections of the form
Batson Iii committed Jan 19, 2021 101 (301)$\sigma^{(r)}_{X,g} = \frac{\int_{g}\sigma^{(r)}_{X}(E)\Phi(E)\text{dE}}{\int_{g}\Phi(E)\text{dE}} ,$
Batson Iii committed Nov 17, 2020 102 103 104 105 106 107 108 109 110 111 112 113 114
where $$\sigma^{(r)}_{X,g}$$ is the shielded MG cross section for reaction type X of resonance nuclide r in group g; $$\sigma^{(r)}_{X}(E)$$ is a PW cross section; and $$\Phi(E)$$ is the PW weighting function, which approximates the flux spectrum per unit of energy for the system of interest. PW cross section values are known from processing evaluated data in ENDF/B files; therefore, resonance self‑shielding depends mainly on determining the problem-dependent flux spectrum $$\Phi(E)$$, which may exhibit significant fine structure variations as a result of resonance reactions.
The essence of the Bondarenko method is to parameterize the flux spectrum corresponding to varying degrees of self-shielding, represented by the background cross section parameter $$\sigma_0$$ (called “sigma-zero”) and the Doppler broadening temperature T. Hence,
Batson Iii committed Jan 19, 2021 115 (302)$\Phi \text{(E)}\to \Phi \text{(E;}\,\sigma _{\text{0,g}}^{\text{(r)}}\text{,T)}\ \ \,,\,\ \text{E}\in \text{g}\ ; \text{and} \ Batson Iii committed Nov 17, 2020 116 117 118 119 120 121 122 123 124 \sigma^{(r)}_{X,g} \rightarrow \sigma^{(r)}_{X,g}(\sigma^{(r)}_{0,g},\text{T})$
With this approach, it is possible to preprocess MG data for different background cross sections representing varying degrees of resonance self-shielding. This allows the MG averaging to be performed during the original MG library processing, so that BONAMI can do a simple interpolation on the background cross section and temperature to obtain self-shielded cross sections. This procedure is much faster than the CENTRM/PMC method in SCALE, which computes a PW flux spectrum by solving the neutron transport equation on a PW energy mesh in CENTRM and then Batson Iii committed Jan 19, 2021 125 evaluates (301). in PMC “on the fly” during a sequence execution.
Batson Iii committed Nov 17, 2020 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152
BONAMI performs two main tasks: (a) computation of background cross sections for all nuclides in each mixture in the system and (b) interpolation of shielded cross sections from the library values tabulated vs. background cross sections and temperature. The BONAMI calculation is essentially isolated from the computation of the tabulated shielded cross sections, which is performed by the AMPX processing code system—the only connection is through the definition of the background cross section used in processing the library values. Various approximations can be used to parameterize the flux spectrum in terms of a background XS, as required by the Bondarenko method. We will first consider several approaches to representing the flux in an infinite medium, which lead to different definitions of the background cross section. BONAMI’s use of equivalence theory to extend the homogeneous methods to address heterogeneous systems, such as reactor lattices, is discussed in the following section.
Parameterized Flux Spectra
Several approximations can be applied to the infinite medium transport equation to parameterize the flux spectrum in terms of a background XS, as required by the Bondarenko method. The resulting homogeneous spectra are used in AMPX to process MG cross sections which can also can be applied to heterogeneous systems (i.e., lattices) by using equivalence theory; thus the key step is determining approximations that provide parameterized solutions for homogeneous media. The neutron transport equation for a homogeneous medium at temperature T, containing a resonance nuclide r mixed with other nuclides can be expressed as
Batson Iii committed Jan 19, 2021 153 (303)$\left( \Sigma _{\text{t}}^{\text{(r)}}\text{(E,T)}\ +\sum\limits_{j\ne r} Batson Iii committed Nov 17, 2020 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 {\Sigma _{\text{t}}^{\text{(j)}}\text{(E,T)}} \right)\ \Phi \text{(E,T)}\ \,\,\,=\ \ \,{{\text{S}}^{\text{(r)}}}(\text{E,T})\ \,+\,\sum\limits_{j\ne r}{{{\text{S}}^{\text{(j)}}}(\text{E,T})} ,$
where $$\Sigma _{\text{t}}^{\text{(r)}}\text{(E,T)}$$ , $$\text{S}_{{}}^{\text{(r)}}\text{(E,T)}$$ are the macroscopic total XS and elastic scattering source for r, respectively; and $$\Sigma _{\text{t}}^{\text{(j)}}\text{(E,T)}$$, $$\text{S}_{{}}^{\text{(j)}}\text{(E,T)}$$ are the macroscopic total cross section and elastic source, respectively, for a nuclide j. The cross sections in all these expressions are Doppler-broadened to the temperature of the medium. The nuclides in the summations (i.e., all nuclides except r) are called background nuclides for the resonance absorber r.
The NR approximation can be used to approximate scattering sources of nuclides for which the neutron energy loss is large compared with the practical widths of resonances for the absorber materials of interest. Applying the NR approximation for the scattering source of background material j gives
Batson Iii committed Jan 19, 2021 169 (304)$\text{S}^{(j)}(\text{E,T}) \rightarrow \Sigma^{(j)}_{p}C(E) \text{for j = a NR-scatterer nuclide}$
Batson Iii committed Nov 17, 2020 170 171 172 173 174 175
where C(E) is a slowly varying function representative of the asymptotic (i.e., no absorption) flux in a homogeneous medium, which approximates the flux between resonances. In the resolved resonance range of most important resonance absorbers, the asymptotic flux per unit energy is represented as,
Batson Iii committed Jan 19, 2021 176 (305)$C(\text{E})\ =\ \ \,\frac{{{\Phi }_{\infty }}}{E}\ \ \ ,$
Batson Iii committed Nov 17, 2020 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195
where $${{\Phi }_{\infty }}$$ is an arbitrary normalization constant that cancels from the MG cross section expression. In the thermal range a Maxwellian spectrum is used for C(E), and in the fast range a fission spectrum is used. The SCALE Cross Section Libraries section of the SCALE documentation gives analytical expressions for C(E) used in AMPX to process MG data with the NR approximation. AMPX also has an option to input numerical values for C(E), obtained for example from a PW slowing-down calculation with CENTRM. This method has been used to process MG data for some nuclides on the SCALE libraries.
Conversely, the wide resonance (WR) approximation has been used to represent elastic scattering sources of nuclides for which the neutron energy loss is small compared with the practical width of the resonance. This approximation tends to be more accurate for heavy nuclides and for lower energies. The limit of infinite mass is usually assumed, so the WR approximation is sometimes called the infinite mass (IM) approximation. Because of the assumption of IM, there is no energy loss due to collisions with WR scatterers. Applying the WR approximation for the slowing-down source of background nuclide j gives
Batson Iii committed Jan 19, 2021 196 (306)$\text{S}^{(j)}(\text{E,T}) \rightarrow \Sigma^{(j)}_{s}(\text{E,T})\Phi(\text{E,T}) ; Batson Iii committed Nov 17, 2020 197 198 199 200 201 202 203 204 \text{for} j = \text{a WR-scatterer nuclide}$
The IR approximation was proposed in the 1960s for scatterers with slowing-down properties intermediate between those of NR and WR scatterers [GC62]. The IR method represents the scattering source for arbitrary nuclide j by a linear combination of NR and WR expressions. This is done by introducing an IR parameter usually called lambda, such that
Batson Iii committed Jan 19, 2021 205 206 (307)$\text{S}_{{}}^{\text{(j)}}(\text{E,T)}\,\ \to \ \,\underbrace{\lambda _{\text{g}}^{\text{(j)}}\Sigma _{\text{p}}^{\text{(j)}}\,C(E)}_{\mathbf{NR scatterer}}\ +\ \ (1-\lambda _{\text{g}}^{\text{(j)}})\,\,\underbrace{\Sigma _{\text{s}}^{\text{(j)}}(\text{E,T})\Phi (\text{E,T})}_{\mathbf{WR scatterer}}\ \,\ \,\ ;\,\,\ \ \text{E}\in \text{g}\,\text{.}$
A value of λ=1 reduces (307) to the NR expression, whereas λ=0 reduces the Batson Iii committed Nov 17, 2020 207 208 209 210 211 212 equation to the WR expression. Fractional λ’s are for IR scatterers. Since the type of scatterer can change with the energy, the IR lambdas are functions of the energy group as well as the nuclide. The λ values represent the moderation “effectiveness” of a given nuclide, compared to hydrogen. The AMPX module LAMBDA was used to compute the IR parameters on the SCALE libraries. (See AMPX documentation distributed with SCALE) Batson Iii committed Jan 19, 2021 213 Substituting (307) into (303) and then dividing by the absorber number Batson Iii committed Nov 17, 2020 214 215 216 density N(r) gives the following IR approximation for the infinite medium transport equation in energy group g
Batson Iii committed Jan 19, 2021 217 (308)$\left( \sigma _{\text{t}}^{\text{(r)}}\text{(E,T)}\ \text{+}\ \sigma _{0}^{\text{(r)}}\text{(E,T) } \right)\,{{\Phi }^{\text{(r)}}}\text{(E,T)}\ \ =\,\ \frac{\text{1}}{{{\text{N}}^{\text{(r)}}}}{{\text{S}}^{\text{(r)}}}\text{(E,T)}\ +\ \frac{\text{1}}{{{\text{N}}^{\text{(r)}}}}\sum\limits_{j\ne r}{\lambda _{\text{g}}^{\text{(j)}}\,\Sigma _{\text{p}}^{\text{(j)}}C(E)\,}$
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where the background cross section of r in the homogeneous medium is defined as
Batson Iii committed Jan 19, 2021 221 222 (309)$\sigma _{0}^{\text{(r)}}\text{(E,T)}\ \ =\ \ \frac{1}{{{\text{N}}^{\text{(r)}}}}\,\,\sum\limits_{j\ne r}{\left( \Sigma _{\text{a}}^{\text{(j)}}(\text{E,T})+\lambda _{\text{g}}^{\text{(j)}}\,\Sigma _{\text{s}}^{\text{(j)}}(\text{E,T})\,\, \right)}$
Although (308) provides the flux spectrum as a function of the background Batson Iii committed Nov 17, 2020 223 224 225 cross section $$\sigma \,_{0}^{(r)}(u,T)$$ it is not in a form that can be preprocessed when the MG library is generated, because the energy variation of $$\sigma \,_{0}^{(r)}(E,T)$$ must be known. If the total cross sections Batson Iii committed Jan 19, 2021 226 of the background nuclides in (309) have different energy variations, the shape of Batson Iii committed Nov 17, 2020 227 228 $$\sigma \,_{0}^{(r)}(E,T)$$ depends on their relative concentrations—which are not known when the MG library is processed. Batson Iii committed Jan 19, 2021 229 However, if the cross sections in (309) are independent of energy, Batson Iii committed Nov 17, 2020 230 so that the background cross section is constant, Batson Iii committed Jan 19, 2021 231 (308) can be solved for any arbitrary value of $$\sigma \,_{0}^{(r)}$$ Batson Iii committed Nov 17, 2020 232 233 234 235 236 237 as a parameter. This obviously occurs for the special case in which nuclide r is the only resonance nuclide in the mixture; i.e., the background materials are nonabsorbing moderators for which the total cross section is equal to the potential cross section. In this case, $$\sigma \,_{0}^{(r)}(E,T)\quad \to \ \ \ \sigma \,_{0,g}^{(r)}$$, where
Batson Iii committed Jan 19, 2021 238 (310)$\sigma \,_{0,g}^{(r)}\,\,=\quad \frac{1}{N_{{}}^{(r)}}\sum\limits_{j\,\ne \,i}{\ N_{{}}^{(j)}\,\lambda _{g}^{(j)}\sigma \,_{p}^{(j)}}$
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If the mixture contains multiple resonance absorbers, as is usually the case, other approximations must be made to obtain a constant background cross section.
The approximation of “no resonance interference” assumes that resonances of background nuclides do not overlap with those of nuclide r, so their total cross sections can be approximated by the potential values within resonances of r where self-shielding occurs. In this Batson Iii committed Jan 19, 2021 246 approximation, the expression in (310) is also used for the background Batson Iii committed Nov 17, 2020 247 248 249 250 251 cross section.
Another approximation is to represent the energy-dependent cross sections of the background nuclides by their group-averaged (i.e., self-shielded cross) values; thus
Batson Iii committed Jan 19, 2021 252 253 (311)$\sigma \,_{a}^{(j)}(E,T)\quad \to \ \ \ \sigma \,_{a,g}^{(j)}\ \quad ;\quad \ \ \quad \sigma \,_{s}^{(j)}(E,T)\quad \to \ \ \ \sigma \,_{s,g}^{(j)}\text{ for }E\in g$
In this case, the background cross section in (309) for nuclide r is the Batson Iii committed Nov 17, 2020 254 255 group-dependent expression,
Batson Iii committed Jan 19, 2021 256 257 (312)$\sigma _{0,g}^{\text{(r)}}\ \ =\ \ \frac{1}{{{\text{N}}^{\text{(r)}}}}\,\,\sum\limits_{j\ne r}{\left( \Sigma _{\text{a,g}}^{\text{(j)}}+\lambda _{\text{g}}^{\text{(j)}}\,\Sigma _{\text{s,g}}^{\text{(j)}}\, \right)}$
An equation similar to (312) is used for the background cross sections of Batson Iii committed Nov 17, 2020 258 259 260 261 262 263 264 265 266 267 all resonance nuclides; thus the self-shielded cross sections of each resonance absorber depend on the shielded cross sections of all other resonance absorbers in the mixture. When self-shielding operations are performed with BONAMI for this approximation, “Bondarenko” iterations are performed to account for the inter-dependence of the shielded cross sections.
Assuming that $$\sigma \,_{0}^{(r)}$$ is represented as a groupwise-constant based on one of the previous approximations, several methods can be used to obtain a parameterized flux spectrum for preprocessing Bondarenko data in the MG libraries. In the simpliest approach, the scattering source of the resonance Batson Iii committed Jan 19, 2021 268 nuclide r in (308) is represented by the NR approximation, Batson Iii committed Nov 17, 2020 269 $${{\text{S}}^{\text{(r)}}}(\text{E,T})$$ to $$\Sigma _{\text{p}}^{\text{(r)}}C(E)$$. Batson Iii committed Jan 19, 2021 270 In this case, (308) can be solved analytically to obtain the following Batson Iii committed Nov 17, 2020 271 272 expression for the flux spectrum used to process MG data as a function of $$\sigma \,_{0}^{(r)}$$:
Batson Iii committed Jan 19, 2021 273 (313)${{\Phi }^{\text{(r)}}}\text{(E;}\,\sigma _{0}^{\text{(r)}}\text{,T)}\ \ =\,\ \frac{\sigma _{\text{p}}^{\text{(r)}}\ +\ \,\frac{\text{1}}{{{\text{N}}^{\text{(r)}}}}\sum\limits_{j\ne r}{\,\Sigma _{\text{p}}^{\text{(j)}}\,}\ }{\sigma _{\text{t}}^{\text{(r)}}\text{(E,T)}\ \text{+}\ \sigma _{0}^{\text{(r)}}}C(E)\ \ \,\ \to \ \ \,\frac{C(E)\ }{\sigma _{\text{t}}^{\text{(r)}}\text{(E,T)}\ \text{+}\ \sigma _{0}^{\text{(r)}}}$
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where C(E) includes is an arbitrary constant multiplier that cancels Batson Iii committed Jan 19, 2021 275 from (301).
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A more accurate approach that does not require using the NR approximation is to directly solve the IR form of the neutron transport equation using PW cross sections, with the assumption of no interference between mixed absorber resonances. The IRFfactor module of AMPX uses XSProc to calculate the self-shielded flux spectrum for MG data processing using one of two options:
1. A homogeneous model corresponding to an infinite medium of the resonance nuclide mixed with hydrogen, in which the ratio of the absorber to hydrogen number densities is varied in CENTRM to obtain the desired background cross section values;
2. A heterogeneous model corresponding to a 2D unit cell from an infinite lattice, in which the cell geometry (e.g., pitch) as well as the absorber number density is varied in CENTRM to obtain the desired background cross section values.
Both of these models provide a numerical solution for the flux spectrum. Details on these approaches are given in reference 2.
Self-Shielded Cross Section Data in SCALE Libraries
The AMPX code system processes self-shielded cross sections using the flux expressions described in the preceding section. For MG libraries in Batson Iii committed Jan 19, 2021 299 SCALE-6.2 and later versions, the NR approximation in (313) is used to Batson Iii committed Nov 17, 2020 300 301 302 303 304 305 306 307 308 309 310 311 312 313 represent the flux spectrum for nuclides with masses below A=40, since the NR approximation is generally accurate for low-mass nuclides and/or high energies. The standard AMPX weight functions are used to represent C(E) over the entire energy range for all nuclides with A<40, except for hydrogen and oxygen which use a calculated C(E) from CENTRM. The NR approximation with a calculated C(E) function is also used to represent the spectrum above the resolved resonance range for nuclides with A>40; but in the resolved resonance range of these nuclides, AMPX processes shielded cross sections with flux spectra obtained from CENTRM calculations using either a homogeneous or heterogeneous model. Regardless of the method used to obtain the flux spectrum, the parameterized shielded cross sections for absorber nuclide “r” are computed from the expression,
Batson Iii committed Jan 19, 2021 314 (314)$\sigma _{\text{X,g}}^{\text{(r)}}(\sigma \,_{0}^{(r)}\,,T)\quad =\quad \,\frac{\int_{g}{\ \ \,\sigma _{X}^{(r)}(E,T)\ \,\Phi (E;\,\,\sigma \,_{0}^{(r)}\,,T)\ dE}}{\int_{g}{\ \,\Phi (E;\,\,\sigma \,_{0}^{(r)}\,,T)\ \,dE}}\quad ,$
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where $$\Phi (E;\,\,\sigma \,_{0}^{(r)}\,,T)$$ is the flux for a given value of $$\sigma \,_{0}^{(r)}$$ and T.
Rather than storing self-shielded cross sections in the master library, AMPX converts them to Bondarenko shielding factors, also called f-factors, defined as the ratio of the shielded cross section to the infinitely dilute cross section. Thus the MG libraries in SCALE contain Bondarenko data consisting of f‑factors defined as
Batson Iii committed Jan 19, 2021 323 (315)$f_{\text{X,g}}^{\text{(r)}}(\sigma \,_{0}^{{}}\,,T)\quad =\quad \,\frac{\sigma _{\text{X,g}}^{\text{(r)}}(\sigma \,_{0}^{{}},T)}{\sigma _{\text{X,g}}^{\text{(r)}}(\infty )}\quad ,$
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and infinitely dilute cross sections defined as,
Batson Iii committed Jan 19, 2021 326 (316)$\sigma _{\text{X,g}}^{\text{(r)}}(\infty )\quad =\quad \,\sigma _{\text{X,g}}^{\text{(r)}}(\sigma \,_{0}^{{}}=\infty ,T={{T}_{ref}}) \to \ \ \,\frac{\int_{g}{\ \sigma _{X}^{(r)}(E,{{T}_{ref}})\ C(E)\ \,dE}}{\int_{g}{\ \,C(E)\ \,dE}}\quad .$
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In AMPX, the reference temperature for the infinitely dilute cross section is normally taken to be 293 K. Bondarenko data on SCALE libraries are provided for all energy groups and for five reaction types: total, radiative capture, fission, within-group scattering, and elastic scatter. Recent SCALE libraries include f-factors at ~10–30 background cross section values (depending on nuclide) ranging from ~10−3 to ~1010 barns, which span the range of self-shielding conditions. Typically the f-factor data are tabulated at five temperature values. Background cross sections and temperatures available for each nuclide in the SCALE MG libraries are given in the SCALE Cross Section Libraries chapter.
Background Cross Section Options in BONAMI
To compute self-shielded cross sections for nuclide r, BONAMI first computes the appropriate background cross section for the system of interest and then interpolates the library Bondarenko data to obtain the f-factor corresponding to this σ0 and nuclide temperature. Several options are available in BONAMI to compute the background cross Batson Iii committed Jan 19, 2021 346 section, based on (310) and (312) in the preceding section. The options are Batson Iii committed Nov 17, 2020 347 348 349 350 351 specified by input parameter “iropt” and have the following definitions:
1. iropt = 0 => NR approximation with Bondarenko iterations:
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Background cross sections for all nuclides are computed using (312) with Batson Iii committed Nov 17, 2020 353 354 λ=1; therefore,
Batson Iii committed Jan 19, 2021 355 (317)$\sigma _{0}^{\text{(r)}}\ =\ \frac{1}{{{\text{N}}^{\text{(r)}}}}\,\,\sum\limits_{j\ne r}{\Sigma _{\text{t,g}}^{\text{(j)}}} .$
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Since the background cross section for each nuclide depends on the shielded total cross sections of all other nuclides in the mixture, “Bondarenko iterations” are performed in BONAMI to obtain a consistent set of shielded cross sections. Bondarenko iterations provide a crude method of accounting for resonance interference effects that are ignored by the Batson Iii committed Jan 19, 2021 361 approximation for $$\sigma \,_{0}^{(r)}$$ in (310). The BONAMI Batson Iii committed Nov 17, 2020 362 363 364 365 366 367 iterative algorithm generally converges in a few iterations. Prior to SCALE-6.2, this option was the only one available in BONAMI, and it is still the default for XSProc.
1. iropt = 1 => IR approximation with no resonance interference (potential cross sections):
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Background cross sections for all nuclides are computed using (310). No Batson Iii committed Nov 17, 2020 369 370 371 372 373 Bondarenko iterations are needed.
1. iropt t = 2 => IR approximation with Bondarenko iterations, but no resonance scattering:
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Background cross sections for all nuclides are computed using (312) with Batson Iii committed Nov 17, 2020 375 376 377 the scattering cross section approximated by the potential value; therefore,
Batson Iii committed Jan 19, 2021 378 (318)$\sigma _{0}^{\text{(r)}}\ \ =\ \ \frac{1}{{{\text{N}}^{\text{(r)}}}}\,\,\sum\limits_{j\ne r}{\left( \Sigma _{\text{a,g}}^{\text{(j)}}+\lambda _{\text{g}}^{\text{(j)}}\,\Sigma _{\text{p}}^{\text{(j)}}\, \right)}$
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Since the background cross section for each resonance nuclide includes the shielded absorption cross sections of all other nuclides, Bondarenko interactions are performed.
1. iropt = 3 => IR approximation with Bondarenko iterations:
Background cross sections for all nuclides are computed using the full Batson Iii committed Jan 19, 2021 386 IR expression in (312). Bondarenko interactions are performed.
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Computation of the background cross sections in BONAMI generally requires group-dependent values for the IR parameter λ. These are calculated by a module in AMPX during the library process and are stored in the MG libraries under the reaction identifier (MT number), MT=2000.
Self-Shielded Cross Sections for Heterogeneous Media
Equivalence theory can be used to obtain shielded cross sections for heterogeneous systems containing one or more “lumps” of resonance absorber mixtures separated by moderators, such as reactor lattices. It can be shown that if the fuel escape probability is represented by the Wigner rational approximation, the collision probability formulation of the neutron transport equation for an absorber body in a heterogeneous Batson Iii committed Jan 19, 2021 400 medium can be reduced to a form identical to (303). This can be done for Batson Iii committed Nov 17, 2020 401 402 403 404 405 406 407 408 409 410 411 412 an “equivalent” infinite homogeneous medium consisting of the same absorber body mixture plus an additional NR scatterer with a constant cross section called the “escape cross section” [Lam66]. Equivalence theory states that the self-shielded cross section for resonance absorber r in the heterogeneous medium is equal to the self-shielded cross section of r in the equivalent infinite homogeneous medium; therefore the f-factors that were calculated for homogenous mixtures can also be used to compute self-shielded cross sections for heterogeneous media by simply interpolating the tabulated f-factors in the library to the modified sigma-zero value of
Batson Iii committed Jan 19, 2021 413 (319)$\hat{\sigma }_{0}^{(r)}\quad =\quad \sigma _{0}^{(r)}\ +\ \ \,\sigma _{esc}^{(r)}$
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where,
$$\hat{\sigma }_{0}^{(r)}$$ = background cross section of r in the absorber lump of the heterogeneous system;
$$\sigma \,_{0}^{(r)}$$ = background cross section defined in Parameterized Flux Spectra for an infinite homogeneous medium of the absorber body mixture;
$$\sigma _{esc}^{(r)}$$ = microscopic escape cross section for nuclide r, defined as
Batson Iii committed Jan 19, 2021 422 (320)$\sigma _{esc}^{(r)}\quad =\quad \frac{{{\Sigma }_{esc}}}{{{N}^{(r)}}}$
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$${{\Sigma }_{esc}}$$ = macroscopic escape cross section for the absorber lump defined in BONAMI as
Batson Iii committed Jan 19, 2021 427 (321)${{\Sigma }_{esc}}\quad =\quad \,\frac{(1\quad -\quad c)A}{\bar{\ell }\ \,\ \left[ 1\quad +\quad \left( A\quad -\quad 1 \right)c \right]}$
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where
$$\bar{\ell }$$ = average chord length of the absorber body = $$4\ \ \,\times \ \frac{volume}{surface\ \ area}$$;
A = Bell factor, used to improve the accuracy of the Wigner rational approximation;
c = lattice Dancoff factor, which is equal to the probability that a neutron escaping from one absorber body will reach another absorber body before colliding in the intervening moderator.
Values for the mean chord length $$\bar{\ell }$$ are computed in BONAMI for slab, sphere, and cylinder absorber bodies. In the most common mode of operation where BONAMI is executed through the XSProc module in SCALE, Dancoff factors for uniform lattices are computed automatically and provided as input to BONAMI. For nonuniform lattices—such as those containing water holes, control rods, etc.—it may be desirable for the user to run the SCALE module MCDancoff to compute Dancoff factors using Monte Carlo for an arbitrary 3D configuration. In this case the values are provided in the MORE DATA input block of XSProc. The Bell factor “A” is a correction factor to account for errors caused by use of the Wigner rational approximation to represent the escape probability from a lump. Two optional Bell factor corrections are included in BONAMI. The first uses expressions developed by Otter that essentially force the Wigner escape probability for an isolated absorber lump to agree with the exact escape probability for the particular geometry by determining a value of A as a function of $${{\Sigma }_{T}}\bar{\ell }$$ for slab, cylindrical, or spherical geometries. Since the Otter expression was developed for isolated bodies, it does not account for errors in the Wigner rational approximation due to lattice effects. BONAMI also includes a Bell factor correction based on a modified formulation developed by Leslie [LHJ65] that is a function of the Dancoff factor.
Interpolation Scheme
After the background cross section for a system has been computed, BONAMI interpolates f-factors at the appropriate σ0 and Batson Iii committed Jan 19, 2021 460 temperature from the tabulated values in the library. Fig. 202 shows Batson Iii committed Nov 17, 2020 461 462 463 464 465 a typical variation of the f-factor vs. background cross sections for the capture cross section of 238U in the SCALE 252 group library.
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Fig. 202 Plot of f-factor variation for 238U capture reaction.
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Interpolation of the f-factors can be problematic, and several different schemes have been developed for this purpose. Some of the interpolation methods that have been used in other codes are constrained Lagrangian, [DYB77] arc-tangent fitting, [Kid74] and an approach developed by Segev [Seg81]. All of these were tested and found to be inadequate for use with the SCALE libraries, which may have multiple energy groups within a single resonance. BONAMI uses a unique interpolation method developed by Greene, which is described in [Gre82]. Greene’s interpolation method is essentially a polynomial approach in which the powers of the Batson Iii committed Jan 19, 2021 477 polynomial terms can vary within a panel, as shown in (325):
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Batson Iii committed Jan 19, 2021 479 (322)$f\left( \sigma \right)\quad =\quad f\left( \sigma {{\,}_{1}} \right)\quad +\quad \frac{\sigma {{\,}^{q(\sigma )}}\quad -\quad \sigma \,_{1}^{q(\sigma )}}{\sigma \,_{2}^{q(\sigma )}\quad -\quad \sigma \,_{1}^{q(\sigma )}}\quad \left( f\left( {{\sigma }_{2}} \right)\quad -\quad f\left( {{\sigma }_{1}} \right) \right)\quad ,$
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where
Batson Iii committed Jan 19, 2021 482 483 (323)$q\left( \sigma \right)\quad =\quad q\left( \sigma {{\,}_{1}} \right)\quad +\quad \frac{\sigma \quad -\quad \sigma \,_{1}^{{}}}{\sigma \,_{2}^{{}}\quad -\quad \sigma \,_{1}^{{}}}\quad \left( q\left( {{\sigma }_{2}} \right)\quad -\quad q\left( {{\sigma }_{1}} \right) \right)\quad .$
Fig. 203 illustrates the expected behavior of (322) caused by varying Batson Iii committed Nov 17, 2020 484 485 486 487 488 489 490 491 492 493 the powers in a panel.
By allowing the power q to vary as a function of independent variable σ, we can move between the various monotonic curves on the graph in a monotonic fashion. Note that when p crosses the p = 1 curve, the shape changes from concave to convex, or vice versa. This shape change means that we can use the scheme to introduce an inflection point, which is exactly the situation needed for interpolating f-factors.
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Fig. 203 Illustration of the effects of varying “powers” in the Greene interpolation method.
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Fig. 204 and Fig. 204 show typical “fits” of the f-factors using Batson Iii committed Nov 17, 2020 497 498 499 500 501 502 503 504 505 the Greene interpolation scheme for two example cases. Note, in particular, that since this scheme has guaranteed monotonicity, it easily accommodates the end panels that have the smooth asymptotic variation. Even considering the extra task of having to determine the powers for temperature and σ0 interpolations, the method is not significantly more time-consuming than the alternative schemes for most applications.
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Fig. 204 Use of Greene’s method to fit the σ0 variation of Bondarenko factors for case 1.
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Fig. 205 Use of Greene’s method to fit the σ0 variation of Bondarenko factors for case 2.
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Input Instructions
BONAMI is most commonly used as an integral component of XSProc through SCALE automated analysis sequences. XSProc automatically prepares all the input data for BONAMI and links it with the other self-shielding modules. During a SCALE sequence execution, the data are provided directly to BONAMI in memory through XSProc. Some of the input parameters can be modified in the MOREDATA block in XSProc.
However, the legacy interface to execute stand-alone BONAMI calculations has been preserved for expert users. The legacy input to BONAMI uses the FIDO schemes described in the FIDO chapter of the SCALE manual. The BONAMI input for standalone execution is given below, where the MOREDATA input keywords are marked in bold.
Data Block 1
0$Logical Unit Assignments [4] 1. masterlib— input master library (Default = 23) 2. mwt—not used 3. msc—not used 4. newlib—output master library (Default = 22) 1$ Case Description [6]
1. cellgeometry—geometry description
0 homogeneous
1 slab
2 cylinder
3 sphere
2. numzones—number of zones or material regions
3. mixlength—mixing table length. This is the total number of entries needed to describe the concentrations of all constituents in all mixtures in the problem.
1. ib—not used
2. crossedt—output edit option
0 no output (Default)
1 input echo
2 iteration list, timing
3 background cross section calculation details
4 shielded cross sections, Bondarenko factors
3. issopt—not used
4. iropt—resonance approximation option
0 NR (Default) (Bondarenko iterations)
1 IR with potential scattering
2 IR with absorption and potential scattering (Bondarenko iterations)
3 IR with absorption and elastic scattering (Bondarenko iterations)
5. bellopt—Bell factor calculation option
0 Otter 1 Leslie (Default)
6. escxsopt—escape cross section calculation option
0 consistent
1 inconsistent (Default)
2* Floating-Point Constants [2]
1. bonamieps—convergence criteria for the Bondarenko iteration (Default = 0.001)
2. bellfact—geometrical escape probability adjustment factor. See notes below on this parameter (Default = 0.0).
T Terminate Data Block 1.
Data Block 2
3$Mixture numbers in the mixing table [mixlength] 4$ Component (nuclide) identifiers in the mixing table [mixlength] 5* Concentrations (atoms/b-cm) in the mixing table [mixlength] 6$Mixtures by zone [numzones] 7* Outer radii (cm) by zone [numzones] 8* Temperature (k) by zone [numzones] 9* Escape cross section (cm-1) by zone [numzones] 10$ Not used 11$Not used 12* Temperature (K) of the nuclide in a one-to-one correspondence with the mixing table arrays. 13* Dancoff factors by zone [numzones] 14* Lbar ($$\bar{\ell }$$) factors by zone [numzones] T Terminate Data Block 2. This concludes the input data required by BONAMI. Notes on input In the 1$ array, cellgeometry specifies the geometry. The geometry information is used in conjunction with the 7* array to calculate mean chord length Lbar if it is not provided by the user in the 14* array.
numzones, the number of zones, may or may not model a real situation. It may, for example, be used to specify numzones independent media to perform a cell calculation in parallel with one or more infinite medium calculations. The geometry description in 1$array applies only to mean chord length calculations unless it is provided in 14*. In the 2* array, bonamieps is used to specify the convergence expected on all macroscopic total values by zone, that is, each $${{\Sigma }_{t}}(g,j)$$ in group g and zone j is converged so that Batson Iii committed Jan 19, 2021 623 (324)$\frac{\left| \,\Sigma \,_{t}^{i}(g,j)\quad -\quad \Sigma \,_{t}^{i-1}(g,j)\, \right|}{\Sigma \,_{t}^{i}(g,j)}\quad \le \quad bonamieps\quad .$ Batson Iii committed Nov 17, 2020 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 The “Bell” factor in the 2* array is the parameter used to adjust the Wigner rational approximation for the escape probability to a more correct value. It has been suggested that if one wishes to use one constant value, the Bell factor should be 1.0 for slabs and 1.35 otherwise. In the ordinary case, BONAMI defaults the Bell factor to zero and uses a prescription by Otter [Ott64] to determine a cross-section geometry-dependent value of the Bell factor for isolated absorber bodies. It uses a prescription by Leslie6 to determine the Dancoff factor–dependent values of the Bell factor for lattices, which are much more accurate than the single value. The user who wishes to determine the constant value can, however, use it by inputting a value other than zero. The 3$, 4$, and 5* arrays are used to specify the concentrations of the constituents of all mixtures in the problem as follows: Entry 3$ (Mixture Number) 4$(Nuclide ID) 5* (Concentrations) 1 2 . . . . mixlength . Because of the manner in which BONAMI references the nuclides in a calculation, each nuclide in the problem must have a unique entry in the mixing table. Thus one cannot specify a mixture and subsequently load it into more than one zone, as can be the case with many modules requiring this type of data. The 12* array is used to allow varying the temperatures by nuclide within a zone. In the event this array is omitted, the 12* array will default by nuclide to the temperature of the zone containing the nuclide. The mixture numbers in each zone are specified in the 6$ array. Mixture numbers are arbitrary and need only match up with those used in the 3\$ array.
The radii in the 7* array are referenced to a zero value at the left boundary of the system.
In the event the temperatures in the 8* array are not bounded by temperature values in the Bondarenko tables, BONAMI will extrapolate using the three temperature points closest to the value. For example, a request for 273 K for a nuclide with Bondarenko sets at 300, 900, and 2,100 K would use the polynomial fit from those three temperature points to extrapolate the 273 K value.
The escape cross sections in the 9* array allow a macro escape cross section ($$\Sigma _{e}^{input}$$) to be specified by zone. (This array can be ignored if Dancoff factors are provided.) If the Dancoff factor for a zone is specified as −1 in the input, then the user-specified escape cross section is used in calculating the background cross sections σ0 as follows:
Batson Iii committed Jan 19, 2021 674 (325)${{\sigma }_{0}}\quad =\quad \frac{\sum\limits_{n\ne i}{{{N}_{n}}\ \sigma \,_{t}^{n}\quad +\quad \Sigma _{e}^{input}}}{{{N}_{i}}}\quad$
Batson Iii committed Nov 17, 2020 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231
Sample Problem
In most cases, the input data to BONAMI are simple and obvious because the complicated parameters are determined internally based on the options selected. The user describes his geometry, the materials contained therein, the temperatures, and a few options.
This problem is for a system of iron-clad uranium (U238 – U235 ) fuel pins arranged in a square lattice in a water pool.
Our number densities are
Fuel:
$${{N}_{{}^{235}U}}$$ = 1.4987 × 10−4
$${{N}_{{}^{238}U}}$$ = 2.0664× 10−-2
$${{N}_{{}^{56}Fe}}$$ = 9.5642× 10−5
Water:
NH = 6.6662 × 10−2
NO = 3.3331 × 10−2
For the problem, we choose iropt = 1 (IR approximation with scattering approximated by λΣp) and crossedt = 4 for the most detailed output edits. An 8-group test library is used for fast execution and a short output file.
The XSProc/CSAS1X SCALE sequence input file, the corresponding i_bonami FIDO input file created by the sequence under the temporary working directory, and an abbreviated copy of the output from this case follows.
=csas1x Assembly pin test-8grp read comp ' fuel u-235 1 0 1.4987e-4 297.15 end u-238 1 0 2.0664e-2 297.15 end ' clad fe-56 2 0 9.5642e-5 297.15 end ' coolant h 3 0 6.6662e-2 297.15 end o 3 0 3.3331e-2 297.15 end end comp ' ==================================================================== read celldata latticecell squarepitch pitch=1.26 3 fuelr=0.405765 1 cladr=0.47498 2 end moredata iropt=1 crossedt=4 end moredata end celldata ' ==================================================================== end
FIDO input i_bonami
-1$$a0001 500000 e 0$$ a0001 11 0 18 1 e 1$$a0001 1 3 5 0 4 1010 1 -1 -1 e 2** a0001 1.00000E-03 0.00000E+00 e t 3$$ a0001 1 1 2 3 3 e 4$$a0001 92235 92238 26056 1001 8016 e 5** a0001 1.49870E-04 2.06640E-02 9.56420E-05 6.66620E-02 3.33310E-02 e 6$$ a0001 1 2 3 e 7** a0001 4.05765E-01 4.74980E-01 7.10879E-01 e 8** a0001 2.97150E+02 2.97150E+02 2.97150E+02 e 9** a0001 1.11870E+00 4.15813E+00 1.78119E-01 e 10$$a0001 92235 92238 26056 1001 8016 e 11$$ a0001 0 0 0 e 13** a0001 2.71260E-01 5.20852E-01 9.24912E-01 e 14** a0001 8.11530E-01 1.38430E-01 4.71798E-01 e 15** a0001 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 e 16$$a0001 2 2 2 e 17$$ a0001 0 0 0 0 e t
program verification information code system: SCALE version: 6.2 program: bonami creation date: unknown library: /home02/u2m/Workfolder/sampletmp test code: bonami version: 6.2.0 jobname: u2m machine name: node22.ornl.gov date of execution: 04_dec_2013 time of execution: 21:43:54.38
1 BONAMI CELL PARAMETERS --------------------------------------------- Bonami Print Option : 4 BellFactor : 0 Bondarenko Iteration eps : 0.001 Resonance Option : 1 Bell Factor Option : LESLIE Escape CrossSection Option : INCONSISTENT CellGeometry : 2 MasterLibrary : Number oF Neutron Groups : 8 First Thermal Neutron Group : 5 __________________________________________ Processing Zone : 1 Mixture Number : 1 Number Of Nuclides : 2 Dancoff Factor : 0.27126 Lbar : 0.81153 Escape Cross Section Input : 1.1187 Material Temeprature : 297.15 Processing Nuclide : 92235 Number Density : 0.00014987 Processing Nuclide : 92238 Number Density : 0.020664 Bondarenko Iterations iteration Nuclide Group MaxChange Selfsig0 Effsig0 1 92235 0 0 0 0 1 92238 0 0 0 0 Total number of Bondarenko Iterations : 1 Max Change in Group : 0 Group Eff Macro Sig0 Escape Xsec 1 0.2351032 0.9075513 2 0.2351032 0.9075513 3 0.2351032 0.9075513 4 0.2351032 0.9075513 5 0.2351032 0.9075513 6 0.2351032 0.9075513 7 0.2351032 0.9075513 8 0.2351032 0.9075513 ---------------------------------------------------
Shielding Nuclide 92235 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 1 1 7612.71875 7.19131 0.999998 7.19129 1 2 7612.71875 10.2521 0.999616 10.2481 1 3 7612.71875 24.9361 1.00241 24.9963 1 4 7612.71875 75.1109 1.05902 79.5436 1 5 7612.71875 56.0286 1.00205 56.1434 1 6 7612.71875 198.645 1.0008 198.805 1 7 7612.71875 347.945 1.00024 348.028 1 8 7612.71875 761.257 1.0066 766.282 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 2 1 7612.71875 3.71448 0.999999 3.71448 2 2 7612.71875 7.63235 0.99935 7.62739 2 3 7612.71875 11.841 0.999444 11.8345 2 4 7612.71875 11.5408 1.00561 11.6055 2 5 7612.71875 12.5449 1.00001 12.545 2 6 7612.71875 14.2501 1.00007 14.2511 2 7 7612.71875 14.8125 1.00003 14.8128 2 8 7612.71875 15.1274 1.00015 15.1297 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 18 1 7612.71875 1.21846 0.999996 1.21846 18 2 7612.71875 1.40834 1.0002 1.40862 18 3 7612.71875 8.92885 1.00132 8.94062 18 4 7612.71875 39.2086 1.06274 41.6686 18 5 7612.71875 32.7026 1.00105 32.737 18 6 7612.71875 153.511 1.00089 153.647 18 7 7612.71875 285.775 1.00026 285.848 18 8 7612.71875 636.445 1.00655 640.611 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 102 1 7612.71875 0.060296 1 0.0602962 102 2 7612.71875 0.317627 1.00352 0.318746 102 3 7612.71875 4.16593 1.01325 4.22113 102 4 7612.71875 24.3615 1.07832 26.2695 102 5 7612.71875 10.781 1.00749 10.8618 102 6 7612.71875 30.8844 1.00074 30.9073 102 7 7612.71875 47.3579 1.0002 47.3671 102 8 7612.71875 109.685 1.00781 110.542 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 1007 1 7612.71875 0 0 0 1007 2 7612.71875 0 0 0 1007 3 7612.71875 0 0 0 1007 4 7612.71875 0 0 0 1007 5 7612.71875 12.5448 1.00001 12.5449 1007 6 7612.71875 14.2501 1.00007 14.2511 1007 7 7612.71875 14.8125 1.00003 14.8129 1007 8 7612.71875 15.1278 1.00015 15.13 ---------------------------------------------------
Shielding Nuclide 92238 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 1 1 44.0034676 7.33815 0.999983 7.33803 1 2 44.0034676 10.3566 1.00418 10.3999 1 3 44.0034676 15.0517 0.976844 14.7032 1 4 44.0034676 15.951 0.983793 15.6925 1 5 44.0034676 9.43867 1.00002 9.43887 1 6 44.0034676 10.1008 1.00008 10.1015 1 7 44.0034676 10.7744 1.00004 10.7748 1 8 44.0034676 12.2124 1.00145 12.2301 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 2 1 44.0034676 4.0228 0.999974 4.0227 2 2 44.0034676 9.05886 1.00575 9.11093 2 3 44.0034676 14.0213 0.979923 13.7398 2 4 44.0034676 11.9032 0.98795 11.7598 2 5 44.0034676 8.86555 0.999984 8.86541 2 6 44.0034676 9.24452 1.00002 9.24471 2 7 44.0034676 9.2797 1.00002 9.27987 2 8 44.0034676 9.3077 1.00009 9.30853 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 18 1 44.0034676 0.376356 1.00001 0.376361 18 2 44.0034676 0.000528746 1.00019 0.000528845 18 3 44.0034676 0.000308061 0.966052 0.000297603 18 4 44.0034676 4.75014e-06 0.967842 4.59738e-06 18 5 44.0034676 2.60878e-06 1.00006 2.60893e-06 18 6 44.0034676 5.27139e-06 1.00071 5.27512e-06 18 7 44.0034676 9.3235e-06 1.00018 9.32514e-06 18 8 44.0034676 1.81868e-05 1.00588 1.82937e-05 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 102 1 44.0034676 0.0554327 1.00006 0.0554359 102 2 44.0034676 0.17972 0.978628 0.175879 102 3 44.0034676 1.03011 0.934934 0.963087 102 4 44.0034676 4.04777 0.971568 3.93268 102 5 44.0034676 0.573119 1.0006 0.573462 102 6 44.0034676 0.856257 1.00068 0.856839 102 7 44.0034676 1.49471 1.00017 1.49497 102 8 44.0034676 2.90465 1.00586 2.92168 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 1007 1 44.0034676 0 0 0 1007 2 44.0034676 0 0 0 1007 3 44.0034676 0 0 0 1007 4 44.0034676 0 0 0 1007 5 44.0034676 8.86549 0.999984 8.86535 1007 6 44.0034676 9.24445 1.00002 9.24463 1007 7 44.0034676 9.27974 1.00002 9.27992 1007 8 44.0034676 9.30769 1.00009 9.30852 Zone Calculation is completed in 0 seconds BONAMI CELL PARAMETERS --------------------------------------------- Bonami Print Option : 4 BellFactor : 0 Bondarenko Iteration eps : 0.001 Resonance Option : 1 Bell Factor Option : LESLIE Escape CrossSection Option : INCONSISTENT CellGeometry : 2 MasterLibrary : Number oF Neutron Groups : 8 First Thermal Neutron Group : 5 __________________________________________ Processing Zone : 2 Mixture Number : 2 Number Of Nuclides : 1 Dancoff Factor : 0.520852 Lbar : 0.13843 Escape Cross Section Input : 4.15813 Material Temeprature : 297.15 Processing Nuclide : 26056 Number Density : 9.5642e-05 Bondarenko Iterations iteration Nuclide Group MaxChange Selfsig0 Effsig0 1 26056 0 0 0 0 Total number of Bondarenko Iterations : 1 Max Change in Group : 0 Group Eff Macro Sig0 Escape Xsec 1 0.0003553244 3.487286 2 0.0003553244 3.487286 3 0.0003553244 3.487286 4 0.0003553244 3.487286 5 0.0003553244 3.487286 6 0.0003553244 3.487286 7 0.0003553244 3.487286 8 0.0003553244 3.487286 ---------------------------------------------------
Shielding Nuclide 26056 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 1 1 36461.8672 3.07957 1.00005 3.07972 1 2 36461.8672 4.68958 1.00091 4.69382 1 3 36461.8672 7.85712 0.999843 7.85589 1 4 36461.8672 12.0029 1 12.0029 1 5 36461.8672 12.3689 1.00001 12.369 1 6 36461.8672 12.8598 1.00003 12.8602 1 7 36461.8672 13.5237 0.999906 13.5224 1 8 36461.8672 15.0714 0.99949 15.0637 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 2 1 36461.8672 2.26476 1.00047 2.26583 2 2 36461.8672 4.6817 1.0009 4.68592 2 3 36461.8672 7.81457 0.999813 7.81311 2 4 36461.8672 11.9143 1 11.9143 2 5 36461.8672 12.0468 1.00001 12.0469 2 6 36461.8672 12.065 1.00002 12.0653 2 7 36461.8672 12.0887 1.00005 12.0893 2 8 36461.8672 12.2042 1.00013 12.2057 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 102 1 36461.8672 0.00206393 1.0015 0.00206702 102 2 36461.8672 0.00787763 1.0035 0.00790524 102 3 36461.8672 0.0425504 1.00623 0.0428155 102 4 36461.8672 0.0885525 1 0.0885529 102 5 36461.8672 0.322101 1.00002 0.322109 102 6 36461.8672 0.794804 1.0002 0.79496 102 7 36461.8672 1.43496 0.998734 1.43314 102 8 36461.8672 2.86723 0.996792 2.85803 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 1007 1 36461.8672 0 0 0 1007 2 36461.8672 0 0 0 1007 3 36461.8672 0 0 0 1007 4 36461.8672 0 0 0 1007 5 36461.8672 12.0468 1.00001 12.0469 1007 6 36461.8672 12.065 1.00002 12.0653 1007 7 36461.8672 12.0887 1.00005 12.0893 1007 8 36461.8672 12.2042 1.00013 12.2057 Zone Calculation is completed in 0 seconds
BONAMI CELL PARAMETERS --------------------------------------------- Bonami Print Option : 4 BellFactor : 0 Bondarenko Iteration eps : 0.001 Resonance Option : 1 Bell Factor Option : LESLIE Escape CrossSection Option : INCONSISTENT CellGeometry : 2 MasterLibrary : Number oF Neutron Groups : 8 First Thermal Neutron Group : 5 __________________________________________ Processing Zone : 3 Mixture Number : 3 Number Of Nuclides : 2 Dancoff Factor : 0.924912 Lbar : 0.471798 Escape Cross Section Input : 0.178119 Material Temeprature : 297.15 Processing Nuclide : 1001 Number Density : 0.066662 Processing Nuclide : 8016 Number Density : 0.033331 Bondarenko Iterations iteration Nuclide Group MaxChange Selfsig0 Effsig0 1 1001 0 0 0 0 1 8016 0 0 0 0 Total number of Bondarenko Iterations : 1 Max Change in Group : 0 Group Eff Macro Sig0 Escape Xsec 1 1.494705 0.1593803 2 1.494705 0.1593803 3 1.494705 0.1593803 4 1.494705 0.1593803 5 1.494705 0.1593803 6 1.494705 0.1593803 7 1.494705 0.1593803 8 1.494705 0.1593803 ---------------------------------------------------
Shielding Nuclide 1001 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 1 1 4.33502197 2.98905 0.999485 2.98751 1 2 4.33502197 9.87269 0.999169 9.86448 1 3 4.33502197 19.9332 0.999972 19.9326 1 4 4.33502197 20.4672 0.998926 20.4453 1 5 4.33502197 21.1735 1.00001 21.1736 1 6 4.33502197 26.1886 0.99995 26.1873 1 7 4.33502197 35.0621 0.999821 35.0558 1 8 4.33502197 54.9507 0.997361 54.8057 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 2 1 4.33502197 2.98901 0.999485 2.98747 2 2 4.33502197 9.8726 0.999168 9.86439 2 3 4.33502197 19.9315 0.999972 19.9309 2 4 4.33502197 20.4556 0.998926 20.4336 2 5 4.33502197 21.1321 1.00001 21.1322 2 6 4.33502197 26.0865 0.99995 26.0852 2 7 4.33502197 34.8778 0.999829 34.8718 2 8 4.33502197 54.5786 0.997396 54.4365 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 102 1 4.33502197 3.56422e-05 1.00003 3.56433e-05 102 2 4.33502197 8.96827e-05 0.998165 8.9518e-05 102 3 4.33502197 0.00171679 0.999794 0.00171643 102 4 4.33502197 0.0116042 1.00002 0.0116044 102 5 4.33502197 0.0413709 1.00001 0.0413714 102 6 4.33502197 0.102043 1.00007 0.10205 102 7 4.33502197 0.184322 0.998389 0.184025 102 8 4.33502197 0.372079 0.992163 0.369163 mt Group sig0 infDiluted Xsec f-factor shielded Xsec 1007 1 4.33502197 0 0 0 1007 2 4.33502197 | 2022-01-20T14:25:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7042841911315918, "perplexity": 1420.3675390184662}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301863.7/warc/CC-MAIN-20220120130236-20220120160236-00154.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Abeg.ismat | # zbMATH — the first resource for mathematics
## Beg, Ismat
Compute Distance To:
Author ID: beg.ismat Published as: Beg, I.; Beg, Ismat; Beg, Izmat Homepage: http://www.lahoreschoolofeconomics.edu.pk/CVs/DrIsmatBeg.aspx External Links: MGP · Wikidata · ORCID · ResearchGate · dblp
Documents Indexed: 229 Publications since 1983 Reviewing Activity: 84 Reviews
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#### Serials
22 The Journal of Fuzzy Mathematics 11 Journal of Applied Mathematics and Stochastic Analysis 6 Demonstratio Mathematica 6 Journal of Intelligent and Fuzzy Systems 5 Journal of Mathematical Analysis and Applications 5 Indian Journal of Mathematics 5 International Journal of Mathematics and Mathematical Sciences 5 Rendiconti del Circolo Matemàtico di Palermo. Serie II 5 Nonlinear Functional Analysis and Applications 5 Fixed Point Theory and Applications 4 Archivum Mathematicum 4 Stochastic Analysis and Applications 4 Fixed Point Theory 4 International Journal of Modern Mathematics 4 Journal of Nonlinear Science and Applications 3 Indian Journal of Pure & Applied Mathematics 3 Mathematica Japonica 3 Approximation Theory and its Applications 3 Journal of Mathematics. The Punjab University 3 Bollettino della Unione Matemàtica Italiana. Serie VII. A 3 Applications and Applied Mathematics 3 Nonlinear Analysis. Theory, Methods & Applications 2 Computers & Mathematics with Applications 2 Fuzzy Sets and Systems 2 Journal of Natural Sciences and Mathematics 2 Mathematica Slovaca 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Results in Mathematics 2 Mathematical and Computer Modelling 2 Advances in Mathematical Sciences and Applications 2 Topological Methods in Nonlinear Analysis 2 Notes on Intuitionistic Fuzzy Sets 2 Communications on Applied Nonlinear Analysis 2 Novi Sad Journal of Mathematics 2 Acta Universitatis Apulensis. Mathematics - Informatics 2 Journal of Applied Mathematics and Computing 2 Carpathian Journal of Mathematics 2 Sarajevo Journal of Mathematics 2 New Mathematics and Natural Computation 2 Applied and Computational Mathematics 2 International Journal of Analysis 2 Journal of Function Spaces 2 Korean Journal of Mathematics 1 Chaos, Solitons and Fractals 1 Analele Universităţii Bucureşti. Matematică 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 1 Archiv der Mathematik 1 The Australian Mathematical Society Gazette 1 Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie. Nouvelle Série 1 Czechoslovak Mathematical Journal 1 Functiones et Approximatio. Commentarii Mathematici 1 Information Sciences 1 The Journal of the Indian Mathematical Society. New Series 1 Matematički Vesnik 1 Le Matematiche 1 The Mathematics Student 1 Numerical Functional Analysis and Optimization 1 Opsearch 1 Soochow Journal of Mathematics 1 Bulletin of the Greek Mathematical Society 1 Southeast Asian Bulletin of Mathematics 1 Complex Variables. Theory and Application 1 Pakistan Journal of Statistics 1 Applied Mathematics Letters 1 Bulletin of the Allahabad Mathematical Society 1 Mathematica Bohemica 1 Panamerican Mathematical Journal 1 Annales de la Société Scientifique de Bruxelles. Série I 1 Atti del Seminario Matematico e Fisico dell’Università di Modena 1 Journal of the Australian Mathematical Society. Series A 1 Bollettino della Unione Matemàtica Italiana. Serie VI. A 1 New Zealand Journal of Mathematics 1 Mathematica Montisnigri 1 Computational and Applied Mathematics 1 Random Operators and Stochastic Equations 1 Discussiones Mathematicae. Differential Inclusions 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Nonlinear Studies 1 Kuwait Journal of Science and Engineering 1 Mathematical Problems in Engineering 1 Mathematical Communications 1 Vietnam Journal of Mathematics 1 Honam Mathematical Journal 1 Soft Computing 1 Journal of Inequalities and Applications 1 Mathematical Sciences Research Hot-Line 1 Mathematical Inequalities & Applications 1 Italian Journal of Pure and Applied Mathematics 1 Journal of Computational Analysis and Applications 1 Nonlinear Analysis Forum 1 Journal of the Australian Mathematical Society 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Cubo Matemática Educacional 1 The Australian Journal of Mathematical Analysis and Applications 1 Journal of Concrete and Applicable Mathematics 1 Iranian Journal of Fuzzy Systems 1 Cubo 1 Journal of Fixed Point Theory and Applications 1 International Journal of Mathematical Analysis (Ruse) 1 Annales Mathematicae et Informaticae ...and 14 more Serials
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#### Fields
127 Operator theory (47-XX) 107 General topology (54-XX) 34 Functional analysis (46-XX) 32 Mathematical logic and foundations (03-XX) 29 Probability theory and stochastic processes (60-XX) 18 Approximations and expansions (41-XX) 18 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Computer science (68-XX) 8 Order, lattices, ordered algebraic structures (06-XX) 6 Real functions (26-XX) 6 Measure and integration (28-XX) 5 Operations research, mathematical programming (90-XX) 3 Numerical analysis (65-XX) 3 Information and communication theory, circuits (94-XX) 2 Difference and functional equations (39-XX) 2 Integral transforms, operational calculus (44-XX) 2 Integral equations (45-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Biology and other natural sciences (92-XX)
#### Citations contained in zbMATH Open
132 Publications have been cited 841 times in 544 Documents Cited by Year
Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces. Zbl 1176.54028
Beg, Ismat; Butt, Asma Rashid
2009
The contraction principle for set valued mappings on a metric space with a graph. Zbl 1201.54029
Beg, Ismat; Butt, Asma Rashid; Radojević, S.
