url
stringlengths 14
2.42k
| text
stringlengths 100
1.02M
| date
stringlengths 19
19
| metadata
stringlengths 1.06k
1.1k
|
|---|---|---|---|
https://tinevez.github.io/msdanalyzer/ | View on GitHub
# Mean square displacement analysis of particle trajectories.
Mean square displacement (MSD) analysis is a technique commonly used in colloidal studies and biophysics to determine what is the mode of displacement of particles followed over time. In particular, it can help determine whether the particle is:
• freely diffusing;
• transported;
• bound and limited in its movement.
On top of this, it can also derive an estimate of the parameters of the movement, such as the diffusion coefficient.
`@msdanalyzer` is a MATLAB per-value class that helps performing this kind of analysis. The user provides several trajectories he measured, and the class can derive meaningful quantities for the determination of the movement modality, assuming that all particles follow the same movement model and sample the same environment.
This tutorial doubles the documentation of the class, that can be accessed in classical ways. We demonstrate here how to use it, using very basic numerical simulations. The literature on MSD analysis is quite dense; in no way this beginner tutorial can hope to replace it. The examples we use are trivial, and we do not discuss the complex but important matter of the results significance. A demanding user is referred to the publications listed in this tutorial, and to the references they link.
## Citing this work.
If you use this tool for your work, we kindly ask you to cite the following article for which it was created:
Nadine Tarantino, Jean-Yves Tinevez, Elizabeth Faris Crowell, Bertrand Boisson, Ricardo Henriques, Musa Mhlanga, Fabrice Agou, Alain Israël, and Emmanuel Laplantine. TNF and IL-1 exhibit distinct ubiquitin requirements for inducing NEMO-IKK supramolecular structures. J Cell Biol (2014) vol. 204 (2) pp. 231-45
## Installation.
Just download the link to the zip file or the tar.gz file and extract the `@msdanalyzer` folder. Drop it in a folder that belongs to the MATLAB path (the @msdanalyzer folder should not be in the path itself).
If everything works, typing
`>> ma = msdanalyzer(2, 'µm', 's')`
should return something like:
``` msdanalyzer with properties:
TOLERANCE: 12
tracks: {}
n_dim: 2
space_units: 'µm'
time_units: 's'
msd: []
vcorr: []
lfit: []
loglogfit: []
drift: []
```
## Brownian motion and mean square displacement.
According to Einstein theory (the first part), an ensemble of particles undergoing brownian motion will have the following density:
$ρ ( r , t ) = ρ 0 4π Dt e - r 2 4Dt$
assuming all the particles where followed from a single point at t=0, that r is the distance to this point, and D the diffusion coefficient. This (and much more) can be found in Einstein historical paper [1].
Using this formula, one can derive the mean square displacement for such particles:
$r 2 = 2 d D t$
where d is the dimensionality of the problem (2 for 2D, etc...) and D the diffusion coefficient. The mean is taken over a whole ensemble of particles: you have to sample many particles, compute $msd i ( τ ) = ( r i ( τ ) - r i ( 0 ) ) 2$ for each particle i and average the resulting $msd i$ over all particles.
We see that the plot of the MSD value as a function of time should be a straight line in the case of diffusing movement. We therefore have a way to check what is the modality of the particle movement. If the MSD is a line, then it is diffusing, and the slope gives us the diffusion coefficient. If the MSD saturates and has a concave curvature, then its movement is impeded: it cannot freely diffuse away from its starting point. On the contrary, if the MSD increases faster than at linear rate, then it must be transported, because Brownian motion could not take it away that fast.
This is great, because to decide whether the erratic movement of a particle that you are observing is freely diffusive, bound, or transported, you would have to follow the particle for an infinite amount of time. This formula gives you a function that can be evaluated to check whether the particle movement is of any type. So we just need a way to evaluate it practically.
Experimentally, the MSD for a single particle is also taken as a mean. If the process is stationary (that is: the "situation", experimental conditions, etc... do not change over time), the ensemble average can be taken as a time average for a single trajectory, and MSD for a single particle can be calculated as
$msd i ( τ ) = ∑ t ( r i ( t + τ ) - r i ( t ) ) 2$
τ is called the delay; the MSD tells you how far can a particle under Brownian motion can go over a time τ. For finite trajectories, obviously the smaller delays τ will be more represented in the average than longer delays. For instance, if a trajectory has N points in it, the delay corresponding to one frame will have N-1 points in the average, and the delay corresponding to N frames will only have one. This has major consequences on measurement certainty, see [2].
## @msdanalyzer: a MATLAB per-value class for MSD analysis.
The class presented here perform these computations automatically, and offers a lot of convenience methods to simplify the analysis of trajectories.
The user must provide the class with particle trajectories, possibly several thousands of them. The class itself cannot generate those trajectories. For this, you want to check single-particle tracking tools. Here are a few examples, drawn from Life-Sciences and my work:
• Fiji ships a tracking tool named TrackMate made by yours truly, that can deal rather well with Brownian motion. The software is a Java program.
• Icy is another Java software dedicated to Life Science that also offers single particle tracking.
• If you already have the positions of all particles, and just need to link them to build tracks, you can use this simple tracker in MATLAB, again made by yours truly. But it has a much simpler capability compared that the two others.
And there are most likely plenty of other solutions out there.
@msdanalyzer can deal with tracks (particle trajectories) that do not start all at the same time, have different lengths, have missing detections (gaps: a particle fails to be detected in one or several frame then reappear), and do not have the same time sampling. As soon as you added your tracks to the class, everything is transparent. It offers facilities to plot and inspect the data, whether for individual particles, or on ensemble average quantities. It has several methods for correcting for drift, which is the main source of error in the analysis. Once corrected, the data can analyzed via the MSD curves or via the velocity autocorrelation. Automated fits of the MSD curves are included (but they require you have the curve fitting toolbox), allowing to derive the type of motion and its characteristics.
`>> doc msdanalyzer`
and will get a page where all methods and fields are detailed.
To document the class, we will play with toy examples, using simulated trajectories, Our simulations will be kept simple, even trivial. There is a deep literature on the modeling of diffusion, but we will skip any complexities, at the expense of scientific relevance. See [3] for details on modeling.
## Tutorial content.
1. Simulating and analyzing Brownian motion. Here we introduce the class using the most simple example: a few particles undergoing a purely diffusive process. We will review all the important functions of the class for calculating and analyzing the MSD curves.
2. Velocities and velocity auto-correlation. In this chapter we quickly review how to exploit the displacement and velocity autocorrelation function to analyze the particles motion.
3. Impact of tracking and localization error. We refine a little bit the plain simulations of the previous chapter, trying to generate tracks that are more resembling experimental measurements. We reproduce some of the results of [4], investigating how these errors impact the final analysis results.
4. Directed motion. We deal with the case of particles that have a directed motion on top of a Brownian motion. We introduce how to distinguish between the two kind of motion, and exploit analysis results to derive motion characteristics.
5. Confined movements. This is just the converse case: for this type of motion, the particle is not free to diffuse, but somehow bound to a fixed structure or hindered in its movement by an invisible fence.
6. Correcting for drift. This chapter details what methods are offered to correct for drift in measurements. It also provides an assessment of the most adequate method. And concludes this tutorial.
Since most of the complexity of the calculation is hidden in the @msdanalyzer class, these tutorial chapters involve mainly MATLAB code to generate and simulate fake particle trajectories. Some hacks are presented to facilitate the task, that I hope you will find useful as well. | 2021-07-28 19:38:29 | {"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": 0.5883575677871704, "perplexity": 811.4738533489058}, "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-2021-31/segments/1627046153791.41/warc/CC-MAIN-20210728185528-20210728215528-00008.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-a-combined-approach-4th-edition/chapter-7-test-page-561/3 | ## Algebra: A Combined Approach (4th Edition)
$\frac{3}{5}$
Step 1: $\frac{3x-6}{5x-10}$ Step 2: $\frac{3(x-2)}{5(x-2)}$ Step 3: Cancelling (x-2), which is common to both the numerator and the denominator, the expression reduces to $\frac{3}{5}$. | 2018-07-18 20:44:31 | {"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": 0.9629977941513062, "perplexity": 332.673484030981}, "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-2018-30/segments/1531676590329.25/warc/CC-MAIN-20180718193656-20180718213656-00178.warc.gz"} |
https://www.r-bloggers.com/2015/03/rolling-sharpe-ratios/ | Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
Similar to my rolling cumulative returns from last post, in this post, I will present a way to compute and plot rolling Sharpe ratios. Also, I edited the code to compute rolling returns to be more general with an option to annualize the returns, which is necessary for computing Sharpe ratios.
In any case, let’s look at some more code. First off, the new running cumulative returns:
"runCumRets" <- function(R, n = 252, annualized = FALSE, scale = NA) {
R <- na.omit(R)
if (is.na(scale)) {
freq = periodicity(R)
switch(freq$scale, minute = { stop("Data periodicity too high") }, hourly = { stop("Data periodicity too high") }, daily = { scale = 252 }, weekly = { scale = 52 }, monthly = { scale = 12 }, quarterly = { scale = 4 }, yearly = { scale = 1 }) } cumRets <- cumprod(1+R) if(annualized) { rollingCumRets <- (cumRets/lag(cumRets, k = n))^(scale/n) - 1 } else { rollingCumRets <- cumRets/lag(cumRets, k = n) - 1 } return(rollingCumRets) } Essentially, a more general variant, with an option to annualize returns over longer (or shorter) periods of time. This is necessary for the following running Sharpe ratio code: "runSharpe" <- function(R, n = 252, scale = NA, volFactor = 1) { if (is.na(scale)) { freq = periodicity(R) switch(freq$scale, minute = {
stop("Data periodicity too high")
}, hourly = {
stop("Data periodicity too high")
}, daily = {
scale = 252
}, weekly = {
scale = 52
}, monthly = {
scale = 12
}, quarterly = {
scale = 4
}, yearly = {
scale = 1
})
}
rollingAnnRets <- runCumRets(R, n = n, annualized = TRUE)
rollingAnnSD <- sapply(R, runSD, n = n)*sqrt(scale)
rollingSharpe <- rollingAnnRets/rollingAnnSD ^ volFactor
return(rollingSharpe)
}
The one little innovation I added is the vol factor parameter, allowing users to place more or less emphasis on the volatility. While changing it from 1 will make the calculation different from the standard Sharpe ratio, I added this functionality due to the Logical Invest strategy I did in the past, and thought that I might as well have this function run double duty.
And of course, this comes with a plotting function.
"plotRunSharpe" <- function(R, n = 252, ...) {
sharpes <- runSharpe(R = R, n = n)
sharpes <- sharpes[!is.na(sharpes[,1]),]
chart.TimeSeries(sharpes, legend.loc="topleft", main=paste("Rolling", n, "period Sharpe Ratio"),
date.format="%Y", yaxis=FALSE, ylab="Sharpe Ratio", auto.grid=FALSE, ...)
meltedSharpes <- do.call(c, data.frame(sharpes))
axisLabels <- pretty(meltedSharpes, n = 10)
axisLabels <- unique(round(axisLabels, 1))
axisLabels <- axisLabels[axisLabels > min(axisLabels) & axisLabels < max(axisLabels)]
axis(side=2, at=axisLabels, label=axisLabels, las=1)
}
So what does this look like, in the case of a 252-day FAA vs. SPY test?
Like this:
par(mfrow = c (2,1))
plotRunSharpe(comparison, n=252)
plotRunSharpe(comparison, n=756)
Essentially, similar to what we saw last time–only having poor performance at the height of the crisis and for a much smaller amount of time than SPY, and always possessing a three-year solid performance. One thing to note about the Sharpe ratio is that the interpretation in the presence of negative returns doesn’t make too much sense. That is, when returns are negative, having a small variance actually works against the Sharpe ratio, so a strategy that may have lost only 10% while SPY lost 50% might look every bit as bad on the Sharpe Ratio plots due to the nature of a small standard deviation punishing smaller negative returns as much as it benefits smaller positive returns.
In conclusion, this is a fast way of computing and plotting a running Sharpe ratio, and this function doubles up as a utility for use with strategies such as the Universal Investment Strategy from Logical Invest.
NOTE: I am a freelance consultant in quantitative analysis on topics related to this blog. If you have contract or full time roles available for proprietary research that could benefit from my skills, please contact me through my LinkedIn here.
R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't. | 2021-12-06 03:32:55 | {"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": 0.2736685872077942, "perplexity": 3362.066642903259}, "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-2021-49/segments/1637964363229.84/warc/CC-MAIN-20211206012231-20211206042231-00469.warc.gz"} |
https://www.physicsforums.com/threads/simulation-of-the-fission-as-a-stochastic-process.78620/ | # Simulation of the fission as a stochastic process
1. Jun 10, 2005
### Heimdall
Hello
I'm a french student, I'm actually not sure this is the good place to ask my question but as it deals with the nuclear fission I try here... don't hesitate to tell me if there is a better forum... thx..
well, I'm trying to solve numerically the Langevin equation, initially for the brownian motion, it is also used in nuclear physics as you probably know, to describe the fission of nuclei...
the Langevin equation is :
$$\ddot{x}+\beta \dot{x} + \frac{1}{m}\frac{\partial U}{\partial x} = \Gamma(t)$$
where $$\beta=\frac{\gamma}{m}$$ is a friction term (from a stocke's law) divided by the mass of the brownian particle. (so $$\beta$$ is $$s^{-1}$$)
$$U(x)$$ is an extern potential
and $$\Gamma(t)$$ is a stochastic force divided my the mass.
well, now I decide, as Kramers did, to tell that my potential U is represented by two parabolas as you can see on http://nicolas.aunai.free.fr/courb.htm [Broken]
I call B the height of the maximum, and $$x_b$$ the correspondant X-coordonnate (assuming that the minimum will be at x=0)
I decide that B will be my caracteristic energy for the problem, and $$x_b$$ my caracteristc length.
I want, in order to solve my equation numerically, to write it without dimension, so I introduce the following new variables :
$$Q = \frac{x}{x_b}$$
$$\Pi = \frac{U}{B}$$
$$t'=\omega t$$ where $$\omega$$ is the caracteristic pulsation of my parabolas
i.e. the equations of the parabolas are :
$$U_1(x)=\frac{1}{2}m\omega^2 x^2$$ for $$x<x_0$$
$$U_2(x)=-\frac{1}{2}m\omega^2(x-x_b)^2 + B$$ for $$x>x_0$$
assuming the continuity of the potential, the functions and the derivatives shoud be equal between them at $$x_0$$ the junction point. these conditions give us the height B which is equals to :
$$\frac{1}{4}m\omega^2 x_b^2$$
well now we have to re-write the langevin equation, replacing by the new variables... and here began my problems....
$$\ddot{x}+\beta \dot{x} + \frac{1}{m}\frac{\partial U}{\partial x} = \Gamma(t)$$
$$\dot{x}$$ means $$\frac{dx}{dt}$$, so since we have $$t'=\omega t$$, the derivation by t' gives us an $$\omega$$
$$\omega^2 x_b\ddot{Q}+\beta \omega x_b \dot{Q} + \frac{B}{m}\frac{\partial \Pi}{\partial Q} \frac{\partial Q}{\partial x} = \Gamma(t)$$
we know that $$\frac{\partial Q}{\partial x} = \frac{1}{x_b}$$
so we have :
$$\omega^2 x_b\ddot{Q}+\beta \omega x_b \dot{Q} + \frac{B}{mx_b}\frac{\partial \Pi}{\partial Q}= \Gamma(t)$$
and with the B value we have :
$$\omega^2 x_b\ddot{Q}+\beta \omega x_b \dot{Q} + \frac{\omega^2 x_b}{4}\frac{\partial \Pi}{\partial Q}= \Gamma(t)$$
finally, dividing by $$\omega^2 x_b$$ we obtain :
$$\ddot{Q}+\frac{\beta}{\omega}\dot{Q} + \frac{1}{4}\frac{\partial \Pi}{\partial Q}= \frac{1}{\omega^2 x_b}\Gamma(t)$$
which I think is almost the result that I'm looking for.. since the first term is without dimention, $$\frac{\beta}{\omega}$$ is without dimension too, and the third term too..
my problem is the stochastic term...
now I don't know how to do with it.... if you have an idea...
I now, that the autocorrelation function of the Langevin Force is :
$$<\Gamma(t)\Gamma(t')> = 2\beta T \delta(t_1-t_2)$$
since $$t_i = \frac{t_i'}{\omega}$$, can I write the following equation :
$$<\Gamma(t)\Gamma(t')> = 2\beta T \delta(\frac{t_1'}{\omega}-\frac{t_2'}{\omega})$$
and with $$\delta(a x)=\frac{1}{a}\delta(x)$$
I find :
$$<\Gamma(t)\Gamma(t')> = 2\omega \beta T \delta(t_1'-t_2')$$
so $$\Gamma(t)$$ should be proportionnal to $$\sqrt{(2\omega\beta T \delta(t_1'-t_2'))}$$
in the nuclear system, k (the Boltzmann constant) is equal to 1, so we can also introduce the new variable :
$$\Theta=\frac{T}{B}$$
so we can put it in our relation :
$$\Gamma(t)\ \ \ \alpha\ \ \ \sqrt{(2\omega\beta B\Theta\delta(t_1'-t_2'))}$$
well... I'm not sure where I'm going with this... can someone help me ?
thanks !
Last edited by a moderator: May 2, 2017 | 2017-07-20 18:43:24 | {"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": 0.8606544733047485, "perplexity": 503.18144033530143}, "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-2017-30/segments/1500549423320.19/warc/CC-MAIN-20170720181829-20170720201829-00460.warc.gz"} |
http://landshape.org/enm/simple-greenhouse-models/ | • Home»
• All»
• Simple Greenhouse Proofs
# Simple Greenhouse Proofs
A reported increase in the longwave downward radiation in the Swiss Alps, proves the ‘‘theory’’ of greenhouse warming with direct radiation observations according to this paper, “Radiative forcing – measured at Earth’s surface – corroborate the increasing greenhouse effect”, by Rolf Philipona, Bruno Durr, Christoph Marty, Atsumu Ohmura and Martin Wild.
Supposed direct observational proofs of the enhanced greenhouse effect have been reviewed here in the past.
1. Rahmstorf, who claimed climate responding faster than expected on the basis of a dubious graph with no statistical test;
2. Harries who claimed to detect the greenhouse effect from CO2 spectral brightening but whose later (underreported) publications were much more equivocal;
3. Soden, whose claims to have detected increase in specific water vapor from
spectral brightening were reported as proof in the IPCC AR4, despite conflicting evidence.
• jae
Hope I can comment, despite being an amateur on radiation. I started reading it and choked on my Coke while reading the first sentence in the Introduction.
• jae
Hope I can comment, despite being an amateur on radiation. I started reading it and choked on my Coke while reading the first sentence in the Introduction.
• Alex Harvey
jae, I would recommend reading this article carefully. Note the authors, including Martin Wild, and Atsumo Ohmura. Then look at this text in section 3:
For a 10% increase of CO2, including respective increases of other greenhouse gases and water vapour feedback, the ECHAM-4 GCM calculates an increase over land in the northern hemisphere of LDRcf of +4.6 Wm-2 and a SDRcf decrease of -1.4 Wm-2. These flux changes induce temperature and absolute humidity increases of +0.74C and +4.4% respectively. Table 2 shows that these model predicted flux and climate parameter changes are in good agreement with ASRB measured variations over the eight years time period.
[9] However, the CO2 increase from 1995 to 2002 was not 10%, but only 12 ppm or 3.3% in central Europe. Hence, although changes of radiative fluxes and subsequent climatic changes observed at the surface are in due proportion with model predicted variations, they are about three times larger than expected from greenhouse gas increases.
Is this not precisely the result that Lindzen finds in Lindzen 2007? The greenhouse effect is observed, but at 1/3 the magnitude of what is expected.
At least half of the increases may therefore not be explicable by direct effects of increased GHGs and associated feedbacks on temperature and humidity, but are rather due to circulation changes over central Europe.1
But they seem to spin the wording, especially in the headings, and in the conclusion, to make it sound as if CO2 is causing 3x the warming we were expecting! I’m puzzled; I wonder if this is to throw their bosses off the scent so their research continues to be published, and they keep their jobs?
Meanwhile, with respect to Miskolczi’s theory, note that they still don’t have measurements of AA to go with their new improved measurements of ED. They do seem to assume that surface heating is caused by downward longwave radiation, whereas M seems to say that it is not. Perhaps someone like might to comment on this.
• Alex Harvey
jae, I would recommend reading this article carefully. Note the authors, including Martin Wild, and Atsumo Ohmura. Then look at this text in section 3:
For a 10% increase of CO2, including respective increases of other greenhouse gases and water vapour feedback, the ECHAM-4 GCM calculates an increase over land in the northern hemisphere of LDRcf of +4.6 Wm-2 and a SDRcf decrease of -1.4 Wm-2. These flux changes induce temperature and absolute humidity increases of +0.74C and +4.4% respectively. Table 2 shows that these model predicted flux and climate parameter changes are in good agreement with ASRB measured variations over the eight years time period.
[9] However, the CO2 increase from 1995 to 2002 was not 10%, but only 12 ppm or 3.3% in central Europe. Hence, although changes of radiative fluxes and subsequent climatic changes observed at the surface are in due proportion with model predicted variations, they are about three times larger than expected from greenhouse gas increases.
Is this not precisely the result that Lindzen finds in Lindzen 2007? The greenhouse effect is observed, but at 1/3 the magnitude of what is expected.
At least half of the increases may therefore not be explicable by direct effects of increased GHGs and associated feedbacks on temperature and humidity, but are rather due to circulation changes over central Europe.1
But they seem to spin the wording, especially in the headings, and in the conclusion, to make it sound as if CO2 is causing 3x the warming we were expecting! I’m puzzled; I wonder if this is to throw their bosses off the scent so their research continues to be published, and they keep their jobs?
Meanwhile, with respect to Miskolczi’s theory, note that they still don’t have measurements of AA to go with their new improved measurements of ED. They do seem to assume that surface heating is caused by downward longwave radiation, whereas M seems to say that it is not. Perhaps someone like might to comment on this.
• Anonymous
Wild et al 2001 on Downward Longwave Radiation by Steve McIntyre on April 13th, 2005
Wild et al. [2001], a blue-chip study, shows that the downward longwave radiation in cold, dry climates is dramatically under-estimated in the GCMs used in IPCC TAR, as shown in the following excerpt from their Figure 4 (from one of the best GCMs). The bias is systemic.
Noted recently here and raised again here for discussion.
• http://landshape.org/enm David Stockwell
Wild et al 2001 on Downward Longwave Radiation by Steve McIntyre on April 13th, 2005
Wild et al. [2001], a blue-chip study, shows that the downward longwave radiation in cold, dry climates is dramatically under-estimated in the GCMs used in IPCC TAR, as shown in the following excerpt from their Figure 4 (from one of the best GCMs). The bias is systemic.
Noted recently here and raised again here for discussion.
• Alex Harvey
David, here is the link to the Wild et al. [2001] article again: http://ams.allenpress.com/archive/1520-0442/14/15/pdf/i1520-0442-14-15-3227.pdf
There are also a lot of other interesting articles that cite this article (find it in google scholar and then click the link ‘cited by 22′). I note that Atsumu Ohmura, and the Swiss Federal Institute of Technology, Institute for Climate Research, is linked to a lot of this literature. Keep in mind Ozawa & Ohmura 1997, and their theory of convection as deriving from the MEP, whilst reading all this. I am finding it all quite intriguing…
• Alex Harvey
David, here is the link to the Wild et al. [2001] article again: http://ams.allenpress.com/archive/1520-0442/14/15/pdf/i1520-0442-14-15-3227.pdf
There are also a lot of other interesting articles that cite this article (find it in google scholar and then click the link ‘cited by 22′). I note that Atsumu Ohmura, and the Swiss Federal Institute of Technology, Institute for Climate Research, is linked to a lot of this literature. Keep in mind Ozawa & Ohmura 1997, and their theory of convection as deriving from the MEP, whilst reading all this. I am finding it all quite intriguing…
• Anonymous
Here is the link for that Alex. It is intriguing as Wild seems to have had a change of heart. Would be good to get him on here to explain it all, if we could phrase some questions.
Here is the link for that Alex. It is intriguing as Wild seems to have had a change of heart. Would be good to get him on here to explain it all, if we could phrase some questions.
• Louis Hissink
In addition atmsopheric electrical currents, whose existence is only now being recognised, are also sources of IR radiation.
This should complicate matters somewhat?
• Louis Hissink
In addition atmsopheric electrical currents, whose existence is only now being recognised, are also sources of IR radiation.
This should complicate matters somewhat?
• Gary Moran
Is this not precisely the result that Lindzen finds in Lindzen 2007? The greenhouse effect is observed, but at 1/3 the magnitude of what is expected.
Surely this is the other way round, the effect is 3 * greater than expected given the GHG increase?
• Gary Moran
Is this not precisely the result that Lindzen finds in Lindzen 2007? The greenhouse effect is observed, but at 1/3 the magnitude of what is expected.
Surely this is the other way round, the effect is 3 * greater than expected given the GHG increase?
• Gary Moran
[QUOTE]Is this not precisely the result that Lindzen finds in Lindzen 2007? The greenhouse effect is observed, but at 1/3 the magnitude of what is expected.[/QUOTE]
Surely this is the other way round, the effect is 3 * greater than expected given the GHG increase?
• Gary Moran
[QUOTE]Is this not precisely the result that Lindzen finds in Lindzen 2007? The greenhouse effect is observed, but at 1/3 the magnitude of what is expected.[/QUOTE]
Surely this is the other way round, the effect is 3 * greater than expected given the GHG increase?
• Alex Harvey
Gary # 7:
Actually, I’m far more confused about what they’re saying after reading it several more times than I had first thought. I hope an expert will comment with their own thoughts.
• Alex Harvey
Gary # 7:
Actually, I’m far more confused about what they’re saying after reading it several more times than I had first thought. I hope an expert will comment with their own thoughts.
• Alex Harvey
To Jan,
Perhaps you can help.
I concede that I have misread, or perhaps refused to accept, what Philipona et al. [2004] is stating in the sections I quoted above.
I went back and checked, by the way, that there is nothing much new in this analysis of P et al. that wasn’t in the Wild et al. [2001], other than the fact that whereas P et al look at a specific latitude (=46N), W et al look at all latitudes, so P et al get away with failing to mention in this paper that ECHAM4 actually overestimates ED (DLR) in the tropics, but underestimates it at mid- to high-latitudes.
But is P et al really saying that GCMs have been underestimating GHG surface temperature forcing by a factor of 3? Or is this spin, for funding agency’s eyes only, as my gut is telling me? In the case of the former, I suppose, this would be a nice antidote to the recent conclusions of Douglass, Lindzen, etc., that the tropospheric hotspot is only 1/3 of the required magnitude. All of a sudden, 1/3 of the required magnitude becomes exactly the magnitude required!
Meanwhile, Ferenc has written (Supplement and background information for Miskolczi’s greenhouse papers, part I / ‘draft1′):
Since AA=ED the IR atmospheric back radiation can not be responsible for the excess surface warming. Further on, this relationship is not consistent with the theoretical expectations of the semi-infinite classic Eddington solution. We recognized that there is something wrong with our knowledge and understanding of the greenhouse effect and we had to go back to the roots of the greenhouse theory.
We all seem to agree that AA cannot be less than ED; not many people want to accept that AA = ED. So, the consensus at present is that AA > ED. I would have thought, and this is why I was excited to find Wild et al. 2001, that the discovery that ED is greater than the models predicted would mean that it must be much closer to AA than previously expected. I suppose, if AA = ED implies, as Ferenc says, that the surface is not heated by IR backradiation, then ED being very close to AA would imply less surface heating than if ED is not as close to AA.
Have I completely misunderstood this? If I haven’t misunderstood this, can we not say that P et al’s lack of detail on their AA measurements / calculations is a bit of a problem for their pro-AGW conclusion?
• Alex Harvey
To Jan,
Perhaps you can help.
I concede that I have misread, or perhaps refused to accept, what Philipona et al. [2004] is stating in the sections I quoted above.
I went back and checked, by the way, that there is nothing much new in this analysis of P et al. that wasn’t in the Wild et al. [2001], other than the fact that whereas P et al look at a specific latitude (=46N), W et al look at all latitudes, so P et al get away with failing to mention in this paper that ECHAM4 actually overestimates ED (DLR) in the tropics, but underestimates it at mid- to high-latitudes.
But is P et al really saying that GCMs have been underestimating GHG surface temperature forcing by a factor of 3? Or is this spin, for funding agency’s eyes only, as my gut is telling me? In the case of the former, I suppose, this would be a nice antidote to the recent conclusions of Douglass, Lindzen, etc., that the tropospheric hotspot is only 1/3 of the required magnitude. All of a sudden, 1/3 of the required magnitude becomes exactly the magnitude required!
Meanwhile, Ferenc has written (Supplement and background information for Miskolczi’s greenhouse papers, part I / ‘draft1′):
Since AA=ED the IR atmospheric back radiation can not be responsible for the excess surface warming. Further on, this relationship is not consistent with the theoretical expectations of the semi-infinite classic Eddington solution. We recognized that there is something wrong with our knowledge and understanding of the greenhouse effect and we had to go back to the roots of the greenhouse theory.
We all seem to agree that AA cannot be less than ED; not many people want to accept that AA = ED. So, the consensus at present is that AA > ED. I would have thought, and this is why I was excited to find Wild et al. 2001, that the discovery that ED is greater than the models predicted would mean that it must be much closer to AA than previously expected. I suppose, if AA = ED implies, as Ferenc says, that the surface is not heated by IR backradiation, then ED being very close to AA would imply less surface heating than if ED is not as close to AA.
Have I completely misunderstood this? If I haven’t misunderstood this, can we not say that P et al’s lack of detail on their AA measurements / calculations is a bit of a problem for their pro-AGW conclusion?
• http://signals.auditblogs.com/ UC
“Rahmstorf, who claimed climate responding faster than expected on the basis of a dubious graph with no statistical test”
JeanS updated that graph with 2008 data,
http://i42.tinypic.com/2hnpf0o.jpg
• http://signals.auditblogs.com/ UC
“Rahmstorf, who claimed climate responding faster than expected on the basis of a dubious graph with no statistical test”
JeanS updated that graph with 2008 data,
http://i42.tinypic.com/2hnpf0o.jpg
• Anonymous
I hope someone writes to Science/Nature about this, as the Rahmstorf paper seems to be becoming one of the most widely cited in history. When I took on Rahmstorf at RC and showed he an no understanding of the statistical methods he was using and the blowout in uncertainty on the ends of these smoothings, all he could say was “see you in print”.
I hope someone writes to Science/Nature about this, as the Rahmstorf paper seems to be becoming one of the most widely cited in history. When I took on Rahmstorf at RC and showed he an no understanding of the statistical methods he was using and the blowout in uncertainty on the ends of these smoothings, all he could say was “see you in print”.
• Jan Pompe
David #12
I don’t understand Eq (1) and why ΔtA should be the residuals and 2/3 the temperature trend due to advection. Where does the number 2/3 come from? It looks like a guess (heuristic?) to me but if the residuals most perplexing perhaps because I’m statistically challenged. I think you’ll be able to help me with this part.
With regard to the 2/3 AND the measured reduction in in insolation of 2 W/m^2 I’d expect a first order effect of a reduction in surface temperature to be given by
$$Delta t_{surface} = frac {Delta SDR} {4 sigma T_{av}^3}$$
so IMO that 2/3 number does not make sense I’d expect the ratio to be greater than 1.
• Jan Pompe
David #12
I don’t understand Eq (1) and why ΔtA should be the residuals and 2/3 the temperature trend due to advection. Where does the number 2/3 come from? It looks like a guess (heuristic?) to me but if the residuals most perplexing perhaps because I’m statistically challenged. I think you’ll be able to help me with this part.
With regard to the 2/3 AND the measured reduction in in insolation of 2 W/m^2 I’d expect a first order effect of a reduction in surface temperature to be given by
$$\Delta t_{surface} = \frac {\Delta SDR} {4 \sigma T_{av}^3}$$
so IMO that 2/3 number does not make sense I’d expect the ratio to be greater than 1.
• Jan Pompe
Re #13
That was in Phillipona’s paper.
• Jan Pompe
Re #13
That was in Phillipona’s paper.
• Jan Pompe
Alex #10
If AA>ED then the surface is cooling due to that radiative component if ED>AA at a given location like the Swiss Alps then the extra heat is coming from advection of warm moist air from the Mediterranean or perhaps the Atlantic and it can warm the surface. I am, however, more inclined to think that it’s the sun with the surface needing to play catchup until equilibrium is achieved.
• Jan Pompe
Alex #10
If AA>ED then the surface is cooling due to that radiative component if ED>AA at a given location like the Swiss Alps then the extra heat is coming from advection of warm moist air from the Mediterranean or perhaps the Atlantic and it can warm the surface. I am, however, more inclined to think that it’s the sun with the surface needing to play catchup until equilibrium is achieved.
• Alex Harvey
Jan #15,
If AA>ED then the surface is cooling due to that radiative component if ED>AA at a given location like the Swiss Alps then the extra heat is coming from advection of warm moist air from the Mediterranean or perhaps the Atlantic and it can warm the surface.
I don’t understand this at all.
If ED (=downward longwave radiation / DLR) is the amount of LW emitted downwards by the atmosphere, and AA is the amount of LW absorbed by the atmosphere, how can we consider ED > AA as a possibility? How can more be emitted than was absorbed? And what has advection (=K, a flux of non-radiative origin) got to do with this?
As far as where the extra heat, as distinct from LW flux, is coming from, the authors happily admit in para. 9 that it comes from the North Atlantic Oscillation (NAO) — advection as you say — and they see no problem with this for their analysis as the T increases are acknowledged by them to be ‘considerably larger than global average’ in central Europe (para. 5).
[Aside: In this way, I still say, the analysis is consistent with Lindzen [2007] because we still have 2/3 (or at least more than 1/2) of the overall (LW + SW + non-radiative) temperature increase at the surface caused by a process — the NOA — that GCMs do not currently model. As such, again, this is not consistent with the IPCC Summary for Policy-makers position “…Only if the human input of greenhouse gases is included does the simulated climate agree with what has been recently observed…” (cited in Lindzen, 2007, p. 944).]
• Alex Harvey
Jan #15,
If AA>ED then the surface is cooling due to that radiative component if ED>AA at a given location like the Swiss Alps then the extra heat is coming from advection of warm moist air from the Mediterranean or perhaps the Atlantic and it can warm the surface.
I don’t understand this at all.
If ED (=downward longwave radiation / DLR) is the amount of LW emitted downwards by the atmosphere, and AA is the amount of LW absorbed by the atmosphere, how can we consider ED > AA as a possibility? How can more be emitted than was absorbed? And what has advection (=K, a flux of non-radiative origin) got to do with this?
As far as where the extra heat, as distinct from LW flux, is coming from, the authors happily admit in para. 9 that it comes from the North Atlantic Oscillation (NAO) — advection as you say — and they see no problem with this for their analysis as the T increases are acknowledged by them to be ‘considerably larger than global average’ in central Europe (para. 5).
[Aside: In this way, I still say, the analysis is consistent with Lindzen [2007] because we still have 2/3 (or at least more than 1/2) of the overall (LW + SW + non-radiative) temperature increase at the surface caused by a process — the NOA — that GCMs do not currently model. As such, again, this is not consistent with the IPCC Summary for Policy-makers position “…Only if the human input of greenhouse gases is included does the simulated climate agree with what has been recently observed…” (cited in Lindzen, 2007, p. 944).]
• Jan Pompe
Alex #16
If ED (=downward longwave radiation / DLR) is the amount of LW emitted downwards by the atmosphere, and AA is the amount of LW absorbed by the atmosphere, how can we consider ED > AA as a possibility?
Remember here we are looking at a fraction of the earth’s surface and advection can bring warmer air from a warmer place. Until it cools to local equilibrium temperature ED>AA. It will radiate according to its temperature and absorb according to it’s temperature and the radiation is always there.
• Jan Pompe
Alex #16
If ED (=downward longwave radiation / DLR) is the amount of LW emitted downwards by the atmosphere, and AA is the amount of LW absorbed by the atmosphere, how can we consider ED > AA as a possibility?
Remember here we are looking at a fraction of the earth’s surface and advection can bring warmer air from a warmer place. Until it cools to local equilibrium temperature ED>AA. It will radiate according to its temperature and absorb according to it’s temperature and the radiation is always there.
• Alex Harvey
Jan # 17,
I see, I thought the AA = ED law was meant to hold both locally AND in the global average (I seem to have misunderstood Ferenc’s comment here http://landshape.org/enm/greenhouse-heat-engine/#comment-168865).
But in any case, don’t we still need to know the local AA, in both the standard and in M theory, before we can be making actual conclusions about the measured strength of the enhanced greenhouse effect? [And what about the tropospheric hotspot: I thought that was the signature of greenhouse warming.] In their conclusion, they state very simply that they’ve ‘proved the “theory” of greenhouse warming with direct observations’ (why is “theory” in quotes?) but they make no mention of magnitude — so I still want to know, was it more or less than the GCMs predicted?
Is the magnitude of ED alone really a measure of the strength of the greenhouse effect — in anyone’s theory?
• Alex Harvey
Jan # 17,
I see, I thought the AA = ED law was meant to hold both locally AND in the global average (I seem to have misunderstood Ferenc’s comment here http://landshape.org/enm/greenhouse-heat-engine/#comment-168865).
But in any case, don’t we still need to know the local AA, in both the standard and in M theory, before we can be making actual conclusions about the measured strength of the enhanced greenhouse effect? [And what about the tropospheric hotspot: I thought that was the signature of greenhouse warming.] In their conclusion, they state very simply that they’ve ‘proved the “theory” of greenhouse warming with direct observations’ (why is “theory” in quotes?) but they make no mention of magnitude — so I still want to know, was it more or less than the GCMs predicted?
Is the magnitude of ED alone really a measure of the strength of the greenhouse effect — in anyone’s theory?
• Jan Pompe
Alex #18
We sometimes forget that M’s is a static or equilibrium model. In this model K has done it’s work and there is nothing more for it to do, and we have a picture of the radiative balance under those circumstances. We can’t really compare directly M’s model with the the results of P’s paper which discusses dynamic conditions but we can apply what we have learnt from it for example Aa=Ed and re-examine P’s in that light.
I agree we need to know Aa but we also need a better way to gauge the effect of advection on temperature that plucking number like 2/3 from the air. Taking the measurements over a period which is a fraction of the period of the Atlantic Multidecadal Oscillation and a rising SST portion of it is not going to help.
• Jan Pompe
Alex #18
We sometimes forget that M’s is a static or equilibrium model. In this model K has done it’s work and there is nothing more for it to do, and we have a picture of the radiative balance under those circumstances. We can’t really compare directly M’s model with the the results of P’s paper which discusses dynamic conditions but we can apply what we have learnt from it for example Aa=Ed and re-examine P’s in that light.
I agree we need to know Aa but we also need a better way to gauge the effect of advection on temperature that plucking number like 2/3 from the air. Taking the measurements over a period which is a fraction of the period of the Atlantic Multidecadal Oscillation and a rising SST portion of it is not going to help.
• Anonymous
Jan: I don’t know where 2/3s comes from. I am very uncomfortable with these magic rations, like 2/3 (invert it an you get M’s 1.5 ). It seems like numerology.
• http://landshape.org/enm davids
Jan: I don’t know where 2/3s comes from. I am very uncomfortable with these magic rations, like 2/3 (invert it an you get M’s 1.5 ). It seems like numerology.
• Jan Pompe
David #20
Numerology? I think you are too polite. IMO it’s fairly obvious it’s a wild guess plucked out of nowhere as opposed to M’s 1.5 where there is some reasoning to follow whether we agree with it or not.
For me a more important objection is the use of trends over a fraction of the period of cyclic source of a significant signal like the Atlantic mutli-decadal oscillation. Especially since that one is in a positive going part of the cycle during the entire period of the study. I don’t see any where in the study where there is a proper accounting of the effect of advection from the Atalantic apart from the 2/3 guess.
If data over a complete cycle even just of temperature alone for the stations involved from say 1940 to 2005 would we not have a better basis for a smarter statistician than I am to do that accounting?
• Jan Pompe
David #20
Numerology? I think you are too polite. IMO it’s fairly obvious it’s a wild guess plucked out of nowhere as opposed to M’s 1.5 where there is some reasoning to follow whether we agree with it or not.
For me a more important objection is the use of trends over a fraction of the period of cyclic source of a significant signal like the Atlantic mutli-decadal oscillation. Especially since that one is in a positive going part of the cycle during the entire period of the study. I don’t see any where in the study where there is a proper accounting of the effect of advection from the Atalantic apart from the 2/3 guess.
If data over a complete cycle even just of temperature alone for the stations involved from say 1940 to 2005 would we not have a better basis for a smarter statistician than I am to do that accounting?
• Alex Harvey
Jan #19,
With respect to M theory, okay, understood. Ferenc is talking about the global average of equilibrium situations, and he discarded atmospheric profiles that weren’t in equilibrium, in order to produce Fig. 2, this being the bit I am forgetting, as you say.
• Alex Harvey
Jan #19,
With respect to M theory, okay, understood. Ferenc is talking about the global average of equilibrium situations, and he discarded atmospheric profiles that weren’t in equilibrium, in order to produce Fig. 2, this being the bit I am forgetting, as you say.
• Ferenc Miskolczi
#22 Alex
Alex, there were no profiles discarded based on the equilibrium condition. InFig 2. M7 there were no extra selection criteria over the 228 profiles. If youselect those situations (out of the 228 profile) where the olr/f=su is stisfied you are getting wery few cases (as indicated in Fig. 25 M4 open circles). The olr/f=su is rarely stisfied locally. It must, however be satisfied for the local and global climatic averages. The main reason is the stochastic variation of the local h2o (around the local climatic average).
• Ferenc Miskolczi
#22 Alex
Alex, there were no profiles discarded based on the equilibrium condition. InFig 2. M7 there were no extra selection criteria over the 228 profiles. If youselect those situations (out of the 228 profile) where the olr/f=su is stisfied you are getting wery few cases (as indicated in Fig. 25 M4 open circles). The olr/f=su is rarely stisfied locally. It must, however be satisfied for the local and global climatic averages. The main reason is the stochastic variation of the local h2o (around the local climatic average).
• Ferenc Miskolczi
# Alex
‘Is the magnitude of ED alone really a measure of the strength of the greenhouse effect — in anyone’s theory?’
From the TIGR results:
g=(Su-OLR)/Su=(379.6-251.2)/379.6=0.338
g=(Ed-Eu)/Su=Ed(1-1/(2A))=310.4(1-1/(2*0.8455))/379.6=0.3341
A=1-Ta=1-0.1545=1-exp(-1.86756)=0.8455
Ed alone is useless….
GCMs are not the proper tools to study the long term planetary greenhouse effect. Their Ed simulations worh nothing, since they model is tuned to give the Ed~344 Wm-2 global average.
The measured (BSRN) Ed=344 Wm-2 is realistic, HARTCODE gives about the same global average using a 0.62 % cloud cover at 2km altitude.
The general problem here is the fact that those experts talk about greenhouse effect without the correct computation of tau_A….
• Ferenc Miskolczi
# Alex
‘Is the magnitude of ED alone really a measure of the strength of the greenhouse effect — in anyone’s theory?’
From the TIGR results:
g=(Su-OLR)/Su=(379.6-251.2)/379.6=0.338
g=(Ed-Eu)/Su=Ed(1-1/(2A))=310.4(1-1/(2*0.8455))/379.6=0.3341
A=1-Ta=1-0.1545=1-exp(-1.86756)=0.8455
Ed alone is useless….
GCMs are not the proper tools to study the long term planetary greenhouse effect. Their Ed simulations worh nothing, since they model is tuned to give the Ed~344 Wm-2 global average.
The measured (BSRN) Ed=344 Wm-2 is realistic, HARTCODE gives about the same global average using a 0.62 % cloud cover at 2km altitude.
The general problem here is the fact that those experts talk about greenhouse effect without the correct computation of tau_A….
• jae
Ferenc: Lurking, but VERY, VERY interested. Learning, I think. Thanks.
• jae
Ferenc: Lurking, but VERY, VERY interested. Learning, I think. Thanks.
• Ferenc Miskolczi
#25 jae
jae, this is out of topic, but the other day you commented that Lindzen’s theory is compatible with the new equations, or at least it can coexists with them. Could you explain me this a bit deeper? In short, what he wants to say with respect to the global energy balance and what is his proofs? You can mail me to [email protected]….Thanks…
• Ferenc Miskolczi
#25 jae
jae, this is out of topic, but the other day you commented that Lindzen’s theory is compatible with the new equations, or at least it can coexists with them. Could you explain me this a bit deeper? In short, what he wants to say with respect to the global energy balance and what is his proofs? You can mail me to [email protected]….Thanks…
• Alex Harvey
Ferenc,
Many thanks for your input & clarifications.
I am still digesting the equations, which seem to follow from the Gn = G / Su = (Sg – OLR) / Sg, of Ramanathan & Inamdar 1997, which unfortunately I don’t have, cited in M7, p. 3.
So even in R&I, the “greenhouse factor” isn’t some linear function of just Ed, so it must be just innuendo, this association of 3x underestimation of LW down, with the conclusion, “this proves the theory of the enhanced greenhouse effect.” I can’t help feeling we’re supposed to read this, and draw the wrong conclusion that the greenhouse effect is stronger than we thought by a factor of 3. Thankyou, this is exactly what I was trying to understand.
How can scientists be WRONG in their predictions about a quantity, in this case Ed, and not just slightly wrong, but quite wrong, then perform some manipulations that apparently statisticians here can’t follow, and then conclude, “Therefore, our theory is correct.” Surely, THIS is a circular argument. The only new “evidence” is just more evidence that scientists and models were wrong, and yet a triumphant conclusion follows, “therefore, we were right.”
Of course I’m sure they had little choice…the forces of the status quo presumably need to be balanced.
• Alex Harvey
Ferenc,
Many thanks for your input & clarifications.
I am still digesting the equations, which seem to follow from the Gn = G / Su = (Sg – OLR) / Sg, of Ramanathan & Inamdar 1997, which unfortunately I don’t have, cited in M7, p. 3.
So even in R&I, the “greenhouse factor” isn’t some linear function of just Ed, so it must be just innuendo, this association of 3x underestimation of LW down, with the conclusion, “this proves the theory of the enhanced greenhouse effect.” I can’t help feeling we’re supposed to read this, and draw the wrong conclusion that the greenhouse effect is stronger than we thought by a factor of 3. Thankyou, this is exactly what I was trying to understand.
How can scientists be WRONG in their predictions about a quantity, in this case Ed, and not just slightly wrong, but quite wrong, then perform some manipulations that apparently statisticians here can’t follow, and then conclude, “Therefore, our theory is correct.” Surely, THIS is a circular argument. The only new “evidence” is just more evidence that scientists and models were wrong, and yet a triumphant conclusion follows, “therefore, we were right.”
Of course I’m sure they had little choice…the forces of the status quo presumably need to be balanced.
• Jan Pompe
Alex #27
I am still digesting the equations, which seem to follow from the Gn = G / Su = (Sg – OLR) / Sg, of Ramanathan & Inamdar 1997, which unfortunately I don’t have, cited in M7, p. 3.
• Jan Pompe
Alex #27
I am still digesting the equations, which seem to follow from the Gn = G / Su = (Sg – OLR) / Sg, of Ramanathan & Inamdar 1997, which unfortunately I don’t have, cited in M7, p. 3.
• jae
Ferenc, 26: I don’t have any detailed information connecting your work and Lindzen’s. Your work shows that there are some mechanisms/special properties of the atmosphere, which may not be well understood, but which work to keep optical depth, cloudiness, and greenhous gas levels at an optimum. I was just making a general observation that Lindzen’s “Iris” mechanism, wherein cloudiness is somehow self-regulated, may be part of the mechanisms involved. Spencer’s work seems to show the same type of cloud self-regulation.
• jae
Ferenc, 26: I don’t have any detailed information connecting your work and Lindzen’s. Your work shows that there are some mechanisms/special properties of the atmosphere, which may not be well understood, but which work to keep optical depth, cloudiness, and greenhous gas levels at an optimum. I was just making a general observation that Lindzen’s “Iris” mechanism, wherein cloudiness is somehow self-regulated, may be part of the mechanisms involved. Spencer’s work seems to show the same type of cloud self-regulation.
• jae
• jae
• Alex Harvey
I am wondering if there is more in common with Roy Spencer’s argument that causes and effects are conflated in GCM models. In Philipona et al., we have here (A) an increase in downward LW flux, and (B) an increase in temperature at the surface. It seems that the model and theory just assume that increased LW down causes increased surface temperature. How do we know that increased surface temperature doesn’t cause the increased LW down? I don’t know if Spencer considered this particular scenario, but it’s a thought…
• Alex Harvey
I am wondering if there is more in common with Roy Spencer’s argument that causes and effects are conflated in GCM models. In Philipona et al., we have here (A) an increase in downward LW flux, and (B) an increase in temperature at the surface. It seems that the model and theory just assume that increased LW down causes increased surface temperature. How do we know that increased surface temperature doesn’t cause the increased LW down? I don’t know if Spencer considered this particular scenario, but it’s a thought…
• Jan Pompe
Alex #31
It seems that the model and theory just assume that increased LW down causes increased surface temperature. How do we know that increased surface temperature doesn’t cause the increased LW down?