2010
Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition. Zbl 1133.54024
Beg, Ismat; Abbas, Mujahid
2006
Common fixed points of two maps in cone metric spaces. Zbl 1197.54056
2008
Common fixed points of fuzzy maps. Zbl 1165.54311
Azam, Akbar; Beg, Ismat
2009
Approximation of random fixed points in normed spaces. Zbl 1034.47027
Beg, Ismat
2002
Fixed points of asymptotically regular multivalued mappings. Zbl 0765.54036
Beg, Ismat; Azam, Akbar
1992
Common fixed points for maps on topological vector space valued cone metric spaces. Zbl 1187.54032
2009
Random fixed points of random multivalued operators on Polish spaces. Zbl 0793.54031
1993
Fixed points of fuzzy contractive and fuzzy locally contractive maps. Zbl 1198.54069
2009
Banach contraction principle on cone rectangular metric spaces. Zbl 1274.54113
2009
Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered dislocated metric space. Zbl 1423.54068
2013
Fixed point in topological vector space-valued cone metric spaces. Zbl 1197.54057
2010
Fixed points for weakly compatible mappings satisfying an implicit relation in partially ordered metric spaces. Zbl 1199.54207
Beg, I.; Butt, A. R.
2009
Iterative procedures for solutions of random operator equations in Banach spaces. Zbl 1093.47057
Beg, Ismat; Abbas, Mujahid
2006
Random fixed point theorems for nonexpansive and contractive-type random operators on Banach spaces. Zbl 0823.47055
1994
Common fixed point for generalized set valued contractions satisfying an implicit relation in partially ordered metric spaces. Zbl 1195.54068
Beg, Ismat; Butt, Asma Rashid
2010
Applications of the proximity map to random fixed point theorems in Hilbert spaces. Zbl 0868.47044
1995
Fixed points and best approximation in Menger convex metric spaces. Zbl 1109.47047
Beg, Ismat; Abbas, Mujahid
2005
Approximation of $$*$$-nonexpansive random multivalued operators on Banach spaces. Zbl 1072.47055
Beg, Ismat; Khan, A. R.; Hussain, N.
2004
Fixed point of set-valued graph contractive mappings. Zbl 1329.54041
Beg, Ismat; Butt, Asma Rashid
2013
Common fuzzy fixed points for fuzzy mappings. Zbl 1409.54015
Azam, Akbar; Beg, Ismat
2013
Equivalence and stability of random fixed point iterative procedures. Zbl 1107.47046
Beg, Ismat; Abbas, Mujahid
2006
Fixed points of multivalued locally contractive mappings. Zbl 0717.54023
Beg, Ismat; Azam, Akbar
1990
Multi-criteria trapezoidal valued intuitionistic fuzzy decision making with Choquet integral based TOPSIS. Zbl 1337.90087
Beg, Ismat; Rashid, Tabasam
2014
Generalized cone metric spaces. Zbl 1203.54035
Beg, Ismat; Abbas, Mujahid; Nazir, Talat
2010
Inequalities in metric spaces with applications. Zbl 0998.47040
Beg, Ismat
2001
Hesitant 2-tuple linguistic information in multiple attributes group decision making. Zbl 1361.91007
Beg, Ismat; Rashid, Tabasam
2016
Coupled fixed points of mixed monotone operators on probabilistic Banach spaces. Zbl 1068.47093
Beg, Ismat; Latif, Abdul; Ali, Rashid; Azam, Akbar
2001
Geometric fixed points for single and multivalued mappings. Zbl 0911.54039
Latif, Abdul; Beg, Ismat
1997
Random fixed points of random operators satisfying semicontractivity conditions. Zbl 0896.47053
Beg, Ismat
1997
Similarity measures for fuzzy sets. Zbl 1194.46115
Beg, Ismat; Ashraf, Samina
2009
Minimal displacement of random variables under Lipschitz random maps. Zbl 1030.47047
Beg, Ismat
2002
Fixed point on a closed ball in ordered dislocated quasi metric spaces. Zbl 1325.54023
2015
Periodic fixed points of random operators. Zbl 1220.47075
Beg, Ismat; Abbas, Mujahid; Azam, Akbar
2010
Existence of fixed points in complete cone metric spaces. Zbl 1203.54034
2010
Random fixed point theorems for Caristi type random operators. Zbl 1148.47044
Beg, Ismat; Abbas, Mujahid
2007
Random approximations and random fixed point theorems. Zbl 0811.47069
1994
Coincidence and common fixed points of noncompatible maps. Zbl 1251.54039
Beg, Ismat; Abbas, Mujahid
2011
Coupled fixed points of set valued mappings in partially ordered metric spaces. Zbl 1295.54043
Beg, Ismat; Butt, Asma Rashid
2010
Fuzzy similarity and measure of similarity with Łukasiewicz implicator. Zbl 1144.03311
Beg, Ismat; Ashraf, Samina
2008
Approximation of fixed points of uniformly $$R$$-subweakly commuting mappings. Zbl 1111.47056
Beg, Ismat; Sahu, D. R.; Diwan, S. D.
2006
Fixed point theorems for weakly inward multivalued maps on a convex metric space. Zbl 1099.54030
Beg, Ismat; Abbas, Mujahid
2006
An application of a random fixed point theorem to random best approximation. Zbl 0956.47023
2000
Some random approximation theorems with applications. Zbl 0931.60054
1999
Structure of the set of fixed points of nonexpansive mappings on convex metric spaces. Zbl 1004.54031
Beg, Ismat
1998
Measurability of fixed point sets of multivalued random operators. Zbl 0913.47057
Xu, Hong-Kun; Beg, Ismat
1998
Fixed points of fuzzy multivalued mappings with values in fuzzy ordered sets. Zbl 0909.47055
Beg, Ismat
1998
Random fixed points of weakly inward operators in conical shells. Zbl 0828.47044
1995
Fixed point theorems and best approximation in convex metric spaces. Zbl 0769.41032
Beg, I.; Shahzad, N.; Iqbal, M.
1992
Common fixed point and coincidence point of generalized contractions in ordered metric spaces. Zbl 06236304
Beg, Ismat; Butt, Asma Rashid
2012
Random fixed point theorems for a random operator on an unbounded subset of a Banach space. Zbl 1172.47042
Beg, Ismat; Abbas, Mujahid
2008
Weak and strong convergence for fixed points of nearly asymptotically non-expansive mappings. Zbl 1223.47095
Sahu, D. R.; Beg, Ismat
2008
An iteration scheme for asymptotically nonexpansive mappings on uniformly convex metric spaces. Zbl 0996.47057
Beg, I.
2001
Common fixed points for commuting and compatible maps. Zbl 0912.47033
Beg, Ismat; Azam, Akbar
1996
On random approximations and a random fixed point theorem for multivalued mappings defined on unbounded sets in Hilbert spaces. Zbl 0874.60062
1996
Common random fixed points of random multivalued operators on metric spaces. Zbl 0857.47039
1995
Fixed points on star-shaped subsets of convex metric spaces. Zbl 0622.54033
Beg, Ismat; Azam, Akbar
1987
Hesitant probabilistic fuzzy linguistic sets with applications in multi-criteria group decision making problems. Zbl 1397.91135
Joshi, Dheeraj Kumar; Beg, Ismat; Kumar, Sanjay
2018
Incomplete interval valued fuzzy preference relations. Zbl 1398.68541
Khalid, Asma; Beg, Ismat
2016
Triangular dense fuzzy sets and new defuzzification methods. Zbl 1365.03035
Sujit, Kumar De; Beg, Ismat
2016
Ideal solutions for hesitant fuzzy soft sets. Zbl 1361.90024
Beg, Ismat; Rashid, Tabasam
2016
Convex hesitant fuzzy sets. Zbl 1364.03079
Rashid, Tabasam; Beg, Ismat
2016
Hesitant intuitionistic fuzzy linguistic term sets. Zbl 1397.91127
Beg, Ismat; Rashid, Tabasam
2014
Fixed point for fuzzy contraction mappings satisfying an implicit relation. Zbl 1349.54084
Beg, Ismat; Ahmed, M. A.
2014
($$\phi, \psi$$)-weak contractions in intuitionistic fuzzy metric spaces. Zbl 1305.54010
2014
Fixed points and invariant approximation in random normed spaces. Zbl 1212.47038
Beg, Ismat; Abbas, Mujahid
2010
Common fixed point theorems in cone metric spaces. Zbl 1173.54317
2009
Common fixed points and best approximation in convex metric spaces. Zbl 1149.47043
Beg, Ismat; Abbas, Mujahid
2007
Random Edelstein theorem. Zbl 1285.47072
Beg, Ismat
2001
A general fixed point theorem for a class of continuous random operators. Zbl 0886.47038
1997
Coincidence points of compatible multivalued mappings. Zbl 0862.54039
Azam, Akbar; Beg, Ismat
1996
Fixed point theorems for Kannan mappings. Zbl 0607.54034
Beg, Ismat; Azam, Akbar
1986
Incomplete interval-valued hesitant fuzzy preference relations in decision making. Zbl 1422.91196
Khalid, A.; Beg, Ismat
2018
Fixed points of contractive dominated mappings on a closed ball in an ordered quasi partial metric space. Zbl 1443.54018
2015
Fixed points of Suzuki type multifunctions on metric spaces. Zbl 1334.54060
Beg, Ismat; Aleomraninejad, S. M. A.
2015
Fixed point theorems in fuzzy metric spaces. Zbl 1268.54020
Beg, Ismat; Sedghi, Shaban; Shobe, Nabi
2013
Periodic points of random multivalued operators. Zbl 1304.47071
Beg, Ismat; Abbas, Mujahid
2012
Common fixed points and best approximation in CAT(0) spaces. Zbl 1257.47060
Beg, Ismat; Abbas, Mujahid
2012
End-point results for multivalued mappings in partially ordered metric spaces. Zbl 1248.54020
Beg, Ismat; Nashine, Hemant Kumar
2012
Common fixed point theorem for $$(\phi, \psi)$$-weak contraction in fuzzy metric space. Zbl 1314.47083
Jha, K.; Abbas, M.; Beg, I.; Pabt, R. P.; Imdad, M.
2011
An iterative process for a family of asymptotically quasi-nonexpansive mappings in CAT(0) spaces. Zbl 1258.47080
Beg, Ismat; Abbas, Mujahid
2011
Common fixed points of Banach operator pair on fuzzy normed spaces. Zbl 1269.47039
Beg, Ismat; Abbas, Mujahid
2011
Invariant approximation for fuzzy nonexpansive mappings. Zbl 1216.47083
Beg, Ismat; Abbas, Mujahid
2011
Solution of random operator equations using general composite implicit iteration process. Zbl 1177.47072
Beg, Ismat; Thakur, Balwant Singh
2009
Fuzzy equivalence relations. Zbl 1207.03061
Beg, Ismat; Ashraf, Samina
2008
Convergence theorems of the iterative schemes in convex metric spaces. Zbl 1120.47057
Beg, Ismat; Abbas, Mujahid; Kim, Jong Kyu
2006
Common random fixed points of noncommuting random operators. Zbl 0955.47033
1999
Continuity of fuzzy multifunctions. Zbl 0926.47056
Beg, Ismat
1999
Fixed point theorems in $$2$$-metric spaces with an application to variational inequalities. Zbl 0960.54506
Beg, Ismat
1998
Fuzzy Archimedean spaces. Zbl 0879.46049
Beg, Ismat; Islam, Misbah Ul
1997
Fuzzy ordered linear spaces. Zbl 0839.06010
Beg, Ismat; Ul Islam, Misbah
1995
Fuzzy Riesz spaces. Zbl 0812.46078
Beg, Ismat; Islam, Misbah Ul
1994
Some fixed point theorems in convex metric spaces. Zbl 0752.54016
Beg, Ismat; Azam, Akbar; Ali, Faryad; Minhas, Tahira
1991
(JCLR) property and fixed point in non-Archimedean fuzzy metric spaces. Zbl 1412.47101
Beg, Ismat; Ahmed, M.; Nafadi, N.
2018
Human attitude analysis based on fuzzy soft differential equations with Bonferroni mean. Zbl 06973233
Beg, Ismat; Rashid, Tabasam; Jamil, Raja Noshad
2018
Fixed points on ordered metric spaces with applications in homotopy theory. Zbl 06858713
Butt, Asma Rashid; Beg, Ismat; Iftikhar, Aqsa
2018
Group decision making using comparative linguistic expression based on hesitant intuitionistic fuzzy sets. Zbl 1331.91057
Beg, Ismat; Rashid, Tabasam
2015
Common fixed points for hybrid pairs of fuzzy and crisp mappings. Zbl 1340.54056
Beg, I.; Ahmed, M. A.; Nafadi, H. A.
2014
Fixed points of Edelstein-type multivalued maps. Zbl 1320.54038
Mehmood, Nayyar; Azam, Akbar; Beg, Ismat
2014
Hesitant probabilistic fuzzy linguistic sets with applications in multi-criteria group decision making problems. Zbl 1397.91135
Joshi, Dheeraj Kumar; Beg, Ismat; Kumar, Sanjay
2018
Incomplete interval-valued hesitant fuzzy preference relations in decision making. Zbl 1422.91196
Khalid, A.; Beg, Ismat
2018
(JCLR) property and fixed point in non-Archimedean fuzzy metric spaces. Zbl 1412.47101
Beg, Ismat; Ahmed, M.; Nafadi, N.
2018
Human attitude analysis based on fuzzy soft differential equations with Bonferroni mean. Zbl 06973233
Beg, Ismat; Rashid, Tabasam; Jamil, Raja Noshad
2018
Fixed points on ordered metric spaces with applications in homotopy theory. Zbl 06858713
Butt, Asma Rashid; Beg, Ismat; Iftikhar, Aqsa
2018
Hesitant 2-tuple linguistic information in multiple attributes group decision making. Zbl 1361.91007
Beg, Ismat; Rashid, Tabasam
2016
Incomplete interval valued fuzzy preference relations. Zbl 1398.68541
Khalid, Asma; Beg, Ismat
2016
Triangular dense fuzzy sets and new defuzzification methods. Zbl 1365.03035
Sujit, Kumar De; Beg, Ismat
2016
Ideal solutions for hesitant fuzzy soft sets. Zbl 1361.90024
Beg, Ismat; Rashid, Tabasam
2016
Convex hesitant fuzzy sets. Zbl 1364.03079
Rashid, Tabasam; Beg, Ismat
2016
Fixed point on a closed ball in ordered dislocated quasi metric spaces. Zbl 1325.54023
2015
Fixed points of contractive dominated mappings on a closed ball in an ordered quasi partial metric space. Zbl 1443.54018
2015
Fixed points of Suzuki type multifunctions on metric spaces. Zbl 1334.54060
Beg, Ismat; Aleomraninejad, S. M. A.
2015
Group decision making using comparative linguistic expression based on hesitant intuitionistic fuzzy sets. Zbl 1331.91057
Beg, Ismat; Rashid, Tabasam
2015
Multi-criteria trapezoidal valued intuitionistic fuzzy decision making with Choquet integral based TOPSIS. Zbl 1337.90087
Beg, Ismat; Rashid, Tabasam
2014
Hesitant intuitionistic fuzzy linguistic term sets. Zbl 1397.91127
Beg, Ismat; Rashid, Tabasam
2014
Fixed point for fuzzy contraction mappings satisfying an implicit relation. Zbl 1349.54084
Beg, Ismat; Ahmed, M. A.
2014
($$\phi, \psi$$)-weak contractions in intuitionistic fuzzy metric spaces. Zbl 1305.54010
2014
Common fixed points for hybrid pairs of fuzzy and crisp mappings. Zbl 1340.54056
Beg, I.; Ahmed, M. A.; Nafadi, H. A.
2014
Fixed points of Edelstein-type multivalued maps. Zbl 1320.54038
Mehmood, Nayyar; Azam, Akbar; Beg, Ismat
2014
Fuzzy relational calculus. Zbl 1303.03080
Beg, Ismat; Ashraf, Samina
2014
Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered dislocated metric space. Zbl 1423.54068
2013
Fixed point of set-valued graph contractive mappings. Zbl 1329.54041
Beg, Ismat; Butt, Asma Rashid
2013
Common fuzzy fixed points for fuzzy mappings. Zbl 1409.54015
Azam, Akbar; Beg, Ismat
2013
Fixed point theorems in fuzzy metric spaces. Zbl 1268.54020
Beg, Ismat; Sedghi, Shaban; Shobe, Nabi
2013
Fixed point for compatible and subsequentially continuous mappings in Menger spaces and applications. Zbl 1299.54084
Beg, Ismat; Chauhan, Sunny
2013
Common fixed point and coincidence point of generalized contractions in ordered metric spaces. Zbl 06236304
Beg, Ismat; Butt, Asma Rashid
2012
Periodic points of random multivalued operators. Zbl 1304.47071
Beg, Ismat; Abbas, Mujahid
2012
Common fixed points and best approximation in CAT(0) spaces. Zbl 1257.47060
Beg, Ismat; Abbas, Mujahid
2012
End-point results for multivalued mappings in partially ordered metric spaces. Zbl 1248.54020
Beg, Ismat; Nashine, Hemant Kumar
2012
Belief aggregation in fuzzy framework. Zbl 1271.91036
Beg, Ismat; Khalid, Asma
2012
Gödel form of fuzzy transitive relations. Zbl 1263.03039
Beg, Ismat; Ashraf, Samina
2012
Fixed points of quasi $$(f, g)$$-nonexpansive multivalued mapping. Zbl 1252.47052
Beg, Ismat; Abbas, Mujahid
2012
Coincidence and common fixed points of noncompatible maps. Zbl 1251.54039
Beg, Ismat; Abbas, Mujahid
2011
Common fixed point theorem for $$(\phi, \psi)$$-weak contraction in fuzzy metric space. Zbl 1314.47083
Jha, K.; Abbas, M.; Beg, I.; Pabt, R. P.; Imdad, M.
2011
An iterative process for a family of asymptotically quasi-nonexpansive mappings in CAT(0) spaces. Zbl 1258.47080
Beg, Ismat; Abbas, Mujahid
2011
Common fixed points of Banach operator pair on fuzzy normed spaces. Zbl 1269.47039
Beg, Ismat; Abbas, Mujahid
2011
Invariant approximation for fuzzy nonexpansive mappings. Zbl 1216.47083
Beg, Ismat; Abbas, Mujahid
2011
Fixed point results in generalized cone metric spaces. Zbl 1274.54115
Beg, Ismat; Abbas, Mujahid; Nazir, Talat
2011
Fixed point of involution mappings in convex metric spaces. Zbl 1260.54057
Beg, Ismat; Olaposi Olatinwo, Memudu
2011
Numerical representation of product transitive complete fuzzy orderings. Zbl 1217.91037
Beg, Ismat; Ashraf, Samina
2011
The contraction principle for set valued mappings on a metric space with a graph. Zbl 1201.54029
Beg, Ismat; Butt, Asma Rashid; Radojević, S.
2010
Fixed point in topological vector space-valued cone metric spaces. Zbl 1197.54057
2010
Common fixed point for generalized set valued contractions satisfying an implicit relation in partially ordered metric spaces. Zbl 1195.54068
Beg, Ismat; Butt, Asma Rashid
2010
Generalized cone metric spaces. Zbl 1203.54035
Beg, Ismat; Abbas, Mujahid; Nazir, Talat
2010
Periodic fixed points of random operators. Zbl 1220.47075
Beg, Ismat; Abbas, Mujahid; Azam, Akbar
2010
Existence of fixed points in complete cone metric spaces. Zbl 1203.54034
2010
Coupled fixed points of set valued mappings in partially ordered metric spaces. Zbl 1295.54043
Beg, Ismat; Butt, Asma Rashid
2010
Fixed points and invariant approximation in random normed spaces. Zbl 1212.47038
Beg, Ismat; Abbas, Mujahid
2010
Strong convergence theorems for common fixed points of Banach operator pair. Zbl 1218.47091
Beg, Ismat; Hussain, N.; Khan, S. H.
2010
Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces. Zbl 1176.54028
Beg, Ismat; Butt, Asma Rashid
2009
Common fixed points of fuzzy maps. Zbl 1165.54311
Azam, Akbar; Beg, Ismat
2009
Common fixed points for maps on topological vector space valued cone metric spaces. Zbl 1187.54032
2009
Fixed points of fuzzy contractive and fuzzy locally contractive maps. Zbl 1198.54069
2009
Banach contraction principle on cone rectangular metric spaces. Zbl 1274.54113
2009
Fixed points for weakly compatible mappings satisfying an implicit relation in partially ordered metric spaces. Zbl 1199.54207
Beg, I.; Butt, A. R.
2009
Similarity measures for fuzzy sets. Zbl 1194.46115
Beg, Ismat; Ashraf, Samina
2009
Common fixed point theorems in cone metric spaces. Zbl 1173.54317
2009
Solution of random operator equations using general composite implicit iteration process. Zbl 1177.47072
Beg, Ismat; Thakur, Balwant Singh
2009
Fuzzy dissimilarity and distance functions. Zbl 1275.03146
Beg, Ismat; Ashraf, Samina
2009
Random coincidence and fixed points for weakly compatible mappings in convex metric spaces. Zbl 1200.54022
Beg, Izmat; Jahangir, Adnan; Azam, Akbar
2009
Common fixed points of two maps in cone metric spaces. Zbl 1197.54056
2008
Fuzzy similarity and measure of similarity with Łukasiewicz implicator. Zbl 1144.03311
Beg, Ismat; Ashraf, Samina
2008
Random fixed point theorems for a random operator on an unbounded subset of a Banach space. Zbl 1172.47042
Beg, Ismat; Abbas, Mujahid
2008
Weak and strong convergence for fixed points of nearly asymptotically non-expansive mappings. Zbl 1223.47095
Sahu, D. R.; Beg, Ismat
2008
Fuzzy equivalence relations. Zbl 1207.03061
Beg, Ismat; Ashraf, Samina
2008
Random fixed points of asymptotically nonexpansive random operators on unbounded domains. Zbl 1199.47236
Beg, Ismat; Abbas, Mujahid
2008
Convergence of multivalued mappings via approximable measurable selectors. Zbl 1142.47324
Beg, Ismat; Abbas, Mujahid
2008
Random fixed point theorems for Caristi type random operators. Zbl 1148.47044
Beg, Ismat; Abbas, Mujahid
2007
Common fixed points and best approximation in convex metric spaces. Zbl 1149.47043
Beg, Ismat; Abbas, Mujahid
2007
Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition. Zbl 1133.54024
Beg, Ismat; Abbas, Mujahid
2006
Iterative procedures for solutions of random operator equations in Banach spaces. Zbl 1093.47057
Beg, Ismat; Abbas, Mujahid
2006
Equivalence and stability of random fixed point iterative procedures. Zbl 1107.47046
Beg, Ismat; Abbas, Mujahid
2006
Approximation of fixed points of uniformly $$R$$-subweakly commuting mappings. Zbl 1111.47056
Beg, Ismat; Sahu, D. R.; Diwan, S. D.
2006
Fixed point theorems for weakly inward multivalued maps on a convex metric space. Zbl 1099.54030
Beg, Ismat; Abbas, Mujahid
2006
Convergence theorems of the iterative schemes in convex metric spaces. Zbl 1120.47057
Beg, Ismat; Abbas, Mujahid; Kim, Jong Kyu
2006
Common random fixed points of compatible random operators. Zbl 1121.47046
Beg, Ismat; Abbas, Mujahid
2006
Fixed points and best approximation in Menger convex metric spaces. Zbl 1109.47047
Beg, Ismat; Abbas, Mujahid
2005
Nearest point projection in uniformly convex metric spaces. Zbl 1082.41021
Beg, Ismat
2005
Approximation of $$*$$-nonexpansive random multivalued operators on Banach spaces. Zbl 1072.47055
Beg, Ismat; Khan, A. R.; Hussain, N.
2004
Fixed point, almost fixed point and best approximation of nonexpansive multivalued mapping in Banach spaces. Zbl 1054.47042
Beg, Ismat; Hussain, Nawab; Khan, Abdul Rahim
2003
Approximation of random fixed points in normed spaces. Zbl 1034.47027
Beg, Ismat
2002
Minimal displacement of random variables under Lipschitz random maps. Zbl 1030.47047
Beg, Ismat
2002
Inequalities in metric spaces with applications. Zbl 0998.47040
Beg, Ismat
2001
Coupled fixed points of mixed monotone operators on probabilistic Banach spaces. Zbl 1068.47093
Beg, Ismat; Latif, Abdul; Ali, Rashid; Azam, Akbar
2001
An iteration scheme for asymptotically nonexpansive mappings on uniformly convex metric spaces. Zbl 0996.47057
Beg, I.
2001
Random Edelstein theorem. Zbl 1285.47072
Beg, Ismat
2001
An application of a random fixed point theorem to random best approximation. Zbl 0956.47023
2000
Some random approximation theorems with applications. Zbl 0931.60054
1999
Common random fixed points of noncommuting random operators. Zbl 0955.47033
1999
Continuity of fuzzy multifunctions. Zbl 0926.47056
Beg, Ismat
1999
Structure of the set of fixed points of nonexpansive mappings on convex metric spaces. Zbl 1004.54031
Beg, Ismat
1998
Measurability of fixed point sets of multivalued random operators. Zbl 0913.47057
Xu, Hong-Kun; Beg, Ismat
1998
Fixed points of fuzzy multivalued mappings with values in fuzzy ordered sets. Zbl 0909.47055
Beg, Ismat
1998
Fixed point theorems in $$2$$-metric spaces with an application to variational inequalities. Zbl 0960.54506
Beg, Ismat
1998
Extension of fuzzy positive linear operators. Zbl 0917.47058
Beg, Ismat
1998
Geometric fixed points for single and multivalued mappings. Zbl 0911.54039
Latif, Abdul; Beg, Ismat
1997
Random fixed points of random operators satisfying semicontractivity conditions. Zbl 0896.47053
Beg, Ismat
1997
A general fixed point theorem for a class of continuous random operators. Zbl 0886.47038
1997
Fuzzy Archimedean spaces. Zbl 0879.46049
Beg, Ismat; Islam, Misbah Ul
1997
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#### Cited in 128 Serials
89 Fixed Point Theory and Applications 25 Journal of Inequalities and Applications 18 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 17 Abstract and Applied Analysis 14 Computers & Mathematics with Applications 13 Journal of Mathematical Analysis and Applications 13 Applied Mathematics Letters 12 Applied Mathematics and Computation 12 Journal of Function Spaces 11 Fuzzy Sets and Systems 11 Rendiconti del Circolo Matemàtico di Palermo. Serie II 11 Mathematical and Computer Modelling 8 International Journal of Mathematics and Mathematical Sciences 8 Stochastic Analysis and Applications 8 Soft Computing 8 Symmetry 7 Journal of the Egyptian Mathematical Society 7 Journal of Fixed Point Theory and Applications 7 Journal of Nonlinear Science and Applications 7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 7 Mathematical Sciences 6 The Journal of Analysis 6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 6 Thai Journal of Mathematics 6 Journal of Mathematics 6 International Journal of Analysis 6 Mathematics 5 Results in Mathematics 5 Random Operators and Stochastic Equations 5 Complexity 5 Journal of Intelligent and Fuzzy Systems 4 Journal of Applied Mathematics and Stochastic Analysis 4 Vietnam Journal of Mathematics 4 Discrete Dynamics in Nature and Society 4 Journal of Applied Mathematics and Computing 4 Asian-European Journal of Mathematics 4 Bulletin of Mathematical Analysis and Applications 4 Journal of Linear and Topological Algebra 4 Nonlinear Analysis. Theory, Methods & Applications 4 Cogent Mathematics 3 Czechoslovak Mathematical Journal 3 Topology and its Applications 3 Applied Mathematics and Mechanics. (English Edition) 3 Journal of Applied Mathematics 3 Analysis in Theory and Applications 3 Iranian Journal of Fuzzy Systems 3 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 3 Applications and Applied Mathematics 3 Advances in Fuzzy Systems 3 Applied General Topology 3 Journal of Mathematics and Computer Science. JMCS 3 Arabian Journal of Mathematics 3 Chinese Journal of Mathematics 3 Korean Journal of Mathematics 2 Chaos, Solitons and Fractals 2 Mathematica Slovaca 2 Numerical Functional Analysis and Optimization 2 Computational and Applied Mathematics 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Positivity 2 Nonlinear Analysis. Modelling and Control 2 Nonlinear Functional Analysis and Applications 2 Tbilisi Mathematical Journal 2 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 2 Fuzzy Information and Engineering 2 Sahand Communications in Mathematical Analysis 2 International Journal of Applied and Computational Mathematics 2 Open Mathematics 2 Transactions of A. Razmadze Mathematical Institute 1 Indian Journal of Pure & Applied Mathematics 1 Ukrainian Mathematical Journal 1 Fortschritte der Physik 1 Acta Mathematica Vietnamica 1 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 1 Demonstratio Mathematica 1 Fasciculi Mathematici 1 Functiones et Approximatio. Commentarii Mathematici 1 Glasgow Mathematical Journal 1 Information Sciences 1 Journal of Mathematical Economics 1 Opsearch 1 Proceedings of the American Mathematical Society 1 Zeitschrift für Analysis und ihre Anwendungen 1 Bulletin of the Iranian Mathematical Society 1 Sequential Analysis 1 Facta Universitatis. Series Mathematics and Informatics 1 International Journal of Approximate Reasoning 1 Aequationes Mathematicae 1 European Journal of Operational Research 1 Journal of Dynamics and Differential Equations 1 Journal of Logic, Language and Information 1 Arab Journal of Mathematical Sciences 1 Mathematical Problems in Engineering 1 Honam Mathematical Journal 1 Matematychni Studiï 1 Acta Mathematica Sinica. English Series 1 CEJOR. Central European Journal of Operations Research 1 Journal of the Australian Mathematical Society 1 Journal of Systems Science and Complexity ...and 28 more Serials
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#### Cited in 31 Fields
366 General topology (54-XX) 308 Operator theory (47-XX) 33 Functional analysis (46-XX) 32 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 31 Probability theory and stochastic processes (60-XX) 25 Mathematical logic and foundations (03-XX) 22 Approximations and expansions (41-XX) 16 Computer science (68-XX) 16 Operations research, mathematical programming (90-XX) 13 Numerical analysis (65-XX) 10 Combinatorics (05-XX) 8 Integral equations (45-XX) 7 Ordinary differential equations (34-XX) 6 Order, lattices, ordered algebraic structures (06-XX) 5 Measure and integration (28-XX) 5 Difference and functional equations (39-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Convex and discrete geometry (52-XX) 4 Real functions (26-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Statistics (62-XX) 2 Sequences, series, summability (40-XX) 2 Algebraic topology (55-XX) 2 Information and communication theory, circuits (94-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX) 1 Systems theory; control (93-XX)
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The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-05-13T18:33:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5325924754142761, "perplexity": 5027.1837778463805}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991943.36/warc/CC-MAIN-20210513173321-20210513203321-00268.warc.gz"} |
https://w3.pppl.gov/info/emacs/Text_and_Binary.html | GNU Emacs Manual. Node: Text and Binary
## 28.4: Text Files and Binary Files
GNU Emacs uses newline characters to separate text lines. This is the convention used on Unix, on which GNU Emacs was developed, and on GNU systems since they are modeled on Unix.
MS-DOS and MS-Windows normally use carriage-return linefeed, a two-character sequence, to separate text lines. (Linefeed is the same character as newline.) Therefore, convenient editing of typical files with Emacs requires conversion of these end-of-line (EOL) sequences. And that is what Emacs normally does: it converts carriage-return linefeed into newline when reading files, and converts newline into carriage-return linefeed when writing files. The same mechanism that handles conversion of international character codes does this conversion also (see Coding Systems).
One consequence of this special format-conversion of most files is that character positions as reported by Emacs (see Position Info) do not agree with the file size information known to the operating system.
Some kinds of files should not be converted, because their contents are not really text. Therefore, Emacs on MS-DOS distinguishes certain files as binary files, and reads and writes them verbatim. (This distinction is not part of MS-DOS; it is made by Emacs only.) These include executable programs, compressed archives, etc. Emacs uses the file name to decide whether to treat a file as binary: the variable `file-name-buffer-file-type-alist` defines the file-name patterns that indicate binary files. Note that if a file name matches one of the patterns for binary files in `file-name-buffer-file-type-alist`, Emacs uses the `no-conversion` coding system (see Coding Systems) which turns off all coding-system conversions, not only the EOL conversion.
In addition, if Emacs recognizes from a file's contents that it uses newline rather than carriage-return linefeed as its line separator, it does not perform conversion when reading or writing that file. Thus, you can read and edit files from Unix or GNU systems on MS-DOS with no special effort, and they will be left with their Unix-style EOLs.
You can visit a file and specify whether to treat a file as text or binary using the commands `find-file-text` and `find-file-binary`. End-of-line conversion is part of the general coding system conversion mechanism, so another way to control whether to treat a file as text or binary is with the commands for specifying a coding system (see Specify Coding). For example, C-x `RET` c undecided-unix `RET` C-x C-f foobar.txt visits the file ``foobar.txt`' without converting the EOLs.
The mode line indicates whether end-of-line translation was used for the current buffer. Normally a colon appears after the coding system letter near the beginning of the mode line. If MS-DOS end-of-line translation is in use for the buffer, this character changes to a backslash.
When you use NFS or Samba to access file systems that reside on computers using Unix or GNU systems, Emacs should not perform end-of-line translation on any files in these file systems--not even when you create a new file. To request this, designate these file systems as untranslated file systems by calling the function `add-untranslated-filesystem`. It takes one argument: the file system name, including a drive letter and optionally a directory. For example,
```(add-untranslated-filesystem "Z:")
```
designates drive Z as an untranslated file system, and
```(add-untranslated-filesystem "Z:\\foo")
```
designates directory ``\foo`' on drive Z as an untranslated file system.
Most often you would use `add-untranslated-filesystem` in your ``_emacs`' file, or in ``site-start.el`' so that all the users at your site get the benefit of it.
To countermand the effect of `add-untranslated-filesystem`, use the function `remove-untranslated-filesystem`. This function takes one argument, which should be a string just like the one that was used previously with `add-untranslated-filesystem`.
MS-DOS File Names MS-DOS MS-DOS Printing | 2018-05-24T17:36:20 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8257020711898804, "perplexity": 5011.62825882935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866733.77/warc/CC-MAIN-20180524170605-20180524190605-00436.warc.gz"} |
https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_(OpenStax)/23%3A_Electromagnetic_Induction%2C_AC_Circuits%2C_and_Electrical_Technologies/23.7%3A_Transformers | $$\require{cancel}$$
# 23.7: Transformers
Transformers do what their name implies—they transform voltages from one value to another (The term voltage is used rather than emf, because transformers have internal resistance). For example, many cell phones, laptops, video games, and power tools and small appliances have a transformer built into their plug-in unit (like that in Figure $$\PageIndex{1}$$) that changes 120 V or 240 V AC into whatever voltage the device uses.
Figure $$\PageIndex{1}$$: The plug-in transformer has become increasingly familiar with the proliferation of electronic devices that operate on voltages other than common 120 V AC. Most are in the 3 to 12 V range. (credit: Shop Xtreme)
Transformers are also used at several points in the power distribution systems, such as illustrated in Figure $$\PageIndex{2}$$. Power is sent long distances at high voltages, because less current is required for a given amount of power, and this means less line loss, as was discussed previously. But high voltages pose greater hazards, so that transformers are employed to produce lower voltage at the user’s location.
Figure $$\PageIndex{2}$$: Transformers change voltages at several points in a power distribution system. Electric power is usually generated at greater than 10 kV, and transmitted long distances at voltages over 200 kV—sometimes as great as 700 kV—to limit energy losses. Local power distribution to neighborhoods or industries goes through a substation and is sent short distances at voltages ranging from 5 to 13 kV. This is reduced to 120, 240, or 480 V for safety at the individual user site.
The type of transformer considered in this text (Figure $$\PageIndex{3}$$) is based on Faraday’s law of induction and is very similar in construction to the apparatus Faraday used to demonstrate magnetic fields could cause currents. The two coils are called the primary and secondary coils. In normal use, the input voltage is placed on the primary, and the secondary produces the transformed output voltage. Not only does the iron core trap the magnetic field created by the primary coil, its magnetization increases the field strength. Since the input voltage is AC, a time-varying magnetic flux is sent to the secondary, inducing its AC output voltage.
Figure $$\PageIndex{3}$$: A typical construction of a simple transformer has two coils wound on a ferromagnetic core that is laminated to minimize eddy currents. The magnetic field created by the primary is mostly confined to and increased by the core, which transmits it to the secondary coil. Any change in current in the primary induces a current in the secondary.
For the simple transformer shown in Figure $$\PageIndex{3}$$, the output voltage $$V_{s}$$ depends almost entirely on the input voltage $$V_{p}$$ and the ratio of the number of loops in the primary and secondary coils. Faraday’s law of induction for the secondary coil gives its induced output voltage $$V_{s}$$ to be
$V_{s} = -N\dfrac{\Delta \Phi}{\Delta t},\label{23.8.1}$
where $$N_{s}$$ is the number of loops in the secondary coil and $$\Delta \Phi / \Delta t$$ is the rate of change of magnetic flux. Note that the output voltage equals the induced emf ($$V_{s} = emf_{s}$$), provided coil resistance is small (a reasonable assumption for transformers). The cross-sectional area of the coils is the same on either side, as is the magnetic field strength, and so $$\Delta \Phi / \Delta t$$ is the same on either side. The input primary voltage $$V_{p}$$ is also related to changing flux by
$V_{p} = -N_{p}\dfrac{\Delta \Phi}{\Delta t}.\label{23.8.2}$
The reason for this is a little more subtle. Lenz’s law tells us that the primary coil opposes the change in flux caused by the input voltage $$V_{p}$$, hence the minus sign (This is an example of self-inductance, a topic to be explored in some detail in later sections). Assuming negligible coil resistance, Kirchhoff’s loop rule tells us that the induced emf exactly equals the input voltage. Taking the ratio of these last two equations yields a useful relationship:
$\dfrac{V_{s}}{V_{p}} = \dfrac{N_{s}}{N_{p}}.\label{23.8.3}$
This is known as the transformer equation, and it simply states that the ratio of the secondary to primary voltages in a transformer equals the ratio of the number of loops in their coils.
The output voltage of a transformer can be less than, greater than, or equal to the input voltage, depending on the ratio of the number of loops in their coils. Some transformers even provide a variable output by allowing connection to be made at different points on the secondary coil. A step-up transformer is one that increases voltage, whereas a step-down transformer decreases voltage. Assuming, as we have, that resistance is negligible, the electrical power output of a transformer equals its input. This is nearly true in practice—transformer efficiency often exceeds 99%. Equating the power input and output,
$P_{p} = I_{p}V_{p} = I_{s}V_{s} = P_{s}.\label{23.8.4}$
Rearranging terms gives
$\dfrac{V_{s}}{V_{p}} = \dfrac{I_{p}}{I_{s}}.\label{23.8.6}$
Combining this with Equation \ref{23.8.3} , we find that
$\dfrac{I_{s}}{I_{p}} = \dfrac{N_{p}}{N_{s}}.\label{23.8.7}$
is the relationship between the output and input currents of a transformer. So if voltage increases, current decreases. Conversely, if voltage decreases, current increases.
Example $$\PageIndex{1}$$: Calculating Characteristics of a Step-Up Transformer
A portable x-ray unit has a step-up transformer, the 120 V input of which is transformed to the 100 kV output needed by the x-ray tube. The primary has 50 loops and draws a current of 10.00 A when in use. (a) What is the number of loops in the secondary? (b) Find the current output of the secondary.
Strategy and Solution for (a):
We solve Equation \ref{23.8.3} for $$N_{s}$$, the number of loops in the secondary, and enter the known values. This gives
\begin{align*} N_{s} &= N_{p}\dfrac{V_{s}}{V_{p}} \\[5pt] &= \left(50\right) \dfrac{100,000 V}{120 V} \\[5pt] &= 4.17 \times 10^{4}. \end{align*}
Discussion for (a):
A large number of loops in the secondary (compared with the primary) is required to produce such a large voltage. This would be true for neon sign transformers and those supplying high voltage inside TVs and CRTs.
Strategy and Solution for (b):
We can similarly find the output current of the secondary by solving Equation \ref{23.8.7} and $$I_{s}$$ and entering known values. This gives
\begin{align*} I_{s} &= I_{p}\dfrac{N_{p}}{N_{s}} \\[5pt] &= \left(10.00 A \right) \dfrac{50}{4.17 \times 10^{4}} \\[5pt] &= 12.0 mA. \end{align*}
Discussion for (b):
As expected, the current output is significantly less than the input. In certain spectacular demonstrations, very large voltages are used to produce long arcs, but they are relatively safe because the transformer output does not supply a large current. Note that the power input here is
\begin{align*}P_{p} = I_{p}V_{p} &= \left(10.00 A \right) \left(120 V \right) \\[5pt] &= 1.20 kW. \end{align*}
This equals the power output
\begin{align*} P_{p} = I_{s}V_{s} &= \left(12.0 mA \right) \left(100kV \right) \\[5pt] &= 1.20 kW \end{align*}
as we assumed in the derivation of the equations used.
The fact that transformers are based on Faraday’s law of induction makes it clear why we cannot use transformers to change DC voltages. If there is no change in primary voltage, there is no voltage induced in the secondary. One possibility is to connect DC to the primary coil through a switch. As the switch is opened and closed, the secondary produces a voltage like that in Figure $$\PageIndex{4}$$. This is not really a practical alternative, and AC is in common use wherever it is necessary to increase or decrease voltages.
Figure $$\PageIndex{4}$$: Transformers do not work for pure DC voltage input, but if it is switched on and off as on the top graph, the output will look something like that on the bottom graph. This is not the sinusoidal AC most AC appliances need.
Example $$\PageIndex{2}$$: Calculating Characteristics of a Step-Down Transformer
A battery charger meant for a series connection of ten nickel-cadmium batteries (total emf of 12.5 V DC) needs to have a 15.0 V output to charge the batteries. It uses a step-down transformer with a 200-loop primary and a 120 V input. (a) How many loops should there be in the secondary coil? (b) If the charging current is 16.0 A, what is the input current?
Strategy and Solution for (a):
You would expect the secondary to have a small number of loops. Solving Equation \ref{23.8.3} for $$N_{s}$$ and entering known values gives
\begin{align*} N_{s} &= N_{p}\dfrac{V_{s}}{V_{p}} \\[5pt] &= \left( 200 \right) \dfrac{15.0 V}{120 V} \\[5pt] &= 25. \end{align*}
Strategy and Solution for (b):
The current input can be obtained by solving Equation \ref{23.8.7} for $$I_{p}$$ and entering known values. This gives
\begin{align*} I_{p} = I_{s}\dfrac{N_{s}}{N_{p}} \\[5pt] &= \left( 16.0 A \right) \dfrac{25}{200} \\[5pt] &= 2.00 A. \end{align*}
Discussion:
The number of loops in the secondary is small, as expected for a step-down transformer. We also see that a small input current produces a larger output current in a step-down transformer. When transformers are used to operate large magnets, they sometimes have a small number of very heavy loops in the secondary. This allows the secondary to have low internal resistance and produce large currents. Note again that this solution is based on the assumption of 100% efficiency—or power out equals power in ($$P_{p} = P_{s}$$)-- reasonable for good transformers. In this case the primary and secondary power is 240 W. (Verify this for yourself as a consistency check.) Note that the Ni-Cd batteries need to be charged from a DC power source (as would a 12 V battery). So the AC output of the secondary coil needs to be converted into DC. This is done using something called a rectifier, which uses devices called diodes that allow only a one-way flow of current.
Transformers have many applications in electrical safety systems, which are discussed in 23.9.
PHET EXPLORATIONS: GENERATOR
Generate electricity with a bar magnet! Discover the physics behind the phenomena by exploring magnets and how you can use them to make a bulb light.
Figure $$\PageIndex{5}$$: Generator
### Summary
• Transformers use induction to transform voltages from one value to another.
• For a transformer, the voltages across the primary and secondary coils are related by $\dfrac{V_{s}}{V_{p}} = \dfrac{N_{s}}{N_{p}},$ where $$V_{p}$$ and $$V_{s}$$ are the voltages across primary and secondary coils having $$N_{p}$$ and $$N_{s}$$ turns.
• The currents $$I_{p}$$ and $$I_{s}$$ in the primary and secondary coils are related by $$\dfrac{I_{s}}{I_{p}} = \dfrac{N_{p}}{N_{s}}.$$
• A step-up transformer increases voltage and decreases current, whereas a step-down transformer decreases voltage and increases current.
### Glossary
transformer
a device that transforms voltages from one value to another using induction
transformer equation
the equation showing that the ratio of the secondary to primary voltages in a transformer equals the ratio of the number of loops in their coils; $$\dfrac{V_{s}}{V_{p}} = \dfrac{N_{s}}{N_{p}}$$
step-up transformer
a transformer that increases voltage
step-down transformer
a transformer that decreases voltage
### Contributors
• Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0). | 2019-01-16T23:24:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9300963878631592, "perplexity": 823.4929650372836}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583657907.79/warc/CC-MAIN-20190116215800-20190117001800-00548.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Aford.kevin-b | # zbMATH — the first resource for mathematics
## Ford, Kevin B.
Compute Distance To:
Author ID: ford.kevin-b Published as: Ford, Kevin; Ford, Kevin B.; Ford, K. External Links: MGP · Wikidata
Documents Indexed: 87 Publications since 1993
all top 5
#### Co-Authors
28 single-authored 19 Konyagin, Sergeĭ Vladimirovich 10 Luca, Florian 7 Zaharescu, Alexandru 6 Pomerance, Carl Bernard 6 Shparlinski, Igor E. 4 Green, Ben Joseph 4 Tao, Terence 3 Bourgain, Jean 3 Eberhard, Sean 3 Maynard, James 2 Alkan, Emre 2 Dilworth, Stephen J. 2 Filaseta, Michael A. 2 Hudson, Richard H. 2 Khan, Mizan R. 2 Kutzarova, Denka N. 2 Lamzouri, Youness 2 Pollack, Paul 2 Tenenbaum, Gérald 1 Addario-Berry, Louigi 1 Banks, William D. 1 Bays, Carter 1 Broughan, Kevin A. 1 Buttkewitz, Yvonne 1 Cobeli, Cristian 1 de la Bretèche, Régis 1 Dewitt, Jonathan 1 Diamond, Harold George 1 Elsholtz, Christian 1 Gabdullin, Mikhail R. 1 Garaev, Moubariz Z. 1 Goldstein, Eli 1 Halberstam, Heini 1 Harper, Adam J. 1 Heath-Brown, Roger 1 Hu, Yong 1 Koukoulopoulos, Dimitris 1 Meng, Xianchang 1 Miller, Steven J. 1 Moree, Pieter 1 Moreland, Gwyneth 1 Palsson, Eyvindur Ari 1 Pappalardi, Francesco 1 Qian, Guoyou 1 Rubinstein, Michael O. 1 Schlage-Puchta, Jan-Christoph 1 Senger, Steven 1 Shallit, Jeffrey O. 1 Sneed, Jason 1 Soundararajan, Kannan 1 Vandehey, Joseph 1 Wooley, Trevor D. 1 Yankov, Christian L. 1 Yu, Gang
all top 5
#### Serials
5 Acta Arithmetica 4 Proceedings of the American Mathematical Society 4 IMRN. International Mathematics Research Notices 3 Bulletin of the London Mathematical Society 3 Duke Mathematical Journal 3 Transactions of the American Mathematical Society 3 Journal of the American Mathematical Society 3 Annals of Mathematics. Second Series 2 Journal of the London Mathematical Society. Second Series 2 Journal of Number Theory 2 Mathematische Annalen 2 Monatshefte für Mathematik 2 The Ramanujan Journal 2 The Quarterly Journal of Mathematics 2 Algebra & Number Theory 1 Bulletin of the Australian Mathematical Society 1 Journal d’Analyse Mathématique 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Periodica Mathematica Hungarica 1 Mathematics of Computation 1 Acta Mathematica 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 Compositio Mathematica 1 Functiones et Approximatio. Commentarii Mathematici 1 Illinois Journal of Mathematics 1 Journal für die Reine und Angewandte Mathematik 1 Mathematika 1 Michigan Mathematical Journal 1 Proceedings of the London Mathematical Society. Third Series 1 Statistics & Probability Letters 1 Combinatorica 1 Acta Mathematica Hungarica 1 Probability Theory and Related Fields 1 Forum Mathematicum 1 The Annals of Applied Probability 1 Geometric and Functional Analysis. GAFA 1 Experimental Mathematics 1 Electronic Research Announcements of the American Mathematical Society 1 Smarandache Notions Journal 1 Journal of the European Mathematical Society (JEMS) 1 Integers 1 Journal of the Australian Mathematical Society 1 International Journal of Number Theory 1 Proceedings of the Steklov Institute of Mathematics 1 Rivista di Matematica della Università di Parma. New Series 1 Moscow Journal of Combinatorics and Number Theory 1 Discrete Analysis
all top 5
#### Fields
78 Number theory (11-XX) 8 Combinatorics (05-XX) 5 Group theory and generalizations (20-XX) 5 Probability theory and stochastic processes (60-XX) 4 Statistics (62-XX) 1 Algebraic geometry (14-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX)
#### Citations contained in zbMATH Open
70 Publications have been cited 478 times in 385 Documents Cited by Year
The distribution of integers with a divisor in a given interval. Zbl 1181.11058
Ford, Kevin
2008
Explicit constructions of RIP matrices and related problems. Zbl 1236.94027
Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka
2011
Vinogradov’s integral and bounds for the Riemann zeta function. Zbl 1034.11044
Ford, Kevin
2002
On the divisibility of Fermat quotients. Zbl 1223.11116
Bourgain, Jean; Ford, Kevin; Konyagin, Sergei V.; Shparlinski, Igor E.
2010
Sums and products from a finite set of real numbers. Zbl 0908.11008
Ford, Kevin
1998
The distribution of totients. Zbl 0914.11053
Ford, Kevin
1998
The number of solutions of $$\varphi (x)=m$$. Zbl 0978.11053
Ford, Kevin
1999
New estimates for mean values of Weyl sums. Zbl 0821.11050
Ford, Kevin B.
1995
Large gaps between consecutive prime numbers. Zbl 1338.11083
Ford, Kevin; Green, Ben; Konyagin, Sergei; Tao, Terence
2016
Long gaps between primes. Zbl 1392.11071
Ford, Kevin; Green, Ben; Konyagin, Sergei; Maynard, James; Tao, Terence
2018
On the maximal difference between an element and its inverse in residue rings. Zbl 1131.11005
Ford, Kevin; Khan, Mizan R.; Shparlinski, Igor E.; Yankov, Christian L.
2005
Sieving by large integers and covering systems of congruences. Zbl 1210.11020
Filaseta, Michael; Ford, Kevin; Konyagin, Sergei; Pomerance, Carl; Yu, Gang
2007
Values of the Euler $$\varphi$$-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields. Zbl 1294.11164
Ford, Kevin; Luca, Florian; Moree, Pieter
2014
On an irreducibility theorem of A. Schinzel associated with coverings of the integers. Zbl 0966.11046
Filaseta, M.; Ford, K.; Konyagin, S.
2000
On the distribution of imaginary parts of zeros of the Riemann zeta function. II. Zbl 1160.11042
Ford, Kevin; Soundararajan, Kannan; Zaharescu, Alexandru
2009
Zero-free regions for the Riemann zeta function. Zbl 1034.11045
Ford, Kevin
2002
Generalized Euler constants. Zbl 1143.11036
Diamond, Harold G.; Ford, Kevin
2008
On the distribution of imaginary parts of zeros of the Riemann zeta function. Zbl 1139.11036
Ford, Kevin; Zaharescu, Alexandru
2005
On Vinogradov’s mean value theorem: strongly diagonal behaviour via efficient congruencing. Zbl 1307.11102
Ford, Kevin; Wooley, Trevor D.
2014
Invariable generation of the symmetric group. Zbl 06754739
Eberhard, Sean; Ford, Kevin; Green, Ben
2017
Common values of the arithmetic functions $$\varphi$$ and $$\sigma$$. Zbl 1205.11010
Ford, Kevin; Luca, Florian; Pomerance, Carl
2010
Integers with a divisor in $$(y,2y]$$. Zbl 1175.11053
Ford, Kevin
2008
Chebyshev’s conjecture and the prime number race. Zbl 1214.11105
Ford, Kevin; Konyagin, Sergei
2002
Chebyshev’s bias for products of two primes. Zbl 1280.11056
Ford, Kevin; Sneed, Jason
2010
Values of the Euler function in various sequences. Zbl 1197.11125
Banks, William D.; Ford, Kevin; Luca, Florian; Pappalardi, Francesco; Shparlinski, Igor E.
2005
Diophantine approximation with arithmetic functions. I. Zbl 1225.11098
Alkan, Emre; Ford, Kevin; Zaharescu, Alexandru
2009
Poisson-Dirichlet branching random walks. Zbl 1278.60129
2013
The prime number race and zeros of $$L$$-functions off the critical line. Zbl 1010.11051
Ford, Kevin; Konyagin, Sergei
2002
Prime chains and Pratt trees. Zbl 1218.11085
Ford, Kevin; Konyagin, Sergei V.; Luca, Florian
2010
The prime number race and zeros of Dirichlet $$L$$-functions off the critical line. III. Zbl 1284.11123
Ford, Kevin; Lamzouri, Youness; Konyagin, Sergei
2013
On the largest prime factor of the Mersenne numbers. Zbl 1178.11061
Ford, Kevin; Luca, Florian; Shparlinski, Igor E.
2009
The representation of numbers as sums of unlike powers. II. Zbl 0866.11054
Ford, Kevin B.
1996
The representation of numbers as sums of unlike powers. Zbl 0816.11049
Ford, Kevin B.
1995
Residue classes free of values of Euler’s function. Zbl 0931.11037
Ford, Kevin; Konyagin, Sergei; Pomerance, Carl
1999
Geometric properties of points on modular hyperbolas. Zbl 1204.11004
Ford, Kevin; Khan, Mizan R.; Shparlinski, Igor E.
2010
Diophantine approximation with arithmetic functions. II. Zbl 1225.11099
Alkan, Emre; Ford, Kevin; Zaharescu, Alexandru
2009
On common values of $$\varphi(n)$$ and $$\sigma(m)$$. II. Zbl 1279.11093
Ford, Kevin; Pollack, Paul
2012
The distribution of totients. Zbl 0888.11003
Ford, Kevin
1998
Zeros of Dirichlet $$L$$-functions near the real axis and Chebyshev’s bias. Zbl 1009.11057
Bays, Carter; Ford, Kevin; Hudson, Richard H.; Rubinstein, Michael
2001
The prime number race and zeros of $$L$$-functions off the critical line. II. Zbl 1056.11051
Ford, Kevin; Konyagin, Sergei
2003
Permutations contained in transitive subgroups. Zbl 1346.05005
Eberhard, Sean; Ford, Kevin; Koukoulopoulos, Dimitris
2016
The image of Carmichael’s $$\lambda$$-function. Zbl 1322.11104
Ford, Kevin; Luca, Florian; Pomerance, Carl
2014
Large gaps between consecutive prime numbers containing perfect powers. Zbl 1391.11125
Ford, Kevin; Heath-Brown, D. R.; Konyagin, Sergei
2015
Permutations fixing a $$k$$-set. Zbl 1404.05004
Eberhard, Sean; Ford, Kevin; Green, Ben
2016
Breaking the $$k^2$$ barrier for explicit RIP matrices. Zbl 1288.68062
Bourgain, Jean; Dilworth, Stephen J.; Ford, Kevin; Konyagin, Sergei V.; Kutzarova, Denka
2011
The Brun-Hooley sieve. Zbl 0978.11049
Ford, Kevin; Halberstam, H.
2000
Sharp probability estimates for random walks with barriers. Zbl 1171.60007
Ford, Kevin
2009
Maximal collections of intersecting arithmetic progressions. Zbl 1046.05077
Ford, K.
2003
Waring’s problem with polynomial summands. Zbl 0964.11044
Ford, Kevin
2000
The normal behavior of the Smarandache function. Zbl 1077.11505
Ford, Kevin
1999
Sign changes in $$\pi_{q,a}(x) - \pi_{q,b}(x)$$. Zbl 0986.11063
Ford, Kevin; Hudson, Richard H.
2001
From Kolmogorov’s theorem on empirical distribution to number theory. Zbl 1369.62103
Ford, Kevin
2007
On groups with perfect order subsets. Zbl 1295.11100
Ford, Kevin; Konyagin, Sergei; Luca, Florian
2012
On common values of $$\varphi(n)$$ and $$\sigma(m)$$. I. Zbl 1265.11092
Ford, Kevin; Pollack, Paul
2011
Unnormalized differences between zeros of $$L$$-functions. Zbl 1319.11057
Ford, Kevin; Zaharescu, Alexandru
2015
Simultaneous distribution of the fractional parts of Riemann zeta zeros. Zbl 1433.11104
Ford, Kevin; Meng, Xianchang; Zaharescu, Alexandru
2017
Extremal properties of product sets. Zbl 1414.05288
Ford, Kevin
2018
Extreme biases in prime number races with many contestants. Zbl 1451.11102
Ford, Kevin; Harper, Adam J.; Lamzouri, Youness
2019
On the smallest simultaneous power nonresidue modulo a prime. Zbl 1422.11003
Ford, Kevin; Garaev, Moubariz Z.; Konyagin, Sergei V.
2017
Sharp probability estimates for generalized Smirnov statistics. Zbl 1229.62059
Ford, Kevin
2008
Localized large sums of random variables. Zbl 1133.60322
Ford, Kevin; Tenenbaum, Gérald
2008
Generalized Smirnov statistics and the distribution of prime factors. Zbl 1229.11122
Ford, Kevin
2007
On two conjectures of Sierpiński concerning the arithmetic functions $$\sigma$$ and $$\varphi$$. Zbl 0931.11032
Ford, Kevin; Konyagin, Sergei
1999
An explicit sieve bound and small values of $$\sigma(\varphi(m))$$. Zbl 0980.11004
Ford, Kevin
2001
The jumping champions of the Farey series. Zbl 1034.11013
Cobeli, Cristian; Ford, Kevin; Zaharescu, Alexandru
2003
A strong form of a problem of R. L. Graham. Zbl 1148.11052
Ford, Kevin
2004
On Bombieri’s asymptotic sieve. Zbl 1125.11053
Ford, Kevin
2005
A problem of Ramanujan, Erdős, and Kátai on the iterated divisor function. Zbl 1266.11100
Buttkewitz, Yvonne; Elsholtz, Christian; Ford, Kevin; Schlage-Puchta, Jan-Christoph
2012
Divisors of the Euler and Carmichael functions. Zbl 1237.11038
Ford, Kevin; Hu, Yong
2008
Integers divisible by a large shifted prime. Zbl 1428.11164
Ford, Kevin
2017
Extreme biases in prime number races with many contestants. Zbl 1451.11102
Ford, Kevin; Harper, Adam J.; Lamzouri, Youness
2019
Long gaps between primes. Zbl 1392.11071
Ford, Kevin; Green, Ben; Konyagin, Sergei; Maynard, James; Tao, Terence
2018
Extremal properties of product sets. Zbl 1414.05288
Ford, Kevin
2018
Invariable generation of the symmetric group. Zbl 06754739
Eberhard, Sean; Ford, Kevin; Green, Ben
2017
Simultaneous distribution of the fractional parts of Riemann zeta zeros. Zbl 1433.11104
Ford, Kevin; Meng, Xianchang; Zaharescu, Alexandru
2017
On the smallest simultaneous power nonresidue modulo a prime. Zbl 1422.11003
Ford, Kevin; Garaev, Moubariz Z.; Konyagin, Sergei V.
2017
Integers divisible by a large shifted prime. Zbl 1428.11164
Ford, Kevin
2017
Large gaps between consecutive prime numbers. Zbl 1338.11083
Ford, Kevin; Green, Ben; Konyagin, Sergei; Tao, Terence
2016
Permutations contained in transitive subgroups. Zbl 1346.05005
Eberhard, Sean; Ford, Kevin; Koukoulopoulos, Dimitris
2016
Permutations fixing a $$k$$-set. Zbl 1404.05004
Eberhard, Sean; Ford, Kevin; Green, Ben
2016
Large gaps between consecutive prime numbers containing perfect powers. Zbl 1391.11125
Ford, Kevin; Heath-Brown, D. R.; Konyagin, Sergei
2015
Unnormalized differences between zeros of $$L$$-functions. Zbl 1319.11057
Ford, Kevin; Zaharescu, Alexandru
2015
Values of the Euler $$\varphi$$-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields. Zbl 1294.11164
Ford, Kevin; Luca, Florian; Moree, Pieter
2014
On Vinogradov’s mean value theorem: strongly diagonal behaviour via efficient congruencing. Zbl 1307.11102
Ford, Kevin; Wooley, Trevor D.
2014
The image of Carmichael’s $$\lambda$$-function. Zbl 1322.11104
Ford, Kevin; Luca, Florian; Pomerance, Carl
2014
Poisson-Dirichlet branching random walks. Zbl 1278.60129
2013
The prime number race and zeros of Dirichlet $$L$$-functions off the critical line. III. Zbl 1284.11123
Ford, Kevin; Lamzouri, Youness; Konyagin, Sergei
2013
On common values of $$\varphi(n)$$ and $$\sigma(m)$$. II. Zbl 1279.11093
Ford, Kevin; Pollack, Paul
2012
On groups with perfect order subsets. Zbl 1295.11100
Ford, Kevin; Konyagin, Sergei; Luca, Florian
2012
A problem of Ramanujan, Erdős, and Kátai on the iterated divisor function. Zbl 1266.11100
Buttkewitz, Yvonne; Elsholtz, Christian; Ford, Kevin; Schlage-Puchta, Jan-Christoph
2012
Explicit constructions of RIP matrices and related problems. Zbl 1236.94027
Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka
2011
Breaking the $$k^2$$ barrier for explicit RIP matrices. Zbl 1288.68062
Bourgain, Jean; Dilworth, Stephen J.; Ford, Kevin; Konyagin, Sergei V.; Kutzarova, Denka
2011
On common values of $$\varphi(n)$$ and $$\sigma(m)$$. I. Zbl 1265.11092
Ford, Kevin; Pollack, Paul
2011
On the divisibility of Fermat quotients. Zbl 1223.11116
Bourgain, Jean; Ford, Kevin; Konyagin, Sergei V.; Shparlinski, Igor E.
2010
Common values of the arithmetic functions $$\varphi$$ and $$\sigma$$. Zbl 1205.11010
Ford, Kevin; Luca, Florian; Pomerance, Carl
2010
Chebyshev’s bias for products of two primes. Zbl 1280.11056
Ford, Kevin; Sneed, Jason
2010
Prime chains and Pratt trees. Zbl 1218.11085
Ford, Kevin; Konyagin, Sergei V.; Luca, Florian
2010
Geometric properties of points on modular hyperbolas. Zbl 1204.11004
Ford, Kevin; Khan, Mizan R.; Shparlinski, Igor E.
2010
On the distribution of imaginary parts of zeros of the Riemann zeta function. II. Zbl 1160.11042
Ford, Kevin; Soundararajan, Kannan; Zaharescu, Alexandru
2009
Diophantine approximation with arithmetic functions. I. Zbl 1225.11098
Alkan, Emre; Ford, Kevin; Zaharescu, Alexandru
2009
On the largest prime factor of the Mersenne numbers. Zbl 1178.11061
Ford, Kevin; Luca, Florian; Shparlinski, Igor E.
2009
Diophantine approximation with arithmetic functions. II. Zbl 1225.11099
Alkan, Emre; Ford, Kevin; Zaharescu, Alexandru
2009
Sharp probability estimates for random walks with barriers. Zbl 1171.60007
Ford, Kevin
2009
The distribution of integers with a divisor in a given interval. Zbl 1181.11058
Ford, Kevin
2008
Generalized Euler constants. Zbl 1143.11036
Diamond, Harold G.; Ford, Kevin
2008
Integers with a divisor in $$(y,2y]$$. Zbl 1175.11053
Ford, Kevin
2008
Sharp probability estimates for generalized Smirnov statistics. Zbl 1229.62059
Ford, Kevin
2008
Localized large sums of random variables. Zbl 1133.60322
Ford, Kevin; Tenenbaum, Gérald
2008
Divisors of the Euler and Carmichael functions. Zbl 1237.11038
Ford, Kevin; Hu, Yong
2008
Sieving by large integers and covering systems of congruences. Zbl 1210.11020
Filaseta, Michael; Ford, Kevin; Konyagin, Sergei; Pomerance, Carl; Yu, Gang
2007
From Kolmogorov’s theorem on empirical distribution to number theory. Zbl 1369.62103
Ford, Kevin
2007
Generalized Smirnov statistics and the distribution of prime factors. Zbl 1229.11122
Ford, Kevin
2007
On the maximal difference between an element and its inverse in residue rings. Zbl 1131.11005
Ford, Kevin; Khan, Mizan R.; Shparlinski, Igor E.; Yankov, Christian L.
2005
On the distribution of imaginary parts of zeros of the Riemann zeta function. Zbl 1139.11036
Ford, Kevin; Zaharescu, Alexandru
2005
Values of the Euler function in various sequences. Zbl 1197.11125
Banks, William D.; Ford, Kevin; Luca, Florian; Pappalardi, Francesco; Shparlinski, Igor E.
2005
On Bombieri’s asymptotic sieve. Zbl 1125.11053
Ford, Kevin
2005
A strong form of a problem of R. L. Graham. Zbl 1148.11052
Ford, Kevin
2004
The prime number race and zeros of $$L$$-functions off the critical line. II. Zbl 1056.11051
Ford, Kevin; Konyagin, Sergei
2003
Maximal collections of intersecting arithmetic progressions. Zbl 1046.05077
Ford, K.
2003
The jumping champions of the Farey series. Zbl 1034.11013
Cobeli, Cristian; Ford, Kevin; Zaharescu, Alexandru
2003
Vinogradov’s integral and bounds for the Riemann zeta function. Zbl 1034.11044
Ford, Kevin
2002
Zero-free regions for the Riemann zeta function. Zbl 1034.11045
Ford, Kevin
2002
Chebyshev’s conjecture and the prime number race. Zbl 1214.11105
Ford, Kevin; Konyagin, Sergei
2002
The prime number race and zeros of $$L$$-functions off the critical line. Zbl 1010.11051
Ford, Kevin; Konyagin, Sergei
2002
Zeros of Dirichlet $$L$$-functions near the real axis and Chebyshev’s bias. Zbl 1009.11057
Bays, Carter; Ford, Kevin; Hudson, Richard H.; Rubinstein, Michael
2001
Sign changes in $$\pi_{q,a}(x) - \pi_{q,b}(x)$$. Zbl 0986.11063
Ford, Kevin; Hudson, Richard H.
2001
An explicit sieve bound and small values of $$\sigma(\varphi(m))$$. Zbl 0980.11004
Ford, Kevin
2001
On an irreducibility theorem of A. Schinzel associated with coverings of the integers. Zbl 0966.11046
Filaseta, M.; Ford, K.; Konyagin, S.
2000
The Brun-Hooley sieve. Zbl 0978.11049
Ford, Kevin; Halberstam, H.
2000
Waring’s problem with polynomial summands. Zbl 0964.11044
Ford, Kevin
2000
The number of solutions of $$\varphi (x)=m$$. Zbl 0978.11053
Ford, Kevin
1999
Residue classes free of values of Euler’s function. Zbl 0931.11037
Ford, Kevin; Konyagin, Sergei; Pomerance, Carl
1999
The normal behavior of the Smarandache function. Zbl 1077.11505
Ford, Kevin
1999
On two conjectures of Sierpiński concerning the arithmetic functions $$\sigma$$ and $$\varphi$$. Zbl 0931.11032
Ford, Kevin; Konyagin, Sergei
1999
Sums and products from a finite set of real numbers. Zbl 0908.11008
Ford, Kevin
1998
The distribution of totients. Zbl 0914.11053
Ford, Kevin
1998
The distribution of totients. Zbl 0888.11003
Ford, Kevin
1998
The representation of numbers as sums of unlike powers. II. Zbl 0866.11054
Ford, Kevin B.
1996
New estimates for mean values of Weyl sums. Zbl 0821.11050
Ford, Kevin B.
1995
The representation of numbers as sums of unlike powers. Zbl 0816.11049
Ford, Kevin B.
1995
all top 5
#### Cited by 455 Authors
26 Shparlinski, Igor E. 25 Ford, Kevin B. 16 Luca, Florian 13 Pollack, Paul 12 Pomerance, Carl Bernard 12 Wooley, Trevor D. 8 Alkan, Emre 8 Konyagin, Sergeĭ Vladimirovich 8 Mixon, Dustin G. 7 Banks, William D. 7 Maynard, James 7 Tao, Terence 6 Fickus, Matthew C. 6 Moree, Pieter 6 Roche-Newton, Oliver 6 Shkredov, Il’ya Dmitrievich 5 Filaseta, Michael A. 5 Fu, Fangwei 5 Lamzouri, Youness 5 Niu, Minyao 5 Rudnev, Misha 5 Zaharescu, Alexandru 4 Baier, Stephan 4 Bourgain, Jean 4 Brüdern, Jörg 4 Chen, Zhixiong 4 Jørgensen, Palle E. T. 3 Chang, Mei-Chu 3 Cilleruelo, Javier 3 Croot, Ernie 3 Elsholtz, Christian 3 Finch, Carrie E. 3 Garunkštis, Ramūnas 3 Garzoni, Daniele 3 Granville, Andrew James 3 Jasper, John 3 Kawada, Koichi 3 Languasco, Alessandro 3 Maier, Helmut 3 Martin, Greg 3 Meng, Xianchang 3 Pintz, Janos 3 Rassias, Michael Th. 3 Shteĭnikov, Yuriĭ Nikolaevich 3 Trudgian, Tim 3 Trudgian, Timothy S. 2 Albeverio, Sergio A. 2 Balog, Antal 2 Bandeira, Afonso S. 2 Bansal, Arpit 2 Bays, Carter 2 Bordignon, Matteo 2 Cho, Ilwoo 2 de la Bretèche, Régis 2 Devin, Lucile 2 Dirksen, Sjoerd 2 Dose, Titus 2 Dubickas, Artūras 2 Dusart, Pierre 2 Dutkay, Dorin Ervin 2 Gao, You 2 Green, Ben Joseph 2 Gun, Sanoli 2 Halupczok, Karin 2 Harper, Adam J. 2 Harrington, Joshua 2 Hart, Derrick N. 2 Hudson, Richard H. 2 Ivić, Aleksandar P. 2 Jankauskas, Jonas 2 Kerr, Bryce 2 Kolpakova, Ol’ga Viktorovna 2 Kotnik, Tadej 2 Laporta, Maurizio B. S. 2 Li, Liangpan 2 Michelen, Marcus 2 Miller, Steven J. 2 Murphy, Brendan 2 Naidu, R. Ramu 2 Narayanan, Bhargav P. 2 Ng, Nathan C. 2 Nielsen, Pace P. 2 Pemantle, Robin 2 Radziwiłł, Maksym 2 Rauhut, Holger 2 Rosenberg, Josh 2 Saad Eddin, Sumaia 2 Saha, Ekata 2 Sha, Min 2 Šimėnas, Raivydas 2 Solymosi, József 2 Stănică, Pantelimon 2 Sun, Zhi-Wei 2 Tenenbaum, Gérald 2 Winterhof, Arne 2 Xue, Boqing 1 Addario-Berry, Louigi 1 Agrawal, Komal 1 Akbary, Amir 1 Alkan, Altug ...and 355 more Authors
all top 5
#### Cited in 134 Serials
33 Journal of Number Theory 20 Mathematics of Computation 17 International Journal of Number Theory 15 Mathematika 11 Proceedings of the American Mathematical Society 11 Journal de Théorie des Nombres de Bordeaux 9 Acta Arithmetica 9 Proceedings of the Steklov Institute of Mathematics 7 Functiones et Approximatio. Commentarii Mathematici 6 Bulletin of the Australian Mathematical Society 6 Israel Journal of Mathematics 6 Mathematical Notes 6 Duke Mathematical Journal 6 The Ramanujan Journal 6 Annals of Mathematics. Second Series 6 Integers 5 Advances in Mathematics 5 Journal of Algebra 5 Mathematische Annalen 5 Monatshefte für Mathematik 4 Journal of Mathematical Analysis and Applications 4 Mathematische Zeitschrift 4 Transactions of the American Mathematical Society 4 Linear Algebra and its Applications 4 Experimental Mathematics 4 Research in Number Theory 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Acta Mathematica Hungarica 3 Constructive Approximation 3 Journal of the American Mathematical Society 3 SIAM Journal on Discrete Mathematics 3 Bulletin of the American Mathematical Society. New Series 3 Applied and Computational Harmonic Analysis 3 Finite Fields and their Applications 2 Lithuanian Mathematical Journal 2 Periodica Mathematica Hungarica 2 Bulletin of the London Mathematical Society 2 Compositio Mathematica 2 Illinois Journal of Mathematics 2 Journal of Applied Probability 2 Michigan Mathematical Journal 2 Proceedings of the London Mathematical Society. Third Series 2 Graphs and Combinatorics 2 Probability Theory and Related Fields 2 Journal of Complexity 2 Discrete & Computational Geometry 2 Designs, Codes and Cryptography 2 Geometric and Functional Analysis. GAFA 2 Indagationes Mathematicae. New Series 2 Advances in Computational Mathematics 2 Journal of Combinatorial Optimization 2 Journal of Group Theory 2 Journal of Integer Sequences 2 Journal of the Australian Mathematical Society 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Advances in Mathematics of Communications 2 Discrete Mathematics, Algorithms and Applications 2 Japanese Journal of Mathematics. 3rd Series 2 Cryptography and Communications 2 Mathematics 1 Communications on Pure and Applied Mathematics 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 Indian Journal of Pure & Applied Mathematics 1 Journal d’Analyse Mathématique 1 Journal of Statistical Physics 1 Rocky Mountain Journal of Mathematics 1 Ukrainian Mathematical Journal 1 The Mathematical Intelligencer 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Mathematica 1 Applied Mathematics and Computation 1 Archiv der Mathematik 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 Inventiones Mathematicae 1 Journal of Approximation Theory 1 Journal of Combinatorial Theory. Series A 1 Journal of Combinatorial Theory. Series B 1 Journal of Functional Analysis 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Nagoya Mathematical Journal 1 Pacific Journal of Mathematics 1 Proceedings of the Japan Academy. Series A 1 Quaestiones Mathematicae 1 Rendiconti del Seminario Matematico della Università di Padova 1 Theoretical Computer Science 1 Statistics & Probability Letters 1 Combinatorica 1 Circuits, Systems, and Signal Processing 1 Chinese Annals of Mathematics. Series B 1 Revista Matemática Iberoamericana 1 Journal of Cryptology 1 Forum Mathematicum 1 The Annals of Applied Probability 1 International Journal of Foundations of Computer Science 1 Proceedings of the National Academy of Sciences of the United States of America 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences ...and 34 more Serials
all top 5
#### Cited in 30 Fields
306 Number theory (11-XX) 43 Information and communication theory, circuits (94-XX) 28 Combinatorics (05-XX) 22 Probability theory and stochastic processes (60-XX) 18 Group theory and generalizations (20-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 13 Numerical analysis (65-XX) 12 Computer science (68-XX) 11 Field theory and polynomials (12-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 8 Algebraic geometry (14-XX) 7 Convex and discrete geometry (52-XX) 7 Statistics (62-XX) 5 Real functions (26-XX) 5 Functional analysis (46-XX) 4 Special functions (33-XX) 4 Operations research, mathematical programming (90-XX) 3 Measure and integration (28-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Commutative algebra (13-XX) 2 Functions of a complex variable (30-XX) 2 Geometry (51-XX) 2 Manifolds and cell complexes (57-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Associative rings and algebras (16-XX) 1 Topological groups, Lie groups (22-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-09-25T00:52:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4341820478439331, "perplexity": 7457.968562009855}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057584.91/warc/CC-MAIN-20210924231621-20210925021621-00355.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=Q004MSR | # ${\boldsymbol m}_{{{\boldsymbol c}}}/{\boldsymbol m}_{{{\boldsymbol s}}}$ MASS RATIO INSPIRE search
VALUE DOCUMENT ID TECN
$\bf{ 11.72 \pm0.25}$ OUR EVALUATION
$11.652$ $\pm0.065$ 1
2015
LATT
$11.747$ $\pm0.019$ ${}^{+0.059}_{-0.043}$ 2
2014 A
LATT
$11.62$ $\pm0.16$ 3
2014
LATT
$11.27$ $\pm0.30$ $\pm0.26$ 4
2012
LATT
$12.0$ $\pm0.3$ 5
2010
LATT
$11.85$ $\pm0.16$ 6
2010
LATT
1 CHAKRABORTY 2015 is a lattice QCD computation on gluon field configurations with 2+1+1 dynamical flavors of HISQ quarks with u/d masses down to the physical value. ${\mathit m}_{{{\mathit c}}}$ and ${\mathit m}_{{{\mathit s}}}$ are tuned from pseudoscalar meson masses.
2 BAZAVOV 2014A is a lattice computation using 4 dynamical flavors of HISQ fermions.
3 CARRASCO 2014 is a lattice QCD computation of light quark masses using 2 + 1 + 1 dynamical quarks, with ${{\mathit m}_{{u}}}$ = ${{\mathit m}_{{d}}}{}\not=$ ${{\mathit m}_{{s}}}{}\not=$ ${{\mathit m}_{{c}}}$. The ${\mathit {\mathit u}}$ and ${\mathit {\mathit d}}$ quark masses are obtained separately by using the ${{\mathit K}}$ meson mass splittings and lattice results for the electromagnetic contributions.
4 DURR 2012 determine ${\mathit m}_{{{\mathit c}}}/{\mathit m}_{{{\mathit s}}}$ using a lattice computation with ${{\mathit N}_{{f}}}$ = 2 dynamical fermions. The result is combined with other determinations of ${\mathit m}_{{{\mathit c}}}$ to obtain ${\mathit m}_{{{\mathit s}}}$(2 GeV) = $97.0$ $\pm2.6$ $\pm2.5~$MeV.
5 BLOSSIER 2010 determine ${\mathit m}_{{{\mathit c}}}/{\mathit m}_{{{\mathit s}}}$ from a computation of the hadron spectrum using ${{\mathit N}_{{f}}}$ = 2 dynamical twisted-mass Wilson fermions.
6 DAVIES 2010 determine ${\mathit m}_{{{\mathit c}}}/{\mathit m}_{{{\mathit s}}}$ from meson masses calculated on gluon fields including ${{\mathit u}}$, ${{\mathit d}}$, and ${{\mathit s}}$ sea quarks with lattice spacing down to 0.045 fm. The Highly Improved Staggered quark formalism is used for the valence quarks.
${\mathit m}_{{{\mathit c}}}/{\mathit m}_{{{\mathit s}}}$ MASS RATIO
References:
CHAKRABORTY 2015
PR D91 054508 High-Precision Quark Masses and QCD Coupling from ${{\mathit n}_{{f}}}$ = 4 Lattice QCD
BAZAVOV 2014A
PR D90 074509 Charmed and Light Pseudoscalar Meson Decay Constants from Four-flavor Lattice QCD with Physical Light Quarks
CARRASCO 2014
NP B887 19 Up, Down, Strange and Charm Quark Masses with $\mathit N_{f}$ = 2+1+1 Twisted Mass Lattice QCD
DURR 2012
PRL 108 122003 Ratio ${\mathit m}_{{{\mathit c}}}/{\mathit m}_{{{\mathit s}}}$ with Wilson Fermions
BLOSSIER 2010
PR D82 114513 Average up/down, strange, and charm Quark Masses with $\mathit N_{f}$=2 Twisted-Mass Lattice QCD
DAVIES 2010
PRL 104 132003 Precise Charm to Strange Mass Ratio and Light Quark Masses from Full Lattice QCD | 2019-01-21T07:35:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8575010299682617, "perplexity": 4541.874348042041}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583763839.28/warc/CC-MAIN-20190121070334-20190121092334-00019.warc.gz"} |
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=913921 | # Publication Citation: Parametric seeding of a microresonator optical frequency comb
NIST Authors in Bold
Author(s): Scott B. Papp; Pascal P. Del'Haye; Scott A. Diddams; Parametric seeding of a microresonator optical frequency comb July 16, 2013 We have investigated parametric seeding of a microresonator frequency comb (microcomb) by way of a pump laser with two intensity modulation sidebands. We show that the pump-sideband spacing is precisely replicated throughout the microcomb's optical spectrum, and we demonstrate a record absolute line spacing stability for microcombs of $1.6\times10^{-13}$ at 1 s. Parametric comb generation is complicated, and often non-equidistant subcombs are observed. Our results demonstrate that parametric seeding can not only control the subcombs, but it can lead to the generation of a strictly equidistant microcomb spectrum. Optics Express 21 15 pp. 1 - 10 frequency metrology;microresonators;nonlinear optics;optical frequency combs Physics | 2014-07-29T00:40:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6697875261306763, "perplexity": 7663.453846467322}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510264270.11/warc/CC-MAIN-20140728011744-00190-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://par.nsf.gov/biblio/10366443-dearth-close-stellar-companions-dwarf-tess-objects-interest | A Dearth of Close-in Stellar Companions to M-dwarf TESS Objects of Interest
Abstract
TESS has proven to be a powerful resource for finding planets, including those that orbit the most prevalent stars in our galaxy: M dwarfs. Identification of stellar companions (both bound and unbound) has become a standard component of the transiting planet confirmation process in order to assess the level of light-curve dilution and the possibility of the target being a false positive. Studies of stellar companions have also enabled investigations into stellar multiplicity in planet-hosting systems, which has wide-ranging implications for both exoplanet detection and characterization, as well as for the formation and evolution of planetary systems. Speckle and AO imaging are some of the most efficient and effective tools for revealing close-in stellar companions; we therefore present observations of 58 M-dwarf TOIs obtained using a suite of speckle imagers at the 3.5 m WIYN telescope, the 4.3 m Lowell Discovery Telescope, and the 8.1 m Gemini North and South telescopes. These observations, as well as near-infrared adaptive optics images obtained for a subset (14) of these TOIs, revealed only two close-in stellar companions. Upon surveying the literature, and cross-matching our sample with Gaia, SUPERWIDE, and the catalog from El-Badry et al., we reveal an additional 15 widely separated more »
Authors:
; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10366443
Journal Name:
The Astronomical Journal
Volume:
163
Issue:
5
Page Range or eLocation-ID:
Article No. 232
ISSN:
0004-6256
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
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M dwarfs are favorable targets for exoplanet detection with current instrumentation, but stellar companions can induce false positives and inhibit planet characterization. Knowledge of stellar companions is also critical to our understanding of how binary stars form and evolve. We have therefore conducted a survey of stellar companions around nearby M dwarfs, and here we present our new discoveries. Using the Differential Speckle Survey Instrument at the 4.3 m Lowell Discovery Telescope, and the similar NN-EXPLORE Exoplanet Stellar Speckle Imager at the 3.5 m WIYN telescope, we carried out a volume-limited survey of M-dwarf multiplicity to 15 parsecs, with a special emphasis on including the later M dwarfs that were overlooked in previous surveys. Additional brighter targets at larger distances were included for a total sample size of 1070 M dwarfs. Observations of these 1070 targets revealed 26 new companions; 22 of these systems were previously thought to be single. If all new discoveries are confirmed, then the number of known multiples in the sample will increase by 7.6%. Using our observed properties, as well as the parallaxes and 2MASSKmagnitudes for these objects, we calculate the projected separation, and estimate the mass ratio and component spectral types, for thesemore »
2. Abstract We present the complete sample of protoplanetary disks from the Gemini- Large Imaging with the Gemini Planet Imager Herbig/T Tauri Survey, which observed bright Herbig Ae/Be stars and T Tauri stars in near-infrared polarized light to search for signatures of disk evolution and ongoing planet formation. The 44 targets were chosen based on their near- and mid-infrared colors, with roughly equal numbers of transitional, pre-transitional, and full disks. Our approach explicitly did not favor well-known, “famous” disks or those observed by the Atacama Large Millimeter/submillimeter Array, resulting in a less-biased sample suitable to probe the major stages of disk evolution during planet formation. Our optimized data reduction allowed polarized flux as low as 0.002% of the stellar light to be detected, and we report polarized scattered light around 80% of our targets. We detected point-like companions for 47% of the targets, including three brown dwarfs (two confirmed, one new), and a new super-Jupiter-mass candidate around V1295 Aql. We searched for correlations between the polarized flux and system parameters, finding a few clear trends: the presence of a companion drastically reduces the polarized flux levels, far-IR excess correlates with polarized flux for nonbinary systems, and systems hosting disks with ringmore »
3. Abstract
We present the first results of a multiyear program to map the orbits of M-dwarf multiples within 25 pc. The observations were conducted primarily during 2019–2020 using speckle interferometry at the Southern Astrophysical Research Telescope in Chile, using the High-Resolution Camera mounted on the adaptive optics module (HRCam+SAM). The sample of nearby M dwarfs is drawn from three sources: multiples from the RECONS long-term astrometric monitoring program at the SMARTS 0.9 m; known multiples, for which these new observations will enable or improve orbit fits; and candidate multiples flagged by their astrometric fits in Gaia Data Release 2 (DR2). We surveyed 333 of our 338 M dwarfs via 830 speckle observations, detecting companions for 63% of the stars. Most notably, this includes new companions for 76% of the subset selected from Gaia DR2. In all, we report the first direct detections of 97 new stellar companions to the observed M dwarfs. Here we present the properties of those detections, the limits of each nondetection, and five orbits with periods 0.67–29 yr already observed as part of this program. Companions detected have projected separations of 0.″024–2.″0 (0.25–66 au) from their primaries and have ΔI≲ 5.0 mag. This multiyear campaign willmore »
4. Abstract
We present the validation of two planets orbiting M dwarfs, TOI-1696b and TOI-2136b. Both planets are mini-Neptunes orbiting nearby stars, making them promising prospects for atmospheric characterization with the James Webb Space Telescope (JWST). We validated the planetary nature of both candidates using high-contrast imaging, ground-based photometry, and near-infrared radial velocities. Adaptive optics images were taken using the ShARCS camera on the 3 m Shane Telescope. Speckle images were taken using the NN-Explore Exoplanet Stellar Speckle Imager on the WIYN 3.5 m telescope. Radii and orbital ephemerides were refined using a combination of the Transiting Exoplanet Survey Satellite, the diffuser-assisted Astrophysical Research Consortium (ARC) Telescope Imaging Camera (ARCTIC) imager on the 3.5 m ARC telescope at Apache Point Observatory, and the 0.6 m telescope at Red Buttes Observatory. We obtained radial velocities using the Habitable-Zone Planet Finder on the 10 m Hobby–Eberly Telescope, which enabled us to place upper limits on the masses of both transiting planets. TOI-1696b (P= 2.5 days;Rp= 3.24R;Mp< 56.6M) falls into a sparsely populated region of parameter space considering its host star’s temperature (Teff= 3168 K, M4.5), as planets of its size are quite rare around mid- to late-M dwarfs. On the other hand, TOI-2136bmore »
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https://fermatslibrary.com/s/q-2020-02-10-229 | Maximum N -body correlations do not in general imply
genuine multipartite entanglement
Christopher Eltschka
1
and Jens Siewert
2,3
1
Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
2
Departamento de Química Física, Universidad del País Vasco UPV/EHU, E-48080 Bilbao, Spain
3
IKERBASQUE Basque Foundation for Science, E-48013 Bilbao, Spain
The existence of correlations between
the parts of a quantum system on the one
hand, and entanglement between them
on the other, are different properties.
Yet, one intuitively would identify
strong N-party correlations with N -party
entanglement in an N -partite quantum
state. If the local systems are qubits,
this intuition is confirmed: The state
with the strongest N-party correlations
is the Greenberger-Horne-Zeilinger
(GHZ) state, which does have genuine
multipartite entanglement. However, for
high-dimensional local systems the state
with strongest N-party correlations may
be a tensor product of Bell states, that
is, partially separable. We show this
by introducing several novel tools for
handling the Bloch representation.
1 Introduction
The expansion of the density operator in
terms of a matrix basis is called the Bloch
representation [1, 2, 3]. Technically, this
representation is rather demanding: A pure
state of N parties each of local dimension d
is characterized by 2d
N
2 real coefficients,
whereas the same state written in the Bloch
representation requires d
2N
1 parameters, just
as any mixed state. On the other hand, this
representation appears to be perfectly adapted to
studying the correlation properties of a quantum
system, because the above-mentioned expansion
corresponds to a decomposition of the state
into all possible correlation contributions (hence
the terms are also called correlation tensors).
Therefore, from a better understanding of the
technical characteristics of this expansion one
may expect significant insight into the physics of
correlated quantum systems.
The systematic investigation of the properties
of the Bloch representation for finite-dimensional
multi-party quantum systems is a relatively
recent subject [4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15], although many important results were
found earlier, mostly relating specific features of
the Bloch picture to the entanglement properties
of the state (e.g., [16, 17, 18, 19, 20, 21, 22,
23, 24, 26, 25]). Currently much activity is
devoted to working out the technical details
and properties for an easier use of the Bloch
representation to solving physics problems. An
essential part of this is to figure out smaller sets
of parameters that carry sufficient amounts of
information to facilitate the characterization of
relevant physical properties for a state given in
the Bloch representation. In this contribution,
we define such a set of parameters, which we call
the “sector distribution” and discuss some of its
key features. Moreover, we illustrate how the
properties of this distribution are reflected in the
correlation properties of the states.
To be more specific, let us preliminarily
introduce the Bloch representation; the precise
definition will be given below. If we enumerate
the parties of an N-party system (of equal local
dimension d) by {1, 2 . . . N} and A is a subset of
parties, then
ρ =
1
d
N
X
A
G
A
1
¯
A
. (1)
Here, G
A
is a Hermitian operator that acts
nontrivially on the parties belonging to the subset
A, and 1
¯
A
is the identity operator for the
complementary set. Consider now the sum of
all those terms in Eq. (1) that act on the same
Accepted in Quantum 2020-02-03, click title to verify. Published under CC-BY 4.0. 1
arXiv:1908.04220v2 [quant-ph] 6 Feb 2020
number k of parties,
S
k
1
d
N
X
|A|=k
G
A
1
¯
A
. (2)
We call S
k
the k-sector” of ρ and the (squared)
Hilbert-Schmidt length of S
k
the k-sector
length” S
k
[27]
S
k
d
N
Tr
S
k
S
k
. (3)
The k-sector length S
k
is a natural quantifier for
the k-party correlations in a state [28]. Clearly,
for an N-partite state there are N sector lengths
(S
0
= 1 for all normalized states). Sector
lengths were discussed earlier [16, 17, 20, 4,
5, 6, 8, 7, 9, 10, 14, 15]. In particular the
N-sector was intuitively linked with the N -party
quantum correlations. Therefore it came as a
surprise that there exist mixed states that are
N-party entangled but do not possess N-party
correlations [29, 30, 31, 32]. Later it was
realized [4] that, in order to witness genuine
multipartite entanglement, it may be necessary
to consider a collection of the highest sector
lengths S
N
, S
N1
, . . . rather than just S
N
. In the
present work we systematically study the set of all
sector lengths {S
k
}. As we will demonstrate the
distribution {S
1
, S
2
. . . S
N
} represents a reduced
set of parameters in the spirit described above
(linear in the system size instead of exponential)
that carries substantial information regarding
some of the correlation properties of the state.
Often it has little meaning to study the sector
lengths S
k
individually; rather, there exists a
variety of strict relations between them that
determine the entire distribution.
We introduce several novel technical concepts,
most importantly the N-sector projector. We use
this toolbox to prove the long-standing conjecture
that for any number N of qubits the GHZ state
maximizes the N-sector length. Subsequently
we analyze the sector distribution for few-party
systems of higher local dimension d > 2. Here we
prove that for higher local dimension the state
with maximum N-sector length may be partially
separable. Moreover, we provide a comprehensive
discussion for the behavior of the N-sector with
increasing number of parties as well as growing
local dimension.
2 Definitions and preliminaries
For the Bloch representation of an N-partite state
with all local dimensions equal to d = 2 the
operators G
A
in Eq. (1) are expanded in local
operators, i.e., a basis of traceless matrices {g
j
},
1 5 j 5 d
2
1, g
0
1, with normalization
Tr
g
j
g
k
=
jk
,
ρ =
1
d
N
X
A
X
j
l
: lA
r
j
1
···j
N
g
j
1
··· g
j
N
1
¯
A
,
(4)
and
r
j
1
···j
N
= Tr
h
g
j
1
··· g
j
N
1
¯
A
i
ρ
. (5)
Here, all indices j
m
, m
¯
A are set to 0. With
this, the k-sector length simply becomes
S
k
=
X
j
l
: lA,|A|=k
|r
j
1
···j
N
|
2
, (6)
where |A| is the number of elements in A. All
the sector lengths are local unitary invariants of
the state. As the actual sector lengths
S
k
equal
the Hilbert-Schmidt norms of S
k
, they obey the
triangle inequality. Because of this, the N-sector
length of a mixture of pure states can never
exceed the largest N-sector length of any of the
pure states. Therefore, throughout this article we
focus on pure states Π, that is, for the purity we
have Tr Π
2
= Tr Π = 1 and, hence, for the sum
of all sector lengths,
P
N
k=0
S
k
= d
N
.
Consider the simplest case of all, that is,
product states
prod
N
j
E
= |ji
N
; here |ji
denotes a state of the computational basis,
j = 0, 1, . . . , (d 1). It is easy to see that
S
k
(prod
N
j
) =
N
k
(d 1)
k
. Remarkably, it was
shown by Tran et al. [6] that among the pure
states only product states have the minimum
N-sector length
min S
N
= (d 1)
N
,
that is, for d > 2 the N-sector is always on the
order of d
N
. It turned out that the opposite
question regarding the states with maximum
N-sector is considerably more complex. A
relevant state for this discussion is the GHZ state
for N parties of local dimension d
GHZ
N
d
E
=
1
d
d1
X
j=0
|ji
N
. (7)
Accepted in Quantum 2020-02-03, click title to verify. Published under CC-BY 4.0. 2
For N -qudit GHZ states we find the sector
distribution (see Appendix)
S
k
(GHZ
N
d
) = (d 1)d
N1
δ
kN
+
+
N
k
!
(d 1)
k
+ (1)
k
(d 1)
d
.
(8)
Tran et al. [6] showed that for odd party
number N of qubits the GHZ state has maximum
N-sector length. They conjectured that this
statement holds also for even N. For d > 2 it
is not clear which state has maximum N -party
correlations. In the following we will prove the
conjecture for even-N qubit GHZ states.
3 The N -sector projector
For the proof we need some mathematical
tools based on universal state inversion [35,
36, 37, 9, 12]. First we define the projection
(super-)operator [38] onto the last (k = N) sector
(or N -sector projector for short whenever there
are no ambiguities)
P(ρ) =
N
Y
j=1
id
1
d
Tr
j
(·) 1
j
ρ . (9)
It is easy to check by writing ρ in the Bloch
representation that P indeed realizes a projection
onto the N-sector, S
N
. The map (9) belongs to
the class of generalized universal state inversions
discussed in Refs. [37, 12] that have the form
I
{α
j
j
}
=
Q
N
j=1
α
j
Tr
j
(·) 1
j
β
j
id
, where
id denotes the identity map and α
j
, β
j
are real
numbers. With definition (9) we get immediately
S
N
(ρ) = d
N
Tr [ρ P(ρ)]
= d
N
X
A
1
d
|A|
Tr
ρ
2
¯
A
, (10)
where A, as before, runs through all subsets
of {1 . . . N} and ρ
¯
A
= Tr
A
ρ is the reduced
state on the subset of parties
¯
A. The equality
Tr
h
(Tr
A
Π)
2
i
= Tr
h
(Tr
¯
A
Π)
2
i
for pure states Π
motivates the definition of another operator
Q(ρ) =
N
Y
j=1
Tr
j
(·) 1
j
1
d
id
ρ , (11)
so that
S
N
= d
N
Tr P(Π)]
= d
N
Tr Q(Π)] = 0 . (12)
Because of the projector property of P and
the Cauchy-Schwarz inequality, kMk
P
q
Tr [M
P(M)] defines a seminorm for operators
M (while the analogous statement does not hold
for Q). By considering the action of Q(Π) in the
Bloch representation relation (12) gives rise to the
astounding equality
d
N
S
N
(Π) =
N
X
k=0
(1)
k
(d
2
1)
Nk
S
k
(Π) ,
(13)
which links the last sector length S
N
with all
others.
Finally we rewrite the well-known purity
condition for reductions of pure states
Tr
h
(Tr
A
|ψihψ|)
2
i
= Tr
h
(Tr
¯
A
|ψihψ|)
2
i
in
terms of sector lengths. This is achieved by
symmetrizing the purity conditions for fixed
|A| and accomplishing the combinatorial
accounting. We find for the k-purity
relation (k = 0, 1, . . . , b
N1
2
c with the floor
function b·c) [33]
d
N2k
k
X
m=0
N m
k m
!
S
m
=
Nk
X
n=0
N n
k
!
S
n
.
(14)
For k = 0 this gives the well-known condition
d
N
=
P
N
0
S
n
. We explicitly write the relations
for k = 1 and k = 2 as they will turn out useful
later:
d
N2
[N + S
1
] = N + (N 1)S
1
+ . . . + 2S
N2
+ S
N1
, (15a)
d
N4
"
N
2
!
+ (N 1)S
1
+ S
2
#
=
N
2
!
+
N 1
2
!
S
1
+ . . . +
3
2
!
S
N3
+ S
N2
. (15b)
Accepted in Quantum 2020-02-03, click title to verify. Published under CC-BY 4.0. 3
Interestingly, Eqs. (14) elucidate the role of the
N-sector for pure states: All sector lengths have
to be adjusted so as to obey the k-purity relations
(k = 1 . . . b
N1
2
c) between the reduced states of
non-empty complementary partitions; note that
the last sector is excluded from establishing this
balance. The last sector serves to fill up the
total length d
N
of the Bloch vector (the “0-purity”
relation).
4 The N -qubit GHZ state maximizes
the N -sector
For odd N we know max S
N
= S
N
(GHZ) =
2
N1
, cf. Ref. [6]. We recall this proof in the
Appendix. We are prepared now to show for even
N qubits that
max S
N
= S
N
(GHZ) = 2
N1
+ 1 .
As here the GHZ state has only even-numbered
sectors, Eq. (13) would imply for a hypothetical
state Π
x
= |xihx| with larger N-sector than GHZ
that S
2m
>
N
2m
for some m < N/2. In order
to obtain information regarding the distribution
of the even-numbered sectors we consider an R
matrix (analogous to Refs. [34, 5, 9]) of ρ
[1]
Tr
{1}
Π
x
after tracing the first party,
R
[1]
ρ
[1]
I
(ρ
[1]
) = ρ
[1]
X
A
(1)
|A|
Tr
¯
A
ρ
[1]
1
¯
A
,
(16)
where I
(σ)
Q
M
j=1
[Tr
j
(·) 1
j
id] σ denotes
the standard universal state inversion for an
M-partite state σ (cf. Refs. [36, 9, 11]). If
we symmetrize over the traced party we can
establish a relation between
P
j
Tr R
[j]
and the
sector lengths S
k
x
) of Π
x
,
0 5 d
N1
N
X
j=1
Tr R
[j]
=
N1
X
k=0
(1)
k
(N k)S
k
.
(17)
The reasoning is exactly the same as the one to
obtain the 1-purity, Eq. (15a). By adding the
latter equation and Eq. (17) (and dividing by
2) we obtain a relation for the even-numbered
sectors,
d
N2
2
N + S
1
+
X
j
d Tr R
[j]
= N + (N 2)S
2
+ (N 4)S
4
+ . . . + 4S
N4
+ 2S
N2
. (18)
We observe that on the right-hand side (r.h.s.)
the prefactors increase with decreasing index,
this is analogous to Eq. (13), only that here
the prefactors increase linearly. Also here the
even-sector distribution of Π
x
would exceed
the result of the GHZ state. Relation (18)
gives us the possibility to directly check the
achievable maximum of the r.h.s. for pure states
by maximizing the terms on the left-hand side.
For qubits this is straightforward and shows that
the maximum is achieved for the GHZ state (we
present this calculation in the Appendix). Hence,
there is no state Π
x
with larger N-sector.
5 Few parties of higher local dimension
The obvious guess from the results so far is that
GHZ
N
d
E
maximizes the N -sector length also for
d > 2. It will turn out that this can only partially
be true. To this end, let us investigate states
with up to six parties. The following results are
obtained by using Eqs. (13), (14) for k = 0, 1, 2,
and increasingly tedious algebra.
N = 2 : We have d
2
= 1 + S
1
+ S
2
, so that
max S
2
= d
2
1
for S
1
= 0, that is, the Bell state
Φ
+
d
E
GHZ
2
d
E
maximizes the 2-sector.
N = 3: Here,
S
3
= (d 1)
2
(d + 2) (d 1)S
1
,
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so that S
1
= 0 leads to max S
3
= (d + 2)(d 1)
2
,
which again is realized by the GHZ state.
N = 4: In this case, there remains more than one
parameter undetermined
S
4
= (d
2
1)
2
1
2
h
(d
2
1)S
1
+ S
3
i
,
but since S
1
, S
3
= 0, the 4-sector gets maximized
for S
1
= S
3
= 0, so that max S
4
= (d
2
1)
2
.
That is, for four-party states the N-sector is not
maximized by the GHZ state, but by a tensor
product of Bell states, i.e., a biseparable state.
Curiously, the case d = 2 is right on the edge,
because the tensor product of a pair of two-qubit
Bell states and the four-qubit GHZ state have the
same 4-sector length, S
4
= 9.
N = 5: Here we find
(d 3)S
5
= (d 1)
3
(d + 2)(d
2
2d 4)
(d 1)
2
(d
2
d 3)S
1
+ (d 1)S
3
.
(19)
This suggests again S
1
= 0 for the N-sector
maximum, however, now the sign of S
3
is
reversed. We note that the maximum k-sector
length of an N-party system is on the order of
N
k
d
k
, so that the 3-sector length S
3
O(d
3
),
and hence for large local dimension d 1
max S
5
(d 1)
3
(d + 1)(d + 2)
1 + O(d
2
) ,
which indicates that the maximum N-sector
is approximated with better than first-order
accuracy for growing d by the polynomial in
the denominator. The latter corresponds to the
tensor product of a Bell state and a three-party
GHZ state,
Φ
+
d
E
GHZ
3
d
E
. Consequently, for
large d also here the state with maximum N-body
correlations may be biseparable. The case d = 3
is special: S
3
= 20 gives the largest 3-sector.
The five-qutrit GHZ state is compatible with
this [cf. Eq. (8)] and has larger 5-sector than
Φ
+
3
E
GHZ
3
3
E
(172 vs. 160). However, in
principle, there might be a state with S
1
= 0,
S
3
= 20 and even larger 5-sector.
N = 6: This case has similar features as N = 5.
The 6-sector obeys
2(d
2
4)S
6
= 2(d 2)(d
2
1)
3
(d + 2)
(d
2
1)
2
(d
2
3)S
1
+
+ (d
2
1)S
3
(d
2
3)S
5
.
(20)
Again we see that for increasing d 1 the
6-sector (max S
6
)/(d
2
1)
3
1 + O(d
3
)
because of the scaling of the sector lengths with
d; the corresponding state is
Φ
+
d
E
3
. Note that
already for d = 3 the 6-sector of
Φ
+
3
E
3
beats
the length of the six-qutrit GHZ state (512 vs.
508).
We summarize the results of this section in
Tables 1–3.
Table 1: Maximum of the N-sector for 2, 3, 4 parties.
N max N-sector S
N
state maximizing S
N
2 d
2
1
Φ
+
d
E
3 (d 1)
2
(d + 2)
GHZ
3
d
E
4 (d
2
1)
2
Φ
+
d
E
2
Table 2: Comparison of N-sectors for N = 5.
S
5
GHZ
5
d
E
GHZ
3
d
E
Φ
+
d
E
d (d 1)
2
× (d 1)
3
×
(d
3
+ 2d
2
2d + 4) (d + 1)(d + 2)
3 172 > 160
4 828 > 810
5 2704 > 2688
6 7000 = 7000
7 15516 < 15552
Table 3: Comparison of N-sectors for N = 6.
S
6
GHZ
6
d
E
Φ
+
d
E
3
d
d1
d
d
6
+ (d 1)
5
+ 1
(d
2
1)
3
2 33 > 27
3 508 < 512
4 3255 < 3375
6 Maximum N -sector for large d and
large N
We can investigate the dominance of N-sectors
numerically. On increasing d, the partially
separable states—that is, a tensor product of Bell
states (even N) or Bell states and a three-party
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Figure 1: N-sector length difference
S
N
(GHZ
N
d
) S
N
(Bell
N
d
). The border between
GHZ-dominated and Bell-dominated is given by a
straight line d ' 0.6275 · N (see text); however, note
the pronounced even-odd effect. For N = 2 and N = 3,
GHZ and Bell are the same state, therefore these cases
have to be counted as ‘undecided’. (a) Small scale
N, d 5 10; (b) larger scale N, d 5 100. Note that the
color scale is logarithmic.
GHZ state (odd N)—appear to dominate (we
will call these states Bell”). In the opposite
case, the GHZ state has larger N-sector. This
behavior is shown in Fig. 1, where the difference
of N-sectors S
N
(GHZ
N
d
)S
N
(Bell
N
d
) is displayed
in a (d, N) plane. We note the formal analogy of
our problem of finding the maximum N-sector
with that of deciding the existence of absolutely
maximimally entangled (AME) states [21, 39,
40, 8, 11] that is suggested by the structure of
Fig. 1. The analogy arises because also the
N-sector problem seems to have two solutions
whose validity regions in the (d, N) plane are
connected and separated by a single line. The
region of GHZ dominance corresponds to ‘AME
state does not exist’, while that of Bell dominance
relates to ‘AME does exist’. The line separating
the two corresponds to the Scott bound [21, 11].
An accurate analytical approximation for this
line is found by equating S
N
(GHZ
N
d
) in Eq. (8)
with S
N
(Bell
N
d
) = (d
2
1)
N/2
(for even N ).
Assuming d = γ
1
N, this leads to an equation
that determines the γ parameter, e
γ
= 1
γ
2
,
from which
d ' 0.6275 · N . (21)
Close to this line there may be exceptions from
the rule, just as in the case of AME states.
In the following we provide arguments why
GHZ and Bell are, if not the dominating, at
least close to the states with dominating N-sector
in the limits of large N and d. Consider first
fixed even N and d 2, N. Our reasoning
is based on the purity relations Eqs. (15) and
on the consideration that to leading order the
maximum k-sector is given by S
k
N
k
d
k
. From
the 0-purity relation S
N
= d
N
S
N1
. . . 1 it
follows that the dominating terms S
N1
+ S
N2
need to be as small as possible in order to obtain
max S
N
. We observe that Eq. (15a) dictates that
S
N2
and S
N1
cannot both vanish, and their
sum needs to be at least of order Nd
N2
. As
S
1
> 0 would only increase the r.h.s., S
1
= 0
is the sensible choice. Moreover, we see that
S
N2
+ S
N1
1
2
d
N2
N + S
N1
, so that
the subleading correction becomes smallest for
S
N1
= 0 and S
N2
N
2
d
N2
. Substituting
this result into Eq. (15b) leads to S
2
N
2
d
2
. In
particular the latter requirement together with
S
1
= 0 can be fulfilled if the state is a Bell tensor
product.
For the opposite limit, N d > 2, general
statements are more difficult to make, because
the sector sum does not correspond to a power
expansion in d any longer. We can discuss at least
the case of states that are more entangled than
GHZ, that is, m-uniform states [21, 39]. A state
is called m-uniform if S
1
= S
2
= ··· = S
m
= 0,
with the extreme case of AME states (m =
bN/2c). For AME states, S
N
' d
N
(1
1
d
2
)
N
is
a fair approximation that applies to some extent
also to m . N/2 if N does not exceed d
2
. Then,
for large d approximately S
N
d
N
e
N
d
2
, which
shows that a substantial fraction of the Bloch
vector length is not in the N -sector, making these
states bad candidates for the maximum S
N
.
On the other hand, for the GHZ state we have
S
N
(GHZ
N
d
) ' d
N
1
1
d
+ d
N1
e
N
d
. (22)
That is, S
N
is essentially given by the first term
in Eq. (22) and the relative error shrinks with
increasing N . This is the expected behavior
for the dominating state, because d
N
1
1
d
is
the absolute maximum the traceless part of a
pure state |ψihψ| can achieve: An offdiagonal
element consisting of orthogonal product states
gives k|jj . . . jihkk . . . k|k
P
= 1, which is the
maximum among all rank-1 operators. An
N-qudit state of local dimension d can have
at most Schmidt rank d in a bipartition
of a single party against the rest. This
amounts to a maximum offdiagonal contribution
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of
1
d
2
d(d 1)d
N
to S
N
which is precisely
the GHZ result. Consequently, for large N the
GHZ state N-sector approaches the maximum for
any rank-1 operator. Evidently, this discussion
cannot exclude the existence of a state that
approaches this maximum even faster.
7 Conclusions
We have analyzed the Bloch sector distribution
for multipartite pure quantum states of N d-level
systems, in particular the properties of the
N-sector. We have demonstrated that the sectors
must not be considered individually; rather, there
are numerous interdependencies that determine
the distribution. One of our main results
based on this insight is the proof that for
qubits the GHZ state has maximum N-sector
also for even N. We have given an extensive
characterization of the N-sector behavior for
arbitrary N and d, which can be viewed as
an algebraic problem analogous to that of the
existence of AME states. Most importantly,
we find that strong N-party correlations (viz
maximum N-sector) do not necessarily imply
genuine multipartite entanglement. Apart from
our physics results, our work provides several
novel technical tools for analyzing the Bloch
representation of pure states and thereby shows
that this is a powerful approach to obtain
new insight into the mathematical properties of
many-body quantum states.
Acknowledgments
This work was funded by the German
Research Foundation Project EL710/2-1
(C.E., J.S.), by Grant PGC2018-101355-B-100
(MCIU/FEDER/UE) and Basque Government
Grant IT986-16 (J.S.). The authors would like
to thank Marcus Huber and Nikolai Wyderka
for stimulating discussions. C.E. and J.S.
acknowledge Klaus Richter’s support of this
project.
Appendix
Sector distribution of GHZ state, Eq. (8)
In order to obtain the sector lengths for the GHZ
state it is not necessary to explicitly calculate the
Bloch representation. Yet we quickly do it for the
qubit example to demonstrate how simple it is.
The density matrix of the N-qubit GHZ state is
Π
GHZ
N
2
=
1
2
|00 . . . 0ih00 . . . 0| +
+ |11 . . . 1ih11 . . . 1| +
+ |00 . . . 0ih11 . . . 1| +
+ |11 . . . 1ih00 . . . 0|
. (A1)
Each term here is a tensor product of N identical
rank-1 single-qubit operators,
|0ih0|
N
=
1
2
N
(1 + Z)
N
|1ih1|
N
=
1
2
N
(1 Z)
N
|0ih1|
N
=
1
2
N
(X + iY )
N
|1ih0|
N
=
1
2
N
(X iY )
N
,
where X σ
1
, Y σ
2
, Z σ
3
are the
Pauli matrices and 1 is the qubit identity matrix.
Hence
Π
GHZ
N
2
=
1
2
N
X
even#Z
ZZ . . . 11 +
+
X
even#Y
(1)
#Y
2
X . . . Y Y . . . X . . . Y Y
,
(A2)
where the sums run over all combinations of
even numbers of Z occurrences padded with 1s
(diagonal) and even numbers of Y occurences
padded with Xs (offdiagonal); for simplicity we
omit the tensor product signs. The difference
between even and odd N is that for even N there
is one N -sector term ZZ . . . Z in the diagonal
part, whereas for odd N the N-sector exclusively
consists of offdiagonal terms. The GHZ state for
d > 2 can be built in an analogous manner.
In order to derive Eq. (8) we can take a shortcut
and use Eq. (10),
S
N
= d
N
X
A
1
d
|A|
Tr
ρ
2
¯
A
. (A3)
The GHZ state is particularly simple as all
reduced states are of rank d and completely
mixed on their span, so that Tr
ρ
2
A
=
1
d
for all
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|A| 6= 0, N. For |A| = 0 and |A| = N we have
Tr (ρ
A
)
2
= 1, so that
S
N
=d
N
1
d
1
1
d
N
+ d
N
1
1
d
(1)
N
d
N
1
d
N+1
1
d
N
=d
N1
(d 1) +
+
1
d
h
(d 1)
N
+ (1)
N
(d 1)
i
. (A4)
For k < N, S
k
is given by the length of the
last sector of the reduced density matrix ρ
A
(|A| = k) times the number of such reduced
density matrices, S
k
= d
k
N
k
kρ
A
k
2
P
. In contrast
to the N-sector we need not include a correction
for the first term, so that
S
k
= d
k
1
d
1
1
d
k
N
k
!
(1)
k
d
k
1
d
k
1
d
k1
=
N
k
!
1
d
h
(d 1)
k
+ (1)
k
(d 1)
i
. (A5)
Proof maximum N sector of odd-N qubit
GHZ state
Here we show the proof that for odd N qubits,
the maximum N-sector length is max S
N
=
S
N
(GHZ) = 2
N1
, which is realized by the GHZ
state [6].
First, we recall that for odd N qubit states
Π = |ψihψ| the degree-2 SL invariant
H = Tr
h
Π Y
N
Π
Y
N
i
= 0 (A6)
always vanishes [5, 6, 10] (here, Y σ
2
is a
Pauli matrix and Π
= |ψ
ihψ
|, where |ψ
i is
the vector with complex conjugate components).