How do we know they don’t rise and fall together due to an underlying cause for both?
• Jan Pompe
Alex #31
It seems that the model and theory just assume that increased LW down causes increased surface temperature. How do we know that increased surface temperature doesn’t cause the increased LW down?
How do we know they don’t rise and fall together due to an underlying cause for both?
• Jan Pompe
jae #29
I was just making a general observation that Lindzen’s “Iris” mechanism, wherein cloudiness is somehow self-regulated, may be part of the mechanisms involved.
It certainly looks to me like Richard Lindzen is on a similar general track. might have to follow up on some of his references.
Hat tip to Alex for the link to Lindzens article.
• Jan Pompe
jae #29
I was just making a general observation that Lindzen’s “Iris†mechanism, wherein cloudiness is somehow self-regulated, may be part of the mechanisms involved.
It certainly looks to me like Richard Lindzen is on a similar general track. might have to follow up on some of his references.
Hat tip to Alex for the link to Lindzens article.
• jae
jan:
“How do we know they don’t rise and fall together due to an underlying cause for both?”
That is where my intuition points me. Perhaps we sometimes make things much more complicated than need be.
• jae
jan:
“How do we know they don’t rise and fall together due to an underlying cause for both?”
That is where my intuition points me. Perhaps we sometimes make things much more complicated than need be.
• Alex Harvey
jae, 34:
Getting the arrows of causality around the right away isn’t over-complicating things in my book, and it also suggests that if M’s Kirchhoff law is correct, I think that Roy Spencer would be interested to know this. Proof of M’s Kirchhoff law, from what I have understood of its implications on the atmosphere’s role in heating the surface, is also proof of Spencer’s theory that cause & effect are conflated in GCM models. This is important; Spencer might be pleased to cite this result, and we’d all be a big step closer to seeing the wider scientific community start looking at this theory a little more carefully.
• Alex Harvey
jae, 34:
Getting the arrows of causality around the right away isn’t over-complicating things in my book, and it also suggests that if M’s Kirchhoff law is correct, I think that Roy Spencer would be interested to know this. Proof of M’s Kirchhoff law, from what I have understood of its implications on the atmosphere’s role in heating the surface, is also proof of Spencer’s theory that cause & effect are conflated in GCM models. This is important; Spencer might be pleased to cite this result, and we’d all be a big step closer to seeing the wider scientific community start looking at this theory a little more carefully.
• Alex Harvey
By the way, looks like they fixed the little bug that was causing LW downward fluxes to be out by a factor of 3.
• Alex Harvey
By the way, looks like they fixed the little bug that was causing LW downward fluxes to be out by a factor of 3.
• Jan Pompe
jae #34
That is where my intuition points me. Perhaps we sometimes make things much more complicated than need be.
I think people sometimes forget that the heat comes in at 1366W/m^2 (Effective T~393K) at the TOA and not the ~ 235 W/m^2 (Effective T ~ 254K) averaged over the globe with globally averaged cloud albedo.
We get a higher portion of it at the tropics than we do at the poles and the wind and ocean currents take their time distributing it meaning the system is never in equilibrium but always chasing it. Doesn’t mean we can use equilibrium models to learn something from them about how the system works but we must keep in mind they are models and do not accurately describe reality.
• Jan Pompe
jae #34
That is where my intuition points me. Perhaps we sometimes make things much more complicated than need be.
I think people sometimes forget that the heat comes in at 1366W/m^2 (Effective T~393K) at the TOA and not the ~ 235 W/m^2 (Effective T ~ 254K) averaged over the globe with globally averaged cloud albedo.
We get a higher portion of it at the tropics than we do at the poles and the wind and ocean currents take their time distributing it meaning the system is never in equilibrium but always chasing it. Doesn’t mean we can use equilibrium models to learn something from them about how the system works but we must keep in mind they are models and do not accurately describe reality.
• Alex Harvey
North Atlantic Oscillation (NAO) one minute, Global Dimming the next
David #20, I wouldn’t lose too much sleep over Philipona et al. 2004′s magic 2/3.
I have just read the latest Philipona et al. paper, this time Philipona, R.,K. Behrens, andC. Ruckstuhl (2009), How declining aerosols and rising greenhouse gases forced rapid warming in Europe since the 1980s, Geophys. Res. Lett., 36 (thanks again, Jan).
Just get a load of this! As we have seen, back in 2004, lead author Philipona showed that GCMs got LW down wrong by a factor of three, and discovered that 2/3 of the temperature trend in Europe since 1980 was probably caused by the North Atlantic Oscillation (para 9):
At least half of the increases may … not be explicable by direct effects of increased GHGs and associated feedbacks on temperature and humidity, but are rather due to circulation changes over central Europe. On the northern hemisphere, non-uniform warming with differing decadal and marked seasonal and regional variations is often related to changes of the North Atlantic Oscillation (NAO) [Hurrell, 1995].
Later, para 10:
…two thirds of the temperature trend that is due to warm air advection…
(I almost forgot to add, thus proving the theory of the enhanced greenhouse effect.)
But now, but now, listen to this:
Philipona et al. 2009, para 15:
Of the rapid temperature rise since the 1980s … about two thirds are shown by our analysis to be likely forced by aerosol decline and related solar brightening that strongly reinforced anthropogenic greenhouse forcing.
There, much better. Out, damned NAO! See, not a single mention of it anywhere in the paper, and certainly no citation for that bad, bad Hurrell, 1995, who put the idea into P’s head in a moment of weakness. No citation to Philipona et al. 2004 either; that could be problematic. How could the IPCC in the forthcoming AR5 cite any nonsense about a mysterious ‘NAO’ that no state-of-the-art GCM has ever predicted causing 2/3 of the warming since 1980 in Europe?
I’m sorry, I shouldn’t speculate, but what the *&*&#$is going on here???? • Alex Harvey North Atlantic Oscillation (NAO) one minute, Global Dimming the next David #20, I wouldn’t lose too much sleep over Philipona et al. 2004′s magic 2/3. I have just read the latest Philipona et al. paper, this time Philipona, R.,K. Behrens, andC. Ruckstuhl (2009), How declining aerosols and rising greenhouse gases forced rapid warming in Europe since the 1980s, Geophys. Res. Lett., 36 (thanks again, Jan). Just get a load of this! As we have seen, back in 2004, lead author Philipona showed that GCMs got LW down wrong by a factor of three, and discovered that 2/3 of the temperature trend in Europe since 1980 was probably caused by the North Atlantic Oscillation (para 9): At least half of the increases may … not be explicable by direct effects of increased GHGs and associated feedbacks on temperature and humidity, but are rather due to circulation changes over central Europe. On the northern hemisphere, non-uniform warming with differing decadal and marked seasonal and regional variations is often related to changes of the North Atlantic Oscillation (NAO) [Hurrell, 1995]. Later, para 10: …two thirds of the temperature trend that is due to warm air advection… (I almost forgot to add, thus proving the theory of the enhanced greenhouse effect.) But now, but now, listen to this: Philipona et al. 2009, para 15: Of the rapid temperature rise since the 1980s … about two thirds are shown by our analysis to be likely forced by aerosol decline and related solar brightening that strongly reinforced anthropogenic greenhouse forcing. There, much better. Out, damned NAO! See, not a single mention of it anywhere in the paper, and certainly no citation for that bad, bad Hurrell, 1995, who put the idea into P’s head in a moment of weakness. No citation to Philipona et al. 2004 either; that could be problematic. How could the IPCC in the forthcoming AR5 cite any nonsense about a mysterious ‘NAO’ that no state-of-the-art GCM has ever predicted causing 2/3 of the warming since 1980 in Europe? I’m sorry, I shouldn’t speculate, but what the *&*&#$ is going on here????
• jae
Alex: LOL. I wonder how these geniuses are going to explain the last 10 years of cooler temperatures…Did Europe go backwards on pollution control, so that solar dimming is now again a problem? Or could the NAO have something to do with it? It’s like the jokers that run the GCMs. They have said for years that only CO2 could possibly explain the rise in temperatures during the 90s (arrogantly presuming, of course, that everything else is perfectly accounted for in the models). Now, they have no explanation as to why temperatures have been dropping, except to babble about natural variation (a concept which is not allowed when temperatures are increasing).
• jae
Alex: LOL. I wonder how these geniuses are going to explain the last 10 years of cooler temperatures…Did Europe go backwards on pollution control, so that solar dimming is now again a problem? Or could the NAO have something to do with it? It’s like the jokers that run the GCMs. They have said for years that only CO2 could possibly explain the rise in temperatures during the 90s (arrogantly presuming, of course, that everything else is perfectly accounted for in the models). Now, they have no explanation as to why temperatures have been dropping, except to babble about natural variation (a concept which is not allowed when temperatures are increasing).
• Alex Harvey
jae: Well, I’m no statistician, but if you take just a look at their Fig. 3, anyone could see that they had to use the year 1980 to make this all work out. If they’d divided the range at 1982 instead of 1980, their politically-correct conclusion would disappear along with their aerosols.
• Alex Harvey
jae: Well, I’m no statistician, but if you take just a look at their Fig. 3, anyone could see that they had to use the year 1980 to make this all work out. If they’d divided the range at 1982 instead of 1980, their politically-correct conclusion would disappear along with their aerosols.
• http://www.ecoengineers.com Steve Short
Just popped back for a quick lurk. Still at it fellows! Will it never end?
As for me I’m still squirming over past gems of tortured dogma from Jan such as:
“Whether you choose to name atmospheric outward flux EU or K doesn’t matter because they are algebraically equal. Eu and K each have one value but 2 degrees of freedom each EU = (F+P) + (ST – AA) and K = HL + HS where HL and HS are latent and sensible heat respectively. So your precious convection is not hidden in ST or TA but out in the open as if for constant F0, EU is also constant then it is obvious that to keep it constant when τ is increased and leads to increased HS, then HS must decrease. If that decreases you end up with less water vapour in the atmosphere and low pan evaporation rates and τ returning to it’s original value. That is negative feedback at its best.”
BTW I’d been reading up on Budyko’s ice-albedo feedback theory etc when I came across this interesting little (2000) paper by some obscure Egyptians scientists published in a Spanish meteorological journal (deja vu rules OK).
Check out the dSu/dAc = 143 W/m^2 and d(Fo-F)/dAc= 64 W/m^2 stuff (where Ac = cloud cover from surface)
• http://www.ecoengineers.com Steve Short
Just popped back for a quick lurk. Still at it fellows! Will it never end?
As for me I’m still squirming over past gems of tortured dogma from Jan such as:
“Whether you choose to name atmospheric outward flux EU or K doesn’t matter because they are algebraically equal. Eu and K each have one value but 2 degrees of freedom each EU = (F+P) + (ST – AA) and K = HL + HS where HL and HS are latent and sensible heat respectively. So your precious convection is not hidden in ST or TA but out in the open as if for constant F0, EU is also constant then it is obvious that to keep it constant when Ï„ is increased and leads to increased HS, then HS must decrease. If that decreases you end up with less water vapour in the atmosphere and low pan evaporation rates and Ï„ returning to it’s original value. That is negative feedback at its best.”
BTW I’d been reading up on Budyko’s ice-albedo feedback theory etc when I came across this interesting little (2000) paper by some obscure Egyptians scientists published in a Spanish meteorological journal (deja vu rules OK).
http://www.biblioteca.org.ar/LIBROS/90618.pdf
Check out the dSu/dAc = 143 W/m^2 and d(Fo-F)/dAc= 64 W/m^2 stuff (where Ac = cloud cover from surface)
• Jan Pompe
Hmmmm
EU = (F+P) + (ST – AA)
I wonder where I said that? It doesn’t look right and I can’t find it. Though the rest of the text sounds familiar.
$$E_U = left( F+P right) + K$$ it should be and $$K = H_S – S_L$$ or non-radiative factors.
The corrected equation just derives from M07 Eqns (1) & (4). In a sort of trial balance FM on page 24 tackles it from another angle:
Based on Eq. (28) [$$S_U = frac {OLR} f$$] we may also give a simple interpretation of $$E_U$$: $$E_U = S_U f – S_U T_A$$. Since the total converted $$F^0 + P^0$$ to OLR is $$S_U f$$, and $$S_U T_A$$ is the transmitted part of the surface radiation, the $$S_U F – S_U T_A$$ difference is the contribution to the OLR from all other energy transfer processes which are not related to LW absorption : $$E_U = F + P +K$$. Substituting this last equation into the energy balance equation at the lower boundary, and using Eq. (3) we get: $$E_D – A_A =0$$ . This is the proof of the Kirchhoff law for the surface-atmosphere system. The validity of the Kirchhoff law requires the thermal equilibrium at the surface. Note, that in obtaining Eq. (28) the Kirchhoff law was not used (see Appendix B). [My comment in brackets and all emphasis mine]
That’s an interesting paper in the abstract
It was found that there was an inverse relationship between longwave radiation and the planetary albedo at both the surface and the top of the atmosphere.
We more or less expect this but then in concluding remarks 5):
The effect of heat absorbed and emitted through $$Delta SW$$ and $$Delta LW$$, indicates a remarkable flux increase with cloud cover. These values on average vary at different locations in mid latitude regions having the values: $$frac {partial SW} {partial A_c} = 64 Wm^{-2}$$ and $$frac {partial LW} {partial A_c} = 143 Wm^{-2}$$.
This is counter intuitive, so looking at their equations 13 to 14 it is quite clear that $$Delta SW$$ and $$Delta LW$$ are differences in the fluxes between the TOA and BOA ie the fluxes don’t increase but the differences in fluxes increase with cloud cover. That is for shortwave $$frac {partial Delta SW} {partial A_c} = 64 Wm^{-2}$$ which makes some more sense.
• Jan Pompe
Hmmmm
EU = (F+P) + (ST – AA)
I wonder where I said that? It doesn’t look right and I can’t find it. Though the rest of the text sounds familiar.
$$E_U = \left( F+P \right) + K$$ it should be and $$K = H_S – S_L$$ or non-radiative factors.
The corrected equation just derives from M07 Eqns (1) & (4). In a sort of trial balance FM on page 24 tackles it from another angle:
Based on Eq. (28) [$$S_U = \frac {OLR} f$$] we may also give a simple interpretation of $$E_U$$: $$E_U = S_U f – S_U T_A$$. Since the total converted $$F^0 + P^0$$ to OLR is $$S_U f$$, and $$S_U T_A$$ is the transmitted part of the surface radiation, the $$S_U F – S_U T_A$$ difference is the contribution to the OLR from all other energy transfer processes which are not related to LW absorption : $$E_U = F + P +K$$. Substituting this last equation into the energy balance equation at the lower boundary, and using Eq. (3) we get: $$E_D – A_A =0$$ . This is the proof of the Kirchhoff law for the surface-atmosphere system. The validity of the Kirchhoff law requires the thermal equilibrium at the surface. Note, that in obtaining Eq. (28) the Kirchhoff law was not used (see Appendix B). [My comment in brackets and all emphasis mine]
That’s an interesting paper in the abstract
It was found that there was an inverse relationship between longwave radiation and the planetary albedo at both the surface and the top of the atmosphere.
We more or less expect this but then in concluding remarks 5):
The effect of heat absorbed and emitted through $$\Delta SW$$ and $$\Delta LW$$, indicates a remarkable flux increase with cloud cover. These values on average vary at different locations in mid latitude regions having the values: $$\frac {\partial SW} {\partial A_c} = 64 Wm^{-2}$$ and $$\frac {\partial LW} {\partial A_c} = 143 Wm^{-2}$$.
This is counter intuitive, so looking at their equations 13 to 14 it is quite clear that $$\Delta SW$$ and $$\Delta LW$$ are differences in the fluxes between the TOA and BOA ie the fluxes don’t increase but the differences in fluxes increase with cloud cover. That is for shortwave $$\frac {\partial \Delta SW} {\partial A_c} = 64 Wm^{-2}$$ which makes some more sense.
• http://www.ecoengineers.com Steve Short
Jan #42
“Hmmmm
EU = (F+P) + (ST – AA)
I wonder where I said that? It doesn’t look right and I can’t find it. Though the rest of the text sounds familiar.”
It should sound familiar. That was Jan #240 in podium mode in Greenhouse Heat Engine #4. In fact the whole quoted paragraph was a farrago. Take the statement: “Whether you choose to name atmospheric outward flux Eu or K doesn’t matter because they are algebraically equal.” Also garbage.
Then there was your confusion between the effect of your own HS and HL – BTW completely ignoring all my prior hard work pointing out that K is comprised of 3 components not two i.e. ~80 W/m^2 latent (HL), ~20 W/m^2 sensible (HS; which BTW does nothing to affect water vapour profile contrary to your claim) and ~20 W/m^2 zonal and meridional heat transfer (from surface to atmosphere and tropics to poles).
Taking the equally silly line EU = (F+P) + (ST – AA) which followed it – where did that equation come from? It doesn’t appear in M4 or M7 or drafdt1.pdf! If F ~ 60 W/m^2 and St ~ 60 W/m^2 and Aa = Ed ~ 310 W/m^2 then this makes Eu = 60 + 60 – 310 ~ – 190 W/m^2!!!
Sure, accepting M Theory we have : Eu = F + K + P + Aa – Ed (net atmosphere) and Fo + Po + Ed – F – K – P – Aa – St = 0 (net surface) therefore if P, Po = 0 and Aa = Ed (as per M) then Fo – Eu – St = 0 therefore Eu = Fo – St therefore Fo – St = F + K i.e. OLR – St = F + K i.e. ~ 240 – 60 ~ 180 ~ 60 + 120 This at least adds up reasonably well and is the non-LW radiative part of the OLR (St being the LW radiative part). No mystery there – just another way of saying Eu = F + K. You won’t find a reference or justification for K ~ 120 W/m^2 anywhere in M4 or M7 please note.
The mystery is why didn’t Ferenc himself ever correct this stuff? Or why did you yourself not pick it up and acknowledge as a wrong? Lengthy self-serving later quotes do not gainsay an annoying propensity to mix clearly wrong whole paragraph-long lectures with good stuff and then just roll on like steam train without back tracking to acknowledge those errors (which are a good bit more than a few mere typos).
Hmmmm “This is counter intuitive, so looking at their equations 13 to 14 it is quite clear that Delta SW and Delta LW are differences in the fluxes between the TOA and BOA i.e the fluxes don’t increase but the differences in fluxes increase with cloud cover…… ”
I am glad you at least read it. Now the challenge is just try expressing the differences in fluxes in an M-type formalism (without mucking up the signs).
• http://www.ecoengineers.com Steve Short
Jan #42
“Hmmmm
EU = (F+P) + (ST – AA)
I wonder where I said that? It doesn’t look right and I can’t find it. Though the rest of the text sounds familiar.”
It should sound familiar. That was Jan #240 in podium mode in Greenhouse Heat Engine #4. In fact the whole quoted paragraph was a farrago. Take the statement: “Whether you choose to name atmospheric outward flux Eu or K doesn’t matter because they are algebraically equal.†Also garbage.
Then there was your confusion between the effect of your own HS and HL – BTW completely ignoring all my prior hard work pointing out that K is comprised of 3 components not two i.e. ~80 W/m^2 latent (HL), ~20 W/m^2 sensible (HS; which BTW does nothing to affect water vapour profile contrary to your claim) and ~20 W/m^2 zonal and meridional heat transfer (from surface to atmosphere and tropics to poles).
Taking the equally silly line EU = (F+P) + (ST – AA) which followed it – where did that equation come from? It doesn’t appear in M4 or M7 or drafdt1.pdf! If F ~ 60 W/m^2 and St ~ 60 W/m^2 and Aa = Ed ~ 310 W/m^2 then this makes Eu = 60 + 60 – 310 ~ – 190 W/m^2!!!
Sure, accepting M Theory we have : Eu = F + K + P + Aa – Ed (net atmosphere) and Fo + Po + Ed – F – K – P – Aa – St = 0 (net surface) therefore if P, Po = 0 and Aa = Ed (as per M) then Fo – Eu – St = 0 therefore Eu = Fo – St therefore Fo – St = F + K i.e. OLR – St = F + K i.e. ~ 240 – 60 ~ 180 ~ 60 + 120 This at least adds up reasonably well and is the non-LW radiative part of the OLR (St being the LW radiative part). No mystery there – just another way of saying Eu = F + K. You won’t find a reference or justification for K ~ 120 W/m^2 anywhere in M4 or M7 please note.
The mystery is why didn’t Ferenc himself ever correct this stuff? Or why did you yourself not pick it up and acknowledge as a wrong? Lengthy self-serving later quotes do not gainsay an annoying propensity to mix clearly wrong whole paragraph-long lectures with good stuff and then just roll on like steam train without back tracking to acknowledge those errors (which are a good bit more than a few mere typos).
Hmmmm “This is counter intuitive, so looking at their equations 13 to 14 it is quite clear that Delta SW and Delta LW are differences in the fluxes between the TOA and BOA i.e the fluxes don’t increase but the differences in fluxes increase with cloud cover…… ”
I am glad you at least read it. Now the challenge is just try expressing the differences in fluxes in an M-type formalism (without mucking up the signs).
• Jan Pompe
Steve #43
It should sound familiar. That was Jan #240 in podium mode in Greenhouse Heat Engine #4.
Greenhouse Heat Engine #4 only goes to 24 and #24o in GHE #3 is a comment by franko I’ve tried key word searches in several threads and haven’t found it. Obviously there is an error in that equation I’m perfectly happy to acknowledge that but I’m trying to find it so I can get to the context because I’m wondering what I was thinking (ST-AA) makes no sense.
Then there was your confusion between the effect of your own HS and HL – BTW completely ignoring all my prior hard work pointing out that K is comprised of 3 components not two i.e. ~80 W/m^2 latent (HL), ~20 W/m^2 sensible (HS; which BTW does nothing to affect water vapour profile contrary to your claim) and ~20 W/m^2 zonal and meridional heat transfer (from surface to atmosphere and tropics to poles).
So we have latent heat ~80W/m^2 and ~20 W/m^2 gobal average from surface to atmosphere so both leaving the surface (i.e. cooling it) global average remember and that eventually radiates to space. That zonal and meridional ~20W/m^2 cools one place the tropics and warms another the poles it does not contribute to the globally averaged radiative energy budget and is already included in the ~ 100W/m^2 Hs +Hl unless of course the tropics is not part of the globe.
You won’t find a reference or justification for K ~ 120 W/m^2 anywhere in M4 or M7 please note.
Nor is there any reason we should, there is no reason to assume that $$S_T =F$$ that I can see. $$E_U = F^0 -S_T = OLR – S_T = F+K$$ 0r $$240 [OLR] – 60 [S_T] approx 180 approx 80[F] + 100[K]$$
As interesting as I found the paper it’s scope is not the same as M&M04 or M07 which examine the affect of IR absorbers in the atmosphere on the radiation budget holding albedo (and consequently cloud cover) constant while the W&H paper explores the effect of variations in cloud cover holding all else constant. I’m sure one day someone will integrate it all into a coherent model but that someone is not likely to be me.
• Jan Pompe
Steve #43
It should sound familiar. That was Jan #240 in podium mode in Greenhouse Heat Engine #4.
Greenhouse Heat Engine #4 only goes to 24 and #24o in GHE #3 is a comment by franko I’ve tried key word searches in several threads and haven’t found it. Obviously there is an error in that equation I’m perfectly happy to acknowledge that but I’m trying to find it so I can get to the context because I’m wondering what I was thinking (ST-AA) makes no sense.
Then there was your confusion between the effect of your own HS and HL – BTW completely ignoring all my prior hard work pointing out that K is comprised of 3 components not two i.e. ~80 W/m^2 latent (HL), ~20 W/m^2 sensible (HS; which BTW does nothing to affect water vapour profile contrary to your claim) and ~20 W/m^2 zonal and meridional heat transfer (from surface to atmosphere and tropics to poles).
So we have latent heat ~80W/m^2 and ~20 W/m^2 gobal average from surface to atmosphere so both leaving the surface (i.e. cooling it) global average remember and that eventually radiates to space. That zonal and meridional ~20W/m^2 cools one place the tropics and warms another the poles it does not contribute to the globally averaged radiative energy budget and is already included in the ~ 100W/m^2 Hs +Hl unless of course the tropics is not part of the globe.
You won’t find a reference or justification for K ~ 120 W/m^2 anywhere in M4 or M7 please note.
Nor is there any reason we should, there is no reason to assume that $$S_T =F$$ that I can see. $$E_U = F^0 -S_T = OLR – S_T = F+K$$ 0r $$240 [OLR] – 60 [S_T] \approx 180 \approx 80[F] + 100[K]$$
As interesting as I found the paper it’s scope is not the same as M&M04 or M07 which examine the affect of IR absorbers in the atmosphere on the radiation budget holding albedo (and consequently cloud cover) constant while the W&H paper explores the effect of variations in cloud cover holding all else constant. I’m sure one day someone will integrate it all into a coherent model but that someone is not likely to be me.
• http://www.ecoengineers.com Steve Short
Yes, I did get the thread wrong. I’ve just now sent you the complete diatribe by direct email (as you did me). Perhaps then you’ll remember it?
“….I’m wondering what I was thinking (ST-AA) makes no sense.” Yeah me too.
“Nor is there any reason we should, there is no reason to assume that S_T =F that I can see. ” Yeah me too. They are certainly similar in magnitude i.e. S_T ~ F (as recourse to any good textbook or relevant paper will show).
But perhaps there is an underlying reason why they are similar in magnitude? After all the whole system clearly displays autocorrelation between outgoing LW and incoming SW terms.
“As interesting as I found the paper it’s scope is not the same as M&M04 or M07 which examine the affect of IR absorbers in the atmosphere on the radiation budget holding albedo (and consequently cloud cover) constant while the W&H paper explores the effect of variations in cloud cover holding all else constant.”
Another copout. After all cloud cover increases with increasing water vapor column amount. I also suggest going back and reading Section 5.2 Global average profiles in M7 viz: ” Cloudy computations also show that Eu – and consequently K – has a maximum around this level, which is favorable for cloud formation. ” or ” OLRA – 2Su/3 ~ -15 W/m^2 is fairly good estimate of the global average cloud forcing. The estimated beta ~ 0.6 is the required cloud cover (at this level) to balance OLRA , which looks realistic. ”
That’s all Miskolczi (possibly at his finest BTW) – not you, not me.
“I’m sure one day someone will integrate it all into a coherent model but that someone is not likely to be me.”
This from someone who pretends to engage in open ended discussion yet is then always so keen to jump up and vigorously ‘straighten people out’ on what M Theory does or does not mean (not always correctly as I’ve just demonstrated) and just as vigorously resists to the max any attempts to tweak M theory or tighten up the formalism with respect to the critical SW F and non-radiative K components yet when it comes to the crunch has to be oh so coy.
Bah humbug.
• http://www.ecoengineers.com Steve Short
Yes, I did get the thread wrong. I’ve just now sent you the complete diatribe by direct email (as you did me). Perhaps then you’ll remember it?
“….I’m wondering what I was thinking (ST-AA) makes no sense.” Yeah me too.
“Nor is there any reason we should, there is no reason to assume that S_T =F that I can see. ” Yeah me too. They are certainly similar in magnitude i.e. S_T ~ F (as recourse to any good textbook or relevant paper will show).
But perhaps there is an underlying reason why they are similar in magnitude? After all the whole system clearly displays autocorrelation between outgoing LW and incoming SW terms.
“As interesting as I found the paper it’s scope is not the same as M&M04 or M07 which examine the affect of IR absorbers in the atmosphere on the radiation budget holding albedo (and consequently cloud cover) constant while the W&H paper explores the effect of variations in cloud cover holding all else constant.”
Another copout. After all cloud cover increases with increasing water vapor column amount. I also suggest going back and reading Section 5.2 Global average profiles in M7 viz: ” Cloudy computations also show that Eu – and consequently K – has a maximum around this level, which is favorable for cloud formation. ” or ” OLRA – 2Su/3 ~ -15 W/m^2 is fairly good estimate of the global average cloud forcing. The estimated beta ~ 0.6 is the required cloud cover (at this level) to balance OLRA , which looks realistic. ”
That’s all Miskolczi (possibly at his finest BTW) – not you, not me.
“I’m sure one day someone will integrate it all into a coherent model but that someone is not likely to be me.”
This from someone who pretends to engage in open ended discussion yet is then always so keen to jump up and vigorously ‘straighten people out’ on what M Theory does or does not mean (not always correctly as I’ve just demonstrated) and just as vigorously resists to the max any attempts to tweak M theory or tighten up the formalism with respect to the critical SW F and non-radiative K components yet when it comes to the crunch has to be oh so coy.
Bah humbug.
• http://www.ecoengineers.com Steve Short
Jan #44
“So we have latent heat ~80W/m^2 and ~20 W/m^2 gobal average from surface to atmosphere so both leaving the surface (i.e. cooling it) global average remember and that eventually radiates to space. That zonal and meridional ~20W/m^2 cools one place the tropics and warms another the poles it does not contribute to the globally averaged radiative energy budget and is already included in the ~ 100W/m^2 Hs +Hl unless of course the tropics is not part of the globe.”
As well as transferring heat from the tropics to the poles (putting aside juvenile cheap shot re tropics), zonal and meridional winds also extract a net ~15 W/m^2 from the surface via non-convective cooling and drying effects (and producing frictional dissipation, orographic and wave cloud formation) etc. As the so-called thermal engineer here you should definitely know all about that. The remainder of the K term (~2 – 5 W/m^2) is largely comprised of frictional losses from falling rain. Thus K totals about 120 W/m^2.
Presumably this is also why Miskolczi assigns a K/St ratio of ~2 in his draft1.pdf (Fig. 18E). However, as you disagree I’m sure you will tell him/us why?
The highest estimate of F I have seen in the literature is about 68 -70 W/m^2. Your value of ~80 W/m^2 is not a value which I have ever seen and it is inconsistent with the mean SW tau which we discussed some time back (you may recall). Please produce a citation and/or tell us how you reconcile it with the known SW tau.
• http://www.ecoengineers.com Steve Short
Jan #44
“So we have latent heat ~80W/m^2 and ~20 W/m^2 gobal average from surface to atmosphere so both leaving the surface (i.e. cooling it) global average remember and that eventually radiates to space. That zonal and meridional ~20W/m^2 cools one place the tropics and warms another the poles it does not contribute to the globally averaged radiative energy budget and is already included in the ~ 100W/m^2 Hs +Hl unless of course the tropics is not part of the globe.”
As well as transferring heat from the tropics to the poles (putting aside juvenile cheap shot re tropics), zonal and meridional winds also extract a net ~15 W/m^2 from the surface via non-convective cooling and drying effects (and producing frictional dissipation, orographic and wave cloud formation) etc. As the so-called thermal engineer here you should definitely know all about that. The remainder of the K term (~2 – 5 W/m^2) is largely comprised of frictional losses from falling rain. Thus K totals about 120 W/m^2.
Presumably this is also why Miskolczi assigns a K/St ratio of ~2 in his draft1.pdf (Fig. 18E). However, as you disagree I’m sure you will tell him/us why?
The highest estimate of F I have seen in the literature is about 68 -70 W/m^2. Your value of ~80 W/m^2 is not a value which I have ever seen and it is inconsistent with the mean SW tau which we discussed some time back (you may recall). Please produce a citation and/or tell us how you reconcile it with the known SW tau.
• jan pompe
Steve #46
K is vertical globally average term from surface to atmosphere and you want to add a horizontal term so please show us all where horizontal movement has a vertical component.
Try not to be so rude while you are at it please.
• jan pompe
Steve #46
K is vertical globally average term from surface to atmosphere and you want to add a horizontal term so please show us all where horizontal movement has a vertical component.
Try not to be so rude while you are at it please.
• http://www.ecoengineers.com Steve Short
No, K = the sum of all non-radiative heat transfers from the surface.
To quote M7 (page 3): ” The net thermal energy to the atmosphere of non-radiative origin is K.”
Further down on page 3 M also says: ” Note, that the K term is not restricted to strict vertical transfer. Due to the permanent motion of the atmosphere K represents a statistical or climatic average.”
Horizontal air movements, commonly known as winds typically exhibit a vertical component when the airstream runs into a mass of cooler air and is forced upwards or when it runs into hills or mountains.
Non-vertical, non-radiative heat transfer to the atmosphere is clearly contained in the K term NOT in the Po term which M7 defines as “total thermal energy from the planetary interior to the surface-atmosphere system.” Thus P0 would presumably take into account ocean upwelling/downwelling effects, geothermal etc.
Miskolczi’s model is not exclusively 1D in any sense. It is also trivially self-evident that it is a globally averaged model.
• http://www.ecoengineers.com Steve Short
No, K = the sum of all non-radiative heat transfers from the surface.
To quote M7 (page 3): ” The net thermal energy to the atmosphere of non-radiative origin is K.”
Further down on page 3 M also says: ” Note, that the K term is not restricted to strict vertical transfer. Due to the permanent motion of the atmosphere K represents a statistical or climatic average.”
Horizontal air movements, commonly known as winds typically exhibit a vertical component when the airstream runs into a mass of cooler air and is forced upwards or when it runs into hills or mountains.
Non-vertical, non-radiative heat transfer to the atmosphere is clearly contained in the K term NOT in the Po term which M7 defines as “total thermal energy from the planetary interior to the surface-atmosphere system.” Thus P0 would presumably take into account ocean upwelling/downwelling effects, geothermal etc.
Miskolczi’s model is not exclusively 1D in any sense. It is also trivially self-evident that it is a globally averaged model.
• jan pompe
Steve #48
No, K = the sum of all non-radiative heat transfers from the surface.
To quote M7 (page 3): ” The net thermal energy to the atmosphere of non-radiative origin is K.”
My point exactly once the heat is in the atmosphere movement within the atmosphere does not add to it. Now it if the atmosphere is warmed more at the poles there will be a thermal potential difference between the tropics and the poles that will lead to a net movement towards the poles i.e. wind turbulence will cause friction losses i.e. some of the net movement is randomised.
There is and can be no increase in the energy content of the atmosphere due to the horizontal or even vertical movement of heat within the atmosphere we can only get an increase in entropy from it.
• jan pompe
Steve #48
No, K = the sum of all non-radiative heat transfers from the surface.
To quote M7 (page 3): †The net thermal energy to the atmosphere of non-radiative origin is K.â€
My point exactly once the heat is in the atmosphere movement within the atmosphere does not add to it. Now it if the atmosphere is warmed more at the poles there will be a thermal potential difference between the tropics and the poles that will lead to a net movement towards the poles i.e. wind turbulence will cause friction losses i.e. some of the net movement is randomised.
There is and can be no increase in the energy content of the atmosphere due to the horizontal or even vertical movement of heat within the atmosphere we can only get an increase in entropy from it.
• http://www.ecoengineers.com Steve Short
I can quote Misckolczi back at you at length to show he does not regard his K term as made up of just vertical latent and sensible heat components.
I can clearly explain what I believe that extra (minor) portion is. You can blithely ignore that completely.
I am obviously not talking about conservative within-atmosphere transfer of heat from tropics to poles and made that crystal clear.
I also made it perfectly clear I am talking about cooling and drying transferring heat FROM THE SURFACE the surface during lateral air movement (winds). Inspection of the literature suggests this about 13% of total K and frictional heat loss from falling rain about 3% of total K.
Classic Pompe! Never any progress to be had with you, eh Jan. Rigor mortis set in long ago. I suggest Haiti for a suitable holiday destination – they used to do a nice line in your type of guy.
• http://www.ecoengineers.com Steve Short
I can quote Misckolczi back at you at length to show he does not regard his K term as made up of just vertical latent and sensible heat components.
I can clearly explain what I believe that extra (minor) portion is. You can blithely ignore that completely.
I am obviously not talking about conservative within-atmosphere transfer of heat from tropics to poles and made that crystal clear.
I also made it perfectly clear I am talking about cooling and drying transferring heat FROM THE SURFACE the surface during lateral air movement (winds). Inspection of the literature suggests this about 13% of total K and frictional heat loss from falling rain about 3% of total K.
Classic Pompe! Never any progress to be had with you, eh Jan. Rigor mortis set in long ago. I suggest Haiti for a suitable holiday destination – they used to do a nice line in your type of guy.
• jan pompe
Steve #50
Classic Pompe! Never any progress to be had with you, eh Jan. Rigor mortis set in long ago. I suggest Haiti for a suitable holiday destination – they used to do a nice line in your type of guy.
Is it possible for you to stop making such childish remarks?
I am perfectly aware that M07 has:
(b) — The temperature or source function profile is the result of the
equilibrium between the IR radiation field and all other sinks and sources of
thermal energy, (latent heat transfer, convection, conduction, advection,
turbulent mixing, short wave absorption, etc.). Note, that the Kterm is not
restricted to strict vertical heat transfer. Due to the permanent motion of the atmosphere K represents a statistical or climatic average.
The emphasised sentence should make it crystal clear that:
I also made it perfectly clear I am talking about cooling and drying transferring heat FROM THE SURFACE the surface during lateral air movement (winds).
And
Inspection of the literature suggests this about 13% of total K and frictional heat loss from falling rain about 3% of total K.
both the 13% and the 3% are still only a portion of K they don’t add to it.
• jan pompe
Steve #50
Classic Pompe! Never any progress to be had with you, eh Jan. Rigor mortis set in long ago. I suggest Haiti for a suitable holiday destination – they used to do a nice line in your type of guy.
Is it possible for you to stop making such childish remarks?
I am perfectly aware that M07 has:
(b) — The temperature or source function profile is the result of the
equilibrium between the IR radiation field and all other sinks and sources of
thermal energy, (latent heat transfer, convection, conduction, advection,
turbulent mixing, short wave absorption, etc.). Note, that the Kterm is not
restricted to strict vertical heat transfer. Due to the permanent motion of the atmosphere K represents a statistical or climatic average.
The emphasised sentence should make it crystal clear that:
I also made it perfectly clear I am talking about cooling and drying transferring heat FROM THE SURFACE the surface during lateral air movement (winds).
And
Inspection of the literature suggests this about 13% of total K and frictional heat loss from falling rain about 3% of total K.
both the 13% and the 3% are still only a portion of K they don’t add to it.
• jae
What jan says
• jae
What jan says
• http://www.ecoengineers.com Steve Short
Jan #51
“..both the 13% and the 3% are still only a portion of K they don’t add to it.”
Holds belly, doubled-up with laughter. What language is this? Nebbish?
• http://www.ecoengineers.com Steve Short
Jan #51
“..both the 13% and the 3% are still only a portion of K they don’t add to it.”
Holds belly, doubled-up with laughter. What language is this? Nebbish?
• jan pompe
Steve #53
“..both the 13% and the 3% are still only a portion of K they don’t add to it.”
Holds belly, doubled-up with laughter. What language is this? Nebbish?
Don’t you understand energy conservation? It’s not hard.
• jan pompe
Steve #53
“..both the 13% and the 3% are still only a portion of K they don’t add to it.â€
Holds belly, doubled-up with laughter. What language is this? Nebbish?
Don’t you understand energy conservation? It’s not hard.
• http://www.ecoengineers.com Steve Short
15/120 ~13%, 4/120 ~ 3%. Arithmetic. Its not hard.
• http://www.ecoengineers.com Steve Short
15/120 ~13%, 4/120 ~ 3%. Arithmetic. Its not hard.
• jan pompe
Steve #45
15/120 ~13%, 4/120 ~ 3%. Arithmetic. Its not hard.
It’s what it means that seems to be the difficult part.
Whether you think K is 120W/m^2 (wherever the heck you got that number from) of K&T 97 102 W/m^2 that % symbol means its a fraction of the whole which include all non-radiative modes the energy leaves the surface to enter the atmosphere. Conversion between energy types does not change the total. For instance the frictional heat lost by falling rain was obtained by K in the first place and converted to potential energy.
Now kindly explain how rearranging the apples in a barrel changes the quantity of apples in the barrel.
• jan pompe
Steve #45
15/120 ~13%, 4/120 ~ 3%. Arithmetic. Its not hard.
It’s what it means that seems to be the difficult part.
Whether you think K is 120W/m^2 (wherever the heck you got that number from) of K&T 97 102 W/m^2 that % symbol means its a fraction of the whole which include all non-radiative modes the energy leaves the surface to enter the atmosphere. Conversion between energy types does not change the total. For instance the frictional heat lost by falling rain was obtained by K in the first place and converted to potential energy.
Now kindly explain how rearranging the apples in a barrel changes the quantity of apples in the barrel.
• jan pompe
#56
which include all non-radiative modes the energy leaves the surface to enter the atmosphere.
I should mention “and leave the atmosphere” also.
• jan pompe
#56
which include all non-radiative modes the energy leaves the surface to enter the atmosphere.
I should mention “and leave the atmosphere” also.
• http://www.ecoengineers.com Steve Short
Funny, in other circumstances you would be the first to deride K&T 97 of course. I repeat:
Presumably this is also why Miskolczi assigns a K/St ratio of ~2 in his draft1.pdf (Fig. 18E). However, as you disagree I’m sure you will tell him/us why?
The highest estimate of F I have seen in the literature is about 68 -70 W/m^2. Your value of ~80 W/m^2 is not a value which I have ever seen and it is inconsistent with the mean SW tau which we discussed some time back (you may recall). Please produce a citation and/or tell us how you reconcile it with the known SW tau.
You didn’t fess-up on either of these. Don’t want to offend the master?
Far be it from me to rank myself with Neal King. I spent about 100 days quietly lurking following you both all over the blogosphere. Neal is a fine mathematician but that is all you did with him too – a never ending (and ultimately totally mind numbing) exercise in ‘slip sliding away…..’.
You wriggled away when I challenged you to try the fairly simple task of expressing the W&H 2000 middle latitude expressions in a Miskolczi formalism. Now I’m going to slip slide away myself to look again at that.
• http://www.ecoengineers.com Steve Short
Funny, in other circumstances you would be the first to deride K&T 97 of course. I repeat:
Presumably this is also why Miskolczi assigns a K/St ratio of ~2 in his draft1.pdf (Fig. 18E). However, as you disagree I’m sure you will tell him/us why?
The highest estimate of F I have seen in the literature is about 68 -70 W/m^2. Your value of ~80 W/m^2 is not a value which I have ever seen and it is inconsistent with the mean SW tau which we discussed some time back (you may recall). Please produce a citation and/or tell us how you reconcile it with the known SW tau.
You didn’t fess-up on either of these. Don’t want to offend the master?
Far be it from me to rank myself with Neal King. I spent about 100 days quietly lurking following you both all over the blogosphere. Neal is a fine mathematician but that is all you did with him too – a never ending (and ultimately totally mind numbing) exercise in ‘slip sliding away…..’.
You wriggled away when I challenged you to try the fairly simple task of expressing the W&H 2000 middle latitude expressions in a Miskolczi formalism. Now I’m going to slip slide away myself to look again at that.
• jan pompe
Steve
“Presumably this is also why Miskolczi assigns a K/St ratio of ~2 in his draft1.pdf (Fig. 18E). However, as you disagree I’m sure you will tell him/us why?”
I’ve already e-mailed Miskolczi regarding Fig 18 and there will be some changes at the very least some explanations on the axes which will come out with part 2. I’m content to wait until that appears before I’ll comment further. I’m sure I’ve told you all this so what is your game?
Now I’m going to slip slide away myself to look again at that.
If you don’t think it’s a waste of time then go for it.
• jan pompe
Steve
“Presumably this is also why Miskolczi assigns a K/St ratio of ~2 in his draft1.pdf (Fig. 18E). However, as you disagree I’m sure you will tell him/us why?”
I’ve already e-mailed Miskolczi regarding Fig 18 and there will be some changes at the very least some explanations on the axes which will come out with part 2. I’m content to wait until that appears before I’ll comment further. I’m sure I’ve told you all this so what is your game?
Now I’m going to slip slide away myself to look again at that.
If you don’t think it’s a waste of time then go for it.
• Geoff Sherrington
While I for one appreciate the dedication and persistence of those debating on this thread, it has become fairly cryptic now and relies upon a new reader going back to the start to comprehend it.
Are we reaching a stage where a summay catch-up is possible, so the main areas of agreement and difference can be clearly elucidated?
It remains the case that F. Miskolczi has made an important contribution in a field rather short in fresh ideas and we need to know if he is right, mainly right or can be proven right or wrong.
• Geoff Sherrington
While I for one appreciate the dedication and persistence of those debating on this thread, it has become fairly cryptic now and relies upon a new reader going back to the start to comprehend it.
Are we reaching a stage where a summay catch-up is possible, so the main areas of agreement and difference can be clearly elucidated?
It remains the case that F. Miskolczi has made an important contribution in a field rather short in fresh ideas and we need to know if he is right, mainly right or can be proven right or wrong.
• jae
jan and Steve: You guys got me confused (more than usual, that is). Isn’t K 102 wm-2 in the K&T scheme? K includes ALL non-radiative energy transfers, including convection, friction, and latent heat. And it doesn’t matter if it’s up, down, or blowing in the wind.
Geoff: I may be wrong, but I don’t think we have moved a mm closer toward establishing validity to M’s ideas in the last several months! Just arguing about peripheral details. As far as I know, M has not been proved incorrect on any of his major ideas. We need some new physics sharks here, perhaps.
• jae
jan and Steve: You guys got me confused (more than usual, that is). Isn’t K 102 wm-2 in the K&T scheme? K includes ALL non-radiative energy transfers, including convection, friction, and latent heat. And it doesn’t matter if it’s up, down, or blowing in the wind.
Geoff: I may be wrong, but I don’t think we have moved a mm closer toward establishing validity to M’s ideas in the last several months! Just arguing about peripheral details. As far as I know, M has not been proved incorrect on any of his major ideas. We need some new physics sharks here, perhaps.
• http://www.ecoengineers.com Steve Short
Jan #59
“I’m content to wait until that appears before I’ll comment further. I’m sure I’ve told you all this so what is your game?”
Yes, we certainly agreed that the method of presentation of Fig 18 was confusing – especially to those coming up to speed on M Theory. However that was all about presentation only and at no point did we/you dispute the approximate ratios such as K/St ~2. So please explain why you did not object to that at the time? There are also some other approximate ratios in Figure 18E which could also be open to question. You did not question those either?
So it is disingenuous for you to now infer that amendments to Fig 18 suggested by you to M were substantive rather than simply in the method of presentation.
“If you don’t think it’s a waste of time then go for it.”
This is the sort of stuff you spout time and again. What really bugs me about your attitude to M Theory in this blog Jan is that you invariably leave no space for anyone to suggest developments, improvements, modification or tweaks to M Theory even amongst those of us who have a whole lot of sympathy and even a decent measure of technical belief in Fernenc’s work.
It is not an open ended discussion because as far as you are concerned you have obtained the received truth from the prophet M and it is complete and definitive in its present form. Even your language frequently betrays how you see this e.g. ” ….I’ve told you all this so what is your game?”.
As someone who did pure, high level academic science research for around 12 years and has worked in applied science for the other part of a 35 year career I find that you have an extremely quaint and totalitarian attitude to how science is meant to be done. It is plain to me and to many here that you often post excellent commentary in some instances and on other occasions post stuff which ranges from confused gobbledegook to completely wrong. I’m not saying we aren’t all periodically guilty of the same thing.
But the point is that for you everything you say is the TOTAL AND ABSOLUTE TRUTH and must be taken as such (even when it is mumbo jumbo) and that then is the end of the matter. FINIS – no further ideas, theory upgrading, mathematical development, nothing.
Well I for one think the way you do this ‘science’ sucks big time and it goes part the way to explaining why we are still locked into a tiny incestuous cabal which is going nowhere rapidly. This is the practice of small exclusive religions – a social environment which is seemingly made for you (and you make it).
It is not at all the nature of real science though – a point you seem incapable of comprehending.
I agree with Geoff #40
“It remains the case that F. Miskolczi has made an important contribution in a field rather short in fresh ideas and we need to know if he is right, mainly right or can be proven right or wrong.”
• http://www.ecoengineers.com Steve Short
Jan #59
“I’m content to wait until that appears before I’ll comment further. I’m sure I’ve told you all this so what is your game?”
Yes, we certainly agreed that the method of presentation of Fig 18 was confusing – especially to those coming up to speed on M Theory. However that was all about presentation only and at no point did we/you dispute the approximate ratios such as K/St ~2. So please explain why you did not object to that at the time? There are also some other approximate ratios in Figure 18E which could also be open to question. You did not question those either?
So it is disingenuous for you to now infer that amendments to Fig 18 suggested by you to M were substantive rather than simply in the method of presentation.
“If you don’t think it’s a waste of time then go for it.”
This is the sort of stuff you spout time and again. What really bugs me about your attitude to M Theory in this blog Jan is that you invariably leave no space for anyone to suggest developments, improvements, modification or tweaks to M Theory even amongst those of us who have a whole lot of sympathy and even a decent measure of technical belief in Fernenc’s work.