In terms of sector lengths Eq. (A6) reads [5, 6, 10]
0 =
P
N
k=0
(1)
k
S
k
, so that
S
even
N1
2
X
k=0
S
2k
=
N1
2
X
k=0
S
2k+1
S
odd
,
(A7)
that is, the sum of the even-numbered sector
lengths S
even
always equals that of the
odd-numbered ones, S
odd
. Because of the
purity-0 constraint
P
N
k=0
S
k
= S
even
+ S
odd
= 2
N
this means that both even and odd sector
length sums are always equal to 2
N1
, so that
the properties of a state are encoded in the
distribution of the even sector lengths among
themselves on the one hand, and separately the
odd ones, on the other hand.
It is quite obvious then that the GHZ state
(odd N) is the one with maximum N-sector:
Here, the entire odd sector length 2
N1
is
shifted to the N-sector, and the other odd
sector lengths vanish. (The peculiarity is that
such a state actually does exist this is by
no means guaranteed by Eq. (A7) and the
purity constraint.) Note also that for the GHZ
state, Eq. (A7) does not say anything about the
distribution of the even-numbered sectors.
Now consider the PQ relation, Eq. (13) from
the main text,
S
N
=
1
2
N
N
X
k=0
(1)
k
3
Nk
S
k
=
1
2
N
N1
2
X
l=0
3
N2l
S
2l
N1
2
X
m=0
3
N2m1
S
2m+1
.
(A8)
We see that also from the point of view of
Eq. (A8) the maximum N-sector for the GHZ
state makes perfect sense: All odd sector
contributions are moved to S
N
where they cause
the ‘least damage’ for maximizing the r.h.s. of the
equation, because S
N
has the smallest prefactor.
Proof maximum l.h.s. of Eq. (18) in main text
In the following we demonstrate the last step
of the proof in the main text that max S
N
=
2
N1
+ 1 for even-N qubit GHZ states. This step
consists in maximizing the left-hand side (l.h.s.)
of Eq. (18) of the manuscript,
S
1
+
X
j
2 Tr R
[j]
max ,
where ρ
[j]
= Tr
{j}
Π
x
and Π
x
= |xihx| is a pure
state.
First, let us consider ρ
[1]
= Tr
{1}
Π
x
. We write
the Schmidt decomposition of |xi with respect to
the first qubit,
|xi =
p
λ
1
|0i|X
0
i +
p
1 λ
1
|1i|X
1
i , (A9)
where {|0i, |1i} is the Schmidt basis on the first
qubit and |X
0
i, |X
1
i two orthogonal odd-(N 1)
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qubit states, the Schmidt vectors on qubits
{2 . . . N}. Hence,
ρ
[1]
= λ
1
|X
0
ihX
0
| + (1 λ
1
) |X
1
ihX
1
| ,
(A10)
so that, as for k-qubit states |φi the inverted state
|
˜
φi = Y
k
|φ
i [cf. [5, 9, 10] and the discussion
below Eq. (A6)],
Tr R
[1]
= Tr
h
ρ
[1]
Y
(N1)
ρ
[1]
Y
(N1)
i
= λ
2
1
|hX
0
|
˜
X
0
i|
2
+ (1 λ
1
)
2
hX
1
|
˜
X
1
i|
2
+
+ λ
1
(1 λ
1
)|hX
0
|
˜
X
1
i|
2
+
+ λ
1
(1 λ
1
)|hX
1
|
˜
X
0
i|
2
= 2λ
1
(1 λ
1
)|hX
0
|
˜
X
1
i|
2
= 2λ
1
(1 λ
1
)|hX
0
|Y
(N1)
X
1
i|
2
,
(A11)
because hφ|
˜
φi = 0 for odd-N qubit states [see also
Eq. (A6)]. For the matrix element in Eq. (A11)
we have
= |hX
0
|Y
(N1)
X
1
i| 5 1 , (A12)
since the operator Y
(N1)
has only eigenvalues
of modulus 1. Consequently we find, if we add
the 1-sector S
(1)
1
of the 1st qubit in Π
x
,
max
|xi
h
S
(1)
1
+ 2 Tr R
[1]
i
=
= max
λ
1
,
h
2λ
2
1
+ 2(1 λ
1
)
2
1 + 4λ
1
(1 λ
1
)∆
2
i
= 1 . (A13)
The states |X
0
i, |X
1
i that realize this maximum
are, e.g., |X
0
i = |0i
(N1)
and |X
1
i = |1i
(N1)
.
That is, an even-N qubit state that maximizes
the l.h.s. of Eq. (A13) is, e.g., the GHZ state |xi =
1
2
|0i
N
+ |1i
N
.
The same reasoning as above can be applied
for all qubits j = 1 . . . N, so that we find for the
symmetrized l.h.s. of Eq. (A13),
max
|xi
S
1
+
X
j
2 Tr R
[j]
= N , (A14)
with the GHZ state attaining the maximum.
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for general N-qubit states, Phys. Rev. Lett.
88, 210401 (2002).
[19] M. Teodorescu-Frumosu and G. Jaeger,
Quantum Lorentz-group invariants of
n-qubit systems, Phys. Rev. A 67, 052305
(2003).
[20] H. Aschauer, J. Calsamiglia, M. Hein,
and H.J. Briegel, Local invariants for
multi-partite entangled states allowing for
a simple entanglement criterion, Quantum
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arXiv.org link.
[21] A. J. Scott, Multipartite entanglement,
quantum error correcting codes, and
entangling power of quantum evolutions,
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the Bloch representation of density matrices,
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[23] J.I. de Vicente, Further results on
entanglement detection and quantification
from the correlation matrix criterion, J.
Phys. A: Math. Theor. 41, 065309 (2008).
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and M. Żukowski, Correlation-tensor
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[26] J.I. de Vicente and M. Huber, Multipartite
entanglement detection from correlation
tensors, Phys. Rev. A 84, 062306 (2011).
[27] We will use the term k-sector length”
instead of “squared k-sector length” following
Ref. [6]. In the present context this does not
lead to confusion.
[28] One may imagine very different correlation
quantifiers, e.g., D. Girolami, T. Tufarelli,
and C.E. Susa, Quantifying Genuine
Multipartite Correlations and their Pattern
Complexity, Phys. Rev. Lett. 119, 140505
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de Rosier, W. Laskowski, T. Paterek, and
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Entanglement without Multipartite
Correlations, Phys. Rev. Lett. 114, 180501
(2015).
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L. Knips, W. Laskowski, T. Paterek,
and H. Weinfurter, Genuine N -partite
entanglement without N-partite correlation
functions, Phys. Rev. A 95, 062331 (2017).
[32] W. Klobus, W. Laskowski, T. Paterek,
M. Wiesniak, and H. Weinfurter,
Higher dimensional entanglement without
correlations, Eur. Phys. J. D 73, 29 (2019).
[33] This relation corresponds to a special case
of the quantum MacWilliams identity, cf.
Ref. [11].
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Distributed entanglement, Phys. Rev. A 61,
052306 (2000).
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Hillery, and G.J. Milburn, Universal state
inversion and concurrence in arbitrary
dimensions, Phys. Rev. A 64, 042315 (2001).
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separability, Phys. Rev. A 72, 022311 (2005).
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S. Rana, and J. Samsonowicz, Sufficient
separability criteria and linear maps, Phys.
Rev. A 93, 042335 (2016).
Accepted in Quantum 2020-02-03, click title to verify. Published under CC-BY 4.0. 10
[38] An in-depth analysis of this projection
operator will be carried out in forthcoming
work.
[39] D. Goyeneche and K. Życzkowski, Genuinely
multipartite entangled states and orthogonal
arrays, Phys. Rev. A 90, 022316 (2014).
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A. Riera, and K. Życzkowski, Absolutely
maximally entangled states, combinatorial
designs, and multiunitary matrices, Phys.
Rev. A 92, 032316 (2015).
Accepted in Quantum 2020-02-03, click title to verify. Published under CC-BY 4.0. 11 | 2022-12-06T03:29:20 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.82236647605896, "perplexity": 9985.763354366962}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711069.79/warc/CC-MAIN-20221206024911-20221206054911-00548.warc.gz"} |
https://par.nsf.gov/biblio/10361566-galactic-chemical-evolution-radioactive-isotopes-process-contribution | Galactic Chemical Evolution of Radioactive Isotopes with an s-process Contribution
Abstract
Analysis of inclusions in primitive meteorites reveals that several short-lived radionuclides (SLRs) with half-lives of 0.1–100 Myr existed in the early solar system (ESS). We investigate the ESS origin of107Pd,135Cs, and182Hf, which are produced byslowneutron captures (thes-process) in asymptotic giant branch (AGB) stars. We modeled the Galactic abundances of these SLRs using theOMEGA+galactic chemical evolution (GCE) code and two sets of mass- and metallicity-dependent AGB nucleosynthesis yields (Monash and FRUITY). Depending on the ratio of the mean-lifeτof the SLR to the average length of time between the formations of AGB progenitorsγ, we calculate timescales relevant for the birth of the Sun. Ifτ/γ≳ 2, we predict self-consistent isolation times between 9 and 26 Myr by decaying the GCE predicted107Pd/108Pd,135Cs/133Cs, and182Hf/180Hf ratios to their respective ESS ratios. The predicted107Pd/182Hf ratio indicates that our GCE models are missing 9%–73% of107Pd and108Pd in the ESS. This missing component may have come from AGB stars of higher metallicity than those that contributed to the ESS in our GCE code. Ifτ/γ≲ 0.3, we calculate instead the time (TLE) from the last nucleosynthesis event that added the SLRs into the presolar matter to the formation of the oldest solids in the ESS. For the 2M,Z= 0.01 more »
Authors:
; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10361566
Journal Name:
The Astrophysical Journal
Volume:
924
Issue:
1
Page Range or eLocation-ID:
Article No. 10
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
Gravitational-wave (GW) detections of binary black hole (BH) mergers have begun to sample the cosmic BH mass distribution. The evolution of single stellar cores predicts a gap in the BH mass distribution due to pair-instability supernovae (PISNe). Determining the upper and lower edges of the BH mass gap can be useful for interpreting GW detections of merging BHs. We useMESAto evolve single, nonrotating, massive helium cores with a metallicity ofZ= 10−5, until they either collapse to form a BH or explode as a PISN, without leaving a compact remnant. We calculate the boundaries of the lower BH mass gap for S-factors in the range S(300 keV) = (77,203) keV b, corresponding to the ±3σuncertainty in our high-resolution tabulated12C(α,γ)16O reaction rate probability distribution function. We extensively test temporal and spatial resolutions for resolving the theoretical peak of the BH mass spectrum across the BH mass gap. We explore the convergence with respect to convective mixing and nuclear burning, finding that significant time resolution is needed to achieve convergence. We also test adopting a minimum diffusion coefficient to help lower-resolution models reach convergence. We establish a new lower edge of the upper mass gap asMlower$60−14+32$Mfrom the ±3σuncertainty inmore » | 2023-01-27T07:25:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6100537776947021, "perplexity": 4278.011598784252}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494974.98/warc/CC-MAIN-20230127065356-20230127095356-00557.warc.gz"} |
http://dlmf.nist.gov/34.14 | # §34.14 Tables
Tables of exact values of the squares of the $3j$ and $6j$ symbols in which all parameters are $\leq 8$ are given in Rotenberg et al. (1959), together with a bibliography of earlier tables of $3j,6j$, and $9j$ symbols on pp. 33–36.
Tables of $3j$ and $6j$ symbols in which all parameters are $\leq 17/2$ are given in Appel (1968) to 6D. Some selected $9j$ symbols are also given. Other tabulations for $3j$ symbols are listed on pp. 11-12; for $6j$ symbols on pp. 16-17; for $9j$ symbols on p. 21.
Biedenharn and Louck (1981) give tables of algebraic expressions for Clebsch–Gordan coefficients and $6j$ symbols, together with a bibliography of tables produced prior to 1975. In Varshalovich et al. (1988) algebraic expressions for the Clebsch–Gordan coefficients with all parameters $\leq 5$ and numerical values for all parameters $\leq 3$ are given on pp. 270–289; similar tables for the $6j$ symbols are given on pp. 310–332, and for the $9j$ symbols on pp. 359, 360, 372–411. Earlier tables are listed on p. 513. | 2015-04-25T23:21:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 21, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8232828974723816, "perplexity": 612.0000683124514}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246651873.94/warc/CC-MAIN-20150417045731-00129-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://dergipark.gov.tr/ieja/issue/25194/266215 | Yıl 2015, Cilt 17, Sayı 17, Sayfalar 105 - 138 2015-06-01
| | | |
DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3: THE p ≥ 5 CASE
C. Bowman [1] , S. R. Doty [2] , S. Martin [3]
244 213
We study the structure of the indecomposable direct summands of tensor products of two restricted rational simple modules for the algebraic group SL3(K), where K is an algebraically closed field of characteristic p ≥ 5. We also give a characteristic-free algorithm for the decomposition of such a tensor product into indecomposable direct summands. The p < 5 case was studied in the authors’ earlier paper [4]. We find that for characteristics p ≥ 5 all the indecomposable summands are rigid, in contrast to the characteristic 3 case.
Algebraic groups, tilting modules, Weyl modules, quivers
Konular JA83CK95UH Makaleler Yazar: C. Bowman Yazar: S. R. Doty Yazar: S. Martin
Bibtex @ { ieja266215, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2015}, volume = {17}, pages = {105 - 138}, doi = {10.24330/ieja.266215}, title = {DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3: THE p ≥ 5 CASE}, key = {cite}, author = {Doty, S. R. and Martin, S. and Bowman, C.} } APA Bowman, C , Doty, S , Martin, S . (2015). DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3: THE p ≥ 5 CASE. International Electronic Journal of Algebra, 17 (17), 105-138. DOI: 10.24330/ieja.266215 MLA Bowman, C , Doty, S , Martin, S . "DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3: THE p ≥ 5 CASE". International Electronic Journal of Algebra 17 (2015): 105-138 Chicago Bowman, C , Doty, S , Martin, S . "DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3: THE p ≥ 5 CASE". International Electronic Journal of Algebra 17 (2015): 105-138 RIS TY - JOUR T1 - DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3: THE p ≥ 5 CASE AU - C. Bowman , S. R. Doty , S. Martin Y1 - 2015 PY - 2015 N1 - doi: 10.24330/ieja.266215 DO - 10.24330/ieja.266215 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 105 EP - 138 VL - 17 IS - 17 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266215 UR - http://dx.doi.org/10.24330/ieja.266215 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3: THE p ≥ 5 CASE %A C. Bowman , S. R. Doty , S. Martin %T DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3: THE p ≥ 5 CASE %D 2015 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 17 %N 17 %R doi: 10.24330/ieja.266215 %U 10.24330/ieja.266215 ISNAD Bowman, C. , Doty, S. R. , Martin, S. . "DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3: THE p ≥ 5 CASE". International Electronic Journal of Algebra 17 / 17 (Haziran 2015): 105-138. http://dx.doi.org/10.24330/ieja.266215 | 2019-01-19T20:42:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.672879695892334, "perplexity": 5469.607117590001}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583681597.51/warc/CC-MAIN-20190119201117-20190119223117-00621.warc.gz"} |
https://www.lessonplanet.com/teachers/proofs-of-derivatives-of-ln-x-and-e6x | # Proofs of Derivatives of Ln(x) and e6x
In this video, Sal takes on the challenge of proving both the derivative of ln x = 1/x and of ex = ex, showing that no circular logic is used in the proof. It contains a clearer version of both proofs shown in the videos titled, _Proof d/dx e^x = e^x” and _Proof: d/dx (ln x) = 1/x.”
Resource Details
11th - Higher Ed
Subjects
Math
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Videos
1 more...
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For Teacher Use
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Flipped Classroom
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Creative Commons
BY-NC-SA: 3.0 | 2019-03-20T11:06:36 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8464200496673584, "perplexity": 9458.927651379332}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202326.46/warc/CC-MAIN-20190320105319-20190320131319-00421.warc.gz"} |
https://googology.wikia.org/wiki/Googolplexiduexitrex | 10,666 Pages
The googolplexiduexitrex is equal to \( 10\uparrow\uparrow\uparrow\)googolplexiduex using arrow notation.[1] The term was coined by Wikia user Username5243.
• In Bird's array notation, it would be equal to \([10,[10,[10,[10,100] ],2],3]\). (Trivially, this is \(\{10,\{10,\{10,\{10,100\}\},2\},3\}\) in BEAF.)
• In the FGH, this is very roughly \(f_4(f_3(f_2^2(100)))\).
## Sources
Community content is available under CC-BY-SA unless otherwise noted. | 2020-11-24T07:04:57 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8568488955497742, "perplexity": 11446.778718864243}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141171126.6/warc/CC-MAIN-20201124053841-20201124083841-00582.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Atemam.roger-m | zbMATH — the first resource for mathematics
Temam, Roger Meyer
Compute Distance To:
Author ID: temam.roger-m Published as: Temam, Roger; Temam, R.; Témam, Roger; Temam, Roger M.; Témam, R.; Temam, R. M. External Links: MGP · Wikidata · GND
Documents Indexed: 482 Publications since 1966, including 41 Books Biographic References: 5 Publications
all top 5
Co-Authors
106 single-authored 59 Foiaş, Ciprian Ilie 25 Jung, Changyeol 21 Wang, Shouhong 18 Tribbia, Joseph J. 17 Manley, Oscar P. 17 Rosa, Ricardo M. S. 16 Lions, Jacques-Louis 15 Wang, Xiaoming 14 Hamouda, Makram 14 Petcu, Madalina 14 Ziane, Mohammed 13 Nicolaenko, Basil 12 Marion, Martine 10 Debussche, Arnaud 10 Ghidaglia, Jean-Michel 10 Jauberteau, François 8 Constantin, Peter 8 Dubois, Thierry 8 Huang, Aimin 8 Miranville, Alain M. 7 Bousquet, Arthur 7 Chen, Qingshan 7 Laminie, Jacques 7 Saut, Jean-Claude 7 Tachim Medjo, Theodore 7 Wirosoetisno, Djoko 6 Gie, Gung-Min 6 Glatt-Holtz, Nathan E. 6 Hong, Youngjoon 6 Rakotoson, Jean-Michel 6 Rousseau, Antoine 5 di Plinio, Francesco 5 Ewald, Brian D. 5 Faure, Sylvain 5 Jolly, Michael S. 5 Sell, George Roger 4 Bensoussan, Alain 4 Bewley, Thomas R. 4 Cao, Yining 4 Chekroun, Mickaël D. 4 Coti Zelati, Michele 4 Cyr, Justin 4 Ekeland, Ivar 4 Giorgini, Andrea 4 Hu, Changbing 4 Kukavica, Igor 4 Qin, Zhen 4 Samelson, Roger M. 4 Scheurer, Bruno 4 Shen, Jie 4 Simonnet, Eric 4 Strang, William Gilbert 3 Abergel, Frédéric 3 Boujot, Jean-Paul 3 Brauner, Claude-Michel 3 Eden, Alp 3 Lichnewsky, Alain 3 Moin, Parviz 3 Moise, Ioana 3 Mossino, Jacqueline 3 Park, Eunhee 3 Penel, Patrick 3 Pham, Du 3 Promislow, Keith Steven 3 Shiue, Ming-Cheng 3 Tang, Sisi 3 Wang, Chuntian 2 Baranger, Jacques 2 Cabral, Marco 2 Cheng, Wenfang 2 Demengel, Françoise 2 Dettori, Lucia 2 Duane, Gregory S. 2 Guillopé, Colette 2 Han, Daozhi 2 Jia, Chuck 2 Kohn, Robert Vita 2 Link, Joshua A. 2 Morera, J. P. 2 Oleĭnik, Ol’ga Arsen’evna 2 Pascal, Frédéric P. 2 Pata, Vittorino 2 Peyret, Roger 2 Rosier, Carole 2 Tawri, Krutika 2 Vicol, Vlad C. 2 Wang, Cheng 2 Wang, Xiaoyan 1 Bardos, Claude Williams 1 Barnhill, Robert E. 1 Bercovici, Hari 1 Bercovier, Michel 1 Böhm, Wolfgang 1 Brefort, B. 1 Bruneau, Charles-Henri 1 Cabannes, Henri 1 Calgaro, Caterina 1 Chattot, Jean-Jacques 1 Chehab, Jean-Paul 1 Chepyzhov, Vladimir V. ...and 38 more Co-Authors
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all top 5
Fields
303 Partial differential equations (35-XX) 232 Fluid mechanics (76-XX) 100 Numerical analysis (65-XX) 77 Geophysics (86-XX) 56 Dynamical systems and ergodic theory (37-XX) 55 Calculus of variations and optimal control; optimization (49-XX) 33 Mechanics of deformable solids (74-XX) 27 Ordinary differential equations (34-XX) 22 Probability theory and stochastic processes (60-XX) 19 Global analysis, analysis on manifolds (58-XX) 14 Functional analysis (46-XX) 14 Operator theory (47-XX) 13 General and overarching topics; collections (00-XX) 9 Systems theory; control (93-XX) 8 Real functions (26-XX) 8 Operations research, mathematical programming (90-XX) 7 Biology and other natural sciences (92-XX) 6 Measure and integration (28-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 History and biography (01-XX) 3 Approximations and expansions (41-XX) 2 Convex and discrete geometry (52-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
Citations contained in zbMATH Open
418 Publications have been cited 16,039 times in 10,142 Documents Cited by Year
Infinite-dimensional dynamical systems in mechanics and physics. 2nd ed. Zbl 0871.35001
Temam, Roger
1997
Infinite-dimensional dynamical systems in mechanics and physics. Zbl 0662.35001
Temam, Roger
1988
Navier-Stokes equations. Theory and numerical analysis. Zbl 0383.35057
Temam, Roger
1977
Convex analysis and variational problems. Translated by Minerva Translations, Ltd., London. Zbl 0322.90046
Ekeland, Ivar; Temam, Roger
1976
Navier-Stokes equations. Theory and numerical analysis. 3rd (rev.) ed. Zbl 0568.35002
Temam, Roger
1984
Navier-Stokes equations. Theory and numerical analysis. Rev. ed. Zbl 0426.35003
Temam, Roger
1979
Some mathematical questions related to the MHD equations. Zbl 0524.76099
Sermange, Michel; Temam, Roger
1983
Navier-Stokes equations. Theory and numerical analysis. Repr. with corr. Repr. with corr. Zbl 0981.35001
Temam, Roger
2001
Convex analysis and variational problems. Unabridged, corrected republication of the 1976 English original. Zbl 0939.49002
Ekeland, Ivar; Témam, Roger
1999
Convex analysis and variational problems. (Analyse convexe et problèmes variationnels.) Zbl 0281.49001
Ekeland, Ivar; Temam, Roger
1974
Navier-Stokes equations and nonlinear functional analysis. 2nd ed. Zbl 0833.35110
Temam, Roger
1995
Navier-Stokes equations and turbulence. Zbl 0994.35002
Foias, C.; Rosa, R.; Manley, O.; Temam, R.
2001
Inertial manifolds for nonlinear evolutionary equations. Zbl 0643.58004
Foias, Ciprian; Sell, George R.; Temam, Roger
1988
Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations. Zbl 0454.35073
Foiaş, Ciprian; Temam, R.
1979
Sur l’approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires. II. Zbl 0207.16904
Témam, R.
1969
Gevrey class regularity for the solutions of the Navier-Stokes equations. Zbl 0702.35203
Foias, C.; Temam, R.
1989
Attractors for Navier-Stokes equations. Zbl 0572.35083
Temam, R.
1985
Navier-Stokes equations and nonlinear functional analysis. Zbl 0522.35002
Temam, Roger
1983
Exponential attractors for dissipative evolution equations. Zbl 0842.58056
Eden, A.; Foias, C.; Nicolaenko, B.; Temam, R.
1994
On the equations of the large-scale ocean. Zbl 0766.35039
Lions, Jacques-Louis; Temam, Roger; Wang, Shouhong
1992
Structure of the set of stationary solutions of the Navier Stokes equations. Zbl 0335.35077
Foiaş, Ciprian; Temam, R.
1977
Integral manifolds and inertial manifolds for dissipative partial differential equations. Zbl 0683.58002
Constantin, P.; Foias, C.; Nicolaenko, B.; Temam, R.
1989
On some control problems in fluid mechanics. Zbl 0708.76106
Abergel, F.; Temam, R.
1990
New formulations of the primitive equations of atmosphere and applications. Zbl 0746.76019
Lions, Jacques Louis; Temam, Roger; Wang, Shouhong
1992
Nonlinear Galerkin methods. Zbl 0683.65083
Marion, Martine; Temam, Roger
1989
Equations stochastiques du type Navier-Stokes. Zbl 0265.60094
Bensoussan, A.; Temam, R.
1973
Une méthode d’approximation de la solution des équations de Navier-Stokes. Zbl 0181.18903
Temam, R.
1968
Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors. Zbl 0592.35013
Nicolaenko, B.; Scheurer, B.; Temam, R.
1985
Modelling of the interaction of small and large eddies in two dimensional turbulent flows. Zbl 0663.76054
Foias, C.; Manley, O.; Temam, R.
1988
On the Euler equations of incompressible perfect fluids. Zbl 0309.35061
Temam, Roger
1975
Attractors representing turbulent flows. Zbl 0567.35070
Constantin, P.; Foiaş, Ciprian; Temam, R.
1985
Attractors for the Bénard problem: Existence and physical bounds on their fractal dimension. Zbl 0646.76098
Foias, C.; Manley, O.; Temam, R.
1987
Sur l’approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires. I. Zbl 0195.46001
Temam, R.
1969
Functions of bounded deformation. Zbl 0472.73031
Temam, Roger; Strang, Gilbert
1980
Stochastic Burgers’ equation. Zbl 0824.35112
Da Prato, Giuseppe; Debussche, Arnaud; Temam, Roger
1994
Problèmes mathématiques en plasticité. Zbl 0547.73026
Temam, Roger
1983
DNS-based predictive control of turbulence: An optimal benchmark for feedback algorithms. Zbl 1036.76027
Bewley, Thomas R.; Moin, Parviz; Temam, Roger
2001
Mathematical problems in plasticity. Zbl 0457.73017
Temam, R.
1980
Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension. Zbl 0694.35028
Foias, C.; Nicolaenko, B.; Sell, G. R.; Temam, R.
1988
Attractors for damped nonlinear hyperbolic equations. Zbl 0572.35071
Ghidaglia, J. M.; Temam, R.
1987
Some global dynamical properties of a class of pattern formation equations. Zbl 0691.35019
Nicolaenko, B.; Scheurer, B.; Temam, R.
1989
Convex functions of a measure and applications. Zbl 0581.46036
Demengel, F.; Temam, R.
1984
Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation. Zbl 0384.35047
Foiaş, Ciprian; Temam, R.
1978
A non-linear eigenvalue problem: the shape at equilibrium of a confined plasma. Zbl 0328.35069
Temam, R.
1975
Dual spaces of stresses and strains, with applications to Hencky plasticity. Zbl 0532.73039
Kohn, Robert V.; Temam, Roger
1983
On the dimension of the attractors in two-dimensional turbulence. Zbl 0658.58030
Constantin, P.; Foias, C.; Temam, R.
1988
Asymptotic analysis of the Navier-Stokes equations. Zbl 0584.35007
Foiaş, Ciprian; Manley, O. P.; Temam, R.; Treve, Y. M.
1983
Determining modes and fractal dimension of turbulent flows. Zbl 0607.76054
Constantin, P.; Foias, C.; Manley, O. P.; Temam, R.
1985
Remarks on the Korteweg-de Vries equation. Zbl 0334.35062
Saut, J. C.; Temam, R.
1976
Boundary layers associated with incompressible Navier-Stokes equations: the noncharacteristic boundary case. Zbl 0997.35042
Temam, R.; Wang, X.
2002
Mathematical theory for the coupled atmosphere-ocean models (CAO III). Zbl 0866.76025
Lions, Jacques-Louis; Temam, Roger; Wang, Shouhong
1995
Some mathematical problems in geophysical fluid dynamics. Zbl 1222.35145
Temam, Roger; Ziane, Mohammed
2004
Behaviour at time t=0 of the solutions of semi-linear evolution equations. Zbl 0446.35057
Temam, R.
1982
Remarks on a free boundary value problem arising in plasma physics. Zbl 0355.35023
Temam, R.
1977
Nonlinear Galerkin methods: The finite elements case. Zbl 0702.65081
Marion, M.; Temam, R.
1990
Determination of the solutions of the Navier-Stokes equations by a set of nodal values. Zbl 0563.35058
Foiaş, Ciprian; Temam, Roger
1984
Feedback control for unsteady flow and its application to the stochastic Burgers equation. Zbl 0810.76012
Choi, Haecheon; Temam, Roger; Moin, Parviz; Kim, John
1993
Sur un problème non linéaire. Zbl 0187.03902
Temam, R.
1969
Inertial manifolds and multigrid methods. Zbl 0715.35039
Temam, R.
1990
Models of the coupled atmosphere and ocean (CAO I). Zbl 0805.76011
Lions, J. L.; Temam, R.; Wang, S.
1993
Generic properties of nonlinear boundary value problems. Zbl 0462.35016
Saut, J. C.; Temam, R.
1979
Navier-Stokes equations in three-dimensional thin domains with various boundary conditions. Zbl 0864.35083
Temam, R.; Ziane, M.
1996
Duality and relaxation in the variational problems of plasticity. Zbl 0465.73033
Temam, Roger; Strang, Gilbert
1980
Pseudo solutions of the time-dependent minimal surface problem. Zbl 0368.49016
Lichnewsky, A.; Temam, R.
1978
Directional derivative of the increasing rearrangement mapping and application to a queer differential equation in plasma physics. Zbl 0476.35031
Mossino, J.; Temam, R.
1981
Spectral barriers and inertial manifolds for dissipative partial differential equations. Zbl 0701.35024
Constantin, P.; Foias, C.; Nicolaenko, B.; Témam, R.
1989
Incremental unknowns, multilevel methods and the numerical simulation of turbulence. Zbl 0948.76070
Dubois, T.; Jauberteau, F.; Temam, R.
1998
On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity. Zbl 1043.35127
Temam, Roger; Wang, Xiaoming
1997
Navier-Sotkes equations: Theory and approximation. Zbl 0921.76040
Marion, Martine; Temam, Roger
1998
Local martingale and pathwise solutions for an abstract fluids model. Zbl 1230.60065
Debussche, Arnaud; Glatt-Holtz, Nathan; Temam, Roger
2011
Equations aux dérivées partielles stochastiques non linéaires. I. Zbl 0241.35009
Bensoussan, A.; Temam, R.
1972
The primitive equations on the large scale ocean under the small depth hypothesis. Zbl 1048.35082
Hu, Changbing; Temam, Roger; Ziane, Mohammed
2003
Navier-Stokes equations. Theory and numerical analysis. (Uravnenie Nav’e - Stoksa. Teoriya i chislennyj analiz). Transl. from the English. Zbl 0529.35002
Temam, Roger
1981
Convex analysis and variational problems. Translated from the English by V. M. Tikhomirov. (Выпуклый анализ и вариационные проблемы.) Zbl 0546.90057
Ekeland, Ivar; Temam, Roger
1979
Numerical analysis of the coupled atmosphere-ocean models (CAO II). Zbl 0805.76052
Lions, J. L.; Temam, R.; Wang, S.
1993
Navier-Stokes equations in thin spherical domains. Zbl 0891.35119
Temam, R.; Ziane, M.
1997
A generalized Norton-Hoff model and the Prandtl-Reuss law of plasticity. Zbl 0615.73035
Temam, Roger
1986
A general framework for robust control in fluid mechanics. Zbl 0981.76026
Bewley, Thomas R.; Temam, Roger; Ziane, Mohammed
2000
Sur la stabilité et la convergence de la méthode des pas fractionnaires. Zbl 0174.45804
Temam, R.
1968
A co-area formula with applications to monotone rearrangement and to regularity. Zbl 0735.49039
Rakotoson, Jean Michel; Temam, Roger
1990
Incremental unknowns for solving partial differential equations. Zbl 0712.65103
Chen, Min; Temam, Roger
1991
New a priori estimates for Navier-Stokes equations in dimension 3. Zbl 0472.35070
Foiaş, Ciprian; Guillopé, Colette; Témam, Roger
1981
On the anti-plane shear problem in finite elasticity. Zbl 0496.73036
Gurtin, Morton E.; Temam, Roger
1981
Asymptotic numerical analysis for the Navier-Stokes equations. Zbl 0555.76030
Foiaş, Ciprian; Temam, R.
1983
Remark on the pressure boundary condition for the projection method. Zbl 0738.76054
Temam, R.
1991
Attractors for the penalized Navier-Stokes equations. Zbl 0696.35131
Brefort, B.; Ghidaglia, J. M.; Temam, R.
1988
Incremental unknowns in finite differences: Condition number of the matrix. Zbl 0773.65080
Chen, Min; Temam, Roger
1993
Asymptotic analysis of Oseen type equations in a channel at small viscosity. Zbl 0881.35097
Temam, Roger; Wang, Xiaoming
1996
Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain. Zbl 1204.35129
Kukavica, Igor; Temam, Roger; Vicol, Vlad C.; Ziane, Mohammed
2011
Some mathematical properties of the planetary geostrophic equations for large-scale ocean circulation. Zbl 1027.86002
Samelson, R.; Temam, R.; Wang, S.
1998
Mathematical modelling in continuum mechanics. 2nd ed. Zbl 1077.76001
Temam, Roger; Miranville, Alain M.
2005
Variétés inertielles des équations différentielles dissipatives. (Inertial manifolds for dissipative differential equations). Zbl 0591.35062
Foiaş, Ciprian; Sell, George R.; Témam, Roger
1985
Generalization of the Sobolev-Lieb-Thirring inequalities and applications to the dimension of attractors. Zbl 0745.46037
Ghidaglia, Jean-Michel; Marion, Martine; Temam, Roger
1988
Attractors for the Navier-Stokes equations: Localization and approximation. Zbl 0698.58040
Temam, R.
1989
Local and global Lyapunov exponents. Zbl 0718.34080
Eden, A.; Foias, C.; Temam, R.
1991
On the large time Galerkin approximation of the Navier-Stokes equations. Zbl 0551.76021
Constantin, P.; Foiaş, Ciprian; Temam, R.
1984
Solution of the incompressible Navier-Stokes equations by the nonlinear Galerkin method. Zbl 0783.76068
Dubois, T.; Jauberteau, F.; Temam, R.
1993
An initial boundary-value problem for the Zakharov-Kuznetsov equation. Zbl 1219.35253
Saut, Jean-Claude; Temam, Roger
2010
A nonlinear Galerkin method for the Navier-Stokes equations. Zbl 0722.76039
Jauberteau, F.; Rosier, C.; Temam, R.
1990
On mathematical problems for the primitive equations of the ocean: The mesoscale midlatitude case. Zbl 0978.76102
Lions, Jacques L.; Temam, Roger; Wang, Shouhong
2000
The Stampacchia maximum principle for stochastic partial differential equations forced by Lévy noise. Zbl 1446.35274
Nguyen, Phuong; Temam, Roger
2020
Review of local and global existence results for stochastic PDEs with Lévy noise. Zbl 1447.35003
Cyr, Justin; Nguyen, Phuong; Tang, Sisi; Temam, Roger
2020
Weak and strong solutions to the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system. Zbl 1452.35151
Giorgini, Andrea; Temam, Roger
2020
Uniqueness and regularity for the Navier-Stokes-Cahn-Hilliard System. Zbl 1419.35160
Giorgini, Andrea; Miranville, Alain; Temam, Roger
2019
Properties of stationary statistical solutions of the three-dimensional Navier-Stokes equations. Zbl 1421.35243
Foias, Ciprian; Rosa, Ricardo M. S.; Temam, Roger M.
2019
Stochastic one layer shallow water equations with Lévy noise. Zbl 1420.35479
Cyr, Justin; Nguyen, Phuong; Temam, Roger
2019
Mathematical analysis of the Jin-Neelin model of El Niño-Southern-Oscillation. Zbl 1405.35079
Cao, Yining; Chekroun, Mickaël D.; Huang, Aimin; Temam, Roger
2019
A result of uniqueness of solutions of the Shigesada-Kawasaki-Teramoto equations. Zbl 1437.35433
Pham, Du; Temam, Roger
2019
Linear diffusion with singular absorption potential and/or unbounded convective flow: the weighted space approach. Zbl 1374.35178
Díaz, Jesus Ildefonso; Gómez-Castro, David; Rakotoson, Jean Michel; Temam, Roger
2018
Singular perturbations and boundary layers. Zbl 1411.35002
Gie, Gung-Min; Hamouda, Makram; Jung, Chang-Yeol; Temam, Roger M.
2018
The Euler equations of an inviscid incompressible fluid driven by a Lévy noise. Zbl 1406.35246
Cyr, Justin; Tang, Sisi; Temam, Roger
2018
Navier-Stokes-Voigt equations with memory in 3D lacking instantaneous kinematic viscosity. Zbl 1384.35059
Di Plinio, Francesco; Giorgini, Andrea; Pata, Vittorino; Temam, Roger
2018
A comparison of two settings for stochastic integration with respect to Lévy processes in infinite dimensions. Zbl 1403.60043
Cyr, Justin; Tang, Sisi; Temam, Roger
2018
Mathematical problems in plasticity. Translated from the French by L. S. Orde. With a new preface and a new appendix by Jean-François Babadjian and the author. Reprint of the English translation published by Gauthier-Villars 1985. Zbl 1406.74002
Temam, Roger
2018
The equations of the multi-phase humid atmosphere expressed as a quasi variational inequality. Zbl 1395.35128
Cao, Yining; Hamouda, Makram; Temam, Roger; Tribbia, Joseph; Wang, Xiaoyan
2018
Boundary layer analysis for the stochastic nonlinear reaction-diffusion equations. Zbl 1398.35119
Hong, Youngjoon; Jung, Chang-Yeol; Temam, Roger
2018
Weak solutions of the Shigesada-Kawasaki-Teramoto equations and their attractors. Zbl 1371.35160
Pham, Du; Temam, Roger
2017
Time discrete approximation of weak solutions to stochastic equations of geophysical fluid dynamics and applications. Zbl 1368.35266
Glatt-Holtz, Nathan; Temam, Roger; Wang, Chuntian
2017
Boundary layer analysis of nonlinear reaction-diffusion equations in a smooth domain. Zbl 1368.35023
Jung, Chang-Yeol; Park, Eunhee; Temam, Roger
2017
Numerical approximation of a variational inequality related to the humid atmosphere. Zbl 1371.35225
Temam, Roger; Wang, Xiaoyan
2017
Local martingale solutions to the stochastic one layer shallow water equations. Zbl 1387.60101
Link, Joshua; Nguyen, Phuong; Temam, Roger
2017
Modeling the lid driven flow: theory and computation. Zbl 1375.76042
Hamouda, Makram; Temam, Roger; Zhang, Le
2017
Recent progresses in boundary layer theory. Zbl 1343.35016
Temam, Roger; Jung, Chang-Yeol; Gie, Gung-Min
2016
The Stampacchia maximum principle for stochastic partial differential equations and applications. Zbl 1343.35247
Chekroun, Mickaël D.; Park, Eunhee; Temam, Roger
2016
On the Cahn-Hilliard-Oono-Navier-Stokes equations with singular potentials. Zbl 1349.35171
Miranville, Alain; Temam, Roger
2016
Boundary layers for the 3D primitive equations in a cube: the supercritical modes. Zbl 1382.35306
Hamouda, Makram; Jung, Chang-Yeol; Temam, Roger
2016
Existence and regularity results for the inviscid primitive equations with lateral periodicity. Zbl 1351.35138
Hamouda, Makram; Jung, Chang-Yeol; Temam, Roger
2016
Towards the modeling of nanoindentation of virus shells: do substrate adhesion and geometry matter? Zbl 1376.92009
Bousquet, Arthur; Dragnea, Bogdan; Tayachi, Manel; Temam, Roger
2016
Finite volume approximation of stiff problems on two-dimensional curvilinear domain. Zbl 1356.65232
Faure, Sylvain; Tekitek, Mohamed Mahdi; Temam, Roger
2016
Preface: In memory of A. V. Balakrishnan. Zbl 1341.01041
Bensoussan, Alain; Kukavica, Igor; Lasiecka, Irena; Mitter, Sanjoy; Temam, Roger; Triggiani, Roberto
2016
The primitive equations of the atmosphere in presence of vapour saturation. Zbl 1308.35233
Zelati, Michele Coti; Huang, Aimin; Kukavica, Igor; Temam, Roger; Ziane, Mohammed
2015
Global existence for fully nonlinear reaction-diffusion systems describing multicomponent reactive flows. Zbl 1323.35076
Marion, Martine; Temam, Roger
2015
Convergence of time averages of weak solutions of the three-dimensional Navier-Stokes equations. Zbl 1357.35246
Foias, Ciprian; Rosa, Ricardo M. S.; Temam, Roger M.
2015
Finite dimensions of the global attractor for 3D primitive equations with viscosity. Zbl 1311.35223
Ju, Ning; Temam, Roger
2015
Grisvard’s shift theorem near $$L^\infty$$ and Yudovich theory on polygonal domains. Zbl 1321.35047
Di Plinio, Francesco; Temam, Roger
2015
The nonlinear 2D supercritical inviscid shallow water equations in a rectangle. Zbl 1326.35275
Huang, Aimin; Petcu, Madalina; Temam, Roger
2015
Singular perturbation analysis of time dependent convection-diffusion equations in a circle. Zbl 1320.35026
Hong, Youngjoon; Jung, Chang-Yeol; Temam, Roger
2015
Numerical simulations of the humid atmosphere above a mountain. Zbl 1364.86014
Bousquet, Arthur; Chekroun, Mickaël D.; Hong, Youngjoon; Temam, Roger M.; Tribbia, Joseph
2015
Formulation of the equations of the humid atmosphere in the context of variational inequalities. Zbl 1321.35175
Temam, Roger; Wu, Kakuen John
2015
The 2d nonlinear fully hyperbolic inviscid shallow water equations in a rectangle. Zbl 1344.35102
Huang, Aimin; Temam, Roger
2015
On the numerical approximations of stiff convection-diffusion equations in a circle. Zbl 1295.65112
Hong, Youngjoon; Jung, Chang-Yeol; Temam, Roger
2014
The linearized 2D inviscid shallow water equations in a rectangle: boundary conditions and well-posedness. Zbl 1293.35247
Huang, Aimin; Temam, Roger
2014
Phase transition models in atmospheric dynamics. Zbl 1319.35181
Bousquet, Arthur; Zelati, Michele Coti; Temam, Roger
2014
The nonlinear 2D subcritical inviscid shallow water equations with periodicity in one direction. Zbl 1310.76015
Huang, Aimin; Temam, Roger
2014
The linear hyperbolic initial and boundary value problems in a domain with corners. Zbl 1304.35390
Huang, Aimin; Temam, Roger
2014
Boundary layer theory for convection-diffusion equations in a circle. Zbl 1307.35025
Jung, C.-Y.; Temam, R.
2014
Finite volume multilevel approximation of the shallow water equations. Zbl 1426.76339
Bousquet, Arthur; Marion, Martine; Temam, Roger
2014
Singularly perturbed problems with a turning point: the non-compatible case. Zbl 1296.34138
Jung, Chang-Yeol; Temam, Roger
2014
Martingale and pathwise solutions to the stochastic Zakharov-Kuznetsov equation with multiplicative noise. Zbl 1329.60211
Glatt-Holtz, Nathan; Temam, Roger; Wang, Chuntian
2014
Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations. (Propriétés des solutions statistiques des équations de Navier-Stokes tridimensionnelles dans le cas évolutif.) Zbl 1304.35486
Foias, Ciprian; Rosa, Ricardo M. S.; Temam, Roger
2013
Attractors for processes on time-dependent spaces. Applications to wave equations. Zbl 1288.35098
Conti, Monica; Pata, Vittorino; Temam, Roger
2013
The equations of the atmosphere with humidity and saturation: uniqueness and physical bounds. Zbl 1286.86013
Coti Zelati, Michele; Frémond, Michel; Temam, Roger; Tribbia, Joseph
2013
The Euler equations in planar nonsmooth convex domains. Zbl 1306.35135
Bardos, Claude; Di Plinio, Francesco; Temam, Roger
2013
Asymptotic analysis for the 3D primitive equations in a channel. Zbl 1262.35078
Hamouda, Makram; Jung, Chang-Yeol; Temam, Roger
2013
The one-dimensional shallow water equations with transparent boundary conditions. Zbl 1277.35241
2013
Boundary conditions for limited area models based on the shallow water equations. Zbl 1373.35232
Bousquet, Arthur; Petcu, Madalina; Shiue, Ming-Cheng; Temam, Roger; Tribbia, Joseph
2013
Finite volume multilevel approximation of the shallow water equations. Zbl 1326.76069
Bousquet, Arthur; Marion, Martine; Temam, Roger
2013
Analysis of mixed elliptic and parabolic boundary layers with corners. Zbl 1272.35094
Gie, Gung-Min; Jung, Chang-Yeol; Temam, Roger
2013
Multilevel finite volume methods and boundary conditions for geophysical flows. Zbl 1365.76140
Bousquet, Arthur; Marion, Martine; Petcu, Madalina; Temam, Roger
2013
An interface problem: the two-layer shallow water equations. Zbl 1277.35242
2013
Global existence and regularity for the 3D stochastic primitive equations of the ocean and atmosphere with multiplicative white noise. Zbl 1246.35194
Debussche, A.; Glatt-Holtz, N.; Temam, R.; Ziane, M.
2012
An initial and boundary-value problem for the Zakharov-Kuznestov equation in a bounded domain. Zbl 1278.35221
Saut, Jean-Claude; Temam, Roger; Wang, Chuntian
2012
The atmospheric equation of water vapor with saturation. Zbl 1256.35174
Coti Zelati, Michele; Temam, Roger
2012
Numerical approximation of the inviscid 3D primitive equations in a limited domain. Zbl 1308.76197
Chen, Qingshan; Shiue, Ming-Cheng; Temam, Roger; Tribbia, Joseph
2012
Singular perturbations and boundary layer theory for convection-diffusion equations in a circle: the generic noncompatible case. Zbl 1261.35013
Jung, Chang-Yeol; Temam, Roger
2012
Asymptotic analysis of the Navier-Stokes equations in a curved domain with a non-characteristic boundary. Zbl 1270.35046
Gie, Gung-Min; Hamouda, Makram; Temam, Roger
2012
The 3-dimensional oscillon equation. Zbl 1256.35155
Di Plinio, Francesco; Duane, Gregory S.; Temam, Roger
2012
Penalty method for the KdV equation. Zbl 1235.35253
Qin, Zhen; Temam, Roger
2012
A penalty method for numerically handling dispersive equations with incompatible initial and boundary data. Zbl 1250.65124
Flyer, Natasha; Qin, Zhen; Temam, Roger
2012
Analysis of a penalty method. Zbl 1254.65105
Chen, Qingshan; Hong, Youngjoon; Temam, Roger
2012
Local martingale and pathwise solutions for an abstract fluids model. Zbl 1230.60065
Debussche, Arnaud; Glatt-Holtz, Nathan; Temam, Roger
2011
Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain. Zbl 1204.35129
Kukavica, Igor; Temam, Roger; Vicol, Vlad C.; Ziane, Mohammed
2011
Boundary layer associated with the Darcy-Brinkman-Boussinesq model for convection in porous media. Zbl 1209.37102
Kelliher, James P.; Temam, Roger; Wang, Xiaoming
2011
Pathwise solutions of the 2-D stochastic primitive equations. Zbl 1225.60105
Glatt-Holtz, Nathan; Temam, Roger
2011
Time-dependent attractor for the oscillon equation. Zbl 1223.37100
Di Plinio, Francesco; Duane, Gregory S.; Temam, Roger
2011
Singular perturbation analysis on a homogeneous ocean circulation model. Zbl 1229.76091
Jung, Chang-Yeol; Petcu, Madalina; Temam, Roger
2011
Cauchy convergence schemes for some nonlinear partial differential equations. Zbl 1209.35103
Glatt-Holtz, Nathan; Temam, Roger
2011
Convection-diffusion equations in a circle: the compatible case. Zbl 1228.35021
Jung, Chang-Yeol; Temam, Roger
2011
Numerical resolution near $$t = 0$$ of nonlinear evolution equations in the presence of corner singularities in space dimension 1. Zbl 1364.35057
Chen, Qingshan; Qin, Zhen; Temam, Roger
2011
The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Zbl 1219.35003
2011
Treatment of incompatible initial and boundary data for parabolic equations in higher dimension. Zbl 1225.35012
Chen, Qingshan; Qin, Zhen; Temam, Roger
2011
The one-dimensional supercritical Shallow Water Equations with topography. Zbl 1249.35213
Huang, Aimin; Petcu, Mădălina; Temam, Roger
2011
Existence theorem for a model of dryland vegetation. Zbl 1230.35140
Goto, Yukie; Hilhorst, Danielle; Meron, Ehud; Temam, Roger
2011
On the inaccuracies of some finite volume discrtizations of the linearized shallow water problem. Zbl 1426.76361
Faure, S.; Petcu, M.; Temam, R.; Tribbia, J.
2011
An initial boundary-value problem for the Zakharov-Kuznetsov equation. Zbl 1219.35253
Saut, Jean-Claude; Temam, Roger
2010
Topological properties of the weak global attractor of the three-dimensional Navier-Stokes equations. Zbl 1191.35204
Foias, Ciprian; Rosa, Ricardo; Temam, Roger
2010
The barotropic mode for the primitive equations. Zbl 1203.86009
Chen, Qingshan; Shiue, Ming-Cheng; Temam, Roger
2010
A note on statistical solutions of the three-dimensional Navier-Stokes equations: the time-dependent case. Zbl 1186.35141
Foias, Ciprian; Rosa, Ricardo M. S.; Temam, Roger
2010
Finite volume approximation of two-dimensional stiff problems. Zbl 1194.65127
Jung, Chang-Yeol; Temam, Roger
2010
Boundary layers in smooth curvilinear domains: parabolic problems. Zbl 1191.35035
Gie, Gung-Min; Hamouda, Makram; Témam, Roger
2010
A note on statistical solutions of the three-dimensional Navier-Stokes equations: The stationary case. (Note sur les solutions statistiques de équations de Navier-Stokes incompressibles en dimension trois d’espace: le cas stationnaire.) Zbl 1186.35142
Foias, Ciprian; Rosa, Ricardo M. S.; Temam, Roger
2010
Asymptotic analysis of the Stokes problem on general bounded domains: the case of a characteristic boundary. Zbl 1191.35034
Gie, Gung-Min; Hamouda, Makram; Temam, Roger
2010
Existence and uniqueness of solutions for the hydrostatic Euler equations on a bounded domain with analytic data. Zbl 1194.35247
Kukavica, Igor; Temam, Roger; Vicol, Vlad; Ziane, Mohammed
2010
Stability of the slow manifold in the primitive equations. Zbl 1218.35032
Temam, R.; Wirosoetisno, D.
2010
Finite volume approximation of one-dimensional stiff convection-diffusion equations. Zbl 1203.65159
Jung, Chang-Yeol; Temam, Roger
2009
Boundary layers for the 2D linearized primitive equations. Zbl 1152.35423
Hamouda, Makram; Jung, Chang-Yeol; Temam, Roger
2009
Handbook of numerical analysis. Vol XIV. Special volume: Computational methods for the atmosphere and the oceans. Zbl 1226.86002
Temam, Roger M.; Tribbia, Joseph J.
2009
Interaction of boundary layers and corner singularities. Zbl 1161.65086
Jung, Chang-Yeol; Temam, Roger
2009
The 3D primitive equations in the absence of viscosity: boundary conditions and well-posedness in the linearized case. Zbl 1137.35057
Rousseau, A.; Temam, R.; Tribbia, J.
2008
A two-grid finite difference method for the primitive equations of the ocean. Zbl 1142.76368
Tachim Medjo, T.; Temam, R.