It is not an open ended discussion because as far as you are concerned you have obtained the received truth from the prophet M and it is complete and definitive in its present form. Even your language frequently betrays how you see this e.g. ” ….I’ve told you all this so what is your game?”.
As someone who did pure, high level academic science research for around 12 years and has worked in applied science for the other part of a 35 year career I find that you have an extremely quaint and totalitarian attitude to how science is meant to be done. It is plain to me and to many here that you often post excellent commentary in some instances and on other occasions post stuff which ranges from confused gobbledegook to completely wrong. I’m not saying we aren’t all periodically guilty of the same thing.
But the point is that for you everything you say is the TOTAL AND ABSOLUTE TRUTH and must be taken as such (even when it is mumbo jumbo) and that then is the end of the matter. FINIS – no further ideas, theory upgrading, mathematical development, nothing.
Well I for one think the way you do this ‘science’ sucks big time and it goes part the way to explaining why we are still locked into a tiny incestuous cabal which is going nowhere rapidly. This is the practice of small exclusive religions – a social environment which is seemingly made for you (and you make it).
It is not at all the nature of real science though – a point you seem incapable of comprehending.
I agree with Geoff #40
“It remains the case that F. Miskolczi has made an important contribution in a field rather short in fresh ideas and we need to know if he is right, mainly right or can be proven right or wrong.”
• http://www.ecoengineers.com Steve Short
If we went along with the old USST 76 atmosphere estimate for Eu (=F+K) then we got Eu = 169 W/m2. Similarly with K&L97 if we go along with K = 102 W/m2 we get 170 W/m^2 for Eu (F = 68 W/m^2 if memory serves me correctly). This means that if it is accepted that Su = 2Eu as per M Theory then Su ~ 340 W/m^2.
But this causes grief with the OLRA – 2SuE/3 ~ -15 W/m^2 global average cloud forcing estimate (for beta ~0.6) as this gives ~ 250 – 227 ~ + 23W/m^2! Thus we are out by almost 40 W/m^2.
Hopefully Jan or jae have a really nice answer for this problem to allow them have their cake and eat it too (assuming they accept M7 Eqns. 8, 9 and 28 of course
• http://www.ecoengineers.com Steve Short
If we went along with the old USST 76 atmosphere estimate for Eu (=F+K) then we got Eu = 169 W/m2. Similarly with K&L97 if we go along with K = 102 W/m2 we get 170 W/m^2 for Eu (F = 68 W/m^2 if memory serves me correctly). This means that if it is accepted that Su = 2Eu as per M Theory then Su ~ 340 W/m^2.
But this causes grief with the OLRA – 2SuE/3 ~ -15 W/m^2 global average cloud forcing estimate (for beta ~0.6) as this gives ~ 250 – 227 ~ + 23W/m^2! Thus we are out by almost 40 W/m^2.
Hopefully Jan or jae have a really nice answer for this problem to allow them have their cake and eat it too (assuming they accept M7 Eqns. 8, 9 and 28 of course
• jan pompe
jae #61
Isn’t K 102 wm-2 in the K&T scheme? K includes ALL non-radiative energy transfers, including convection, friction, and latent heat. And it doesn’t matter if it’s up, down, or blowing in the wind.
Yes I agree but K&T scheme and Miskolczi turn up different numbers but k&T is useful because they tabulate results from different researchers some of which show quite a deal of variation and one can’t possible agree with them all.
If we use the TIGR profile data (or just use M07 sect 7 & 8) the
$$OLR = 250 Wm^{-2}$$ see fig 11.
$$S_U = frac {OLR} f = frac {2 times OLR} {1 + 1.87 +exp(-1.87))} = 378 W m^{-2}$$ See fig 12
$$S_T = S_U times exp(-1.87) = 58 W m^{-2}$$
Then
$$E_U = OLR – S_T = 250 – 58 = 192 W/m^{-2}$$
and
$$2 times E_U = 384 W/m^2$$ not too far from the measured TIGR average ~383.6 Wm^2 for <T > =286.6K.
now if Steve is right about it $$K = 2S_T = 116$$
The only thing that M 7 has to say about the value of F is this at the top of page 26
Unfortunately, our static model can not deal with the dynamical factors represented by the variables K and F. The decomposition of $$E_U$$ into its several components is beyond the scope of this study
F is not evaluated and the means to evaluate are not given in the paper so going to K&T 97 who give values from various different researchers for Satm (F) in Table 1 ranging from 65 – 86 W/m^2 (So much for Steve’s “Your value of ~80 W/m^2 is not a value which I have ever seen“) so take your pick. That rather large range tends to suggest quite a bit of uncertainty in any case and make a breakdown of EU into it’s component parts rather difficult.
I’m sure though that one can be found in that list so that $$K + F = E_U$$ exactly in fact a value in the middle say 75.5 +116 looks pretty close to 192 to me.
The whole point is to obtain a better mathematical description that will obtain the surface temperature/radiative flux from the OLR and atmospheric absorber effects than the current standard Schwarzschild-Milne equations do then I think he has achieved that and you can see the comparison in M7 fig 12.
You can also see in fig 12 the greatest divergence is in the tropical zones but this may be due to a lack of profiles (this was availability rather than selection) in that zone and that needs to be checked in order to do that he needs TIGR 3 profiles and does not have that as I found out this morning.
For my part I’m still stuck on finding different ways to test empirically equation 4 and I would like to poke around the virial some more but it’s a question of available time and I have already spent far more time on this post than I would have liked.
• jan pompe
jae #61
Isn’t K 102 wm-2 in the K&T scheme? K includes ALL non-radiative energy transfers, including convection, friction, and latent heat. And it doesn’t matter if it’s up, down, or blowing in the wind.
Yes I agree but K&T scheme and Miskolczi turn up different numbers but k&T is useful because they tabulate results from different researchers some of which show quite a deal of variation and one can’t possible agree with them all.
If we use the TIGR profile data (or just use M07 sect 7 & 8) the
$$OLR = 250 Wm^{-2}$$ see fig 11.
$$S_U = \frac {OLR} f = \frac {2 \times OLR} {1 + 1.87 +exp(-1.87))} = 378 W m^{-2}$$ See fig 12
$$S_T = S_U \times exp(-1.87) = 58 W m^{-2}$$
Then
$$E_U = OLR – S_T = 250 – 58 = 192 W/m^{-2}$$
and
$$2 \times E_U = 384 W/m^2$$ not too far from the measured TIGR average ~383.6 Wm^2 for <T > =286.6K.
now if Steve is right about it $$K = 2S_T = 116$$
The only thing that M 7 has to say about the value of F is this at the top of page 26
Unfortunately, our static model can not deal with the dynamical factors represented by the variables K and F. The decomposition of $$E_U$$ into its several components is beyond the scope of this study
F is not evaluated and the means to evaluate are not given in the paper so going to K&T 97 who give values from various different researchers for Satm (F) in Table 1 ranging from 65 – 86 W/m^2 (So much for Steve’s “Your value of ~80 W/m^2 is not a value which I have ever seen“) so take your pick. That rather large range tends to suggest quite a bit of uncertainty in any case and make a breakdown of EU into it’s component parts rather difficult.
I’m sure though that one can be found in that list so that $$K + F = E_U$$ exactly in fact a value in the middle say 75.5 +116 looks pretty close to 192 to me.
The whole point is to obtain a better mathematical description that will obtain the surface temperature/radiative flux from the OLR and atmospheric absorber effects than the current standard Schwarzschild-Milne equations do then I think he has achieved that and you can see the comparison in M7 fig 12.
You can also see in fig 12 the greatest divergence is in the tropical zones but this may be due to a lack of profiles (this was availability rather than selection) in that zone and that needs to be checked in order to do that he needs TIGR 3 profiles and does not have that as I found out this morning.
For my part I’m still stuck on finding different ways to test empirically equation 4 and I would like to poke around the virial some more but it’s a question of available time and I have already spent far more time on this post than I would have liked.
• http://www.ecoengineers.com Steve Short
Jan #64
“F is not evaluated and the means to evaluate are not given in the paper so going to K&T 97 who give values from various different researchers for Satm (F) in Table 1 ranging from 65 – 86 W/m^2 (So much for Steve’s “Your value of ~80 W/m^2 is not a value which I have ever seen“) so take your pick. That rather large range tends to suggest quite a bit of uncertainty in any case and make a breakdown of EU into it’s component parts rather difficult.”
K&T97 is rather an old paper. It is also one which has come in for a lot of criticism on NM, including by Miskolczi and youself. Putting that aside (!), clearly my memory that it had ‘opted’ for 68 W/m^2 for F may be faulty. But the middle value of the range you quote is 75.5 as you say – so let’s agree to opt for 76 W/m^2 (at least pre-1998 ;-). It is my impression that about 70 is the upper limit of more recent papers published over the last decade but I am happy to stand corrected.
Needless to say, it still didn’t take you more than a few extra seconds to figure out, weasel like, that even 76 W/m^2 would still not ‘get you over the line’ regarding the ~15 W/m^2 negative forcing by clouds. Hence you then immediately say next:
“I’m sure though that one can be found in that list so that K + F = E_U exactly in fact a value in the middle say 75.5 +116 looks pretty close to 192 to me. ”
Looks pretty close to 192 to you does it? Of course it would!
But hang on a minute! Haven’t you just spent a whole bunch of posts really lambasting me for proposing K should about 120 W/m^2 (and impugning my motives for the extra 15 + 3-5 for the extra bit over 100 W/m^2), with jae’s support that is about 100 W/m^2 (jae quoting 102 from K&T 97).
So where does your extra 14 – 16 W/m^2 (on top of 100 – 102 W/m^2) for K come from to get you up to 192 W/m^2 for E_U?
I won’t quote the rest of your post. It’s just your usual pedantic posturing to hide the fact that you just sneakily adopted 116 W/m^2 for K in the face of having jackboot-like rejected anything over 102 W/m^2 from me in your last half dozen posts!!
And this from the guy who generally steadfastly ‘refuses’ to mess around with refining our understanding of the (to my mind critical) non LW IR terms of M Theory!
Fair crack of the whip, Jan. There you are doing it yet again! One rule for yourself, another rule for the rest. The sophistry just rolls on like a stream train. How many hundreds of examples do we need, for chrissakes?
I’m sure you’ll slip slide away from this little corker as well – boring and predictable as it is – it is precisely what I’ve come to expect from you.
• http://www.ecoengineers.com Steve Short
Jan #64
“F is not evaluated and the means to evaluate are not given in the paper so going to K&T 97 who give values from various different researchers for Satm (F) in Table 1 ranging from 65 – 86 W/m^2 (So much for Steve’s “Your value of ~80 W/m^2 is not a value which I have ever seen“) so take your pick. That rather large range tends to suggest quite a bit of uncertainty in any case and make a breakdown of EU into it’s component parts rather difficult.”
K&T97 is rather an old paper. It is also one which has come in for a lot of criticism on NM, including by Miskolczi and youself. Putting that aside (!), clearly my memory that it had ‘opted’ for 68 W/m^2 for F may be faulty. But the middle value of the range you quote is 75.5 as you say – so let’s agree to opt for 76 W/m^2 (at least pre-1998 ;-). It is my impression that about 70 is the upper limit of more recent papers published over the last decade but I am happy to stand corrected.
Needless to say, it still didn’t take you more than a few extra seconds to figure out, weasel like, that even 76 W/m^2 would still not ‘get you over the line’ regarding the ~15 W/m^2 negative forcing by clouds. Hence you then immediately say next:
“I’m sure though that one can be found in that list so that K + F = E_U exactly in fact a value in the middle say 75.5 +116 looks pretty close to 192 to me. ”
Looks pretty close to 192 to you does it? Of course it would!
But hang on a minute! Haven’t you just spent a whole bunch of posts really lambasting me for proposing K should about 120 W/m^2 (and impugning my motives for the extra 15 + 3-5 for the extra bit over 100 W/m^2), with jae’s support that is about 100 W/m^2 (jae quoting 102 from K&T 97).
So where does your extra 14 – 16 W/m^2 (on top of 100 – 102 W/m^2) for K come from to get you up to 192 W/m^2 for E_U?
I won’t quote the rest of your post. It’s just your usual pedantic posturing to hide the fact that you just sneakily adopted 116 W/m^2 for K in the face of having jackboot-like rejected anything over 102 W/m^2 from me in your last half dozen posts!!
And this from the guy who generally steadfastly ‘refuses’ to mess around with refining our understanding of the (to my mind critical) non LW IR terms of M Theory!
Fair crack of the whip, Jan. There you are doing it yet again! One rule for yourself, another rule for the rest. The sophistry just rolls on like a stream train. How many hundreds of examples do we need, for chrissakes?
I’m sure you’ll slip slide away from this little corker as well – boring and predictable as it is – it is precisely what I’ve come to expect from you.
• http://www.ecoengineers.com Steve Short
Quick scan of papers in my files dated around a decade or so ago.
Ramanathan et al. (1995) F = 52 W/m^2
Kiehl (1998) F = 54 W/m^2
Braswell and Lindzen (1998) F = 61 W/m^2
Collins (2001) F = 49 W/m^2
The lower values may have the known underestimation bias in CCM2 of ~20 W/m^2 and the higher values may have the known underestimation bias in CCM3 of ~15 W/m^2 so an absolute UPPER BOUND to F is definitely around 75 – 76 W/m^2. If Eu really is 192 W/m^2 this means that K >=116 W/m^2. Just trying to box Jan in a little bit more, but of course we are dealing with an Houdini here who vaporizes whole boxes with the mere wave of a hand (;-)
On a more constructive note:
http://www.atmos.washington.edu/~ken/PUB/swabs.pdf
• http://www.ecoengineers.com Steve Short
Quick scan of papers in my files dated around a decade or so ago.
Ramanathan et al. (1995) F = 52 W/m^2
Kiehl (1998) F = 54 W/m^2
Braswell and Lindzen (1998) F = 61 W/m^2
Collins (2001) F = 49 W/m^2
The lower values may have the known underestimation bias in CCM2 of ~20 W/m^2 and the higher values may have the known underestimation bias in CCM3 of ~15 W/m^2 so an absolute UPPER BOUND to F is definitely around 75 – 76 W/m^2. If Eu really is 192 W/m^2 this means that K >=116 W/m^2. Just trying to box Jan in a little bit more, but of course we are dealing with an Houdini here who vaporizes whole boxes with the mere wave of a hand (;-)
On a more constructive note:
http://www.atmos.washington.edu/~ken/PUB/swabs.pdf
• jan pompe
Steve #65
I am happy to stand corrected.
Thank you.
Looks pretty close to 192 to you does it? Of course it would!
Well is it close or not?
Needless to say, it still didn’t take you more than a few extra seconds to figure out, weasel like, that even 76 W/m^2 would still not ‘get you over the line’ regarding the ~15 W/m^2 negative forcing by clouds. Hence you then immediately say next:
Has it not occurred to you that I haven’t even looked at cloud forcing?
There is a reason assumption at the top of the list:
(a) — The available SW flux is totally absorbed in the system. In the process of thermalization $$F^0$$ is instantly converted to isotropic upward and downward LW radiation. The absorption of the SW photons and emission of the LW radiation are based on independent microphysical processes.
While the paper glosses over this stuff that you think is crucial I don’t don’t think it’s essential to the main thrust of the paper where by and large cloud effects are ignored. Future work perhaps but for now I’m just not interested.
No weasels here that’s just your perception and I really can’t help that.
<blockquoteBut hang on a minute! Haven’t you just spent a whole bunch of posts really lambasting me for proposing K should about 120 W/m^2
No Steve there is something faulty with your perceptions again. I disagreed that horizontal transport is additional to K, it’s not, it’s part of what ever the total value is. It’s pretty clear jae understood, it but why didn’t you?
• jan pompe
Steve #65
I am happy to stand corrected.
Thank you.
Looks pretty close to 192 to you does it? Of course it would!
Well is it close or not?
Needless to say, it still didn’t take you more than a few extra seconds to figure out, weasel like, that even 76 W/m^2 would still not ‘get you over the line’ regarding the ~15 W/m^2 negative forcing by clouds. Hence you then immediately say next:
Has it not occurred to you that I haven’t even looked at cloud forcing?
There is a reason assumption at the top of the list:
(a) — The available SW flux is totally absorbed in the system. In the process of thermalization $$F^0$$ is instantly converted to isotropic upward and downward LW radiation. The absorption of the SW photons and emission of the LW radiation are based on independent microphysical processes.
While the paper glosses over this stuff that you think is crucial I don’t don’t think it’s essential to the main thrust of the paper where by and large cloud effects are ignored. Future work perhaps but for now I’m just not interested.
No weasels here that’s just your perception and I really can’t help that.
<blockquoteBut hang on a minute! Haven’t you just spent a whole bunch of posts really lambasting me for proposing K should about 120 W/m^2
No Steve there is something faulty with your perceptions again. I disagreed that horizontal transport is additional to K, it’s not, it’s part of what ever the total value is. It’s pretty clear jae understood, it but why didn’t you?
• jan pompe
Steve #66
Just trying to box Jan in a little bit more, but of course we are dealing with an Houdini here who vaporizes whole boxes with the mere wave of a hand (;-)
No you are a 60 year old who can’t recognise when someone else doesn’t want to play his silly games.
• jan pompe
Steve #66
Just trying to box Jan in a little bit more, but of course we are dealing with an Houdini here who vaporizes whole boxes with the mere wave of a hand (;-)
No you are a 60 year old who can’t recognise when someone else doesn’t want to play his silly games.
• http://www.ecoengineers.com Steve Short
Steve #43
“Sure, accepting M Theory we have : Eu = F + K + P + Aa – Ed (net atmosphere) and Fo + Po + Ed – F – K – P – Aa – St = 0 (net surface) therefore if P, Po = 0 and Aa = Ed (as per M) then Fo – Eu – St = 0 therefore Eu = Fo – St therefore Fo – St = F + K i.e. OLR – St = F + K i.e. ~ 240 – 60 ~ 180 ~ 60 + 120 This at least adds up reasonably well and is the non-LW radiative part of the OLR (St being the LW radiative part). No mystery there – just another way of saying Eu = F + K. You won’t find a reference or justification for K ~ 120 W/m^2 anywhere in M4 or M7 please note.
Presumably this is also why Miskolczi assigns a K/St ratio of ~2 in his draft1.pdf (Fig. 18E). However, as you disagree I’m sure you will tell him/us why?”
Steve #46
“As well as transferring heat from the tropics to the poles (putting aside juvenile cheap shot re tropics), zonal and meridional winds also extract a net ~15 W/m^2 from the surface via non-convective cooling and drying effects (and producing frictional dissipation, orographic and wave cloud formation) etc. As the so-called thermal engineer here you should definitely know all about that. The remainder of the K term (~2 – 5 W/m^2) is largely comprised of frictional losses from falling rain. Thus K totals about 120 W/m^2.”
Jan #67
“No Steve there is something faulty with your perceptions again. I disagreed that horizontal transport is additional to K, it’s not, it’s part of what ever the total value is. It’s pretty clear jae understood, it but why didn’t you?”
Mate, you just gotta be totally twisted.
• http://www.ecoengineers.com Steve Short
Steve #43
“Sure, accepting M Theory we have : Eu = F + K + P + Aa – Ed (net atmosphere) and Fo + Po + Ed – F – K – P – Aa – St = 0 (net surface) therefore if P, Po = 0 and Aa = Ed (as per M) then Fo – Eu – St = 0 therefore Eu = Fo – St therefore Fo – St = F + K i.e. OLR – St = F + K i.e. ~ 240 – 60 ~ 180 ~ 60 + 120 This at least adds up reasonably well and is the non-LW radiative part of the OLR (St being the LW radiative part). No mystery there – just another way of saying Eu = F + K. You won’t find a reference or justification for K ~ 120 W/m^2 anywhere in M4 or M7 please note.
Presumably this is also why Miskolczi assigns a K/St ratio of ~2 in his draft1.pdf (Fig. 18E). However, as you disagree I’m sure you will tell him/us why?”
Steve #46
“As well as transferring heat from the tropics to the poles (putting aside juvenile cheap shot re tropics), zonal and meridional winds also extract a net ~15 W/m^2 from the surface via non-convective cooling and drying effects (and producing frictional dissipation, orographic and wave cloud formation) etc. As the so-called thermal engineer here you should definitely know all about that. The remainder of the K term (~2 – 5 W/m^2) is largely comprised of frictional losses from falling rain. Thus K totals about 120 W/m^2.”
Jan #67
“No Steve there is something faulty with your perceptions again. I disagreed that horizontal transport is additional to K, it’s not, it’s part of what ever the total value is. It’s pretty clear jae understood, it but why didn’t you?”
Mate, you just gotta be totally twisted.
• http://www.ecoengineers.com Steve Short
Steve #48
“Non-vertical, non-radiative heat transfer to the atmosphere is clearly contained in the K term NOT in the Po term which M7 defines as “total thermal energy from the planetary interior to the surface-atmosphere system.” Thus P0 would presumably take into account ocean upwelling/downwelling effects, geothermal etc.”
Steve #50
“I also made it perfectly clear I am talking about cooling and drying transferring heat FROM THE SURFACE the surface during lateral air movement (winds). Inspection of the literature suggests this about 13% of total K and frictional heat loss from falling rain about 3% of total K.”
Jan #67
“No Steve there is something faulty with your perceptions again. I disagreed that horizontal transport is additional to K, it’s not, it’s part of what ever the total value is. It’s pretty clear jae understood, it but why didn’t you?”
Faulty perceptions? Fawlty Towers more like.
• http://www.ecoengineers.com Steve Short
Steve #48
“Non-vertical, non-radiative heat transfer to the atmosphere is clearly contained in the K term NOT in the Po term which M7 defines as “total thermal energy from the planetary interior to the surface-atmosphere system.†Thus P0 would presumably take into account ocean upwelling/downwelling effects, geothermal etc.”
Steve #50
“I also made it perfectly clear I am talking about cooling and drying transferring heat FROM THE SURFACE the surface during lateral air movement (winds). Inspection of the literature suggests this about 13% of total K and frictional heat loss from falling rain about 3% of total K.”
Jan #67
“No Steve there is something faulty with your perceptions again. I disagreed that horizontal transport is additional to K, it’s not, it’s part of what ever the total value is. It’s pretty clear jae understood, it but why didn’t you?â€
Faulty perceptions? Fawlty Towers more like.
• jan pompe
Steve #69
As well as transferring heat from the tropics to the poles (putting aside juvenile cheap shot re tropics), zonal and meridional winds also extract a net ~15 W/m^2 from the surface via non-convective cooling and drying effects (and producing frictional dissipation, orographic and wave cloud formation) etc. As the so-called thermal engineer here you should definitely know all about that. The remainder of the K term (~2 – 5 W/m^2) is largely comprised of frictional losses from falling rain.
This extra 17 – 20 W/m^2 you want to add to just what exactly?
• jan pompe
Steve #69
As well as transferring heat from the tropics to the poles (putting aside juvenile cheap shot re tropics), zonal and meridional winds also extract a net ~15 W/m^2 from the surface via non-convective cooling and drying effects (and producing frictional dissipation, orographic and wave cloud formation) etc. As the so-called thermal engineer here you should definitely know all about that. The remainder of the K term (~2 – 5 W/m^2) is largely comprised of frictional losses from falling rain.
This extra 17 – 20 W/m^2 you want to add to just what exactly?
• jan pompe
Steve #70
also made it perfectly clear I am talking about cooling and drying transferring heat FROM THE SURFACE the surface during lateral air movement (winds). Inspection of the literature suggests this about 13% of total K and frictional heat loss from falling rain about 3% of total K.”
you want to add this 18% to what value of K obtained from where?
• jan pompe
Steve #70
also made it perfectly clear I am talking about cooling and drying transferring heat FROM THE SURFACE the surface during lateral air movement (winds). Inspection of the literature suggests this about 13% of total K and frictional heat loss from falling rain about 3% of total K.”
you want to add this 18% to what value of K obtained from where?
• http://www.ecoengineers.com Steve Short
Oi! Gevalt!
• http://www.ecoengineers.com Steve Short
Oi! Gevalt!
• jan pompe
Steve #73
Oi! Gevalt!
Never mind the yiddish lesson just answer.
• jan pompe
Steve #73
Oi! Gevalt!
Never mind the yiddish lesson just answer.
• Alex Harvey
Dear Steve & Jan,
Can I suggest that this stuff really isn’t worth drawing pistols at ten paces over. I understand the frustration, but I don’t think anyone’s mistakes, tangents, misunderstandings, are deliberate efforts to mislead, weasel, slip, slide or even speak Nebbish.
May I recommend that both of you look at the following diagram:
http://www.theaustralian.news.com.au/common/imagedata/0,,6465299,00.jpg
• Alex Harvey
Dear Steve & Jan,
Can I suggest that this stuff really isn’t worth drawing pistols at ten paces over. I understand the frustration, but I don’t think anyone’s mistakes, tangents, misunderstandings, are deliberate efforts to mislead, weasel, slip, slide or even speak Nebbish.
May I recommend that both of you look at the following diagram:
http://www.theaustralian.news.com.au/common/imagedata/0,,6465299,00.jpg
• http://www.ecoengineers.com Steve Short
I’m very sorry for you if you are genuinely that dense, Jan.
I have been suggesting all along in, in what for me was simple plain English (not Yiddish – I got that from Mutti as you did perhaps too) that there is a problem with the K term in M Theory IF (as your yourself have suggested – but M hasn’t) it is only comprised of sensible and latent heat component totaling only ~100 W/m^2. For E-U = F + K and S-U = 2E+u etc etc then K has to ~120 W/m^2. OR E-U = F + K + what?
Therefore an all embracing non-radiative K would have to INCLUDE a ‘missing’ component/term adding to ~20 W/m^2. I have proposed what I think it might be. In that aspect I could be wrong.
NOWHERE, NOWHERE in any of my posts have I EVER EVER suggested an ADDITIONAL term separate from K. How you deduced that (if you are not simply yanking my chain in the name of mental cruelty) is totally beyond me. The fawlty perception is entirely yours.
• http://www.ecoengineers.com Steve Short
I’m very sorry for you if you are genuinely that dense, Jan.
I have been suggesting all along in, in what for me was simple plain English (not Yiddish – I got that from Mutti as you did perhaps too) that there is a problem with the K term in M Theory IF (as your yourself have suggested – but M hasn’t) it is only comprised of sensible and latent heat component totaling only ~100 W/m^2. For E-U = F + K and S-U = 2E+u etc etc then K has to ~120 W/m^2. OR E-U = F + K + what?
Therefore an all embracing non-radiative K would have to INCLUDE a ‘missing’ component/term adding to ~20 W/m^2. I have proposed what I think it might be. In that aspect I could be wrong.
NOWHERE, NOWHERE in any of my posts have I EVER EVER suggested an ADDITIONAL term separate from K. How you deduced that (if you are not simply yanking my chain in the name of mental cruelty) is totally beyond me. The fawlty perception is entirely yours.
• jan pompe
Steve #76
that there is a problem with the K term in M Theory IF (as your yourself have suggested – but M hasn’t) it is only comprised of sensible and latent heat component totaling only ~100 W/m^2.
It’s where that number 100W/m^2 that bother’s me and adding another 20W/m^2 to that number. I don’t think it’s necessary.
What we are dealing with here is averages over time and space the net effect will be 116W/m^2 according to the numbers in M7 derived from the TIGR profiles not 100 W/m^2. Then 2E_U = 2 x 192 =384 again shown in #64.
The numbers are internally consistent as I showed in #64 so I don’t think there isn’t a problem there.
Which is why I asked what value of K are you wanting to add your extra to and where it came from more particularly where it came from. It was obviously not Ferenc’s paper.
As for the value of F whatever it turns out to be eventually I expect it will be constant as there will always be enough N2 and O2 to scatter and absorb the short wave. New K&T has it at 78 it think it needs more work yet.
Now I’m not going to press you for an answer but want you to think about
also made it perfectly clear I am talking about cooling and drying transferring heat FROM THE SURFACE the surface during lateral air movement (winds).
and how this is NOT sensible heat (cooling) and latent heat (drying) even though it is assisted by lateral air movements.
yes i did enjoy a beer thanks. feel free to do the same and BTW
I don’t think i ever suggested this:
NOWHERE, NOWHERE in any of my posts have I EVER EVER suggested an ADDITIONAL term separate from K.
What I was saying that the cooling and the drying were not separate from sensible and latent heat therefore already included in K I didn’t think that you were suggesting to add an extra term.
FYI all who are interested
New Kiehl Trenberth and Fasullo This time if you look at the cartoon at the end they have a .9W/m^2 continuous warming signal in it.
I hope you didn’t run out of cold beer tomorrow promises to be warmer.
• jan pompe
Steve #76
that there is a problem with the K term in M Theory IF (as your yourself have suggested – but M hasn’t) it is only comprised of sensible and latent heat component totaling only ~100 W/m^2.
It’s where that number 100W/m^2 that bother’s me and adding another 20W/m^2 to that number. I don’t think it’s necessary.
What we are dealing with here is averages over time and space the net effect will be 116W/m^2 according to the numbers in M7 derived from the TIGR profiles not 100 W/m^2. Then 2E_U = 2 x 192 =384 again shown in #64.
The numbers are internally consistent as I showed in #64 so I don’t think there isn’t a problem there.
Which is why I asked what value of K are you wanting to add your extra to and where it came from more particularly where it came from. It was obviously not Ferenc’s paper.
As for the value of F whatever it turns out to be eventually I expect it will be constant as there will always be enough N2 and O2 to scatter and absorb the short wave. New K&T has it at 78 it think it needs more work yet.
Now I’m not going to press you for an answer but want you to think about
also made it perfectly clear I am talking about cooling and drying transferring heat FROM THE SURFACE the surface during lateral air movement (winds).
and how this is NOT sensible heat (cooling) and latent heat (drying) even though it is assisted by lateral air movements.
yes i did enjoy a beer thanks. feel free to do the same and BTW
I don’t think i ever suggested this:
NOWHERE, NOWHERE in any of my posts have I EVER EVER suggested an ADDITIONAL term separate from K.
What I was saying that the cooling and the drying were not separate from sensible and latent heat therefore already included in K I didn’t think that you were suggesting to add an extra term.
FYI all who are interested
New Kiehl Trenberth and Fasullo This time if you look at the cartoon at the end they have a .9W/m^2 continuous warming signal in it.
I hope you didn’t run out of cold beer tomorrow promises to be warmer.
• jan pompe
Alex #75
LOL
• jan pompe
Alex #75
LOL
• http://www.ecoengineers.com Steve Short
Jan #77
“It’s where that number 100W/m^2 that bother’s me and adding another 20W/m^2 to that number. I don’t think it’s necessary.
What we are dealing with here is averages over time and space the net effect will be 116W/m^2 according to the numbers in M7 derived from the TIGR profiles not 100 W/m^2. Then 2E_U = 2 x 192 =384 again shown in #64.”
I’m sorry but I beg to think it is necessary (or some functional M Thoery compatible equivalent).
It doesn’t really matter how you get to an E_U of 192. Even if one accepts Kiehl Trenberth and Fasullo (2008) and sets F at 78 W/m^2 then this means that to get an E_U of 192 then K still has to be 114 W/m^2. If you have a problem (as I do with a ‘K’ that is comprised of only (your) H_S and H_L then the highest value for K seen in the literature is some 102 W/m^2. 102 + 78 still only = 180. For OLR = 250 this gives a positive cloud forcing of ~ 10 W/m^2. This means that there is still a shortfall in E_U of 12 W/m^2 to get to the OLRA – 2S_UE/3 ~ -15 W/m^2 given on page 19 (Section 5.2) in M7.
I happen to believe that the last paragraph on page 19 in M7 is a brillinat statement by Ferenc of how the system works. Allow me to quote it:
The OLRA – 2S_UE /3 ≈ − 15 W m-2 is a fairly good estimate of the global
average cloud forcing. The estimated β ≈ 0.6 is the required cloud cover (at this level) to balance OLRA , which looks realistic. We believe that the β parameter is governed by the maximum entropy principle, the system tries to convert as much SW radiation to LW radiation as possible, while obeying the 2OLR/(3 f ) = F0 + P0 condition. The cloud altitude, where the clear-sky OLRE = OLRA = ED depends only on the SW characteristics of the system (surface and cloud albedo, SW solar input) and alone, is a very important climate parameter.”
Higher up on the same page Miskolczi also says (significantly) that:
“Since the Earth-atmosphere system must have a way to reduce the clear
sky OLRE to the observed OLRA we assume the existence of an effective
cloud layer at about 2.05 km altitude. The corresponding optical depth is
τA = 1.47 . Fig. 6 shows the dependences of the OLR and ED on the cloud top altitude and EU on the cloud bottom altitude. At this cloud level the source function is SC = 332.8 W m-2. We also assume that the cloud layer is in thermal equilibrium with the surrounding air and radiates as a perfect blackbody. Clear sky simulations show that at this level the A
OLR ≈ OLR ≈ ED and the layer is close to the radiative equilibrium. Cloudy computations also show that EU – and consequently K – has a maximum around this level, which is favorable for cloud formation.”
Note that up at the cloud layer according to M S_C = 333 W/m^2 Two thirds of this is only 222 W/m^2 BTW!
Even with the most modern upwards revised F of 78 W/m^ and the most optimistic H-S + H_L of 102 W/m^2 we still have a short fall in K of the order of 12 W/m^2 just to get to ~6 W/m^2 global forcing by the (approx. 60%) cloud cover (assuming global mean OLR = 250 W/m^2 as per M4). Thus if you don’t like the idea that K is higher than (say) 100 W/m^2 you do need another extra term Q of about 14 W/m^2 to any significant negative forcing (say >6 W/m^2) at 60% cloud cover.
If you don’t want to permit a total K term of the order of 115 – 116 W/m^2 then there is no negative cloud forcing at all and Miskolczi does not have a convenient explanation for homeostasis or static equilibrium (or whatever term you prefer this week).
I am pouring over K, T & F (2008) and I thank you for the reference.
But us having both said all this I hope you also downloaded Takahashi (2008) who has a very nice discussion (p5) of the problems of accurately estimation SW absorption in the atmosphere. SW absorption is not at all just about O2 and N2 absorption bands. Let me quote from Takahashi (2008):
“It is only recently that climate models are converging towards producing realistic (sufficiently strong) tropospheric clear-sky shortwave absorption (Wild et al., 2006). Although the physics behind this absorption are well understood from fi rst principles, subtle de ficiencies in the depiction of the spectroscopic properties of water vapor have substantial consequences for the clear-sky absorption of shortwave radiation (e.g. Collins et al.,
2006b). Furthermore, the convergence in present-day absorption does not necessarily translate to the climate change case and, as shown by Collins et al. (2006a), there is relatively large inter-model discrepancies in the
changes in clear-sky surface shortwave flux associated with water vapor.”
On top of this there is the global SW dimming caused by an increased flux of biogenic organic and inorganic aerosols getting into the atmosphere. The Eurocentric suggestion by Phillipona et al over many years that it was/is all direct industrial aerosol pollution is nonsense – including from a careful reading of the literature.
BTW I hope you have noticed during this current (relatively clear sky high summer insolation) heat wave in the Sydney area just how dense the ‘smog’ is. I have recently been in the Shoalhaven Valley area as usual working on my block and the biogenic ‘smog’ is as thick all across Morton and Budawang National Parks as it is in the Sydney Basin. Those trees are just pumping it out (under current conditions) I’ll bet the cyanobacteria all along our coastal shelf are doing just the same as lateral coastal air visibility is down to about 5 km or less.
So perhaps the ‘problem’ is not with K (although increased aerosol concentration does enhance latent heat release due to more rapid nucleation) but more with the global mean size of the SW absorption term F? Either way there is a ‘problem’.
Interestingly using the deltaLW/delta cloud cover and deltaSW/delta cloud cover mid-latitude ratios from that little W&H 2000 paper seem to give a hint of where the problem lies. I’ll save that for another time.
• http://www.ecoengineers.com Steve Short
Jan #77
“It’s where that number 100W/m^2 that bother’s me and adding another 20W/m^2 to that number. I don’t think it’s necessary.
What we are dealing with here is averages over time and space the net effect will be 116W/m^2 according to the numbers in M7 derived from the TIGR profiles not 100 W/m^2. Then 2E_U = 2 x 192 =384 again shown in #64.”
I’m sorry but I beg to think it is necessary (or some functional M Thoery compatible equivalent).
It doesn’t really matter how you get to an E_U of 192. Even if one accepts Kiehl Trenberth and Fasullo (2008) and sets F at 78 W/m^2 then this means that to get an E_U of 192 then K still has to be 114 W/m^2. If you have a problem (as I do with a ‘K’ that is comprised of only (your) H_S and H_L then the highest value for K seen in the literature is some 102 W/m^2. 102 + 78 still only = 180. For OLR = 250 this gives a positive cloud forcing of ~ 10 W/m^2. This means that there is still a shortfall in E_U of 12 W/m^2 to get to the OLRA – 2S_UE/3 ~ -15 W/m^2 given on page 19 (Section 5.2) in M7.
I happen to believe that the last paragraph on page 19 in M7 is a brillinat statement by Ferenc of how the system works. Allow me to quote it:
The OLRA – 2S_UE /3 ≈ − 15 W m-2 is a fairly good estimate of the global
average cloud forcing. The estimated β ≈ 0.6 is the required cloud cover (at this level) to balance OLRA , which looks realistic. We believe that the β parameter is governed by the maximum entropy principle, the system tries to convert as much SW radiation to LW radiation as possible, while obeying the 2OLR/(3 f ) = F0 + P0 condition. The cloud altitude, where the clear-sky OLRE = OLRA = ED depends only on the SW characteristics of the system (surface and cloud albedo, SW solar input) and alone, is a very important climate parameter.”
Higher up on the same page Miskolczi also says (significantly) that:
“Since the Earth-atmosphere system must have a way to reduce the clear
sky OLRE to the observed OLRA we assume the existence of an effective
cloud layer at about 2.05 km altitude. The corresponding optical depth is
Ï„A = 1.47 . Fig. 6 shows the dependences of the OLR and ED on the cloud top altitude and EU on the cloud bottom altitude. At this cloud level the source function is SC = 332.8 W m-2. We also assume that the cloud layer is in thermal equilibrium with the surrounding air and radiates as a perfect blackbody. Clear sky simulations show that at this level the A
OLR ≈ OLR ≈ ED and the layer is close to the radiative equilibrium. Cloudy computations also show that EU – and consequently K – has a maximum around this level, which is favorable for cloud formation.”
Note that up at the cloud layer according to M S_C = 333 W/m^2 Two thirds of this is only 222 W/m^2 BTW!
Even with the most modern upwards revised F of 78 W/m^ and the most optimistic H-S + H_L of 102 W/m^2 we still have a short fall in K of the order of 12 W/m^2 just to get to ~6 W/m^2 global forcing by the (approx. 60%) cloud cover (assuming global mean OLR = 250 W/m^2 as per M4). Thus if you don’t like the idea that K is higher than (say) 100 W/m^2 you do need another extra term Q of about 14 W/m^2 to any significant negative forcing (say >6 W/m^2) at 60% cloud cover.
If you don’t want to permit a total K term of the order of 115 – 116 W/m^2 then there is no negative cloud forcing at all and Miskolczi does not have a convenient explanation for homeostasis or static equilibrium (or whatever term you prefer this week).
I am pouring over K, T & F (2008) and I thank you for the reference.
But us having both said all this I hope you also downloaded Takahashi (2008) who has a very nice discussion (p5) of the problems of accurately estimation SW absorption in the atmosphere. SW absorption is not at all just about O2 and N2 absorption bands. Let me quote from Takahashi (2008):
“It is only recently that climate models are converging towards producing realistic (sufficiently strong) tropospheric clear-sky shortwave absorption (Wild et al., 2006). Although the physics behind this absorption are well understood from fi rst principles, subtle de ficiencies in the depiction of the spectroscopic properties of water vapor have substantial consequences for the clear-sky absorption of shortwave radiation (e.g. Collins et al.,
2006b). Furthermore, the convergence in present-day absorption does not necessarily translate to the climate change case and, as shown by Collins et al. (2006a), there is relatively large inter-model discrepancies in the
changes in clear-sky surface shortwave flux associated with water vapor.”
On top of this there is the global SW dimming caused by an increased flux of biogenic organic and inorganic aerosols getting into the atmosphere. The Eurocentric suggestion by Phillipona et al over many years that it was/is all direct industrial aerosol pollution is nonsense – including from a careful reading of the literature.
BTW I hope you have noticed during this current (relatively clear sky high summer insolation) heat wave in the Sydney area just how dense the ‘smog’ is. I have recently been in the Shoalhaven Valley area as usual working on my block and the biogenic ‘smog’ is as thick all across Morton and Budawang National Parks as it is in the Sydney Basin. Those trees are just pumping it out (under current conditions) I’ll bet the cyanobacteria all along our coastal shelf are doing just the same as lateral coastal air visibility is down to about 5 km or less.
So perhaps the ‘problem’ is not with K (although increased aerosol concentration does enhance latent heat release due to more rapid nucleation) but more with the global mean size of the SW absorption term F? Either way there is a ‘problem’.
Interestingly using the deltaLW/delta cloud cover and deltaSW/delta cloud cover mid-latitude ratios from that little W&H 2000 paper seem to give a hint of where the problem lies. I’ll save that for another time.
• Geoff Sherrington
Steve or Jan,
To save us labouring through the new Trenbeth, it would be a great service for you to make some dot points where it appears to advance understanding. There are so many issues going on at once that the generalist is kept very busy.
Steve, Remember that it was before 1800 that the Blue Mountains were named, it is thought because of biogenic emissions like eucalyptus oils.
• Geoff Sherrington
Steve or Jan,
To save us labouring through the new Trenbeth, it would be a great service for you to make some dot points where it appears to advance understanding. There are so many issues going on at once that the generalist is kept very busy.
Steve, Remember that it was before 1800 that the Blue Mountains were named, it is thought because of biogenic emissions like eucalyptus oils.
• Jan Pompe
Geoff #80
I’ve only just skimmed through the paper and it’s a preprint so I’m not sure if it will stay the same as I mentioned to Steve I’m not to happy to get into a flap over something that might not yet be finished. I did a double take on the .9W/m^2 in the cartoon that I have not, while doing a quick search, been able to find explained in the text.
That’s 28 Mega Joules cumulatively absorbed per square metre over the course of a year today at one o’clock well see what 17 MJ not cumulatively absorbed over 6 hours (that’s assuming 800W/m^2 incoming and not counting outgoing). One can only wonder how long this thermal imbalance is supposed to have been going on.
However I do think it’s best to wait to see the final result and hope that someone who they’ll listen to will point out what I consider an obvious problem with their budget as it stands.
• Jan Pompe
Geoff #80
I’ve only just skimmed through the paper and it’s a preprint so I’m not sure if it will stay the same as I mentioned to Steve I’m not to happy to get into a flap over something that might not yet be finished. I did a double take on the .9W/m^2 in the cartoon that I have not, while doing a quick search, been able to find explained in the text.
That’s 28 Mega Joules cumulatively absorbed per square metre over the course of a year today at one o’clock well see what 17 MJ not cumulatively absorbed over 6 hours (that’s assuming 800W/m^2 incoming and not counting outgoing). One can only wonder how long this thermal imbalance is supposed to have been going on.
However I do think it’s best to wait to see the final result and hope that someone who they’ll listen to will point out what I consider an obvious problem with their budget as it stands.
• Geoff Sherrington
Jan #81
I skimmed it too. It is prudent to delay detailed comment until the final version (and a good scientific principle also).
I suspect I say for many readers that we hope that the dialogue between you and Herb and BPL etc does not give rise to personal differences. The dialogue could result in a most productive consensus and we hope that civility is not threatened to the point of extinction. You guys have a lot to teach we generalists.
• Geoff Sherrington
Jan #81
I skimmed it too. It is prudent to delay detailed comment until the final version (and a good scientific principle also).
I suspect I say for many readers that we hope that the dialogue between you and Herb and BPL etc does not give rise to personal differences. The dialogue could result in a most productive consensus and we hope that civility is not threatened to the point of extinction. You guys have a lot to teach we generalists.
• Jan Pompe
Steve #79
There is I think some cross over of purpose.
If you have a problem (as I do with a ‘K’ that is comprised of only (your) H_S and H_L
My issue is that your cooling and drying, due to lateral movement of wind are still only sensible heat ($$H_S$$) and latent heat ($$H_L$$) respectively i.e. vertical components. The the lateral movements of wind represent an energy that has as it’s source the sensible, latent and radiant heat even the lightning and thunder as far as I can see has the same three sources. Therefore I suggest we get Ferenc to clarify this too:
Note, that the Kterm is not restricted to strict vertical heat transfer. Due to the permanent motion of the atmosphere K represents a statistical or climatic average.
You want to do it or shall I.
Geoff #81 I’m sure Steve and I have the same aims just somewhat different personalities and different focuses and priorities & despite all apparent appearances here I quite like the guy. Just wish he wasn’t quite so ornery and he probably thinks the same about me.
There are a lot of problems in the paper with regard to clarity. I think a bigger problem looms than the value F & K and how Ferenc has (or hasn’t) dealt with them, and that is with how he has determined the boundary condition for the integral equation in appendix B which has it’s roots in Kirchhoff’s law and thermodynamic and hydrostatic equilibrium that is to say in Equations 4 and 8. If it’s going to unravel it’s going to be there IMHO. There is an awful lot invested in the semi-infinite/semi-grey mathematical model it will die hard if die it must.
I’f Steve has some insight s to offer there I’d be only to happy to hear/see or otherwise find out about them.
I’ll look at the rest of Steve’s post after I’ve recovered from the beer that I’m about to consume.
• Jan Pompe
Steve #79
There is I think some cross over of purpose.
If you have a problem (as I do with a ‘K’ that is comprised of only (your) H_S and H_L
My issue is that your cooling and drying, due to lateral movement of wind are still only sensible heat ($$H_S$$) and latent heat ($$H_L$$) respectively i.e. vertical components. The the lateral movements of wind represent an energy that has as it’s source the sensible, latent and radiant heat even the lightning and thunder as far as I can see has the same three sources. Therefore I suggest we get Ferenc to clarify this too:
Note, that the Kterm is not restricted to strict vertical heat transfer. Due to the permanent motion of the atmosphere K represents a statistical or climatic average.
You want to do it or shall I.
Geoff #81 I’m sure Steve and I have the same aims just somewhat different personalities and different focuses and priorities & despite all apparent appearances here I quite like the guy. Just wish he wasn’t quite so ornery and he probably thinks the same about me.
There are a lot of problems in the paper with regard to clarity. I think a bigger problem looms than the value F & K and how Ferenc has (or hasn’t) dealt with them, and that is with how he has determined the boundary condition for the integral equation in appendix B which has it’s roots in Kirchhoff’s law and thermodynamic and hydrostatic equilibrium that is to say in Equations 4 and 8. If it’s going to unravel it’s going to be there IMHO. There is an awful lot invested in the semi-infinite/semi-grey mathematical model it will die hard if die it must.
I’f Steve has some insight s to offer there I’d be only to happy to hear/see or otherwise find out about them.
I’ll look at the rest of Steve’s post after I’ve recovered from the beer that I’m about to consume.
• http://www.ecoengineers.com Steve Short
Jan #81
So it seems that pre-print version of K,T&F (2008) has the following numbers for CERES May 2000 – May 2004:
Fo = 239.4 W/m^2
OLR = 238.5
F = 78.2
K = 97.0
S_T = 63.0
By definition this gives E_U = 78.2 + 97.0 = 175.2
Thus if we accept Miskolczi’s virial relation S_U = 2 E_U (based on KE/PE arguments of course) then the Miskolczi relation global OLR – 2Su/3 gives 238.5 – (4 x 175.2/3) = 238.5 – 233.5 = +4.9 W/m^2
So either there is either no net negative global cloud forcing or/and the virial relation S_U = 2E_U doesn’t hold up (noting a bit of both is also possible).
However, it is also noted that OLR = E_U + S_T in the bounded or semi-transparent atmosphere according to M Theory. Thus E_U = OLR -S_T = 238.5 – 63.0 = 175.5. This agrees very well with the 175.2 estimated via E_U = F + K.
So it would appear that if we were to accept the pre-print K, L & T (2008) values, the problem to which I have been referring does not lie so much with the estimation of E_U (as F + K) but more likely with the actual virial relation Su = 2E_U itself.
Another way of looking at this is of course to consider Jan’s ‘proof’ of the virial relation S_U + S_V = 3OLR/2 which set S_V = S_T/2 – E_D/10 as per M& Eqn. 9. Noting that E_U/E_D = 3/5 we then have S_U + S_T/2 – E_D/10 = 350.4 + 31.5 – 29.2 = 352.7
Thus 2(S_U + S_V)/3 = 235.1
Thus OLR-2(S_U + S_V)/3 = 238.5 – 235.1 = +3.4 W/m^2 so not much improvement there. Clouds still heating us up!
Jan #77
“The numbers are internally consistent as I showed in #64 so I don’t think there isn’t (sic) a problem there. ”
Now even Jan’s double negative typos are getting prescient (;-)
• http://www.ecoengineers.com Steve Short
Jan #81
So it seems that pre-print version of K,T&F (2008) has the following numbers for CERES May 2000 – May 2004:
Fo = 239.4 W/m^2
OLR = 238.5
F = 78.2
K = 97.0
S_T = 63.0
By definition this gives E_U = 78.2 + 97.0 = 175.2
Thus if we accept Miskolczi’s virial relation S_U = 2 E_U (based on KE/PE arguments of course) then the Miskolczi relation global OLR – 2Su/3 gives 238.5 – (4 x 175.2/3) = 238.5 – 233.5 = +4.9 W/m^2
So either there is either no net negative global cloud forcing or/and the virial relation S_U = 2E_U doesn’t hold up (noting a bit of both is also possible).
However, it is also noted that OLR = E_U + S_T in the bounded or semi-transparent atmosphere according to M Theory. Thus E_U = OLR -S_T = 238.5 – 63.0 = 175.5. This agrees very well with the 175.2 estimated via E_U = F + K.
So it would appear that if we were to accept the pre-print K, L & T (2008) values, the problem to which I have been referring does not lie so much with the estimation of E_U (as F + K) but more likely with the actual virial relation Su = 2E_U itself.
Another way of looking at this is of course to consider Jan’s ‘proof’ of the virial relation S_U + S_V = 3OLR/2 which set S_V = S_T/2 – E_D/10 as per M& Eqn. 9. Noting that E_U/E_D = 3/5 we then have S_U + S_T/2 – E_D/10 = 350.4 + 31.5 – 29.2 = 352.7
Thus 2(S_U + S_V)/3 = 235.1
Thus OLR-2(S_U + S_V)/3 = 238.5 – 235.1 = +3.4 W/m^2 so not much improvement there. Clouds still heating us up!
Jan #77
“The numbers are internally consistent as I showed in #64 so I don’t think there isn’t (sic) a problem there. ”
Now even Jan’s double negative typos are getting prescient (;-)
• Jan Pompe
Steve #84
I make E_U 199 W/^2 (or 238.5 -40) in this one and S_U 396 W/m^2 2 x E_U = 398 (or 397) which I think is in the ballpark. Its not a difference I would hang a career on.
Then also the amount in the atmospheric window ($$S_T$$) is 40W/m^2 the 63W/m^2 is made up of Kirchhoff’s law denying upward re-radiation of $$A_A$$ of 23 W/m^2 + 40 W/m^2 $$S_T$$ so its $$OLR – S_T = 238.5 – 40 = 197.5 W/m^2$$. The only thing that both papers agree on is that $$S_U=2E_U$$
The only thing there is reasonable agreement between sources they cite is that $$S_U approx 396 Wm^{-2}$$.
For arguments sake let’s say they don’t agree with the Virial I still don’t understand your issue with “negative cloud forcing” in this context.
What is this?
OLR – 2Su/3 gives 238.5 – (4 x 175.2/3) = 238.5 – 233.5 = +4.9 W/m^2
Neither M-7 nor K&T 97 or FKT08 relate F+K to SU in that way. I don’t understand what you are trying to say here.
However, it is also noted that OLR = E_U + S_T in the bounded or semi-transparent atmosphere according to M Theory. Thus E_U = OLR -S_T = 238.5 – 63.0 = 175.5. This agrees very well with the 175.2 estimated via E_U = F + K.
I don’t particularly think hat K&T 97 or FKT08 quite have ST right (I for one think 63 W/m^2 is closer to the truth) but 40 W/m^2 is what they say for that. Now from 97 -> 08 SU, ED, OLR, K (the sum) and presumably tau ($$CO_2 uparrow$$) all change but not ST does that not strike you as a just a little weird? Of course that $$A_A neq E_D$$ does not change either, but we expect that. However that 23 W/m^2 is not where it belongs. Like I said if you are right about $$frac K {S_T} approx 2$$ then in M7 $$K approx 120 W/m^2$$ and there is not 23 W/m^2 A<sub?A uncompensated by ED.
Now apart from the fact that this is NOT “Jan’s ‘proof’” but Ferenc’s explanation ( who many times is this now that I’ve mentioned it?) what is this
Another way of looking at this is of course to consider Jan’s ‘proof’ of the virial relation S_U + S_V = 3OLR/2 which set S_V = S_T/2 – E_D/10 as per M& Eqn. 9. Noting that E_U/E_D = 3/5 we then have S_U + S_T/2 – E_D/10 = 350.4 + 31.5 – 29.2 = 352.7
and why does $$frac {E_U}{E_D} = frac 3 5$$ when in both KT97 & FKT $$S_U neq frac 3 2 OLR$$? You need to go to M&M 04 to find out that OLRs are generally understated (in this case about 12W/m^2) because those early birds carried colour blind spectrometers that generally could not see IR at frequencies below $$400 cm-1$$
Sometimes, due to technical or engineering constraints, the spectral sensitivity of a detector or instrument design sets the spectral boundaries.
In fact if you to the archives or various papers you’ll see the $$400 cm-1$$ spectral limit is fairly consistent. The main purpose behind MM4 is to correct for that error. Already in OLR alone you have an error more than three times your 3.4 W/m^2 “cloud forcing and that misplaced 23W/m^2 AA is six time the cloud forcing.
I would be the first to agree that the fact that $$S_U = 2E_U$$ in both these papers is a fluke but that really doesn’t help us with any of the rest. It certainly doesn’t give me confidence that we can rely on it for the value of either K or F.
Now even Jan’s double negative typos are getting prescient (;-)
maybe I know you better than I know myself :- heaven forbid. 8)
• Jan Pompe
Steve #84
I make E_U 199 W/^2 (or 238.5 -40) in this one and S_U 396 W/m^2 2 x E_U = 398 (or 397) which I think is in the ballpark. Its not a difference I would hang a career on.
Then also the amount in the atmospheric window ($$S_T$$) is 40W/m^2 the 63W/m^2 is made up of Kirchhoff’s law denying upward re-radiation of $$A_A$$ of 23 W/m^2 + 40 W/m^2 $$S_T$$ so its $$OLR – S_T = 238.5 – 40 = 197.5 W/m^2$$. The only thing that both papers agree on is that $$S_U=2E_U$$
The only thing there is reasonable agreement between sources they cite is that $$S_U \approx 396 Wm^{-2}$$.
For arguments sake let’s say they don’t agree with the Virial I still don’t understand your issue with “negative cloud forcing” in this context.
What is this?
OLR – 2Su/3 gives 238.5 – (4 x 175.2/3) = 238.5 – 233.5 = +4.9 W/m^2
Neither M-7 nor K&T 97 or FKT08 relate F+K to SU in that way. I don’t understand what you are trying to say here.
However, it is also noted that OLR = E_U + S_T in the bounded or semi-transparent atmosphere according to M Theory. Thus E_U = OLR -S_T = 238.5 – 63.0 = 175.5. This agrees very well with the 175.2 estimated via E_U = F + K.
I don’t particularly think hat K&T 97 or FKT08 quite have ST right (I for one think 63 W/m^2 is closer to the truth) but 40 W/m^2 is what they say for that. Now from 97 -> 08 SU, ED, OLR, K (the sum) and presumably tau ($$CO_2 \uparrow$$) all change but not ST does that not strike you as a just a little weird? Of course that $$A_A \neq E_D$$ does not change either, but we expect that. However that 23 W/m^2 is not where it belongs. Like I said if you are right about $$\frac K {S_T} \approx 2$$ then in M7 $$K \approx 120 W/m^2$$ and there is not 23 W/m^2 A<sub?A uncompensated by ED.
Now apart from the fact that this is NOT “Jan’s ‘proof’” but Ferenc’s explanation ( who many times is this now that I’ve mentioned it?) what is this
Another way of looking at this is of course to consider Jan’s ‘proof’ of the virial relation S_U + S_V = 3OLR/2 which set S_V = S_T/2 – E_D/10 as per M& Eqn. 9. Noting that E_U/E_D = 3/5 we then have S_U + S_T/2 – E_D/10 = 350.4 + 31.5 – 29.2 = 352.7
and why does $$\frac {E_U}{E_D} = \frac 3 5$$ when in both KT97 & FKT $$S_U \neq \frac 3 2 OLR$$? You need to go to M&M 04 to find out that OLRs are generally understated (in this case about 12W/m^2) because those early birds carried colour blind spectrometers that generally could not see IR at frequencies below $$400 cm-1$$
Sometimes, due to technical or engineering constraints, the spectral sensitivity of a detector or instrument design sets the spectral boundaries.
In fact if you to the archives or various papers you’ll see the $$400 cm-1$$ spectral limit is fairly consistent. The main purpose behind MM4 is to correct for that error. Already in OLR alone you have an error more than three times your 3.4 W/m^2 “cloud forcing and that misplaced 23W/m^2 AA is six time the cloud forcing.
I would be the first to agree that the fact that $$S_U = 2E_U$$ in both these papers is a fluke but that really doesn’t help us with any of the rest. It certainly doesn’t give me confidence that we can rely on it for the value of either K or F.
Now even Jan’s double negative typos are getting prescient (;-)
maybe I know you better than I know myself :- heaven forbid. 8)
• http://www.ecoengineers.com Steve Short
Jan #85
“I make E_U 199 W/^2 (or 238.5 -40) in this one and S_U 396 W/m^2 2 x E_U = 398 (or 397) which I think is in the ballpark. Its not a difference I would hang a career on.”
I’ll go along with the last sentence only. You are wrong otherwise. In fact K,T&F (2008) give 63.0 W/m^2 for S_T. It’s there is black and white in Table 2b in the 2nd last column as Net LW (denoted ‘This paper’). BTW, the other 3 studies cited give a bracketing range from 48.5 – 72.8 W/m^2.
Looks to me like you have simply picked your value of 40 W/m^2 for S_T out of your numerological hat again.
Given that M7 p211 clearly defines OLR = S_T + E_U then I make E-U = 238.5 – 63.0 = 175.5 W/m^2.
After all, a value of 63.0 W/m^2 is eminently reasonable for S_T given that M&M4 found 61 W/m^2 for the global value of S_T from the HARTCODE output. M&M4 also got an arithmetic mean of 69 and standard deviation of 13 W/m^2 for S_T. The whole set ranged from 22 through 112. This also makes your mystery value of 40 look a bit sick.
“Then also the amount in the atmospheric window (S_T) is 40W/m^2 the 63W/m^2 is made up of Kirchhoff’s law denying upward re-radiation of A_A of 23 W/m^2 + 40 W/m^2 S_T so its OLR – S_T = 238.5 – 40 = 197.5 W/m^2. The only thing that both papers agree on is that S_U=2E_U”
How can A_A (or even A-A/10) be as low as 23 W/m^2? According to M7 A_A = E_D by Kirchoff and by definition E_D = S_U – S_T (M7 p6) so we have from K,T&F (2008) E_D = 396 – 63 = 333 W/m^2. Thus A_A ~ 333 W/m^2. Therefore where do you get your statement above “….denying upward re-radiation of A_A of 23 W/m^2″? This makes nonsense of the general magnitude of A_A (or E_D)!
BTW, we also know from M7 Eqn 9 (page 7) that supposedly E_U/E-D = 3/5 therefore E_D = 5E-U/3 = 5 x 175.5/3 = 292.5. Thus once again there is no way A_A (or A-A/10) is as low as 23 W/m^2!
“The only thing there is reasonable agreement between sources they cite is that S_U approx 396 Wm^{-2}.”
Agreed.
“For arguments sake let’s say they don’t agree with the Virial I still don’t understand your issue with “negative cloud forcing” in this context.
What is this?
OLR – 2Su/3 gives 238.5 – (4 x 175.2/3) = 238.5 – 233.5 = +4.9 W/m^2
Neither M-7 nor K&T 97 or FKT08 relate F+K to SU in that way. I don’t understand what you are trying to say here. ”
Rubbish. M7 Eqn 5 (page 6) says E_U = F + K + P
Thus if P0= 0 and thus P = 0 as is usually the case then E_U = F + K.
Further, as I have quoted at least twice now but here goes yet again (!) M7 page 19:
“The OLRA − 2SU/3 ≈ − 15 W m-2 is a fairly good estimate of the global
average cloud forcing. The estimated β ≈ 0.6 is the required cloud cover (at
this level) to balance OLRA , which looks realistic. We believe that the β
parameter is governed by the maximum entropy principle, the system tries to convert as much SW radiation to LW radiation as possible, while obeying the 2OLR/(3 f ) = F0 + P0 condition. The cloud altitude, where the clear-sky OLRA = OLR = E_D depends only on the SW characteristics of the system (surface and cloud albedo, SW solar input) and alone, is a very important climate parameter.”
I don’t know why you still have such a problem with Miskolczi’s own text in M7?
Put simply – I happen to think that M Theory could well be very much less attractive if it too predicted a positive cloud forcing. I don’t think any genuine sceptics would have a problem with that proposition, do you?
Furthermore, I had pointed out in Steve #84: OLR = E_U + S_T in the bounded or semi-transparent atmosphere according to M Theory (M7 Section 4.2 Bounded atmosphere page 13). Thus E_U = OLR -S_T = 238.5 – 63.0 = 175.5.
This agrees very well with the 175.2 estimated via E_U = F + K.
I would say this further confirms an E_U of about 175 W/m^2, wouldn’t you?
“I don’t particularly think that K&T 97 or FKT08 quite have ST right (I for one think 63 W/m^2 is closer to the truth) but 40 W/m^2 is what they say for that.”
No K,T&F (2008) doesn’t say 40 W/m^2.
“Already in OLR alone you have an error more than three times your 3.4 W/m^2 “cloud forcing and that misplaced 23W/m^2 AA is six time the cloud forcing.”
Rubbish again. I don’t accept that because A_A does not = 23 W/m^2 as you claim. In fact even A_A (or E_D)/10 does not = 23 W/m^2. As I have shown above A_A = E_D = 333 W/m^2 therefore A_A/10 = 33 W/m^2. So there goes your virial fiddling up the spout.
Unless K,T&F (2008) is bedevilled by a circular logic to get estimates of F and K and you obviously haven’t demonstrated that yet – although I’d really like to see you put it in plain, logical, easy to follow, non-opaque English if possible, then the fact remains that they get 396 W/m^2 for S_U and 175.2 – 175.5 W/m^2 for E_U.
Bottom line is that in K,T&F (2008) S_U = 396 W/m^2 and E_U = 175.5 W/m^2 therefore 2E_U = 351 W/m^2 thus S_U does not equal 2E_U and so K,T&F (2008) definitely does not support Misckolczi’s virial relation.
This much and only this much we can agree on.
Other than that, most of your #85 post is pretty much your usual obscure, quasi-religious (‘only I have the received truth from on high’) numerological shuffling around of the goal posts as far as I can see.
• http://www.ecoengineers.com Steve Short
Jan #85
“I make E_U 199 W/^2 (or 238.5 -40) in this one and S_U 396 W/m^2 2 x E_U = 398 (or 397) which I think is in the ballpark. Its not a difference I would hang a career on.”
I’ll go along with the last sentence only. You are wrong otherwise. In fact K,T&F (2008) give 63.0 W/m^2 for S_T. It’s there is black and white in Table 2b in the 2nd last column as Net LW (denoted ‘This paper’). BTW, the other 3 studies cited give a bracketing range from 48.5 – 72.8 W/m^2.
Looks to me like you have simply picked your value of 40 W/m^2 for S_T out of your numerological hat again.
Given that M7 p211 clearly defines OLR = S_T + E_U then I make E-U = 238.5 – 63.0 = 175.5 W/m^2.
After all, a value of 63.0 W/m^2 is eminently reasonable for S_T given that M&M4 found 61 W/m^2 for the global value of S_T from the HARTCODE output. M&M4 also got an arithmetic mean of 69 and standard deviation of 13 W/m^2 for S_T. The whole set ranged from 22 through 112. This also makes your mystery value of 40 look a bit sick.
“Then also the amount in the atmospheric window (S_T) is 40W/m^2 the 63W/m^2 is made up of Kirchhoff’s law denying upward re-radiation of A_A of 23 W/m^2 + 40 W/m^2 S_T so its OLR – S_T = 238.5 – 40 = 197.5 W/m^2. The only thing that both papers agree on is that S_U=2E_U”
How can A_A (or even A-A/10) be as low as 23 W/m^2? According to M7 A_A = E_D by Kirchoff and by definition E_D = S_U – S_T (M7 p6) so we have from K,T&F (2008) E_D = 396 – 63 = 333 W/m^2. Thus A_A ~ 333 W/m^2. Therefore where do you get your statement above “….denying upward re-radiation of A_A of 23 W/m^2″? This makes nonsense of the general magnitude of A_A (or E_D)!
BTW, we also know from M7 Eqn 9 (page 7) that supposedly E_U/E-D = 3/5 therefore E_D = 5E-U/3 = 5 x 175.5/3 = 292.5. Thus once again there is no way A_A (or A-A/10) is as low as 23 W/m^2!
“The only thing there is reasonable agreement between sources they cite is that S_U \approx 396 Wm^{-2}.”
Agreed.
“For arguments sake let’s say they don’t agree with the Virial I still don’t understand your issue with “negative cloud forcing†in this context.
What is this?
OLR – 2Su/3 gives 238.5 – (4 x 175.2/3) = 238.5 – 233.5 = +4.9 W/m^2
Neither M-7 nor K&T 97 or FKT08 relate F+K to SU in that way. I don’t understand what you are trying to say here. ”
Rubbish. M7 Eqn 5 (page 6) says E_U = F + K + P
Thus if P0= 0 and thus P = 0 as is usually the case then E_U = F + K.
Further, as I have quoted at least twice now but here goes yet again (!) M7 page 19:
“The OLRA − 2SU/3 ≈ − 15 W m-2 is a fairly good estimate of the global
average cloud forcing. The estimated β ≈ 0.6 is the required cloud cover (at
this level) to balance OLRA , which looks realistic. We believe that the β
parameter is governed by the maximum entropy principle, the system tries to convert as much SW radiation to LW radiation as possible, while obeying the 2OLR/(3 f ) = F0 + P0 condition. The cloud altitude, where the clear-sky OLRA = OLR = E_D depends only on the SW characteristics of the system (surface and cloud albedo, SW solar input) and alone, is a very important climate parameter.”
I don’t know why you still have such a problem with Miskolczi’s own text in M7?
Put simply – I happen to think that M Theory could well be very much less attractive if it too predicted a positive cloud forcing. I don’t think any genuine sceptics would have a problem with that proposition, do you?
Furthermore, I had pointed out in Steve #84: OLR = E_U + S_T in the bounded or semi-transparent atmosphere according to M Theory (M7 Section 4.2 Bounded atmosphere page 13). Thus E_U = OLR -S_T = 238.5 – 63.0 = 175.5.
This agrees very well with the 175.2 estimated via E_U = F + K.
I would say this further confirms an E_U of about 175 W/m^2, wouldn’t you?
“I don’t particularly think that K&T 97 or FKT08 quite have ST right (I for one think 63 W/m^2 is closer to the truth) but 40 W/m^2 is what they say for that.”
No K,T&F (2008) doesn’t say 40 W/m^2.
“Already in OLR alone you have an error more than three times your 3.4 W/m^2 “cloud forcing and that misplaced 23W/m^2 AA is six time the cloud forcing.”
Rubbish again. I don’t accept that because A_A does not = 23 W/m^2 as you claim. In fact even A_A (or E_D)/10 does not = 23 W/m^2. As I have shown above A_A = E_D = 333 W/m^2 therefore A_A/10 = 33 W/m^2. So there goes your virial fiddling up the spout.
Unless K,T&F (2008) is bedevilled by a circular logic to get estimates of F and K and you obviously haven’t demonstrated that yet – although I’d really like to see you put it in plain, logical, easy to follow, non-opaque English if possible, then the fact remains that they get 396 W/m^2 for S_U and 175.2 – 175.5 W/m^2 for E_U.
Bottom line is that in K,T&F (2008) S_U = 396 W/m^2 and E_U = 175.5 W/m^2 therefore 2E_U = 351 W/m^2 thus S_U does not equal 2E_U and so K,T&F (2008) definitely does not support Misckolczi’s virial relation.
This much and only this much we can agree on.
Other than that, most of your #85 post is pretty much your usual obscure, quasi-religious (‘only I have the received truth from on high’) numerological shuffling around of the goal posts as far as I can see.
• Jan Pompe
Steve #86
In fact K,T&F (2008) give 63.0 W/m^2 for S_T. It’s there is black and white in Table 2b in the 2nd last column as Net LW (denoted ‘This paper’).
That says LW not what is passing through the window which is what S_T is you need to look at the cartoon to see how they’ve divided that up.
Looks to me like you have simply picked your value of 40 W/m^2 for S_T out of your numerological hat again.
Try and look at want the authors are actually trying to tell you instead of putting your own interpretation on it.
• Jan Pompe
Steve #86
In fact K,T&F (2008) give 63.0 W/m^2 for S_T. It’s there is black and white in Table 2b in the 2nd last column as Net LW (denoted ‘This paper’).
That says LW not what is passing through the window which is what S_T is you need to look at the cartoon to see how they’ve divided that up.
Looks to me like you have simply picked your value of 40 W/m^2 for S_T out of your numerological hat again.
Try and look at want the authors are actually trying to tell you instead of putting your own interpretation on it.
• Jan Pompe
Steve #86
OLR – 2Su/3 gives 238.5 – (4 x 175.2/3) = 238.5 – 233.5 = +4.9 W/m^2
Here you imply $$S_U = frac {4 E_U} 3 = frac {4 times 175.2} 3$$ somehow I don’t think this comes from M-7 but $$S_U = 2E_U$$ does.
The OLRA − 2SU/3 ≈ − 15 W m-2 is a fairly good estimate of the global
average cloud forcing. The estimated β ≈ 0.6 is the required cloud cover (at
this level) to balance OLRA , which looks realistic. We believe that the β
parameter is governed by the maximum entropy principle, the system tries to convert as much SW radiation to LW radiation as possible, while obeying the 2OLR/(3 f ) = F0 + P0 condition. The cloud altitude, where the clear-sky OLRA = OLR = E_D depends only on the SW characteristics of the system (surface and cloud albedo, SW solar input) and alone, is a very important climate parameter.
• Jan Pompe
Steve #86
OLR – 2Su/3 gives 238.5 – (4 x 175.2/3) = 238.5 – 233.5 = +4.9 W/m^2
Here you imply $$S_U = \frac {4 E_U} 3 = \frac {4 \times 175.2} 3$$ somehow I don’t think this comes from M-7 but $$S_U = 2E_U$$ does.
The OLRA − 2SU/3 ≈ − 15 W m-2 is a fairly good estimate of the global
average cloud forcing. The estimated β ≈ 0.6 is the required cloud cover (at
this level) to balance OLRA , which looks realistic. We believe that the β
parameter is governed by the maximum entropy principle, the system tries to convert as much SW radiation to LW radiation as possible, while obeying the 2OLR/(3 f ) = F0 + P0 condition. The cloud altitude, where the clear-sky OLRA = OLR = E_D depends only on the SW characteristics of the system (surface and cloud albedo, SW solar input) and alone, is a very important climate parameter.
• http://www.ecoengineers.com Steve Short
Jan #87
“That says LW not what is passing through the window which is what S_T is you need to look at the cartoon to see how they’ve divided that up.”
I agree it says 40 in the cartoon (Figure 1). But I think this is a mistake (typo)? This is a preprint remember.
If you look carefully at the cartoon (Figure 1) the total of F + K = 175 W/m^2. But above the clouds they have 169 + 30 = 199 departing (excluding their so called S-T of 40 ‘passing up through the clouds’)! Thus they do not actually have a balance above the clouds. If you subtract 175 from 199 you will get 24. Add 24 to 40 and you get 64. This was good enough for me. I simply assumed that, being a preprint they had stuffed-up the cartoon.
I also note that the cartoon has 396 for S-U leaving the surface and 333 for the A_A returning to the surface. Regardless of any arguments about whether A-A = E_D etc, this also suggests a net LW component of 63 W/m^2 is passing up through the clouds. So it is looking more and more like S_T = 63, n’est pas?
BTW, before my posting ( #84) I was also prudent enough to run a search on ’40′ and 40 W/m^2′ through the pdf. You will not find them anywhere. In other words other than in the cartoon there is not one single textual statement to suggest S_T = 40 W/m^2.
Thus I concluded (quite reasonably I think) that the value of 63 W/m^2 designated ‘Net LW’ in Figure 2b (in the company of other so-called ‘Net LW’ values from other studies) was the actual S_T. Presumably we agree this also closely similar to both the global value, arithmetic means ± one s.d. for S-T given in M&M4.
Jan #87
“Try and look at want the authors are actually trying to tell you instead of putting your own interpretation on it.”
Hmmmm- I can say here Jan is that, on the available evidence (as carefully explained above), and noting it is a preprint I think I have a significantly sounder basis for concluding that FKT (2008) is claiming a value 63.0 for S_T than you have for concluding it is claiming 40 W/m^2 (from a cartoon only).
So who do you really think rushed to judgement – me or you???
I’d really like to solve this S-T puzzle first before arguing with you at length about all the other stuff but, strangely enough to you perhaps yes, I do happen to think that IF AND ONLY IF:
S_U = 2E_U
then 2S_U/3 should =2x2E_U/3
= 4E_U/3
It is after all only just simple arithmetic!
• http://www.ecoengineers.com Steve Short
Jan #87
“That says LW not what is passing through the window which is what S_T is you need to look at the cartoon to see how they’ve divided that up.”
I agree it says 40 in the cartoon (Figure 1). But I think this is a mistake (typo)? This is a preprint remember.
If you look carefully at the cartoon (Figure 1) the total of F + K = 175 W/m^2. But above the clouds they have 169 + 30 = 199 departing (excluding their so called S-T of 40 ‘passing up through the clouds’)! Thus they do not actually have a balance above the clouds. If you subtract 175 from 199 you will get 24. Add 24 to 40 and you get 64. This was good enough for me. I simply assumed that, being a preprint they had stuffed-up the cartoon.
I also note that the cartoon has 396 for S-U leaving the surface and 333 for the A_A returning to the surface. Regardless of any arguments about whether A-A = E_D etc, this also suggests a net LW component of 63 W/m^2 is passing up through the clouds. So it is looking more and more like S_T = 63, n’est pas?
BTW, before my posting ( #84) I was also prudent enough to run a search on ’40′ and 40 W/m^2′ through the pdf. You will not find them anywhere. In other words other than in the cartoon there is not one single textual statement to suggest S_T = 40 W/m^2.
Thus I concluded (quite reasonably I think) that the value of 63 W/m^2 designated ‘Net LW’ in Figure 2b (in the company of other so-called ‘Net LW’ values from other studies) was the actual S_T. Presumably we agree this also closely similar to both the global value, arithmetic means ± one s.d. for S-T given in M&M4.
Jan #87
“Try and look at want the authors are actually trying to tell you instead of putting your own interpretation on it.”
Hmmmm- I can say here Jan is that, on the available evidence (as carefully explained above), and noting it is a preprint I think I have a significantly sounder basis for concluding that FKT (2008) is claiming a value 63.0 for S_T than you have for concluding it is claiming 40 W/m^2 (from a cartoon only).
So who do you really think rushed to judgement – me or you???
I’d really like to solve this S-T puzzle first before arguing with you at length about all the other stuff but, strangely enough to you perhaps yes, I do happen to think that IF AND ONLY IF:
S_U = 2E_U
then 2S_U/3 should =2x2E_U/3
= 4E_U/3
It is after all only just simple arithmetic!
• Jan Pompe
Steve #89
So who do you really think rushed to judgement – me or you???
You Steve it’s your impatience see Jan #81
as I mentioned to Steve I’m not to happy to get into a flap over something that might not yet be finished.
I was quite happy to leave it lie until the final comes out. Can you think of another instance where something similar has happened?
Apart from your impatience there are other issues.
$$E_U$$ is the radiation from the atmosphere clearly labelled as 169 + 30 =199 W/m^2 in the cartoon, not mentioned in the text either, but consistent with $$E_U = OLR – S_T$$.
The 40 W/m^2 is actually there in both papers and not mentioned in the text in either in and this paper really only discusses changes from the last one without spelling out how the did things.
Do you think they are such donkeys to trip over the same stone twice?
Since they don’t hold with M’s theory we can be fairly sure that they don’t think that $$A_A=E_D$$ they clearly label the absorbed upward ($$A_A$$) as 356 W/m^2 and downward ($$E_D$$) as 333 W/m^2 that’s a difference of 23W/m^2 which they’ve put in the wrong place. It is however counted among the absorbed not what is passing up through the clouds. It is consistent though with an $$S_T = 40 Wm^{-2}$$ and $$A_A neq E_D$$ but $$S_U – A_A = S_T$$.
They are consistent.
Personally I think it little more than an interesting curiosity that they have $$S_U approx 2E_U$$ . I wouldn’t be getting into a flap over it and I have no intention of doing so and I don’t particularly like seeing you waste so much time over this. I don’t expect to find compatibility of any sort with M7 in these papers and I consider the line you are following pointless.0
I’m sure you have better things to do.
• Jan Pompe
Steve #89
So who do you really think rushed to judgement – me or you???
You Steve it’s your impatience see Jan #81
as I mentioned to Steve I’m not to happy to get into a flap over something that might not yet be finished.
I was quite happy to leave it lie until the final comes out. Can you think of another instance where something similar has happened?
Apart from your impatience there are other issues.
$$E_U$$ is the radiation from the atmosphere clearly labelled as 169 + 30 =199 W/m^2 in the cartoon, not mentioned in the text either, but consistent with $$E_U = OLR – S_T$$.
The 40 W/m^2 is actually there in both papers and not mentioned in the text in either in and this paper really only discusses changes from the last one without spelling out how the did things.
Do you think they are such donkeys to trip over the same stone twice?
Since they don’t hold with M’s theory we can be fairly sure that they don’t think that $$A_A=E_D$$ they clearly label the absorbed upward ($$A_A$$) as 356 W/m^2 and downward ($$E_D$$) as 333 W/m^2 that’s a difference of 23W/m^2 which they’ve put in the wrong place. It is however counted among the absorbed not what is passing up through the clouds. It is consistent though with an $$S_T = 40 Wm^{-2}$$ and $$A_A \neq E_D$$ but $$S_U – A_A = S_T$$.
They are consistent.
Personally I think it little more than an interesting curiosity that they have $$S_U \approx 2E_U$$ . I wouldn’t be getting into a flap over it and I have no intention of doing so and I don’t particularly like seeing you waste so much time over this. I don’t expect to find compatibility of any sort with M7 in these papers and I consider the line you are following pointless.0
I’m sure you have better things to do.
• http://www.ecoengineers.com Steve Short
You Steve it’s your impatience see Jan #81
” as I mentioned to Steve I’m not to happy to get into a flap over something that might not yet be finished.”
In #81 you prove zilch. I think it is you who has impatiently accepted the cartoon of a preprint at the expense of the paper itself.
Jan #90
“E_U is the radiation from the atmosphere clearly labelled as 169 + 30 =199 W/m^2 in the cartoon, not mentioned in the text either, but consistent with E_U = OLR – S_T.”
Hang on. In FKT (2008) Fig. 2b OLR = 239 and S_T = 63 therefore E-U = 176 W/m^2.
The cartoon clearly shows F0 = 341 – 79 -23 = 238
This matches the OLR. If OLR – S_T = 239 – 40 = 199 = Eu = F+ K then (PLEASE!) how come F + K adds up to 79 + (17 + 80) = 176 W.m^2? Your logic error #1.
In a way Jan it is you who really has the math problem because you just can’t abide non-radiative terms and so you can’t even live with non LW radiative equalities like E_U = F + K.
Tell me, if E_U really is 199 W/m^2 as you say then where does your extra 23 W/m^2 (in E_U; over and above F + K) come from? Tell me that. What exactly is its nature? You need to explain that. If you can’t (or won’t) this is your logic error #2?
“Personally I think it little more than an interesting curiosity that they have S_U approx 2E_U . ”
They don’t. It is your wishful thinking. You may think they do by your reading of a partly flawed cartoon which has an obvious inbalance above the clouds (based on F + K) but there is no inbalance in Fig. 2b, nor ironically is there any inbalance in the incoming SW part of the cartoon!
“Since they don’t hold with M’s theory we can be fairly sure that they don’t think that A_A=E_D they clearly label the absorbed upward (A_A) as 356 W/m^2 and downward (E_D) as 333 W/m^2 that’s a difference of 23W/m^2 which they’ve put in the wrong place. It is however counted among the absorbed not what is passing up through the clouds. It is consistent though with an S_T = 40 Wm^{-2} and A_A neq E_D but S_U – A_A = S_T.
They are consistent.”
Well no, actually they are not. I agree they have A_A as 356 and E_D as 333.
BUT that is still clearly a graphical problem for them because above the cloud they still have a heat flux inbalance. Furthermore, A_A = 356 does not agree with the content of data Table. 5b.
If not then need to say what the ***** is ‘Net LW’ meant to mean? Where does the 63 W/m^2 come from? What does it signify? Explain me that as well….! Your logic error #3.
“Do you think they are such donkeys to trip over the same stone twice? ”
No, I am more inclined to think your interpretation is riddled with logical errors (as identified above). Not real good at constantly juggling a logically consistent dataset are you. I’m thrashing Excel about 5 hours per day.
Thus I am unconvinced by your old blogster’s vague hand waving references to past consistency by Kiehl et al. and more inclined to think that this is simply a graphical stuff-up by the junior author in the cartoon only. Junior authors do tend to trip over the same stone especially if they are given control over something like a cartoon only. Maybe Kiehl has been too lazy to check this – he is fairly arrogant (having personally seen him on TV in Colorado).
Yes, I do have better things to do. Check out Takahashi (2008). Web reference previously given. Stuff like delta (H_L + F)/delta T_S = 9/4 and delata H_L /delta T_S = 5/4 etc., viz:
“The inter-model di fferences in the rate of change in SWabs can not be solely accounted for by di fferences in the radiative transfer schemes or in the modeled changes in the global water vapor content,which suggests that subtler aspects of the change in the water vapor distribution might be important for the change in SWabs. However, the results from the RTMIP project suggest that climate models generally underestimate the change in the clear-sky SWabs by water vapor relative to detailed line-by- line calculations. In the light of the results presented here, this would suggest that the climate models might be overestimating the rate of increase in the global hydrological cycle with global warming.”
• http://www.ecoengineers.com Steve Short
You Steve it’s your impatience see Jan #81
” as I mentioned to Steve I’m not to happy to get into a flap over something that might not yet be finished.”
In #81 you prove zilch. I think it is you who has impatiently accepted the cartoon of a preprint at the expense of the paper itself.
Jan #90
“E_U is the radiation from the atmosphere clearly labelled as 169 + 30 =199 W/m^2 in the cartoon, not mentioned in the text either, but consistent with E_U = OLR – S_T.”
Hang on. In FKT (2008) Fig. 2b OLR = 239 and S_T = 63 therefore E-U = 176 W/m^2.
The cartoon clearly shows F0 = 341 – 79 -23 = 238
This matches the OLR. If OLR – S_T = 239 – 40 = 199 = Eu = F+ K then (PLEASE!) how come F + K adds up to 79 + (17 + 80) = 176 W.m^2? Your logic error #1.
In a way Jan it is you who really has the math problem because you just can’t abide non-radiative terms and so you can’t even live with non LW radiative equalities like E_U = F + K.
Tell me, if E_U really is 199 W/m^2 as you say then where does your extra 23 W/m^2 (in E_U; over and above F + K) come from? Tell me that. What exactly is its nature? You need to explain that. If you can’t (or won’t) this is your logic error #2?
“Personally I think it little more than an interesting curiosity that they have S_U \approx 2E_U . ”
They don’t. It is your wishful thinking. You may think they do by your reading of a partly flawed cartoon which has an obvious inbalance above the clouds (based on F + K) but there is no inbalance in Fig. 2b, nor ironically is there any inbalance in the incoming SW part of the cartoon!
“Since they don’t hold with M’s theory we can be fairly sure that they don’t think that A_A=E_D they clearly label the absorbed upward (A_A) as 356 W/m^2 and downward (E_D) as 333 W/m^2 that’s a difference of 23W/m^2 which they’ve put in the wrong place. It is however counted among the absorbed not what is passing up through the clouds. It is consistent though with an S_T = 40 Wm^{-2} and A_A \neq E_D but S_U – A_A = S_T.
They are consistent.”
Well no, actually they are not. I agree they have A_A as 356 and E_D as 333.
BUT that is still clearly a graphical problem for them because above the cloud they still have a heat flux inbalance. Furthermore, A_A = 356 does not agree with the content of data Table. 5b.
If not then need to say what the ***** is ‘Net LW’ meant to mean? Where does the 63 W/m^2 come from? What does it signify? Explain me that as well….! Your logic error #3.
“Do you think they are such donkeys to trip over the same stone twice? ”
No, I am more inclined to think your interpretation is riddled with logical errors (as identified above). Not real good at constantly juggling a logically consistent dataset are you. I’m thrashing Excel about 5 hours per day.
Thus I am unconvinced by your old blogster’s vague hand waving references to past consistency by Kiehl et al. and more inclined to think that this is simply a graphical stuff-up by the junior author in the cartoon only. Junior authors do tend to trip over the same stone especially if they are given control over something like a cartoon only. Maybe Kiehl has been too lazy to check this – he is fairly arrogant (having personally seen him on TV in Colorado).
Yes, I do have better things to do. Check out Takahashi (2008). Web reference previously given. Stuff like delta (H_L + F)/delta T_S = 9/4 and delata H_L /delta T_S = 5/4 etc., viz:
“The inter-model di fferences in the rate of change in SWabs can not be solely accounted for by di fferences in the radiative transfer schemes or in the modeled changes in the global water vapor content,which suggests that subtler aspects of the change in the water vapor distribution might be important for the change in SWabs. However, the results from the RTMIP project suggest that climate models generally underestimate the change in the clear-sky SWabs by water vapor relative to detailed line-by- line calculations. In the light of the results presented here, this would suggest that the climate models might be overestimating the rate of increase in the global hydrological cycle with global warming.”
• Jan Pompe
Steve #91
In #81 you prove zilch. I think it is you who has impatiently accepted the cartoon of a preprint at the expense of the paper itself.
Steve sorry but you are the one who claimed to find a mistake in it.
Hang on. In FKT (2008) Fig. 2b OLR = 239 and S_T = 63 therefore E-U = 176 W/m^2.
The cartoon clearly shows F0 = 341 – 79 -23 = 238
I give up have a good life Steve.
• Jan Pompe
Steve #91
In #81 you prove zilch. I think it is you who has impatiently accepted the cartoon of a preprint at the expense of the paper itself.
Steve sorry but you are the one who claimed to find a mistake in it.
Hang on. In FKT (2008) Fig. 2b OLR = 239 and S_T = 63 therefore E-U = 176 W/m^2.
The cartoon clearly shows F0 = 341 – 79 -23 = 238
I give up have a good life Steve.
• http://www.ecoengineers.com Steve Short
Hot off the presses, the pre-print version of K,T&F (2008) has the following numbers for CERES May 2000 – May 2004 (all from Table 5b):
Fo = 239.4 W/m^2
OLR = 238.5 = F0 no problems there
F = 78.2 consistent with known range of SW tau
K = 97.0 consistent with literature
S_T = 63.0 (allowing for error in cartoon but correctly given in Table 5b)
S_U = 396 no problems there
E_U = F + K = 175.2 = OLR – S_T = 175.5 down about 20 W/m^2 on K&T (1997)
A_A = 333 = S_U – S_T no problems there
Thus
TauA = ln (S_T/S_U) = 1.838 consistent with Miskolczi
TA = 1-A = exp(-tauA) = 0.159 consistent with Miskolczi
OLR/S_U = 238.5/396 = 0.602 = 3/5 i.e. 10% away from Miskolczi General Solution (OLR /S_U = (3 + 2TA)/5 = 0.664). Hmmm could mean a little problem with the surface temperature discontinuity perhaps?
But the one thing that markedly doesn’t agree with Miskolczi is:
S_U not equal to 2E_U the so-called virial relation, i.e. here Su/E_U = 396/238.5 = 1.660 ~ 5/3
Thus OLR not even equal to 3E_U-E_D. However, if the books are cooked by adding 20 W/m^2 to BOTH E_U AND to E_D we get 3×199 – 356 = 241 ~238
But this is one of those nasty Catch 22′s – can’t simultaneously add 20 W/m^2 to BOTH E_U AND E_D ……..otherwise Kirchoff (A_A = E_D) flies out the window too! Little problem of an overconstrained system I’d say, what with S_U meant to =2E_U and A_A meant to =E_D BOTH AT THE SAME TIME.
TA DAH!
Remember all that KE/PE ratio stuff back in July, August and September between Neal King, Jan and Nick Stokes (Pliny)? I’m sure Franko does! Strong sense of deja vu building up here. No wonder Jan’s blood pressure is up. Maybe when some things (like matters of ego) are at stake a certain someone might even consider it worthwhile shafting Ferenc himself.
Someone be really chewing their lip over the ‘problem of the missing 20 W/m^2′. Of course finding that pesky extra 20 W/M^2 needed up there in (say) a 3rd component of K or ….P is just out of the question. Someone else already came up with that solution long ago, so ergo baby, it just didn’t count fer nuthin (;-)
Tragicomedy or just farce?
• http://www.ecoengineers.com Steve Short
Hot off the presses, the pre-print version of K,T&F (2008) has the following numbers for CERES May 2000 – May 2004 (all from Table 5b):
Fo = 239.4 W/m^2
OLR = 238.5 = F0 no problems there
F = 78.2 consistent with known range of SW tau
K = 97.0 consistent with literature
S_T = 63.0 (allowing for error in cartoon but correctly given in Table 5b)
S_U = 396 no problems there
E_U = F + K = 175.2 = OLR – S_T = 175.5 down about 20 W/m^2 on K&T (1997)
A_A = 333 = S_U – S_T no problems there
Thus
TauA = ln (S_T/S_U) = 1.838 consistent with Miskolczi
TA = 1-A = exp(-tauA) = 0.159 consistent with Miskolczi
OLR/S_U = 238.5/396 = 0.602 = 3/5 i.e. 10% away from Miskolczi General Solution (OLR /S_U = (3 + 2TA)/5 = 0.664). Hmmm could mean a little problem with the surface temperature discontinuity perhaps?
But the one thing that markedly doesn’t agree with Miskolczi is:
S_U not equal to 2E_U the so-called virial relation, i.e. here Su/E_U = 396/238.5 = 1.660 ~ 5/3
Thus OLR not even equal to 3E_U-E_D. However, if the books are cooked by adding 20 W/m^2 to BOTH E_U AND to E_D we get 3×199 – 356 = 241 ~238
But this is one of those nasty Catch 22′s – can’t simultaneously add 20 W/m^2 to BOTH E_U AND E_D ……..otherwise Kirchoff (A_A = E_D) flies out the window too! Little problem of an overconstrained system I’d say, what with S_U meant to =2E_U and A_A meant to =E_D BOTH AT THE SAME TIME.
TA DAH!
Remember all that KE/PE ratio stuff back in July, August and September between Neal King, Jan and Nick Stokes (Pliny)? I’m sure Franko does! Strong sense of deja vu building up here. No wonder Jan’s blood pressure is up. Maybe when some things (like matters of ego) are at stake a certain someone might even consider it worthwhile shafting Ferenc himself.
Someone be really chewing their lip over the ‘problem of the missing 20 W/m^2′. Of course finding that pesky extra 20 W/M^2 needed up there in (say) a 3rd component of K or ….P is just out of the question. Someone else already came up with that solution long ago, so ergo baby, it just didn’t count fer nuthin (;-)
Tragicomedy or just farce?
• http://www.ecoengineers.com Steve Short
Typo in my #93 above
Should read: S_U not equal to 2E_U the so-called virial relation, i.e. here S_U/E_U = 396/175 = 2.263 ~9/4
What I find amazing about the T,F&K 08 dataset is that of we accept S_T = 63 W/m^2 which BTW is required to get M’s tauA = 1.838 i.e. nearly spot on to his 1.841 for a General Solution AND we force A_A = E_D = 333 on the grounds that:
(1) the cartoon has a mistake; and that
(2) Miskolczi knows his surface radiative balance science really well (all my reading supports that),
then we get S_U/E_U = 2.263 i.e. almost exactly 9/4.
However, if we accept an S_T of only 40 W/m^2 this puts LW tauA at ln(-40/396) = 2.293 but it does put S_U = 396/195 = 2.031 ~2.00 within error.
Putting the possible (single) cartoon error aside, the outcome of T,F&K 08) seems to be unequivocally that you can’t have the Kirchoff A_A = E_D AND Virial S_U = 2E_U AND a LW tauA ~1.85 all at the same time.
So, bottom line Jan would seem to want to have S_U = 2E_U at the expense of getting a LW tauA of 2.293 i.e. a long way from M’s ~1.85 as well as junking Kirchoff A_A = E_D.
I happen to think that that the so-called S_U = 2E_U virial relation is probably the least important part of Miskolczi Theory. A lot of other stuff in M Theory comes good if one is prepared to junk that relationship as nothing more than empirically approximately correct.
After all, E_U is essentially comprised of a combination of SW absorption, sensible heat and latent heat fluxes – all linked to S_U via a quite complex system involving cloud density and altitude, aerosol concentrations and types, modes and rates of generation of clouds and aerosols etc etc etc.
With respect to Miskolczi Theory I am much more comfortable with an 8% error in the S_U=2E_U relation over only a 4 year period than I am with:
a 7% error in A_A = E_D PLUS a 25% error in mean LW tauA.
• http://www.ecoengineers.com Steve Short
Typo in my #93 above
Should read: S_U not equal to 2E_U the so-called virial relation, i.e. here S_U/E_U = 396/175 = 2.263 ~9/4
What I find amazing about the T,F&K 08 dataset is that of we accept S_T = 63 W/m^2 which BTW is required to get M’s tauA = 1.838 i.e. nearly spot on to his 1.841 for a General Solution AND we force A_A = E_D = 333 on the grounds that:
(1) the cartoon has a mistake; and that
(2) Miskolczi knows his surface radiative balance science really well (all my reading supports that),
then we get S_U/E_U = 2.263 i.e. almost exactly 9/4.
However, if we accept an S_T of only 40 W/m^2 this puts LW tauA at ln(-40/396) = 2.293 but it does put S_U = 396/195 = 2.031 ~2.00 within error.
Putting the possible (single) cartoon error aside, the outcome of T,F&K 08) seems to be unequivocally that you can’t have the Kirchoff A_A = E_D AND Virial S_U = 2E_U AND a LW tauA ~1.85 all at the same time.
So, bottom line Jan would seem to want to have S_U = 2E_U at the expense of getting a LW tauA of 2.293 i.e. a long way from M’s ~1.85 as well as junking Kirchoff A_A = E_D.
I happen to think that that the so-called S_U = 2E_U virial relation is probably the least important part of Miskolczi Theory. A lot of other stuff in M Theory comes good if one is prepared to junk that relationship as nothing more than empirically approximately correct.
After all, E_U is essentially comprised of a combination of SW absorption, sensible heat and latent heat fluxes – all linked to S_U via a quite complex system involving cloud density and altitude, aerosol concentrations and types, modes and rates of generation of clouds and aerosols etc etc etc.
With respect to Miskolczi Theory I am much more comfortable with an 8% error in the S_U=2E_U relation over only a 4 year period than I am with:
a 7% error in A_A = E_D PLUS a 25% error in mean LW tauA.
• Alex Harvey
Steve #94:
With respect to Miskolczi Theory I am much more comfortable with an 8% error in the S_U=2E_U relation over only a 4 year period than I am with: a 7% error in A_A = E_D PLUS a 25% error in mean LW tauA.
What I would really love to see would be a Ferenc Miskolczi audit of the TFK08 energy budget Steve McIntyre-style. SM, with all his experience in obtaining data from difficult places, might even be able to assist.
• Alex Harvey
Steve #94:
With respect to Miskolczi Theory I am much more comfortable with an 8% error in the S_U=2E_U relation over only a 4 year period than I am with: a 7% error in A_A = E_D PLUS a 25% error in mean LW tauA.
What I would really love to see would be a Ferenc Miskolczi audit of the TFK08 energy budget Steve McIntyre-style. SM, with all his experience in obtaining data from difficult places, might even be able to assist.
• Alex Harvey
I would encourage those with suitably-sized brains to consider the recent publication of an article Pelkowski et al. 2008:
ABSTRACT
We apply the semi-gray model of our previous paper to the particular case of the Earth’s atmosphere, in order to illustrate quantitatively the inverse problem associated with the direct problem we dealt with before. From given climatological values of the atmosphere’s spherical albedo and transmittance for visible radiation, the single-scattering albedo and the optical thickness in the visible are inferred, while the infrared optical thickness is deduced for given global average surface temperature. Eventually, temperature distributions in terms of the infrared optical depth will be shown for a terrestrial atmosphere assumed to be semi-gray and, locally, in radiative and thermodynamic equilibrium.
Pelkowski, J.; Chevallier, L.; Rutily, B.; Titaud, O. 2008: Exact results in modeling planetary atmospheres-III The general theory applied to the Earth’s semi-gray atmosphere, JQSRT.