2008
...and 318 more Documents
all top 5
Cited by 8,540 Authors
182 Temam, Roger Meyer 107 Titi, Edriss Saleh 94 He, Yinnian 75 Guo, Boling 73 Miranville, Alain M. 61 Foiaş, Ciprian Ilie 57 Tachim Medjo, Theodore 52 Zhou, Shengfan 45 Kukavica, Igor 44 Zelik, Sergey V. 43 Rakotoson, Jean-Michel 43 Robinson, James Cooper 41 Caraballo Garrido, Tomás 40 Zhao, Caidi 40 Zhong, Chengkui 38 Chueshov, Igor’ Dmitrievich 38 Langa, Jose’ Antonio 38 Wang, Bixiang 37 Duan, Jinqiao 37 Grasselli, Maurizio 37 Kunisch, Karl 37 Li, Jian 37 Li, Kaitai 36 Rojas-Medar, Marko Antonio 35 Jolly, Michael S. 35 Pata, Vittorino 34 Wang, Xiaoming 33 Valero, José 32 Shen, Jie 31 Chepyzhov, Vladimir V. 31 Hou, Yanren 30 Brzeźniak, Zdzisław 30 Jung, Changyeol 30 Yamazaki, Kazuo 29 Diaz Diaz, Jesus Ildefonso 29 Gunzburger, Max D. 29 Kapustyan, Oleksiy V. 29 Sun, Chunyou 28 Cung The Anh 28 Kasyanov, Pavlo O. 27 Gao, Hongjun 27 Guillén González, Francisco M. 27 Nolasco de Carvalho, Alexandre 26 Codina, Ramon 26 Debussche, Arnaud 26 Feireisl, Eduard 26 Li, Yangrong 26 Łukaszewicz, Grzegorz 25 Guermond, Jean-Luc 25 Marín-Rubio, Pedro 25 Repin, Sergeĭ Igorevich 25 Vicol, Vlad C. 25 Wang, Shouhong 24 Shang, Yueqiang 23 Lasiecka, Irena 23 Rebholz, Leo G. 23 Vishik, Marko Iosifovich 23 Winkler, Michael 23 Zhang, Zujin 22 Bessaih, Hakima 22 Constantin, Peter 22 Conti, Monica C. 22 Flandoli, Franco 22 Gal, Ciprian Gheorghe Sorin 22 Li, Yongsheng 22 You, Bo 21 Gala, Sadek 21 Ma, Yichen 21 Ziane, Mohammed 20 Gibbon, John D. 20 Glatt-Holtz, Nathan E. 20 Kloeden, Peter Eris 20 Kozono, Hideo 20 Real Anguas, José 20 Sofonea, Mircea 19 Boţ, Radu Ioan 19 Razafimandimby, Paul André 19 Simsen, Jacson 19 Wu, Hao 19 Wu, Jiahong 18 Berselli, Luigi Carlo 18 Casas, Eduardo 18 Chae, Dongho 18 Chen, Zhangxin 18 Fan, Jishan 18 Fernández-Cara, Enrique 18 Fuchs, Martin 18 Lu, Kening 18 Si, Zhiyong 18 Sritharan, Sivaguru S. 18 Yang, Meihua 17 Alduncin, Gonzalo 17 Goubet, Olivier 17 Grujić, Zoran 17 Hintermüller, Michael 17 Hoang, Luan Thach 17 Ma, Tian 17 Neustupa, Jiří 17 Orlov, Vladimir P. 17 Rodríguez-Bernal, Aníbal ...and 8,440 more Authors
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Cited in 587 Serials
542 Journal of Mathematical Analysis and Applications 485 Journal of Differential Equations 364 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 205 Journal of Computational Physics 192 Archive for Rational Mechanics and Analysis 188 Physica D 187 Computer Methods in Applied Mechanics and Engineering 146 Discrete and Continuous Dynamical Systems. Series B 134 Applied Mathematics and Computation 132 Journal of Computational and Applied Mathematics 132 Nonlinear Analysis. Real World Applications 131 Discrete and Continuous Dynamical Systems 128 Nonlinear Analysis. Theory, Methods & Applications 122 Numerische Mathematik 120 ZAMP. Zeitschrift für angewandte Mathematik und Physik 120 Journal of Mathematical Fluid Mechanics 117 Computers & Mathematics with Applications 117 Applied Mathematics Letters 112 Journal of Mathematical Physics 112 Mathematical Methods in the Applied Sciences 110 Applied Numerical Mathematics 110 Journal of Dynamics and Differential Equations 106 Numerical Functional Analysis and Optimization 104 Applicable Analysis 101 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 100 Communications in Mathematical Physics 99 Computers and Fluids 96 Journal of Scientific Computing 95 Journal of Functional Analysis 92 Applied Mathematics and Optimization 92 Journal of Mathematical Sciences (New York) 91 Journal of Optimization Theory and Applications 87 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 87 Communications on Pure and Applied Analysis 77 Communications in Partial Differential Equations 76 RAIRO. Modélisation Mathématique et Analyse Numérique 75 Mathematics of Computation 75 Journal de Mathématiques Pures et Appliquées. Neuvième Série 72 Acta Applicandae Mathematicae 71 Journal of Fluid Mechanics 68 SIAM Journal on Mathematical Analysis 61 Annali di Matematica Pura ed Applicata. Serie Quarta 61 Abstract and Applied Analysis 57 Acta Mathematicae Applicatae Sinica. English Series 57 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 55 Numerical Methods for Partial Differential Equations 54 Comptes Rendus. Mathématique. Académie des Sciences, Paris 51 Calculus of Variations and Partial Differential Equations 50 Physics of Fluids 49 Mathematical Notes 49 Transactions of the American Mathematical Society 49 Applied Mathematics and Mechanics. (English Edition) 49 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 45 Stochastic Analysis and Applications 45 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 44 Journal of Nonlinear Science 41 NoDEA. Nonlinear Differential Equations and Applications 40 International Journal for Numerical Methods in Fluids 40 SIAM Journal on Numerical Analysis 39 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 38 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 38 SIAM Journal on Control and Optimization 38 Applications of Mathematics 38 Boundary Value Problems 36 Journal of Statistical Physics 36 Chinese Annals of Mathematics. Series B 36 Acta Mathematica Sinica. English Series 35 Quarterly of Applied Mathematics 35 Stochastic Processes and their Applications 34 International Journal of Engineering Science 34 Communications in Nonlinear Science and Numerical Simulation 33 Nonlinearity 33 Journal of Evolution Equations 32 Journal of Elasticity 31 Proceedings of the American Mathematical Society 31 Siberian Mathematical Journal 31 Differential Equations 31 Evolution Equations and Control Theory 30 Mathematical and Computer Modelling 30 Journal of Mathematical Imaging and Vision 29 Rendiconti del Seminario Matematico della Università di Padova 29 Advances in Computational Mathematics 28 Discrete and Continuous Dynamical Systems. Series S 27 Communications on Pure and Applied Mathematics 26 Doklady Mathematics 26 Science China. Mathematics 25 Computational Optimization and Applications 25 SIAM Journal on Scientific Computing 24 Mathematische Zeitschrift 24 Japan Journal of Industrial and Applied Mathematics 24 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 23 Advances in Mathematics 23 Journal of Global Optimization 22 Physics Letters. A 22 Journal of Soviet Mathematics 22 Mathematische Annalen 22 Zeitschrift für Analysis und ihre Anwendungen 22 Optimization 22 Russian Mathematics 22 Mathematical Problems in Engineering ...and 487 more Serials
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Cited in 59 Fields
6,397 Partial differential equations (35-XX) 4,344 Fluid mechanics (76-XX) 1,845 Numerical analysis (65-XX) 1,251 Calculus of variations and optimal control; optimization (49-XX) 1,177 Dynamical systems and ergodic theory (37-XX) 947 Mechanics of deformable solids (74-XX) 701 Probability theory and stochastic processes (60-XX) 469 Ordinary differential equations (34-XX) 427 Systems theory; control (93-XX) 387 Operator theory (47-XX) 322 Geophysics (86-XX) 306 Operations research, mathematical programming (90-XX) 275 Biology and other natural sciences (92-XX) 225 Classical thermodynamics, heat transfer (80-XX) 224 Functional analysis (46-XX) 212 Statistical mechanics, structure of matter (82-XX) 153 Global analysis, analysis on manifolds (58-XX) 146 Real functions (26-XX) 113 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 108 Information and communication theory, circuits (94-XX) 86 Optics, electromagnetic theory (78-XX) 80 Integral equations (45-XX) 80 Computer science (68-XX) 73 Harmonic analysis on Euclidean spaces (42-XX) 71 Measure and integration (28-XX) 60 Mechanics of particles and systems (70-XX) 51 Differential geometry (53-XX) 46 Statistics (62-XX) 40 General topology (54-XX) 37 Approximations and expansions (41-XX) 36 Quantum theory (81-XX) 33 Difference and functional equations (39-XX) 24 Convex and discrete geometry (52-XX) 22 Potential theory (31-XX) 16 Astronomy and astrophysics (85-XX) 14 Functions of a complex variable (30-XX) 11 General and overarching topics; collections (00-XX) 11 History and biography (01-XX) 11 Manifolds and cell complexes (57-XX) 9 Combinatorics (05-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 9 Relativity and gravitational theory (83-XX) 8 Algebraic topology (55-XX) 7 Special functions (33-XX) 5 Group theory and generalizations (20-XX) 5 Abstract harmonic analysis (43-XX) 5 Integral transforms, operational calculus (44-XX) 4 Sequences, series, summability (40-XX) 3 Mathematical logic and foundations (03-XX) 3 Algebraic geometry (14-XX) 3 Topological groups, Lie groups (22-XX) 2 Number theory (11-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Geometry (51-XX) 2 Mathematics education (97-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX)
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https://www.zbmath.org/authors/?q=ai%3Aying.lexing | # zbMATH — the first resource for mathematics
## Ying, Lexing
Compute Distance To:
Author ID: ying.lexing Published as: Ying, Lexing External Links: MGP · Wikidata
Documents Indexed: 100 Publications since 2004
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#### Co-Authors
12 single-authored 15 Lin, Lin 13 Lu, Jianfeng 11 Engquist, Bjorn E. 10 Demanet, Laurent 7 Fan, Yuwei 7 Ho, Kenneth L. 7 Yang, Haizhao 6 Damle, Anil 6 E, Weinan 6 Tsuji, Paul 5 Candès, Emmanuel J. 5 Minden, Victor 5 Poulson, Jack 4 Khoo, Yuehaw 4 Li, Yingzhou 3 Biros, George 3 Feliu-Fabà, Jordi 3 Qian, Jianliang 3 Zorin, Denis N. 2 Hu, Jingwei 2 Maxwell, Nicholas 2 Schmitz, Phillip G. 2 Yang, Chao 2 Zepeda-Núñez, Leonardo 1 An, Jing 1 Bao, Gang 1 Benson, Austin R. 1 Cai, Zhenning 1 Car, Roberto 1 Donoho, David Leigh 1 Ferrara, Matthew 1 Fomel, Sergey 1 Jiang, Shidong 1 Li, Siwei 1 Li, Wuchen 1 Li, Zhihan 1 Lindsey, Michael 1 Martin, Eileen R. 1 Meza, Juan C. 1 Orozco Bohorquez, Cindy 1 Ren, Bo 1 Tran, Kenneth 1 Xia, Jianlin 1 Xiu, Dongbin 1 Xu, Ze 1 Ye, Xin 1 Zhang, Hai
all top 5
#### Serials
22 Journal of Computational Physics 20 Multiscale Modeling & Simulation 16 SIAM Journal on Scientific Computing 6 Communications in Mathematical Sciences 4 Journal of Scientific Computing 4 Research in the Mathematical Sciences 3 Communications on Pure and Applied Mathematics 3 Applied and Computational Harmonic Analysis 2 Mathematics of Computation 2 SIAM Journal on Imaging Sciences 1 ACM Transactions on Mathematical Software 1 Journal of Computational and Applied Mathematics 1 Numerische Mathematik 1 Chinese Annals of Mathematics. Series B 1 SIAM Journal on Matrix Analysis and Applications 1 Communications in Partial Differential Equations 1 SIAM Journal on Mathematical Analysis 1 SIAM Review 1 Foundations of Computational Mathematics 1 Acta Numerica 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Frontiers of Mathematics in China 1 Science China. Mathematics 1 International Journal for Uncertainty Quantification 1 Information and Inference 1 Annals of Mathematical Sciences and Applications
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#### Fields
90 Numerical analysis (65-XX) 35 Partial differential equations (35-XX) 15 Optics, electromagnetic theory (78-XX) 9 Statistical mechanics, structure of matter (82-XX) 8 Computer science (68-XX) 7 Integral transforms, operational calculus (44-XX) 6 Quantum theory (81-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Information and communication theory, circuits (94-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral equations (45-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Probability theory and stochastic processes (60-XX) 3 Mechanics of deformable solids (74-XX) 3 Geophysics (86-XX) 3 Biology and other natural sciences (92-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Statistics (62-XX) 2 Fluid mechanics (76-XX) 2 Operations research, mathematical programming (90-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX)
#### Citations contained in zbMATH Open
86 Publications have been cited 1,196 times in 734 Documents Cited by Year
A kernel-independent adaptive fast multipole algorithm in two and three dimensions. Zbl 1053.65095
Ying, Lexing; Biros, George; Zorin, Denis
2004
Fast discrete curvelet transforms. Zbl 1122.65134
Candès, Emmanuel; Demanet, Laurent; Donoho, David; Ying, Lexing
2006
Sweeping preconditioner for the Helmholtz equation: moving perfectly matched layers. Zbl 1228.65234
Engquist, Björn; Ying, Lexing
2011
Sweeping preconditioner for the Helmholtz equation: hierarchical matrix representation. Zbl 1229.35037
Engquist, Björn; Ying, Lexing
2011
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains. Zbl 1105.65115
Ying, Lexing; Biros, George; Zorin, Denis
2006
A fast solver for the Stokes equations with distributed forces in complex geometries. Zbl 1047.76065
Biros, George; Ying, Lexing; Zorin, Denis
2004
Fast directional multilevel algorithms for oscillatory kernels. Zbl 1180.65006
Engquist, Björn; Ying, Lexing
2007
A fast butterfly algorithm for the computation of Fourier integral operators. Zbl 1184.65125
Candès, Emmanuel; Demanet, Laurent; Ying, Lexing
2009
A fast direct solver for elliptic problems on general meshes in 2D. Zbl 1408.65022
Schmitz, Phillip G.; Ying, Lexing
2012
Hierarchical interpolative factorization for elliptic operators: differential equations. Zbl 1353.35142
Ho, Kenneth L.; Ying, Lexing
2016
Fast construction of hierarchical matrix representation from matrix-vector multiplication. Zbl 1218.65038
Lin, Lin; Lu, Jianfeng; Ying, Lexing
2011
Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems. Zbl 1182.65072
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Car, Roberto; E, Weinan
2009
Hierarchical interpolative factorization for elliptic operators: integral equations. Zbl 1344.65123
Ho, Kenneth L.; Ying, Lexing
2016
Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation. Zbl 1197.65156
Qian, Jianliang; Ying, Lexing
2010
A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations. Zbl 1275.65073
Poulson, Jack; Engquist, Björn; Li, Siwei; Ying, Lexing
2013
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework. I: Total energy calculation. Zbl 1251.82008
Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
2012
A fast directional algorithm for high frequency acoustic scattering in two dimensions. Zbl 1182.65178
Engquist, Björn; Ying, Lexing
2009
Wave atoms and sparsity of oscillatory patterns. Zbl 1132.68068
Demanet, Laurent; Ying, Lexing
2007
Fast computation of Fourier integral operators. Zbl 1157.65522
Candès, Emmanuel; Demanet, Laurent; Ying, Lexing
2007
Sparse Fourier transform via butterfly algorithm. Zbl 1207.65169
Ying, Lexing
2009
Fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beams for the wave equation. Zbl 1223.65076
Qian, Jianliang; Ying, Lexing
2010
The phase flow method. Zbl 1110.65119
Ying, Lexing; Candès, Emmanuel J.
2006
Butterfly factorization. Zbl 1317.44004
Li, Yingzhou; Yang, Haizhao; Martin, Eileen R.; Ho, Kenneth L.; Ying, Lexing
2015
SelInv – an algorithm for selected inversion of a sparse symmetric matrix. Zbl 1365.65069
Lin, Lin; Yang, Chao; Meza, Juan C.; Lu, Jianfeng; Ying, Lexing; E, Weinan
2011
A fast spectral algorithm for the quantum Boltzmann collision operator. Zbl 1260.82068
Hu, Jingwei; Ying, Lexing
2012
A sweeping preconditioner for time-harmonic Maxwell’s equations with finite elements. Zbl 1251.78013
Tsuji, Paul; Engquist, Bjorn; Ying, Lexing
2012
Synchrosqueezed curvelet transform for two-dimensional mode decomposition. Zbl 1297.42053
Yang, Haizhao; Ying, Lexing
2014
A kernel independent fast multipole algorithm for radial basis functions. Zbl 1089.65018
Ying, Lexing
2006
A butterfly algorithm for synthetic aperture radar imaging. Zbl 1250.65033
Demanet, Laurent; Ferrara, Matthew; Maxwell, Nicholas; Poulson, Jack; Ying, Lexing
2012
Synchrosqueezed wave packet transform for 2D mode decomposition. Zbl 1282.65036
Yang, Haizhao; Ying, Lexing
2013
Sparsifying preconditioner for the Lippmann-Schwinger equation. Zbl 1317.65087
Ying, Lexing
2015
Fast geodesics computation with the phase flow method. Zbl 1110.65118
Ying, Lexing; Candès, Emmanuel J.
2006
A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations. Zbl 1230.65039
Lin, Lin; Yang, Chao; Lu, Jianfeng; Ying, Lexing; E, Weinan
2011
Discrete symbol calculus. Zbl 1210.65194
Demanet, Laurent; Ying, Lexing
2011
Pole-based approximation of the Fermi-Dirac function. Zbl 1188.41007
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Weinan, E.
2009
Fast wave computation via Fourier integral operators. Zbl 1245.65140
Demanet, Laurent; Ying, Lexing
2012
Wave atoms and time upscaling of wave equations. Zbl 1179.65129
Demanet, Laurent; Ying, Lexing
2009
A parallel butterfly algorithm. Zbl 1290.65127
Poulson, Jack; Demanet, Laurent; Maxwell, Nicholas; Ying, Lexing
2014
Recursive sweeping preconditioner for the three-dimensional Helmholtz equation. Zbl 1376.65035
Liu, Fei; Ying, Lexing
2016
Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions. Zbl 1252.65196
Jiang, Shidong; Ren, Bo; Tsuji, Paul; Ying, Lexing
2011
Sweeping preconditioners for elastic wave propagation with spectral element methods. Zbl 1423.74950
Tsuji, Paul; Poulson, Jack; Engquist, Björn; Ying, Lexing
2014
Crystal image analysis using 2D synchrosqueezed transforms. Zbl 1336.74016
Yang, Haizhao; Lu, Jianfeng; Ying, Lexing
2015
A recursive skeletonization factorization based on strong admissibility. Zbl 1365.65286
Minden, Victor; Ho, Kenneth L.; Ying, Lexing
2017
Optimized local basis set for Kohn-Sham density functional theory. Zbl 1250.82002
Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
2012
A sweeping preconditioner for Yee’s finite difference approximation of time-harmonic Maxwell’s equations. Zbl 1253.78049
Tsuji, Paul; Ying, Lexing
2012
Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost. Zbl 1349.81020
Lu, Jianfeng; Ying, Lexing
2015
A multiscale butterfly algorithm for multidimensional Fourier integral operators. Zbl 1317.44005
Li, Yingzhou; Yang, Haizhao; Ying, Lexing
2015
Additive sweeping preconditioner for the Helmholtz equation. Zbl 1338.65077
Liu, Fei; Ying, Lexing
2016
Fast spatial Gaussian process maximum likelihood estimation via skeletonization factorizations. Zbl 1378.65092
Minden, Victor; Damle, Anil; Ho, Kenneth L.; Ying, Lexing
2017
A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices. Zbl 1349.65598
Schmitz, Phillip G.; Ying, Lexing
2014
SCDM-k: localized orbitals for solids via selected columns of the density matrix. Zbl 1375.81255
Damle, Anil; Lin, Lin; Ying, Lexing
2017
Fast directional algorithms for the Helmholtz kernel. Zbl 1379.65103
Engquist, Björn; Ying, Lexing
2010
A technique for updating hierarchical skeletonization-based factorizations of integral operators. Zbl 1329.65317
Minden, Victor; Damle, Anil; Ho, Kenneth L.; Ying, Lexing
2016
Multidimensional butterfly factorization. Zbl 1390.44016
Li, Yingzhou; Yang, Haizhao; Ying, Lexing
2018
A fast algorithm for multilinear operators. Zbl 1247.65176
Yang, Haizhao; Ying, Lexing
2012
Scattering in flatland: Efficient representations via wave atoms. Zbl 1197.65192
Demanet, Laurent; Ying, Lexing
2010
Fast computation of partial Fourier transforms. Zbl 1186.65166
Ying, Lexing; Fomel, Sergey
2009
Fast directional computation of high frequency boundary integrals via local FFTs. Zbl 1317.65244
Ying, Lexing
2015
Sparsifying preconditioner for pseudospectral approximations of indefinite systems on periodic structures. Zbl 1317.65086
Ying, Lexing
2015
Recursively preconditioned hierarchical interpolative factorization for elliptic partial differential equations. Zbl 1437.65172
Feliu-Fabà, Jordi; Ho, Kenneth L.; Ying, Lexing
2020
A simple solver for the fractional Laplacian in multiple dimensions. Zbl 1437.65242
Minden, Victor; Ying, Lexing
2020
Distributed-memory hierarchical interpolative factorization. Zbl 1375.65141
Li, Yingzhou; Ying, Lexing
2017
A convergent multiscale Gaussian-beam parametrix for the wave equation. Zbl 1302.35485
Bao, Gang; Qian, Jianliang; Ying, Lexing; Zhang, Hai
2013
Directional preconditioner for 2D high frequency obstacle scattering. Zbl 1317.65245
Ying, Lexing
2015
Solving electrical impedance tomography with deep learning. Zbl 1453.65041
Fan, Yuwei; Ying, Lexing
2020
Fast algorithm for periodic density fitting for Bloch waves. Zbl 1381.65098
Lu, Jianfeng; Ying, Lexing
2016
Sparsify and sweep: an efficient preconditioner for the Lippmann-Schwinger equation. Zbl 1392.65035
Liu, Fei; Ying, Lexing
2018
SwitchNet: a neural Network Model for forward and inverse scattering problems. Zbl 1425.65208
Khoo, Yuehaw; Ying, Lexing
2019
A fast directional algorithm for high-frequency electromagnetic scattering. Zbl 1220.78049
Tsuji, Paul; Ying, Lexing
2011
Sparsifying preconditioner for soliton calculations. Zbl 1349.65606
Lu, Jianfeng; Ying, Lexing
2016
Convex relaxation approaches for strictly correlated density functional theory. Zbl 1423.49033
Khoo, Yuehaw; Ying, Lexing
2019
Adaptively compressed polarizability operator for accelerating large scale ab initio phonon calculations. Zbl 1369.82020
Lin, Lin; Xu, Ze; Ying, Lexing
2017
An entropic Fourier method for the Boltzmann equation. Zbl 1406.65093
Cai, Zhenning; Fan, Yuwei; Ying, Lexing
2018
Fast algorithms for high frequency wave propagation. Zbl 1248.65114
Engquist, Björn; Ying, Lexing
2012
A pedestrian introduction to fast multipole methods. Zbl 1259.65187
Ying, Lexing
2012
A multiscale neural network based on hierarchical matrices. Zbl 1435.65181
Fan, Yuwei; Lin, Lin; Ying, Lexing; Zepeda-Núñez, Leonardo
2019
A parallel directional fast multipole method. Zbl 1305.78017
Benson, Austin R.; Poulson, Jack; Tran, Kenneth; Engquist, Björn; Ying, Lexing
2014
Fast algorithms for boundary integral equations. Zbl 1159.65365
Ying, Lexing
2009
Mirror descent algorithms for minimizing interacting free energy. Zbl 1453.65145
Ying, Lexing
2020
Fast algorithms for integral formulations of steady-state radiative transfer equation. Zbl 1451.65234
Fan, Yuwei; An, Jing; Ying, Lexing
2019
BCR-net: A neural network based on the nonstandard wavelet form. Zbl 1451.65244
Fan, Yuwei; Orozco Bohorquez, Cindy; Ying, Lexing
2019
Pole expansion for solving a type of parametrized linear systems in electronic structure calculations. Zbl 1310.65047
Damle, Anil; Lin, Lin; Ying, Lexing
2014
Semidefinite relaxation of multimarginal optimal transport for strictly correlated electrons in second quantization. Zbl 1456.49037
Khoo, Yuehaw; Lin, Lin; Lindsey, Michael; Ying, Lexing
2020
Localized sparsifying preconditioner for periodic indefinite systems. Zbl 1369.65153
Liu, Fei; Ying, Lexing
2017
Computing localized representations of the Kohn-Sham subspace via randomization and refinement. Zbl 1382.82022
Damle, Anil; Lin, Lin; Ying, Lexing
2017
Hessian transport gradient flows. Zbl 1427.35282
Li, Wuchen; Ying, Lexing
2019
Recursively preconditioned hierarchical interpolative factorization for elliptic partial differential equations. Zbl 1437.65172
Feliu-Fabà, Jordi; Ho, Kenneth L.; Ying, Lexing
2020
A simple solver for the fractional Laplacian in multiple dimensions. Zbl 1437.65242
Minden, Victor; Ying, Lexing
2020
Solving electrical impedance tomography with deep learning. Zbl 1453.65041
Fan, Yuwei; Ying, Lexing
2020
Mirror descent algorithms for minimizing interacting free energy. Zbl 1453.65145
Ying, Lexing
2020
Semidefinite relaxation of multimarginal optimal transport for strictly correlated electrons in second quantization. Zbl 1456.49037
Khoo, Yuehaw; Lin, Lin; Lindsey, Michael; Ying, Lexing
2020
SwitchNet: a neural Network Model for forward and inverse scattering problems. Zbl 1425.65208
Khoo, Yuehaw; Ying, Lexing
2019
Convex relaxation approaches for strictly correlated density functional theory. Zbl 1423.49033
Khoo, Yuehaw; Ying, Lexing
2019
A multiscale neural network based on hierarchical matrices. Zbl 1435.65181
Fan, Yuwei; Lin, Lin; Ying, Lexing; Zepeda-Núñez, Leonardo
2019
Fast algorithms for integral formulations of steady-state radiative transfer equation. Zbl 1451.65234
Fan, Yuwei; An, Jing; Ying, Lexing
2019
BCR-net: A neural network based on the nonstandard wavelet form. Zbl 1451.65244
Fan, Yuwei; Orozco Bohorquez, Cindy; Ying, Lexing
2019
Hessian transport gradient flows. Zbl 1427.35282
Li, Wuchen; Ying, Lexing
2019
Multidimensional butterfly factorization. Zbl 1390.44016
Li, Yingzhou; Yang, Haizhao; Ying, Lexing
2018
Sparsify and sweep: an efficient preconditioner for the Lippmann-Schwinger equation. Zbl 1392.65035
Liu, Fei; Ying, Lexing
2018
An entropic Fourier method for the Boltzmann equation. Zbl 1406.65093
Cai, Zhenning; Fan, Yuwei; Ying, Lexing
2018
A recursive skeletonization factorization based on strong admissibility. Zbl 1365.65286
Minden, Victor; Ho, Kenneth L.; Ying, Lexing
2017
Fast spatial Gaussian process maximum likelihood estimation via skeletonization factorizations. Zbl 1378.65092
Minden, Victor; Damle, Anil; Ho, Kenneth L.; Ying, Lexing
2017
SCDM-k: localized orbitals for solids via selected columns of the density matrix. Zbl 1375.81255
Damle, Anil; Lin, Lin; Ying, Lexing
2017
Distributed-memory hierarchical interpolative factorization. Zbl 1375.65141
Li, Yingzhou; Ying, Lexing
2017
Adaptively compressed polarizability operator for accelerating large scale ab initio phonon calculations. Zbl 1369.82020
Lin, Lin; Xu, Ze; Ying, Lexing
2017
Localized sparsifying preconditioner for periodic indefinite systems. Zbl 1369.65153
Liu, Fei; Ying, Lexing
2017
Computing localized representations of the Kohn-Sham subspace via randomization and refinement. Zbl 1382.82022
Damle, Anil; Lin, Lin; Ying, Lexing
2017
Hierarchical interpolative factorization for elliptic operators: differential equations. Zbl 1353.35142
Ho, Kenneth L.; Ying, Lexing
2016
Hierarchical interpolative factorization for elliptic operators: integral equations. Zbl 1344.65123
Ho, Kenneth L.; Ying, Lexing
2016
Recursive sweeping preconditioner for the three-dimensional Helmholtz equation. Zbl 1376.65035
Liu, Fei; Ying, Lexing
2016
Additive sweeping preconditioner for the Helmholtz equation. Zbl 1338.65077
Liu, Fei; Ying, Lexing
2016
A technique for updating hierarchical skeletonization-based factorizations of integral operators. Zbl 1329.65317
Minden, Victor; Damle, Anil; Ho, Kenneth L.; Ying, Lexing
2016
Fast algorithm for periodic density fitting for Bloch waves. Zbl 1381.65098
Lu, Jianfeng; Ying, Lexing
2016
Sparsifying preconditioner for soliton calculations. Zbl 1349.65606
Lu, Jianfeng; Ying, Lexing
2016
Butterfly factorization. Zbl 1317.44004
Li, Yingzhou; Yang, Haizhao; Martin, Eileen R.; Ho, Kenneth L.; Ying, Lexing
2015
Sparsifying preconditioner for the Lippmann-Schwinger equation. Zbl 1317.65087
Ying, Lexing
2015
Crystal image analysis using 2D synchrosqueezed transforms. Zbl 1336.74016
Yang, Haizhao; Lu, Jianfeng; Ying, Lexing
2015
Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost. Zbl 1349.81020
Lu, Jianfeng; Ying, Lexing
2015
A multiscale butterfly algorithm for multidimensional Fourier integral operators. Zbl 1317.44005
Li, Yingzhou; Yang, Haizhao; Ying, Lexing
2015
Fast directional computation of high frequency boundary integrals via local FFTs. Zbl 1317.65244
Ying, Lexing
2015
Sparsifying preconditioner for pseudospectral approximations of indefinite systems on periodic structures. Zbl 1317.65086
Ying, Lexing
2015
Directional preconditioner for 2D high frequency obstacle scattering. Zbl 1317.65245
Ying, Lexing
2015
Synchrosqueezed curvelet transform for two-dimensional mode decomposition. Zbl 1297.42053
Yang, Haizhao; Ying, Lexing
2014
A parallel butterfly algorithm. Zbl 1290.65127
Poulson, Jack; Demanet, Laurent; Maxwell, Nicholas; Ying, Lexing
2014
Sweeping preconditioners for elastic wave propagation with spectral element methods. Zbl 1423.74950
Tsuji, Paul; Poulson, Jack; Engquist, Björn; Ying, Lexing
2014
A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices. Zbl 1349.65598
Schmitz, Phillip G.; Ying, Lexing
2014
A parallel directional fast multipole method. Zbl 1305.78017
Benson, Austin R.; Poulson, Jack; Tran, Kenneth; Engquist, Björn; Ying, Lexing
2014
Pole expansion for solving a type of parametrized linear systems in electronic structure calculations. Zbl 1310.65047
Damle, Anil; Lin, Lin; Ying, Lexing
2014
A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations. Zbl 1275.65073
Poulson, Jack; Engquist, Björn; Li, Siwei; Ying, Lexing
2013
Synchrosqueezed wave packet transform for 2D mode decomposition. Zbl 1282.65036
Yang, Haizhao; Ying, Lexing
2013
A convergent multiscale Gaussian-beam parametrix for the wave equation. Zbl 1302.35485
Bao, Gang; Qian, Jianliang; Ying, Lexing; Zhang, Hai
2013
A fast direct solver for elliptic problems on general meshes in 2D. Zbl 1408.65022
Schmitz, Phillip G.; Ying, Lexing
2012
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework. I: Total energy calculation. Zbl 1251.82008
Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
2012
A fast spectral algorithm for the quantum Boltzmann collision operator. Zbl 1260.82068
Hu, Jingwei; Ying, Lexing
2012
A sweeping preconditioner for time-harmonic Maxwell’s equations with finite elements. Zbl 1251.78013
Tsuji, Paul; Engquist, Bjorn; Ying, Lexing
2012
A butterfly algorithm for synthetic aperture radar imaging. Zbl 1250.65033
Demanet, Laurent; Ferrara, Matthew; Maxwell, Nicholas; Poulson, Jack; Ying, Lexing
2012
Fast wave computation via Fourier integral operators. Zbl 1245.65140
Demanet, Laurent; Ying, Lexing
2012
Optimized local basis set for Kohn-Sham density functional theory. Zbl 1250.82002
Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
2012
A sweeping preconditioner for Yee’s finite difference approximation of time-harmonic Maxwell’s equations. Zbl 1253.78049
Tsuji, Paul; Ying, Lexing
2012
A fast algorithm for multilinear operators. Zbl 1247.65176
Yang, Haizhao; Ying, Lexing
2012
Fast algorithms for high frequency wave propagation. Zbl 1248.65114
Engquist, Björn; Ying, Lexing
2012
A pedestrian introduction to fast multipole methods. Zbl 1259.65187
Ying, Lexing
2012
Sweeping preconditioner for the Helmholtz equation: moving perfectly matched layers. Zbl 1228.65234
Engquist, Björn; Ying, Lexing
2011
Sweeping preconditioner for the Helmholtz equation: hierarchical matrix representation. Zbl 1229.35037
Engquist, Björn; Ying, Lexing
2011
Fast construction of hierarchical matrix representation from matrix-vector multiplication. Zbl 1218.65038
Lin, Lin; Lu, Jianfeng; Ying, Lexing
2011
SelInv – an algorithm for selected inversion of a sparse symmetric matrix. Zbl 1365.65069
Lin, Lin; Yang, Chao; Meza, Juan C.; Lu, Jianfeng; Ying, Lexing; E, Weinan
2011
A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations. Zbl 1230.65039
Lin, Lin; Yang, Chao; Lu, Jianfeng; Ying, Lexing; E, Weinan
2011
Discrete symbol calculus. Zbl 1210.65194
Demanet, Laurent; Ying, Lexing
2011
Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions. Zbl 1252.65196
Jiang, Shidong; Ren, Bo; Tsuji, Paul; Ying, Lexing
2011
A fast directional algorithm for high-frequency electromagnetic scattering. Zbl 1220.78049
Tsuji, Paul; Ying, Lexing
2011
Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation. Zbl 1197.65156
Qian, Jianliang; Ying, Lexing
2010
Fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beams for the wave equation. Zbl 1223.65076
Qian, Jianliang; Ying, Lexing
2010
Fast directional algorithms for the Helmholtz kernel. Zbl 1379.65103
Engquist, Björn; Ying, Lexing
2010
Scattering in flatland: Efficient representations via wave atoms. Zbl 1197.65192
Demanet, Laurent; Ying, Lexing
2010
A fast butterfly algorithm for the computation of Fourier integral operators. Zbl 1184.65125
Candès, Emmanuel; Demanet, Laurent; Ying, Lexing
2009
Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems. Zbl 1182.65072
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Car, Roberto; E, Weinan
2009
A fast directional algorithm for high frequency acoustic scattering in two dimensions. Zbl 1182.65178
Engquist, Björn; Ying, Lexing
2009
Sparse Fourier transform via butterfly algorithm. Zbl 1207.65169
Ying, Lexing
2009
Pole-based approximation of the Fermi-Dirac function. Zbl 1188.41007
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Weinan, E.
2009
Wave atoms and time upscaling of wave equations. Zbl 1179.65129
Demanet, Laurent; Ying, Lexing
2009
Fast computation of partial Fourier transforms. Zbl 1186.65166
Ying, Lexing; Fomel, Sergey
2009
Fast algorithms for boundary integral equations. Zbl 1159.65365
Ying, Lexing
2009
Fast directional multilevel algorithms for oscillatory kernels. Zbl 1180.65006
Engquist, Björn; Ying, Lexing
2007
Wave atoms and sparsity of oscillatory patterns. Zbl 1132.68068
Demanet, Laurent; Ying, Lexing
2007
Fast computation of Fourier integral operators. Zbl 1157.65522
Candès, Emmanuel; Demanet, Laurent; Ying, Lexing
2007
Fast discrete curvelet transforms. Zbl 1122.65134
Candès, Emmanuel; Demanet, Laurent; Donoho, David; Ying, Lexing
2006
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains. Zbl 1105.65115
Ying, Lexing; Biros, George; Zorin, Denis
2006
The phase flow method. Zbl 1110.65119
Ying, Lexing; Candès, Emmanuel J.
2006
A kernel independent fast multipole algorithm for radial basis functions. Zbl 1089.65018
Ying, Lexing
2006
Fast geodesics computation with the phase flow method. Zbl 1110.65118
Ying, Lexing; Candès, Emmanuel J.
2006
A kernel-independent adaptive fast multipole algorithm in two and three dimensions. Zbl 1053.65095
Ying, Lexing; Biros, George; Zorin, Denis
2004
A fast solver for the Stokes equations with distributed forces in complex geometries. Zbl 1047.76065
Biros, George; Ying, Lexing; Zorin, Denis
2004
all top 5
#### Cited by 1,108 Authors
56 Ying, Lexing 19 Lu, Jianfeng 19 Yang, Haizhao 18 Darve, Eric 17 Lin, Lin 14 Biros, George 14 Gander, Martin Jakob 12 Greengard, Leslie F. 12 Qian, Jianliang 11 Demanet, Laurent 10 Martinsson, Per-Gunnar 10 Tornberg, Anna-Karin 9 Barnett, Alex H. 9 Jiang, Shidong 9 Leung, Shingyu 9 Xia, Jianlin 9 Zorin, Denis N. 8 de Hoop, Maarten V. 8 Gillman, Adrianna 8 Ho, Kenneth L. 8 Li, Yingzhou 8 Saad, Yousef 7 Cai, Wei 7 Quaife, Bryan D. 7 Runborg, Olof 7 Veerapaneni, Shravan Kumar 7 Wei, Guowei 7 Zepeda-Núñez, Leonardo 6 Bao, Gang 6 Damle, Anil 6 Fan, Yuwei 6 Grohs, Philipp 6 Keyes, David Elliot 6 Melenk, Jens Markus 6 Xing, Xin 6 You, Guoqiao 5 Börm, Steffen 5 Bremer, James C. 5 Chow, Edmond G. W. 5 Daubechies, Ingrid Chantal 5 E, Weinan 5 Geuzaine, Christophe A. 5 Helsing, Johan 5 Hu, Guanghui 5 Hu, Jingwei 5 Kutyniok, Gitta 5 Labate, Demetrio 5 Li, Xiaoye Sherry 5 Pérez-Arancibia, Carlos 5 Rachh, Manas 5 Rahimian, Abtin 5 Shelley, Michael J. 5 Spence, Euan A. 5 Stolk, Christiaan C. 5 Tsuji, Paul 5 Xi, Yuanzhe 5 Zhang, Hui 5 Zhao, Hongkai 4 Ambikasaran, Sivaram 4 Bonnet, Marc 4 Bui-Thanh, Tan 4 Calo, Victor Manuel 4 Chaillat, Stéphanie 4 Chen, Duan 4 Cordero, Elena 4 Dolean, Victorita 4 Engquist, Bjorn E. 4 Ghattas, Omar N. 4 Ghysels, Pieter 4 Graham, Ivan G. 4 Hu, Qiya 4 Huang, Jingfang 4 Jin, Shi 4 Klöckner, Andreas 4 Levitt, Antoine 4 Minden, Victor 4 Nicola, Fabio 4 Oseledets, Ivan V. 4 Pardo, David 4 Paszyński, Maciej 4 Plonka, Gerlind 4 Rouet, François-Henry 4 Steidl, Gabriele 4 Turc, Catalin 4 Turkiyyah, George M. 4 Vuik, Cornelis 4 Xu, Zhenli 4 Yang, Xu 4 Ying, Wenjun 4 Zhuang, Xiaosheng 3 Alger, Nick 3 Andersson, Fredrik K. 3 Antoine, Xavier 3 Balakrishnan, Venkataramanan 3 Beale, J. Thomas 3 Bermejo-Moreno, Iván 3 Burridge, Robert 3 Calandra, Henri 3 Cambier, Léopold 3 Cauley, Stephen ...and 1,008 more Authors
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#### Cited in 119 Serials
176 Journal of Computational Physics 79 SIAM Journal on Scientific Computing 46 Applied and Computational Harmonic Analysis 29 Journal of Scientific Computing 29 Multiscale Modeling & Simulation 20 Computers & Mathematics with Applications 17 Advances in Computational Mathematics 15 SIAM Journal on Matrix Analysis and Applications 15 Engineering Analysis with Boundary Elements 13 Computer Methods in Applied Mechanics and Engineering 12 Mathematics of Computation 12 Journal of Computational and Applied Mathematics 11 Numerische Mathematik 11 Numerical Linear Algebra with Applications 9 International Journal of Wavelets, Multiresolution and Information Processing 8 Journal of Fluid Mechanics 8 SIAM Journal on Numerical Analysis 7 BIT 7 SIAM Journal on Imaging Sciences 6 International Journal for Numerical Methods in Engineering 6 Numerical Algorithms 6 The Journal of Fourier Analysis and Applications 6 Research in the Mathematical Sciences 5 Applied Numerical Mathematics 5 Computational Mechanics 5 Acta Numerica 4 Communications on Pure and Applied Mathematics 4 Inverse Problems 4 Wave Motion 4 Journal of Mathematical Imaging and Vision 4 Foundations of Computational Mathematics 4 Science China. Mathematics 3 Computers and Fluids 3 ACM Transactions on Mathematical Software 3 Signal Processing 3 International Journal of Computer Mathematics 3 SIAM Journal on Applied Mathematics 3 SIAM Journal on Mathematical Analysis 3 Mathematical Problems in Engineering 3 Computational Geosciences 2 Applicable Analysis 2 Computer Physics Communications 2 Journal of Mathematical Analysis and Applications 2 Journal of Mathematical Physics 2 Applied Mathematics and Computation 2 Information Sciences 2 Journal of Approximation Theory 2 Chinese Annals of Mathematics. Series B 2 Computer Aided Geometric Design 2 Multidimensional Systems and Signal Processing 2 Pattern Recognition 2 SIAM Review 2 Computational Statistics and Data Analysis 2 Differential Equations and Dynamical Systems 2 Computational Methods in Applied Mathematics 2 Sādhanā 2 Inverse Problems in Science and Engineering 2 Frontiers of Mathematics in China 2 Journal of Pseudo-Differential Operators and Applications 2 SIAM/ASA Journal on Uncertainty Quantification 1 Journal of Engineering Mathematics 1 Mathematical Methods in the Applied Sciences 1 Rocky Mountain Journal of Mathematics 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Functional Analysis 1 Results in Mathematics 1 SIAM Journal on Control and Optimization 1 Transactions of the American Mathematical Society 1 ACM Transactions on Graphics 1 Constructive Approximation 1 Statistical Science 1 Revista Matemática Iberoamericana 1 COMPEL 1 Journal of the American Mathematical Society 1 Mathematical and Computer Modelling 1 Neural Computation 1 Differential Geometry and its Applications 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Applied Mathematical Modelling 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Linear Algebra and its Applications 1 Archive of Applied Mechanics 1 Journal of Nonlinear Science 1 Computational Optimization and Applications 1 Communications in Numerical Methods in Engineering 1 Physics of Fluids 1 ETNA. Electronic Transactions on Numerical Analysis 1 Discrete and Continuous Dynamical Systems 1 Computing and Visualization in Science 1 Abstract and Applied Analysis 1 Mathematical Methods of Operations Research 1 Chaos 1 Communications in Nonlinear Science and Numerical Simulation 1 Annales Henri Poincaré 1 Advances in Difference Equations 1 Oberwolfach Reports 1 Boundary Value Problems 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis ...and 19 more Serials
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#### Cited in 44 Fields
559 Numerical analysis (65-XX) 236 Partial differential equations (35-XX) 84 Optics, electromagnetic theory (78-XX) 82 Fluid mechanics (76-XX) 65 Information and communication theory, circuits (94-XX) 63 Computer science (68-XX) 62 Harmonic analysis on Euclidean spaces (42-XX) 42 Mechanics of deformable solids (74-XX) 34 Statistical mechanics, structure of matter (82-XX) 30 Statistics (62-XX) 29 Quantum theory (81-XX) 26 Approximations and expansions (41-XX) 25 Integral equations (45-XX) 24 Linear and multilinear algebra; matrix theory (15-XX) 20 Biology and other natural sciences (92-XX) 16 Geophysics (86-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 13 Dynamical systems and ergodic theory (37-XX) 12 Probability theory and stochastic processes (60-XX) 12 Operations research, mathematical programming (90-XX) 11 Integral transforms, operational calculus (44-XX) 10 Potential theory (31-XX) 9 Ordinary differential equations (34-XX) 8 Mechanics of particles and systems (70-XX) 7 Operator theory (47-XX) 6 Functional analysis (46-XX) 6 Global analysis, analysis on manifolds (58-XX) 6 Systems theory; control (93-XX) 5 Special functions (33-XX) 3 Real functions (26-XX) 3 Difference and functional equations (39-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Functions of a complex variable (30-XX) 2 Manifolds and cell complexes (57-XX) 1 Mathematical logic and foundations (03-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Abstract harmonic analysis (43-XX) 1 Differential geometry (53-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
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https://pos.sissa.it/396/047/ | Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Poster
Quantum State Preparation for the Schwinger Model
G. Pederiva*, A. Bazavov, B. Henke, L. Hostetler, D. Lee, H.W. Lin and A. Shindler
Full text: pdf
Pre-published on: May 16, 2022
Published on:
Abstract
It is not possible, using standard lattice techniques in Euclidean space, to calculate the complete fermionic spectrum of a quantum field theory. Algorithms running on quantum computers have the potential to access the theory with real-time evolution, enabling a direct computation. As a testing ground we consider the 1+1-dimensional Schwinger model with the presence of a $\theta$ term using a staggered fermions discretization. We study the convergence properties of two different algorithms -adiabatic evolution and the Quantum Approximate Optimization Algorithm- with an emphasis on their cost in terms of CNOT gates. This is crucial to understand the feasibility of these algorithms, because calculations on near-term quantum devices depend on their rapid convergence. We also propose a blocked algorithm that has the first indications of a better scaling behavior with the dimensionality of the problem.
DOI: https://doi.org/10.22323/1.396.0047
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5 728 publications · Export
O. M. Mulyava
Let $F$ and $G$ be analytic functions given by Dirichlet series with exponents increasing to $+\infty$ and zero abscissa of absolute convergence.The growth of $F$ with respect to $G$ is studied through the generalized order$$\varrho^0_{\alpha,\beta}[F]_G=\varlimsup\limits_{\sigma\uparrow 0}\dfrac{\alpha(1/|M^{-1}_G(M_F(\sigma)|)}{\beta(1/|\sigma|)}$$and the generalized lower order $$\lambda^0_{\alpha,\beta}[F]_G=\varliminf\limits_{\sigma\uparrow 0} \dfrac{\alpha(1/|M^{-1}_G(M_F(\sigma)|)}{\beta(1/|\sigma|)},$$ where $M_F(\sigma)=\sup\{|F(\sigma+it)|:\,t\in{\mathbb R}\},$ $M^{-1}_G(x)$ is the function inverse to $M_G(\sigma)$ and $\alpha$ and $\beta$ are positive increasing to $+\infty$ functions.Formulas are found for the finding these quantities.
2021, № 1, p. 44-50
Scopus
M. V. Pratsiovytyi, Ya. V. Goncharenko, N. V. Dyvliash, S. P. Ratushniak
We consider structural, integral, differential properties of function defined by equality$$I(\Delta^{Q_2^*}_{\alpha_1\alpha_2...\alpha_n...})=\Delta^{Q_2^*}_{[1-\alpha_1][1-\alpha_2]...[1-\alpha_n]...}, \quad \alpha_n\in A\equiv\{0,1\}$$for two-symbol polybasic non-self-similar representation of numbers of closed interval $[0;1]$ that is a generalization of classic binary representation and self-similar two-base $Q_2$-representation.For additional conditions on the sequence of bases, singularity of the function and self-affinity of the graph are proved.Namely, the derivative is equal to zero almost everywhere in the sense of Lebesgue measure.The integral of the function is calculated.
2021, № 1, p. 37-43
Scopus
Ya. M. Chabanyuk, A. V. Nikitin, U. T. Khimka
A stochastic approximation procedure and a limit generator of the original problem are constructed for a system of stochastic differential equations with Markov switching and impulse perturbation under Levy approximation conditions with control, which is determined by the condition for the extremum of the quality criterion function.The control problem using the stochastic optimization procedure is a generalization of the control problem with the stochastic approximation procedure, which was studied in previous works of the authors. This generalization is not simple and requires non-trivial approaches to solving the problem. In particular we discuss how the behavior of the boundary process depends on the prelimiting stochastic evolutionary system in the ergodic Markov environment. The main assumption is the condition for uniform ergodicity of the Markov switching process, that is, the existence of a stationary distribution for the switching process over large time intervals. This allows one to construct explicit algorithms for the analysis of the asymptotic behavior of a controlled process. An important property of the generator of the Markov switching process is that the space in which it is defined splits into the direct sum of its zero-subspace and a subspace of values, followed by the introduction of a projector that acts on the subspace of zeros.For the first time, a model of the control problem for the diffusion transfer process using the stochastic optimization procedure for control problem is proposed. A singular expansion in the small parameter of the generator of the three-component Markov process is obtained, and the problem of a singular perturbation with the representation of the limiting generator of this process is solved.
2021, № 1, p. 107-112
Scopus
O. V. Lopotko
A generalization of P. A. Minlos, V. V. Sazonov’s theorem is proved in the case of bounded evenly positive definite function given in a Hilbert space. The integral representation is obtained for a family of bounded commutative self-adjoint operators which are connected by algebraic relationship.
2021, № 1, p. 85-93
Scopus
A. I. Bandura, O. B. Skaskiv, T. M. Salo
We study the following question: Let $f\colon \mathbb{C}\to \mathbb{C}$ be an entire function of bounded $l$-index, $\Phi\colon \mathbb{C}^n\to \mathbb{C}$ an be entire function, $n\geq2,$ $l\colon \mathbb{C}\to \mathbb{R}_+$ be a continuous function. What is a positive continuous function $L\colon \mathbb{C}^n\to \mathbb{R}_+$ and a direction $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}$ such that the composite function $f(\Phi(z))$ has bounded $L$-index in the direction~$\mathbf{b}$?'' In the present paper, early known result on boundedness of $L$-index in direction for the composition of entire functions $f(\Phi(z))$ is modified. We replace a condition that a directional derivative of the inner function $\Phi$ in a direction $\mathbf{b}$ does not equal zero. The condition is replaced by a construction of greater function $L(z)$ for which $f(\Phi(z))$ has bounded $L$-index in a direction. We relax the condition $|\partial_{\mathbf{b}}^k\Phi(z)|\le K|\partial_{\mathbf{b}}\Phi(z)|^k$ for all $z\in\mathbb{C}^n$,where $K\geq 1$ is a constant and ${\partial_{\mathbf{b}} F(z)}:=\sum\limits_{j=1}^{n}\!\frac{\partial F(z)}{\partial z_{j}}{b_{j}},$ $\partial_{\mathbf{b}}^k F(z):=\partial_{\mathbf{b}}\big(\partial_{\mathbf{b}}^{k-1} F(z)\big).$ It is replaced by the condition $|\partial_{\mathbf{b}}^k\Phi(z)|\le K(l(\Phi(z)))^{1/(N(f,l)+1)}|\partial_{\mathbf{b}}\Phi(z)|^k,$ where $N(f,l)$ is the $l$-index of the function $f.$The described result is an improvement of previous one.
2021, № 1, p. 51-56
Scopus
I. V. Protasov
A coarse structure $\mathcal{E}$ on a set $X$ is called finitary if, for each entourage $E\in \mathcal{E}$, there exists a natural number $n$ such that $E[x]< n$ for each $x\in X$. By a finitary approximation of a coarse structure $\mathcal{E}^\prime$, we mean any finitary coarse structure $\mathcal{E}$ such that $\mathcal{E}\subseteq \mathcal{E}^\prime$.If $\mathcal{E}^\prime$ has a countable base and $E[x]$ is finite for each $x\in X$ then $\mathcal{E}^\prime$has a cellular finitary approximation $\mathcal{E}$ such that the relations of linkness on subsets of $( X,\mathcal{E}^\prime)$ and $( X, \mathcal{E})$ coincide.This answers Question 6 from [8]: the class of cellular coarse spaces is not stable under linkness. We define and apply the strongest finitary approximation of a coarse structure.
2021, № 1, p. 33-36
Scopus
Kh. V. Mamalyha, M. M. Osypchuk
This article is aimed at determining existence conditions of single layer potentials for pseudo-differential equations related to some linear transformations of a rotationally invariant stable stochastic process in a multidimensional Euclidean space and investigating their properties as well. The carrier surface of the potential is smooth enough. In this article, we consider two main cases: the first, when this surface is bounded and closed; the second, when it is unbounded, but could be presented by an explicit equation in some coordinate system. The density of this potential is a continuous function. It is bounded with respect to the spatial variable and, probably, has an integrable singularity with respect to the time variable at zero. Classic properties of this potential, including a jump theorem of the action result of some operator (an analog of the co-normal differential) at its surface points, considered.
 A rotationally invariant $\alpha$-stable stochastic process in $\mathbb{R}^d$ is a L\'{e}vy process with the characte\-ristic function of its value in the moment of time $t>0$ defined by the expression $\exp\{-tc|\xi|^\alpha\}$, $\xi\in\mathbb{R}^d$, where $\alpha\in(0,2]$, $c>0$ are some constants. If $\alpha=2$ and $c=1/2$, we get Brownian motion and classic theory of potential. There are many different results in this case. The situation of $\alpha\in(1,2)$ is considered in this paper. We study constant and invertible linear transformations of the rotationally invariant $\alpha$-stable stochastic process. The related pseudo-differential equation is the parabolic equation of the order $\alpha$ of the heat'' type in which the operator with respect to the spatial variable is the process generator. The single layer potential is constructed in the same way as the single layer potential for the heat equation in the classical theory of potentials. That is, we use the fundamental solution of the equation, which is the transition probability density of the related process. In our theory, the role of the gradient operator is performed by some vector pseudo-differential operator of the order $\alpha-1$. We have already studied the following main properties of the single layer potentials: the single layer potential is a solution of the relating equation outside of the carrier surface and the jump theorem is held. These properties can be useful to solving initial boundary value problems for the considered equations.
2021, № 1, p. 94-106
Scopus
P.V. Danchev
We investigate a few special decompositions in arbitrary rings and matrix rings over indecomposable rings into nilpotent and idempotent elements. Moreover, we also define and study the nilpotent sum trace number of nilpotent matrices over an arbitrary ring. Some related notions are explored as well.
2021, № 1, p. 24-32
Scopus
D. Bedoya, M. Ortega, W. Ramírez, A. Urieles
We introduce two biparametric families of Apostol-Frobenius-Euler polynomials of level-$m$. We give some algebraic properties, as well as some other identities which connect these polynomial class with the generalized $\lambda$-Stirling type numbers of the second kind, the generalized Apostol--Bernoulli polynomials, the generalized Apostol--Genocchi polynomials, the generalized Apostol--Euler polynomials and Jacobi polynomials. Finally, we will show the differential properties of this new family of polynomials.
2021, № 1, p. 10-23
Scopus
P. Sahoo, G. Biswas
In this paper, we study the value distribution of the differential polynomial $\varphi f^2f^{(k)}-1$, where $f(z)$ is a transcendental meromorphic function, $\varphi (z)\;(\not\equiv 0)$ is a small function of $f(z)$ and $k\;(\geq 2)$ is a positive integer. We obtain an inequality concerning the Nevanlinna Characteristic function $T(r,f)$ estimated by reduced counting function only. Our result extends the result due to J.F. Xu and H.X. Yi [J. Math. Inequal., 10 (2016), 971-976].
2021, № 1, p. 64-75
Scopus | 2021-04-14T08:09:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8448532223701477, "perplexity": 310.96014388205606}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038077336.28/warc/CC-MAIN-20210414064832-20210414094832-00605.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action;jsessionid=BFAC96E851BA1DC3429CFE993F3B2306?node=S025MSS&init=0 | # Stable Charged Heavy Lepton (${{\mathit L}^{\pm}}$) MASS LIMITS INSPIRE search
VALUE (GeV) CL% DOCUMENT ID TECN
$\bf{>102.6}$ 95
2001 B
L3
• • • We do not use the following data for averages, fits, limits, etc. • • •
$>28.2$ 95 1
1990 C
TOPZ
$\text{none 18.5 - 42.8}$ 95
1990 O
OPAL
$>26.5$ 95
1990 F
ALEP
$\text{none } {\mathit m}_{{{\mathit \mu}}}-36.3$ 95
1990
MRK2
1 ADACHI 1990C put lower limits on the mass of stable charged particles with electric charge $\mathit Q$ satisfying 2/3 $<$ $\mathit Q/{{\mathit e}}$ $<$ 4/3 and with spin 0 or 1/2. We list here the special case for a stable charged heavy lepton.
References:
ACHARD 2001B
PL B517 75 Search for Heavy Neutral and Charged Leptons in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Annihilation at LEP
PL B252 290 Search for Pair Produced Stable Singly-Charged Heavy Particles in ${{\mathit Z}^{0}}$ Decays
PL B236 511 A Search for New Quarks and Leptons from ${{\mathit Z}^{0}}$ Decay
PRL 64 2980 A Search for Pair Production of Heavy Stable Charged Particles in ${{\mathit Z}^{0}}$ Decays | 2018-02-23T06:38:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5686876773834229, "perplexity": 4514.598402341355}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814493.90/warc/CC-MAIN-20180223055326-20180223075326-00785.warc.gz"} |
https://par.nsf.gov/biblio/10350421-stellar-revival-repeated-flares-deeply-plunging-tidal-disruption-events | This content will become publicly available on March 1, 2023
Stellar Revival and Repeated Flares in Deeply Plunging Tidal Disruption Events
Abstract Tidal disruption events with tidal radius r t and pericenter distance r p are characterized by the quantity β = r t / r p , and “deep encounters” have β ≫ 1. It has been assumed that there is a critical β ≡ β c ∼ 1 that differentiates between partial and full disruption: for β < β c a fraction of the star survives the tidal interaction with the black hole, while for β > β c the star is completely destroyed, and hence all deep encounters should be full. Here we show that this assumption is incorrect by providing an example of a β = 16 encounter between a γ = 5/3, solar-like polytrope and a 10 6 M ⊙ black hole—for which previous investigations have found β c ≃ 0.9—that results in the reformation of a stellar core post-disruption that comprises approximately 25% of the original stellar mass. We propose that the core reforms under self-gravity, which remains important because of the compression of the gas both near pericenter, where the compression occurs out of the orbital plane, and substantially after pericenter, where compression is within the plane. We find that the core forms on more »
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10350421
Journal Name:
The Astrophysical Journal Letters
Volume:
927
Issue:
2
Page Range or eLocation-ID:
L25
ISSN:
2041-8205
We develop a Newtonian model of a deep tidal disruption event (TDE), for which the pericenter distance of the star,rp, is well within the tidal radius of the black hole,rt, i.e., whenβrt/rp≫ 1. We find that shocks form forβ≳ 3, but they are weak (with Mach numbers ∼1) for allβ, and that they reach the center of the star prior to the time of maximum adiabatic compression forβ≳ 10. The maximum density and temperature reached during the TDE follow much shallower relations withβthan the previously predicted$ρmax∝β3$and$Tmax∝β2$scalings. Belowβ≃ 10, this shallower dependence occurs because the pressure gradient is dynamically significant before the pressure is comparable to the ram pressure of the free-falling gas, while aboveβ≃ 10, we find that shocks prematurely halt the compression and yield the scalings$ρmax∝β1.62$and$Tmax∝β1.12$. We find excellent agreement between our results and high-resolution simulations. Our results demonstrate that, in the Newtonian limit, the compression experienced by the star is completely independent of the mass of the black hole. We discuss our results in the context of existing (affine) models, polytropic versus non-polytropic stars, and general relativistic effects, which become important when the pericenter ofmore »
The tidal disruption of stars by supermassive black holes (SMBHs) probes relativistic gravity. In the coming decade, the number of observed tidal disruption events (TDEs) will grow by several orders of magnitude, allowing statistical inferences of the properties of the SMBH and stellar populations. Here we analyze the probability distribution functions of the pericenter distances of stars that encounter an SMBH in the Schwarzschild geometry, where the results are completely analytic, and the Kerr metric. From this analysis we calculate the number of observable TDEs, defined to be those that come within the tidal radiusrtbut outside the direct capture radius (which is, in general, larger than the horizon radius). We find that relativistic effects result in a steep decline in the number of stars that have pericenter distancesrp≲ 10rg, whererg=GM/c2, and that for maximally spinning SMBHs the distribution function ofrpat such distances scales as$frp∝rp4/3$, or in terms ofβrt/rpscales asfββ−10/3. We find that spin has little effect on the TDE fraction until the very-high-mass end, where instead of being identically zero the rate is small (≲1% of the expected rate in the absence of relativistic effects). Effectively independent of spin, if the progenitorsmore » | 2022-12-01T14:41:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7329221963882446, "perplexity": 1358.5789205275523}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710813.48/warc/CC-MAIN-20221201121601-20221201151601-00460.warc.gz"} |
https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/valcount.htm | Dataplot Vol 2 Vol 1
# VALUE COUNT
Name:
VALUE COUNT (LET)
Type:
Let Subcommand
Purpose:
Compute the number of elements in a variable that are equal to a specified value.
Syntax:
LET <par> = VALUE COUNT <x1>
<SUBSET/EXCEPT/FOR qualification>
where <x1> is the variable for which the size is to be computed;
<par> is a parameter where the size is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET XVALUE = 6
LET NVAL = VALUE COUNT Y
Note:
The value that is being checked is specified by entering the command
LET XVALUE = <value>
before entering the VALUE COUNT command.