• Alex Harvey
I would encourage those with suitably-sized brains to consider the recent publication of an article Pelkowski et al. 2008:
ABSTRACT
We apply the semi-gray model of our previous paper to the particular case of the Earth’s atmosphere, in order to illustrate quantitatively the inverse problem associated with the direct problem we dealt with before. From given climatological values of the atmosphere’s spherical albedo and transmittance for visible radiation, the single-scattering albedo and the optical thickness in the visible are inferred, while the infrared optical thickness is deduced for given global average surface temperature. Eventually, temperature distributions in terms of the infrared optical depth will be shown for a terrestrial atmosphere assumed to be semi-gray and, locally, in radiative and thermodynamic equilibrium.
Pelkowski, J.; Chevallier, L.; Rutily, B.; Titaud, O. 2008: Exact results in modeling planetary atmospheres-III The general theory applied to the Earth’s semi-gray atmosphere, JQSRT.
• http://www.ecoengineers.com Steve Short
Alex #85
“What I would really love to see would be a Ferenc Miskolczi audit of the TFK08 energy budget Steve McIntyre-style.”
I heartily agree. The M&M04 and M7 papers have concentrated our minds on the overall mechanics of the Earth’s climate system like no others. I am convinced that somewhere in there is the beginning of a great idea.
We are still learning much about how the Earth’s climate operates and if anyone needed a proof the obvious heat flux balance error of about 24 W/m^2 ‘above the clouds’ in TFK08 while at the same time claiming a net surface absorption of 0.9 W/m^2 is one such.
Miskolczi Theory deserves to be a work in vigorous progress, not a church with a single high priest.
I welcome such a timely audit by Ferenc. It would also help to clarify for us his present views.
• http://www.ecoengineers.com Steve Short
Alex #85
“What I would really love to see would be a Ferenc Miskolczi audit of the TFK08 energy budget Steve McIntyre-style.”
I heartily agree. The M&M04 and M7 papers have concentrated our minds on the overall mechanics of the Earth’s climate system like no others. I am convinced that somewhere in there is the beginning of a great idea.
We are still learning much about how the Earth’s climate operates and if anyone needed a proof the obvious heat flux balance error of about 24 W/m^2 ‘above the clouds’ in TFK08 while at the same time claiming a net surface absorption of 0.9 W/m^2 is one such.
Miskolczi Theory deserves to be a work in vigorous progress, not a church with a single high priest.
I welcome such a timely audit by Ferenc. It would also help to clarify for us his present views.
• jae
“I welcome such a timely audit by Ferenc. It would also help to clarify for us his present views.”
Me, too. Methinks you may be creating strawpeople.
• jae
“I welcome such a timely audit by Ferenc. It would also help to clarify for us his present views.”
Me, too. Methinks you may be creating strawpeople.
• Alex Harvey
Responding to my own #96, cringing as I re-read it, I trust the ‘brainsize’ remark was understood to be a joke at my own expense, and no one else’s.
• Alex Harvey
Responding to my own #96, cringing as I re-read it, I trust the ‘brainsize’ remark was understood to be a joke at my own expense, and no one else’s.
• Nick Stokes
Steve #97
There’s no typo in Fig 1. Nor would you expect one – this stuff has been thought about for a long time, and although a preprint, this ms has been reviewed. You’re forgetting that, as well as the 78 W/m2 SW absorbed, and the 17+80 K, there is a nett absorption of 396-333=23 W/m2 LW. Total 198, which, with rounding, balances the 199 W/m2 upward IR.
And yes, I did register as Pliny at CA.
• Nick Stokes
Steve #97
There’s no typo in Fig 1. Nor would you expect one – this stuff has been thought about for a long time, and although a preprint, this ms has been reviewed. You’re forgetting that, as well as the 78 W/m2 SW absorbed, and the 17+80 K, there is a nett absorption of 396-333=23 W/m2 LW. Total 198, which, with rounding, balances the 199 W/m2 upward IR.
And yes, I did register as Pliny at CA.
• http://www.ecoengineers.com Steve Short
Nick #100
“….You’re forgetting that, as well as the 78 W/m2 SW absorbed, and the 17+80 K, there is a nett absorption of 396-333=23 W/m2 LW. ”
Sorry, but I get for 396 – 333 some 63 w/m^2 (;-) However, being reasonable, I guess you probably meant 356 – 333 = 23 W/m^2? So there is still some 23 W/m^2 left over from the fact that A_A does not equal E-D (in M parlance) which passes up through the clouds (and clearly contributes to the OLR)?
Given that no-one can label each little bit of LW IR (from BOA) it seems to me that S_T is still then 40 + 23 = 63 W/m^2 and hence tauLW = -ln (63/396) = 1.838? As you may have noticed Jan was insisting S_T = 40 W/m^2.
I’d also be interested in your comment about the difference between the sum of SWabs + sensible + latent = 78 + 17 + 80 = 175 W/m^2 and the 169 W/m^2 contributing to the OLR i.e. this extra 6 W/m^2? Is that why the LW IR passing from the clouds to the OLR is shown as 30 (~ 23 + 6)?
If so that would tend to make a true S_T neither 63 nor 40 but 40 + 23 – 6 = 57 W/m^2. This would suggest the surface to TOA tauLW = – ln (57/396) = 1.938, n’est pas?
This is a bit like fishing around inside a good spaghetti bolognaise!
• http://www.ecoengineers.com Steve Short
Nick #100
“….You’re forgetting that, as well as the 78 W/m2 SW absorbed, and the 17+80 K, there is a nett absorption of 396-333=23 W/m2 LW. ”
Sorry, but I get for 396 – 333 some 63 w/m^2 (;-) However, being reasonable, I guess you probably meant 356 – 333 = 23 W/m^2? So there is still some 23 W/m^2 left over from the fact that A_A does not equal E-D (in M parlance) which passes up through the clouds (and clearly contributes to the OLR)?
Given that no-one can label each little bit of LW IR (from BOA) it seems to me that S_T is still then 40 + 23 = 63 W/m^2 and hence tauLW = -ln (63/396) = 1.838? As you may have noticed Jan was insisting S_T = 40 W/m^2.
I’d also be interested in your comment about the difference between the sum of SWabs + sensible + latent = 78 + 17 + 80 = 175 W/m^2 and the 169 W/m^2 contributing to the OLR i.e. this extra 6 W/m^2? Is that why the LW IR passing from the clouds to the OLR is shown as 30 (~ 23 + 6)?
If so that would tend to make a true S_T neither 63 nor 40 but 40 + 23 – 6 = 57 W/m^2. This would suggest the surface to TOA tauLW = – ln (57/396) = 1.938, n’est pas?
This is a bit like fishing around inside a good spaghetti bolognaise!
• http://www.ecoengineers.com Steve Short
jae #98
“Methinks you may be creating strawpeople.”
Heaven forbid! When two or more strawpeople get together they are liable to make hayseeds while the sun shines.
• http://www.ecoengineers.com Steve Short
jae #98
“Methinks you may be creating strawpeople.”
Heaven forbid! When two or more strawpeople get together they are liable to make hayseeds while the sun shines.
• jan pompe
Nick #100
There’s no typo in Fig 1. Nor would you expect one – this stuff has been thought about for a long time, and although a preprint, this ms has been reviewed.
I agree 100%
• jan pompe
Nick #100
There’s no typo in Fig 1. Nor would you expect one – this stuff has been thought about for a long time, and although a preprint, this ms has been reviewed.
I agree 100%
• Nick Stokes
Steve,
“Given that no-one can label each little bit of LW IR (from BOA) it seems to me that S_T is still then 40 + 23 = 63 W/m^2″
You can identify the LW by frequency. The 40 W/m2 is in the 8-13 micron atmospheric window, and shows in the spectrum as coming from ground temp. The 23 (yes, I meant 356, thanks) is mostly in other bands; you can, with more difficulty, say something about it from the spectrum. But it isn’t to be included in S_T.
I think the arithmetic goes like this – there’s a total of 199 (198) W/m2 added to the atmosphere (clouds) plus air, including fluxes from below, and this balances the total upward emission. The reason that that is split into 169+30 is to distinguish what is emitted by clouds (30) and by air (169). These fluxes are seen differently by the satellites. But they are part of the same budget.
• Nick Stokes
Steve,
“Given that no-one can label each little bit of LW IR (from BOA) it seems to me that S_T is still then 40 + 23 = 63 W/m^2″
You can identify the LW by frequency. The 40 W/m2 is in the 8-13 micron atmospheric window, and shows in the spectrum as coming from ground temp. The 23 (yes, I meant 356, thanks) is mostly in other bands; you can, with more difficulty, say something about it from the spectrum. But it isn’t to be included in S_T.
I think the arithmetic goes like this – there’s a total of 199 (198) W/m2 added to the atmosphere (clouds) plus air, including fluxes from below, and this balances the total upward emission. The reason that that is split into 169+30 is to distinguish what is emitted by clouds (30) and by air (169). These fluxes are seen differently by the satellites. But they are part of the same budget.
• http://www.ecoengineers.com Steve Short
All good and clear. Thank you.
But what happens to the 6 W/m^2 discrepancy between the 169 W/m^2 emitted upwards by air above the clouds and the total of SWabs + thermals + latent heat = 78 + 17 + 80 = 175 W/m^2?
Is this included in the 30 W/m^2 radiated upwards by clouds and if so, why?
• http://www.ecoengineers.com Steve Short
All good and clear. Thank you.
But what happens to the 6 W/m^2 discrepancy between the 169 W/m^2 emitted upwards by air above the clouds and the total of SWabs + thermals + latent heat = 78 + 17 + 80 = 175 W/m^2?
Is this included in the 30 W/m^2 radiated upwards by clouds and if so, why?
• Nick Stokes
Steve,
No, it’s all aggregated. The 6 W/m2 in your sum is the difference between the 30 W/m2 up from clouds, and the 23 (356-333) difference in up/down LW. But there’s no reason to associate these numbers particularly. The 23 is just a contribution to the 198 coming in, and the 30 is just a part of the 199 going out.
• Nick Stokes
Steve,
No, it’s all aggregated. The 6 W/m2 in your sum is the difference between the 30 W/m2 up from clouds, and the 23 (356-333) difference in up/down LW. But there’s no reason to associate these numbers particularly. The 23 is just a contribution to the 198 coming in, and the 30 is just a part of the 199 going out.
• Geoff Sherrington
Re Alex #96,
I cannot comprehend the purpose of the word “Eventually” in the last line of the Pelkowski extract. Can you illuminate? It is not a customary word in a scientific paper used this way.
How is the solution to linear algebra going among the regular posters?
• Geoff Sherrington
Re Alex #96,
I cannot comprehend the purpose of the word “Eventually” in the last line of the Pelkowski extract. Can you illuminate? It is not a customary word in a scientific paper used this way.
How is the solution to linear algebra going among the regular posters?
• http://www.ecoengineers.com Steve Short
Nick Stokes #100, #104, #106
If as soundly based as it appears this (TFK08) is then a fairly severe blow for Miskolczi Theory.
It means that a 4 year mean tauA = 2.29 some 22% away from 1.87, that A_A differs from E_D by about 7%, and E_U does not really equal F+K+P (other than approximately) because S_U can only be made to =E_U by means of the use of the emission/back radiation difference between A_A and E_D. Any claim that there is a ‘virial relation ‘ based on a fixed KE/PE = -2 ratio that supports an atmospheric S_U = 2E_U then becomes IMO a hollow claim.
Is there a ‘superglue’ to stop the M pack of cards collapsing?
• http://www.ecoengineers.com Steve Short
Nick Stokes #100, #104, #106
If as soundly based as it appears this (TFK08) is then a fairly severe blow for Miskolczi Theory.
It means that a 4 year mean tauA = 2.29 some 22% away from 1.87, that A_A differs from E_D by about 7%, and E_U does not really equal F+K+P (other than approximately) because S_U can only be made to =E_U by means of the use of the emission/back radiation difference between A_A and E_D. Any claim that there is a ‘virial relation ‘ based on a fixed KE/PE = -2 ratio that supports an atmospheric S_U = 2E_U then becomes IMO a hollow claim.
Is there a ‘superglue’ to stop the M pack of cards collapsing?
• Nick Stokes
Steve #108
Well, I’ve never been a fan of M theory. TFK08 is not so radically different from K&T97, as their section “Intent of article” explains. When the theory in M theory started to look wobbly, M and Z fell back on a claim that it was empirically substantiated, but the empirical claims were not described at publication level and had no support from actual radiation measurements, relying instead on Hartcode modelling. There is a lot of real empirical information out there.
• Nick Stokes
Steve #108
Well, I’ve never been a fan of M theory. TFK08 is not so radically different from K&T97, as their section “Intent of article” explains. When the theory in M theory started to look wobbly, M and Z fell back on a claim that it was empirically substantiated, but the empirical claims were not described at publication level and had no support from actual radiation measurements, relying instead on Hartcode modelling. There is a lot of real empirical information out there.
• jae
“but the empirical claims were not described at publication level and had no support from actual radiation measurements, relying instead on Hartcode modelling. There is a lot of real empirical information out there.”
?? I don’t think that is correct. SOME is based on Hartcode, MOST is from radiosonde data, AFIK.
• jae
“but the empirical claims were not described at publication level and had no support from actual radiation measurements, relying instead on Hartcode modelling. There is a lot of real empirical information out there.”
?? I don’t think that is correct. SOME is based on Hartcode, MOST is from radiosonde data, AFIK.
• jae
Nick: I’m kinda shocked by your statements. Have you actually read M’s works?
• jae
Nick: I’m kinda shocked by your statements. Have you actually read M’s works?
• Nick Stokes
jae Yes, of course I’ve read M’s papers. Probably more than anyone here (do you want to talk about Appendix B?). Anyway, enough to know the empirical data that he uses. The TIGR radiosonde data includes pressure, temperature, and various gas concentrations. There are no measurements of radiation.
• Nick Stokes
jae Yes, of course I’ve read M’s papers. Probably more than anyone here (do you want to talk about Appendix B?). Anyway, enough to know the empirical data that he uses. The TIGR radiosonde data includes pressure, temperature, and various gas concentrations. There are no measurements of radiation.
• jan pompe
Nick #112
The TIGR radiosonde data includes pressure, temperature, and various gas concentrations. There are no measurements of radiation.
So do doubt HARTCODE’s ability to convert that radiosonde data to radiation data?
It has been pretty well validated as a simple web search will reveal and it is one of the ways the satellite instrument calibration is checked not to mention ground based instruments like pyrgeometers.
Do we need to go over all that again for you?
• jan pompe
Nick #112
The TIGR radiosonde data includes pressure, temperature, and various gas concentrations. There are no measurements of radiation.
So do doubt HARTCODE’s ability to convert that radiosonde data to radiation data?
It has been pretty well validated as a simple web search will reveal and it is one of the ways the satellite instrument calibration is checked not to mention ground based instruments like pyrgeometers.
Do we need to go over all that again for you?
• Nick Stokes
Jan #113
I was responding to the statement “SOME is based on Hartcode, MOST is from radiosonde data, AFIK.”. You are, as so often, twisting that into something else.
• Nick Stokes
Jan #113
I was responding to the statement “SOME is based on Hartcode, MOST is from radiosonde data, AFIK.”. You are, as so often, twisting that into something else.
• jan pompe
Nick #114
I was responding to the statement “SOME is based on Hartcode, MOST is from radiosonde data, AFIK.”. You are, as so often, twisting that into something else.
I’m well aware of what you are responding to but what is the issue here is whether HARTCODE + radiosonde can provide radiation data the implication in this sentence
There are no measurements of radiation.
that it can’t. At least that is how I understood it are you saying I misunderstood?
• jan pompe
Nick #114
I was responding to the statement “SOME is based on Hartcode, MOST is from radiosonde data, AFIK.â€. You are, as so often, twisting that into something else.
I’m well aware of what you are responding to but what is the issue here is whether HARTCODE + radiosonde can provide radiation data the implication in this sentence
There are no measurements of radiation.
that it can’t. At least that is how I understood it are you saying I misunderstood?
• jae
Nick is interpreting it correctly; I forgot that the radiosonde data didn’t include the radiation info.
• jae
Nick is interpreting it correctly; I forgot that the radiosonde data didn’t include the radiation info.
• jan pompe
jae #116
Nick is interpreting it correctly; I forgot that the radiosonde data didn’t include the radiation info.
I understood that much. There is however a deeper implication related to an earlier comment by Nick that you also queried:
When the theory in M theory started to look wobbly, M and Z fell back on a claim that it was empirically substantiated, but the empirical claims were not described at publication level and had no support from actual radiation measurements, relying instead on Hartcode modelling. There is a lot of real empirical information out there.
implying the work of taking the radiosonde profiles and converting that to radiation data is not empirical work. The principles involved are really no different to obtaining empirical data with radiometers, which uses the effect of temperature on a thermocouple array warmed (or cooled) through a spectrally selective window.
See this paper or this for some more background or the Michelson interferometer used as a spectrometer by running the varying electromagnetic intensity signal through a fast fourier model to turn the data into a spectrum.
It just seems to me that Nick has the mistaken impression that the work in M&M04 and M07 does not have an empirical basis to begin with.
• jan pompe
jae #116
Nick is interpreting it correctly; I forgot that the radiosonde data didn’t include the radiation info.
I understood that much. There is however a deeper implication related to an earlier comment by Nick that you also queried:
When the theory in M theory started to look wobbly, M and Z fell back on a claim that it was empirically substantiated, but the empirical claims were not described at publication level and had no support from actual radiation measurements, relying instead on Hartcode modelling. There is a lot of real empirical information out there.
implying the work of taking the radiosonde profiles and converting that to radiation data is not empirical work. The principles involved are really no different to obtaining empirical data with radiometers, which uses the effect of temperature on a thermocouple array warmed (or cooled) through a spectrally selective window.
See this paper or this for some more background or the Michelson interferometer used as a spectrometer by running the varying electromagnetic intensity signal through a fast fourier model to turn the data into a spectrum.
It just seems to me that Nick has the mistaken impression that the work in M&M04 and M07 does not have an empirical basis to begin with.
• Alex Harvey
Nick #112,
I’m still interested in Appendix B, as I’ve been discussing it with Jan, and trying to figure it out in the historical context.
In Collins [2003], p. 254 found here http://bifrost.cwru.edu/personal/collins/astrobook/AbookC10.pdf, Collins’s eqn (10.1.4) corresponds with M’s eqn (B1).
Then, on p. 256, Collins states that ‘The general classical solution for the two streams can then be written as’ and he introduces eqn. (10.1.5) which differs from M’s (B3) by the equivalent of the Bg * exp(-3/2 tauA) term.
To justify the removal of this term Collins says:
One further complication must be dealt with before we can use this description of a stellar atmosphere. In general, stellar atmospheres can be regarded as being infinitely thick. Since the influence of the lower boundary diminishes as exp(tau-tau0), and since this optical depth will exceed several hundred within a few thousand kilometers of the surface for main sequence stars, we can take it to be infinity.
In other words, the term can be disregarded because the stellar atmosphere exceeds several thousand kilometers in thickness, and tau >several hundred. Anything to the power of minus several hundred is going to be so close to 0 that it seems reasonable to disregard it.
But surely you would agree that this simplifying assumption is not valid for the earth’s atmosphere, where the tau is closer to 1.87?
• Alex Harvey
Nick #112,
I’m still interested in Appendix B, as I’ve been discussing it with Jan, and trying to figure it out in the historical context.
In Collins [2003], p. 254 found here http://bifrost.cwru.edu/personal/collins/astrobook/AbookC10.pdf, Collins’s eqn (10.1.4) corresponds with M’s eqn (B1).
Then, on p. 256, Collins states that ‘The general classical solution for the two streams can then be written as’ and he introduces eqn. (10.1.5) which differs from M’s (B3) by the equivalent of the Bg * exp(-3/2 tauA) term.
To justify the removal of this term Collins says:
One further complication must be dealt with before we can use this description of a stellar atmosphere. In general, stellar atmospheres can be regarded as being infinitely thick. Since the influence of the lower boundary diminishes as exp(tau-tau0), and since this optical depth will exceed several hundred within a few thousand kilometers of the surface for main sequence stars, we can take it to be infinity.
In other words, the term can be disregarded because the stellar atmosphere exceeds several thousand kilometers in thickness, and tau >several hundred. Anything to the power of minus several hundred is going to be so close to 0 that it seems reasonable to disregard it.
But surely you would agree that this simplifying assumption is not valid for the earth’s atmosphere, where the tau is closer to 1.87?
• Alex Harvey
Jan/jae #117 etc:
The other issue is, is TFK08 purely based on direct measurements of radiation, or are they still using RT codes to get some quantities, such as AA. If they’re still using RT codes like MODTRAN to get AA, then they have no greater claim to being more empirical. Finally, doesn’t the ERBE measurements of MM04 contain direct radiation measurements that M compared his results with?
• Alex Harvey
Jan/jae #117 etc:
The other issue is, is TFK08 purely based on direct measurements of radiation, or are they still using RT codes to get some quantities, such as AA. If they’re still using RT codes like MODTRAN to get AA, then they have no greater claim to being more empirical. Finally, doesn’t the ERBE measurements of MM04 contain direct radiation measurements that M compared his results with?
• jan pompe
Alex #119
The other issue is, is TFK08 purely based on direct measurements of radiation, or are they still using RT codes to get some quantities, such as AA.
I have no idea if they say in the text I’ve missed it. If there is a direct way to measure $$A_A live I don’t know of it. We can of course in a laboratory where the source is hotter than the gas and re-radiation is insignificant. Finally, doesn’t the ERBE measurements of MM04 contain direct radiation measurements that M compared his results with? I would say so. • jan pompe Alex #119 The other issue is, is TFK08 purely based on direct measurements of radiation, or are they still using RT codes to get some quantities, such as AA. I have no idea if they say in the text I’ve missed it. If there is a direct way to measure$$A_A\$ live I don’t know of it. We can of course in a laboratory where the source is hotter than the gas and re-radiation is insignificant.
Finally, doesn’t the ERBE measurements of MM04 contain direct radiation measurements that M compared his results with?
I would say so.
• Nick Stokes
Alex #118
I mentioned App B because I had been puzzling over it. And indeed, it looks like B1 comes from 10.1.4.
But Collins is describing a very different situation. The energy being radiated is produced by the gas. In fact he says following your quote, that the surface is generally unilluminated. So 10.1.4 cites the source term S. And it has the constant μ, which in B1 would be 2/3.
But 10.1.4 comes from the inhomogeneous linear equation 10.1.1, and I can’t see any similar eqn in M theory. The nearest is M12, but it has only a constant on the right – so there’s no implied μ. And in fact the equation analogous to 10.1.4 seems to be M15, but it is quite different, reflecting the absence of an energy source.
It’s true that just before B3 M makes it clear that B is being regarded as the source. It’s possible that this can all be made consistent, but at the moment there is something missing. I can’t see why B1 and its consequences are needed in addition to M12-M15, which seem to stand alone without any “semi-infinite” assumption.
• Nick Stokes
Alex #118
I mentioned App B because I had been puzzling over it. And indeed, it looks like B1 comes from 10.1.4.
But Collins is describing a very different situation. The energy being radiated is produced by the gas. In fact he says following your quote, that the surface is generally unilluminated. So 10.1.4 cites the source term S. And it has the constant μ, which in B1 would be 2/3.
But 10.1.4 comes from the inhomogeneous linear equation 10.1.1, and I can’t see any similar eqn in M theory. The nearest is M12, but it has only a constant on the right – so there’s no implied μ. And in fact the equation analogous to 10.1.4 seems to be M15, but it is quite different, reflecting the absence of an energy source.
It’s true that just before B3 M makes it clear that B is being regarded as the source. It’s possible that this can all be made consistent, but at the moment there is something missing. I can’t see why B1 and its consequences are needed in addition to M12-M15, which seem to stand alone without any “semi-infinite” assumption.
• Nick Stokes
Alex #119
I don’t believe TFK use a RT code, and they don’t quote A_A directly – they give a surface radiation figure and an atmospheric window transmission. The latter could be deduced from analysing the spectrum. You can also say things about the transmitted radiation from directional analysis; in effect it’s the part that transmits surface detail, while E_U is just shine.
• Nick Stokes
Alex #119
I don’t believe TFK use a RT code, and they don’t quote A_A directly – they give a surface radiation figure and an atmospheric window transmission. The latter could be deduced from analysing the spectrum. You can also say things about the transmitted radiation from directional analysis; in effect it’s the part that transmits surface detail, while E_U is just shine.
• jan pompe
Nick #121
It’s possible that this can all be made consistent, but at the moment there is something missing. I can’t see why B1 and its consequences are needed in addition to M12-M15, which seem to stand alone without any “semi-infinite” assumption.
I’m not sure what you mean “in addition to M12-M15″ it would have that B1 and it’s consequences were “instead of M12 -M15″.
Would you agree that if the integrals in appendix B were evaluated over the interval $$left(o,infty right)$$ (semi-infinite case) all those $$e ^ {-tilde tau}$$ (missing from M15 – M17) would disappear?
I could be mistaken but I’m sure we need that exponential term to cope with a transmission window in the atmosphere. As it stands I’m not sure that Eqns M16 and M17 (or Eqns 1 &2 of Lorenz & Mckay ) can cope with an atmospheric IR window See Weaver & Ramanathan (GRL June 1995) “Deductions From a Simple Climate Model: Factors Governing Surface Temperature and Atmospheric Thermal Structure”.
Abstract here
• jan pompe
Nick #121
It’s possible that this can all be made consistent, but at the moment there is something missing. I can’t see why B1 and its consequences are needed in addition to M12-M15, which seem to stand alone without any “semi-infinite†assumption.
I’m not sure what you mean “in addition to M12-M15″ it would have that B1 and it’s consequences were “instead of M12 -M15″.
Would you agree that if the integrals in appendix B were evaluated over the interval $$\left(o,\infty \right)$$ (semi-infinite case) all those $$e ^ {-\tilde \tau}$$ (missing from M15 – M17) would disappear?
I could be mistaken but I’m sure we need that exponential term to cope with a transmission window in the atmosphere. As it stands I’m not sure that Eqns M16 and M17 (or Eqns 1 &2 of Lorenz & Mckay ) can cope with an atmospheric IR window See Weaver & Ramanathan (GRL June 1995) “Deductions From a Simple Climate Model: Factors Governing Surface Temperature and Atmospheric Thermal Structure”.
Abstract here
• http://www.ecoengineers.com Steve Short
Jan #123
“I could be mistaken but I’m sure we need that exponential term to cope with a transmission window in the atmosphere. As it stands I’m not sure that Eqns M16 and M17 (or Eqns 1 &2 of Lorenz & Mckay ) can cope with an atmospheric IR window See Weaver & Ramanathan (GRL June 1995) “Deductions From a Simple Climate Model: Factors Governing Surface Temperature and Atmospheric Thermal Structure”.”
I got this article about 5 years ago and happily the math in it is quite easy to follow. I am able to send a copy to anyone who emails me. However, the authors do caution that:
“However, we point out that simple models such as the
present one cannot be depended upon for quantitative accuracy;
hence they should be used with extreme care to avoid
misinterpretations a nd erroneousc onclusions. For example,
it is well known that water vapor and CO2 absorption do not
follow semigrey gas models. It is for this reason that we
focus on the optically thick limit for which the influence of
the spectral details is expected to be minimal.”
The paper is a fairly clear approach to a formalism that deals with the window and outlines the consequences of that for a diatomic atmosphere like Earth (and a triatomic atmosphers like Venus).
The following from R&W97 is interesting:
“First, the modified SGM shows that the temperature jump
between the surface and the immediately overlying atmosphere
vanishes inversely as the total optical depth weighted
by the size of the spectral window. If we use( 12) with a
nonzero beta and allow the optical depth to be high somewhere
in the spectrum (as it is in the centers of the primary
vibration-rotation bands of CO2 and H2O), we find that the
discontinuity should be small. Indeed, this has been shown
to be true for the model of Manabe and Strickler [ 1964], who
state that the discontinuity is small due to very strong
absorption near the line centers as well as upward radiation
from the surface through the nearly transparent regions in
the line wings and the water vapor window.”
Beta is the transparent fraction of the total thermal spectrum – the width of the window if you will.
However, I am not at all sure that M7 Appendix B1 is an acceptable solution to the window issue. This is why I expressed the opinion several times here that Miskolczi would have been much better off presenting his solution as a separate initial paper on the issues of both the window and the surface/atmosphere temperature discontinuity in a mainstream journal first. It is completely unclear how much Miskolczi’s formalism relates to the logic of Manabe and Strickler, 1964 and Ramanathan and Weaver, 1995.
• http://www.ecoengineers.com Steve Short
Jan #123
“I could be mistaken but I’m sure we need that exponential term to cope with a transmission window in the atmosphere. As it stands I’m not sure that Eqns M16 and M17 (or Eqns 1 &2 of Lorenz & Mckay ) can cope with an atmospheric IR window See Weaver & Ramanathan (GRL June 1995) “Deductions From a Simple Climate Model: Factors Governing Surface Temperature and Atmospheric Thermal Structureâ€.”
I got this article about 5 years ago and happily the math in it is quite easy to follow. I am able to send a copy to anyone who emails me. However, the authors do caution that:
“However, we point out that simple models such as the
present one cannot be depended upon for quantitative accuracy;
hence they should be used with extreme care to avoid
misinterpretations a nd erroneousc onclusions. For example,
it is well known that water vapor and CO2 absorption do not
follow semigrey gas models. It is for this reason that we
focus on the optically thick limit for which the influence of
the spectral details is expected to be minimal.”
The paper is a fairly clear approach to a formalism that deals with the window and outlines the consequences of that for a diatomic atmosphere like Earth (and a triatomic atmosphers like Venus).
The following from R&W97 is interesting:
“First, the modified SGM shows that the temperature jump
between the surface and the immediately overlying atmosphere
vanishes inversely as the total optical depth weighted
by the size of the spectral window. If we use( 12) with a
nonzero beta and allow the optical depth to be high somewhere
in the spectrum (as it is in the centers of the primary
vibration-rotation bands of CO2 and H2O), we find that the
discontinuity should be small. Indeed, this has been shown
to be true for the model of Manabe and Strickler [ 1964], who
state that the discontinuity is small due to very strong
absorption near the line centers as well as upward radiation
from the surface through the nearly transparent regions in
the line wings and the water vapor window.”
Beta is the transparent fraction of the total thermal spectrum – the width of the window if you will.
However, I am not at all sure that M7 Appendix B1 is an acceptable solution to the window issue. This is why I expressed the opinion several times here that Miskolczi would have been much better off presenting his solution as a separate initial paper on the issues of both the window and the surface/atmosphere temperature discontinuity in a mainstream journal first. It is completely unclear how much Miskolczi’s formalism relates to the logic of Manabe and Strickler, 1964 and Ramanathan and Weaver, 1995.
• jae
Steve, Jan: I confess that you guys have got my mind in such a swirl that I don’t know what’s going on. I wish we could have a few beers together and get on the same playing field, but I think there are a few thousand miles between us. Maybe someone (David?) could summarize just where we are on the Miskolczi File.
• jae
Steve, Jan: I confess that you guys have got my mind in such a swirl that I don’t know what’s going on. I wish we could have a few beers together and get on the same playing field, but I think there are a few thousand miles between us. Maybe someone (David?) could summarize just where we are on the Miskolczi File.
• jan pompe
jae #125
Maybe someone (David?) could summarize just where we are on the Miskolczi File.
• jan pompe
jae #125
Maybe someone (David?) could summarize just where we are on the Miskolczi File.
• Nick Stokes
Jan #123
I’m not sure what you mean “in addition to M12-M15″ it would have that B1 and it’s consequences were “instead of M12 -M15″.
Would you agree that if the integrals in appendix B were evaluated over the interval left(o,infty right) (semi-infinite case) all those e ^ {-tilde tau} (missing from M15 – M17) would disappear?
Why instead of? Are M12-15 wrong? They seem to give the quantities needed.
The exponentials would not disappear on an infinite interval – in fact, they are absolutely needed to make the integral itself finite. See Collins 10.1.6. The reason they are missing in 15-17 is that these are not equations involving I.
I don’t agree that the exponentials have anything to do with the atmospheric window. They are needed as part of a gray-body model, which the window is never consistent with – that’s one reason why this stuff has no connection with practical atmospheric computations. Any equation which uses average tau as a variable is gray-body. At the window frequencies the OD is zero – so they exponentials would actually go away.
I think what is happening here is that M12-15 assume radiative equilibrium (~constant H, all assumed following M11). 10.1.4 does not, and B1, derived from it, is potentially more general, because convection and latent heat could be included as sources. But FM doesn’t do that; he just uses B as the source. The equations look different, because they are expressed in terms of I, but it isn’t clear to me that they add anything.
• Nick Stokes
Jan #123
I’m not sure what you mean “in addition to M12-M15″ it would have that B1 and it’s consequences were “instead of M12 -M15″.
Would you agree that if the integrals in appendix B were evaluated over the interval \left(o,\infty \right) (semi-infinite case) all those e ^ {-\tilde \tau} (missing from M15 – M17) would disappear?
Why instead of? Are M12-15 wrong? They seem to give the quantities needed.
The exponentials would not disappear on an infinite interval – in fact, they are absolutely needed to make the integral itself finite. See Collins 10.1.6. The reason they are missing in 15-17 is that these are not equations involving I.
I don’t agree that the exponentials have anything to do with the atmospheric window. They are needed as part of a gray-body model, which the window is never consistent with – that’s one reason why this stuff has no connection with practical atmospheric computations. Any equation which uses average tau as a variable is gray-body. At the window frequencies the OD is zero – so they exponentials would actually go away.
I think what is happening here is that M12-15 assume radiative equilibrium (~constant H, all assumed following M11). 10.1.4 does not, and B1, derived from it, is potentially more general, because convection and latent heat could be included as sources. But FM doesn’t do that; he just uses B as the source. The equations look different, because they are expressed in terms of I, but it isn’t clear to me that they add anything.
• Nick Stokes
OK, I’ve figured out where App B fits in. As we’ve discussed before, M12 is a first order linear de (a very simple one), and you can only apply one boundary condition (BC). Usually, this is done at TOA, and M15 is the result. There’s good reason for that – TOA is where the assumption of radiative equilibrium really works, and you do know the OLR that has to be matched. The result is a solution of M12 that is valid going downwards, but might not satisfy the BC when you encounter a surface.
The purpose of App B is to instead use the radiative transfer equations to apply the right BC at the ground. You can do that, but it won’t be right at TOA. That’s serious – you don’t get the right exiting OLR, and there is a global energy imbalance. I think the TOA version, which goes back to Schwarzschild, is much preferable. The ground (and nearby) is exactly where radiative equilibrium is known not to apply, because of large convection and latent heat fluxes. H was assumed constant in both M12-15 and App B because the energy flux must be constant, but the upward energy flux is actually H+K.
That’s what is wrong with this whole approach. K is small in the upper atmosphere, so M12 works there, and the BC used is correct. Worrying about a discontinuity at the ground is illogical, because by then K matters, and M12 is no longer a good approx. Trying to apply M12 with a ground BC only makes this worse.
• Nick Stokes
OK, I’ve figured out where App B fits in. As we’ve discussed before, M12 is a first order linear de (a very simple one), and you can only apply one boundary condition (BC). Usually, this is done at TOA, and M15 is the result. There’s good reason for that – TOA is where the assumption of radiative equilibrium really works, and you do know the OLR that has to be matched. The result is a solution of M12 that is valid going downwards, but might not satisfy the BC when you encounter a surface.
The purpose of App B is to instead use the radiative transfer equations to apply the right BC at the ground. You can do that, but it won’t be right at TOA. That’s serious – you don’t get the right exiting OLR, and there is a global energy imbalance. I think the TOA version, which goes back to Schwarzschild, is much preferable. The ground (and nearby) is exactly where radiative equilibrium is known not to apply, because of large convection and latent heat fluxes. H was assumed constant in both M12-15 and App B because the energy flux must be constant, but the upward energy flux is actually H+K.
That’s what is wrong with this whole approach. K is small in the upper atmosphere, so M12 works there, and the BC used is correct. Worrying about a discontinuity at the ground is illogical, because by then K matters, and M12 is no longer a good approx. Trying to apply M12 with a ground BC only makes this worse.
• http://www.ecoengineers.com Steve Short
Thanks Nick. Well explained. I always thought it was all about the K term but around here – it was ‘recant heretic or get burned’. Even R&W97 consider lapse rate. BTW, have you seen Ken Takahashi’s two 2008 papers?
• http://www.ecoengineers.com Steve Short
Thanks Nick. Well explained. I always thought it was all about the K term but around here – it was ‘recant heretic or get burned’. Even R&W97 consider lapse rate. BTW, have you seen Ken Takahashi’s two 2008 papers?
• Anonymous
I don’t really want to start it up with my views, partly becasue I’m not really expert enough in the physics to contribute, and I have other things on. Its OK to let it die here. FM has feedback for the next iteration, we learned a lot about atmospheric radiation physics, had some fun.
• http://landshape.org/enm David Stockwell
I don’t really want to start it up with my views, partly becasue I’m not really expert enough in the physics to contribute, and I have other things on. Its OK to let it die here. FM has feedback for the next iteration, we learned a lot about atmospheric radiation physics, had some fun.
• http://www.ecoengineers.com Steve Short
This bright fellow has the decency to post his publications as pdfs for those who want to keep learning and his papers are very readable too.
http://www.atmos.washington.edu/~ken/
• http://www.ecoengineers.com Steve Short
This bright fellow has the decency to post his publications as pdfs for those who want to keep learning and his papers are very readable too.
http://www.atmos.washington.edu/~ken/
• Nick Stokes
I’m very sympathetic to the idea of calling an end to the discussion. But I’ve realised a solution to a long-term puzzle, and thought I should report it.
I’ve been puzzled about FM’s use of “semi-infinite” and asked for anyone to explain it, without success. But I see the word is used by Collins. It is not appropriate for the Schwarzschild solution, which is just the TOA solution going down, with no infinite assumption.
However, what FM has done is to work out the ground BC solution of M12, and shows that it is different (and to that extent, I believe, wrong). He then shows that for an infinitely thick atmosphere, the difference goes away, so he calls M15 a semi-infinite approximation. But it isn’t. Schwarzschild’s solution makes no such assumption. The fact that it becomes consistent with the ground BC solution when the ground is at infinity is interesting, but a separate fact.
• Nick Stokes
I’m very sympathetic to the idea of calling an end to the discussion. But I’ve realised a solution to a long-term puzzle, and thought I should report it.
I’ve been puzzled about FM’s use of “semi-infinite” and asked for anyone to explain it, without success. But I see the word is used by Collins. It is not appropriate for the Schwarzschild solution, which is just the TOA solution going down, with no infinite assumption.
However, what FM has done is to work out the ground BC solution of M12, and shows that it is different (and to that extent, I believe, wrong). He then shows that for an infinitely thick atmosphere, the difference goes away, so he calls M15 a semi-infinite approximation. But it isn’t. Schwarzschild’s solution makes no such assumption. The fact that it becomes consistent with the ground BC solution when the ground is at infinity is interesting, but a separate fact.
• jan pompe
David
Its OK to let it die here.
Fair enough. We’ll see what transpires next iteration.
• jan pompe
David
Its OK to let it die here.
Fair enough. We’ll see what transpires next iteration.
• http://www.ecoengineers.com Steve Short
Nick #132
“He then shows that for an infinitely thick atmosphere, the difference goes away, so he calls M15 a semi-infinite approximation. But it isn’t. Schwarzschild’s solution makes no such assumption. The fact that it becomes consistent with the ground BC solution when the ground is at infinity is interesting, but a separate fact.”
I’ll ‘fess up. It sucked me in.
BTW, it is interesting to note that TFK08 gets a 4 year mean LW tauA = 2.29 – say 2.3 (hat tip to Jan ;-). This is very close to the required LW tau for the maximum partition ratio of convective heat flux/surface upward LW radiation according to MEP (Ozawa and Ohmura, 1997) i.e. K/S_U = 97/396 = 0.245
• http://www.ecoengineers.com Steve Short
Nick #132
“He then shows that for an infinitely thick atmosphere, the difference goes away, so he calls M15 a semi-infinite approximation. But it isn’t. Schwarzschild’s solution makes no such assumption. The fact that it becomes consistent with the ground BC solution when the ground is at infinity is interesting, but a separate fact.”
I’ll ‘fess up. It sucked me in.
BTW, it is interesting to note that TFK08 gets a 4 year mean LW tauA = 2.29 – say 2.3 (hat tip to Jan ;-). This is very close to the required LW tau for the maximum partition ratio of convective heat flux/surface upward LW radiation according to MEP (Ozawa and Ohmura, 1997) i.e. K/S_U = 97/396 = 0.245
• Geoff Sherrington
Re Nick at #132 and others
Some of us have left the considerable detective work to you folk and would feel anti-climactic if you just dropped it. Is there are chance that the half dozen or fewer main participants can work behindthe dcenes to produce a series of dot points, which would be immensely interesting when we others read Ferenc again.
• Geoff Sherrington
Re Nick at #132 and others
Some of us have left the considerable detective work to you folk and would feel anti-climactic if you just dropped it. Is there are chance that the half dozen or fewer main participants can work behindthe dcenes to produce a series of dot points, which would be immensely interesting when we others read Ferenc again.
• Alex Harvey
More on Philipona et al.
Philipona, R., B. Dürr, A. Ohmura, and C. Ruckstuhl (2005), Anthropogenic greenhouse forcing and strong water vapor feedback increase temperature in Europe, Geophys. Res. Lett., 32, L19809, doi:10.1029/2005GL023624.
Europe’s temperature increases considerably faster than the northern hemisphere average. Detailed month-by-month analyses show temperature and humidity changes for individual months that are similar for all Europe, indicating large-scale weather patterns uniformly influencing temperature. However, superimposed to these changes a strong west-east gradient is observed for all months. The gradual temperature and humidity increases from west to east are not related to circulation but must be due to non-uniform water vapour feedback. Surface radiation measurements in central Europe manifest anthropogenic greenhouse forcing and strong water vapor feedback, enhancing the forcing and temperature rise by about a factor of three. Solar radiation decreases and changing cloud amounts show small net radiative effects. However, high correlation of increasing cloud-free longwave downward radiation with temperature (r = 0.99) and absolute humidity (r = 0.89), and high correlation between ERA-40 integrated water vapor and CRU surface temperature changes (r = 0.84), demonstrates greenhouse forcing with strong water vapor feedback.
Then this:
http://www.agu.org/sci_soc/prrl/prrl0538.html
“The authors, led by Rolf Philipona of the World Radiation Center in Davos, show experimentally that 70 percent of the rapid temperature increase is very likely caused by water vapor feedback. They indicate that remaining 30 percent is likely due to increasing manmade greenhouse gases.”
Then at the bottom:
“Notes for Journalists
Journalists (only) may obtain a pdf copy of this paper upon request to Jonathan Lifland: [email protected]. Please provide your name, name of publication, phone, and email address. The paper and this press release are not under embargo.”
So basically,
P in 2004: 2/3 of the unpredicted warming was caused by the NAO -> therefore OMG the greenhouse effect is real!
P in 2005: 2/3 of the unpredicted warming caused by extraordinary water vapour feedback -> therefore OMG the greenhouse effect is real!
P in 2009: 2/3 of the unpredicted warming caused by anthropogenic-global-un-dimming -> therefore OMG the greenhouse effect is real!
• Alex Harvey
More on Philipona et al.
Philipona, R., B. Dürr, A. Ohmura, and C. Ruckstuhl (2005), Anthropogenic greenhouse forcing and strong water vapor feedback increase temperature in Europe, Geophys. Res. Lett., 32, L19809, doi:10.1029/2005GL023624.
Europe’s temperature increases considerably faster than the northern hemisphere average. Detailed month-by-month analyses show temperature and humidity changes for individual months that are similar for all Europe, indicating large-scale weather patterns uniformly influencing temperature. However, superimposed to these changes a strong west-east gradient is observed for all months. The gradual temperature and humidity increases from west to east are not related to circulation but must be due to non-uniform water vapour feedback. Surface radiation measurements in central Europe manifest anthropogenic greenhouse forcing and strong water vapor feedback, enhancing the forcing and temperature rise by about a factor of three. Solar radiation decreases and changing cloud amounts show small net radiative effects. However, high correlation of increasing cloud-free longwave downward radiation with temperature (r = 0.99) and absolute humidity (r = 0.89), and high correlation between ERA-40 integrated water vapor and CRU surface temperature changes (r = 0.84), demonstrates greenhouse forcing with strong water vapor feedback.
Then this:
http://www.agu.org/sci_soc/prrl/prrl0538.html
“The authors, led by Rolf Philipona of the World Radiation Center in Davos, show experimentally that 70 percent of the rapid temperature increase is very likely caused by water vapor feedback. They indicate that remaining 30 percent is likely due to increasing manmade greenhouse gases.”
Then at the bottom:
“Notes for Journalists
Journalists (only) may obtain a pdf copy of this paper upon request to Jonathan Lifland: [email protected]. Please provide your name, name of publication, phone, and email address. The paper and this press release are not under embargo.”
So basically,
P in 2004: 2/3 of the unpredicted warming was caused by the NAO -> therefore OMG the greenhouse effect is real!
P in 2005: 2/3 of the unpredicted warming caused by extraordinary water vapour feedback -> therefore OMG the greenhouse effect is real!
P in 2009: 2/3 of the unpredicted warming caused by anthropogenic-global-un-dimming -> therefore OMG the greenhouse effect is real!
• Alex Harvey
Geoff #135,
By the way, I would be happy to summarise for you in an email where there has been general areas of agreement amongst participants in the Miskolczi discussion. My email address is alexharv074 at gmail dot com.
Belated thanks to Nick for the response above, and all his other responses, too.
• Alex Harvey
Geoff #135,
By the way, I would be happy to summarise for you in an email where there has been general areas of agreement amongst participants in the Miskolczi discussion. My email address is alexharv074 at gmail dot com.
Belated thanks to Nick for the response above, and all his other responses, too.
• http://www.ecoengineers.com Steve Short
Geoff #135
“Is there are chance that the half dozen or fewer main participants can work behind the scenes to produce a series of dot points, which would be immensely interesting when we others read Ferenc again.”
This is an easy one. We now know from the 5 years May 2000 – May 2004 of CERES program that all the so-called empirical relations which were established by M&M04 and M07 simply do not exist.
The pre-print version of K,T&F (2008) has the following numbers for CERES May 2000 – May 2004:
Fo = 239.4 W/m^2
OLR = 238.5 W/m^2
F = 78.2 W/m^2
K = 17 (H_S) + 80 (H_L) = 97.0 W/m^2
S_T = 40 W/m^2
S_U = 396 W/m^2
E_U = OLR – S_T = 238.5 – 40 = 198.5 W/m^2
A_A = 356 W/m^2
E_D = 333 W/m^2
‘Dot points’ follow:
Thus from we have S_T = 0.101 ~ 1/10 Miskolczi said ~1/6 (0.167)
We have transmittance T_A = S_T/S_U ~1/10 Miskolczi said ~1/6
We have tauA = -lnS_T/S_U) = 2.29 Miskolczi said ~1.87
We also have S_U/OLR = 396/238.5 = 1.660 ~ 5/3 Miskolczi said ~3/2 (1.500)
We also have A_A/E_D = 356/333 = 1.069 ~15/14 Miskolczi said A_A/E_D~ 1
We also have S_U/E_U = 396/198.5 = 1.995 Miskolczi said S_U = 2E_U
So of all these so-called ‘empirical relationships’ the only one, the so-called virial relation S_U = 2E_U is the one that appears to hold up to better than 5% deviation.
The so-called Kirchoff law relation A_A = E_D fares very badly and may be taken as disproven.
Interestingly, the only relation which appears to hold up to better than 5%, but in an unexpected way, is the very one downplayed by Miskolczi and particularly by Jan that is the one E_U = F + K + P
Interestingly, if we stick strictly to Miskolczi’s definition and note that the period May 2000 – May 2004 did not include any globally significantly volcanoes, then F + K = 78.2 + 97.0 = 175.2 which differs from OLR – S_T = 238.5 – 40 = 198.5 by 23.3 W/m^2. But this is almost exactly the difference between A_A (the absorbed LW radiation) and E_D (the downwards atmospheric emittance) i.e. A_A – E_D = 356 – 333 = 23!
As Nick Stokes shows, Miskolczi’s ‘proof’ of the lack of a temperature difference at the surface is no such thing. There is such a difference, and the lack of concordance in the lower troposphere between A_A and E_D is clear confirmation.
If the participants in the Miskolczi discussion can reach any general degree of agreement it should therefore be that:
(1) the so-called Miskolczi ‘proof’ of no temperature discontinuity at or very near to the surface is dead in the water; and that
(2) the A_A/E_D = 1 so-called Kirchoff Law relation ‘discoverd’ by Miskolczi is also dead in the water; but that intriguingly
(3) the so-called virial relation S_U = 2E_U relation not only appears to be good but that, in the absence of a geothermal P term input (to E_U) then E_U = F + K + A_A – E_D = OLR – S_T = S_U/2
In other words Equations 1, 2 and 3 in M7 still hold, as they should, because they were and are simple expressions of the energy balance of the atmosphere. But any further assertion that they show a radiative balance of the atmosphere is plain wrong because some of the terms remain non-radiative and E_U is never just = F+K+P i.e. E_U always = F + K + A_A – E_D + P
It would be interesting to see how Neal King reacts to the finding that S_U still = 2E_U in K,T&F (2008) because it appears to be a linchpin feature of the atmosphere. Whether it is actually equivalent to the ‘total gravitational potential energy equal to two times the internal kinetic energy’ remains an intriguing question.
This suggests that Sections 3.1 and 3.2 of M07 deserve some continued attention but with a big ‘grain of salt’ as follows:
If we look at Misckolczi’s so-called additive virial term in M07 i.e. S_V = S_T/2 – E_D/10 we now find that it actually approximates 20 – 33.3 = -13.3 and hence S_U + S_T/2 – E_D/10 = 396 – 13.3 = 383.3 = 1.607 not equal 3OLR/2 so Miskolczi obviously got it wrong with his Eqn. 9.
This brings crashing down the obviously circular reasoning of M7 Eqn. 10. In actual fact, where E_D ~ 8S_T or LW transmittance T_A ~1/10, Eqn. 9 would not take the form of Eqn.8 at all but actually S_U = 5OLR/3 as I noted above. The way it stands at the moment:
OLR = S_T + F + K + A_A – E-D
i.e.
OLR = 2S_U/20 + 4S_U/20 + 5S-U/20 + 18S_U/20 – 17S_U/20
= 12S_U/20
=3S_U/5
Now there’s some really nice numerology for you – and to better than 5% as well (spot the S_V if you can folks ;-)!
BTW, as an aside may I recommend the very fine historical novel ‘Creation’ by the wonderful Gore Vidal. It has some truly great stuff about the immensely powerful effects of ‘prophets’, ‘revealed truths’ and ‘high priests’ on the poor and numberless masses in the story of man. Timeless, ageless and ever so true ……at all scales.
• http://www.ecoengineers.com Steve Short
Geoff #135
“Is there are chance that the half dozen or fewer main participants can work behind the scenes to produce a series of dot points, which would be immensely interesting when we others read Ferenc again.”
This is an easy one. We now know from the 5 years May 2000 – May 2004 of CERES program that all the so-called empirical relations which were established by M&M04 and M07 simply do not exist.
The pre-print version of K,T&F (2008) has the following numbers for CERES May 2000 – May 2004:
Fo = 239.4 W/m^2
OLR = 238.5 W/m^2
F = 78.2 W/m^2
K = 17 (H_S) + 80 (H_L) = 97.0 W/m^2
S_T = 40 W/m^2
S_U = 396 W/m^2
E_U = OLR – S_T = 238.5 – 40 = 198.5 W/m^2
A_A = 356 W/m^2
E_D = 333 W/m^2
‘Dot points’ follow:
Thus from we have S_T = 0.101 ~ 1/10 Miskolczi said ~1/6 (0.167)
We have transmittance T_A = S_T/S_U ~1/10 Miskolczi said ~1/6
We have tauA = -lnS_T/S_U) = 2.29 Miskolczi said ~1.87
We also have S_U/OLR = 396/238.5 = 1.660 ~ 5/3 Miskolczi said ~3/2 (1.500)
We also have A_A/E_D = 356/333 = 1.069 ~15/14 Miskolczi said A_A/E_D~ 1
We also have S_U/E_U = 396/198.5 = 1.995 Miskolczi said S_U = 2E_U
So of all these so-called ‘empirical relationships’ the only one, the so-called virial relation S_U = 2E_U is the one that appears to hold up to better than 5% deviation.
The so-called Kirchoff law relation A_A = E_D fares very badly and may be taken as disproven.
Interestingly, the only relation which appears to hold up to better than 5%, but in an unexpected way, is the very one downplayed by Miskolczi and particularly by Jan that is the one E_U = F + K + P
Interestingly, if we stick strictly to Miskolczi’s definition and note that the period May 2000 – May 2004 did not include any globally significantly volcanoes, then F + K = 78.2 + 97.0 = 175.2 which differs from OLR – S_T = 238.5 – 40 = 198.5 by 23.3 W/m^2. But this is almost exactly the difference between A_A (the absorbed LW radiation) and E_D (the downwards atmospheric emittance) i.e. A_A – E_D = 356 – 333 = 23!
As Nick Stokes shows, Miskolczi’s ‘proof’ of the lack of a temperature difference at the surface is no such thing. There is such a difference, and the lack of concordance in the lower troposphere between A_A and E_D is clear confirmation.
If the participants in the Miskolczi discussion can reach any general degree of agreement it should therefore be that:
(1) the so-called Miskolczi ‘proof’ of no temperature discontinuity at or very near to the surface is dead in the water; and that
(2) the A_A/E_D = 1 so-called Kirchoff Law relation ‘discoverd’ by Miskolczi is also dead in the water; but that intriguingly
(3) the so-called virial relation S_U = 2E_U relation not only appears to be good but that, in the absence of a geothermal P term input (to E_U) then E_U = F + K + A_A – E_D = OLR – S_T = S_U/2
In other words Equations 1, 2 and 3 in M7 still hold, as they should, because they were and are simple expressions of the energy balance of the atmosphere. But any further assertion that they show a radiative balance of the atmosphere is plain wrong because some of the terms remain non-radiative and E_U is never just = F+K+P i.e. E_U always = F + K + A_A – E_D + P
It would be interesting to see how Neal King reacts to the finding that S_U still = 2E_U in K,T&F (2008) because it appears to be a linchpin feature of the atmosphere. Whether it is actually equivalent to the ‘total gravitational potential energy equal to two times the internal kinetic energy’ remains an intriguing question.
This suggests that Sections 3.1 and 3.2 of M07 deserve some continued attention but with a big ‘grain of salt’ as follows:
If we look at Misckolczi’s so-called additive virial term in M07 i.e. S_V = S_T/2 – E_D/10 we now find that it actually approximates 20 – 33.3 = -13.3 and hence S_U + S_T/2 – E_D/10 = 396 – 13.3 = 383.3 = 1.607 not equal 3OLR/2 so Miskolczi obviously got it wrong with his Eqn. 9.
This brings crashing down the obviously circular reasoning of M7 Eqn. 10. In actual fact, where E_D ~ 8S_T or LW transmittance T_A ~1/10, Eqn. 9 would not take the form of Eqn.8 at all but actually S_U = 5OLR/3 as I noted above. The way it stands at the moment:
OLR = S_T + F + K + A_A – E-D
i.e.
OLR = 2S_U/20 + 4S_U/20 + 5S-U/20 + 18S_U/20 – 17S_U/20
= 12S_U/20
=3S_U/5
Now there’s some really nice numerology for you – and to better than 5% as well (spot the S_V if you can folks ;-)!
BTW, as an aside may I recommend the very fine historical novel ‘Creation’ by the wonderful Gore Vidal. It has some truly great stuff about the immensely powerful effects of ‘prophets’, ‘revealed truths’ and ‘high priests’ on the poor and numberless masses in the story of man. Timeless, ageless and ever so true ……at all scales.
• Anonymous
That is a very impressive round-up Steve. You know, it just feels like real science, the effort it has taken to get somewhere, the not straying far from empiricism, the dissection of assumptions.
Am I right in saying that the upshot of the relaxation of the ‘Kirchhoff constraint’, but keeping the ‘Virial constraint’ is that the climate system no longer adjusts back to the stable state with GHG perturbation, but that the instantaneous forcing estimated by FM still holds? These are low of course, a 2xCO2 climate sensitivity of less than a degree if I remember, but in line with Spencer and others.
That is a very impressive round-up Steve. You know, it just feels like real science, the effort it has taken to get somewhere, the not straying far from empiricism, the dissection of assumptions.
Am I right in saying that the upshot of the relaxation of the ‘Kirchhoff constraint’, but keeping the ‘Virial constraint’ is that the climate system no longer adjusts back to the stable state with GHG perturbation, but that the instantaneous forcing estimated by FM still holds? These are low of course, a 2xCO2 climate sensitivity of less than a degree if I remember, but in line with Spencer and others.
• http://www.ecoengineers.com Steve Short
“You know, it just feels like real science, the effort it has taken to get somewhere, the not straying far from empiricism, the dissection of assumptions.
…….Am I right in saying that the upshot of the relaxation of the ‘Kirchhoff constraint’, but keeping the ‘Virial constraint’ is that the climate system no longer adjusts back to the stable state with GHG perturbation, but that the instantaneous forcing estimated by FM still holds?”
Yes, I think so. This is why I still find what Misckolczi has done fascinating.
As I hope I was able to hint at in my post #138, despite everything, I still think it is not yet over for Miskolczi i.e. the fat lady is not singing yet!
When I realized that the measured difference between A_A and E_D in K,T&F08 instantly supplied the missing ~20 W/m^2 which I have been trying for months to ‘tack on’ to the K term (to the endless irritation of Jan and the cause of numerous heavy tit-for-tat posts) to supply a plausible net heat balance for the atmosphere, I almost fell off my chair.
Sticking with M’s formalism (which does not excessively simplify reality to not be able to describe the system adequately) I am therefore still captured by the evident fact that E_U = F + K + A_A – E_D (+ P) = S_ U – S_T = S_U/2 i.e. the so-called virial relation – even by the determinations of K,T&F08!
Why? How? And how come the AGW orthodoxy haven’t noticed/addressed this issue? I am convinced this relation indicates a sort of homeostasis is buried in the system which can only act to reduce CO2 sensitivity.
If you scour the literature there have been hints for many years before Spencer that something like this is going on. Lindzen seems to me to be the person who has the strongest sense of it but I also earlier quoted an obscure paper from 2000 by two Egyptian meteorologists which is tantalising in this regard. I suspect Ken Takahashi of NOAA knows it is there too.
BTW, I take it you have noticed the global SW flux simply reflected off the surface due to surface albedo given by K,T&F08 is also 23 W/m^2 – precisely equal to the global (LW) difference between A_A and E_D given by them! Another coincidence? Maybe it is and maybe it isn’t.
• http://www.ecoengineers.com Steve Short
“You know, it just feels like real science, the effort it has taken to get somewhere, the not straying far from empiricism, the dissection of assumptions.
…….Am I right in saying that the upshot of the relaxation of the ‘Kirchhoff constraint’, but keeping the ‘Virial constraint’ is that the climate system no longer adjusts back to the stable state with GHG perturbation, but that the instantaneous forcing estimated by FM still holds?”
Yes, I think so. This is why I still find what Misckolczi has done fascinating.
As I hope I was able to hint at in my post #138, despite everything, I still think it is not yet over for Miskolczi i.e. the fat lady is not singing yet!
When I realized that the measured difference between A_A and E_D in K,T&F08 instantly supplied the missing ~20 W/m^2 which I have been trying for months to ‘tack on’ to the K term (to the endless irritation of Jan and the cause of numerous heavy tit-for-tat posts) to supply a plausible net heat balance for the atmosphere, I almost fell off my chair.
Sticking with M’s formalism (which does not excessively simplify reality to not be able to describe the system adequately) I am therefore still captured by the evident fact that E_U = F + K + A_A – E_D (+ P) = S_ U – S_T = S_U/2 i.e. the so-called virial relation – even by the determinations of K,T&F08!
Why? How? And how come the AGW orthodoxy haven’t noticed/addressed this issue? I am convinced this relation indicates a sort of homeostasis is buried in the system which can only act to reduce CO2 sensitivity.
If you scour the literature there have been hints for many years before Spencer that something like this is going on. Lindzen seems to me to be the person who has the strongest sense of it but I also earlier quoted an obscure paper from 2000 by two Egyptian meteorologists which is tantalising in this regard. I suspect Ken Takahashi of NOAA knows it is there too.
BTW, I take it you have noticed the global SW flux simply reflected off the surface due to surface albedo given by K,T&F08 is also 23 W/m^2 – precisely equal to the global (LW) difference between A_A and E_D given by them! Another coincidence? Maybe it is and maybe it isn’t.
• Geoff Sherrington
Re Steve Short #138,
You sure take a tough line on rejecting balances that are slightly different! I read through your list and put a tick against most and then you came along and gave a fail.
I do not want to preempt the fat lady in song, but I do not think that you can truly state that
“(1) the so-called Miskolczi ‘proof’ of no temperature discontinuity at or very near to the surface is dead in the water”
My reasoning is that the measurement of temperatures at this interface is wide open to interpretation, convention, definition or whatever. There really is no such creature as surface sea temperature. There is a gradient which is mixed to various degrees. With what part of the gradient are you comparing the atmosphere? Likewise, the atmosphere, from mast experiments, is a horrible mishmash until you get above a few hundred m altitude. If you are comparing with a surface compilation like HADCRU, then the extensive literature on blogs about the problems with this are legendary.
For reasons like this, I’m pleased that the effort will not stop here. Please take my sincere thanks for your combined works to date.
• Geoff Sherrington
Re Steve Short #138,
You sure take a tough line on rejecting balances that are slightly different! I read through your list and put a tick against most and then you came along and gave a fail.
I do not want to preempt the fat lady in song, but I do not think that you can truly state that
“(1) the so-called Miskolczi ‘proof’ of no temperature discontinuity at or very near to the surface is dead in the water”
My reasoning is that the measurement of temperatures at this interface is wide open to interpretation, convention, definition or whatever. There really is no such creature as surface sea temperature. There is a gradient which is mixed to various degrees. With what part of the gradient are you comparing the atmosphere? Likewise, the atmosphere, from mast experiments, is a horrible mishmash until you get above a few hundred m altitude. If you are comparing with a surface compilation like HADCRU, then the extensive literature on blogs about the problems with this are legendary.
For reasons like this, I’m pleased that the effort will not stop here. Please take my sincere thanks for your combined works to date.
• jae
Geoff:
“You sure take a tough line on rejecting balances that are slightly different! I read through your list and put a tick against most and then you came along and gave a fail.”
Just what I was thinking. Why should we expect the datasets to agree exactly?
• jae
Geoff:
“You sure take a tough line on rejecting balances that are slightly different! I read through your list and put a tick against most and then you came along and gave a fail.”
Just what I was thinking. Why should we expect the datasets to agree exactly?
• http://www.ecoengineers.com Steve Short
Geoff Sherrington #141
“You sure take a tough line on rejecting balances that are slightly different! ”
jae #142
“Just what I was thinking. Why should we expect the datasets to agree exactly?”
Hhhmmmm….K,T&F08 is a review paper just like K&T97 was. BTW, Nick Stokes previously made this point.
K,T&F08 compare their 9CERES) estimates (for effectively all the terms I covered) from the 5 year CERES study with three other quite separate studies (i.e. datasets) – the ICCP FD, the NRA and JRA studies. The references for these other three studies/datsets are given. Indeed, for the oceans they also checked K (i.e. H_S and H_L) against two further studies as well. This is understandable given that global mean oceanic convective sensible and latent heat fluxes are so contentious (e.g. Spencer et al. etc).
Sorry guys, but IMHO both of your comments would ring rather hollow to anyone who has actually read right through the K,T&F08 review paper and perhaps followed up on the other studies.
• http://www.ecoengineers.com Steve Short
Geoff Sherrington #141
“You sure take a tough line on rejecting balances that are slightly different! ”
jae #142
“Just what I was thinking. Why should we expect the datasets to agree exactly?”
Hhhmmmm….K,T&F08 is a review paper just like K&T97 was. BTW, Nick Stokes previously made this point.
K,T&F08 compare their 9CERES) estimates (for effectively all the terms I covered) from the 5 year CERES study with three other quite separate studies (i.e. datasets) – the ICCP FD, the NRA and JRA studies. The references for these other three studies/datsets are given. Indeed, for the oceans they also checked K (i.e. H_S and H_L) against two further studies as well. This is understandable given that global mean oceanic convective sensible and latent heat fluxes are so contentious (e.g. Spencer et al. etc).
Sorry guys, but IMHO both of your comments would ring rather hollow to anyone who has actually read right through the K,T&F08 review paper and perhaps followed up on the other studies.
• Geoff Sherrington
Steve Short #143
Given that this is Niche Modeling, the Power of Numeracy, I would have expected to see some error estimates on the raw figures. I simply do not know if comparisons are statistically different at any chosen level of confidence. I fully accept that it is easy to sit back and ask this, for it is not a simple task, but you might have some informal feel for accuracy that would help set relevance. I’m not sniping, I just don’t know how confident you are.
• Geoff Sherrington
Steve Short #143
Given that this is Niche Modeling, the Power of Numeracy, I would have expected to see some error estimates on the raw figures. I simply do not know if comparisons are statistically different at any chosen level of confidence. I fully accept that it is easy to sit back and ask this, for it is not a simple task, but you might have some informal feel for accuracy that would help set relevance. I’m not sniping, I just don’t know how confident you are.
• http://www.ecoengineers.com Steve Short
Geoff Sherrington #144
“I simply do not know if comparisons are statistically different at any chosen level of confidence. ”
All I can say Geoff, as someone who is very interested in Miskolczi’s work as I am that you re-read Section 6. Error Estimates, Section 7. Greenhouse parameters and Section 8. Zonal distributions in M07. To his credit Miskolczi discussed the issue of relative error bounds to his parameters especially the transfer functions and various LW taus and their implications. See for example Fig. 7. For example, simple arithmetic shows is hard to a reconcile the global mean LW tau of 2.29 of K, T &F 08 with Misckolci’s predicted 1.87 (a 24.5% difference on the mean) with his theoretical error predictions.
• http://www.ecoengineers.com Steve Short
Geoff Sherrington #144
“I simply do not know if comparisons are statistically different at any chosen level of confidence. ”
All I can say Geoff, as someone who is very interested in Miskolczi’s work as I am that you re-read Section 6. Error Estimates, Section 7. Greenhouse parameters and Section 8. Zonal distributions in M07. To his credit Miskolczi discussed the issue of relative error bounds to his parameters especially the transfer functions and various LW taus and their implications. See for example Fig. 7. For example, simple arithmetic shows is hard to a reconcile the global mean LW tau of 2.29 of K, T &F 08 with Misckolci’s predicted 1.87 (a 24.5% difference on the mean) with his theoretical error predictions.
• Anonymous
Steve, In your accounting, the one main difference is the amount of transmittance S_T isn’t it. M uses 1/6 but KT&F; is a lot less, 1/10. Would that difference account for the differences you are looking at. How accurate are estimates of transmittance anyway? Isn’t that a really grey area.
Steve, In your accounting, the one main difference is the amount of transmittance S_T isn’t it. M uses 1/6 but KT&F is a lot less, 1/10. Would that difference account for the differences you are looking at. How accurate are estimates of transmittance anyway? Isn’t that a really grey area.
• http://www.ecoengineers.com Steve Short
“Steve, In your accounting, the one main difference is the amount of transmittance S_T isn’t it. M uses 1/6 but KT&F is a lot less, 1/10. Would that difference account for the differences you are looking at. How accurate are estimates of transmittance anyway? Isn’t that a really grey area.”
According to the KT&F08 review (noting my earlier comments about the comparison included therein with two other studies), IR transmitted up through the atmosphere (S_T) is 40 W/m^2. For an S_U of 396 this give a LW tauA of 2.29. I have checked the literature repeatedly over recent years and very few papers give S_T around 60 as Miskolczi does (which gives him S_T/S_U of ~1/6).
So it appears that Miskolczi has always overestimated S_T by 20 – 25 W/m^2. It just so happens that this is approximately equivalent to the reflected SW (~23 W/m^2) which, together with the SW reflected by the clouds and atmospheric aerosols (~79 W/m^2) gives the total reflected SW which provides the Earth’s albedo (102/341 = 0.299).
You will recall I had a discussion with Miskolczi which showed he was quite clear about the magnitude of the SW absorption (~75 W/m^2) as a fraction of the albedo-correction incident SW (Fo; = 341 – 102 = 239)?
Yet I find it curious that Miskolczi should consistently promote an S_T around 60 – 70 through two papers and in numerous other venues (e.g. the Heartland Institute conference and various Zagoni presentations etc) in the face of other literature which always suggested it was nearer 40 W/m^2. After all, this number has been kicking around the literature since the early 90s. I also note that his S_U is consistently low by about 20 – 25 W/m^2 from the values that generally appeared in the literature over the same period.
It seems to me that some ‘mystery offset’ of around 20 – 25 W/m^2 has often consistently appeared throughout in Miskolczi’s work to cause all sorts of ‘havoc’ e.g.
(1) to shift LW tauA down from around 2.3 to around 1.9 (noting that until he came along tau was generally considered to lie between 2 and 3);
(2) to shift S_T up by about 20 – 25 W/m^2 (noting it was generally considered to be around 40) ;
(3) to shift S_U down by about 20 – 25 W/m^2 (noting it was generally considered to be around 390) ;
(4) to shift E_D up by about 20 – 25 W/m^2 (producing A_A = E_D)
I just find it curious that this offset is always in the same ballpark as the surface reflected SW.
Perhaps Miskolczi may have coded one of his many circular arguments into the Fortran of his HARTCODE…….
• http://www.ecoengineers.com Steve Short
“Steve, In your accounting, the one main difference is the amount of transmittance S_T isn’t it. M uses 1/6 but KT&F is a lot less, 1/10. Would that difference account for the differences you are looking at. How accurate are estimates of transmittance anyway? Isn’t that a really grey area.”
According to the KT&F08 review (noting my earlier comments about the comparison included therein with two other studies), IR transmitted up through the atmosphere (S_T) is 40 W/m^2. For an S_U of 396 this give a LW tauA of 2.29. I have checked the literature repeatedly over recent years and very few papers give S_T around 60 as Miskolczi does (which gives him S_T/S_U of ~1/6).
So it appears that Miskolczi has always overestimated S_T by 20 – 25 W/m^2. It just so happens that this is approximately equivalent to the reflected SW (~23 W/m^2) which, together with the SW reflected by the clouds and atmospheric aerosols (~79 W/m^2) gives the total reflected SW which provides the Earth’s albedo (102/341 = 0.299).
You will recall I had a discussion with Miskolczi which showed he was quite clear about the magnitude of the SW absorption (~75 W/m^2) as a fraction of the albedo-correction incident SW (Fo; = 341 – 102 = 239)?
Yet I find it curious that Miskolczi should consistently promote an S_T around 60 – 70 through two papers and in numerous other venues (e.g. the Heartland Institute conference and various Zagoni presentations etc) in the face of other literature which always suggested it was nearer 40 W/m^2. After all, this number has been kicking around the literature since the early 90s. I also note that his S_U is consistently low by about 20 – 25 W/m^2 from the values that generally appeared in the literature over the same period.
It seems to me that some ‘mystery offset’ of around 20 – 25 W/m^2 has often consistently appeared throughout in Miskolczi’s work to cause all sorts of ‘havoc’ e.g.
(1) to shift LW tauA down from around 2.3 to around 1.9 (noting that until he came along tau was generally considered to lie between 2 and 3);
(2) to shift S_T up by about 20 – 25 W/m^2 (noting it was generally considered to be around 40) ;
(3) to shift S_U down by about 20 – 25 W/m^2 (noting it was generally considered to be around 390) ;
(4) to shift E_D up by about 20 – 25 W/m^2 (producing A_A = E_D)
I just find it curious that this offset is always in the same ballpark as the surface reflected SW.
Perhaps Miskolczi may have coded one of his many circular arguments into the Fortran of his HARTCODE…….
• Nick Stokes
How accurate are estimates of transmittance anyway?
Good, I think. It’s basically a Beer’s Law calculation for a LBL code, which is simpler than IR with re-emission. Experimentally, you can estimate it directly from spectra. In the Fig 8.2a that I’m always going on about, there is a part of the spectrum (the atmospheric window) that tracks the ground temperature BB emission curve. You just have to integrate the power over that, with a small amount extra from the fringes. Incidentally, it looks like a large fraction there, but a lot of the shorter wavelength part of the IR spectrum is missing.
• Nick Stokes
How accurate are estimates of transmittance anyway?
Good, I think. It’s basically a Beer’s Law calculation for a LBL code, which is simpler than IR with re-emission. Experimentally, you can estimate it directly from spectra. In the Fig 8.2a that I’m always going on about, there is a part of the spectrum (the atmospheric window) that tracks the ground temperature BB emission curve. You just have to integrate the power over that, with a small amount extra from the fringes. Incidentally, it looks like a large fraction there, but a lot of the shorter wavelength part of the IR spectrum is missing.
• jae
“In the Fig 8.2a that I’m always going on about, ”
LOL. That figure is ingrained into my brain!
• jae
“In the Fig 8.2a that I’m always going on about, ”
LOL. That figure is ingrained into my brain!
• Jan Pompe
Nick #148
but a lot of the shorter wavelength part of the IR spectrum is missing.
The smaller the wave number the longer the wavelength
• Jan Pompe
Nick #148
but a lot of the shorter wavelength part of the IR spectrum is missing.
The smaller the wave number the longer the wavelength
• Nick Stokes
Jan #150 – you’re right, I meant longer wavelength.
• Nick Stokes
Jan #150 – you’re right, I meant longer wavelength.
• Anonymous
It does seem like the transmittance would be accurate to less than the factor between the two theories. I seem to remember reading statement by FM about this a few times. No doubt there is more to it than oversight.
• http://landshape.org/enm David Stockwell
It does seem like the transmittance would be accurate to less than the factor between the two theories. I seem to remember reading statement by FM about this a few times. No doubt there is more to it than oversight.
• http://www.friendsofscience.org Ken Gregory
Steve Short’s summary (#138)shows:
Su = 396 W/m2
Ed = 333 W/m2
Aa = 356 W/m2
Aa could not exactly equal Ed because the average temperature of the atmosphere at the mean altitude where Ed is emitted is colder than the atmosphere at the surface due to the lapse rate. Do we agree that the actual time average temperature of the atmosphere at the surface is equal to the surface temperature, since they are in physical contact?
I read somewhere that the mean optical path of a photon from the surface to absorption by a GHG molecule is about 20 m, but I don’t know if this is a good estimate.
The article “The new climate theory of Dr. Ferenc Miskolczi” (on this website) states in the Cabauw measurements section:
“In fact, the graph illustrates simply that, because the mean free path of the photons that interact with atmospheric components is so short, on the order of meters, no appreciable temperature differences along that path occur.”
Is there a good scientific measurement or estimate of this mean free path of the photons?
If the dry adiabatic lapse rate is 9.8 C/km, in 20 m the temperature changes by 0.196 C. Doesn’t this suggest that Ed must be very close to Aa, unless the mean free path is much greater than 20 m?
Ignoring the fact the average of a 4th power is not the same as the 4th power of an average, the Su of 396 W/m2 corresponds to 15.93 C (Su = T Sigma^4: Sigma = 5.67 E-8 W/(m2K)). At 0.196 C lower temperature black body emits 394.93 W/m2 or only 1.07 W/m2 less. Does this imply that Ed should be only about 1 w/m2 less than Aa if the mean free path length is about 20 m?
• http://www.friendsofscience.org Ken Gregory
Steve Short’s summary (#138)shows:
Su = 396 W/m2
Ed = 333 W/m2
Aa = 356 W/m2
Aa could not exactly equal Ed because the average temperature of the atmosphere at the mean altitude where Ed is emitted is colder than the atmosphere at the surface due to the lapse rate. Do we agree that the actual time average temperature of the atmosphere at the surface is equal to the surface temperature, since they are in physical contact?
I read somewhere that the mean optical path of a photon from the surface to absorption by a GHG molecule is about 20 m, but I don’t know if this is a good estimate.
The article “The new climate theory of Dr. Ferenc Miskolczi” (on this website) states in the Cabauw measurements section:
“In fact, the graph illustrates simply that, because the mean free path of the photons that interact with atmospheric components is so short, on the order of meters, no appreciable temperature differences along that path occur.”
Is there a good scientific measurement or estimate of this mean free path of the photons?
If the dry adiabatic lapse rate is 9.8 C/km, in 20 m the temperature changes by 0.196 C. Doesn’t this suggest that Ed must be very close to Aa, unless the mean free path is much greater than 20 m?
Ignoring the fact the average of a 4th power is not the same as the 4th power of an average, the Su of 396 W/m2 corresponds to 15.93 C (Su = T Sigma^4: Sigma = 5.67 E-8 W/(m2K)). At 0.196 C lower temperature black body emits 394.93 W/m2 or only 1.07 W/m2 less. Does this imply that Ed should be only about 1 w/m2 less than Aa if the mean free path length is about 20 m?
• jan pompe
Ken #153
Is there a good scientific measurement or estimate of this mean free path of the photons?
using the empirically measured extinction coefficient here we see
E = 20.2 m2/mol * 0.0159 mol/m3 * 10 m = 3.21
As the transmission T = 10-3.21 is 0.6 per mille, we conclude that the relative absorption around the peak is 1-T = 99.94% which takes place already within a 10 m layer near ground.
As for this:
Do we agree that the actual time average temperature of the atmosphere at the surface is equal to the surface temperature, since they are in physical contact?
I certainly do agree but would note that if one is silly enough to account for radiative transport alone then owing to the inverse square law for electromagnetic field intensity there will be a temperature discontinuity at thermal equilibrium.
• jan pompe
Ken #153
Is there a good scientific measurement or estimate of this mean free path of the photons?
using the empirically measured extinction coefficient here we see
E = 20.2 m2/mol * 0.0159 mol/m3 * 10 m = 3.21
As the transmission T = 10-3.21 is 0.6 per mille, we conclude that the relative absorption around the peak is 1-T = 99.94% which takes place already within a 10 m layer near ground.
As for this:
Do we agree that the actual time average temperature of the atmosphere at the surface is equal to the surface temperature, since they are in physical contact?
I certainly do agree but would note that if one is silly enough to account for radiative transport alone then owing to the inverse square law for electromagnetic field intensity there will be a temperature discontinuity at thermal equilibrium.
• Nick Stokes
Ken: I read somewhere that the mean optical path of a photon from the surface to absorption by a GHG molecule is about 20 m, but I don’t know if this is a good estimate.
Everything is very frequency dependent, so these gray-body concepts aren’t very useful. About 10% of the flux is through the frequencies of the IR atmospheric window, where the mean path is almost infinite. If you include that in a mean, the answer won’t be 20m. A harmonic mean might give such an answer, but if that kind of artifice is needed, the concept is not useful.
Doesn’t this suggest that Ed must be very close to Aa, unless the mean free path is much greater than 20 m?
Maybe close, but not “very close”, because of the frequency issue. The atmospheric window does not contribute much to either Ed or Aa, but the fringe frequencies are more significant. Then there is a whole range of effective emission heights. You’re right to focus on this, though, because it is a way of seeing an aspect of the greenhouse effect. The fact that Su comes from a warm surface, and Ed comes back from colder air is the mode of nett energy transmission for a significant part of the spectrum. And the effect of more GHG is to ensure that Ed comes back from lower, warmer air, reeducing the nett transmission.
• Nick Stokes
Ken: I read somewhere that the mean optical path of a photon from the surface to absorption by a GHG molecule is about 20 m, but I don’t know if this is a good estimate.
Everything is very frequency dependent, so these gray-body concepts aren’t very useful. About 10% of the flux is through the frequencies of the IR atmospheric window, where the mean path is almost infinite. If you include that in a mean, the answer won’t be 20m. A harmonic mean might give such an answer, but if that kind of artifice is needed, the concept is not useful.
Doesn’t this suggest that Ed must be very close to Aa, unless the mean free path is much greater than 20 m?
Maybe close, but not “very close”, because of the frequency issue. The atmospheric window does not contribute much to either Ed or Aa, but the fringe frequencies are more significant. Then there is a whole range of effective emission heights. You’re right to focus on this, though, because it is a way of seeing an aspect of the greenhouse effect. The fact that Su comes from a warm surface, and Ed comes back from colder air is the mode of nett energy transmission for a significant part of the spectrum. And the effect of more GHG is to ensure that Ed comes back from lower, warmer air, reeducing the nett transmission.
• http://www.ecoengineers.com Steve Short
jan #154
“I certainly do agree but would note that if one is silly enough to account for radiative transport alone then owing to the inverse square law for electromagnetic field intensity there will be a temperature discontinuity at thermal equilibrium.”
Similarly of course that if one is silly enough to assume convective transfer of heat (both sensible and latent) from the surface is strictly continuous and hence not associated with characteristic pressure differences or other aspects of fluid dynamics it will not have any such thing as a frequency and there will also not be a temperature discontinuity at thermal equilibrium.
However we all know it doesn’t rain continuously – don’t we?
• http://www.ecoengineers.com Steve Short
jan #154
“I certainly do agree but would note that if one is silly enough to account for radiative transport alone then owing to the inverse square law for electromagnetic field intensity there will be a temperature discontinuity at thermal equilibrium.”
Similarly of course that if one is silly enough to assume convective transfer of heat (both sensible and latent) from the surface is strictly continuous and hence not associated with characteristic pressure differences or other aspects of fluid dynamics it will not have any such thing as a frequency and there will also not be a temperature discontinuity at thermal equilibrium.
However we all know it doesn’t rain continuously – don’t we?
• jae
Nick: You triggered again my probably boring continual question with this statement:
“And the effect of more GHG is to ensure that Ed comes back from lower, warmer air, reeducing the nett transmission.”
Yes, that’s part of the AGW creed, but I’m still trying to find a way to actually “observe” this mystical greenhouse effect. So, I have been waiting for some 3 years for someone to explain to me why it’s hotter in a low-elevation desert in July than it is in a tropical area near water at the same latitude and elevation. The greenhouse gas concentration in the humid area is over three (3) times the concentration in the desert. Where is this radiative greenhouse effect from all the extra water vapor in the tropical area? The effects should be immediately apparent, if it is a radiative effect, since EMR travels at the speed of light. One should be able to actually feel all this extra IR (as well as measure its effect with a thermometer). Why does it never get hotter in Guam than about 33 C, whereas 50 C is common in the great deserts around 30 N Latitude? Does the energy for evaporation cancel it out (if so, that is a negative feedback, folks)? Is this a matter of the logarithmic effect between ghg concentration and radiation?
The ghg concentrations in the tropical paradises is about 25,000 ppm (V/V), which is 2.5% of the atmosphere. It’s roughly 7,700 ppm, or 0.77 % in the dryest (and hottest) of the deserts. Why are the deserts so much hotter? I’ve been told that it is because of rainshadows and Froehn winds (adiabatic compression of down welling air), and this may play some role. But is this effect even more powerful than the greenhouse effect that has putatively caused a 33 C difference on a planet with vs. without GHGs?
And please, nobody give me any mythical statements about how it freezes in the desert at night and boils eggs in the day Indeed, it is hotter in the desert, even at night, unless it is a high-altitude desert–and then the effect is due to altitude and not to lack of moisture. It’s true that the dirunal variation is a function of moisture and is much greater in dry areas, but this is almost certainly related to the lapse rate, not to the presence of “radiating gases” and “greenhouse effects.”
• jae
Nick: You triggered again my probably boring continual question with this statement:
“And the effect of more GHG is to ensure that Ed comes back from lower, warmer air, reeducing the nett transmission.”
Yes, that’s part of the AGW creed, but I’m still trying to find a way to actually “observe” this mystical greenhouse effect. So, I have been waiting for some 3 years for someone to explain to me why it’s hotter in a low-elevation desert in July than it is in a tropical area near water at the same latitude and elevation. The greenhouse gas concentration in the humid area is over three (3) times the concentration in the desert. Where is this radiative greenhouse effect from all the extra water vapor in the tropical area? The effects should be immediately apparent, if it is a radiative effect, since EMR travels at the speed of light. One should be able to actually feel all this extra IR (as well as measure its effect with a thermometer). Why does it never get hotter in Guam than about 33 C, whereas 50 C is common in the great deserts around 30 N Latitude? Does the energy for evaporation cancel it out (if so, that is a negative feedback, folks)? Is this a matter of the logarithmic effect between ghg concentration and radiation?
The ghg concentrations in the tropical paradises is about 25,000 ppm (V/V), which is 2.5% of the atmosphere. It’s roughly 7,700 ppm, or 0.77 % in the dryest (and hottest) of the deserts. Why are the deserts so much hotter? I’ve been told that it is because of rainshadows and Froehn winds (adiabatic compression of down welling air), and this may play some role. But is this effect even more powerful than the greenhouse effect that has putatively caused a 33 C difference on a planet with vs. without GHGs?
And please, nobody give me any mythical statements about how it freezes in the desert at night and boils eggs in the day Indeed, it is hotter in the desert, even at night, unless it is a high-altitude desert–and then the effect is due to altitude and not to lack of moisture. It’s true that the dirunal variation is a function of moisture and is much greater in dry areas, but this is almost certainly related to the lapse rate, not to the presence of “radiating gases” and “greenhouse effects.”
• Nick Stokes
jae #154
Well, my standard response is that GHG fluxes are rather small but cumulative (for the Earth), and horizontal transport is large but not cumulative, so you shouldn’t look for local greenhouse effect temp variations. But there’s another factor you might like to think about.
Latent heat transport is quite large on average near the surface. About 80 W/m2, as I recall. It’s measured by rainfall. Now of course it is not evenly distributed – it’s much larger in humid areas, and there’s very little in the desert (cf rain). So in the desert almost all the heat from the surface up is IR, and that needs a high temperature to drive it. In humid areas, you could easily have an LH flux of 150 W/m2, say, and the IR flux can be much less, with correspondingly less surface temperature driving it.
• Nick Stokes
jae #154
Well, my standard response is that GHG fluxes are rather small but cumulative (for the Earth), and horizontal transport is large but not cumulative, so you shouldn’t look for local greenhouse effect temp variations. But there’s another factor you might like to think about.
Latent heat transport is quite large on average near the surface. About 80 W/m2, as I recall. It’s measured by rainfall. Now of course it is not evenly distributed – it’s much larger in humid areas, and there’s very little in the desert (cf rain). So in the desert almost all the heat from the surface up is IR, and that needs a high temperature to drive it. In humid areas, you could easily have an LH flux of 150 W/m2, say, and the IR flux can be much less, with correspondingly less surface temperature driving it.
• Geoff Sherrington
Re Nick #155
You write “And the effect of more GHG is to ensure that Ed comes back from lower, warmer air, reeducing the nett transmission.”
Without having done the maths, I’d guess that this effect was insignficant. Do you have a feel for the numbers? From what I have seen, the “fringe” frequencies are typically distributed towards short penetration half-lengths rather than long. It’s dangerous ground to talk about average distances with exponential decay. In radioactice work we tended to talk about 10 half-lives as approaching zero effect, but seldom used half life to express a practical physical effect, like how far you needed to stand from a source to be safe. (Short haf lives mean greater decay rate and so greater danger on approach, depending on mode of decay, alpha, beta, gamma etc).
• Geoff Sherrington
Re Nick #155
You write “And the effect of more GHG is to ensure that Ed comes back from lower, warmer air, reeducing the nett transmission.”
Without having done the maths, I’d guess that this effect was insignficant. Do you have a feel for the numbers? From what I have seen, the “fringe” frequencies are typically distributed towards short penetration half-lengths rather than long. It’s dangerous ground to talk about average distances with exponential decay. In radioactice work we tended to talk about 10 half-lives as approaching zero effect, but seldom used half life to express a practical physical effect, like how far you needed to stand from a source to be safe. (Short haf lives mean greater decay rate and so greater danger on approach, depending on mode of decay, alpha, beta, gamma etc).
• Geoff Sherrington
jae
If you contact me by email at sherro1 at optusnet com au I’ll send you some rough work in progress that might help your argument. Geoff.
• Geoff Sherrington
jae
If you contact me by email at sherro1 at optusnet com au I’ll send you some rough work in progress that might help your argument. Geoff.
• jae
Nick: Sorry, none of that seems to address my question.
• jae
Nick: Sorry, none of that seems to address my question.
• Geoff Sherrington
For the usual suspects,
I have been studying 17 sites selected from the BOM RCS network as truly rural. About half are by the sea and about half are desert.
Annual average rainfall (mm) and number of rain days per year is shown below, together with mean maximum annual temp.
Broome 532, 44, 32.1
Carnarvon 227, 40, 27.4
Ceduna 300, 93, 23.6
Charleville 490, 60, 28.3
Cobar 400, 60, 25.0
Esperance 620, 135, 21.8
Forrest WA 353, 66, 25.8
Giles n/a, n/a, n/a
Gove 1460, 120, 30.7
Halls Creek 560, 62, 33.5
Learmonth 260, 26, 31.8
Longreach 444, 47, 31.5
(Lord Howe Is) , ,
(Macquarie Is) , ,
Meekatharra 237, 46, 29.0
Tennant Creek 462, 50, 31.9
Woomera 187, 50, 25.8
So you can get together with some desert versus humid data to see if rain does affect things all that much. It does not vary a great deal in this dataset, Gove aside. The number of rain days is more steady than I would have imagined. Tmax is my calculation for the period of more reliable data 1968-2008 incl.
Why not plug these into a multiple regression to see what goes with what (statistically, of course). Let me know if you need other variables like altitude, distance from sea, population, etc.
Hidden catch/warning. There is a rather large difference in the rate of cooling of some of these sites over the 41 years of data. If you project the trends (which I refuse to do) 500 years back or forth, you would have strange times indeed. So there is an unreported strong signal that we can talk about when you arrive at consensus on this set of figures.
• Geoff Sherrington
For the usual suspects,
I have been studying 17 sites selected from the BOM RCS network as truly rural. About half are by the sea and about half are desert.
Annual average rainfall (mm) and number of rain days per year is shown below, together with mean maximum annual temp.
Broome 532, 44, 32.1
Carnarvon 227, 40, 27.4
Ceduna 300, 93, 23.6
Charleville 490, 60, 28.3
Cobar 400, 60, 25.0
Esperance 620, 135, 21.8
Forrest WA 353, 66, 25.8
Giles n/a, n/a, n/a
Gove 1460, 120, 30.7
Halls Creek 560, 62, 33.5
Learmonth 260, 26, 31.8
Longreach 444, 47, 31.5
(Lord Howe Is) , ,
(Macquarie Is) , ,
Meekatharra 237, 46, 29.0
Tennant Creek 462, 50, 31.9
Woomera 187, 50, 25.8
So you can get together with some desert versus humid data to see if rain does affect things all that much. It does not vary a great deal in this dataset, Gove aside. The number of rain days is more steady than I would have imagined. Tmax is my calculation for the period of more reliable data 1968-2008 incl.
Why not plug these into a multiple regression to see what goes with what (statistically, of course). Let me know if you need other variables like altitude, distance from sea, population, etc.
Hidden catch/warning. There is a rather large difference in the rate of cooling of some of these sites over the 41 years of data. If you project the trends (which I refuse to do) 500 years back or forth, you would have strange times indeed. So there is an unreported strong signal that we can talk about when you arrive at consensus on this set of figures.
• Nick Stokes
Geoff #159
I described an elementary way of doing the maths here:
http://climateaudit.org/phpBB3/viewtopic.php?f=4&t=667&st=0&sk=t&sd=a&start=80#p13694
It’s major – about 10% of IR gets out directly. The other 90% is emitted from GHG.
For this purpose, half-life (or something close) is the relevant number. Sure traces will penetrate much further, but it’s the power they carry that counts. Or statistically, on average how often does a photon get absorbed and reemitted before it gets through (with the caveat that it isn’t the same (or even a related) photon, but that’s the idea).
• Nick Stokes
Geoff #159
I described an elementary way of doing the maths here:
http://climateaudit.org/phpBB3/viewtopic.php?f=4&t=667&st=0&sk=t&sd=a&start=80#p13694
It’s major – about 10% of IR gets out directly. The other 90% is emitted from GHG.
For this purpose, half-life (or something close) is the relevant number. Sure traces will penetrate much further, but it’s the power they carry that counts. Or statistically, on average how often does a photon get absorbed and reemitted before it gets through (with the caveat that it isn’t the same (or even a related) photon, but that’s the idea).
• Nick Stokes
jae #161
Yes, it does address your question. We agree that humid air obstructs the progress of IR, and all else being equal, that would make such places warmer. But humid regions have another way of transporting heat, via latent heat transport. Their insolation is similar, so that means they have to emit less IR to maintain balance. They can do this, even through a more resistive pathway, because the flux is less, and can be moved with a smaller temperature differential.
• Nick Stokes
jae #161
Yes, it does address your question. We agree that humid air obstructs the progress of IR, and all else being equal, that would make such places warmer. But humid regions have another way of transporting heat, via latent heat transport. Their insolation is similar, so that means they have to emit less IR to maintain balance. They can do this, even through a more resistive pathway, because the flux is less, and can be moved with a smaller temperature differential.
• jae
“Yes, it does address your question. We agree that humid air obstructs the progress of IR, and all else being equal, that would make such places warmer. But humid regions have another way of transporting heat, via latent heat transport. Their insolation is similar, so that means they have to emit less IR to maintain balance. They can do this, even through a more resistive pathway, because the flux is less, and can be moved with a smaller temperature differential.”
WOW. WTF?
• jae
“Yes, it does address your question. We agree that humid air obstructs the progress of IR, and all else being equal, that would make such places warmer. But humid regions have another way of transporting heat, via latent heat transport. Their insolation is similar, so that means they have to emit less IR to maintain balance. They can do this, even through a more resistive pathway, because the flux is less, and can be moved with a smaller temperature differential.”
WOW. WTF?
• jae
Geoff: I don’t see how one can derive any trends/relationships from such yearly data. You need to use seasonal,preferably monthly, data and you need average temperatures and humidities, preferably absolute humidities. You can have situations where all the rain is in one season and others where it is spread througout the year. Seaside locations are also very different from interior locations, due to ocean effects.
• jae
Geoff: I don’t see how one can derive any trends/relationships from such yearly data. You need to use seasonal,preferably monthly, data and you need average temperatures and humidities, preferably absolute humidities. You can have situations where all the rain is in one season and others where it is spread througout the year. Seaside locations are also very different from interior locations, due to ocean effects.
• jae
Nick:
“Well, my standard response is that GHG fluxes are rather small but cumulative (for the Earth), and horizontal transport is large but not cumulative, so you shouldn’t look for local greenhouse effect temp variations. ”
I know. I’ve thought about this a lot, and it doesn’t do much for me. If the GHG fluxes are small, how do we get a 33 C rise from a no-GHG scenario? Are you saying that they are small, due to the logarithmic effect? If so, how can you have a significant “positive water vapor feedback” from OCO increases?
• jae
Nick:
“Well, my standard response is that GHG fluxes are rather small but cumulative (for the Earth), and horizontal transport is large but not cumulative, so you shouldn’t look for local greenhouse effect temp variations. ”
I know. I’ve thought about this a lot, and it doesn’t do much for me. If the GHG fluxes are small, how do we get a 33 C rise from a no-GHG scenario? Are you saying that they are small, due to the logarithmic effect? If so, how can you have a significant “positive water vapor feedback” from OCO increases?
• jae
• jae
• Anonymous
Long article. Care to give us a bottom line for you jae? Does this mean he agrees that IR transmittance should be more like 1/6 as Miskolczi suggests, and not 1/10 as K&T; think?
Long article. Care to give us a bottom line for you jae? Does this mean he agrees that IR transmittance should be more like 1/6 as Miskolczi suggests, and not 1/10 as K&T think?
• http://www.ecoengineers.com Steve Short
jae #168
“Hah, Jeffifer Marohasy has a great article on how GHGs work! ”
Jeffifer eh? Try Juniper (apologies to Steven Georgiou aka Yusuf Islam).
Well, a quick read through at the start of a work day suggests that Hammer’s logic is probably dodgy.
What we really need of course is our resident ‘hot shot’ heat engineer Jan to give it the once over as there are a lot of allusions to Stefan’s Law etc.
If Hammer can find a flaw in the Kiehl and Trenberth model it would be nice.
After all, if a top notch radiation physicist like Ferenc Miskolczi can somehow ‘lose’ about 20 – 25 W/m^2 in the global heat balance anything is possible in this ‘best of all possible worlds’.
• http://www.ecoengineers.com Steve Short
jae #168
“Hah, Jeffifer Marohasy has a great article on how GHGs work! ”
Jeffifer eh? Try Juniper (apologies to Steven Georgiou aka Yusuf Islam).
Well, a quick read through at the start of a work day suggests that Hammer’s logic is probably dodgy.
What we really need of course is our resident ‘hot shot’ heat engineer Jan to give it the once over as there are a lot of allusions to Stefan’s Law etc.
If Hammer can find a flaw in the Kiehl and Trenberth model it would be nice.
After all, if a top notch radiation physicist like Ferenc Miskolczi can somehow ‘lose’ about 20 – 25 W/m^2 in the global heat balance anything is possible in this ‘best of all possible worlds’.
• Nick Stokes
Key parts of Hammer’s article – he estimates the IR flux through the atmospheric window at 143 W/m2, assuming perfect transmission. K&T’s corresponding figure is 9 W/m2. The difference is probably in the allowances for AW fringe effects etc. The issue is the allowance for cloud effects. K&T make an “ad hoc” adjustment based on satellite (ISCCP) observartions of 62% cloud cover. And Hammer:
“Only a portion of the Earth’s surface at any given time is cloud covered and much of the dense cloud is low altitude cloud, thus a reasonable estimate for the Earth as a whole would be that clouds reduce the energy escaping to space in the atmospheric window by no more than about 15% to 20%.”