Note:
Dataplot statistics can be used in a number of commands. For details, enter
Note that the VALUE COUNT statistic can also be computed using
LET VALCNT = SIZE Y SUBSET Y = VALUE
However, the VALUE COUNT command becomes more convenient when used with these various statistics. In particular, it is useful for obtaining counts with the various cross tabulation statistics. This is demonstrated in the Program 2 example below.
Default:
None
Synonyms:
None
Related Commands:
SIZE = Compute the number of elements in a vector.
Applications:
Data Management
Implementation Date:
2014/04
Program 1:
let y = normal rand numb for i = 1 1 100
let y2 = y
let y2 = 3 subset y > 3
let y2 = -3 subset y < -3
.
let xvalue = 3
let nouth = value count y2
let xvalue = -3
let noutl = value count y2
.
set write decimals 3
print nouth noutl
The following output is generated.
PARAMETERS AND CONSTANTS--
NOUTH -- 0.000
NOUTL -- 1.000
Program 2:
skip 25
let yout = y
let yout = -1 subset y < 0.2
let yout = 1 subset y > 0.4
.
set let cross tabulate collapse
let x1id = cross tabulate group one x1 x2
let x2id = cross tabulate group two x1 x2
let ycnt = cross tabulate size x1 x2
let xvalue = -1
let ylow = cross tabulate value count yout x1 x2
let xvalue = 1
let yhigh = cross tabulate value count yout x1 x2
.
set write decimals 0
print ycnt ylow yhigh x1id x2id
The following output is generated.
---------------------------------------------------------------------------
YCNT YLOW YHIGH X1ID X2ID
---------------------------------------------------------------------------
4 2 0 1 1
4 0 0 1 2
4 1 0 1 3
4 0 0 2 1
4 0 3 2 2
4 0 1 2 3
4 4 0 3 1
4 1 0 3 2
4 1 0 3 3
NIST is an agency of the U.S. Commerce Department.
Date created: 06/23/2014
Last updated: 06/23/2014 | 2018-05-26T09:58:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2536473274230957, "perplexity": 8064.64203198323}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867416.82/warc/CC-MAIN-20180526092847-20180526112847-00560.warc.gz"} |
https://conferences.lbl.gov/event/195/contributions/1057/ | # RIKEN Berkeley Workshop: Quantum Information Science
25-29 January 2019
LBL-Hill
US/Pacific timezone
## Faster classical sampling from distributions defined by quantum circuits
26 Jan 2019, 11:30
40m
Building 66- Auditorium (LBL-Hill)
### Building 66- Auditorium
#### LBL-Hill
Lawrence Berkeley National Lab Berkeley, California
Foundations of quantum computing
### Speaker
Igor Markov (University of Michigan)
### Description
The leading candidate task for benchmarking quantum computers against classical computers entails sampling from the output distribution defined by a random quantum circuit. We develop a massively-parallel simulation package that does not require inter-process communication (IPC) or proprietary hardware. We introduce two ways to trade circuit fidelity for computational speedups, so as to match the fidelity of a given quantum computer. Our software achieves massive speedups for the sampling task over prior software from Microsoft, IBM, Alibaba and Google, as well as supercomputer and GPU-based simulations. By using publicly available Google Cloud Computing, we price such simulations and enable comparisons by total cost across hardware platforms. We simulate approximate sampling from the output of a circuit with $7\times 8$ qubits and depth 1+40+1 by producing one million bitstring probabilities with fidelity 0.5 percent, at an estimated cost of USD 35184. Simulating circuits of depth to 1+48+1 would cost one million dollars.
### Primary author
Igor Markov (University of Michigan)
### Co-authors
Ms Aneeqa Fatima (Univ. of Michigan) Dr Sergei Isakov (Google Zurich) Dr Sergio Boixo (Google)
### Presentation Materials
There are no materials yet. | 2022-06-28T06:46:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4189765155315399, "perplexity": 12197.077256379403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103355949.26/warc/CC-MAIN-20220628050721-20220628080721-00523.warc.gz"} |
https://www.bls.gov/opub/hom/cex/calculation.htm | United States Department of Labor
The .gov means it's official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you're on a federal government site.
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The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.
## Consumer Expenditures and Income: Calculation
The Bureau of Labor Statistics (BLS) processes and prepares Consumer Expenditures Survey (CE) microdata for analysis and publication. At a high level, this processing includes ensuring consistency among reported values, identifying and correcting errors (e.g., misclassified expenditures) in the data, imputing missing values (see below), and classifying (or “mapping”) expenditures to BLS spending categories. In addition, the primary statistic calculated is the average annual expenditure per consumer unit (CU). It is a weighted average whose calculation follows well-established statistical principles. BLS computes weights to allow the sample data results to reflect the population, measured in CUs. In addition, BLS adjusts data by adding sales tax, netting out reimbursements, and excluding business-related expenses.
BLS adjusts data to two surveys: Interview Survey and Diary Survey.
#### Interview Survey
BLS completes three major types of CE data adjustment routines: imputation; allocation; and time adjustment. Imputation routines are used for income tax estimation, and to “fill in” or correct missing or invalid entries. Imputation addresses all types of the data (demographics, income, and expenditures) except assets. Allocation routines are used for respondents who provide insufficient detail to meet tabulation requirements. For example, combined expenditures for the fuels and utilities group are allocated among the components of that group, such as natural gas and electricity. Time adjustment routines are used to classify expenditures reported quarterly by month of occurrence, prior to aggregation of the data to calendar-year expenditures.
#### Diary Survey
Two types of data adjustment routines, imputation and allocation, improve the Diary Survey estimates. BLS imputes missing attributes, such as age, sex, or expenditure amount. Allocation routines transform reports of nonspecific items into specific ones. For example, when respondents report expenditures for meat rather than beef or pork, allocations are made, using proportions derived from item-specific reports in other completed diaries. Income tax data are not estimated for the Diary Survey because the published integrated information uses Interview Survey after-tax income information, and because of the limited amount of background detail collected in the Diary Survey.
#### Imputation
To publish an accurate estimation of spending for CUs, BLS imputes values for missing or inconsistent data fields. There are four broad types of missing values imputed in the CE: demographic characteristics about the CU and its members; missing values for reported expenditure items; and attributes about a reported expenditure (e.g., whether a car is purchased new or used); and income. Depending on what type of data fields are being imputed, different methods of imputation are used. These methods include:
• Hot deck imputation, where values are copied from other CUs that share similar characteristics;
• Cold deck imputation, where values are copied from households with similar characteristics in another data source;
• Weighted mean imputation, where a weighted average of all values reported by CUs that share similar characteristics is used for the missing value;
• Percent distribution imputation, used for non-numeric attribute information (such as demographic information about members in the CU) where a value is randomly assigned based on the distribution of reported values;
• Regression analysis, where values are predicted using a model of independent variables;
• Multiple imputation, used for income imputation, in which the model is ”shocked” with noise to obtain five estimates of income. More details on income imputation can be found in the Data Adjustments section in CE FAQs and the user's guide to income imputation in the CE; and
• Income tax estimation, where all state and federal income taxes are estimated for all CUs in the Interview Survey, which is used for publication tables. BLS uses an internal version of the National Bureau of Economic Research’s TAXSIM software in estimating tax liabilities. Tax liabilities reflect only what TAXSIM estimates is owed, but not necessarily the actual amount that the CU paid. Along with tax liabilities, refundable credits owed to a CU (e.g., additional child tax credit, earned income tax credit) are estimated for each CU regardless of whether the CU received them. For more information about income tax estimation, see the Data Adjustments section in CE FAQs.
#### Allocation
BLS allocates data to provide information at a sufficient level of detail to meet tabulation requirements. This situation arises when a respondent does not provide the required amount of detail for an expenditure (e.g., the respondent reports “various household appliances” instead of separate reports of a “microwave” and a “blender”). Similar to imputation, BLS uses different methods of allocation dependent on the type of expenditure: distribution ratio, fixed ratio, and probability distribution ratio.
• The distribution ratio is used when specific items within a combined reported item is known and the reported value is assigned in a proportional amount as determined by reported records to those items.
• Fixed ratios are used to assign a proportion of the reported value to specific items based on proportions identified from other data sources.
• The probability distribution ratio is used when specific items in each category are unknown. Percentiles are determined for all potential items in the category and a selected subset of target item codes for which the lower quartile is less than the expenditure reported that requires allocation. A random selection of 6 to 12 targets are chosen, and the mean value for each selected item is subtracted from the combined reported expenditure. This is repeated until the total amount of the reported expenditure is exhausted.
### Calculation methodology
After collecting expenditure data from a representative sample of CUs across the nation, the sample is weighted to produce estimates for the U.S. population of CUs as a whole. For this purpose, each CU in the survey is assigned a weight equal to the number of similar CUs in the nation that it represents.
Several factors are involved in computing the weight of each CU from which a usable interview is received. Each CU is initially assigned a base weight equal to the inverse of its probability of being selected for the sample. The probability is the number of addresses selected for the sample divided by the total number of addresses in the Census Bureau’s master address file. CE base weights are typically around 10,000, which means a CU in the sample represents 10,000 CUs in the U.S. civilian noninstitutional population―itself plus 9,999 other CUs that were not selected for the sample. The base weight is then adjusted by the following factors to correct for certain nonsampling errors:
Weighting control factor adjusts for subsampling in the field. Subsampling occurs when a data collector visits a particular address and discovers multiple housing units where only one housing unit was expected.
Noninterview adjustment factor adjusts for interviews that cannot be conducted in occupied housing units because of a CU’s refusal to participate in the survey or the inability to contact anyone at the housing unit despite repeated contact attempts. This adjustment is based on region of the country, CU size, number of contact attempts, and the average adjusted gross income in the CU’s zip code according to a publicly available database from the Internal Revenue Service.
Calibration factor adjusts the weights to 35 known population counts to account for frame undercoverage. These known population counts are for age, race, household tenure (owner or renter), division of the country, urbanicity (urban or rural), and ethnicity (Hispanic or non-Hispanic). The population counts are updated quarterly using the Current Population Survey (CPS) estimates.1 Each CU is given its own unique calibration factor. There are infinitely many sets of calibration factors that can make the weights add up to the 35 known population counts. BLS uses nonlinear programming to select the set that minimizes the amount of change made to the “initial weights” (initial weight = base weight x weighting control factor x noninterview adjustment factor).
After adjusting the base weights by these factors, the final weights are typically around 25,000, which means an interviewed CU represents 25,000 CUs in the U.S. civilian noninstitutional population―itself plus 24,999 other CUs that did not participate in the survey.
### Using the weights
Using these weights, the average expenditure per CU on a particular item is estimated with the standard weighted average formula:
where,
For example, if is the expenditure on eggs made by the CU in the sample during a given time period, then is an estimate of the average expenditure on eggs made by all CUs in the U.S. civilian noninstitutional population during that period.
### Calculation precision
The precision of the estimator is measured by its standard error. Standard errors measure the sampling variability of the CE estimates. That is, standard errors measure the uncertainty in the survey estimates caused by the fact that a random sample of CUs from across the United States is used instead of every CU in the nation. (See table 1.)
The CE’s standard errors are estimated by using the method of “balanced repeated replication.” In this method, the sampled PSUs are divided into 43 groups (called strata), and the CUs within each stratum are randomly divided into two half samples. Half of the CUs are assigned to one half sample, and the other half are assigned to the other half sample. Then 44 different estimates of are created using data from only one half sample per stratum. There are many combinations of half samples that can be used to create these replicate estimates, and the CE uses 44 of them that are created in a “balanced” way with a 44x44 Hadamard matrix. The standard error of is then estimated by:
where is the r th replicate estimate of .
The coefficient of variation is a related measure of sampling variability that measures the variability of the survey estimate relative to the mean. It is defined by the equation:
Table 1. Precision of the Consumer Expenditure Surveys expenditure estimates, integrated Diary and Interview Survey data, 2019
Item Average annual expenditure per consumer unit Standard error, SE(ȳ) Coefficient of variation, CV(ȳ) (in percent)
Total expenditures
$63,036$578 0.92
Food
8,169 119 1.45
Housing
20,679 195 0.94
Apparel
1,883 69 3.64
Transportation
10,742 194 1.81
Healthcare
5,193 70 1.35
Entertainment
3,090 129 4.19
Personal care
786 14 1.76
92 6 7.03
Education
1,443 86 5.93
Tobacco products and smoking supplies
320 11 3.57
Miscellaneous
899 43 4.73
Cash contributions
1,995 109 5.48
Personal insurance and pensions
7,165 131 1.83
Source: U.S. Bureau of Labor Statistics.
### Integrated survey data
Integrated data from the Interview and Diary Surveys provide an approximately complete accounting of consumer expenditures which neither survey component alone is designed to do. For example, most food expenditures in the integrated data tables come from the Diary Survey, which includes detailed items (e.g., rice, strip steak, breakfast purchased from full-service restaurants) not collected in the Interview Survey, while rent, mortgage interest, utilities, and major appliances, which are less likely to be observed during the week of Diary Survey participation, come from the Interview Survey, for which respondents report based on a three-month recall period.
The Interview Survey collects data on expenditures for overnight travel and information on insurance reimbursements for medical care costs and automobile repairs, which are not collected in the Diary Survey. Based on integrated Interview and Diary Surveys data, expenditure data that come exclusively from the Interview Survey, along with global estimates, such as those for food and alcoholic beverages, average about 95 percent of total estimated spending.
For items unique to one or the other survey, the choice of which survey to use as the source of data is obvious. However, there is considerable overlap in coverage between the surveys. Because of the overlap, the integration of the data presents the problem of determining the appropriate survey component from which to select the expenditure items. When data are available from both survey sources, the more reliable of the two is selected, as determined by statistical methods. The selection of the survey source is evaluated every two years. For more information on the source selection process, see the 2011 Anthology article CE source selection for publication tables.
###### Notes
1 The CPS estimates the total number of people in the U.S. civilian noninstitutional population every month, and BLS averages the three monthly population estimates for its quarterly population estimates. The CPS generates its monthly population estimates by taking the Census Bureau’s “official” population estimates from the previous year and updating them to account for the births, deaths, and net migration (immigration minus emigration) that occur each month. | 2023-01-29T07:20:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5496775507926941, "perplexity": 3177.8115720128167}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499700.67/warc/CC-MAIN-20230129044527-20230129074527-00470.warc.gz"} |
https://geodynamics.org/cig/software/conman/ | Status:
Actively supported, maintained and upgraded by community contributors.
## How to Cite
Community:
Geodynamics Forum
Bug reports:
Github Issue Tracker
# ConMan
ConMan is a finite element program for the solution of the equations of incompressible, infinite-Prandtl number convection in two dimensions, originally written by Scott King, Arthur Raefsky, and Brad Hager.
ConMan is a public domain program and is distributed free of charge to anyone who wishes to use it, and may be freely copied and modified. ConMan is written in Standard Fortran 77 with cray pointers and runs on most UNIX systems with many Fortran compilers. Porting it to other systems should be straightforward. As with anything free, ConMan comes with no guarantees, but it has been benchmarked against other existing codes.
There are several significant differences that the user familiar with past versions of ConMan will find in the 3.0 version. First, we removed the clunky memory manager library (a set of routines wrapped around the c function malloc) and replaced them with FORTRAN 90's allocate and deallocate functions.?This eliminates many of the compilation problems people experienced with the 2.0 version.?Most of these routines were in files subroutines input and elminp.
As part of a general clean up, we replaced the separate input and elminp (both input subroutines) and created a new input subroutine. As part of this we removed the element library' function (eglib.F and eg2.F) which was a structure originally designed for different formulations 2D Cartesian, 3D Cartesian, spherical axysymmetric, ...). Because these were never fully developed, it made on sense to retain the cumbersome structure. We also moved all out the subroutines associated with output, into new output subroutine. The user does not need to hunt through the time_driver subroutine to find out where the specific output subroutines are called. Thus, subroutines geoid, fluxke, masflx, print, output_rheol, print_compbm_data, and stress are all in subroutine output.
We also changed the names of many of the subroutines to take advantage of longer subroutine names allowed by modern FORTRAN. Thus f_tlhs has become form_temp_matrix, f_vres has become form_vel-ocity_rhs, f_vstf has become form_velocity_stiffness_matrix. Similarly, subroutine timdrv has become time_driver. As you look through the code there are examples where this could have been carried further.
Second, Picard iteration for the temperature equation is now a runtime option as opposed to a compiler option. This necessitated specifying both implicit and explicit subroutines for the temperature right hand side, form_temp_rhs_implicit and form_temp_rhs_explicit, a well as a form_temp_matrix for the implicit temperature matrix and form_temp_mass_matrix for the lumped mass matrix that has traditionally been used for the explicit version of the temperature solver.
Third, we added the EBA, TALA, and ALA formulations as described in [King et al, 2010]. The compressible formulation is described in Chapter 3 of the manual. This required a number of changes throughout the form_temperature and form_velocity subroutines. We provide a test suite that runs a subset of the problems from [King et al., 2010] that can be used to verify the installation version 3.0.0
Finally, we have added a cookbook of subduction wedge problems based on problems from the subduction zone benchmark paper [vanKeken et al., 2008] and one based on the compressible convection benchmark paper [King et al., 2010]. This required adding a new 'fault' subroutine and a subroutine to implement the Batchelor corner flow boundary conditions. These can be found in the subduct.src directory.
## Current Release
### Source Packages
ConMan-3.0.0.tar.gz [2020-01-31]
v 3.0 has several significant differences than previous versions See release notes.
### View Prior Source Releases
[show] [hide]
ConMan-2.0.0.tar.gz [2008-09-17]
Latest release solves equations of 2D Cartesian incompressible thermal convection with an explicit or Picard time iteration scheme.
## User Resources
User Manual
The ConMan user manual is available online.
Community Wiki
Visit the ConMan Wiki page for additional support with building, using, or modifying ConMan.
ConMan Publications List
Research publications using ConMan.
Community Discussion
Browse the CIG Mailing List Archive to find past discussions and previous troubleshooting help, or post to the CIG forum with questions or comments.
## Developer Resources
Development Version
If you are interested in getting the development version of this code from the CIG repository, use the following git command:
git clone --recursive https://github.com/geodynamics/conman.git`
You can also browse the history of modifications in the Git repository.
Issue/Bug Tracker on Github
Browse and/or submit new issues at our Github Issues Tracker.
Doxygen Documentation
Auto-generated Doxygen documentation is available for the Development codebase.
## ConMan Users Map
Shows location of all users who downloaded ConMan in the past year (image updated daily.)
This image was generated using GMT: The Generic Mapping Tools which is released under the GNU LGPL3+. Location data is based on MaxMind's GeoLite database which is released under the Creative Commons CC-BY-SA 3.0. | 2020-07-09T05:21:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22132202982902527, "perplexity": 4197.51078297757}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655898347.42/warc/CC-MAIN-20200709034306-20200709064306-00169.warc.gz"} |
https://wiki.cosmos.esa.int/planckpla/index.php?title=Cosmological_Parameters&oldid=5290 | # Cosmological parameter results
## Description
The cosmological parameter results explore a variety of cosmological models with combinations of Planck and other data. We provide results from MCMC exploration chains, as well as best fits, and sets of parameter tables. Definitions, conventions and reference are contained in #planck2013-p11.
## Production process
Parameter chains are produced using CosmoMC, a sampling package available from [1]. This includes the sample analysis package GetDist, and the scripts for managing and analysing the full grid or runs. Chain products provided here have had burn in removed. Some results with additional data are produced by importance sampling.
## Caveats and known issues
Confidence intervals are derived from the MCMC samples, and assume the input likelihoods are exactly correct, so there is no quantification for systematic errors other than via the covariance, foreground and beam error models assumed in the likelihood codes. We had some issues producing reliable results from the minimizer used to produce the best fits, so in some cases the quoted fits may be significantly improved.
## Related products
Results of the parameter exploration runs should be reproducible using CosmoMC with the Planck likelihood code.
## Parameter Tables
These list paramter constraints for each considered model and data combination separately
There are also summary comparison tables, showing how constraints for selected models vary with data used to constrain them:
## Parameter Chains
We provide the full chains and getdist outputs for our parameter results.
The download contains a hierarchy of directories, with each separate chain in a separate directory. The structure for the directories is
base_AAA_BBB/XXX_YYY_.../
where AAA and BBB are any additional parameters that are variend in addition to the six parameters of the baseline model. XXX, YYY, etc encode the data combinations used. The parameter tags are defined in #planck2013-p11. Data combination tags are as follows (see the parameters paper for full description and references):
Data tags
Tag Data
planck high-L Planck temperature (CamSpec, 50 <= l <= 2500)
lowl low-L: Planck temperature (2 <= l <= 49)
lensing Planck lensing power spectrum reconstruction
lowLike low-L WMAP 9 polarization
tauprior A Gaussian prior on the optical depth, tau = 0.09 +- 0.013
BAO Baryon oscillation data from DR7, DR9 and and 6DF
SNLS Supernova data from the Supernova Legacy Survey
Union2 Supernova data from the Union compilation
HST Hubble parameter constraint from HST (Riess et al)
WMAP The full WMAP (temperature and polarization) 9 year data
Data likelihoods are either included when running the chains, or by importance sampling. Data combinations that are added by importance sampling appear at the end of the list, following the {\tt post{\textunderscore}} tag. WMAP9 chains are run from the WMAP9 likelihood code with the same baseline assumptions as \textit{Planck}, and hence may different slightly from those available on Lambda (e.g. the baseline model has non-zero neutrino mass). Note that the best fits are merely examples of parameter combinations that fit the data well, due to parameter degeneracies there may be other combinations of parameters that fit the data nearly equally well.
Beneath each table is the minus log Likelihood $\chi^2_{\rm eff}$ for each best fit model, and also the contributions coming from each separate part of the likelihood. The $R-1$ value is also given, which measures the convergence of the sampling chains, with small values being better converged. The sampling uncertainty on quoted mean values are typically of order $R-1$ in units of the standard deviation.
## References
<biblio force=false>
1. References
</biblio> | 2021-10-28T21:19:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6970013976097107, "perplexity": 2936.7449387678807}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588526.57/warc/CC-MAIN-20211028193601-20211028223601-00304.warc.gz"} |
https://fermi.gsfc.nasa.gov/ssc/data/analysis/gbm/gbm_data_tools/gdt-docs/notebooks/Visualizations.html | # Visualizations¶
The GBM data tools would be incomplete if we didn’t provide a way to visualize the data. We provide a number of different levels of plotting. At the most basic level (and the level we hope you don’t sink to), there is a library of plotting functions in gbm.plot.lib. The next level up, we have plotting classes in gbm.plot.gbmplot which contain a variety of special plotting elements designed for the data tools. An example of one of these plot elements is a Histo class which, yes, plots a histogram. But it is special in that we want to plot histograms that may have gaps in it (i.e. SAA passage). These plot elements can be added to a new plot with little effort as long as you instantiate them correctly.
At the highest level are plotting classes for specific views that can keep track of various plot elements in a single plot. For example, plotting a lightcurve with a background model and signal selection requires us to keep track of Histo, HistoErrorbars, LightcurveBackground, and HistoFilled plot objects. We’ll show a few characteristics of how plotting works, but the full capability is somewhat limited in Jupyter. If you are making plots in ipython, you can interactively modify the plots through the ipython environment.
## Lightcurves and Spectra¶
Let’s revisit the example in the PHA Export tutorial:
[1]:
from gbm import test_data_dir
from gbm.data import TTE
from gbm.binning.unbinned import bin_by_time
from gbm.background import BackgroundFitter
from gbm.background.binned import Polynomial
# some selections
erange = (8.0, 900.0)
bkgd_times = [(-20.0, -5.0), (75.0, 200.0)]
src_time = (6.0, 8.0)
# open TTE and bin
tte = TTE.open(test_data_dir+'/glg_tte_n9_bn090131090_v00.fit')
phaii = tte.to_phaii(bin_by_time, 1.024, time_ref=0.0)
lc_data = phaii.to_lightcurve(energy_range=erange)
# fit background
backfitter = BackgroundFitter.from_phaii(phaii, Polynomial, time_ranges=bkgd_times)
backfitter.fit(order=1)
bkgd = backfitter.interpolate_bins(phaii.data.tstart, phaii.data.tstop)
lc_bkgd = bkgd.integrate_energy(*erange)
# source selection
src_lc = phaii.to_lightcurve(time_range=src_time, energy_range=erange)
By default, the plot will show the full extent of the data
[2]:
%matplotlib inline
from gbm.plot import Lightcurve
lcplot = Lightcurve(data=lc_data, background=lc_bkgd)
But you can adjust axis plot properties by setting them as attributes:
[3]:
lcplot = Lightcurve(data=lc_data, background=lc_bkgd)
lcplot.xlim = (-5.0, 20.0)
lcplot.ylim = (1000.0, 5500.)
You can access the various plot elements in the plot, also as attributes:
[4]:
lcplot.lightcurve, lcplot.errorbars, lcplot.background, lcplot.selections
[4]:
(<gbm.plot.gbmplot.Histo at 0x127b72910>,
<gbm.plot.gbmplot.HistoErrorbars at 0x127b8f990>,
<gbm.plot.gbmplot.LightcurveBackground at 0x127b88950>,
[<gbm.plot.gbmplot.HistoFilled at 0x127ae3f50>])
And each plot element has its own set of properties that can be modified. Sometimes we may want to hide a plot element, or want to change the plot element’s color or alpha. You can retrieve this information as attributes, and you can set them like attributes as well.
[5]:
print('Errorbars visible? {}'.format(lcplot.errorbars.visible))
print('Lightcurve color: {}'.format(lcplot.lightcurve.color))
print('Selection alpha: {}'.format(lcplot.selections[0].alpha))
Errorbars visible? True
Lightcurve color: #394264
Selection alpha: 0.2
Say we want to remove the errorbars, change the background model color to purple, and make the selection more opaque:
[6]:
lcplot = Lightcurve(data=lc_data, background=lc_bkgd)
lcplot.xlim = (-5.0, 20.0)
lcplot.ylim = (1000.0, 5500.)
lcplot.errorbars.hide()
lcplot.background.color='purple'
lcplot.selections[0].alpha=0.8
This is particularly elegant in ipython because you can perform these commands interactively without having to remake the whole plot. Plotting the spectrum is similar:
[7]:
from gbm.plot import Spectrum
# our spectral data
spec_data = phaii.to_spectrum(time_range=src_time)
spec_bkgd = bkgd.integrate_time(*src_time)
spec_selection = phaii.to_spectrum(time_range=src_time, energy_range=erange)
specplot = Spectrum(data=spec_data, background=spec_bkgd)
You can set the scale in the plot much the same way you set the view ranges. Plot the spectrum y-axis in linear scale (not sure why you would want to do this though):
[8]:
specplot = Spectrum(data=spec_data, background=spec_bkgd)
specplot.yscale = 'linear'
## Sky Maps¶
Sky map plots are usually used to show the GBM detector pointings and Earth occultation at a given time, or to show the GBM localization of an event on the sky. They have more general functionality however, and you can use various plot elements to add to and customize your sky map plot.
Here’s an example of how you might show the detector pointing for a single detector over the course of a day:
[9]:
import numpy as np
from gbm.data import PosHist
from gbm.plot import SkyPlot
from gbm.plot.gbmplot import SkyPoints # plot element for plotting a single point or many points on the sky
# generate an array of times covering the poshist with frequency 1/minute
poshist = PosHist.open(test_data_dir+'/glg_poshist_all_170101_v00.fit')
times = np.linspace(*poshist.time_range, 14400)
# detector RA, Dec pointings for each of our times
n0_ra, n0_dec = poshist.detector_pointing('n0', times)
s = SkyPlot() # initialize
# plot the points as green dots with marker size 5
pts = SkyPoints(n0_ra, n0_dec, s.ax, color='green', s=5)
Instead, we could plot the detector pointing as a continuous line. Don’t worry, the meridian clipping is already handled for you.
[10]:
from gbm.plot.gbmplot import SkyLine # plot element for plotting a line on the sky
s = SkyPlot()
line = SkyLine(n0_ra, n0_dec, s.ax, color='green')
Similarly, you can plot circles on the sky of whatever size you want. The Earth and detector pointing circles are special cases of the SkyCircle class.
[11]:
from gbm.plot.gbmplot import SkyCircle # plot element for plotting a (shaded) circle on the sky
ras = np.array([244.7, 289.6, 145.4, 104.27, 222.7, 101.6, 26.4, 44.1, 314.5, 91.0])
decs = np.array([-49., -74.0 , -14.3, 80.2, 36.9, -24.5 , 8.6, 59.6, 15.4, 12.3])
colors = np.random.random(size=(10,4))
s = SkyPlot()
circles = [SkyCircle(ras[i], decs[i], radii[i], s.ax, color=colors[i,:]) for i in range(10)]
You can also plot polygons on the sky. These are most useful for plotting confidence regions.
[12]:
from gbm.plot.gbmplot import SkyPolygon # plot element for plotting a (shaded) polygon on the sky
ra_pts = np.array([270.0, 180.0, 90.0])
dec_pts = np.array([15.0, 60.0, 15.0])
s = SkyPlot()
poly = SkyPolygon(ra_pts, dec_pts, s.ax, color='red', alpha=0.6)
Another thing you can do is plot a heatmap on the sky. This is essentially a color gradient that maps a parameter onto the sky, such as localization posterior density.
[13]:
from gbm.data import GbmHealPix
from gbm.plot.gbmplot import SkyHeatmap
loc = GbmHealPix.open(test_data_dir+'/glg_healpix_all_bn190915240_v00.fit')
# converts the healpix grid to grid on the sky for plotting
prob, ra_grid, dec_grid = loc.prob_array(numpts_ra=720, numpts_dec=180)
s = SkyPlot()
heatmap = SkyHeatmap(ra_grid, dec_grid, prob, s.ax)
You can change the color of the heatmap, but this means you need to choose a colormap instead of just a color. Advanced users can create their own. Additionally, you can add a normalization to the colormap that will change how the gradient is distributed. Finally, you can adjust the alpha “gradient” of the map. That is, lower heatmap values will become more transparent than higher heatmap values. The default is to make this gradient go from 0 to 1, but that can be changed.
[14]:
from matplotlib.colors import PowerNorm # power-law normalization for colormaps
# "plasma colormap with 0.3 power-law normalization"
s = SkyPlot()
heatmap = SkyHeatmap(ra_grid, dec_grid, prob, s.ax, color='plasma', norm=PowerNorm(0.3))
[15]:
# and now defining alpha_min=1 (no alpha gradient)
s = SkyPlot()
heatmap = SkyHeatmap(ra_grid, dec_grid, prob, s.ax, color='plasma', norm=PowerNorm(0.3), alpha_min=1.0)
Ok, you should be getting the gist of it now. For all the plot classes, you can add various plot elements or change their plotting properties, like color, alpha, plot symbols, etc. For any of the plot classes, you can hide/show each plot element if you have its reference and modify various properties. While we can demo this here, you should try this in ipython because you can see the plots update dynamically as you enter commands! | 2023-03-23T14:49:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47443336248397827, "perplexity": 6161.561340402222}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945168.36/warc/CC-MAIN-20230323132026-20230323162026-00642.warc.gz"} |
http://wikimechanics.org/definition-binary | Definition: Binary Description
Noun Definition Binary Descriptors $\sf{\text{A mutually exclusive pair of characteristics.}}$ 2-1
Logical Antecedents
Nouns Definition Reference Sensations $\sf{\text{Standards to judge and recognize all perceptions.}}$ 1-1
Note to editors: the layout for this page is determined by this template.
page revision: 7, last edited: 29 Jan 2013 22:44
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License | 2017-09-25T06:07:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6450846195220947, "perplexity": 10570.90519376435}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818690340.48/warc/CC-MAIN-20170925055211-20170925075211-00480.warc.gz"} |
https://simulationresearch.lbl.gov/modelica/userGuide/glossary.html | # 7. Glossary¶
2nd order low pass filter
A second order low pass filter is an input-output block that computes
$\begin{split}\dot x(t) = \begin{pmatrix} r & 0 \\ -r & r \end{pmatrix} \, x(t) + \begin{pmatrix} -r \\ 0 \end{pmatrix} \, u(t)\end{split}$
and
$y(t) = (0, \, 1) \, x(t),$
where $$r$$ is a positive real number. This causes the input signal $$u(\cdot)$$ to be converted to an output signal $$y(\cdot)$$ that is differentiable in time. See the plot of a filtered step response.
compressible flow
The opposite of incompressible flow.
incompressible flow
In fluid mechanics, incompressible flow refers to flow where the mass density is constant within a fluid volume that moves with the fluid.
iterative solver
An iterative solver is a numerical solver that iterates until the approximate solution satisfies a convergence test. Examples include Newton solvers for nonlinear systems of equations, and ordinary differential equation solvers with adaptive time step length.
numerical noise
In numerical solutions, numerical noise refers to fast but small changes in variables whose magnitude is typically smaller than the solver tolerance.
regularization
By regularization, we mean approximating a non-differentiable function by another function that is differentiable and has continuous and bounded derivatives, i.e., a function that is continuously differentiable. Continuous differentiability is a necessary condition for Newton-based solvers to solve nonlinear equations.
state variables
State variables are variables whose time rate of change is defined by a differential equation.
thermo-fluid system
Thermo-fluid systems are systems that compute combined mass and energy flow, such as a heat exchanger in which heat is added to the medium that flows through it.
valve authority
For a control valve, the valve authority $$N$$ is defined as
$N = \frac{\Delta p_v(1)}{\Delta p_v(1) + \Delta p_0},$
where $$\Delta p_v(1)$$ is the pressure drop across the fully open valve, and $$\Delta p_v(1) + \Delta p_0$$ is the pressure drop across the whole flow leg whose mass flow rate is controlled by the valve. Valves should be designed such that $$N$$ is around 0.5, but not higher. | 2021-07-28T01:16:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7388782501220703, "perplexity": 541.4741674879638}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153515.0/warc/CC-MAIN-20210727233849-20210728023849-00273.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/proc.2003.2003.375 | Article Contents
Article Contents
# A global semi-Lagrangian spectral model for the reformulated shallow water equations
• In this paper, we study the semi-Lagrangian spectral method for the shallow-water equations in a rotating, spherical geometry. With the reformulation of a vector calculus identity for spherical geometries, we are able to write the vorticity and divergence equations in advective form and directly apply the semi-Lagrangian, spectral method. The scalar vorticity and divergence equations are used to avoid the pole problems. Shape preserving interpolation is used for the calculation of departure point values for all fields. The results of the standard test set are presented showing accuracy, stability and regularity properties of the method for atmospheric flows.
Mathematics Subject Classification: Primary: 35Q35, 65Q99, 76M22, 86A10.
Citation:
Open Access Under a Creative Commons license | 2023-03-27T19:10:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.20867444574832916, "perplexity": 731.6993230368109}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948684.19/warc/CC-MAIN-20230327185741-20230327215741-00424.warc.gz"} |
https://www.mcs.anl.gov/research/projects/otc/InteriorPoint/abstracts/Kruk-etal-1.html | ## The Gauss-Newton Direction in Semidefinite Programming
### Serge Kruk, Masakazu Muramatsu, Franz Rendl, Robert J. Vanderbei, Henry Wolkowicz
Primal-dual interior-point methods have proven to be very successful for both linear programming (LP) and, more recently, for semidefinite programming (SDP) problems. Many of the techniques that have been so successful for LP have been extended to SDP. In fact, interior point methods are currently the only successful techniques for SDP. We present a new paradigm for deriving these methods: 1) using the optimality conditions from the dual log-barrier problem, we obtain primal feasibility, dual feasibility, and perturbed complementary slackness equations; 2) the perturbed complementary slackness condition is quite nonlinear, so we modify this condition to obtain a bilinear condition, i.e. a condition that is less nonlinear; 3) we now find a search direction by applying the Gauss-Newton method to the least squares problem for these optimality conditions; equivalently we find the least squares solution of the linearized perturbed optimality conditions. In the case of LP, the Gauss-Newton direction for the least squares problem is equivalent to the Newton direction applied to solving the modified (square) nonlinear system of optimality conditions. Though this paradigm does not directly provide a new search direction for linear programming, it does provide a new approach for convergence proofs as well as motivation for step lengths larger than one. However, there is one major difference between LP and SDP that raises several interesting questions. That difference is the form of the perturbed complementarity condition used in the optimality conditions. In LP this condition is modified to be $ZX - \mu I = 0.$ The primal matrix $X$ and the dual slack matrix $Z$ are diagonal in LP but may only be symmetric in SDP; this results in $ZX$ not being symmetric in general, i.e. the optimality conditions in the SDP case end up as an overdetermined system of nonlinear equations. There have been various approaches which modify the complementarity condition so that the linearization of the optimality conditions are square'', i.e. map between the same spaces. These approaches can have several drawbacks, e.g. numerical instability near the optimum and lack of positive definiteness after symmetrization. Our least squares approach requires no symmetrization and does not suffer from these drawbacks. We concentrate on solving the overdetermined, system in the best way possible. In particular, we use Gauss-Newton type methods. This leads to numerically stable as well as excellent search directions which lead to the central path. Though the numerical efficient calculation of the Gauss-Newton direction is still an open question, we present a preliminary top down'' elimination approach that is competitive timewise and empirical evidence suggests that it is often more robust than other directions currently in use.
Contact: [email protected] | 2019-09-15T22:54:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6703341603279114, "perplexity": 435.3839342892289}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572436.52/warc/CC-MAIN-20190915215643-20190916001643-00354.warc.gz"} |
https://pdglive.lbl.gov/Particle.action?node=S126&init=0 | GAUGE AND HIGGS BOSONS INSPIRE search
#### ${{\mathit H}^{0}}$
$J$ = $0$
In the following ${{\mathit H}^{0}}$ refers to the signal that has been discovered in the Higgs searches. Whereas the observed signal is labeled as a spin 0 particle and is called a Higgs Boson, the detailed properties of ${{\mathit H}^{0}}$ and its role in the context of electroweak symmetry breaking need to be further clarified. These issues are addressed by the measurements listed below. Concerning mass limits and cross section limits that have been obtained in the searches for neutral and charged Higgs bosons, see the sections “Searches for Neutral Higgs Bosons” and “Searches for Charged Higgs Bosons (${{\mathit H}^{\pm}}$ and ${{\mathit H}^{\pm\pm}}$)”, respectively.
${{\mathit H}^{0}}$ MASS $125.25 \pm0.17$ GeV (S = 1.5)
${{\mathit H}^{0}}$ SPIN AND $\mathit CP$ PROPERTIES
${{\mathit H}^{0}}$ DECAY WIDTH $3.2 {}^{+2.8}_{-2.2}$ MeV
${{\mathit H}^{0}}$ SIGNAL STRENGTHS IN DIFFERENT CHANNELS
Combined Final States $1.13 \pm0.06$
${{\mathit W}}{{\mathit W}^{*}}$ Final State $1.19 \pm0.12$
${{\mathit Z}}{{\mathit Z}^{*}}$ Final State $1.01 \pm0.07$
${{\mathit \gamma}}{{\mathit \gamma}}$ Final State $1.10 \pm0.07$
${{\mathit c}}{{\overline{\mathit c}}}$ Final State $37 \pm20$
${{\mathit b}}{{\overline{\mathit b}}}$ Final State $0.98 \pm0.12$
${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ Final State $1.19 \pm0.34$
${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ Final State $1.15 {}^{+0.16}_{-0.15}$
${{\mathit Z}}{{\mathit \gamma}}$ Final State $<3.6$ CL=95.0%
${{\mathit \gamma}^{*}}{{\mathit \gamma}}$ Final State $1.5 \pm0.5$
Higgs Yukawa couplings
top Yukawa coupling
OTHER ${{\mathit H}^{0}}$ PRODUCTION PROPERTIES
${{\mathit t}}{{\overline{\mathit t}}}{{\mathit H}^{0}}$ Production $1.10 \pm0.18$
${{\mathit H}^{0}}{{\mathit H}^{0}}$ Production
${{\mathit t}}{{\mathit H}^{0}}$ production $6 \pm4$
${{\mathit H}^{0}}$ Production Cross Section in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 TeV $56 \pm4$ pb
$\Gamma_{1}$ ${{\mathit W}}{{\mathit W}^{*}}$
$\Gamma_{2}$ ${{\mathit Z}}{{\mathit Z}^{*}}$
$\Gamma_{3}$ ${{\mathit \gamma}}{{\mathit \gamma}}$ 62625
$\Gamma_{4}$ ${{\mathit b}}{{\overline{\mathit b}}}$
$\Gamma_{5}$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $<3.6\times 10^{-4}$ CL=95% 62625
$\Gamma_{6}$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ 62625
$\Gamma_{7}$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ 62600
$\Gamma_{8}$ ${{\mathit Z}}{{\mathit \gamma}}$ 29431
$\Gamma_{9}$ ${{\mathit Z}}{{\mathit \rho}{(770)}}$ $<1.21\%$ CL=95% 29423
$\Gamma_{10}$ ${{\mathit Z}}{{\mathit \phi}{(1020)}}$ $<3.6\times 10^{-3}$ CL=95% 29417
$\Gamma_{11}$ ${{\mathit Z}}{{\mathit \eta}_{{c}}}$ 29315
$\Gamma_{12}$ ${{\mathit Z}}{{\mathit J / \psi}}$ 29306
$\Gamma_{13}$ ${{\mathit \gamma}^{*}}{{\mathit \gamma}}$ 62625
$\Gamma_{14}$ ${{\mathit J / \psi}}{{\mathit \gamma}}$ $<3.5\times 10^{-4}$ CL=95% 62587
$\Gamma_{15}$ ${{\mathit J / \psi}}{{\mathit J / \psi}}$ $<1.8\times 10^{-3}$ CL=95% 62548
$\Gamma_{16}$ ${{\mathit \psi}{(2S)}}{{\mathit \gamma}}$ $<2.0\times 10^{-3}$ CL=95% 62571
$\Gamma_{17}$ ${{\mathit \Upsilon}{(1S)}}{{\mathit \gamma}}$ $<4.9\times 10^{-4}$ CL=95% 62268
$\Gamma_{18}$ ${{\mathit \Upsilon}{(2S)}}{{\mathit \gamma}}$ $<5.9\times 10^{-4}$ CL=95% 62224
$\Gamma_{19}$ ${{\mathit \Upsilon}{(3S)}}{{\mathit \gamma}}$ $<5.7\times 10^{-4}$ CL=95% 62197
$\Gamma_{20}$ ${{\mathit \Upsilon}{(nS)}}{{\mathit \Upsilon}{(mS)}}$ $<1.4\times 10^{-3}$ CL=95%
$\Gamma_{21}$ ${{\mathit \rho}{(770)}}{{\mathit \gamma}}$ $<8.8\times 10^{-4}$ CL=95% 62623
$\Gamma_{22}$ ${{\mathit \phi}{(1020)}}{{\mathit \gamma}}$ $<4.8\times 10^{-4}$ CL=95% 62621
$\Gamma_{23}$ ${{\mathit e}}{{\mathit \mu}}$ $<6.1\times 10^{-5}$ CL=95% 62625
$\Gamma_{24}$ ${{\mathit e}}{{\mathit \tau}}$ $<2.2\times 10^{-3}$ CL=95% 62612
$\Gamma_{25}$ ${{\mathit \mu}}{{\mathit \tau}}$ $<1.5\times 10^{-3}$ CL=95% 62612
$\Gamma_{26}$ ${\mathrm {invisible}}$ $<19\%$ CL=95%
$\Gamma_{27}$ ${{\mathit \gamma}}$ ${\mathrm {invisible}}$
FOOTNOTES | 2022-08-16T15:52:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8328842520713806, "perplexity": 1374.3543937271659}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572408.31/warc/CC-MAIN-20220816151008-20220816181008-00197.warc.gz"} |
http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/twofact.htm | Dataplot Vol 1 Vol 2
TWO FACTOR PLOT
Name:
TWO FACTOR PLOT
Type:
Graphics Command
Purpose:
Given a response variable and associated variables containing laboratory id's and material id's, generate either a "laboratories within materials" or a "materials" within laboratories" plot.
Description:
This is essentially a run sequence plot sorted by the two factor variables.
This plot is motivated by the desire to plot residuals for the "phase 3" analysis related to the ASTM E691 standard. The phase 3 analysis is a row-linear model for the data in a E691 study and was proposed by John Mandel (see the References below) as an additional step in the E691 analysis. In particular, Mandel recommended a plot of the standardized residuals from the row-linear model (specific plots for the h- and k-statistics are implemented with the H CONSISTENCY PLOT and K CONSISTENCY PLOT commands).
Although motivated by the E691 analysis, this plot can be used for any two factor data set from a full factorial design (i.e., all combinations of levels from the two factors are included). If there is replication within a cell, the mean of the replicates will be used.
Syntax:
TWO FACTOR PLOT <y> <labid> <matid>
<SUBSET/EXCEPT/FOR qualification>
where <y> is a response variable;
<labid> is a variable that specifies the lab-id;
<matid> is a variable that specifies the material-id;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
TWO FACTOR PLOT Y LABID MATID
Note:
If there is replication within the cells and you would like to plot something other than the mean value, you can use the LET CROSS TABULATE command. For example, to plot the standard deviations, do something like
SET LET CROSS TABULATE COLLAPSE
LET YSD = CROSS TABULATE SD Y X1 X2
LET X1D = CROSS TABULATE GROUP ONE X1 X2
LET X2D = CROSS TABULATE GROUP TWO X1 X2
TWO FACTOR PLOT YSD X1D X2D
Note:
There are two formats for the plots. By default, the values are plotted linearly. That is, given three laboratories and three materials, the x-axis is laid out as
LAB: 1 2 3 1 2 3 1 2 3
MAT: 1 1 1 2 2 2 3 3 3
X: 1 2 3 4 5 6 7 8 9
Alternatively, you can stack the lab values so that the x-axis is laid out as
LAB: 1 1 1
2 2 2
3 3 3
MAT: 1 2 3
X: 1 2 3
To specify the stacked alternative, enter the command
SET TWO FACTOR PLOT TYPE STACKED
To reset the line linear option, enter the command
SET TWO FACTOR PLOT TYPE DEFAULT
Note:
By default, the x-axis is defined by "laboratories within materials".
To define the x-axis as "materials within laboratories", enter the command
SET TWO FACTOR PLOT MATERIALS WITHIN LABORATORIES
To reset the default, enter
SET TWO FACTOR PLOT LABORATORIES WITHIN MATERIALS
We find it useful to generate both versions of the plot. Although the information being displayed is the same, different types of patterns may be clearer in one or the other of these plots.
Note:
For better separation between laboratories (or materials), you can enter the command
SET TWO FACTOR PLOT GAP <value>
where <value> is a non-negative integer. So in the above example,
SET TWO FACTOR PLOT GAP 1
yields
LAB: 1 2 3 1 2 3 1 2 3
MAT: 1 1 1 2 2 2 3 3 3
X: 1 2 3 5 6 7 9 10 11
Note:
In some studies, the number of laboratories may be fairly large. In these cases, you may want to split the laboratories into multiple plots for better resolution.
To address this, the following commands were added
SET TWO FACTOR PLOT LABORATORY FIRST <value>
SET TWO FACTOR PLOT LABORATORY LAST <value>
SET TWO FACTOR PLOT MATERIAL FIRST <value>
SET TWO FACTOR PLOT MATERIAL LAST <value>
These commands allow you to specify the range of laboratories (or materials) to be displayed. Note that these commands limit you to contiguous ranges of laboratories or materials.
Default:
None
Synonyms:
None
Related Commands:
E691 INTERLAB = Perform an interlaboratory analysis based on the E691 standard. H CONSISTENCY PLOT = Generate an h-consistency plot. TWO WAY ROW PLOT = Generate a plot based on Mandel's row linear analysis for two-way tables.
References:
"Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method", ASTM International, 100 Barr Harbor Drive, PO BOX C700, West Conshohoceken, PA 19428-2959, USA.
Mandel (1994), "Analyzing Interlaboratory Data According to ASTM Standard E691", Quality and Statistics: Total Quality Management, ASTM STP 1209, Kowalewski, Ed., American Society for Testing and Materials, Philadelphia, PA 1994, pp. 59-70.
Mandel (1993), "Outliers in Interlaboratory Testing", Journal of Testing and Evaluation, Vol. 21, No. 2, pp. 132-135.
Mandel (1995), "Structure and Outliers in Interlaboratory Studies", Journal of Testing and Evaluation, Vol. 23, No. 5, pp. 364-369.
Mandel (1991), "Evaluation and Control of Measurements", Marcel Dekker, Inc.
Applications:
Interlaboratory Studies
Implementation Date:
2015/5
Program:
. Step 1: Read the data
.
dimension 40 columns
skip 25
read mandel7.dat y x1 x2
.
let nlab = unique x1
let nmat = unique x2
let ntot = nlab*nmat
.
variable label y Stress
variable label x1 Lab-ID
variable label x2 Rubber
let nlab = unique x1
let ncol = unique x2
.
. Step 2: Define some default plot control settings
.
case asis
title case asis
title offset 2
label case asis
tic mark offset units screen
tic mark offset 3 3
.
. Step 3: Generate the two way row plot
.
x1label Column Average
character blank all
line dash all
loop for k = 1 1 nlab
let kindex = (k-1)*2 + 1
let plot character kindex = ^k
let plot line kindex = blank
end of loop
.
set two way plot factor label value
set two way plot factor decimal 4
set two way plot anova table on
set two way plot anova table decimals 4
set write decimals 4
title Stress in Kg/cm**2 at 100% Elongation for Natural Rubber Vulcaizates
y1label Data by Laboratory
.
two way row plot y x1 x2
.
. Step 4: Now generate the two factor plot of the residuals
.
skip 1
read dpst3f.dat labid matid junk1 junk2 junk3 resstd
skip 0
y1label Standardized Residuals
x1label Lab-ID/Rubber-ID
legend 1 MATERIAL:
legend 2 LAB:
legend 1 justification right
legend 2 justification right
legend 1 coordinates 14 15
legend 2 coordinates 14 12
legend 1 size 1.7
legend 2 size 1.7
.
x1label
x1tic mark label off
xlimits 1 ntot
major x1tic mark number ntot
minor x1tic mark number 0
x1tic mark offset 1 1
.
line blank
character blank
spike on
spike base 0
two factor plot resstd labid matid
line solid
drawdata 1 0 ntot 0
.
. Step 5: Draw lines separating the labs and add tic labels
. to identify labs/materials
.
let ycoorz = 16
let xcoor = 1
justification center
height 0.7
.
loop for k = 1 1 ntot
moveds xcoor ycoorz
let ktemp = mod(k-1,nmat) + 1
text ^ktemp
let xcoor = xcoor + 1
end of loop
.
height 1.5
let ycoorz = 12
let xcoor = (nmat/2)+0.5
line color red
line dash
loop for k = 1 1 nlab
moveds xcoor ycoorz
let ival = k
text ^ival
if k < nlab
let xcoor2 = xcoor + (nmat/2)
drawdsds xcoor2 20 xcoor2 90
end of if
let xcoor = xcoor + nmat
end of loop
line color black
line blank
The following output is generated
Parameters of Row-Linear Fit for Stress
-------------------------------------------------------------------------------------
Standard Error Correlation
Lab-ID Height Slope RESSD of Slope Coefficient
-------------------------------------------------------------------------------------
1.0000 4.9300 1.0909 0.1168 0.0268 0.9985
2.0000 4.5957 1.0990 0.0851 0.0195 0.9992
3.0000 4.8043 1.0613 0.1547 0.0355 0.9972
4.0000 5.5200 0.9777 0.1818 0.0417 0.9955
5.0000 5.0671 0.8575 0.1844 0.0423 0.9940
6.0000 4.8657 0.8960 0.1289 0.0296 0.9973
7.0000 4.7729 0.8063 0.1784 0.0409 0.9936
8.0000 4.8543 1.0869 0.1006 0.0231 0.9989
9.0000 5.2386 1.0304 0.2197 0.0504 0.9941
10.0000 4.8571 1.0696 0.1045 0.0240 0.9987
11.0000 4.8457 1.0244 0.1773 0.0407 0.9961
Standard Deviation of Slopes: 0.1024
Pooled Standard Deviation of Fit: 0.1616
Column Averages
---------------------------
Column
Rubber Average
---------------------------
1.0000 3.2291
2.0000 3.5927
3.0000 4.0418
4.0000 4.4273
5.0000 5.0791
6.0000 5.7345
7.0000 8.4827
Mean of Column Means: 4.9410
ANOVA Table for Row-Linear Fit
-----------------------------------------------------------------
Degrees of Sum of Mean
Source Freedom Squares Square
-----------------------------------------------------------------
Total 76 216.8951 2.8539
Rows 10 4.4471 0.4447
Column 6 209.1488 34.8581
Error 60 3.2991 0.0550
Residuals 50 1.3054 0.0261
Slopes 10 1.9937 0.1994
Concurrence 1 0.0496 0.0496
Non-Concurrence 9 1.9441 0.2160
NIST is an agency of the U.S. Commerce Department.
Date created: 07/08/2015
Last updated: 07/08/2015
Please email comments on this WWW page to alan.heckert.gov. | 2017-10-22T06:17:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5894274711608887, "perplexity": 10866.485024467256}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187825147.83/warc/CC-MAIN-20171022060353-20171022080353-00262.warc.gz"} |
https://read.dukeupress.edu/demography/article/58/4/1301/173455/Does-the-Impact-of-Motherhood-on-Women-s | ## Abstract
Women's ability to control their fertility through contraception and abortion has been shown to contribute to improvements in education and employment. At the same time, their employment and wages decline substantially when they transition to motherhood. About one-third of births are unintended, and it is unknown whether the impact of motherhood on employment, hours, and wages is smaller for women who planned their transition into motherhood compared with those who did not. To explore this, we examine fixed-effects models that estimate labor market outcomes using panel data from the National Longitudinal Survey of Youth, 1979–2014. We estimate models for Black and White women and find that the relationship between motherhood and employment is significantly more negative among White women who plan their transition into motherhood than among those who have an unplanned first birth. Among those who remain employed, we find that those with a planned first birth work fewer hours and have lower wages relative to those with unplanned births. We do not find significant evidence that the association between motherhood and labor market outcomes differs by fertility planning among Black women. Prior research shows how women's choices are structurally constrained by sociocultural norms and expectations and by a labor market that may not readily accommodate motherhood. In this context, our findings may reflect differences in women's motherhood and employment preferences and their ability to act on those preferences. Our analysis also makes a novel contribution to the large body of research that associates unplanned births with negative outcomes.
## Introduction
For many women, having children poses challenges that appear to adversely affect their employment and wage trajectories. This highlights the importance of research into the structural and individual factors contributing to the impact of motherhood on women's employment and wages. Research has shown that increased access to contraception in the United States has contributed to improvements in women's education and employment (Bailey 2013; Bailey et al. 2012; Goldin and Katz 2000, 2002). Contraception may help women avoid becoming pregnant before they want to, allowing them to invest in their education or career or to stop childbearing once they have all the children they want. It also enables women not to have children if they so desire. For the overwhelming majority of women who expect to and do have children, this logic suggests that women's ability to plan when to have their first birth helps explain associations between contraception and improvements in education and employment. However, although research has consistently shown that women are less likely to be employed and earn lower wages after they become mothers than would be expected had they not given birth (e.g., Amuedo-Dorantes and Kimmel 2005; Budig and England 2001; DeNavas-Walt and Proctor 2015; England et al. 2016; England et al. 2012; Florian 2018; Glauber 2007; Hill 1979; Neumark and Korenman 1992; Taniguchi 1999; Waldfogel 1997; Wilde et al. 2010), we are unaware of any prior research that has analyzed whether planning status of first birth plays a role in employment and wage differences. To address this gap in the literature, we examine two competing hypotheses about the impact that the transition to motherhood has on women's employment and wages according to whether their first birth was planned or unplanned.
Women do a disproportionate amount of the work of raising children, and employers and policy-makers historically have not provided substantial social supports to ameliorate work–family conflict (England 2005). Some women may plan their first birth to minimize the likely disruption to their career or employment. If planning a first birth helps a woman address challenges she may face at work, then a woman who does so may experience fewer adverse impacts on her employment and wages than a woman who does not. We refer to this as Hypothesis 1 (H1).
Structural factors, such as discrimination, contribute to the relationship between motherhood and employment and earnings, and women may experience tensions between their roles as employees and as mothers (Correll et al. 2007; Gerson 1986; Stone 2007). Although women may plan childbearing in response, it may do little to mitigate this conflict. Consequently, we posit that women may plan their first birth as they become more willing or more able to reduce their employment commitment in order to care for children, motivated by the understanding that the labor market may not readily accommodate motherhood. Thus, we argue that planned first births will plausibly be more negatively associated with labor market outcomes than unplanned first births. We refer to this as Hypothesis 2 (H2).
Planned fertility has been associated with socioeconomic advantage (Mosher et al. 2012; Musick et al. 2009), so if H1 is correct—that planning reduces motherhood penalties—then unplanned fertility could compound economic inequality. In contrast, H2 hinges on women's knowledge that employers, the state, and male partners are unlikely to substantially mitigate their work–family conflict (Arendell 2000; Hays 1996; Stone 2007; Waite and Stolzenberg 1976). Evidence in support of H2 would thus emphasize the importance of improving social policies that address challenges of raising children, which fall disproportionately on women.
Relatedly, the associations between motherhood and labor market outcomes are stronger for some groups of women than others. The negative associations between motherhood and employment and between motherhood and wages are larger among White women than Black women (Budig and England 2001; England et al. 2016; Florian 2018; Waldfogel 1997; Wilde et al. 2010). Evidence also suggests that the wage penalty is associated with skill (Wilde et al. 2010), although this association holds for White women but not Black women (England et al. 2016). Thus, to address possible confounding, we should test our hypotheses separately by race and skill.
A conceptual challenge is that demography and public health typically identify “planned” births as those following “intended” pregnancies, based on a survey measure that asks women whether a given pregnancy was wanted at the time, whether it came before it was wanted, or whether they had not wanted to have any (more) children. However, this measure of intention does not actually measure intentionality. A woman may become pregnant regardless of whether she had intended to but may feel (and report) that the pregnancy came when it was wanted.
To address these issues, we analyze panel data from the National Longitudinal Survey of Youth (NLSY79). With these data, we can identify planned births using additional information on whether a woman was actually trying to conceive. We observe women's employment and wages both before and after they became mothers, and we estimate fixed-effects models to compare the association between motherhood and three labor market outcomes—employment, hours, and wages—for women who planned their first birth compared with women who did not.
## Literature
Planned childbearing can be achieved through several mechanisms: manipulating sexual activity (e.g., having sex only when trying to conceive), using contraception, and abortion. Of these three, contraception as a method of family planning has been the most widely studied in regard to its potential impact on employment and earnings. Prior studies have exploited spatiotemporal variation in access to contraception using difference-in-difference techniques to estimate plausibly causal effects on education, employment, and earnings. Goldin and Katz (2000, 2002) analyzed variation across states in the availability of oral contraceptives due to changes in state laws in the 1960s and the 1970s, finding that access to contraception was a major factor in the growing numbers of women obtaining a college education and pursuing advanced professional degrees. In addition, Bailey et al. (2012) provided persuasive evidence that changes in contraceptive access during this period significantly contributed to young women's joining the paid labor force and pursuing professional occupations, and other analyses likewise suggested that the legalization of abortion was associated with increased education and employment (Angrist and Evans 2000; Klein 1997). These changes, in turn, contributed to women's increased earning power and to a reduction in the long-standing gender gap in pay (Bailey 2013; Bailey et al. 2012; Goldin and Katz 2000, 2002).
The embedded assumption of these dynamics is that women were better able to plan their births and to do so in a way that best met their educational and employment aspirations. Undoubtedly, the use of highly effective birth control allowed women to delay fertility and family formation or to avoid childbearing altogether, making it easier to complete college and enter the labor market. However, these studies were unable to address the mechanisms through which individual women's contraceptive use directly contributed to their increased education and employment.
Researchers have discussed a number of structural factors that could contribute to these relationships. These mechanisms include gender discrimination by employers; valorization of continuous work experience, which affects future employability and wages; fixed working hours with limited flexibility; low levels of societal support for balancing work and childcare; and a gendered concept of an “ideal worker” devoted to and available for their job above all else (Acker 1990; Correll et al. 2007; Gerson 1986; Stone 2007).
We hypothesize that planning one's transition to motherhood would not substantially address or counteract these structural and cultural factors. For example, it is not apparent that employers would discriminate less if a woman planned her birth. Indeed, even as gender earnings inequality has declined over time because of faster increases in women's earnings compared with men's, an analysis of the Current Population Surveys suggests that the impact of motherhood on women's employment and wages accounts for a larger proportion of the gender pay gap than it did in earlier periods (Juhn and McCue 2017).
We suspect that birth planning cannot completely or substantially counter structural factors, but we also posit that planning may be a response to the external and internal tensions between motherhood and employment caused or exacerbated by these larger constraints. We identify two potential rationales for why women who plan childbearing may be more likely to disinvest in the labor market upon motherhood.
First, women may plan their births to occur when they are most willing or most able to exit or spend less time in the labor market. When a woman decides to try to become pregnant, she may also be signaling that she is willing and/or wants to focus on domestic responsibilities, even if that means a reduction in time spent in the labor market.
Second, women who plan childbearing may be more responsive to the tension between motherhood and employment. Consistent with this view, data from the National Survey of Fertility Barriers suggest that planned childbearing is most salient to women who describe themselves as career-conscious (Simoni et al. 2017). However, women who originally anticipated continued employment after their first birth may find it more challenging than anticipated to maintain their expected level of labor market commitment (Stone 2007; Waite and Stolzenberg 1976).
Either of these behaviors could conceivably be contingent on household resources. However, research has shown that husbands' earnings have a limited association with wives' employment and that motherhood substantially relates to women's labor force participation across socioeconomic strata (Killewald and Gough 2013; Killewald and Zhuo 2019). Work conducted around the time that women in the NLSY79 were having children has explored how sociocultural norms can influence women's decisions to disinvest or withdraw from the labor market even when it is not in their economic interest to do so (or may even be counter to it). Gerson (1986:204), in her qualitative study of White women in geographically and socially diverse neighborhoods in the San Francisco Bay area, further discussed such influences as “sufficient behavioral similarity among women to provide mutually reinforcing support for female domesticity.”
The tension between family and work has been referred to as a set of competing devotions that may stem from cultural narratives around motherhood and domesticity (Blair-Loy and Dehart 2003). For middle-class White women, motherhood ideologies such as intensive mothering—a mothering paradigm in which a good mother is self-sacrificing and engages in an all-consuming form of childcare, which necessarily conflicts with employment—have long been in development and continue to influence behavior (Arendell 2000; Hays 1996; Romagnoli and Wall 2012). In this context, in which their choices are socially constrained (Gerson 1986), many women may thus form preferences that differ from those predicted by a rational actor model.
However, ideologies and their impacts are not universal. Black women have experienced a different set of cultural narratives about self-sufficiency and economic pressures, working outside the home at historically higher rates than White women (Barnes 2015; Collins 2000; Florian 2018; Marsh et al. 2013; Roberts 1993). The intensive mothering paradigm, for example, is rooted in historical cultural norms of a permanent marriage in which the husband provides household income (Arendell 2000; Gerson 1986; Romagnoli and Wall 2012). However, economic circumstances among Black families, shaped by structural racism, have often required that all adult family members contribute to the family income, making the intensive mothering paradigm less feasible.
Similarly, several scholars have argued that although Black and White women alike may experience a double bind of being pulled toward both work and domesticity, a Black motherhood ideology exists that distinctly places importance on economic self-sufficiency (Barnes 2015; Collins 2000; Florian 2018; Marsh et al. 2013; Roberts 1993). Because of the economic impacts of structural racism, Black women tend to live in poorer households and contribute to a greater share of household income, and they therefore have more of an economic burden compared with White women (Dow 2016; Yoon and Waite 1994). In addition, some qualitative studies have found that Black mothers experience less social disapproval for continuing employment upon motherhood than do White women (Barnes 2015; Landry 2002). In sum, economic necessity and differences in the importance of economic self-sufficiency could contribute to a smaller relationship between motherhood and employment among Black mothers relative to White mothers.
Relatedly, the negative associations between motherhood and employment and between motherhood and wages are larger among White women than Black women (Budig and England 2001; England et al. 2016; Florian 2018). This may be for the reasons discussed earlier, as well as because of the double discrimination (by race and gender) that Black women experience irrespective of motherhood.
In addition to sociocultural pressures, individual differences in opportunity costs may contribute to heterogeneity in how motherhood relates to labor market outcomes. Wilde and colleagues (2010) argued that high-skill women experience the largest wage penalty because they have steeper average wage trajectories before motherhood. In subsequent analyses that disaggregated skill and race, England and colleagues (2016) found skill heterogeneity in the wage penalty among White women but not Black women; specifically, highly skilled White women in high-wage jobs experienced the largest wage penalty due to differences in the return to cumulative work experience.1 This finding may be important because wage trajectory differences between women may affect their employment behaviors as they navigate the tension between work and motherhood. More broadly, a salient point is that both race and measures of cognitive skill predict differences in job characteristics and other factors, including exposure to different sociocultural norms and assortative mating—all of which may lead to heterogeneity in the relationship between motherhood and women's labor market outcomes (as other studies have addressed) and in how birth planning moderates this relationship. For these reasons, we test our hypotheses separately by race and, secondarily, by a proxy for skill.
## Methods
### Data and Variables
We use nationally representative data from the NLSY79. This panel represents the cohort of U.S. women who were born between 1958 and 1965. The respondents were first interviewed in 1979 at ages 14–21. Data were collected annually through 1994 and every two years thereafter until 2014, when the cohort was aged 49–58 and had largely completed childbearing.
We examine three dependent variables: whether a woman was employed at the time of the interview, her reported number of work hours per week, and her hourly rate of pay. This information comes from the NLSY79 work history file.2 We take the natural logs of wages and hours to estimate proportionate changes using least squares, and we employ binomial logistic regression for employment. We convert wages to constant 1996 dollars using the consumer price index; we bottom code and top code wages at $0.50 and$250 for consistency with other recent studies (Budig and Hodges 2010; England et al. 2016). We top-code hours at the 99th percentile, at 65 per week. To address unobserved heterogeneity and selection, we employ person-fixed-effects models, which require at least two observations for each respondent. Of the 5,171 women first interviewed in 1979, 4,685 women reported wages and hours at least twice. Like England et al. (2016), we exclude person-years during which women were enrolled in school (secondary school or higher education) because employment and wages in those years may be misleading.3 After we exclude observations with missing data on the covariates of analyses of hours and wages, our analytic sample includes 34,757 person-years of data from 3,036 non-Hispanic White women and 17,087 person-years from 1,329 non-Hispanic Black women. For the fixed-effect logistic probability models for the dichotomous measure of employment, we have 33,249 person-years of data from 2,166 White women and 19,410 person-years of data from 1,054 Black women.
Our independent variables of interest are years since the first birth and planning status of the pregnancy. Years since the first birth is a categorical variable comparing mothers with nonmothers and, among mothers, the time they have been mothers. This variable indicates whether a woman had a birth and, if so, the number of years since the birth. Killewald and Zhou's (2019) sequence analysis suggests that typical patterns of post-motherhood employment for women in this data set include a single employment status or a period of around either 6 or 11 years of non-employment. Thus, to compare between short- and long-term impacts of motherhood, we distinguish between “not yet had a birth,” “years 1–6 after the first birth,” “years 7–11 after the first birth,” and “later years.”4
This variable contrasts with the conventional measure of pregnancy intentions. The conventional measure focuses on timing—that is, whether a pregnancy was retrospectively considered wanted by the time it was conceived—and does not incorporate contraceptive use or whether a woman was trying to become pregnant. Our measure, in contrast, additionally considers intentionality and thus is better suited to our analyses.
The reference categories in our analyses are never/not yet given birth for the four-category variable for years since first birth and planned for the four-category variable for birth planning. These are the most appropriate comparison groups because our hypotheses relate to differences between women experiencing a planned first birth and those experiencing an unplanned first birth. When never/not yet given birth equals 1, all other categories of both the years since first birth and planning status variables equal 0.
### Analytic Strategy
We test our hypotheses separately by race so that differences by race are not confounded with differences by planning status. Our unit of analysis is the person-year, standard errors are adjusted to account for the nonindependence of observations within persons, and sampling characteristics are accounted for in the regressions.
We generate a series of models to test whether the impact of motherhood differs by planning status. Model 1 includes several time-varying controls measured at each wave. We include indicators for the survey year to adjust for secular trends. We include quadratic terms for age at interview, and categorical variables for educational attainment at interview (less than high school, high school, some college, and college), region (Northeast, North Central, South, and West), metropolitan statistical area classification, and whether the respondent lived in an urban area at interview.
Some research has argued that the impact of motherhood may vary according to the number of children a respondent has had (e.g., Budig and England 2001; England et al. 2016), and women with unintended fertility typically have more children (Musick et al. 2009). To account for this potential bias, following Wilde et al. (2010), Model 2 controls for the number of additional children the respondent has had.
Marriage is associated with both motherhood and employment. Additionally, spousal earnings may allow some women to reduce their time spent in employment; however, research has suggested that women may be more responsive to spouses' hours (Cha and Weeden 2014). For these reasons, Model 3 includes a dichotomous control for marital status as well as quadratic terms for the spouse's hours and annual earnings.
We additionally examine our hypotheses separately among skill groups. Like Wilde et al. (2010) and England et al. (2016), we measure cognitive skill using age-adjusted scores from a standardized test—the Armed Forces Qualifying Test (AFQT)—administered during the second wave. This variable predicts women holding professional jobs with higher earnings potential (England et al. 2016; Wilde et al. 2010) and has been found to affect the motherhood wage penalty for White women because time spent out of the labor force has a more substantial impact on their wages. Other research showed that AFQT is moderately and positively correlated with earnings (England et al. 2000; Farkas et al. 1997; Neal and Johnson 1996). Although skill is not the only possible predictor of professional jobs with higher earning potential, we follow Wilde et al. (2010) in the view that skill is a more plausibly exogenous predictor than other potential measures, such as educational attainment. We group women into race-specific terciles, such that equal proportions of White women and Black women are apportioned into each group, and we compare women in the top tercile with women in the lowest and middle terciles.
We present results from models estimated separately by race or separately by race and skill,6 which is equivalent to fully interacting all variables with race or with race and skill, respectively. Our most saturated model for binomial logistic regressions that estimate employment (with equivalent least squares equations used for log hours and log wages) may be described as follows:
$logit employedijt=∑j=01∑k=01(motherit×LENGTHitβ1jk+motherit×INTENTIONitβ2jk+additional childrenitβ3jk+ageitβ4jk+ageit2β5jk+EDUCATIONitβ6jk+marriageitβ7jk+spouse’s earningsitβ8jk+spouse’s earningsit2β9jk+spouse’s hoursitβ10jk+spouse’s hoursit2β11jk+REGIONitβ12jk+MSAitβ13jk+urbanitβ14jk+YEARitβ15jk)+αi+uit.$
The subscript t indexes the waves so that it uniquely identifies person-years. The person fixed effects are indicated by $αi$, capturing time-invariant unobserved heterogeneity between respondents, and $uit$ is an error term. The subscript j indexes skill and k indexes race, and thus the coefficients $β1$ through $β17$ are indexed jk because the estimated associations vary by race and skill. This specification is equivalent to estimating models for each combination of the race and skill categories.
For describing sample characteristics, we also utilize the work and family aspirations question previously explored by Waite and Stolzenberg (1976; Stolzenberg and Waite 1977). In the years 1979–1986, women were asked, “What would you like to be doing when you are 35 years old?” Women could indicate either “Working” or “Married, raising a family.” Those who provided the latter response were then asked whether they would also like to be working. We retain the latest response given before the first birth and examine whether women's answers differed according to whether they went on to have a planned or an unplanned first birth.
### Sensitivity Analyses
We conducted several supplemental analyses to test the sensitivity of our results to different assumptions (Tables A3–A6 in the online appendix).
Several of our sensitivity tests were related to the independent variable in our models measuring motherhood duration, the length of time since the woman had her first birth. In our preferred specification, we delineate motherhood length with indicator variables delineating the first six years, the next years up through the eleventh, and later years following the first birth. This specification is informed, as mentioned earlier, by Killewald and Zhou's (2019) sequence analysis of employment spells following motherhood in the NLSY79. In sensitivity checks, we reestimated our models (1) measuring time since the most recent birth (i.e., years since the birth of the youngest child; Model 3B); and (2) using the same categories as in Wilde et al. (2010), comparing the first four years, the fifth through ninth, and later years of motherhood (Model 3C).
We also examined models that interacted planning status with both motherhood and motherhood length (Model 3D). We present results from the simpler specification because results are similar in either specification, and the former substantially eases the exposition.
As described earlier, our models address compositional differences by marital status, including spouses' earnings and hours. We also considered the possibility that married women, who could be more likely to plan their first birth, experience a different relationship between motherhood and employment. To confirm that this would not affect our results, we also examined models that simultaneously interacted motherhood with marital status and marital status at the time of the birth, again with similar results (Model 3E).
Finally, as a robustness check for our analyses comparing skill groups, we reestimated our models separately for women grouped by their completed education (i.e., as measured in the latest wave), comparing women who graduated from college by 2014 with those who did not.
## Descriptive Findings
Examining the distribution of first birth planning status in our data, we see that among White women, two-thirds of first births were planned (67%), 24% were mistimed (not wanted at the time they occurred), and 4% unwanted (the respondent reported that she never wanted to have children; Table 1). Among Black women, planned births were less common than unplanned births: 58% of first births were either mistimed (44%) or unwanted (14%), and 34% were planned. The percentage of wanted unplanned first births is relatively small for both groups: 4% among White women and 8% among Black women. Examining these patterns separately by skill (Table A2, online appendix) shows that planned births are more common among both Black and White women in the highest skill tercile than in the lower terciles.
Examining the bivariate relationship between planned childbearing and 2014 employment, we see that nearly three-quarters of women in the sample were employed regardless of race or planning status, and those who were employed generally worked approximately 37–39 hours per week (Table 2). This finding suggests that although socioeconomic advantage is associated with planned fertility (Musick et al. 2009; Mosher et al. 2012), women with planned and unplanned births exhibit similar levels of employment in the long run.
In contrast to employment, the average wages of women in 2014 do appear to have differed by planning status of the first birth. White women who planned childbearing earned nearly $3 more per hour than those who did not, and the corresponding figure for Black women was approximately$2; however, this difference reached statistical significance only among White women.
We also examine women's responses to a question they answered in 1979–1986, when they were 16–29 years old, asking, “What would you like to be doing when you are 35 years old?” About two-thirds of White women who later had planned (67%) and mistimed (66%) first births responded with “Working” (Figure 2, panel a). This response was more common among Black women, for whom the corresponding figures were 80% and 87%, respectively. Among women who reported that their first birth was unplanned but wanted, however, significantly fewer—50% of White women and 56% of Black women—responded “Working.” Women who responded “Married, raising a family” were then asked, “Would you also like to be working in addition to this?” More than one-half, regardless of whether they went on to have a planned or unplanned first birth, answered in the affirmative (Figure 2, panel b). These results suggest that at baseline, most women expected to be employed at age 35. Women's attitudes about whether they wanted to participate in the labor market were similar across first-birth planning status except for the small proportion who went on to have an unplanned but wanted first birth.
When examining their employment trajectories before their first birth according to planning status, we find that a larger proportion of both Black and White women who planned their first birth were employed than were women who went on to have a mistimed or unwanted first birth (Figure 3). After they gave birth (denoted in Figure 3 with the break between line segments), however, these differences became smaller. The smallest proportion of women were employed in the year just after they became mothers, during which time women who planned their first birth remained substantially more likely to be employed than women who did not. A few years after the first birth, however, differences in employment levels by planning status were no longer evident among White women and were seen only among Black women.
We next test whether differences by planning status in employment, hours, and wages are evident after adjusting for differences in women's characteristics.
## Regression Estimates
### Employment
Planning status of first births is associated with subsequent employment only for White women (Table 3). In particular, relative to women who had a planned first birth, those who indicated that the birth was mistimed were significantly more likely to work after becoming mothers. Estimates across all specifications support H2, with odds ratios between 1.61–1.79 and the coefficient for mistimed declining significantly (p < .001, χ2 test) after we control for husbands' characteristics. The small subset of White women who indicated that the birth was unwanted were also more likely to be employed than those with a planned birth, although this association is only marginally significant and weakens to the point of nonsignificance when spouses' characteristics are taken into account.
Among Black women, the impact of motherhood on employment does not appear to differ by birth planning. In addition to being nonsignificant, the odds ratios for mistimed are close to unity (0.98–0.99) in all models.
The significant differences by planning status observed among White mothers are relative to a substantial negative baseline effect of motherhood on employment. Specifically, the odds ratios for employment are 0.14–0.19 within the first six years after the first birth, 0.19–0.29 within the subsequent five years, and 0.46–0.70 for later years, depending on the model. Smaller but still meaningful associations are seen among Black women, for whom the likelihood of employment also decreased after first birth; specifically, the odds ratios for Black women's employment are 0.39 within approximately the first six years since the first birth regardless of the model and 0.62–0.66 for later years, depending on the model. However, differences in the later years are only marginally significant after we control for the spouses' characteristics. These patterns suggest that the likelihood of being employed increases substantially with the passage of time following motherhood, even after age is controlled for.
In sum, the proportion of women who were employed declined substantially after they became mothers. However, this decline was significantly larger among White women who planned their first birth than among those who did not.
### Hours
As with employment, planning status of first births for White women is also associated with the subsequent number of hours a woman spends on market labor (Table 4). Relative to women who had a planned first birth, those who indicated that the birth was mistimed worked an average of 6% to 7% more hours upon motherhood.
The corresponding coefficients are similar in size for the small subset of White women who indicated that the birth was unwanted and for those who indicated that their births were wanted but unplanned—at .06 log points in Model 3. However, these coefficients are not statistically significant in any model.
The estimates presented in Table 4, as with those previously discussed, are consistent with H2, which predicts that the association between motherhood and women's labor market outcomes is more negative for women with a planned first birth. Among Black women, we find no support for H2: the coefficients for mistimed and unwanted births are small and nonsignificant regardless of the specification. An exception to this general pattern is that for the small subset of Black women with an unplanned but wanted first birth, the coefficients are negative.
Differences in hours by birth planning status are somewhat small in absolute terms among women still employed. However, they are substantial when measured relative to the baseline effect of motherhood. In Model 3, in which the estimated differences between mothers and nonmothers are smallest, this difference ranges from about 19% fewer hours (e–.21 – 1) in the first six years of motherhood to 10% in later years. These patterns are less pronounced for Black women: baseline coefficients range from −0.04 to −0.05 log points (depending on the specification) and do not differ with the length of motherhood in any model, and the associations are only marginally significant in some instances.
In sum, in models estimating hours among employed White women, we find evidence consistent with H2: mistimed births are associated with an approximately 6% smaller reduction in work hours compared with planned births. Among Black women, in contrast, the coefficient for mistimed is nonsignificant and is at most 0.01 log points in any model.
### Wages
Among White women, we see little difference in the motherhood wage penalty by birth planning status, with one exception (Table 5). Mothers with an unwanted first birth earned 23% to 26% higher wages (e.21 to e.23) than mothers with a planned first birth. These differences are substantial relative to the baseline wage penalty, which ranges from −7% to −8% in the first six years after the first birth, −11% to −15% over the next five years (e–.12 to e–.16), and −12% to −16% in later years (e–.13 to e–.18), depending on the specification. Differences in the wages of those with planned and mistimed first births are nonsignificant and approach 0.
Among White women, we see clear evidence of the motherhood wage penalty. Regardless of the number of years since the first birth, those with a child earned less than women without. In contrast, the number of years since the first birth is not strongly associated with Black women’s wages in any model. Moreover, wages do not differ significantly between Black women with planned births and those with mistimed or unwanted births. However, as with hours, we find evidence that Black mothers with an unplanned but wanted first birth earned lower wages than those with a planned first birth.
### Employment, Hours, and Wages by Skill
For brevity, we report estimates from our most saturated model when reviewing results by skill (Table 6). Differences by planning status in the impact of motherhood on White women's employment are evident regardless of skill level: relative to White women with a planned first birth, those who indicated that the birth was mistimed were more likely to work in both the low- to mid-skill group (odds ratio = 1.54) and the high-skill group (odds ratio = 1.98).
We also find evidence that employed White women with an unplanned first birth worked more hours than those with a planned first birth. This result is significant only among those who did not score in the highest skill tercile, for whom we estimate a 7% difference in hours.
In models estimating White women's wages, as with the models which averaged across skill groups, we find differences by planning in the association between motherhood and wages only when comparing women who had a planned first birth with those who had an unplanned and unwanted first birth. In models estimated separately by skill, however, the coefficient among high-skill women (at .38 log points) is statistically significant, whereas the coefficient for low- to mid-skill women is not.
In models estimating employment, hours, or wages by skill among Black women, as with the results discussed earlier averaging across skill groups, we find no significant differences between women with planned first births and those with mistimed or unwanted first births.
An exception to the general pattern of results is seen among the small proportion of White women with an unplanned but wanted first birth in the top skill tercile, who were less likely to be employed than those with a planned first birth. We see a similar exception in the unplanned but wanted coefficient in models estimating employed Black women's hours, which is also evident in the models averaging across skill groups.
Consistent with prior research (England et al. 2016; Florian 2018), when examining the baseline associations between motherhood and employment, hours, or wages, we find more substantial evidence of negative associations among White women than among Black women. These associations are evident among White women regardless of skill group for all dependent variables—employment, log hours, and log wages—whereas none of the baseline associations are statistically significant among Black women except in the models estimating employment.
Thus, we find the most significant evidence for a negative association between motherhood and employment, hours, and wages among high-skill White women with a planned first birth. However, differences by skill group are not statistically significant.
### Summary
In summary, we find evidence that the impact of motherhood on White women's employment, hours, and wages differs by planning status of the first birth and is largest among those who plan the transition to motherhood. For Black women, in contrast, we do not find evidence that the impact of motherhood on the probability of employment and, among employed women, hours and wages is larger for women with a planned first birth.
### Limitations
The conventional measure used to assess pregnancy intentions in the large body of sexual and reproductive health research has been criticized for being imprecise and one-dimensional and for not considering the affective component of pregnancy reactions (Aiken et al. 2016; Mumford et al. 2016; Potter et al. 2019; Santelli et al. 2003). Our measure of birth intentions addresses some of these concerns—for example, by taking into account contraceptive use and pregnancy planning—but it is not without shortcomings. Barrett and colleagues (Barrett et al. 2004; Barrett and Wellings 2002) showed that some women may not use the word “planned” to describe a birth unless they engaged in preparatory behaviors, such as having discussions with their partners in addition to trying to become pregnant. Our measure of planning likely includes women who did not explicitly engage in these planning behaviors. Also, we do not know how long a woman was trying to become pregnant and thus how well-timed a planned birth was. If a subset of women were able to mitigate the tension between work and family through extensive planning, then our estimates of how much larger motherhood effects are for women with planned births may be conservative.
It is conceivable that some women may prefer not to work for pay when they become mothers and that this preference is higher among women who plan their first birth. If any women had such a time-invariant preference, it is addressed with the fixed effects. Women's preferences may change over time, however. Addressing the potential that a woman's ability to exercise this preference is contingent on her marital situation, we note that the moderating effect of birth planning on employment remains substantial and significant in models that adjust for marital status and the earnings and hours of the spouse, and it is nearly identical in supplemental models that simultaneously interact motherhood with contemporaneous marital status and marital status at the time of the birth (Table 3 and Table A3, online appendix). Additionally, although we do not know how individual women's attitudes toward employment and child-rearing evolved over time, we are able to analyze baseline measures of women's expectations about work and family. The vast majority of women indicated that they would prefer to work at age 35. Moreover, we find no significant differences in these preferences between women who planned their first birth and women who had a mistimed or unwanted first birth. Thus, although we cannot be absolutely sure that our finding of greater negative effects on employment upon motherhood for women who planned their births is partly or entirely a reflection of the greater preference for being a stay-at-home mother among women who planned their first birth, we believe that this is unlikely given our various modeling choices.
Another limitation of our analysis is that our inferences about differences between mothers who have a planned first birth and those who have an unplanned first birth may not generalize to unplanned pregnancies that end in abortion. Some women may have terminated a pregnancy before a first birth specifically because they wanted to improve their employment outcomes, for example, if the pregnancy occurred before they finished school or at a time that was detrimental to their employment opportunities.
In addition, the fertility postponement literature generally argues that earlier births, if anything, may hinder socioeconomic attainment (Diaz and Fiel 2016). Thus, it is possible that our estimates are slightly conservative.
Finally, an exception to the general pattern of results is a more negative association between motherhood and employment among the small proportion of high-skill White women with an unplanned but wanted first birth. Among Black women, we likewise find exceptions to the general pattern, with more negative associations if their first birth was unplanned but wanted, but in this case with respect to hours and wages rather than employment. Women with an unplanned but wanted first birth may be distinctly different. For example, they were less likely at baseline to report wanting to work and more likely to report wanting to be “Married, raising a family” than women who had a planned, mistimed, or unwanted first birth (Figure 2, panel a). Although these women may not have planned the pregnancy, per se, they may have been motivated to reduce their labor market engagement because of a long-standing commitment to prioritizing family obligations over work. These exceptions to the generalizations from our analysis remind us that women are diverse by race and other factors, and our conclusions may not apply to all groups.
## Discussion
A substantial literature within sociology, economics, and demography has found that having children negatively affects women's odds of employment and their earnings. To explain these findings, researchers have discussed a number of structural factors, such as gender discrimination and a labor market that does not readily accommodate motherhood (Acker 1990; Amuedo-Dorantes and Kimmel 2005; Arendell 2000; Blair-Loy and Dehart 2003; Budig and England 2001; Correll et al. 2007; DeNavas-Walt and Proctor 2015; England et al. 2016; England et al. 2012; Florian 2018; Gerson 1986; Glauber 2007; Hays 1996; Hill 1979; Neumark and Korenman 1992; Romagnoli and Wall 2012; Stone 2007; Taniguchi 1999; Waite and Stolzenberg 1976; Waldfogel 1997; Wilde et al. 2010). A smaller body of literature has discussed the association between access to family planning and historical increases in women's earnings; such an association suggests that at the individual level, women using contraception may be able to plan their transition into motherhood to moderate its impact on their employment and earnings (Bailey 2013; Bailey et al. 2012; Goldin and Katz 2000, 2002). Planned fertility is positively associated with socioeconomic status (Mosher et al. 2012; Musick et al. 2009). If planning helps some women reduce the impact of motherhood on their labor market outcomes, then this could compound economic inequality, and such findings could buttress the promotion of planned child-rearing as a preferential behavioral norm. However, we find the opposite—that women who plan their births in higher numbers experience the effects of motherhood, particularly on employment. Because more-privileged women are the ones who most often plan their first pregnancy, these motherhood penalties are not exacerbating inequality within women. The motherhood penalties that we find instead emphasize the importance of improving public and employer policies to reduce work–parenthood conflict and changing sociocultural norms and expectations that contribute to a continuing gendered division of labor.
Scholars have discussed how long-standing, prevailing ideologies surrounding work and motherhood affect behavior (Arendell 2000; Blair-Loy and Dehart 2003; Gerson 1986; Hays 1996; Romagnoli and Wall 2012; Stone 2007; Waite and Stolzenberg 1976). Such ideologies include a valorization of motherhood that is apparent across classes, from socioeconomically marginalized groups to higher-earning professional women (Edin and Kefalas 2005; Stone 2007). In light of this extant literature, we hypothesized that women who plan childbearing could be more likely—rather than less likely—to disinvest in the labor market upon motherhood. Women may plan their births to occur when they are most willing or most able to exit or spend less time in the labor market; alternatively, those who plan their births may be more responsive to the tension between motherhood and employment (Simoni et al. 2017; Stone 2007; Waite and Stolzenberg 1976).
Consistent with this valorization of female domesticity, our analyses indicate that the negative relationship between motherhood and women's labor market outcomes is largest among White women who planned their first birth. This finding is evident in models with a robust set of controls (Tables 35), regardless of skill group (Table 6), and across an extensive series of sensitivity analyses (Tables A3–A6, online appendix).
We also find larger associations between motherhood and women's labor market outcomes among White women than among Black women, which echoes the findings of earlier studies (Budig and England 2001; England et al. 2016; Florian 2018; Waldfogel 1997; Wilde et al. 2010). This association between motherhood and labor market outcomes is consistently evident for White women across all outcomes in the early and later years of motherhood. Among Black women, in contrast, women with a child were less likely to be employed and worked fewer hours than those with no children, but we do not observe a significant difference in hourly wages between women with and without a birth.
As noted earlier, prior work has discussed how women's choices are structurally constrained not only by a labor market that may not readily accommodate motherhood but also by sociocultural norms and expectations (Arendell 2000; Blair-Loy and Dehart 2003; Gerson 1986; Hays 1996; Romagnoli and Wall 2012; Stone 2007; Waite and Stolzenberg 1976). Although women, regardless of race, would be expected to experience work–family tension, qualitative studies have consistently found evidence of dissimilar sociocultural experiences and expectations—for example, the valorization of economic self-sufficiency among Black women in contrast to domesticity among White women (Barnes 2015; Collins 2000; Florian 2018; Marsh et al. 2013; Roberts 1993). Consistent with these race differences in the valorization of domesticity relative to economic self-sufficiency, we find substantial differences by planning status among White women but not Black women.
In light of work focusing on historical improvements in access to contraception and abortion, our findings present some irony. Contraception can help women control their fertility, and prior research on the association between socioeconomic disadvantage and unintended pregnancy suggests that women who have more socioeconomic resources are more likely to plan their pregnancies. However, we find that mistimed first births are less negatively associated with White women's employment outcomes than are planned ones.
These findings should not be interpreted to indicate that fertility postponement does not contribute to increases in women's economic attainment. Access to family planning has contributed to historic increases in women's acquisition of human capital, consistent with our descriptive results, and fertility postponement is associated with smaller wage penalties in some occupations (Bailey 2013; Bailey et al. 2012; Goldin and Katz 2000, 2002; Landivar 2020).
However, although one can use family planning to postpone fertility in order to accumulate human capital, we argue that it does not necessarily follow that one can use family planning to start a family at the time of one's choosing and to eliminate mothers' work–family tension.
As Potter and colleagues (2019:1) noted, unintended pregnancy has been used in the fields of public health and demography to motivate investments in family planning in a way that “contributes to stigmatization among already-marginalized groups.” Unplanned pregnancies, as shown here, can also be wanted. More central to our point, we find no evidence that unplanned births contribute to worse labor market outcomes than planned births. This is a novel contribution to the pregnancy intentions literature, which thus far has generally associated unintended pregnancies with negative outcomes. Additionally, our findings raise questions about the extent to which differences in pregnancy planning reflect differences in reproductive autonomy. Along with literature exploring the conceptualization of unintended pregnancy, we hope our findings motivate asking comprehensive questions about the reasons why women plan or postpone fertility.
As prior research has suggested, women adapt their priorities and preferences in response to external influences (Gerson 1986). We suspect that reducing the impact of child-rearing on women's employment will require that access to family planning is complemented with a shift in caretaking norms and supported by policies, such as subsidized childcare, that enable both parents to continue working if they so desire (Budig et al. 2012). Care work, including parenting, can be viewed as a social good, and women disproportionately take on this burden (England 2005). This evidence can inform policy-makers as they attempt to ensure that women have the tools to fulfill both their fertility and professional goals.
## Acknowledgments
We thank Rachel Jones, Paula England, and Kathryn Kost for their invaluable input and support. This article was made possible by an anonymous donor. The donor had no role in study design, data analysis, decision to publish, or preparation of the manuscript, and the findings and conclusions contained within are those of the authors and do not necessarily reflect positions or policies of the donor.
## Notes
1
Budig and Hodges (2010) posited an alternate view. They argued that among White women but not Black women, the wage penalty was larger for low-wage than high-wage women. However, they misinterpreted conditional quantile regression coefficients with respect to the marginal wage distribution. For a detailed discussion of this issue, see England et al. (2016).
3
For a discussion of this issue, see England et al. (2016: endnote 10).
4
We later discuss alternative specifications when we address sensitivity analyses.
5
We adopt the term “mistimed” as a useful abbreviation to refer to births occurring sooner than desired from the pregnancy intentions literature. It is a subcategorization of births that followed from pregnancies that, when they were conceived, were not wanted (at the time), in order to distinguish these from excess fertility.
6
For sample means by race and planning status, see Table A1 in the online appendix.
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https://us.edugain.com/questions/Prove-that-the-lengths-of-tangents-drawn-from-an-external-point-A-to-the-points-P-and-Q-on-the-circle-are-equal | ### Prove that the lengths of tangents drawn from an external point $A$ to the points $P$ and $Q$ on the circle are equal.
Answer:
Step by Step Explanation:
1. It is given that two tangents are drawn from an external point $A$ to the points $P$ and $Q$ on the circle.
The given situation is represented by the below image.
We have to prove that the length $AP$ is equal to length $AQ$.
2. Let us join the point $O$ to points $P, Q,$ and $A.$
We get
$AP$ is a tangent at $P$ and $OP$ is the radius through $P$.
We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
$\implies OP \perp AP$
Also, $AQ$ is a tangent at $Q$ and $OQ$ is the radius through $Q$.
We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
$\implies OQ \perp AQ$
3. In right- angled triangle $OPA$ and $OQA$, we have \begin{aligned} & OP = OQ && \text{[Radius of the same circle]} \\ & OA = OA && \text{[Common]} \\ \implies & \triangle OPA \cong \triangle OQA && \text{[By RHS-congruence]} \end{aligned}
4. As the corresponding parts of congruent triangle are equal, we have $AP = AQ$.
5. Thus, the lengths of tangents drawn from an external point $A$ to the points $P$ and $Q$ on the circle are equal.
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Creative Commons License | 2022-12-06T17:05:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9392765164375305, "perplexity": 207.31182637126776}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711111.35/warc/CC-MAIN-20221206161009-20221206191009-00499.warc.gz"} |
https://par.nsf.gov/biblio/10342460-stellar-merger-scenario-black-holes-pair-instability-gap | The Stellar Merger Scenario for Black Holes in the Pair-instability Gap
Abstract The recent detection of GW190521 stimulated ideas on how to populate the predicted black hole (BH) pair-instability (PI) mass gap. One proposal is the dynamical merger of two stars below the PI regime forming a star with a small core and an oversized envelope. We outline the main challenges this scenario faces to form one BH in the gap. In particular, the core needs to avoid growing during the merger, and the merger product needs to retain enough mass, including in the subsequent evolution, and at core collapse (CC). We explore this scenario with detailed stellar evolution calculations, starting with ad hoc initial conditions enforcing no core growth during the merger. We find that these massive merger products are likely to be helium-rich and spend most of their remaining lifetime within regions of instabilities in the Herzsprung–Russell diagram, such as luminous blue variable eruptions. An energetic estimate of the amount of mass loss neglecting the back reaction of the star suggests that the total amount of mass that can be removed at low metallicity is ≲1 M ⊙ . This is small enough that at CC our models are retaining sufficient mass to form BHs in the PI gap more »
Authors:
; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10342460
Journal Name:
The Astrophysical Journal Letters
Volume:
904
Issue:
2
Page Range or eLocation-ID:
L13
ISSN:
2041-8205 | 2023-02-06T03:21:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5834541320800781, "perplexity": 1773.7865896820097}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500303.56/warc/CC-MAIN-20230206015710-20230206045710-00776.warc.gz"} |
http://itl.nist.gov/div898/software/dataplot/refman1/auxillar/diffprop.htm | Dataplot Vol 1 Vol 2
# DIFFERENCE OF PORPORTION CONFIDENCE LIMITS
Name:
DIFFERENCE OF PROPORTION CONFIDENCE LIMITS
Type:
Analysis Command
Purpose:
Generates a confidence interval for the difference between two proportions.
Description:
Given a set of N1 observations in a variable X1 and a set of N2 observations in a variable X2, we can compute the proportion of successes in each sample as p1 and p2. We can then compute the difference of the proportions as P1 - P2. In addition, the DIFFERENCE OF PROPORTION CONFIDENCE LIMITS command computes a confidence interval for the difference between the two proportions of successes.
In Dataplot, you define a success by entering the command
ANOP LIMITS <lower limit> <upper limit>
before entering the DIFFERENCE OF PROPORTION CONFIDENCE LIMITS command. That is, you specify the lower and upper values that define a success. Then the estimate for the proportion of successes in each sample is simply the number of points in the success region divided by the total number of points. The difference of proportions is then the difference between these two sample proportions. Note that in many programs you would simply enter your data as a series of 0's and 1's where one of these defines a success and the other defines a failure. If your data is already in this format, simply define appropiate limits (e.g., ANOP LIMITS 0.5 1.5).
If there are P1 successes in N1 observations for sample 1 and P2 successes in N2 observations for sample 2, and the significance level is alpha (e.g., 0.05), then the 2-sided confidence interval for the difference of proportions of successes is computed as:
$$p_{\mbox{diff}} = p_1 - p_2$$
$$p_{\mbox{se}} = \sqrt{\frac{p_1(1 - p_1)} {n_1} + \frac{p_2(1 - p_2)}{n_2}}$$
$$p_{\mbox{diff}} \pm p_{se} \Phi^{-1}(1 - \alpha/2)$$
with $$\Phi^{-1}$$ denoting the percent point function of the standard normal distribution.
Dataplot computes this inverval for a number of different probability levels.
Syntax:
DIFFERENCE OF PROPORTION CONFIDENCE LIMITS <y1> <y2>
<SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
<y2> is the second response variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
ANOP LIMITS 0.80 1.0
DIFFERENCE OF PROPORTION CONFIDENCE LIMITS Y1 Y2
ANOP LIMITS 0.80 1.0
DIFFERENCE OF PROPORTION CONFIDENCE LIMITS Y1 Y2 ...
SUBSET TAG > 2
Note:
A table of confidence intervals is printed for alpha levels of 50.0, 75.0, 90.0, 95.0, 99.0, 99.9, 99.99, and 99.999. The sample size, sample number of successes, and sample proportion of successes are also printed.
Default:
None
Synonyms:
None
Related Commands:
ANOP LIMITS = Specify success region for proportions. PROPORTION CONFIDENCE LIMITS = Compute a proportions confidence interval. ANOP PLOT = Generate an analysis of proportions plot. CONFIDENCE LIMITS = Generate the confidence limits for the mean.
Reference:
"Statistical Methods", Eigth Edition, Snedecor and Cochran, 1989, Iowa State University Press, pp. 125-128.
Applications:
Confirmatory Data Analysis
Implementation Date:
1999/5
Program:
SKIP 25
ANOP LIMITS 138 142
SET WRITE DECIMALS 5
DIFFERENCE OF PROPORTION CONFIDENCE LIMITS Y1 Y2
This command generates the following output.
Two-Sided Confidence Limits for
the Difference of Proportions
First Response Variable: Y1
Second Response Variable: Y2
Sample 1:
Number of Observations: 10
Number of Successes: 5
Proportion of Successes: 0.50000
Sample 2:
Number of Observations: 10
Number of Successes: 9
Proportion of Successes: 0.90000
Difference Between Proportions: -0.40000
Warning: if either sample size is less
than 20, the normal approximation
may not be accurate.
------------------------------------------
Confidence Lower Upper
Value (%) Limit Limit
------------------------------------------
50.000 -0.52437 -0.27563
75.000 -0.61211 -0.18789
90.000 -0.70330 -0.09670
95.000 -0.76140 -0.03860
99.000 -0.87496 0.07496
99.900 -1.00674 0.20674
99.990 -1.11739 0.31739
99.999 -1.21449 0.41449
NIST is an agency of the U.S. Commerce Department.
Date created: 6/5/2001
Last updated: 10/13/2015 | 2016-09-28T17:02:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8625031113624573, "perplexity": 3732.4254835557836}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738661640.68/warc/CC-MAIN-20160924173741-00079-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://par.nsf.gov/biblio/10250956-linear-stochastic-approximation-fine-grained-polyak-ruppert-non-asymptotic-concentration | On Linear Stochastic Approximation: Fine-grained Polyak-Ruppert and Non-Asymptotic Concentration
We undertake a precise study of the asymptotic and non-asymptotic properties of stochastic approximation procedures with Polyak-Ruppert averaging for solving a linear system $\bar{A} \theta = \bar{b}$. When the matrix $\bar{A}$ is Hurwitz, we prove a central limit theorem (CLT) for the averaged iterates with fixed step size and number of iterations going to infinity. The CLT characterizes the exact asymptotic covariance matrix, which is the sum of the classical Polyak-Ruppert covariance and a correction term that scales with the step size. Under assumptions on the tail of the noise distribution, we prove a non-asymptotic concentration inequality whose main term matches the covariance in CLT in any direction, up to universal constants. When the matrix $\bar{A}$ is not Hurwitz but only has non-negative real parts in its eigenvalues, we prove that the averaged LSA procedure actually achieves an $O(1/T)$ rate in mean-squared error. Our results provide a more refined understanding of linear stochastic approximation in both the asymptotic and non-asymptotic settings. We also show various applications of the main results, including the study of momentum-based stochastic gradient methods as well as temporal difference algorithms in reinforcement learning.
Authors:
; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10250956
Journal Name:
Proceedings of Thirty Third Conference on Learning Theory
Volume:
125
Page Range or eLocation-ID:
2947-2997
We study the problem of solving strongly convex and smooth unconstrained optimization problems using stochastic first-order algorithms. We devise a novel algorithm, referred to as \emph{Recursive One-Over-T SGD} (\ROOTSGD), based on an easily implementable, recursive averaging of past stochastic gradients. We prove that it simultaneously achieves state-of-the-art performance in both a finite-sample, nonasymptotic sense and an asymptotic sense. On the nonasymptotic side, we prove risk bounds on the last iterate of \ROOTSGD with leading-order terms that match the optimal statistical risk with a unity pre-factor, along with a higher-order term that scales at the sharp rate of $O(n^{-3/2})$ under the Lipschitz condition on the Hessian matrix. On the asymptotic side, we show that when a mild, one-point Hessian continuity condition is imposed, the rescaled last iterate of (multi-epoch) \ROOTSGD converges asymptotically to a Gaussian limit with the Cram\'{e}r-Rao optimal asymptotic covariance, for a broad range of step-size choices. | 2023-02-03T01:38:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8178673982620239, "perplexity": 587.8586043777113}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500041.2/warc/CC-MAIN-20230202232251-20230203022251-00393.warc.gz"} |
https://www.abs.gov.au/research/economy/price-indexes-and-inflation/consumer-price-index-australia/implementation-plan-annually-re-weight-australian-cpi | # An implementation plan to annually re-weight the Australian CPI
The ABS maintains a program of periodic reviews of the Consumer Price Index (CPI) which examines CPI concepts, methodologies and data sources
Release date and time
## Preface
The Australian Bureau of Statistics (ABS) maintains a program of periodic reviews of the Consumer Price Index (CPI) to ensure it continues to meet community needs. The 16th Series CPI Review (ABS 2010) was the last comprehensive review which examined CPI concepts, methodologies and data sources. A number of topics and strategies were considered to maintain the relevance of the CPI in a dynamic environment, particularly given recent developments in methods and data sources. These developments present new opportunities to enhance the CPI.
The ABS has primarily used the Household Expenditure Survey (HES) to derive CPI weights at the published level (expenditure class level and above) and have updated these weights in line with the release of the HES data, currently every six years. The International Labour Organization (ILO) Resolution on CPIs recommends published level CPI weights are updated at least every five years. Conducting a more frequent HES would deliver benefits to the measurement of household inflation and to other users. However, a more frequent HES requires additional funding. The use of alternative data sources relating to household expenditure has been investigated by the ABS to enable the more frequent update of CPI expenditure weights, irrespective of the frequency of the HES.
In July 2016, the ABS released the information paper Increasing the Frequency of CPI Expenditure Class Weight Updates (cat. no. 6401.0.60.002), which investigated the feasibility of using Household Final Consumption Expenditure (HFCE) data from the National Accounts to more frequently update Australia's CPI expenditure class (EC) weights. This paper discusses the consultation undertaken by the ABS as part of this investigation, and outlines an implementation plan to annually re-weight the CPI.
The authors of this paper are staff from the Consumer Price Index Section of the ABS.
## Executive summary
In 2016, the ABS proposed annually re-weighting the Australian Consumer Price Index (CPI) using Household Final Consumption Expenditure (HFCE) data from the Australian National Accounts. This proposal was described in the information paper Increasing the Frequency of CPI Expenditure Class Weight Updates (cat. no. 6401.0.60.002). The research presented in this paper found empirical support for the theory that higher frequency re-weighting of the CPI at the expenditure class (EC) level better captures consumers’ substitution effects. Annually re-weighting the CPI using HFCE data also ensures greater coherence across macroeconomic statistics; and improved alignment with international standards.
The ABS consulted broadly in the development of the proposal and methods outlined in the 2016 paper. Development consultation included an external review by Mr Paul McCarthy, an international Price Statistics and National Accounts expert. Following the release of the 2016 paper, the ABS undertook an extensive stakeholder engagement program, including a call for public submissions. The ABS also conducted numerous bilateral and multilateral consultations with key stakeholders, including: the Reserve Bank of Australia; the Treasury; Department of Social Services; Department of Finance; and State Treasuries.
Stakeholders and public submissions were supportive of the ABS proposal and methodology to annually re-weight the Australian CPI. Noting this support, the ABS will:
• update EC level weights for the CPI and Selected Living Cost Indexes (SLCIs) in the December quarter 2017. The principal data source for updating the weights in the December quarter 2017 will be the 2015-16 Household Expenditure Survey (HES) data; and
• update EC level weights in the CPI annually each December quarter. The principal data source for updating the weights for the inter-HES years will be HFCE data from the National Accounts. HES data will continue to be used in the years that it is conducted.
Consultation with key stakeholders raised additional topics for further ABS research. These include:
• methods and data sources to more frequently re-weight the SLCIs; and
• documenting methods to calculate contributions to percentage change with annually re-weighted indexes.
Methods to calculate contributions to change for annually re-weighted indexes can be found in the Appendix.
Additionally, in the coming months the ABS will:
• publish an information paper in early November 2017 containing the new weights that will be implemented in the CPI and SLCIs in the December quarter 2017. This paper will also estimate the amount of upper level substitution bias present in the Australian CPI for the period 2011 to 2017; and
• investigate methods for more frequently updating the weights of the SLCIs. This work will be published following the December quarter 2017 re-weight of the CPI and SLCIs.
For any questions or feedback relating to this paper, please contact [email protected]. The ABS Privacy Policy outlines how the ABS will handle any personal information that you provide to us.
## Implementation plan
### 1 Introduction
1.1 The Australian Consumer Price Index (CPI) is a robust indicator of household inflation that has served Australia well for many decades. While the CPI is a well-respected ABS output, there are particular aspects of the CPI that can be enhanced, particularly with recent developments in methods and the availability of new data sources. In light of this, the ABS commenced a research program in August 2015 aimed at enhancing the Australian CPI through re-examining current approaches to collecting data and the methods used to compile the CPI.
1.2 The Australian CPI measures the change over time in the prices paid by households for a basket of goods and services. The basket reflects the composition of household consumption preferences; is compiled according to international standards; and is based on robust data collection and compilation methodologies. In compiling aggregate measures of price change, the role of expenditure weights is to reflect the economic importance of each item to the total expenditure of Australian households. Therefore, in practice, National Statistical Offices (NSOs) periodically update expenditure weights to accurately reflect the changing purchasing patterns of households.
1.3 The information paper Enhancing the Australian CPI: A roadmap (cat. no. 6401.0.60.001) outlined a research program to enhance the Australian CPI. The research program examined approaches to data collection and methods used to compile the CPI. The research focused on (i) annually re-weighting the CPI; and (ii) maximising the use of transactions data in the CPI.
1.4 The information paper Increasing the Frequency of CPI Expenditure Class Weight Updates (cat. no. 6401.0.60.002) discussed the feasibility of using Household Final Consumption Expenditure (HFCE) data from the National Accounts to more frequently update Australia’s CPI expenditure class (EC) weights. The research identified and addressed the challenges of using HFCE data and conducted an empirical assessment using experimental series. The paper concluded the empirical results supported the theory that higher frequency re-weighting at the EC level more accurately captures consumer substitution effects.
1.5 The ABS has consulted widely on the proposal to more frequently update the CPI EC weights. Public submissions were also sought with the ABS receiving several submissions.
1.6 This paper presents the results of the consultation process, and provides an implementation plan to annually re-weight the CPI. Also discussed is additional research to be conducted by the ABS on topics raised through consultation with the Australian community and key stakeholders.
### 2 Using HFCE data to re-weight the CPI
2.1 HFCE measures expenditure by resident households on goods and services, whether the expenditure is made within the domestic territory or by Australian residents abroad, and expenditure by Non-Profit Institutions Serving Households (NPISH). Conceptually, the measurement of HFCE closely aligns with the HES. HFCE data captures household expenditure, including the Goods and Services Tax (GST). Both HFCE and HES data cover expenditure by Australian households only and exclude expenditure by non-residents in Australia.
2.2 The HES is used as a major benchmark in the compilation of the HFCE series. Benchmarking is a technique used in the National Accounts, where less frequent (e.g. annual) data sources are used to validate more frequent (e.g. quarterly) estimates of HFCE. The other major benchmark used for HFCE is the Retail and Wholesale Industries (cat. no. 8622.0).
2.3 The use of HFCE data for CPI weights has many potential benefits for both internal and external users of inflation statistics. The primary benefit is that more representative weights enhance the CPI in its principal purpose as a macro-economic indicator of household inflation. There are, however, several challenges with using HFCE data for CPI weighting purposes. These challenges can be grouped together as:
• Overarching challenges - encompassing classification, scope, coverage, and revision challenges; and
• Specific EC challenges - encompassing a case-by-case assessment of using HFCE data for specific CPI ECs.
2.4 Challenges arise because the CPI and HFCE estimates are produced for different purposes and use different data sources. Proposed treatments to each of these challenges were addressed in the chapter Methods and practical considerations of the information paper (cat. no. 6401.0.60.002).
2.5 The ABS has conducted an empirical assessment of the proposed change to annually re-weight the CPI EC level weights. Experimental HFCE price indexes were produced between 2005 and 2015 to compare the annually re-weighted series with the existing CPI series. The results revealed that the experimental HFCE series reported lower average annual household inflation measures relative to the CPI. This supported the theory that higher frequency (annual) re-weighting at the EC level captures a greater amount of consumer substitution when compared to the current CPI (six yearly) re-weighting process.
### 3 Consultation
3.1 The ABS has undertaken broad consultation regarding the proposal and methods to annually re-weight the CPI. The method to use HFCE data for CPI weighting purposes underwent an external review by Mr Paul McCarthy, an international Price Statistics and National Accounts expert. Following the release of the paper in 2016, the ABS sought the views of the Australian community through a call for public submissions, which occurred between July and November 2016. Several submissions were received during the consultation period.
3.2 In addition to the call for public submissions, the ABS conducted numerous bilateral and multilateral consultations with key stakeholders, including: the Reserve Bank of Australia; the Treasury; Department of Social Services; Department of Finance; and State Treasuries.
3.3 Stakeholders and public submissions were supportive of the proposal and methods outlined to annually re-weight the Australian CPI.
3.4 Consultation with key stakeholders raised additional topics of further research for the ABS to consider. These topics include: (i) the possibility of more frequently updating the weights of the Selected Living Cost Indexes (SLCIs)(footnote 1) ; and (ii) the ABS to document methods to calculate contributions to percentage change with annually re-weighted indexes.
3.5 As a result of the feedback received, the ABS has conducted research into methods to calculate contributions to change with annually re-weighted indexes. This information can be found in the Appendix.
3.6 In coming months, the ABS will also conduct further research into methods allowing for more frequent re-weighting of the SLCIs. Both theoretical and empirical research will be undertaken with the results to be published following the December quarter 2017 re-weight of the CPI and SLCIs.
### 4 Implementation
4.1 Updated expenditure class level weights will be implemented into the CPI and SLCIs in the December quarter 2017, due for release on 31 January 2018 and 7 February 2018 respectively. The principal source for the updated weights will be the 2015-16 HES data.
4.2 An information paper will be published in early November 2017 containing the new weights. In addition to this, the ABS will construct a retrospective superlative Fisher-type(footnote 2) index between 2011 and 2017 to estimate the amount of upper level substitution bias in the CPI.
4.3 Following this, the EC level weights in the CPI will be updated annually each December quarter. The primary data source for updating the weights for the inter-HES years will be HFCE data from the National Accounts. The December quarter 2018 will be the first instance where HFCE data is used as the principal data source for the CPI re-weight. The ABS will continue to use HES as the primary data source to re-weight the CPI for the years where it is available.
### Footnotes
1. HFCE data is not available for different household groups. Therefore, the information paper Increasing the Frequency of CPI Expenditure Class Weight Updates (cat. no. 6401.0.60.002) proposed to continue to update the SLCI weights using the six yearly HES data.
2. See detailed information on index theory and aggregation in chapter 4 Price index theory of the CPI Concepts, Sources and Methods (cat. no. 6461.0).
## Appendix - calculating contributions to percentage change
### Show all
#### Introduction
1 As of the December quarter 2017, the Australian Bureau of Statistics (ABS) will move to annual re-weighting of the Consumer Price Index (CPI) expenditure class (EC) weights. The Household Expenditure Survey (HES) will continue to be used to update the weights in the years that it is available. For the inter-HES years, Household Final Consumption Expenditure (HFCE) data from the National Accounts will be used to re-weight the CPI ECs.
2 These short-term CPI series will be chain-linked together to form longer term series. In consultations with users about this change, a number of stakeholders sought advice from the ABS to document methods to calculate contributions to percentage change with annually re-weighted indexes.