On that “reasonable estimate” the refutation of K&T is based.
• Nick Stokes
Key parts of Hammer’s article – he estimates the IR flux through the atmospheric window at 143 W/m2, assuming perfect transmission. K&T’s corresponding figure is 9 W/m2. The difference is probably in the allowances for AW fringe effects etc. The issue is the allowance for cloud effects. K&T make an “ad hoc” adjustment based on satellite (ISCCP) observartions of 62% cloud cover. And Hammer:
“Only a portion of the Earth’s surface at any given time is cloud covered and much of the dense cloud is low altitude cloud, thus a reasonable estimate for the Earth as a whole would be that clouds reduce the energy escaping to space in the atmospheric window by no more than about 15% to 20%.â€
On that “reasonable estimate” the refutation of K&T is based.
• Nick Stokes
typo – K&T’s AW figure is 99 W/m2, not 9
• Nick Stokes
typo – K&T’s AW figure is 99 W/m2, not 9
• http://www.ecoengineers.com Steve Short
Nick #172
“typo – K&T’s AW figure is 99 W/m2, not 9″
Now reduced by T,F&K08 to…….63 W/m^2?
BTW, let me emphasize that I don’t endorse T,F&K08. It produces an ‘acceptable’ global energy balance only. Reading it is still a shocking experience even to a hardened old experimental scientist. It clearly shows how much uncertainty there still is over some of the individual fluxes. Numerous papers of even the most recent years continue to persistently highlight this. T,F&K08 is in fact an indictment of the massive dune of shifting sands which is the mountain of AGW rectitude.
Yet so far the other side could only come up with is a half-baked theory cobbled together by a gifted but dogmatically eccentric outsider who insisted you had to take on faith every single nail in his edifice or be damned to you – and hence damned himself! In this context I say to Hammer – good on you – go for it. Sooner or later the one true prophet might appear… perhaps.
• http://www.ecoengineers.com Steve Short
Nick #172
“typo – K&T’s AW figure is 99 W/m2, not 9″
Now reduced by T,F&K08 to…….63 W/m^2?
BTW, let me emphasize that I don’t endorse T,F&K08. It produces an ‘acceptable’ global energy balance only. Reading it is still a shocking experience even to a hardened old experimental scientist. It clearly shows how much uncertainty there still is over some of the individual fluxes. Numerous papers of even the most recent years continue to persistently highlight this. T,F&K08 is in fact an indictment of the massive dune of shifting sands which is the mountain of AGW rectitude.
Yet so far the other side could only come up with is a half-baked theory cobbled together by a gifted but dogmatically eccentric outsider who insisted you had to take on faith every single nail in his edifice or be damned to you – and hence damned himself! In this context I say to Hammer – good on you – go for it. Sooner or later the one true prophet might appear… perhaps.
• Nick Stokes
Steve #173
No, I think 63 W/m2 is nett upward LW from the surface. I don’t think they revisited the AW transmission figures at all.
As far as TFK08 is concerned, some of the accountancy is uncertain, including this figure of 40 W/m2 transmitted. However, many of those figures don’t really matter for heat balance. Whwther IR gets through without ever being absorbed, or if a fraction was absorbed and reemitted once, doesn’t change the energy figures much.
The figure that counts for AGW is the nett in/out imbalance, and that is currently too small (expected to be about 2 W/m2) to show up reliably in the budget measurements, and has to be inferred from modelling etc. But not for too much longer. We’re close to being able to both measure incoming SW and outgoing LW accurately enough to measure the AGW imbalance directly. And we’re close to being able to close the budget by good ocean heat measurements to again check the imbalance independently.
• Nick Stokes
Steve #173
No, I think 63 W/m2 is nett upward LW from the surface. I don’t think they revisited the AW transmission figures at all.
As far as TFK08 is concerned, some of the accountancy is uncertain, including this figure of 40 W/m2 transmitted. However, many of those figures don’t really matter for heat balance. Whwther IR gets through without ever being absorbed, or if a fraction was absorbed and reemitted once, doesn’t change the energy figures much.
The figure that counts for AGW is the nett in/out imbalance, and that is currently too small (expected to be about 2 W/m2) to show up reliably in the budget measurements, and has to be inferred from modelling etc. But not for too much longer. We’re close to being able to both measure incoming SW and outgoing LW accurately enough to measure the AGW imbalance directly. And we’re close to being able to close the budget by good ocean heat measurements to again check the imbalance independently.
• Anonymous
Steve: Yeah, nobody is perfect. I like that Ferenc was very willing to talk about and explain his work quite patiently. Not like some others. There value in putting all of your speculations into one paper, and seeing what sticks. Theres a downside too.
But on another issue, about the latest Shaviv offering on the ocean heat content. Is it really the case that nobody noticed before that periodic ocean heat flux is 5-7 times the TSI periodic flux? I mean, it seems so obvious, its either brilliant, or already done isn’t it? Last thing I heard about ocean heat content (OHC), was by someone at Scripps Institute in San Diego five years ago, telling the press OHC has the fingerprints of AGW and anyone who denied global warming after his results was a moron.
Steve: Yeah, nobody is perfect. I like that Ferenc was very willing to talk about and explain his work quite patiently. Not like some others. There value in putting all of your speculations into one paper, and seeing what sticks. Theres a downside too.
But on another issue, about the latest Shaviv offering on the ocean heat content. Is it really the case that nobody noticed before that periodic ocean heat flux is 5-7 times the TSI periodic flux? I mean, it seems so obvious, its either brilliant, or already done isn’t it? Last thing I heard about ocean heat content (OHC), was by someone at Scripps Institute in San Diego five years ago, telling the press OHC has the fingerprints of AGW and anyone who denied global warming after his results was a moron.
• jae
174, Nick: “The figure that counts for AGW is the nett in/out imbalance, and that is currently too small (expected to be about 2 W/m2) to show up reliably in the budget measurements, and has to be inferred from modelling etc. But not for too much longer. We’re close to being able to both measure incoming SW and outgoing LW accurately enough to measure the AGW imbalance directly. And we’re close to being able to close the budget by good ocean heat measurements to again check the imbalance independently.”
I doubt it, because as Admin says:
“But on another issue, about the latest Shaviv offering on the ocean heat content. Is it really the case that nobody noticed before that periodic ocean heat flux is 5-7 times the TSI periodic flux? I mean, it seems so obvious, its either brilliant, or already done isn’t it? Last thing I heard about ocean heat content (OHC), was by someone at Scripps Institute in San Diego five years ago, telling the press OHC has the fingerprints of AGW and anyone who denied global warming after his results was a moron.”
There will probably always be too much lag to develop some budget accurate to a few watts.
BTW, I’m still trying to digest the Hammer paper. It is an interesting take by an expert in radiation.
• jae
174, Nick: “The figure that counts for AGW is the nett in/out imbalance, and that is currently too small (expected to be about 2 W/m2) to show up reliably in the budget measurements, and has to be inferred from modelling etc. But not for too much longer. We’re close to being able to both measure incoming SW and outgoing LW accurately enough to measure the AGW imbalance directly. And we’re close to being able to close the budget by good ocean heat measurements to again check the imbalance independently.”
I doubt it, because as Admin says:
“But on another issue, about the latest Shaviv offering on the ocean heat content. Is it really the case that nobody noticed before that periodic ocean heat flux is 5-7 times the TSI periodic flux? I mean, it seems so obvious, its either brilliant, or already done isn’t it? Last thing I heard about ocean heat content (OHC), was by someone at Scripps Institute in San Diego five years ago, telling the press OHC has the fingerprints of AGW and anyone who denied global warming after his results was a moron.”
There will probably always be too much lag to develop some budget accurate to a few watts.
BTW, I’m still trying to digest the Hammer paper. It is an interesting take by an expert in radiation.
• http://www.ecoengineers.com Steve Short
Nick #174
“We’re close to being able to both measure incoming SW and outgoing LW accurately enough to measure the AGW imbalance directly. And we’re close to being able to close the budget by good ocean heat measurements to again check the imbalance independently.”
I think we’ll be doing a lot more than just ‘holding the ‘phone’ on that one – especially since the OCO satellite ended up in the ocean somewhere off Antarctica.
I hope y’all caught Paul Biggs’ post on CCNet today?
It is a lucid exposition of the current state of play in the context of the issues raised by Tsonis et al, GRL 2007, Wang, Swanson and Tsonis, 2009 and an even newer paper by Swanson and Tsonis which all claimed that in 2001/02 climate shifted away from the consistent warming trend for the period 1976/77 to 2001/02 against a background of global CO2 emissions increasing at a rate of 3.5% per year since 2000.
I think it is worthwhile quoting parts of the remainder of what Biggs says:
“Meanwhile, Nir Shaviv’s latest paper finds more evidence of an unknown solar amplification mechanism, where the radiative forcing associated with small changes in Total Solar Irradiance (TSI) over the 11-year solar cycle are multiplied by 5 to 7 times. ”
“On 21st December 2006 NASA’s David Hathaway was predicting that solar cycle 24 would be bigger than cycle 23. By January 2009 he changed his mind and predicted a smaller cycle 24. Hathaway also predicts a very small cycle 25, and Milivoje Vukcevic claims to have a formula that predicts cycle 26 that will be even lower than cycle 25. In their 2008 GRL paper Weiss et al asked ‘For how long will the current grand maximum of solar activity persist?’ The answer was probably not very long, but they couldn’t predict the level of the ensuing minimum and they remained loyal to the greenhouse warming ‘consensus’ by stating that any cooling would be “insignificant compared with the global warming caused by greenhouse gases. ”
“So, the lack of cycle 24 sunspots continues and the ‘grand maximum’ of solar activity we enjoyed during the 20th century may be coming to an end. Small changes in the Sun may have much larger effects on climate, and the Pacific Decadal Oscillation (PDO) seems to have entered a cool phase that could last between 21 to 25 years. If the global non-warming since 2002 continues for 30 years as Kyle Swanson suggests, then we have to consider the possibility that, rather than going into hiding, CO2 isn’t the all powerful climate driver that some would have us believe.”
So, to paraphrase Biggs:
Rather than developing a (new) ’30 year hiding place for CO2′ hypothesis [the very latest example of AGW high wire acrobatics which Swanson and Held revealed on the 3rd March!!!!] we can look to the collective behaviour of long-known climate cycles such as the Pacific Decadal Oscillation, the North Atlantic Oscillation, the El Nino/Southern Oscillation, and the North Pacific Oscillation, plus poorly understood solar factors as a big part of the explanation for climate change.
IMHO when we get to look back on all this in about 25 – 30 years (hopefully I can hold out that long), we’ll see what a giant exercise in bad science the AGW movement really was. Then perhaps we’ll be done with the curse of the rise of late 20th century ‘post-modernist science’ and it’s outrageously double- and triple-jointed attitude to truth once and for all.
• http://www.ecoengineers.com Steve Short
Nick #174
“We’re close to being able to both measure incoming SW and outgoing LW accurately enough to measure the AGW imbalance directly. And we’re close to being able to close the budget by good ocean heat measurements to again check the imbalance independently.”
I think we’ll be doing a lot more than just ‘holding the ‘phone’ on that one – especially since the OCO satellite ended up in the ocean somewhere off Antarctica.
I hope y’all caught Paul Biggs’ post on CCNet today?
It is a lucid exposition of the current state of play in the context of the issues raised by Tsonis et al, GRL 2007, Wang, Swanson and Tsonis, 2009 and an even newer paper by Swanson and Tsonis which all claimed that in 2001/02 climate shifted away from the consistent warming trend for the period 1976/77 to 2001/02 against a background of global CO2 emissions increasing at a rate of 3.5% per year since 2000.
I think it is worthwhile quoting parts of the remainder of what Biggs says:
“Meanwhile, Nir Shaviv’s latest paper finds more evidence of an unknown solar amplification mechanism, where the radiative forcing associated with small changes in Total Solar Irradiance (TSI) over the 11-year solar cycle are multiplied by 5 to 7 times. ”
“On 21st December 2006 NASA’s David Hathaway was predicting that solar cycle 24 would be bigger than cycle 23. By January 2009 he changed his mind and predicted a smaller cycle 24. Hathaway also predicts a very small cycle 25, and Milivoje Vukcevic claims to have a formula that predicts cycle 26 that will be even lower than cycle 25. In their 2008 GRL paper Weiss et al asked ‘For how long will the current grand maximum of solar activity persist?’ The answer was probably not very long, but they couldn’t predict the level of the ensuing minimum and they remained loyal to the greenhouse warming ‘consensus’ by stating that any cooling would be “insignificant compared with the global warming caused by greenhouse gases. ”
“So, the lack of cycle 24 sunspots continues and the ‘grand maximum’ of solar activity we enjoyed during the 20th century may be coming to an end. Small changes in the Sun may have much larger effects on climate, and the Pacific Decadal Oscillation (PDO) seems to have entered a cool phase that could last between 21 to 25 years. If the global non-warming since 2002 continues for 30 years as Kyle Swanson suggests, then we have to consider the possibility that, rather than going into hiding, CO2 isn’t the all powerful climate driver that some would have us believe.”
So, to paraphrase Biggs:
Rather than developing a (new) ’30 year hiding place for CO2′ hypothesis [the very latest example of AGW high wire acrobatics which Swanson and Held revealed on the 3rd March!!!!] we can look to the collective behaviour of long-known climate cycles such as the Pacific Decadal Oscillation, the North Atlantic Oscillation, the El Nino/Southern Oscillation, and the North Pacific Oscillation, plus poorly understood solar factors as a big part of the explanation for climate change.
IMHO when we get to look back on all this in about 25 – 30 years (hopefully I can hold out that long), we’ll see what a giant exercise in bad science the AGW movement really was. Then perhaps we’ll be done with the curse of the rise of late 20th century ‘post-modernist science’ and it’s outrageously double- and triple-jointed attitude to truth once and for all.
• Anonymous
“Are you now, or have you evern been a believer in AGW?”
• http://landshape.org/enm David Stockwell
“Are you now, or have you evern been a believer in AGW?”
• Alex Harvey
Steve #177,
…we can look to the collective behaviour of long-known climate cycles such as the Pacific Decadal Oscillation, the North Atlantic Oscillation, the El Nino/Southern Oscillation, and the North Pacific Oscillation, plus poorly understood solar factors as a big part of the explanation for climate change.
You’ve probably already seen this, as I found it cited in Lindzen 2007, but in case you haven’t there’s a very interesting article here:
Tsonis, A. A., K. Swanson, and S. Kravtsov (2007), A new dynamical mechanism for major climate shifts, Geophys. Res. Lett., 34, L13705, doi:10.1029/2007GL030288.
http://www.nosams.whoi.edu/PDFs/papers/tsonis-grl_newtheoryforclimateshifts.pdf
Lindzen’s 2007 article seems to be the only one citing it at this stage (well, based on Google Scholar). So it looks like this is yet another skeptical theory that is being just ignored.
Is there a proper name for the fallacy of refutation by pretending not to be able to hear any counter-arguments?
• Alex Harvey
Steve #177,
…we can look to the collective behaviour of long-known climate cycles such as the Pacific Decadal Oscillation, the North Atlantic Oscillation, the El Nino/Southern Oscillation, and the North Pacific Oscillation, plus poorly understood solar factors as a big part of the explanation for climate change.
You’ve probably already seen this, as I found it cited in Lindzen 2007, but in case you haven’t there’s a very interesting article here:
Tsonis, A. A., K. Swanson, and S. Kravtsov (2007), A new dynamical mechanism for major climate shifts, Geophys. Res. Lett., 34, L13705, doi:10.1029/2007GL030288.
http://www.nosams.whoi.edu/PDFs/papers/tsonis-grl_newtheoryforclimateshifts.pdf
Lindzen’s 2007 article seems to be the only one citing it at this stage (well, based on Google Scholar). So it looks like this is yet another skeptical theory that is being just ignored.
Is there a proper name for the fallacy of refutation by pretending not to be able to hear any counter-arguments?
• http://www.ecoengineers.com Steve Short
IMO there is an actual sensitivity to atmospheric CO2 but it is highly likely less than 1.5 K and quite likely less than 1 K. I accord the reason for the difficulty in discerning the actual value to the fact that the world climate system contains an evolved biotic homeostasis applying in the presence of natural physical internal oscillations and external perturbations which act to mask that value.
Succinct enough for you?
• http://www.ecoengineers.com Steve Short
IMO there is an actual sensitivity to atmospheric CO2 but it is highly likely less than 1.5 K and quite likely less than 1 K. I accord the reason for the difficulty in discerning the actual value to the fact that the world climate system contains an evolved biotic homeostasis applying in the presence of natural physical internal oscillations and external perturbations which act to mask that value.
Succinct enough for you?
• Anonymous
Steve: Do you have a url for that article by Biggs?
Alex: Confirmation bias I think, also ‘cherry picking’. Its regarded as acceptable in climate science. I have given up trying to argue against it. The reviewers simply say ‘well the statement(s) are not wrong’. See the reviews of my manuscript to AMM. The reviewer states ‘the conclusions in the summary are consistent with the text of the report’, while ignoring the fact that the observational results were not reported in the summary, presumably because they directly contradict the forecasts of the models (of increasing drought). I have other examples of failed submission using the same arguments. See the bristle-cones. In the real world the omissions of salient information are called misleading statements. ‘Misleading’ is not in the vocabulary of climate liberals.
• http://landshape.org/enm David Stockwell
Steve: Do you have a url for that article by Biggs?
Alex: Confirmation bias I think, also ‘cherry picking’. Its regarded as acceptable in climate science. I have given up trying to argue against it. The reviewers simply say ‘well the statement(s) are not wrong’. See the reviews of my manuscript to AMM. The reviewer states ‘the conclusions in the summary are consistent with the text of the report’, while ignoring the fact that the observational results were not reported in the summary, presumably because they directly contradict the forecasts of the models (of increasing drought). I have other examples of failed submission using the same arguments. See the bristle-cones. In the real world the omissions of salient information are called misleading statements. ‘Misleading’ is not in the vocabulary of climate liberals.
• http://www.ecoengineers.com Steve Short
Don’t lose heart David. In a 15 year pure research ‘previous life’ (including 11 years as a SRS in an Aust. Federal Govt. agency) I found cliques in which gross dissembling and misleading statements are stock in trade to perpetuate their pet lines and ‘paradigms’ are not uncommon in science. Having also worked in Western Europe and the US I perceived the effect was (is?) particularly bad ‘Downunder’, extending right into CSIRO publishing with some editors exhibiting a finely-tuned rat-like ‘nose’ for just which (clique-based) ‘key’ reviewers to send manuscripts to. On one key discovery of mine which copped a real nasty hammering (only) down here, I got the last laugh (albeit a few years later), with it now applied worldwide.
The post by Paul Biggs was on today’s CCNet. I thought you may have been on Benny Peiser’s wonderful mailing list (which FYI a lot of ‘closet denier’ politicians receive)? For those who are interested:
CCNet is a scholarly electronic network edited by Benny Peiser. To subscribe, send an e-mail to [email protected] (“subscribe cambridge-conference”). To unsubscribe send an e-mail to [email protected] (“unsubscribe cambridge-conference”). Information circulated on this network is for scholarly and educational use only.
The attached information may not be copied or reproduced for any other purposes without prior permission of the copyright holders. DISCLAIMER:
The opinions, beliefs and viewpoints expressed in the articles and texts and in other CCNet contributions do not necessarily reflect the opinions, beliefs and viewpoints of the editor.
http://www.staff.livjm.ac.uk/spsbpeis/
• http://www.ecoengineers.com Steve Short
Don’t lose heart David. In a 15 year pure research ‘previous life’ (including 11 years as a SRS in an Aust. Federal Govt. agency) I found cliques in which gross dissembling and misleading statements are stock in trade to perpetuate their pet lines and ‘paradigms’ are not uncommon in science. Having also worked in Western Europe and the US I perceived the effect was (is?) particularly bad ‘Downunder’, extending right into CSIRO publishing with some editors exhibiting a finely-tuned rat-like ‘nose’ for just which (clique-based) ‘key’ reviewers to send manuscripts to. On one key discovery of mine which copped a real nasty hammering (only) down here, I got the last laugh (albeit a few years later), with it now applied worldwide.
The post by Paul Biggs was on today’s CCNet. I thought you may have been on Benny Peiser’s wonderful mailing list (which FYI a lot of ‘closet denier’ politicians receive)? For those who are interested:
CCNet is a scholarly electronic network edited by Benny Peiser. To subscribe, send an e-mail to [email protected] (“subscribe cambridge-conference”). To unsubscribe send an e-mail to [email protected] (“unsubscribe cambridge-conference”). Information circulated on this network is for scholarly and educational use only.
The attached information may not be copied or reproduced for any other purposes without prior permission of the copyright holders. DISCLAIMER:
The opinions, beliefs and viewpoints expressed in the articles and texts and in other CCNet contributions do not necessarily reflect the opinions, beliefs and viewpoints of the editor.
http://www.staff.livjm.ac.uk/spsbpeis/
• http://www.ecoengineers.com Steve Short
Alex #179
“Is there a proper name for the fallacy of refutation by pretending not to be able to hear any counter-arguments?”
As it is such a very worthwhile endeavour, I hereby formally name this fallacy (and claim originality) as the ‘Flutterby Effect’.
Just as with the well-known Butterfly Effect, it too may be borne out of chaos (not to mention MEP ;-), viz:
We construct a network of observed climate indices in
the period 1900–2000 and investigate their collective
behavior. The results indicate that this network
synchronized several times in this period. We find that in
those cases where the synchronous state was followed by a
steady increase in the coupling strength between the indices,
the synchronous state was destroyed, after which a new
climate state emerged. These shifts are associated with
significant changes in global temperature trend and in
ENSO variability. The latest such event is known as the
great climate shift of the 1970s. We also find the evidence
for such type of behavior in two climate simulations using a
state-of-the-art model. This is the first time that this
mechanism, which appears consistent with the theory of
synchronized chaos, is discovered in a physical system of
the size and complexity of the climate system.
Citation: Tsonis, A. A., K. Swanson, and S. Kravtsov (2007),
A new dynamical mechanism for major climate shifts, Geophys.
Res. Lett., 34, L13705, doi:10.1029/2007GL030288.
• http://www.ecoengineers.com Steve Short
Alex #179
“Is there a proper name for the fallacy of refutation by pretending not to be able to hear any counter-arguments?”
As it is such a very worthwhile endeavour, I hereby formally name this fallacy (and claim originality) as the ‘Flutterby Effect’.
Just as with the well-known Butterfly Effect, it too may be borne out of chaos (not to mention MEP ;-), viz:
We construct a network of observed climate indices in
the period 1900–2000 and investigate their collective
behavior. The results indicate that this network
synchronized several times in this period. We find that in
those cases where the synchronous state was followed by a
steady increase in the coupling strength between the indices,
the synchronous state was destroyed, after which a new
climate state emerged. These shifts are associated with
significant changes in global temperature trend and in
ENSO variability. The latest such event is known as the
great climate shift of the 1970s. We also find the evidence
for such type of behavior in two climate simulations using a
state-of-the-art model. This is the first time that this
mechanism, which appears consistent with the theory of
synchronized chaos, is discovered in a physical system of
the size and complexity of the climate system.
Citation: Tsonis, A. A., K. Swanson, and S. Kravtsov (2007),
A new dynamical mechanism for major climate shifts, Geophys.
Res. Lett., 34, L13705, doi:10.1029/2007GL030288.
• jae
OT, but there is no “unthreaded” here.
My wife rented a copy of the movie, Australia (which we will watch sometime this weekend). Since so many folks from the Down-Under frequent this blog, I thought I’d ask if the movie is worth watching, from an Austrailian’s perspective. Anyone?
• jae
OT, but there is no “unthreaded” here.
My wife rented a copy of the movie, Australia (which we will watch sometime this weekend). Since so many folks from the Down-Under frequent this blog, I thought I’d ask if the movie is worth watching, from an Austrailian’s perspective. Anyone?
• http://www.ecoengineers.com Steve Short
“A given surface air temperature change is consistent with either a relatively large heating which is penetrating rapidly into the oceans and delaying some of the surface warming (i.e., a high climate sensitivity and a high ocean diffusivity), or a relatively small heating which is penetrating slowly into the oceans so the surface warming is quickly experienced (i.e., a low climate sensitivity and a low ocean diffusivity). Our analysis suggests that one promising avenue to decide whether the true climate sensitivity is indeed located in the heavy upper tail of current estimates is through improving the skill of the existing ocean observation system to estimate the anthropogenic heat uptake.”
Urban, Nathan M., and Klaus Keller, 2009. Complementary observational constraints on climate sensitivity. Geophys. Res. Lett., 36, L04708, doi:10.1029/2008GL036457, February 25, 2009, preprint online at http://www.geosc.psu.edu/~kkeller/Urban_Keller_grl_08_submitted.pdf
RE: URBAN & KELLER (2009)
Nir Shaviv [[email protected]]
Guys,
Urban and Keller use the standard 1750-2000 forcing (see end of page 1 of their paper). However, this does not include the real solar forcing which is much higher. As such, you need a large sensitivity from the (wrong) small forcing in order to get the heat content change. Thus, the climate sensitivity they calculate is meaningless.
Cheers
— Nir
Roy Spencer [[email protected]]
Theirs is not the only possibility. Another is that for a given temperature change AND a given ocean diffusivity, then it can either be the result of
(1) large forcing and low climate sensitivity, or
(2) small forcing and a high climate sensitivity.
I believe it is the former, and I now have satellite evidence of not only low climate sensitivity, but also that the large forcing is due to nature, not mankind.
-Roy
• http://www.ecoengineers.com Steve Short
“A given surface air temperature change is consistent with either a relatively large heating which is penetrating rapidly into the oceans and delaying some of the surface warming (i.e., a high climate sensitivity and a high ocean diffusivity), or a relatively small heating which is penetrating slowly into the oceans so the surface warming is quickly experienced (i.e., a low climate sensitivity and a low ocean diffusivity). Our analysis suggests that one promising avenue to decide whether the true climate sensitivity is indeed located in the heavy upper tail of current estimates is through improving the skill of the existing ocean observation system to estimate the anthropogenic heat uptake.â€
Urban, Nathan M., and Klaus Keller, 2009. Complementary observational constraints on climate sensitivity. Geophys. Res. Lett., 36, L04708, doi:10.1029/2008GL036457, February 25, 2009, preprint online at http://www.geosc.psu.edu/~kkeller/Urban_Keller_grl_08_submitted.pdf
RE: URBAN & KELLER (2009)
Nir Shaviv [[email protected]]
Guys,
Urban and Keller use the standard 1750-2000 forcing (see end of page 1 of their paper). However, this does not include the real solar forcing which is much higher. As such, you need a large sensitivity from the (wrong) small forcing in order to get the heat content change. Thus, the climate sensitivity they calculate is meaningless.
Cheers
— Nir
Roy Spencer [[email protected]]
Theirs is not the only possibility. Another is that for a given temperature change AND a given ocean diffusivity, then it can either be the result of
(1) large forcing and low climate sensitivity, or
(2) small forcing and a high climate sensitivity.
I believe it is the former, and I now have satellite evidence of not only low climate sensitivity, but also that the large forcing is due to nature, not mankind.
-Roy
• Anonymous
Steve: “is in fact an indictment of the massive dune of shifting sands which is the mountain of AGW rectitude.” A very nice turn of phrase. They always said that coulds were the greatest uncertainty, but I didn’t realize that ocean heat flux was in the same boat.
• http://landshape.org/enm David Stockwell
Steve: “is in fact an indictment of the massive dune of shifting sands which is the mountain of AGW rectitude.” A very nice turn of phrase. They always said that coulds were the greatest uncertainty, but I didn’t realize that ocean heat flux was in the same boat.
• http://www.ecoengineers.com Steve Short
Yet more of the Flutterby Effect:
Roger Pielke Sr has commented on the Urban & Keller paper on his weblog:
http://climatesci.org/2009/03/05/is-there-climate-heating-in-the-pipeline/
By “unrealized warming in the pipeline”, they mean heat that is being stored within the ocean, which can subsequently be released into the ocean atmosphere. It is erroneous to consider this heat as “unrealized warming”, if the Joules of heat are actually being stored in the ocean. The heat is “realized”; it would just not be entering the atmosphere yet.
As discussed in the Physics Today paper: Pielke Sr., R.A., 2008: A broader view of the role of humans in the climate system. (Physics Today, 61, Vol. 11, 54-55), there has been no heating of the upper ocean since mid-2003. Moreover, there has been no heating within the troposphere (e.g. see Figure 7 of the RSS MSU data).
Thus, there is no “warming in the pipeline” using the author’s terminology, nor any heating within the atmosphere! Perhaps the heating that was observed prior to 2003 will begin again, however, it is scientifically incorrect to report that there is any heat that has not yet been realized within the climate system.
The answer to the question posted in this weblog “Is There Climate Heating In “The Pipeline”? is NO.
Also, the Pielke Sr and Christy comment on Hansen et al 2005 “Earth’s Energy Imbalance: Confirmation and Implications” was bizarrely rejected by Science:
http://www.climatesci.org/publications/pdf/Hansen-Science.pdf
• http://www.ecoengineers.com Steve Short
Yet more of the Flutterby Effect:
Roger Pielke Sr has commented on the Urban & Keller paper on his weblog:
http://climatesci.org/2009/03/05/is-there-climate-heating-in-the-pipeline/
By “unrealized warming in the pipeline”, they mean heat that is being stored within the ocean, which can subsequently be released into the ocean atmosphere. It is erroneous to consider this heat as “unrealized warming”, if the Joules of heat are actually being stored in the ocean. The heat is “realized”; it would just not be entering the atmosphere yet.
As discussed in the Physics Today paper: Pielke Sr., R.A., 2008: A broader view of the role of humans in the climate system. (Physics Today, 61, Vol. 11, 54-55), there has been no heating of the upper ocean since mid-2003. Moreover, there has been no heating within the troposphere (e.g. see Figure 7 of the RSS MSU data).
Thus, there is no “warming in the pipeline” using the author’s terminology, nor any heating within the atmosphere! Perhaps the heating that was observed prior to 2003 will begin again, however, it is scientifically incorrect to report that there is any heat that has not yet been realized within the climate system.
The answer to the question posted in this weblog “Is There Climate Heating In “The Pipeline”? is NO.
Also, the Pielke Sr and Christy comment on Hansen et al 2005 “Earth’s Energy Imbalance: Confirmation and Implications” was bizarrely rejected by Science:
http://www.climatesci.org/publications/pdf/Hansen-Science.pdf
• Pingback: sam waltonman
• Pingback: iherb coupon
• Pingback: iherb coupon
• Pingback: iherb coupon
• Pingback: iherb promo code
• Pingback: iherb coupon code
• Pingback: highline residences 2 bedroom
• Pingback: Free Online Games
• Pingback: Escalate Internet
• Pingback: best friv games
• Pingback: sex live cams
• Pingback: Polygraph
• Pingback: ???????????? ????? ??????????????
• Pingback: stop premature ejaculation tablets
• Pingback: xbox live codes
• Pingback: Throne Rush Gems gennerator
• Pingback: Seo
• Pingback: 4 link suspension kit
• Pingback: Hardened PC Security
• Pingback: capture his heart review
• Pingback: http://kolikkopelit.widezone.net/
• Pingback: iherb coupon code
• Pingback: mark cobb
• Pingback: hairy anus
• Pingback: queens
• Pingback: best priced gold in africa
• Pingback: gopro hero3 black
• Pingback: iherb coupon
• Pingback: bonville.org
• Pingback: iherb.com coupon
• Pingback: new books on lung cancer
• Pingback: rv dealer donna
• Pingback: how to detox your body
• Pingback: clash of clans hack
• Pingback: bankruptcy attorney Miami
• Pingback: nokia pc suite windows 8
• Pingback: clash of clans cheats
• Pingback: Weight Loss
• Pingback: Primerica scam
• Pingback: Diindolylmethane
• Pingback: We Buy Houses in East Lyme, CT
• Pingback: San Antonio SEO Experts
• Pingback: clash of clans hack
• Pingback: gu10 led bulb
• Pingback: Splinter Cell Blacklist Trainer
• Pingback: browse around this website
• Pingback: pressure cooking eggs
• Pingback: global travel
• Pingback: alkaline water benefits
• Pingback: kratom extrakt
• Pingback: plano roofing company
• Pingback: Tanie kwatery
• Pingback: Omen Interactive
• Pingback: physicians medical center carraway
• Pingback: weight loss
• Pingback: Core Products
• Pingback: class d airspace
• Pingback: Logo design
• Pingback: rent a boat
• Pingback: creare site
• Pingback: geo news live urdu video
• Pingback: check out this site
• Pingback: weight loss diet
• Pingback: blucarpet.com
• Pingback: pipeline maintenance services
• Pingback: muscle gaining secrets ebook
• Pingback: metodo del ritmo como se calcula
• Pingback: Chapter 13
• Pingback: burçlar
• Pingback: social media management
• Pingback: Ranking filmów
• Pingback: clash of clans hack
• Pingback: kitchen planner
• Pingback: Party Store
• Pingback: alkaline water
• Pingback: ??????????? ?Θ??? ????Σ
• Pingback: cleaners
• Pingback: niezwykly wpis o bmw
• Pingback: karol hubert rostworowski
• Pingback: Multiple Search Engine
• Pingback: autoskup040.pl
• Pingback: quattroskup.pl
• Pingback: immigration lawyer savannah ga
• Pingback: napedy do bram przesuwnych
• Pingback: UK Lingerie
• Pingback: paleo recipe book review
• Pingback: M88
• Pingback: Nutrilite Supplements
• Pingback: free coins for slotomania
• Pingback: rental homes for sale
• Pingback: Joyería
• Pingback: File Recovery
• Pingback: Manifestation Miracle Review
• Pingback: new zombie show
• Pingback: fajsdgjfashdjfaksjdhkfa
• Pingback: Altieri Gilmore LLP Attorneys
• Pingback: visit the website
• Pingback: free medical billing software
• Pingback: o wienie
• Pingback: noclegi elblag
• Pingback: szkolenia niepelnosprawni
• Pingback: wyniki lotto
• Pingback: Montblanc Scratch Remover
• Pingback: WP Dollar
• Pingback: cd dvd label maker
• Pingback: free annual credit report
• Pingback: Logistics
• Pingback: SizeGenetics Penile Extender
• Pingback: how to make a poster on word
• Pingback: Out Of The Box SEO
• Pingback: arkitekter
• Pingback: Low-budget Shopping Online
• Pingback: Find Out More
• Pingback: free movie expendables 3
• Pingback: JavaTpoint
• Pingback: jobs at my mcdonalds
• Pingback: gogol spain
• Pingback: granier
• Pingback: gta 5 hack
• Pingback: clean cleanse
• Pingback: gnld carotenoid complex
• Pingback: tabasco
• Pingback: why not check here
• Pingback: Puppy Separation Anxiety
• Pingback: napoleon hill jesus christ
• Pingback: Political blog
• Pingback: next page
• Pingback: Frontline Commando 2 hack no survey
• Pingback: marilyn burns tribute
• Pingback: see here,
• Pingback: check over here
• Pingback: kangen water
• Pingback: gra gieldowa
• Pingback: Pulse induction
• Pingback: sonicare
• Pingback: Joe Garza
• Pingback: california
• Pingback: how to meditate
• Pingback: Cheap sunglasses
• Pingback: Flash
• Pingback: surgical tweezers
• Pingback: AVONDALE ELECTRICAL CONTRACTOR
• Pingback: epic fails
• Pingback: sterling silver jewellery
• Pingback: banned commercials
• Pingback: used-generators
• Pingback: buiness health & saftey insurance
• Pingback: bay area
• Pingback: shop
• Pingback: last longer tips
• Pingback: get rid of toenail fungus
• Pingback: paleo recipe book
• Pingback: kaffeevollautomat lidl
• Pingback: porter cable hand planer
• Pingback: psoriasis
• Pingback: christian store
• Pingback: tubeviperx review
• Pingback: criminal lawyer
• Pingback: shower design
• Pingback: Tube Viper X Software
• Pingback: Dryer vent cleaning
• Pingback: shooting game
• Pingback: Jamila Hartsook
• Pingback: Dodecanese
• Pingback: Erick Kiesz
• Pingback: Ideas
• Pingback: silicone needles
• Pingback: relationship
• Pingback: bare minerals brushes
• Pingback: Coupons
• Pingback: HERE
• Pingback: residential drain cleaning conroe
• Pingback: sports
• Pingback: Earn Money
• Pingback: Movie
• Pingback: Mens Underwear johannesburg
• Pingback: FX Education & training
• Pingback: auto loans
• Pingback: personal loans fast
• Pingback: Globetrotter
• Pingback: Cambia
• Pingback: Coffee dehydration
• Pingback: montecristo cigars
• Pingback: reviews of GreenSmoke
• Pingback: cuban cigars online
• Pingback: penyakit jantung
• Pingback: bar para festas
• Pingback: Garcinia Cambogia Extreme
• Pingback: love finding
• Pingback: dryer vent repair Alexandria Va
• Pingback: Box Mod
• Pingback: click clone cash review
• Pingback: instagram users search engine
• Pingback: LIve Scores
• Pingback: Chicago Wedding Cinematographer
• Pingback: how to make yourself taller
• Pingback: hair system replacement
• Pingback: Mudco Drywall
• Pingback: kabuki
• Pingback: Fence Repair
• Pingback: berkeley california decking
• Pingback: events sicily
• Pingback: find out here now
• Pingback: please click the next web page
• Pingback: santa
• Pingback: Flat Fee MLS Realtor IL
• Pingback: blog www
• Pingback: wholesale makeup
• Pingback: unblocked games
• Pingback: wholesale makeup
• Pingback: dog poop bags bulk
• Pingback: triglyceride fish oil
• Pingback: how long average man last in bed
• Pingback: PTCSmarty
• Pingback: ice bucket challenge fails
• Pingback: whatsapp hack
• Pingback: openappmkt
• Pingback: busy z Niemiec do Polski
• Pingback: skup samochodów uzywanych
• Pingback: odd news
• Pingback: hydrocodone online
• Pingback: address book template free
• Pingback: race cycler comp plan
• Pingback: perth web designers
• Pingback: Tempe Glass Repair
• Pingback: Pest Control Houston Texas
• Pingback: plum lipstick
• Pingback: xlovecam hack tool 2013
• Pingback: how to get my ex back
• Pingback: videos jovencitas follando
• Pingback: dubai escorts
• Pingback: giochi di cucina
• Pingback: foder conas peludas
• Pingback: teen network
• Pingback: how to cheat andorid games
• Pingback: amazing animals
• Pingback: dishtv
• Pingback: cialis
• Pingback: comment gagner de l'argent
• Pingback: Fixstone Computer Service
• Pingback: banana blue
• Pingback: epic fails 2014
• Pingback: iniciar sesion en hotmail
• Pingback: Find More
• Pingback: houston affordable seo
• Pingback: Samsung Galaxy Case
• Pingback: divorce papers
• Pingback: zobacz oferte
• Pingback: loyal 9 reviews
• Pingback: Miriam
• Pingback: trail-gear
• Pingback: pet waste bags
• Pingback: tangkasnet
• Pingback: buy real soundcloud plays
• Pingback: sehack
• Pingback: donice drewniane
• Pingback: noclegi wroclaw
• Pingback: Continue
• Pingback: skuteczne pozycjonowanie semstar
• Pingback: samaa tv
• Pingback: GreenSmoke ecigarettes
• Pingback: Android Apps
• Pingback: mini perfumes
• Pingback: alldoza.net
• Pingback: Pegawai Tadbir Diplomatik Gred M41
• Pingback: gold teeth grills
• Pingback: Real Estate School License
• Pingback: atm hire
• Pingback: atms for event | 2014-09-17 11:32:57 | {"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": 0.602889358997345, "perplexity": 2381.9402588018083}, "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-2014-41/segments/1410657123284.86/warc/CC-MAIN-20140914011203-00096-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://hal-cea.archives-ouvertes.fr/cea-03468071 | How ion pair formation drives adsorption in the electrical double layer: Molecular dynamics of charged silica-water interfaces in the presence of divalent alkaline earth ions - Archive ouverte HAL Access content directly
Journal Articles Journal of Physical Chemistry C Year : 2021
## How ion pair formation drives adsorption in the electrical double layer: Molecular dynamics of charged silica-water interfaces in the presence of divalent alkaline earth ions
Kunyu Wang
• Function : Author
Bertrand Siboulet
Connectez-vous pour contacter l'auteur
Diane Rebiscoul
Jean-François Dufreche
Connectez-vous pour contacter l'auteur
#### Abstract
The study by numerical methods of ionic distributions in charged solid-liquid interfaces allows the interpretation of many concepts and phenomena such as the $\zeta$ potential or ion adsorption. Molecular dynamics (MD) can reveal detailed information about electric double layer (EDL), especially the Stern layer, by including electrostatic, van der Waals, and molecular forces. Here, we aim at analyzing the chemical species and the correlations between the ions and the surface including three-body e!ects, one particle belonging to the surface and two to the solution. Correlations are specified on the basis of interionic distance screening. An extensive description is provided from simulations of three alkaline earth metal chlorides (Mg$^{2+}$, Ca$^{2+}$, and Ba$^{2+}$) aqueous solutions at 0.6 mol/L$^{-1}$ in the centers of negatively charged silica nanochannels. The resulting McMillan-Mayer potentials of mean force (PMF) exhibit a decreasing affinity of deprotonated silanol along with the series Mg$^{2+}$ > Ca$^{2+}$ > Ba$^{2+}$, while the formation of bulk M$^{2+}$-Cl$^-$ pairs is in reverse order. A similar trend is obtained for the association constants and the residence times. Over 40% of surface-bound Ba$^{2+}$ ions are correlated with surface-bound Cl$^-$, while the other two cations do not show such trend. When the surface-bound and surface-correlated ions are taken apart, the remaining free ion distributions fit the Poisson-Boltzmann equation well, i.e., the Gouy-Chapman model. This work demonstrates the necessity to account for three-body associations on oxide surface at least for divalent ions.
#### Domains
Chemical Sciences
### Dates and versions
cea-03468071 , version 1 (06-12-2021)
### Identifiers
• HAL Id : cea-03468071 , version 1
• DOI :
### Cite
Kunyu Wang, Bertrand Siboulet, Diane Rebiscoul, Jean-François Dufreche. How ion pair formation drives adsorption in the electrical double layer: Molecular dynamics of charged silica-water interfaces in the presence of divalent alkaline earth ions. Journal of Physical Chemistry C, 2021, 125, pp.20551-20569. ⟨10.1021/acs.jpcc.1c05570⟩. ⟨cea-03468071⟩
### Export
BibTeX TEI Dublin Core DC Terms EndNote Datacite
34 View | 2023-03-28 13:09:33 | {"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": 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": 0.3939683139324188, "perplexity": 9856.641378576252}, "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/1679296948858.7/warc/CC-MAIN-20230328104523-20230328134523-00322.warc.gz"} |
https://r.prevos.net/euler-problem-28/ | # The Ulam Spiral: Euler Problem 28
Euler Problem 28 takes us to the world of the Ulam Spiral. This is a spiral that contains sequential positive integers in a square spiral, marking the prime numbers. Stanislaw Ulam discovered that a lot of primes are located along the diagonals. These diagonals can be described as polynomials. The Ulam Spiral is thus a way of generating quadratic primes (Euler Problem 27).
Ulam Spiral (WikiMedia).
## Euler Problem 28 Definition
Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:
21 22 23 24 25
20 07 08 09 10
19 06 01 02 11
18 05 04 03 12
17 16 15 14 13
It can be verified that the sum of the numbers on the diagonals is 101. What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
## Proposed Solution
To solve this problem we do not need to create a matrix. This code calculates the values of the corners of a matrix with size $n$. The lowest number in the matrix with size $n$ is $n(n-3)+4$. The numbers increase by $n-1$.
The code steps through all matrices from size 3 to 1001. The solution uses only the uneven sized matrices because these have a centre. The answer to the problem is the sum of all numbers.
```size <- 1001 # Size of matrix
answer <- 1 # Starting number
# Define corners of subsequent matrices
for (n in seq(from = 3, to = size, by = 2)) {
corners <- seq(from = n * (n - 3) + 3, by = n - 1, length.out = 4)
}
```
## Plotting the Ulam Spiral
We can go beyond Euler Problem 28 and play with the mathematics. This code snippet plots all the prime numbers in the Ulam Spiral. Watch the video for an explanation of the patterns that appear along the diagonals.
Ulam Spiral prime numbers.
The code creates a matrix of the required size and fills it with the Ulam Spiral. The code then identifies all primes using the is.prime function from Euler Problem 7. A heat map visualises the results.
```# Ulam Spiral
size <- 201 # Size of matrix
ulam <- matrix(ncol = size, nrow = size)
mid <- floor(size / 2 + 1)
ulam[mid, mid] <- 1
for (n in seq(from = 3, to = size, by = 2)) {
numbers <- (n * (n - 4) + 5) : ((n + 2) * ((n + 2) - 4) + 4)
d <- mid - floor(n / 2)
l <- length(numbers)
ulam[d, d:(d + n - 1)] <- numbers[(l - n + 1):l]
ulam[d + n - 1, (d + n - 1):d] <- numbers[(n - 1):(n - 2 + n)]
ulam[(d + 1):(d + n - 2), d] <- numbers[(l - n):(l - 2 * n + 3)]
ulam[(d + 1):(d + n - 2), d + n - 1] <- numbers[1:(n - 2)]
}
ulam.primes <- apply(ulam, c(1, 2), is.prime)
# Visualise
library(ggplot2)
library(reshape2)
ulam.primes <- melt(ulam.primes)
ggplot(ulam.primes, aes(x=Var1, y=Var2, fill=value)) + geom_tile() +
scale_fill_manual(values = c("white", "black")) +
guides(fill=FALSE) +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_blank()) +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank(),
axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()
)
```
## 8 thoughts on “The Ulam Spiral: Euler Problem 28”
1. Actually, you should replace:
ulam <- numbers[(l – n + 1):l]
ulam <- numbers[(n – 1):(n – 2 + n)]
with:
ulam[c, c:(c + n -1)] <- numbers[(l – n + 1):l]
ulam[c + n -1, (c + n -1):c] <- numbers[(n – 1):(n – 2 + n)]
• Indeed, see my response to your previous comment. Thanks again for helping out.
• Great!
Thanks for interesting article.
2. Something wrong in the code – first you create a matrix:
ulam <- matrix(ncol = size, nrow = size)
next you correctly set the middle number:
ulam[mid, mid] <- 1
but later, you reference it as a variable:
ulam <- numbers[(l – n + 1):l]
It can't work this way!
• Hi World Observer,
Thanks for pointing this out. The SyntaxHighlighter plugin removed some of the code because it was confused by “[c”. Now that I have changed the variable c to d, the code displays correctly.
I have updated the code in the post.
Peter | 2018-03-24 09:44:47 | {"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": 0, "img_math": 4, "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": 0.6928895115852356, "perplexity": 892.7979770706205}, "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-2018-13/segments/1521257650188.31/warc/CC-MAIN-20180324093251-20180324113251-00794.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Ageorgiadis.h-g | Compute Distance To:
Documents Indexed: 56 Publications since 1985 Co-Authors: 19 Co-Authors with 45 Joint Publications 109 Co-Co-Authors
all top 5
### Co-Authors
9 single-authored 14 Brock, Louis M. 9 Gourgiotis, Panos A. 6 Lykotrafitis, G. 5 Rigatos, A. P. 5 Vardoulakis, Ioannis G. 3 Anagnostou, D. S. 3 Charalambakis, Nicolas Ch. 3 Grentzelou, C. G. 3 Theocaris, Pericles S. 2 Papadopoulos, George A. 2 Velgaki, E. G. 1 Ammar, Faouzi Ben 1 Hanson, Mark T. 1 Markoyannis, Triantafilos 1 Mouskos, S. C. 1 Neocleous, I. 1 Rodgers, Michael J. 1 Sifnaiou, M. D. 1 Vamvatsikos, D.
all top 5
### Serials
14 International Journal of Solids and Structures 8 Journal of Elasticity 5 Journal of Applied Mechanics 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Acta Mechanica 4 Wave Motion 3 International Journal of Engineering Science 2 Computational Mechanics 2 Archive of Applied Mechanics 2 Mathematics and Mechanics of Solids 1 IMA Journal of Applied Mathematics 1 International Journal of Plasticity 1 Indian Journal of Pure & Applied Mathematics 1 Journal of the Mechanics and Physics of Solids 1 Quarterly Journal of Mechanics and Applied Mathematics 1 International Journal of Fracture
all top 5
### Fields
56 Mechanics of deformable solids (74-XX) 5 Integral equations (45-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Partial differential equations (35-XX) 3 Numerical analysis (65-XX) 2 Integral transforms, operational calculus (44-XX) 1 Functions of a complex variable (30-XX) 1 Operator theory (47-XX)
### Citations contained in zbMATH Open
47 Publications have been cited 435 times in 252 Documents Cited by Year
The mode III crack problem in microstructured solids governed by dipolar gradient elasticity: static and dynamic analysis. Zbl 1110.74453
2003
Torsional surface waves in a gradient-elastic half-space. Zbl 1074.74567
Georgiadis, H. G.; Vardoulakis, I.; Lykotrafitis, G.