3 This appendix explains how the contributions of ECs to quarterly and annual CPI percentage changes are currently derived, then outlines how these contributions can be calculated under an annually re-weighted CPI. An approximation is provided for contributions to the annual inflation rate with an annually re-weighted CPI, which distinguishes between the effect of price changes of the ECs, and changes in the expenditure shares (footnote 1) .
4 The ABS will conduct empirical testing of the method outlined and publish the results in an information paper, which will also introduce the new CPI weights, to be released in November 2017.
#### Current practice
5 The current Australian CPI is a Lowe-type price index. This is an index where at the upper level of aggregation, the price indexes of the ECs are aggregated using fixed quantity, price-updated weights.
6 Points contributions allow users to understand how much an EC contributes to the overall All groups CPI. Points contributions for each EC are published in Tables 7 and 12 of the Time Series Spreadsheets released with the CPI each quarter (cat. no. 6401.0). The weight of EC n to the All groups CPI in quarter t can be estimated using points contributions:
$$w_{n}^{t}=\frac{P C_{n}^{t}}{P C_{A g}^{t}} \times 100$$ (1)
where $$w_{n}^{t}$$ is the weight (%) of EC n to All groups CPI, $$P C_{n}^{t}$$ is the points contribution of EC n and $$P C_{A g}^{t}$$ is the points contribution (or price index) of the All groups CPI, all in quarter t.
7 These weights can be used in the calculation of contributions to the percentage change (footnote 2) . Under a Lowe-type price index, the contribution of individual EC n to the quarterly percentage change in the All groups CPI in quarter t is given by:
$$\operatorname{Cont}_{n q}^{t}=w_{n}^{t-1}\left(\frac{P_{n}^{t}}{P_{n}^{t-1}}-1\right)$$ (2)
where $$P_{n}^{t}$$ represents the price index of EC n in quarter t. Note that $$\frac{P_{n}^{t}}{P_{n}^{t-1}}-1$$is the percentage change of EC n between quarter t-1 and t.
8 The sum of the quarterly contributions of all ECs from (2) is equal to the quarterly percentage change in the All groups CPI.
9 Similarly, the contribution of EC n to the annual percentage change in the All groups CPI is given by the following:
$$\operatorname{Cont}_{n a}^{t}=w_{n}^{t-4}\left(\frac{P_{n}^{t}}{P_{n}^{t-4}}-1\right)$$ (3)
where $$\left(\frac{P_{n}^{t}}{P_{n}^{t-4}}-1\right)$$ is the annual percentage change of EC n.
#### Annual re-weighting and chaining
10 Under annual re-weighting, short-term CPI series (five quarters in length) will be constructed, each with their own set of weights. These series will then be chain-linked together to form a longer continuous time series. For an explanation and examples of chaining, see paragraphs 12.9 to 12.13 of the CPI Concepts, Sources and Methods publication (cat. no. 6461.0).
11 Under annual re-weighting, each quarterly percentage change of the chained CPI utilises a single set of weights. Therefore, calculating contributions to quarterly percentage change of the chained CPI does not pose an issue and can be derived in the same way as is currently done. For example, the contribution of EC n to the All groups CPI quarterly percentage movement in December quarter 2018 would be given by the following:
$$\large\operatorname{cont}_{n q}^{2018 Q_{4}}=w_{n}^{2018 Q 3}\times\left(\frac{p_{n}^{2018 Q 4}}{P_{n}^{2018 Q 3}}-1\right)$$ (4)
where 2018Q3 and 2018Q4 refer to the third and fourth quarters of 2018 respectively (i.e. the September and December quarters). This is the same expression as (2). Again, summing these contributions for all ECs will equal the quarterly percentage change in the All groups CPI in the December quarter 2018.
#### Decomposing annual percentage changes
12 Annual re-weighting does however pose a challenge when calculating contributions to the annual percentage change in the CPI. This is because the contribution will depend not only on changes in prices, but also changes in the weights.
13 As chaining is a multiplicative operation, and due to the arithmetic form of the short-term price index, it is not possible to calculate exact contributions of the ECs to the annual percentage change of the chained CPI. However, an approximation can be derived which distinguishes between the effects of annual percentage price change, and changes in the weights of the ECs. For the contribution of EC n to the annual percentage change between March quarter 2018 and March quarter 2019, the approximation is given by:
$$\large\operatorname{Cont}_{n a}^{2019 \mathrm{Q} 1} \approx w_{n}^{2018 \mathrm{Q} 1}\left(\frac{P_{n}^{2019 \mathrm{Q} 1}}{P_{n}^{2018 \mathrm{Q} 1}}-1\right)+\frac{P_{n}^{2019 \mathrm{Q} 1} / P_{n}^{2018 \mathrm{Q} 3}}{\hat{P}^{2019 \mathrm{Q} 1} / \hat{P}^{2018 \mathrm{Q} 3}}\left(w_{n}^{2018 \mathrm{Q} 3}-\hat{w}_{n}^{2018 \mathrm{Q} 3}\right)$$ (5)
where $$\hat{P}^{2019 \mathrm{Q} 1}$$ is the price index for the All groups CPI in March quarter 2019 using the weights of the previous short-term series and $$\hat{w}_{n}^{2018 \mathrm{Q} 3}$$is the weight of EC n in September quarter 2018 under the previous short-term series.
14 The first term in the expression represents the contribution due to the annual percentage price change, while the second term measures the contribution due to relative quantity (or weight) changes. The latter term is calculated with reference to the September quarter, which is the link quarter that connects the short-term series.
15 The ABS will provide additional information on the derivation of the approximation to interested users upon request. Requests can be sent to [email protected].
16 Further work will see the ABS conduct empirical testing of the decomposition shown in (5). The results of this will be published in an information paper to be released in November 2017.
#### Conclusion
17 As of the December quarter 2017, the ABS will move to annually updating the CPI EC weights. The primary data source to update the weights for the inter-HES years will be National Accounts HFCE data.
18 Updating the EC weights and chain-linking the short-term (Lowe-type) CPI series in this way does not change the method of calculating EC contributions to quarterly percentage changes. This is because each quarterly percentage change of the chained CPI utilises a single set of weights. The contributions are calculated in the same way as has traditionally been done for the Lowe-type CPI with fixed quantity weights.
19 However, with annually updated weights, the contribution of an EC to the annual percentage change in the All groups CPI has to be approximated. A decomposition has been provided in this appendix which distinguishes between the contribution due to price change, and that due to changes in the weights. The ABS will provide additional information on the derivation of the approximation to interested users upon request.
20 The ABS will conduct empirical testing of the decomposition and publish the results in a November 2017 information paper.
#### Footnotes
1 The ABS acknowledges the input and advice provided by Professor Jan de Haan of Statistics Netherlands and Delft University of Technology in the development of this method.
2 This contribution is different to the contribution to change published in Table 6 of the Time Series Spreadsheets released with the CPI each quarter. The values reported in this table measure an EC's contribution to the change in index points of the All groups CPI, rather than the percentage change.
## Bibliography
### Show all
ABS (Australian Bureau of Statistics) 2010, Outcome of the 16th Series Australian Consumer Price Index Review, cat. no. 6469.0, ABS, Canberra.
ABS 2015, Enhancing the Australian CPI: A roadmap, cat. no. 6401.0.60.001, ABS, Canberra.
ABS 2016, Increasing the Frequency of CPI Expenditure Class Weight Updates, cat. no, 6401.0.60.002, ABS, Canberra
ABS 2017, Consumer Price Index: Concepts, Sources and Methods, 2016, cat. no. 6461.0, ABS, Canberra.
Balk, B.M. 2017. Mixed-Form Indices: A Study of Their Properties. Paper presented at the 15th Meeting of the Ottawa Group. Altville am Rhein, 10-12 May.
International Labour Office 2004, Consumer price index manual : theory and practice, International Labour Office, Geneva.
Ribe, M 1999. Effects of Subcomponents on Chained Price Indices Like the HICPs and the MUICP. Statistics Sweden, Stockholm.
Walschots, J 2016. Contributions to and Impacts on Inflation. Statistics Netherlands, The Hague.
### Previous catalogue number
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https://www.zbmath.org/authors/?q=ai%3Awei.juncheng | # zbMATH — the first resource for mathematics
## Wei, Juncheng
Compute Distance To:
Author ID: wei.juncheng Published as: Wei, J.; Wei, J. C.; Wei, Jun Cheng; Wei, Jun-Cheng; Wei, Jun-cheng; Wei, Juncheng; Wei, Juncheng C. Homepage: http://www.math.ubc.ca/~jcwei/ External Links: MGP · Wikidata · dblp
Documents Indexed: 445 Publications since 1994, including 4 Books Reviewing Activity: 2 Reviews
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#### Co-Authors
22 single-authored 51 Winter, Matthias 42 Del Pino, Manuel A. 29 Ren, Xiaofeng 26 Ward, Michael J. 25 Musso, Monica 21 Kolokolnikov, Theodore 20 Lin, Chang-Shou 18 Ao, Weiwei 18 Kowalczyk, Michał 16 Guo, Zongming 14 Yan, Shusen 13 Lin, Taichia 12 Dávila, Juan 12 Liu, Yong 12 Wang, Kelei 11 Yang, Wen 9 Dancer, Edward Norman 9 Wang, Liping 9 Yang, Jun 8 Santra, Sanjiban 8 Zhou, Feng 7 Chan, Hardy 7 D’Aprile, Teresa 7 Gui, Changfeng 7 Pacard, Frank 7 Xu, Xingwang 7 Ye, Dong 6 Ni, Wei-Ming 6 Zhang, Lei 6 Zhao, Chunyi 5 Berestycki, Henri 5 González, María del Mar 5 Iron, David 5 Sire, Yannick 5 Weth, Tobias 5 Yao, Wei 4 Ding, Yanheng 4 Gomez, Daniel 4 Guo, Yuxia 4 Lin, Fang Hua 4 Lu, Guozhen 4 Zhou, Yifu 3 Agudelo, Oscar Mauricio 3 DelaTorre, Azahara 3 Fazly, Mostafa 3 Felmer, Patricio L. 3 Guo, Yujin 3 Hyder, Ali 3 Ma, Li 3 Malchiodi, Andrea 3 Pistoia, Angela 3 Rey, Olivier 3 Rumsey, John R. 3 Wu, Yuanze 2 Bandle, Catherine 2 Cao, Daomin 2 Chen, Guoyuan 2 Chen, Wenyi 2 Du, Zhuoran 2 Dupaigne, Louis 2 Esposito, Pierpaolo 2 Fadai, Nabil T. 2 Flucher, Martin 2 Grossi, Massimo 2 Hebey, Emmanuel 2 Jevnikar, Aleks 2 Jiang, Meiyue 2 Kikuchi, Hiroaki 2 Kim, Seunghyeok 2 Leach, Jannie A. 2 Li, Bo 2 Li, Shuai 2 Liu, Zhongyuan 2 Luo, Senping 2 Mei, Linfeng 2 Norbury, John W. 2 Noussair, Ezzat S. 2 Ren, Xiaofengg 2 Robert, Frédéric 2 Sun, Wentao 2 Terracini, Susanna 2 Ting, Fan 2 Tse, Wang Hung 2 Tzou, J. C. 2 Wang, Guofang 2 Wang, Xuefeng 2 Zeng, Xiaoyu 2 Zheng, Youquan 1 Ai, Jun 1 Alcolado, Adam 1 Bartsch, Thomas J. 1 Cerami, Giovanna 1 Chang, Yanming 1 Chen, Xianjin 1 Cheng, Yongkuan 1 Chern, I-Liang 1 Choe, Hi Jun 1 Chou, Kai-Seng 1 Deng, Bin 1 Deng, Shengbing ...and 41 more Co-Authors
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#### Serials
30 Journal of Differential Equations 29 Calculus of Variations and Partial Differential Equations 22 SIAM Journal on Mathematical Analysis 20 Journal of Functional Analysis 14 Physica D 14 Discrete and Continuous Dynamical Systems 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 10 Archive for Rational Mechanics and Analysis 10 Proceedings of the American Mathematical Society 10 European Journal of Applied Mathematics 10 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 SIAM Journal on Applied Mathematics 8 Pacific Journal of Mathematics 8 Transactions of the American Mathematical Society 8 Communications in Partial Differential Equations 8 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 8 Journal of Nonlinear Science 7 Communications on Pure and Applied Mathematics 7 Nonlinearity 7 Advances in Mathematics 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 6 Journal of Mathematical Physics 6 Indiana University Mathematics Journal 6 Manuscripta Mathematica 6 Studies in Applied Mathematics 5 Journal d’Analyse Mathématique 5 Mathematische Annalen 5 IMRN. International Mathematics Research Notices 5 Analysis & PDE 4 Communications in Mathematical Physics 4 Journal of Mathematical Biology 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Methods and Applications of Analysis 4 Interfaces and Free Boundaries 4 Communications on Pure and Applied Analysis 3 Duke Mathematical Journal 3 Journal of the London Mathematical Society. Second Series 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Nachrichten 3 Mathematische Zeitschrift 3 Asymptotic Analysis 3 Differential and Integral Equations 3 Journal of Dynamics and Differential Equations 3 NoDEA. Nonlinear Differential Equations and Applications 3 Advances in Differential Equations 3 Journal of the European Mathematical Society (JEMS) 3 Communications in Contemporary Mathematics 3 Discrete and Continuous Dynamical Systems. Series B 3 SIAM Journal on Applied Dynamical Systems 2 Reviews in Mathematical Physics 2 American Journal of Mathematics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Inventiones Mathematicae 2 Journal of Differential Geometry 2 Memoirs of the American Mathematical Society 2 Proceedings of the London Mathematical Society. Third Series 2 Geometric and Functional Analysis. GAFA 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Mathematical Research Letters 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Journal of Fixed Point Theory and Applications 1 IMA Journal of Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Bulletin de la Société Mathématique de France 1 Canadian Journal of Mathematics 1 Commentarii Mathematici Helvetici 1 Journal of the Mathematical Society of Japan 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Revista de la Unión Matemática Argentina 1 Tohoku Mathematical Journal. Second Series 1 Chinese Annals of Mathematics. Series B 1 Revista Matemática Iberoamericana 1 Applied Mathematics Letters 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Japan Journal of Industrial and Applied Mathematics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Proceedings of the National Academy of Sciences of the United States of America 1 SIAM Review 1 Communications in Analysis and Geometry 1 Topological Methods in Nonlinear Analysis 1 Electronic Research Announcements of the American Mathematical Society 1 Chaos 1 Annals of Mathematics. Second Series 1 Acta Mathematica Sinica. English Series 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Advanced Nonlinear Studies 1 Milan Journal of Mathematics 1 Pure and Applied Mathematics Quarterly 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Applied Mathematical Sciences 1 GAKUTO International Series. Mathematical Sciences and Applications 1 Science China. Mathematics 1 Nonlinear Analysis. Theory, Methods & Applications 1 Journal of Elliptic and Parabolic Equations 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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#### Fields
422 Partial differential equations (35-XX) 67 Biology and other natural sciences (92-XX) 31 Differential geometry (53-XX) 31 Statistical mechanics, structure of matter (82-XX) 27 Operator theory (47-XX) 24 Global analysis, analysis on manifolds (58-XX) 15 Calculus of variations and optimal control; optimization (49-XX) 14 Dynamical systems and ergodic theory (37-XX) 14 Quantum theory (81-XX) 12 Ordinary differential equations (34-XX) 12 Fluid mechanics (76-XX) 5 Integral equations (45-XX) 4 Potential theory (31-XX) 4 Functional analysis (46-XX) 4 Optics, electromagnetic theory (78-XX) 2 General and overarching topics; collections (00-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Mechanics of deformable solids (74-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Relativity and gravitational theory (83-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Algebraic topology (55-XX) 1 Numerical analysis (65-XX)
#### Citations contained in zbMATH Open
399 Publications have been cited 7,248 times in 2,852 Documents Cited by Year
Ground state of $$N$$ coupled nonlinear Schrödinger equations in $$\mathbb R^n$$, $$n \leq 3$$. Zbl 1119.35087
Lin, Tai-Chia; Wei, Juncheng
2005
On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems. Zbl 0838.35009
Ni, Wei-Ming; Wei, Juncheng
1995
Classification of solutions of higher order conformally invariant equations. Zbl 0940.35082
Wei, Juncheng; Xu, Xingwang
1999
Multiple interior peak solutions for some singularly perturbed Neumann problems. Zbl 1061.35502
Gui, Changfeng; Wei, Juncheng
1999
Spikes in two coupled nonlinear Schrödinger equations. Zbl 1080.35143
Lin, Tai-Chia; Wei, Juncheng
2005
A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system. Zbl 1191.35121
Dancer, E. N.; Wei, Juncheng; Weth, Tobias
2010
Concentrating standing waves for the fractional nonlinear Schrödinger equation. Zbl 1322.35162
Dávila, Juan; Del Pino, Manuel; Wei, Juncheng
2014
Bound states for a coupled Schrödinger system. Zbl 1153.35390
Bartsch, Thomas; Wang, Zhi-Qiang; Wei, Juncheng
2007
Radial solutions and phase separation in a system of two coupled Schrödinger equations. Zbl 1161.35051
Wei, Juncheng; Weth, Tobias
2008
On De Giorgi’s conjecture in dimension $$N\geq 9$$. Zbl 1238.35019
Del Pino, Manuel; Kowalczyk, Michał; Wei, Juncheng
2011
Concentration on curves for nonlinear Schrödinger equations. Zbl 1123.35003
Del Pino, Manuel; Kowalczyk, Michal; Wei, Jun-Cheng
2007
The stability of spike solutions to the one-dimensional Gierer-Meinhardt model. Zbl 0983.35020
Iron, David; Ward, Michael J.; Wei, Juncheng
2001
On interacting bumps of semi-classical states of nonlinear Schrödinger equations. Zbl 1217.35065
Kang, Xiaosong; Wei, Juncheng
2000
On bound states concentrating on spheres for the Maxwell-Schrödinger equation. Zbl 1096.35017
D’Aprile, Teresa; Wei, Juncheng
2005
Multiple boundary peak solutions for some singularly perturbed Neumann problems. Zbl 0944.35020
Gui, Changfeng; Wei, Juncheng; Winter, Matthias
2000
Strongly interacting bumps for the Schrödinger-Newton equations. Zbl 1189.81061
Wei, Juncheng; Winter, Matthias
2009
On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems. Zbl 0949.35052
Gui, Changfeng; Wei, Juncheng
2000
Uniqueness of positive solutions to some coupled nonlinear Schrödinger equations. Zbl 1264.35237
Wei, Juncheng; Yao, Wei
2012
On the boundary spike layer solutions to a singularly perturbed Neumann problem. Zbl 0873.35007
Wei, Juncheng
1997
On single interior spike solutions of the Gierer-Meinhardt system: Uniqueness and spectrum estimates. Zbl 1014.35005
Wei, Juncheng
1999
Spikes in two-component systems of nonlinear Schrödinger equations with trapping potentials. Zbl 1105.35117
Lin, Tai-Chia; Wei, Juncheng
2006
Infinitely many solutions for the prescribed scalar curvature problem on $$\mathbb S^N$$. Zbl 1209.53028
Wei, Juncheng; Yan, Shusen
2010
Nonradial symmetric bound states for a system of coupled Schrödinger equations. Zbl 1229.35019
Wei, Juncheng; Weth, Tobias
2007
On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem. Zbl 0865.35011
Wei, Juncheng
1996
Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model. Zbl 1030.35011
Ward, M. J.; Wei, J.
2003
On a two-dimensional elliptic problem with large exponent in nonlinearity. Zbl 0804.35042
Ren, Xiaofeng; Wei, Juncheng
1994
On the role of mean curvature in some singularly perturbed Neumann problems. Zbl 0942.35058
del Pino, Manuel; Felmer, Patricio L.; Wei, Juncheng
1999
Stationary solutions for the Cahn-Hilliard equation. Zbl 0910.35049
Wei, Juncheng; Winter, Matthias
1998
Infinitely many positive solutions for the nonlinear Schrödinger equations in $$\mathbb R^N$$. Zbl 1189.35106
Wei, Juncheng; Yan, Shusen
2010
Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials. Zbl 1131.35075
Ding, Yanheng; Wei, Juncheng
2007
On the number of interior peak solutions for a singularly perturbed Neumann problem. Zbl 1170.35424
Lin, Fang-Hua; Ni, Wei-Ming; Wei, Jun-Cheng
2007
Asymptotic behaviour of solutions of planar elliptic systems with strong competition. Zbl 1132.35482
Wei, Juncheng; Weth, Tobias
2008
Spikes for the Gierer-Meinhardt system in two dimensions: the strong coupling case. Zbl 1042.35005
Wei, Juncheng; Winter, Matthias
2002
Spikes for the two-dimensional Gierer-Meinhardt system: the weak coupling case. Zbl 1141.35345
Wei, J.; Winter, M.
2001
Convergence for a Liouville equation. Zbl 0987.35056
Ma, Li; Wei, Juncheng C.
2001
Stationary states of nonlinear Dirac equations with general potentials. Zbl 1170.35082
Ding, Yanheng; Wei, Juncheng
2008
Classification and nondegeneracy of $$SU(n+1)$$ Toda system with singular sources. Zbl 1258.35089
Lin, Chang-Shou; Wei, Juncheng; Ye, Dong
2012
Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory. Zbl 0964.35047
Grossi, Massimo; Pistoia, Angela; Wei, Juncheng
2000
Stability analysis of Turing patterns generated by the Schnakenberg model. Zbl 1057.92011
Iron, David; Wei, Juncheng; Winter, Matthias
2004
On the multiplicity of solutions of two nonlocal variational problems. Zbl 0973.49007
Ren, Xiaofeng; Wei, Juncheng
2000
On positive solutions concentrating on spheres for the Gierer-Meinhardt system. Zbl 1090.35023
Ni, Wei-Ming; Wei, Juncheng
2006
Mathematical aspects of pattern formation in biological systems. Zbl 1295.92013
Wei, Juncheng; Winter, Matthias
2014
Standing waves in the Maxwell-Schrödinger equation and an optimal configuration problem. Zbl 1207.35129
D’Aprile, Teresa; Wei, Juncheng
2006
Spike solutions in coupled nonlinear Schrödinger equations with attractive interaction. Zbl 1163.35034
Dancer, E. N.; Wei, Juncheng
2009
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime. Zbl 1136.35003
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Multiple clustered layer solutions for semilinear Neumann problems on a ball. Zbl 1207.35141
Malchiodi, A.; Ni, Wei-Ming; Wei, Juncheng
2005
On phase-separation models: asymptotics and qualitative properties. Zbl 1263.35095
Berestycki, Henri; Lin, Tai-Chia; Wei, Juncheng; Zhao, Chunyi
2013
Stationary multiple spots for reaction-diffusion systems. Zbl 1141.92007
Wei, Juncheng; Winter, Matthias
2008
The existence and stability of asymmetric spike patterns for the Schnakenberg model. Zbl 1152.35397
Ward, Michael J.; Wei, Juncheng
2002
Self-similar solutions for the anisotropic affine curve shortening problem. Zbl 1086.35035
Ai, Jun; Chou, Kai-Seng; Wei, Juncheng
2001
On the interior spike layer solutions to a singularly perturbed Neumann problem. Zbl 0918.35024
Wei, Juncheng
1998
On conformal deformations of metrics on $$S^n$$. Zbl 0924.58120
Wei, Juncheng; Xu, Xingwang
1998
On entire solutions of an elliptic system modeling phase separations. Zbl 1282.35022
Berestycki, Henri; Terracini, Susanna; Wang, Kelei; Wei, Juncheng
2013
Multiple-end solutions to the Allen-Cahn equation in $$\mathbb R^2$$. Zbl 1203.35108
del Pino, Manuel; Kowalczyk, Michał; Pacard, Frank; Wei, Juncheng
2010
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: The low feed-rate regime. Zbl 1145.65328
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain. Zbl 1178.35039
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2009
Concentrating solutions for the Hénon equation in $$\mathbb R^{2}$$. Zbl 1173.35504
Esposito, Pierpaolo; Pistoia, Angela; Wei, Juncheng
2006
On energy minimizers of the diblock copolymer problem. Zbl 1031.49035
Ren, Xiaofeng; Wei, Juncheng
2003
On the location and profile of spike-layer solutions to a singularly perturbed semilinear Dirichlet problem: Intermediate solutions. Zbl 0946.35007
Ni, Wei-Ming; Takagi, Izumi; Wei, Juncheng
1998
A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem. Zbl 1317.35054
Dávila, Juan; Dupaigne, Louis; Wang, Kelei; Wei, Juncheng
2014
On the two-dimensional Gierer-Meinhardt system with strong coupling. Zbl 0955.35006
Wei, Juncheng; Winter, Matthias
1999
Multi-peak solutions for some singular perturbation problems. Zbl 0974.35041
del Pino, Manuel; Felmer, Patricio L.; Wei, Juncheng
2000
Single-point condensation and least-energy solutions. Zbl 0845.35012
Ren, Xiaofeng; Wei, Juncheng
1996
Existence and stability of multiple-spot solutions for the Gray-Scott model in $$\mathbb{R}^2$$. Zbl 1014.37036
Wei, Juncheng; Winter, Matthias
2003
Finite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation. Zbl 1263.35198
Musso, Monica; Pacard, Frank; Wei, Juncheng
2012
Spherical solutions to a nonlocal free boundary problem from diblock copolymer morphology. Zbl 1153.35091
Ren, Xiaofeng; Wei, Juncheng
2008
Many droplet pattern in the cylindrical phase of diblock copolymer morphology. Zbl 1145.82007
Ren, Xiaofeng; Wei, Juncheng
2007
Mesa-type patterns in the one-dimensional Brusselator and their stability. Zbl 1108.35088
Kolokolnikov, T.; Erneux, T.; Wei, J.
2006
Hopf bifurction of spike solutions for the shadow Gierer-Meinhardt model. Zbl 1063.35030
Ward, M. J.; Wei, J.
2003
Asymmetric spike patterns for the one-dimensional Gierer-Meinhardt model: Equilibria and stability. Zbl 1010.35002
Ward, M. J.; Wei, J.
2002
Pattern formations in two-dimensional Gray-Scott model: Existence of single-spot solutions and their stability. Zbl 0981.35026
Wei, Juncheng
2001
On the effect of domain geometry on the existence of nodal solutions in singular perturbations problems. Zbl 0907.35011
Noussair, Ezzat S.; Wei, Juncheng
1997
The Toda system and multiple-end solutions of autonomous planar elliptic problems. Zbl 1197.35114
del Pino, Manuel; Kowalczyk, Michał; Pacard, Frank; Wei, Juncheng
2010
On a fourth order nonlinear elliptic equation with negative exponent. Zbl 1175.35144
Guo, Zongming; Wei, Juncheng
2009
Properties of positive solutions to an elliptic equation with negative exponent. Zbl 1136.35036
Ma, Li; Wei, J. C.
2008
Bubbling solutions for an anisotropic Emden-Fowler equation. Zbl 1159.35402
Wei, Juncheng; Ye, Dong; Zhou, Feng
2007
Asymptotic behavior of a nonlinear fourth order eigenvalue problem. Zbl 0872.35013
Wei, Juncheng
1996
The existence and stability of spike patterns in a chemotaxis model. Zbl 1073.35118
Sleeman, B. D.; Ward, Michael J.; Wei, J. C.
2005
Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity. I: $$N=3$$. Zbl 1134.35049
Rey, Olivier; Wei, Juncheng
2004
On the role of distance function in some singular perturbation problems. Zbl 0949.35054
del Pino, Manuel; Felmer, Patricio L.; Wei, Juncheng
2000
Regularization of point vortices pairs for the Euler equation in dimension two. Zbl 1293.35223
Cao, Daomin; Liu, Zhongyuan; Wei, Juncheng
2014
The stability of a stripe for the Gierer-Meinhardt model and the effect of saturation. Zbl 1210.35016
Kolokolnikov, Theodore; Sun, Wentao; Ward, Michael; Wei, Juncheng
2006
Nonlocal $$s$$-minimal surfaces and Lawson cones. Zbl 1394.53012
Dávila, Juan; del Pino, Manuel; Wei, Juncheng
2018
Sign-changing blowing-up solutions for supercritical Bahri-Coron’s problem. Zbl 1408.35007
Musso, Monica; Wei, Juncheng
2016
Classification of blowup limits for $$\mathrm{SU}(3)$$ singular Toda systems. Zbl 1322.35038
Lin, Chang-Shou; Wei, Jun-Cheng; Zhang, Lei
2015
Infinitely many solutions for the Schrödinger equations in $$\mathbb R^N$$ with critical growth. Zbl 1235.35104
Chen, Wenyi; Wei, Juncheng; Yan, Shusen
2012
A Neumann problem with critical exponent in nonconvex domains and Lin-Ni’s conjecture. Zbl 1204.35093
Wang, Liping; Wei, Juncheng; Yan, Shusen
2010
Existence and stability of spikes for the Gierer-Meinhardt system. Zbl 1223.35007
Wei, Juncheng
2008
Fast and slow decay solutions for supercritical elliptic problems in exterior domains. Zbl 1147.35030
Dávila, Juan; del Pino, Manuel; Musso, Monica; Wei, Juncheng
2008
The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime. Zbl 1304.35051
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2014
Entire solutions of the Allen-Cahn equation and complete embedded minimal surfaces of finite total curvature in $$\mathbb{R}^3$$. Zbl 1275.53015
del Pino, Manuel; Kowalczyk, Michal; Wei, Juncheng
2013
The Toda system and clustering interfaces in the Allen-Cahn equation. Zbl 1163.35017
Del Pino, Manuel; Kowalczyk, Michał; Wei, Juncheng
2008
Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations. Zbl 1105.35116
Lin, Tai-Chia; Wei, Juncheng
2006
On the location of spikes of solutions with two sharp layers for a singularly perturbed semilinear Dirichlet problem. Zbl 1087.35507
Dancer, E. N.; Wei, Juncheng
1999
On the profile of solutions with two sharp layers to a singularly perturbed semilinear Dirichlet problem. Zbl 0882.35052
Dancer, E. N.; Wei, Juncheng
1997
Infinitely many positive solutions for nonlinear equations with non-symmetric potentials. Zbl 1311.35077
Ao, Weiwei; Wei, Juncheng
2014
Infinitely many turning points for an elliptic problem with a singular non-linearity. Zbl 1186.35081
Guo, Zongming; Wei, Juncheng
2008
Existence, classification and stability analysis of multiple-peaked solutions for the Gierer-Meinhardt system in $$\mathbb R^1$$. Zbl 1195.35033
Wei, Juncheng; Winter, Matthias
2007
On the spectra of three-dimensional lamellar solutions of the diblock copolymer problem. Zbl 1055.35041
Ren, Xiaofeng; Wei, Juncheng
2003
On the fractional Lane-Emden equation. Zbl 06730678
Dávila, Juan; Dupaigne, Louis; Wei, Juncheng
2017
Estimates for Liouville equation with quantized singularities. Zbl 07309956
Wei, Juncheng; Zhang, Lei
2021
Singularity formation for the two-dimensional harmonic map flow into $$S^2$$. Zbl 1445.35082
Dávila, Juan; del Pino, Manuel; Wei, Juncheng
2020
Infinite-time blow-up for the 3-dimensional energy-critical heat equation. Zbl 1435.35081
del Pino, Manuel; Musso, Monica; Wei, Juncheng
2020
Gluing methods for vortex dynamics in Euler flows. Zbl 1439.35382
Davila, Juan; Del Pino, Manuel; Musso, Monica; Wei, Juncheng
2020
A gluing approach for the fractional Yamabe problem with isolated singularities. Zbl 1448.35539
Ao, Weiwei; DelaTorre, Azahara; González, María del Mar; Wei, Juncheng
2020
Bound state solutions for the supercritical fractional Schrödinger equation. Zbl 07187825
Ao, Weiwei; Chan, Hardy; González, María del Mar; Wei, Juncheng
2020
Ground states of nonlinear Schrödinger systems with mixed couplings. Zbl 1448.35176
Wei, Juncheng; Wu, Yuanze
2020
Stable and unstable periodic spiky solutions for the Gray-Scott system and the Schnakenberg system. Zbl 1437.35054
Gomez, Daniel; Mei, Linfeng; Wei, Juncheng
2020
The $$\operatorname{SU}(3)$$ Toda system with multiple singular sources. Zbl 1441.35127
Hyder, Ali; Lin, Changshou; Wei, Juncheng
2020
On Delaunay solutions of a biharmonic elliptic equation with critical exponent. Zbl 1437.35390
Guo, Zongming; Huang, Xia; Wang, Liping; Wei, Juncheng
2020
Nonhexagonal lattices from a two species interacting system. Zbl 1437.82008
Luo, Senping; Ren, Xiaofeng; Wei, Juncheng
2020
Nondegeneracy of harmonic maps from $$\mathbb{R}^2$$ to $$\mathbb{S}^2$$. Zbl 1436.53045
Chen, Guoyuan; Liu, Yong; Wei, Juncheng
2020
On higher-dimensional singularities for the fractional Yamabe problem: a nonlocal mazzeo-pacard program. Zbl 1440.35127
Ao, Weiwei; Chan, Hardy; Delatorre, Azahara; Fontelos, Marco A.; González, María Del Mar; Wei, Juncheng
2019
Type II blow-up in the 5-dimensional energy critical heat equation. Zbl 1417.35074
del Pino, Manuel; Musso, Monica; Wei, Jun Cheng
2019
Finite Morse index implies finite ends. Zbl 1418.35190
Wang, Kelei; Wei, Juncheng
2019
Ground states of two-component attractive Bose-Einstein condensates. I: Existence and uniqueness. Zbl 1405.35038
Guo, Yujin; Li, Shuai; Wei, Juncheng; Zeng, Xiaoyu
2019
Infinite time blow-up for the fractional heat equation with critical exponent. Zbl 1452.35244
Musso, Monica; Sire, Yannick; Wei, Juncheng; Zheng, Youquan; Zhou, Yifu
2019
Ground states of two-component attractive Bose-Einstein condensates. II: Semi-trivial limit behavior. Zbl 1421.35088
Guo, Yujin; Li, Shuai; Wei, Juncheng; Zeng, Xiaoyu
2019
Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3. Zbl 1420.35104
del Pino, Manuel; Musso, Monica; Román, Carlos; Wei, Juncheng
2019
The linear stability of symmetric spike patterns for a bulk-membrane coupled Gierer-Meinhardt model. Zbl 1419.35107
Gomez, Daniel; Ward, Michael J.; Wei, Juncheng
2019
Blow-up for the 3-dimensional axially symmetric harmonic map flow into $$S^2$$. Zbl 1425.35107
Dávila, Juan; Del Pino, Manuel; Pesce, Catalina; Wei, Juncheng
2019
Desingularization of Clifford torus and nonradial solutions to the Yamabe problem with maximal rank. Zbl 1439.35175
Medina, Maria; Musso, Monica; Wei, Juncheng
2019
Refined stability thresholds for localized spot patterns for the Brusselator model in $$\mathbb{R}^2$$. Zbl 1427.35107
Chang, Y.; Tzou, J. C.; Ward, M. J.; Wei, J. C.
2019
Second order estimate on transition layers. Zbl 1428.35023
Wang, Kelei; Wei, Juncheng
2019
Superfluids passing an obstacle and vortex nucleation. Zbl 1437.35237
Lin, Fanghua; Wei, Juncheng
2019
Non-radial solutions to a bi-harmonic equation with negative exponent. Zbl 1435.35178
Hyder, Ali; Wei, Juncheng
2019
On Serrin’s overdetermined problem and a conjecture of Berestycki, Caffarelli and Nirenberg. Zbl 1418.35191
Wang, Kelei; Wei, Juncheng
2019
Multi-bump ground states of the fractional Gierer-Meinhardt system on the real line. Zbl 1411.35276
Wei, Juncheng; Yang, Wen
2019
On the Helmholtz equation and Dancer’s-type entire solutions for nonlinear elliptic equations. Zbl 1409.35064
Liu, Yong; Wei, Juncheng
2019
Stable boundary spike clusters for the two-dimensional Gierer-Meinhardt system. Zbl 1406.35023
Ao, Weiwei; Wei, Juncheng; Winter, Matthias
2019
Nonlocal $$s$$-minimal surfaces and Lawson cones. Zbl 1394.53012
Dávila, Juan; del Pino, Manuel; Wei, Juncheng
2018
Existence theorems of the fractional Yamabe problem. Zbl 1377.53056
Kim, Seunghyeok; Musso, Monica; Wei, Juncheng
2018
Degree counting and shadow system for Toda system of rank two: one bubbling. Zbl 1394.35166
Lee, Youngae; Lin, Chang-Shou; Wei, Juncheng; Yang, Wen
2018
Multi-bump solutions of $$-\Delta = K(x)u^{\frac{n+2}{n-2}}$$ on lattices in $$\mathbb{R}^n$$. Zbl 1410.35047
Li, Yanyan; Wei, Juncheng; Xu, Haoyuan
2018
Pattern formation in a reaction-diffusion system with space-dependent feed rate. Zbl 1397.35023
Kolokolnikov, Theodore; Wei, Juncheng
2018
On rank-2 Toda systems with arbitrary singularities: local mass and new estimates. Zbl 1383.35078
Lin, Chang-Shou; Wei, Jun-cheng; Yang, Wen; Zhang, Lei
2018
Classification of blow-up limits for the sinh-Gordon equation. Zbl 1449.35224
Jevnikar, Aleks; Wei, Juncheng; Yang, Wen
2018
On the topological degree of the mean field equation with two parameters. Zbl 1405.35041
Jevnikar, Aleks; Wei, Juncheng; Yang, Wen
2018
Existence of positive weak solutions for fractional Lane-Emden equations with prescribed singular sets. Zbl 1429.35193
Ao, Weiwei; Chan, Hardy; del Mar González, María; Wei, Juncheng
2018
Nondegeneracy of half-harmonic maps from $$\mathbb {R}$$ into $$\mathbb {S}^1$$. Zbl 1410.35278
Sire, Yannick; Wei, Juncheng; Zheng, Youquan
2018
On De Giorgi’s conjecture: recent progress and open problems. Zbl 1402.35023
Chan, Hardy; Wei, Juncheng
2018
Boundary concentrations on segments for the Lin-Ni-Takagi problem. Zbl 1396.35011
Ao, Weiwei; Chan, Hardy; Wei, Juncheng
2018
Anomalous scaling of Hopf bifurcation thresholds for the stability of localized spot patterns for reaction-diffusion systems in two dimensions. Zbl 1391.35225
Tzou, J. C.; Ward, M. J.; Wei, J. C.
2018
Stabilizing a homoclinic stripe. Zbl 1425.35100
Kolokolnikov, Theodore; Ward, Michael; Tzou, Justin; Wei, Juncheng
2018
Nondegeneracy of the Gauss curvature equation with negative conic singularity. Zbl 1406.35130
Wei, Juncheng; Zhang, Lei
2018
Toda systems and hypergeometric equations. Zbl 1402.35106
Lin, Chang-Shou; Nie, Zhaohu; Wei, Juncheng
2018
On the fractional Lane-Emden equation. Zbl 06730678
Dávila, Juan; Dupaigne, Louis; Wei, Juncheng
2017
Delaunay-type singular solutions for the fractional Yamabe problem. Zbl 1378.35321
DelaTorre, Azahara; del Pino, Manuel; González, María del Mar; Wei, Juncheng
2017
On finite Morse index solutions of higher order fractional Lane-Emden equations. Zbl 1372.35334
Fazly, Mostafa; Wei, Juncheng
2017
Stable spike clusters for the one-dimensional Gierer-Meinhardt system. Zbl 1386.35165
Wei, Juncheng; Winter, Matthias
2017
A non-compactness result on the fractional Yamabe problem in large dimensions. Zbl 1378.53051
Kim, Seunghyeok; Musso, Monica; Wei, Juncheng
2017
Local uniqueness and refined spike profiles of ground states for two-dimensional attractive Bose-Einstein condensates. Zbl 1380.35093
Guo, Yujin; Lin, Changshou; Wei, Juncheng
2017
Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation. Zbl 1386.31005
Guo, Zongming; Wei, Juncheng; Zhou, Feng
2017
Global minimizers of the Allen-Cahn equation in dimension $$n\geq 8$$. Zbl 1380.35071
Liu, Yong; Wang, Kelei; Wei, Juncheng
2017
Stable spike clusters for the precursor Gierer-Meinhardt system in $$\mathbb {R}^2$$. Zbl 1386.35166
Wei, Juncheng; Winter, Matthias; Yang, Wen
2017
Traveling wave solutions for bistable fractional Allen-Cahn equations with a pyramidal front. Zbl 1372.35331
Chan, Hardy; Wei, Juncheng
2017
A bifurcation diagram of solutions to an elliptic equation with exponential nonlinearity in higher dimensions. Zbl 1390.35093
Kikuchi, Hiroaki; Wei, Juncheng
2017
Infinitely many positive solutions of fractional nonlinear Schrödinger equations with non-symmetric potentials. Zbl 1370.35091
Ao, Weiwei; Wei, Juncheng; Yang, Wen
2017
Multiplicity of semiclassical solutions to nonlinear Schrödinger equations. Zbl 1364.35330
Ding, Yanheng; Wei, Juncheng
2017
On a transcendental equation involving quotients of gamma functions. Zbl 1371.33007
Luo, Senping; Wei, Juncheng; Zou, Wenming
2017
Two-end solutions to the Allen-Cahn equation in $$\mathbb{R}^3$$. Zbl 1386.35120
Gui, Changfeng; Liu, Yong; Wei, Juncheng
2017
Delayed reaction kinetics and the stability of spikes in the Gierer-Meinhardt model. Zbl 1368.35021
Fadai, Nabil T.; Ward, Michael J.; Wei, Juncheng
2017
The spectrum of the torus profile to a geometric variational problem with long range interaction. Zbl 1378.49050
Ren, Xiaofeng; Wei, Juncheng
2017
Sign-changing blowing-up solutions for supercritical Bahri-Coron’s problem. Zbl 1408.35007
Musso, Monica; Wei, Juncheng
2016
On the uniqueness of solutions of a nonlocal elliptic system. Zbl 1375.35615
Wang, Kelei; Wei, Juncheng
2016
New blow-up phenomena for $$\mathrm{SU}(n+1)$$ Toda system. Zbl 1418.35139
Musso, Monica; Pistoia, Angela; Wei, Juncheng
2016
On non-topological solutions of the $$\mathbf{G}_2$$ Chern-Simons system. Zbl 1358.58013
Ao, Weiwei; Lin, Chang-Shou; Wei, Juncheng
2016
On stable solutions of the fractional Hénon-Lane-Emden equation. Zbl 1344.35163
Fazly, Mostafa; Wei, Juncheng
2016
Local profile of fully bubbling solutions to $$\mathrm {SU} (n+1)$$ Toda systems. Zbl 1350.35085
Lin, Chang-Shou; Wei, Juncheng; Zhang, Lei
2016
Solutions without any symmetry for semilinear elliptic problems. Zbl 1341.35060
Ao, Weiwei; Musso, Monica; Pacard, Frank; Wei, Juncheng
2016
$$2\pi$$-periodic self-similar solutions for the anisotropic affine curve shortening problem. II. Zbl 1326.34071
Jiang, Meiyue; Wei, Juncheng
2016
Higher-dimensional catenoid, Liouville equation, and Allen-Cahn equation. Zbl 1404.35197
Agudelo, Oscar; del Pino, Manuel; Wei, Juncheng
2016
Uniqueness and nondegeneracy of sign-changing radial solutions to an almost critical elliptic problem. Zbl 1375.35025
Ao, Weiwei; Wei, Juncheng; Yao, Wei
2016
Clustering layers for the Fife-Greenlee problem in $${\mathbb R}^n$$. Zbl 1342.35104
Du, Zhuoran; Wei, Juncheng
2016
Qualitative analysis of rupture solutions for a MEMS problem. Zbl 1350.35093
Dávila, Juan; Wang, Kelei; Wei, Juncheng
2016
Layered solutions for a fractional inhomogeneous Allen-Cahn equation. Zbl 1359.35213
Du, Zhuoran; Gui, Changfeng; Sire, Yannick; Wei, Juncheng
2016
Traveling vortex helices for Schrödinger map equations. Zbl 1342.35059
Wei, Juncheng; Yang, Jun
2016
On variational characterization of four-end solutions of the Allen-Cahn equation in the plane. Zbl 1350.35076
Gui, Changfeng; Liu, Yong; Wei, Juncheng
2016
On nonradial singular solutions of supercritical biharmonic equations. Zbl 1355.35061
Guo, Zongming; Wei, Juncheng; Yang, Wen
2016
Non-compactness and infinite number of conformal initial data sets in high dimensions. Zbl 1331.58027
Premoselli, Bruno; Wei, Juncheng
2016
On non-topological solutions of the $$\mathbf{A}_2$$ and $$\mathbf{B}_2$$ Chern-Simons system. Zbl 1330.35123
Ao, Weiwei; Lin, Chang-Shou; Wei, Juncheng
2016
Positive solutions of nonlinear Schrödinger equation with peaks on a Clifford torus. Zbl 1436.35100
Santra, Sanjiban; Wei, Juncheng
2016
An introduction to the finite and infinite dimensional reduction methods. Zbl 1343.35004
del Pino, Manuel; Wei, Juncheng
2016
On a singular perturbed problem in an annulus. Zbl 1347.35024
Santra, Sanjiban; Wei, Juncheng
2016
Classification of blowup limits for $$\mathrm{SU}(3)$$ singular Toda systems. Zbl 1322.35038
Lin, Chang-Shou; Wei, Jun-Cheng; Zhang, Lei
2015
Intermediate reduction method and infinitely many positive solutions of nonlinear Schrödinger equations with non-symmetric potentials. Zbl 1319.35249
del Pino, Manuel; Wei, Juncheng; Yao, Wei
2015
Nondegeneracy of nodal solutions to the critical Yamabe problem. Zbl 1328.35047
Musso, Monica; Wei, Juncheng
2015
Serrin’s overdetermined problem and constant mean curvature surfaces. Zbl 1342.35188
Del Pino, Manuel; Pacard, Frank; Wei, Juncheng
2015
A double bubble assembly as a new phase of a ternary inhibitory system. Zbl 1309.35172
Ren, Xiaofeng; Wei, Juncheng
2015
Solutions with multiple catenoidal ends to the Allen-Cahn equation in $$\mathbb{R}^3$$. Zbl 1305.35079
Agudelo, Oscar; del Pino, Manuel; Wei, Juncheng
2015
End-to-end construction for the Allen-Cahn equation in the plane. Zbl 1311.35115
Kowalczyk, Michał; Liu, Yong; Pacard, Frank; Wei, Juncheng
2015
On a general $$\mathrm{SU}(3)$$ Toda system. Zbl 1339.35118
Gladiali, Francesca; Grossi, Massimo; Wei, Juncheng
2015
A pointwise inequality for the fourth-order Lane-Emden equation. Zbl 1328.35035
Fazly, Mostafa; Wei, Jun-cheng; Xu, Xingwang
2015
Convergence rate, location and $$\partial_z^2$$ condition for fully bubbling solutions to $$\mathrm{SU}(n + 1)$$ Toda systems. Zbl 1328.35040
Lin, Chang-Shou; Wei, Juncheng; Zhang, Lei
2015
Singly periodic solutions of the Allen-Cahn equation and the Toda lattice. Zbl 1321.35054
Kowalczyk, Michał; Liu, Yong; Wei, Juncheng
2015
On a fractional Henon equation and applications. Zbl 1342.35439
Sire, Yannick; Wei, Jun-Cheng
2015
On Toda system with Cartan matrix $$G_{2}$$. Zbl 1321.35039
Ao, Weiwei; Lin, Chang-Shou; Wei, Juncheng
2015
Existence and stability of a spike in the central component for a consumer chain model. Zbl 1375.35247
Wei, Juncheng; Winter, Matthias
2015
Concentrating standing waves for the fractional nonlinear Schrödinger equation. Zbl 1322.35162
Dávila, Juan; Del Pino, Manuel; Wei, Juncheng
2014
Mathematical aspects of pattern formation in biological systems. Zbl 1295.92013
Wei, Juncheng; Winter, Matthias
2014
...and 299 more Documents
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#### Cited by 2,227 Authors
263 Wei, Juncheng 54 Pistoia, Angela 46 Del Pino, Manuel A. 45 Ward, Michael J. 40 Guo, Zongming 40 Musso, Monica 38 Lin, Chang-Shou 38 Yan, Shusen 36 Peng, Shuangjie 36 Tang, Xianhua 36 Zou, Wenming 31 Wang, Jun 31 Wang, Zhi-Qiang 31 Yang, Minbo 30 Ding, Yanheng 28 Cao, Daomin 28 Malchiodi, Andrea 27 Kolokolnikov, Theodore 27 Ren, Xiaofeng 27 Winter, Matthias 25 Grossi, Massimo 25 Tang, Zhongwei 25 Zhang, Fubao 24 Kowalczyk, Michał 23 Clapp, Mónica 22 Ambrosio, Vincenzo 22 Ao, Weiwei 22 Byeon, Jaeyoung 22 Dancer, Edward Norman 22 D’Aprile, Teresa 22 Yang, Wen 21 Dávila, Juan 19 Weth, Tobias 18 Bartsch, Thomas J. 18 Guo, Yuxia 18 Shi, Junping 18 Tavares, Hugo 18 Terracini, Susanna 18 Wang, Kelei 18 Xu, Junxiang 18 Zhang, Zhitao 17 Alves, Claudianor Oliveira 17 Gui, Changfeng 17 Micheletti, Anna Maria 17 Mo, Jiaqi 17 Zhang, Jihui 16 Sire, Yannick 16 Valdinoci, Enrico 16 Wu, Yuanze 16 Zhang, Jianjun 15 Chen, Sitong 15 Fazly, Mostafa 15 Soave, Nicola 15 Wang, Liping 15 Ye, Dong 15 Zhou, Feng 14 Deng, Shengbing 14 Ghimenti, Marco G. 14 Kim, Seunghyeok 14 Li, Congming 14 Liu, Zuhan 14 Mahmoudi, Fethi 14 Santra, Sanjiban 14 Wang, Chunhua 14 Zhang, Jian 13 Esposito, Pierpaolo 13 Lee, Youngae 13 Lei, Yutian 13 Liu, Weiming 13 Liu, Yong 13 Sourdis, Christos 13 Zhang, Wen 12 Chen, Zhijie 12 Dipierro, Serena 12 Do Ó, João M. Bezerra 12 Doelman, Arjen 12 Miyamoto, Yasuhito 12 Yang, Jun 12 Zhao, Fukun 11 Battaglia, Luca 11 Bonheure, Denis 11 Chen, Xinfu 11 Dai, Wei 11 Gao, Fashun 11 Ghergu, Marius 11 Guo, Yujin 11 Iron, David 11 Jevnikar, Aleks 11 Noris, Benedetta 11 Pacard, Frank 11 Zhang, Lei 10 Chen, Chaonien 10 Farina, Alberto 10 Gladiali, Francesca 10 He, Xiaoming 10 Ianni, Isabella 10 Lai, Baishun 10 Liang, Sihua 10 Lin, Taichia 10 Liu, Zhaoli ...and 2,127 more Authors
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#### Cited in 235 Serials
279 Journal of Differential Equations 200 Calculus of Variations and Partial Differential Equations 178 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 148 Journal of Mathematical Analysis and Applications 116 Discrete and Continuous Dynamical Systems 89 Journal of Functional Analysis 66 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 62 Journal of Mathematical Physics 62 Communications on Pure and Applied Analysis 55 Communications in Contemporary Mathematics 49 Communications in Partial Differential Equations 43 Archive for Rational Mechanics and Analysis 43 Proceedings of the American Mathematical Society 43 Physica D 42 Advanced Nonlinear Studies 41 ZAMP. Zeitschrift für angewandte Mathematik und Physik 41 NoDEA. Nonlinear Differential Equations and Applications 38 Advances in Mathematics 37 Journal de Mathématiques Pures et Appliquées. Neuvième Série 34 Transactions of the American Mathematical Society 32 Annali di Matematica Pura ed Applicata. Serie Quarta 29 Communications in Mathematical Physics 28 Nonlinear Analysis. Real World Applications 28 Science China. Mathematics 26 Complex Variables and Elliptic Equations 24 Nonlinearity 24 Applied Mathematics Letters 24 SIAM Journal on Mathematical Analysis 23 Applicable Analysis 23 Mathematical Methods in the Applied Sciences 22 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 22 Comptes Rendus. Mathématique. Académie des Sciences, Paris 22 Boundary Value Problems 21 Computers & Mathematics with Applications 20 European Journal of Applied Mathematics 19 Journal of Dynamics and Differential Equations 19 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 18 Mathematische Annalen 18 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 18 Journal of Nonlinear Science 18 SIAM Journal on Applied Dynamical Systems 18 Advances in Nonlinear Analysis 17 Journal of Fixed Point Theory and Applications 16 Applied Mathematics and Computation 16 Discrete and Continuous Dynamical Systems. Series B 15 Communications on Pure and Applied Mathematics 15 Journal of Mathematical Biology 15 Manuscripta Mathematica 14 Journal d’Analyse Mathématique 12 The Journal of Geometric Analysis 12 Journal of the European Mathematical Society (JEMS) 12 Acta Mathematica Sinica. English Series 11 Journal für die Reine und Angewandte Mathematik 10 Studies in Applied Mathematics 10 Applied Mathematics and Mechanics. (English Edition) 10 Chinese Annals of Mathematics. Series B 10 Acta Applicandae Mathematicae 10 SIAM Journal on Applied Mathematics 10 Discrete and Continuous Dynamical Systems. Series S 9 Journal of Computational Physics 9 Mathematische Nachrichten 9 Mathematische Zeitschrift 9 Revista Matemática Iberoamericana 9 Abstract and Applied Analysis 8 Bulletin of Mathematical Biology 8 Archiv der Mathematik 8 Duke Mathematical Journal 8 Pacific Journal of Mathematics 8 Acta Mathematicae Applicatae Sinica. English Series 8 Japan Journal of Industrial and Applied Mathematics 8 Topological Methods in Nonlinear Analysis 8 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 Chaos 8 Milan Journal of Mathematics 8 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 7 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 7 Analysis & PDE 6 Journal of Scientific Computing 6 Potential Analysis 6 Annales Henri Poincaré 6 Mediterranean Journal of Mathematics 5 Rocky Mountain Journal of Mathematics 5 Journal of Geometry and Physics 5 Indiana University Mathematics Journal 5 Inventiones Mathematicae 5 Quarterly of Applied Mathematics 5 Journal of Mathematical Chemistry 4 Journal of Computational and Applied Mathematics 4 Journal of the London Mathematical Society. Second Series 4 Memoirs of the American Mathematical Society 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Proceedings of the London Mathematical Society. Third Series 4 Applied Mathematical Modelling 4 Electronic Journal of Differential Equations (EJDE) 4 Taiwanese Journal of Mathematics 4 Discrete Dynamics in Nature and Society 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 4 Advances in Difference Equations 4 Journal of Elliptic and Parabolic Equations ...and 135 more Serials
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#### Cited in 49 Fields
2,580 Partial differential equations (35-XX) 268 Global analysis, analysis on manifolds (58-XX) 215 Biology and other natural sciences (92-XX) 173 Differential geometry (53-XX) 156 Calculus of variations and optimal control; optimization (49-XX) 136 Ordinary differential equations (34-XX) 112 Statistical mechanics, structure of matter (82-XX) 111 Quantum theory (81-XX) 109 Dynamical systems and ergodic theory (37-XX) 105 Operator theory (47-XX) 81 Numerical analysis (65-XX) 64 Integral equations (45-XX) 59 Fluid mechanics (76-XX) 39 Mechanics of deformable solids (74-XX) 37 Potential theory (31-XX) 35 Optics, electromagnetic theory (78-XX) 30 Functional analysis (46-XX) 27 Real functions (26-XX) 18 Probability theory and stochastic processes (60-XX) 18 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 16 Convex and discrete geometry (52-XX) 12 Mechanics of particles and systems (70-XX) 11 Relativity and gravitational theory (83-XX) 9 Functions of a complex variable (30-XX) 8 Classical thermodynamics, heat transfer (80-XX) 6 Measure and integration (28-XX) 6 Systems theory; control (93-XX) 5 Special functions (33-XX) 5 Abstract harmonic analysis (43-XX) 4 Nonassociative rings and algebras (17-XX) 4 Difference and functional equations (39-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Geometry (51-XX) 3 General and overarching topics; collections (00-XX) 3 Number theory (11-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Topological groups, Lie groups (22-XX) 3 Algebraic topology (55-XX) 3 Statistics (62-XX) 3 Astronomy and astrophysics (85-XX) 3 Geophysics (86-XX) 2 Combinatorics (05-XX) 2 Algebraic geometry (14-XX) 2 Integral transforms, operational calculus (44-XX) 2 Manifolds and cell complexes (57-XX) 2 Computer science (68-XX) 1 History and biography (01-XX) 1 Category theory; homological algebra (18-XX) 1 Several complex variables and analytic spaces (32-XX)
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