2000
Dispersive Rayleigh-wave propagation in microstructured solids characterized by dipolar gradient elasticity. Zbl 1058.74045
Georgiadis, H. G.; Vardoulakis, I.; Velgaki, E. G.
2004
High-frequency Rayleigh waves in materials with micro-structure and couple-stress effects. Zbl 1087.74567
Georgiadis, H. G.; Velgaki, E. G.
2003
SH surface waves in a homogeneous gradient-elastic half-space with surface energy. Zbl 0912.73016
1997
Problems of the Flamant-Boussinesq and Kelvin type in dipolar gradient elasticity. Zbl 1180.74007
Georgiadis, H. G.; Anagnostou, D. S.
2008
Energy theorems and the $$J$$-integral in dipolar gradient elasticity. Zbl 1120.74341
Georgiadis, H. G.; Grentzelou, C. G.
2006
On the reflection of waves in half-spaces of microstructured materials governed by dipolar gradient elasticity. Zbl 1454.74075
Gourgiotis, P. A.; Georgiadis, H. G.; Neocleous, I.
2013
Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity. Zbl 1193.74008
Gourgiotis, P. A.; Georgiadis, H. G.
2009
Distributed dislocation approach for cracks in couple-stress elasticity: shear modes. Zbl 1260.74007
Gourgiotis, P. A.; Georgiadis, H. G.
2007
Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity. Zbl 1119.74549
Grentzelou, C. G.; Georgiadis, H. G.
2005
A method based on the Radon transform for three-dimensional elastodynamic problems of moving loads. Zbl 1205.74064
2001
Steady-state transonic motion of a line load over an elastic half-space: The corrected Cole/Huth solution. Zbl 0805.73020
Georgiadis, H. G.; Barber, J. R.
1993
Anti-plane shear Lamb’s problem treated by gradient elasticity with surface energy. Zbl 1074.74566
1998
An approach based on distributed dislocations and disclinations for crack problems in couple-stress elasticity. Zbl 1273.74443
Gourgiotis, P. A.; Georgiadis, H. G.
2008
On the super-Rayleigh/subseismic elastodynamic indentation problem. Zbl 0782.73068
Georgiadis, H. G.; Barber, J. R.
1993
Balance laws and energy release rates for cracks in dipolar gradient elasticity. Zbl 1167.74325
Grentzelou, C. G.; Georgiadis, H. G.
2008
The three-dimensional steady-state thermo-elastodynamic problem of moving sources over a half space. Zbl 1025.74010
2003
Three-dimensional thermoelastic wave motions in a half-space under the action of a buried source. Zbl 1048.74016
Lykotrafitis, G.; Georgiadis, H. G.; Brock, L. M.
2001
Steady-state motion of a line mechanical/heat source over a half-space: A thermoelastodynamic solution. Zbl 0927.74019
Brock, L. M.; Georgiadis, H. G.
1997
Shear and torsional impact of cracked viscoelastic bodies – a numerical integral equation/transform approach. Zbl 0803.73020
1993
Numerical implementation of the integral-transform solution to Lamb’s point-load problem. Zbl 0981.74079
Georgiadis, H. G.; Vamvatsikos, D.; Vardoulakis, I.
1999
Asymmetrically cracked cylinder under torsion. Zbl 0586.73157
1986
Cracked orthotropic strip with clamped boundaries. Zbl 0675.73062
1988
An integral equation approach to self-similar plane-elastodynamic crack problems. Zbl 0731.73064
1991
Elastostatics of the orthotropic double-cantilever-beam fracture specimen. Zbl 0728.73059
1990
Plane impact of a cracked viscoelastic body. Zbl 0825.73113
Georgiadis, H. G.; Theocaris, P. S.; Mouskos, S. C.
1991
Multiple-zone sliding contact with friction on an anisotropic thermoelastic half-space. Zbl 1127.74029
Brock, L. M.; Georgiadis, H. G.
2007
Thermoelastodynamic disturbances in a half-space under the action of a buried thermal/mechanical line source. Zbl 0955.74018
Georgiadis, H. G.; Rigatos, A. P.; Brock, L. M.
1999
The Cerruti problem in dipolar gradient elasticity. Zbl 1329.74015
Anagnostou, D. S.; Gourgiotis, P. A.; Georgiadis, H. G.
2015
Moving punch on a highly orthotropic elastic layer. Zbl 0621.73128
1987
An illustration of sliding contact at any constant speed on highly elastic half-spaces. Zbl 1065.74051
Brock, L. M.; Georgiadis, H. G.
2001
The Boussinesq problem in dipolar gradient elasticity. Zbl 1341.74021
Georgiadis, H. G.; Gourgiotis, P. A.; Anagnostou, D. S.
2014
Tangential-displacement effects in the wedge indentation of an elastic half-space – an integral-equation approach. Zbl 0918.73066
1998
Static frictional indentation of an elastic half-plane by a rigid unsymmetrical punch. Zbl 0807.73065
Brock, L. M.; Georgiadis, H. G.; Charalambakis, N.
1994
Transient SIF results for a cracked viscoelastic strip under concentrated impact loading – An integral-transform/function-theoretic approach. Zbl 0953.74563
Georgiadis, H. G.; Rigatos, A. P.
1996
An approach based on integral equations for crack problems in standard couple-stress elasticity. Zbl 1396.74092
Georgiadis, H. G.; Gourgiotis, P. A.
2010
On the solution of steady-state elastodynamic crack problems by using complex variable methods. Zbl 0553.73090
Georgiadis, H. G.; Theocaris, P. S.
1985
Dynamic indentation of an elastic half-plane by a rigid wedge: Frictional and tangential-displacement effects. Zbl 0918.73076
Georgiadis, H. G.; Brock, L. M.; Rigatos, A. P.
1995
Rayleigh waves generated by a thermal source: a three-dimensional transient thermoelasticity solution. Zbl 1111.74414
2005
Dynamic stress concentration around a hole in a viscoelastic plate. Zbl 0863.73011
Georgiadis, H. G.; Rigatos, A. P.; Charalambakis, N. C.
1995
A correspondence principle connecting IBVPs of wave propagation and heat conduction. Zbl 0825.73141
1992
Dynamic frictional identation of an elastic half-plane by a rigid punch. Zbl 0823.73057
Brock, L. M.; Georgiadis, H. G.
1994
Exact elastodynamic analysis of some fracture specimen models involving strip geometries. Zbl 0943.74549
Georgiadis, H. G.; Brock, L. M.
1994
The Keldysh-Sedov method for a closed-form elastodynamic solution of the cracked strip under anti-plane shear. Zbl 0587.73141
Georgiadis, H. G.; Theocaris, P. S.
1986
An asymptotic solution for short-time transient heat conduction between two dissimilar bodies in contact. Zbl 0734.73005
Georgiadis, H. G.; Barber, J. R.; Ammar, F. Ben
1991
Rapid indentation of transversely isotropic or orthotropic half-spaces. Zbl 1110.74356
Brock, L. M.; Georgiadis, H. G.; Hanson, M. T.
2001
The Cerruti problem in dipolar gradient elasticity. Zbl 1329.74015
Anagnostou, D. S.; Gourgiotis, P. A.; Georgiadis, H. G.
2015
The Boussinesq problem in dipolar gradient elasticity. Zbl 1341.74021
Georgiadis, H. G.; Gourgiotis, P. A.; Anagnostou, D. S.
2014
On the reflection of waves in half-spaces of microstructured materials governed by dipolar gradient elasticity. Zbl 1454.74075
Gourgiotis, P. A.; Georgiadis, H. G.; Neocleous, I.
2013
An approach based on integral equations for crack problems in standard couple-stress elasticity. Zbl 1396.74092
Georgiadis, H. G.; Gourgiotis, P. A.
2010
Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity. Zbl 1193.74008
Gourgiotis, P. A.; Georgiadis, H. G.
2009
Problems of the Flamant-Boussinesq and Kelvin type in dipolar gradient elasticity. Zbl 1180.74007
Georgiadis, H. G.; Anagnostou, D. S.
2008
An approach based on distributed dislocations and disclinations for crack problems in couple-stress elasticity. Zbl 1273.74443
Gourgiotis, P. A.; Georgiadis, H. G.
2008
Balance laws and energy release rates for cracks in dipolar gradient elasticity. Zbl 1167.74325
Grentzelou, C. G.; Georgiadis, H. G.
2008
Distributed dislocation approach for cracks in couple-stress elasticity: shear modes. Zbl 1260.74007
Gourgiotis, P. A.; Georgiadis, H. G.
2007
Multiple-zone sliding contact with friction on an anisotropic thermoelastic half-space. Zbl 1127.74029
Brock, L. M.; Georgiadis, H. G.
2007
Energy theorems and the $$J$$-integral in dipolar gradient elasticity. Zbl 1120.74341
Georgiadis, H. G.; Grentzelou, C. G.
2006
Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity. Zbl 1119.74549
Grentzelou, C. G.; Georgiadis, H. G.
2005
Rayleigh waves generated by a thermal source: a three-dimensional transient thermoelasticity solution. Zbl 1111.74414
2005
Dispersive Rayleigh-wave propagation in microstructured solids characterized by dipolar gradient elasticity. Zbl 1058.74045
Georgiadis, H. G.; Vardoulakis, I.; Velgaki, E. G.
2004
The mode III crack problem in microstructured solids governed by dipolar gradient elasticity: static and dynamic analysis. Zbl 1110.74453
2003
High-frequency Rayleigh waves in materials with micro-structure and couple-stress effects. Zbl 1087.74567
Georgiadis, H. G.; Velgaki, E. G.
2003
The three-dimensional steady-state thermo-elastodynamic problem of moving sources over a half space. Zbl 1025.74010
2003
A method based on the Radon transform for three-dimensional elastodynamic problems of moving loads. Zbl 1205.74064
2001
Three-dimensional thermoelastic wave motions in a half-space under the action of a buried source. Zbl 1048.74016
Lykotrafitis, G.; Georgiadis, H. G.; Brock, L. M.
2001
An illustration of sliding contact at any constant speed on highly elastic half-spaces. Zbl 1065.74051
Brock, L. M.; Georgiadis, H. G.
2001
Rapid indentation of transversely isotropic or orthotropic half-spaces. Zbl 1110.74356
Brock, L. M.; Georgiadis, H. G.; Hanson, M. T.
2001
Torsional surface waves in a gradient-elastic half-space. Zbl 1074.74567
Georgiadis, H. G.; Vardoulakis, I.; Lykotrafitis, G.
2000
Numerical implementation of the integral-transform solution to Lamb’s point-load problem. Zbl 0981.74079
Georgiadis, H. G.; Vamvatsikos, D.; Vardoulakis, I.
1999
Thermoelastodynamic disturbances in a half-space under the action of a buried thermal/mechanical line source. Zbl 0955.74018
Georgiadis, H. G.; Rigatos, A. P.; Brock, L. M.
1999
Anti-plane shear Lamb’s problem treated by gradient elasticity with surface energy. Zbl 1074.74566
1998
Tangential-displacement effects in the wedge indentation of an elastic half-space – an integral-equation approach. Zbl 0918.73066
1998
SH surface waves in a homogeneous gradient-elastic half-space with surface energy. Zbl 0912.73016
1997
Steady-state motion of a line mechanical/heat source over a half-space: A thermoelastodynamic solution. Zbl 0927.74019
Brock, L. M.; Georgiadis, H. G.
1997
Transient SIF results for a cracked viscoelastic strip under concentrated impact loading – An integral-transform/function-theoretic approach. Zbl 0953.74563
Georgiadis, H. G.; Rigatos, A. P.
1996
Dynamic indentation of an elastic half-plane by a rigid wedge: Frictional and tangential-displacement effects. Zbl 0918.73076
Georgiadis, H. G.; Brock, L. M.; Rigatos, A. P.
1995
Dynamic stress concentration around a hole in a viscoelastic plate. Zbl 0863.73011
Georgiadis, H. G.; Rigatos, A. P.; Charalambakis, N. C.
1995
Static frictional indentation of an elastic half-plane by a rigid unsymmetrical punch. Zbl 0807.73065
Brock, L. M.; Georgiadis, H. G.; Charalambakis, N.
1994
Dynamic frictional identation of an elastic half-plane by a rigid punch. Zbl 0823.73057
Brock, L. M.; Georgiadis, H. G.
1994
Exact elastodynamic analysis of some fracture specimen models involving strip geometries. Zbl 0943.74549
Georgiadis, H. G.; Brock, L. M.
1994
Steady-state transonic motion of a line load over an elastic half-space: The corrected Cole/Huth solution. Zbl 0805.73020
Georgiadis, H. G.; Barber, J. R.
1993
On the super-Rayleigh/subseismic elastodynamic indentation problem. Zbl 0782.73068
Georgiadis, H. G.; Barber, J. R.
1993
Shear and torsional impact of cracked viscoelastic bodies – a numerical integral equation/transform approach. Zbl 0803.73020
1993
A correspondence principle connecting IBVPs of wave propagation and heat conduction. Zbl 0825.73141
1992
An integral equation approach to self-similar plane-elastodynamic crack problems. Zbl 0731.73064
1991
Plane impact of a cracked viscoelastic body. Zbl 0825.73113
Georgiadis, H. G.; Theocaris, P. S.; Mouskos, S. C.
1991
An asymptotic solution for short-time transient heat conduction between two dissimilar bodies in contact. Zbl 0734.73005
Georgiadis, H. G.; Barber, J. R.; Ammar, F. Ben
1991
Elastostatics of the orthotropic double-cantilever-beam fracture specimen. Zbl 0728.73059
1990
Cracked orthotropic strip with clamped boundaries. Zbl 0675.73062
1988
Moving punch on a highly orthotropic elastic layer. Zbl 0621.73128
1987
Asymmetrically cracked cylinder under torsion. Zbl 0586.73157
1986
The Keldysh-Sedov method for a closed-form elastodynamic solution of the cracked strip under anti-plane shear. Zbl 0587.73141
Georgiadis, H. G.; Theocaris, P. S.
1986
On the solution of steady-state elastodynamic crack problems by using complex variable methods. Zbl 0553.73090
Georgiadis, H. G.; Theocaris, P. S.
1985
all top 5 | 2022-11-30 14:01:19 | {"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": 0.8954042792320251, "perplexity": 12430.288271146343}, "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/1669446710764.12/warc/CC-MAIN-20221130124353-20221130154353-00500.warc.gz"} |
https://www.codingame.com/playgrounds/21973/introduction-to-cmake/cmake-project-file | Introduction to cmake
raphaelmeyer
17.4K views
CMake Project File
The entry point for a CMake project is a file called CMakeLists.txt.
Exercise 1
Let's set up the top level CMakeLists.txt in the project root folder.
[project]/
+--- CMakeLists.txt
+--- ...
The top level CMakeLists.txt must start with command cmake_minimum_required. For this exercise we will be using CMake version 3.10.
Next is the project command. Our time machine project should be named TimeMachine, should have version 1.0.2 and its language should be set to C++.
Run CMake
Building a CMake project
In order to build a CMake project we need a working directory for the build. In our example we use a folder build in the project folder.
For project initialization you must change into the build folder. But you only need to initialize a build folder once.
# create the build folder
mkdir -p /project/build
# for initialization we must change into the build folder
cd /project/build
cmake -G Ninja /project
# build the project
cmake --build /project/build
The option -G of the cmake command line tool sets the generator. There are generators for different build systems like make or ninja. Also, there are generators to create projects for IDEs like eclipse or visual studio. | 2021-04-20 09:52:06 | {"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": 0.3406112492084503, "perplexity": 8374.06008555956}, "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/1618039388763.75/warc/CC-MAIN-20210420091336-20210420121336-00493.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/dcdss.2019127 | # American Institute of Mathematical Sciences
November 2019, 12(7): 1955-1975. doi: 10.3934/dcdss.2019127
## Branching and bifurcation
1 Department of Mathematics, University of Maryland, 4176 Campus Dr, College Park, MD 20742, USA 2 INDAM, Dipartimento di Scienze Matematiche, Politecnico di Torino, Duca degli Abruzzi 24, 10129 Torino, Italy
* Corresponding author
Dedicated to Norman Dancer
Received January 2018 Revised August 2018 Published December 2018
Fund Project: J. Pejsachowicz is supported by GNAMPA-INDAM.
By relating the set of branch points $\mathcal{B} (f)$ of a Fredholm mapping $f$ to linearized bifurcation, we show, among other things, that under mild local assumptions at a single point, the set $\mathcal B(f)$ is sufficiently large to separate the domain of the mapping. In the variational case, we will also provide estimates from below for the number of connected components of the complement of $\mathcal B(f).$
Citation: Patrick M. Fitzpatrick, Jacobo Pejsachowicz. Branching and bifurcation. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 1955-1975. doi: 10.3934/dcdss.2019127
##### References:
show all references
Dedicated to Norman Dancer
##### References:
[1] Vladimir Müller, Aljoša Peperko. Lower spectral radius and spectral mapping theorem for suprema preserving mappings. Discrete & Continuous Dynamical Systems, 2018, 38 (8) : 4117-4132. doi: 10.3934/dcds.2018179 [2] Yin Yang, Yunqing Huang. Spectral Jacobi-Galerkin methods and iterated methods for Fredholm integral equations of the second kind with weakly singular kernel. Discrete & Continuous Dynamical Systems - S, 2019, 12 (3) : 685-702. doi: 10.3934/dcdss.2019043 [3] Joel Kübler, Tobias Weth. Spectral asymptotics of radial solutions and nonradial bifurcation for the Hénon equation. Discrete & Continuous Dynamical Systems, 2020, 40 (6) : 3629-3656. doi: 10.3934/dcds.2020032 [4] Ana Cristina Mereu, Marco Antonio Teixeira. Reversibility and branching of periodic orbits. Discrete & Continuous Dynamical Systems, 2013, 33 (3) : 1177-1199. doi: 10.3934/dcds.2013.33.1177 [5] Ken Ono. Parity of the partition function. Electronic Research Announcements, 1995, 1: 35-42. [6] Xijun Hu, Li Wu. Decomposition of spectral flow and Bott-type iteration formula. Electronic Research Archive, 2020, 28 (1) : 127-148. doi: 10.3934/era.2020008 [7] Juan Campos, Rafael Obaya, Massimo Tarallo. Recurrent equations with sign and Fredholm alternative. Discrete & Continuous Dynamical Systems - S, 2016, 9 (4) : 959-977. doi: 10.3934/dcdss.2016036 [8] Dejian Chang, Huili Liu, Jie Xiong. A branching particle system approximation for a class of FBSDEs. Probability, Uncertainty and Quantitative Risk, 2016, 1 (0) : 9-. doi: 10.1186/s41546-016-0007-y [9] Gerald Sommer, Di Zang. Parity symmetry in multi-dimensional signals. Communications on Pure & Applied Analysis, 2007, 6 (3) : 829-852. doi: 10.3934/cpaa.2007.6.829 [10] Fengbo Hang, Fanghua Lin. Topology of Sobolev mappings IV. Discrete & Continuous Dynamical Systems, 2005, 13 (5) : 1097-1124. doi: 10.3934/dcds.2005.13.1097 [11] Carlangelo Liverani. Fredholm determinants, Anosov maps and Ruelle resonances. Discrete & Continuous Dynamical Systems, 2005, 13 (5) : 1203-1215. doi: 10.3934/dcds.2005.13.1203 [12] Björn Sandstede, Arnd Scheel. Relative Morse indices, Fredholm indices, and group velocities. Discrete & Continuous Dynamical Systems, 2008, 20 (1) : 139-158. doi: 10.3934/dcds.2008.20.139 [13] Feride Tığlay. Integrating evolution equations using Fredholm determinants. Electronic Research Archive, 2021, 29 (2) : 2141-2147. doi: 10.3934/era.2020109 [14] Marcello Delitala, Tommaso Lorenzi. Evolutionary branching patterns in predator-prey structured populations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2267-2282. doi: 10.3934/dcdsb.2013.18.2267 [15] Tapio Rajala. Improved geodesics for the reduced curvature-dimension condition in branching metric spaces. Discrete & Continuous Dynamical Systems, 2013, 33 (7) : 3043-3056. doi: 10.3934/dcds.2013.33.3043 [16] Anna-Lena Horlemann-Trautmann, Alessandro Neri. A complete classification of partial MDS (maximally recoverable) codes with one global parity. Advances in Mathematics of Communications, 2020, 14 (1) : 69-88. doi: 10.3934/amc.2020006 [17] Thomas Westerbäck. Parity check systems of nonlinear codes over finite commutative Frobenius rings. Advances in Mathematics of Communications, 2017, 11 (3) : 409-427. doi: 10.3934/amc.2017035 [18] Konstantinos Drakakis, Rod Gow, Scott Rickard. Parity properties of Costas arrays defined via finite fields. Advances in Mathematics of Communications, 2007, 1 (3) : 321-330. doi: 10.3934/amc.2007.1.321 [19] Emily McMillon, Allison Beemer, Christine A. Kelley. Extremal absorbing sets in low-density parity-check codes. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021003 [20] Huiyan Xue, Antonella Zanna. Generating functions and volume preserving mappings. Discrete & Continuous Dynamical Systems, 2014, 34 (3) : 1229-1249. doi: 10.3934/dcds.2014.34.1229
2019 Impact Factor: 1.233 | 2021-06-23 20:27:53 | {"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": 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": 0.6971597671508789, "perplexity": 8057.620494258152}, "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-2021-25/segments/1623488540235.72/warc/CC-MAIN-20210623195636-20210623225636-00536.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/151346-proving-abel-s-theorem-natural-irrationalities-using-galois-theory.html | ## Proving Abel's theorem of 'natural irrationalities' using Galois Theory
Hi,
In Ian Stewart's book "Galois Theory", there's a discussion on Abel and Ruffini's original work on the general quintic, where he explains the gap in Ruffini's proof which was subsequently fixed by Abel with his theorem on "Natural Irrationalities".
Let $t_{1}, ..., t_{n}$ be independent complex variables, $s_{1}, ..., s_{n}$ the corresponding elementary symmetric polynomials, $L=C(t_{1}, ..., t_{n})$, $K=C(s_{1}, ..., s_{n})$ (where C is the field of complex numbers), so that the general polynomial $F(x)=(x-t_{1})...(x-t_{n})$ splits over the extension $L:K$.
Abel's theorem on Natural Irrationalities is then stated as follows:
If $L$ contains an element $x$ that lies in some radical extension $R:K$, then there exists a radical extension $R':K$ with $x \in R'$ and $R' \subseteq L$
Stewart proceeds to give Abel's original proof of this, but remarks that a proof using Galois theory is straightforward, and indeed sets this as an exercise much later on in the book. So what I'm having trouble with is just that: proving the above theorem in a more straightforward manner using the Galois correspondence.
Any help would be greatly appreciated...apparently this should be 'straightforward' but I've only made myself more confused trying to work it out. Several other texts refer to a "Theorem of Natural Irrationalities", but these are all different in nature, and I've been unable to translate them back into a proof of the above statement.
Thanks. | 2017-01-22 13:44:23 | {"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": 12, "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": 0.8916982412338257, "perplexity": 336.7161571880525}, "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-2017-04/segments/1484560281424.85/warc/CC-MAIN-20170116095121-00211-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://chem-bla-ics.blogspot.com/2008/12/state-of-cdk-120.html | ## Friday, December 26, 2008
### State of CDK 1.2.0...
The reason why I have not blogged in more than two weeks, was that I was hoping to blog about the CDK 1.2.0 release. This was originally aimed at September, slipped into October, November and then December. There were only three show stoppers (see this wiki page), one of which the IChemObject interfaces were not properly tested.
The problem was that the unit tests for the methods in superinterfaces were not applied to implementations of subinterfaces. For example, the unit test for IElement.getSymbol() was not applied to the class Atom, which implements IAtom which is a subinterfaces of IElement.
In fixing this, I had to take some hurdles. For example: the unit test classes used a set up following the implementations; CDK 1.2.x has three implementations of the interfaces: data, datadebug and nonotify. The last does not send around update notifications, and rough tests indicate it is about 10% faster. The second implementation sends messages to the debugger for every modification of the data classes, which is, clearly, useful for debugging purposes.
However, the JUnit4 test classes were basically doing the same. The unit test DebugAtomTest inherited form AtomTest, and only overwrote customizations. AtomTest, itself, inherited from ElementTest. That's where things got broken. In the single implementation set up, this would have been fine, but to allow testing of all three implementations, getBuilder() had to be used.
And when I implemented that, I did not realize that ElementTest would do a test like:
IElement element = builder.newElement();// test IElement functionality
However, while the use of builder ensure testing of all three implementations, it does not run these tests on IAtom implementations.
The followed a long series of patches to get this fixed. One major first patch, was to define unit test frameworks like AbstractElementTest which formalized running unit tests on any implementation, as I noticed that quite a few tests were still testing one particular implementation. This allowed DebugElementTest to extend AbstractElementTest, instead of ElementTest, which would now extend AbstractElementTest too.
OK, with that out of the way, it was time to fix running the unit test for IElement.getSymbol() on IAtom.getSymbol(), which required the removal of the use of IChemObjectBuilder implementations. So, I introduced newChemObject() which would return a fresh instance of the actually tested implementation. That is, DebugAtomTest would return a new DebugAtom, and the getSymbol() test would now run on DebugAtom and not DebugElement. Good.
No, not good. The actual implementation I was using, looks like:
public class DebugElementTest extend AbstractElementTest { @BeforeClass public static void setup() { setChemObject(new DebugElement()); }}public abstract class AbstractElementTest extend AbstractChemObjectTest { @Test public void testGetSymbol() { IElement element = (IElement)newChemObject(); // do testing }}public abstract class AbstractChemObjectTest { private IChemObject testedObject; public static setChemObject(IChemObject object) { this.testedObject = object; } public IChemObject setChemObject(IChemObject object) { return (IChemObject)testedObject.clone(); } // just imagine it has try/catch here too // and here the tests for the IChemObject API @Test public void testGetProperties() { IChemObject element = (IChemObject)newChemObject(); // do testing }}
Excellent! No.
Well, yes. The above system works, but made many unit tests fail, because of bugs in clone() methods. The full scope has to be explored, but at least IPolymer.clone() is not doing what I would expect it to do. Either I am wrong, and need to overwrite the clone unit tests of superinterfaces in AbstractPolymerTest, or the implementations needs fixing. I emailed the cdk-devel mailing list and filed a bug report. But having about 1000 unit tests fail, because of clone broken, is something I did not like. For example, as it makes bug fixing more difficult.
So, next step was to find an approach that did not require clone, but give some interesting insights in the Java language. JUnit4 requires the @BeforeClass method to be static. This means I cannot have a non-static DebugElementTest method return an instance. And, you cannot overwrite a static method! That had never occured to me in the past. DebugElementTest.newChemObject() does not overwrite AbstractChemObjectTest.newChemObject which is somewhere upstream.
But, after discussing matters with Carl, I ended up with this approach:
public abstract class AbstractChemObjectTest extends CDKTestCase { private static ITestObjectBuilder builder; public static void setTestObjectBuilder(ITestObjectBuilder builder) { AbstractChemObjectTest.builder = builder; } public static IChemObject newChemObject() { return AbstractChemObjectTest.builder.newTestObject(); }}public interface ITestObjectBuilder { public IChemObject newTestObject();}public class DebugAtomTest extends AbstractAtomTest { @BeforeClass public static void setUp() { setTestObjectBuilder(new ITestObjectBuilder() { public IChemObject newTestObject() { return new DebugAtom(); } }); }} | 2018-09-22 21:32:57 | {"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": 0.2057988941669464, "perplexity": 5643.601138613255}, "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-2018-39/segments/1537267158691.56/warc/CC-MAIN-20180922201637-20180922222037-00212.warc.gz"} |
http://math.stackexchange.com/questions/249269/2-connected-planar-graph | # 2-connected planar graph
Let $G$ a simple $2$-connected planar graph so that all vertices are incident with the infinite region. Suppose that every bounded region of $G$ has length $3$ (so is a cycle of length $3$). Let $k$ be the number of vertices of degree $2$ in $G$, and let $r$ be the number of regions of $G$ sharing no edges with the infinite region.
If $|V(G)| > 3$, show that \begin{align} k = r + 2 \end{align} I'm trying to figure out how to go about this. So, I think that these could be of help:
• $|E|−|V|=|R|−2$
• Every edge bounds two regions
• If the region shares no edge with the infinite region, then it only shares edges with other regions of length 3.
• $\sum\deg(v)=2|E(G)|$
• $12≤ \sum[6−\deg(v)]$ so $\sum\deg(v)≤6|V(G)|−12$
• for $2$-connected graphs, every vertex has $\deg(v)≥2$
Any ideas?
-
• $k=$ degree-1 nodes of the tree,
• $r=$ degree-3 nodes of the tree.
Contract all the degree one tree nodes. This gives almost a full binary tree, if you select one of the degree-3 nodes as root. "Almost", since the root has 3 children. For such a tree we have by induction #leaves=#interior nodes +2. And hence $k=r+2$. | 2015-10-04 15:57:22 | {"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": 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": 0.9712796211242676, "perplexity": 181.2719037176967}, "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-2015-40/segments/1443736675218.1/warc/CC-MAIN-20151001215755-00229-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://www.tcs.tifr.res.in/events/bernoulli-factory | # Bernoulli Factory
Speaker:
## Time:
Friday, 28 March 2014, 14:30 to 16:00
## Venue:
• D-405 (D-Block Seminar Room)
## Organisers:
Abstract: Necessary and sufficient conditions on a function $f(p)$ are given for the existence of a simulation procedure to simulate a Bernoulli random variable with success probability $f(p)$ from independent Bernoulli random variables with success probability $p$, with $p$ being constrained to lie in a subset of $[0,1]$ but otherwise unknown. | 2023-02-05 18:06:23 | {"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": 0.7742739915847778, "perplexity": 323.226125798725}, "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/1674764500273.30/warc/CC-MAIN-20230205161658-20230205191658-00715.warc.gz"} |
https://proofwiki.org/wiki/Function_Larger_than_Divergent_Function_is_Divergent | # Push Theorem
## Theorem
Let $f$ be a real function which is continuous on the open interval $\left({a \,.\,.\, +\infty}\right)$, $a \in \R$, such that:
$\displaystyle \lim_{x \to +\infty} \ f \left({x}\right) = +\infty$
Let $g$ be a real function defined on some interval $\left({b \,.\,.\, +\infty}\right)$ such that, for sufficiently large $x$:
$\forall x: x \in \left({a \,.\,.\, +\infty}\right) \cap \left({b \,.\,.\, +\infty}\right) \implies g \left({x}\right) > f \left({x}\right)$
Then:
$\displaystyle \lim_{x \to +\infty} \ g \left({x}\right) = +\infty$
## Proof
Let $\displaystyle \lim_{x \to +\infty} \ f \left({x}\right) = +\infty$
By the definition of infinite limits at infinity, this means:
$\forall M_1 \in \R_{>0}: \exists N_1 \in \R_{>0}: x > N_1 \implies f \left({x}\right) > M_1$
Now, the assertion that $g \left({x}\right) \to +\infty$ is:
$\forall M_2 \in \R_{>0}: \exists N_2 \in \R_{>0}: x > N_2 \implies g \left({x}\right) > M_2$
For $N_2$, choose $N_1$.
$\blacksquare$ | 2015-07-02 03:36:25 | {"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": 0.9908739924430847, "perplexity": 154.42920732617083}, "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-2015-27/segments/1435375095373.99/warc/CC-MAIN-20150627031815-00242-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://collegemathteaching.wordpress.com/2011/08/08/quantum-mechanics-and-undergraduate-mathematics-viii-time-evolution-of-expectation-of-an-observable/ | # College Math Teaching
## August 8, 2011
### Quantum Mechanics and Undergraduate Mathematics VIII: Time Evolution of Expectation of an Observable
Filed under: advanced mathematics, applied mathematics, physics, probability, quantum mechanics, science — collegemathteaching @ 3:12 pm
Back to our series on QM: one thing to remember about observables: they are operators with a set collection of eigenvectors and eigenvalues (allowable values that can be observed; “quantum levels” if you will). These do not change with time. So $\frac{d}{dt} (A (\psi)) = A (\frac{\partial}{\partial t} \psi)$. One can work this out by expanding $A \psi$ if one wants to.
So with this fact, lets see how the expectation of an observable evolves with time (given a certain initial state):
$\frac{d}{dt} E(A) = \frac{d}{dt} \langle \psi, A \psi \rangle = \langle \frac{\partial}{\partial t} \psi, A \psi \rangle + \langle \psi, A \frac{\partial}{\partial t} \psi \rangle$
Now apply the Hamiltonian to account for the time change of the state vector; we obtain:
$\langle -\frac{i}{\hbar}H \psi, A \psi \rangle + \langle \psi, -\frac{i}{\hbar}AH \psi \rangle = \overline{\frac{i}{\hbar}} \langle H \psi, A \psi \rangle + -\frac{i}{\hbar} \langle \psi, AH \psi \rangle$
Now use the fact that both $H$ and $A$ are Hermitian to obtain:
$\frac{d}{dt} A = \frac{i}{\hbar} \langle \psi, (HA - AH) \psi \rangle$.
So, we see the operator $HA - AH$ once again; note that if $A, H$ commute then the expectation of the state vector (or the standard deviation for that matter) does not evolve with time. This is certainly true for $H$ itself. Note: an operator that commutes with $H$ is sometimes called a “constant of motion” (think: “total energy of a system in classical mechanics).
Note also that $|\frac{d}{dt} A | = |\frac{i}{\hbar} \langle \psi, (HA - AH) \psi \rangle | \leq 2 \Delta A \Delta H$
If $A$ does NOT correspond with a constant of motion, then it is useful to define an evolution time $T_A = \frac{\Delta A}{\frac{E(A)}{dt}}$ where $\Delta A = (V(A))^{1/2}$ This gives an estimate of how much time must elapse before the state changes enough to equal the uncertainty in the observable.
Note: we can apply this to $H$ and $A$ to obtain $T_A \Delta H \ge \frac{\hbar}{2}$
Consequences: if $T_A$ is small (i. e., the state changes rapidly) then the uncertainty is large; hence energy is impossible to be well defined (as a numerical value). If the energy has low uncertainty then $T_A$ must be large; that is, the state is very slowly changing. This is called the time-energy uncertainty relation. | 2018-06-20 13:31:51 | {"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": 20, "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": 0.8822752833366394, "perplexity": 377.47612518911393}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "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-2018-26/segments/1529267863519.49/warc/CC-MAIN-20180620124346-20180620144346-00470.warc.gz"} |
https://mtg.github.io/JAAH/ | Welcome to Jazz Audio-Aligned Harmony (JAAH) Dataset’s documentation!¶
Dataset statistics¶
Contains 113 tracks Time period 1917 - 1989 Number of Chord Segments 17600 Mean BPM 164.560654012 Mean Harmonic Rhythm 3.6651136363636363
Chord Usage Summary
Chord Beats Number Beats % Duration (seconds) Duration %
maj 18591 27.1124398425 6606.114 26.4232764649
min 13172 19.209566866 4680.954 18.7229802062
dom 29786 43.4388216421 10557.523 42.2282069328
hdim7 1280 1.86670555637 511.15 2.04450873313
dim 1677 2.44567595158 582.86 2.33133592916
N 3986 5.81303777162 2032.415 8.12929710818
unclassified 78 0.113752369841 30.1 0.120394625584
Top Bigrams¶
(see Bigram in glossary)
Top N-grams¶
(see N-gram in glossary)
Chroma Statistics¶
Chord type chroma distribution ternary plot
Glossary¶
Bigram
Bigram represents chords transition event. “Absolute” chord pitches are omitted, bigram is denoted by:
• first chord quality (i.e. Maj, Min, Dom, HDim7, Dim)
• interval between first and second chord roots encoded by:
• Letter: Perfect, Major or minor
• number (2 for second, 3 for third, etc)
• second chord quality
The approach is taken from [BS13].
N-gram
Represent sequence of chord transition events. “Absolute” chord pitches are omitted, only chord qualities and inter-root intervals are considered (see Bigram).
Chord type chroma distribution ternary plot
Lead sheet chord chart is the backbone of performance in many jazz styles. But each performance and style has it’s own “sonic aura” determined by how conceived chords are realized by musicians. The main idea of these plots is to provide visual profiles for each of main chord types used in jazz (major, minor, dominant seventh, halfdiminished seventh and diminished) for the whole dataset and for each track. Chroma distribution plots show:
• What degrees (relative to a chord’s root) are actually presented, and quantitative measurement of their presence.
• Joint distribution of the degrees (it shows e.g. how often certain degrees are played together or are they used independently)
• Dispersion of degree usage
How are they produced?
1. NNLS Chroma features (http://www.isophonics.net/nnls-chroma , [MD10]) are extracted for each frame of audio recordings. Each chroma is a 12-dimensional vector, with components representing 12 semitone pitch classes.
1. Pitch-class based chroma converted to degree-based chroma. I.e. chroma vectors corresponding to each particular chord are transposed to the common root, so the new vector’s first component represents intensity of chord root pitch, the following - intensity of minor second, etc.
1. For each beat, “beat predominant chroma” is calculated. This is a single 12d vector which represents predominant chroma around this beat. To estimate it, we convolve per-frame chroma vectors with Hanning window (https://en.wikipedia.org/wiki/Hann_function) and then use vectors corresponding to beat frames. Thus, maximum weights are given to frames, close to the beat and weights are decreased as frames are moving away from the beat.
1. We rather interested in proportion of chroma components in a certain sound segment, but not in it’s absolute values, so we normalize them with $$l1$$ norm. So they are sum up to one (and they are non-negative by definition).
2. Normalized chroma vectors don’t fill the whole 12D space. They are distributed on standard 11-simplex (https://en.wikipedia.org/wiki/Simplex): $$\{x\in \mathbb {R} ^{12}:x_{0}+\dots +x_{11}=1,x_{i}\geq 0,i=0,\dots ,11\}$$. To visualize it’s distribution we borrow techniques from Compositional Data Analysis (e.g. [vdBTD13]). Such techniques are used when proportions of parts is explored (e.g. chemical composition or budget composition). Our 11-d simplex has 12 vertices corresponding to 12 semitones addressed as chord degrees. It’s confined by 220 triangle faces (each face corresponds to unique triple combination of the degrees, e.g. I-III-V). To see what’s inside, we produce two dimensional projections of the simplex content to it’s faces, representing density with color. For each triple we marginalize out chroma components which are not inculded in the triple and obtain distribution of 3 chord degrees which is defined on a triangle. Resulted figure is called Ternary plot (https://en.wikipedia.org/wiki/Ternary_plot). Out of 220 triangles, we show only six, related to the most “significant” chord degrees. (“Significance” here means that chroma components for these degrees have highest average values throughout the whole dataset), triangles are arranged into hexagons adjoined by identical edges for presentation simplicity.
Mean harmonic rhythm
Rate (in chords per beat) at which chords are changed. See e.g.: https://en.wikipedia.org/wiki/Harmonic_rhythm
References¶
[BS13] Yuri Broze and Daniel Shanahan. Diachronic Changes in Jazz Harmony: A Cognitive Perspective. Music Perception: An Interdisciplinary Journal, 3(1):32–45, 2013. URL: http://www.jstor.org/stable/10.1525/mp.2013.31.1.32 http://www.jstor.org/page/info/about/policies/terms.jsp, doi:10.1525/mp.2013.31.1.32.
[MD10] Matthias Mauch and Simon Dixon. Approximate note transcription for the improved identification of difficult chords. In Proceedings of the International Conference on Music Information Retrieval (ISMIR), number 1, 135–140. 2010. URL: https://www.eecs.qmul.ac.uk/{~}simond/pub/2010/Mauch-Dixon-ISMIR-2010.pdf.
[vdBTD13] K. Gerald van den Boogaart and Raimon Tolosana-Delgado. Fundamental Concepts of Compositional Data Analysis. In Analyzing Compositional Data with R, pages 13–50. Springer Berlin Heidelberg, Berlin, Heidelberg, 2013. URL: http://link.springer.com/10.1007/978-3-642-36809-7{\_}2, doi:10.1007/978-3-642-36809-7_2. | 2021-05-07 14:10:39 | {"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": 0.6506443023681641, "perplexity": 10224.915810231561}, "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-2021-21/segments/1620243988793.99/warc/CC-MAIN-20210507120655-20210507150655-00565.warc.gz"} |
http://juliagraphics.github.io/Luxor.jl/dev/tutorial/basictutorial/ | # A tutorial
Experienced Julia users and programmers fluent in other languages and graphics systems should have no problem using Luxor by referring to the rest of the documentation. For others, here is a tutorial to help you get started.
## What you need
If you've already downloaded Julia, and have added the Luxor package successfully (using ] add Luxor):
\$ julia
_
_ _ _(_)_ | Documentation: https://docs.julialang.org
(_) | (_) (_) |
_ _ _| |_ __ _ | Type "?" for help, "]?" for Pkg help.
| | | | | | |/ _ | |
| | |_| | | | (_| | | Version 1.6.0 (2021-03-24)
_/ |\__'_|_|_|\__'_| | Official https://julialang.org/ release
|__/ |
(v1.6) pkg> add Luxor
You can work in a Jupyter or Pluto notebook, or perhaps use the Atom/Juno or VSCode editor/development environment. It's also possible to work in a text editor (make sure you know how to run a file of Julia code), or, at a pinch, you could use the Julia REPL directly.
Ready? Let's begin. The goal of this tutorial is to do a bit of basic 'compass and ruler' Euclidean geometry, to introduce the basic concepts of Luxor drawings.
## First steps
We'll have to load just one package for this tutorial:
using Luxor
Here's an easy shortcut for making drawings in Luxor. It's a Julia macro, and it's a good way to test that your system's working. Evaluate this code:
@png begin
text("Hello world")
circle(Point(0, 0), 200, action = :stroke)
end
What happened? Can you see this image somewhere?
If you're using Juno, the image should appear in the Plots window. If you're working in a Jupyter or Pluto notebook, the image should appear below or above the code. If you're using Julia in a terminal or text editor, the image should have opened up in some other application, or, at the very least, it should have been saved in your current working directory (as luxor-drawing-(time stamp).png). If nothing happened, or if something bad happened, we've got some set-up or installation issues probably unrelated to Luxor...
Let's press on. The @png macro is an easy way to make a drawing; all it does is save a bit of typing. (The macro expands to enclose your drawing commands with calls to the Drawing(), origin, finish, and preview functions.) There are also @svg and @pdf macros, which do a similar thing. PNGs and SVGs are good because they show up in Juno and Jupyter. SVGs are usually higher quality too, but they're text-based so can become very large and difficult to load if the image is complex. PDF documents are always higher quality, and usually open up in a separate application.
This example illustrates a few things about Luxor drawings:
• There are default values which you don't have to set if you don't want to (file names, colors, font sizes, and so on).
• Positions on the drawing are specified with x and y coordinates stored in the Point type, and you can sometimes omit positions altogether.
• The text was placed at the origin point (0/0), and by default it's left aligned.
• The circle wasn't filled, but stroked. We passed the :stroke symbol as an action to the circle function. Many drawing functions expect some action, such as :fill or :stroke, and sometimes :clip or :fillstroke. This works either as an argument (:fill) or as a keyword argument (action=:fill).
• Did the first drawing takes a few seconds to appear? The Cairo drawing engine takes a little time to warm up. Once it's running, drawings appear much faster.
Once more, with more black, and some rulers:
@png begin
text("Hello again, world!", Point(0, 250))
circle(Point(0, 0), 200, action = :fill)
rulers()
end
The x-coordinates usually run from left to right, the y-coordinates from top to bottom. So here, Point(0, 250) is a point at the left/right center, but at the bottom of the drawing.
## Euclidean eggs
For the main section of this tutorial, we'll attempt to draw Euclid's egg, which involves a bit of geometry.
For now, you can continue to store all the drawing instructions between the @png macro's begin and end markers. Technically, however, working like this at the top-level in Julia (ie without storing instructions in functions which Julia can compile) isn't considered to be 'best practice', because the unit of compilation in Julia is the function. (Look up 'global scope' in the documentation.)
@png begin
and first define the variable radius to hold a value of 80 units (there are 72 units in a traditional inch):
radius=80
Select gray dotted lines. To specify a color you can supply RGB (or HSB or LAB or LUV) values or use named colors, such as "red" or "green". "gray0" is black, and "gray100" is white. (For more information about colors, see Colors.jl.)
setdash("dot")
sethue("gray30")
(You can use setcolor instead of sethue — the latter doesn't affect the current opacity setting.)
Next, make two points, A and B, which will lie either side of the origin point. This line uses an array comprehension - notice the square brackets enclosing a for loop.
A, B = [Point(x, 0) for x in [-radius, radius]]
x uses two values from the inner array, and a Point using each value is created and stored in its own variable. It seems hardly worth doing for two points, but it shows how you can assign more than one variable at the same time, and also how to generate points.
With two points defined, draw a line from A to B, and stroke it.
line(A, B, action = :stroke)
Draw a stroked circle too. The center of the circle is placed at the origin. You can use the letter O as a short cut for Origin, ie the Point(0, 0).
circle(O, radius, action = :stroke)
end
### Labels and dots
It's a good idea to label points in geometrical constructions, and to draw small dots to indicate their location clearly. For the latter task, small filled circles will do. For labels, there's a special label function we can use, which positions a text string close to a point, using angles or points of the compass, so :N places the label to the north of a point.
Edit your previous code by adding instructions to draw some labels and circles:
@png begin
setdash("dot")
sethue("gray30")
line(A, B, action = :stroke)
circle(Point(0, 0), radius, action = :stroke)
# >>>>
label("A", :NW, A)
label("O", :N, O)
label("B", :NE, B)
circle.([A, O, B], 2, action = :fill)
circle.([A, B], 2radius, action = :stroke)
end
While we could have drawn all the circles as usual, we've taken the opportunity to introduce a powerful Julia feature called broadcasting. The dot (.) just after the function name in the last two circle function calls tells Julia to apply the function to all the arguments. We supplied an array of three points, and filled circles were placed at each one. Then we supplied an array of two points and stroked circles were placed there. Notice that we didn't have to supply an array of radius values or an array of actions — in each case Julia did the necessary broadcasting (from scalar to vector) for us.
### Intersect this
We're now ready to tackle the job of finding the coordinates of the two points where two circles intersect. There's a Luxor function called intersectionlinecircle that finds the point or points where a line intersects a circle. So we can find the two points where one of the circles crosses an imaginary vertical line drawn through O. Because of the symmetry, we'll only have to do circle A.
@png begin
# as before
setdash("dot")
sethue("gray30")
line(A, B, action = :stroke)
circle(O, radius, action = :stroke) # use letter O for Point(0, 0)
label("A", :NW, A)
label("O", :N, O)
label("B", :NE, B)
circle.([A, O, B], 2, action = :fill)
circle.([A, B], 2radius, action = :stroke)
The intersectionlinecircle takes four arguments: two points to define the line and a point/radius pair to define the circle. It returns the number of intersections (probably 0, 1, or 2), followed by the two points.
The line is specified with two points with an x value of 0 and y values of ± twice the radius, written in Julia's math-friendly style. The circle is centered at A and has a radius of AB (which is 2radius). Assuming that there are two intersections, we feed these to circle and label for drawing and labeling using our new broadcasting superpowers.
# >>>>
nints, C, D =
if nints == 2
circle.([C, D], 2, action = :fill)
label.(["D", "C"], :N, [D, C])
end
end
### The upper circle
Now for the trickiest part of this construction: a small circle whose center point sits on top of the inner circle and that meets the two larger circles near the point D.
Finding this new center point C1 is easy enough, because we can again use intersectionlinecircle to find the point where the central circle crosses a line from O to D.
@png begin
# >>>>
nints, C1, C2 = intersectionlinecircle(O, D, O, radius)
if nints == 2
circle(C1, 3, action = :fill)
label("C1", :N, C1)
end
end
The two other points that define this circle lie on the intersections of the large circles with imaginary lines through points A and B passing through the center point C1. We're looking for the lines A-C1-ip, where ip is somewhere on the circle between D and B, and B-C1-ip, where ip is somewhere between A and D.
To find (and draw) these points is straightforward. We'll mark these as intermediate for now, because there are in fact four intersection points but we want just the two nearest the top:
# >>>>
nints, I3, I4 = intersectionlinecircle(A, C1, A, 2radius)
nints, I1, I2 = intersectionlinecircle(B, C1, B, 2radius)
circle.([I1, I2, I3, I4], 2, action = :fill)
So we can use the distance function to find the distance between two points, and it's simple enough to compare the values and choose the shortest.
# >>>>
if distance(C1, I1) < distance(C1, I2)
ip1 = I1
else
ip1 = I2
end
if distance(C1, I3) < distance(C1, I4)
ip2 = I3
else
ip2 = I4
end
label("ip1", :N, ip1)
label("ip2", :N, ip2)
circle(C1, distance(C1, ip1), action = :stroke)
end
We now know all the points on the egg's perimeter, and the centers of the circular arcs. To draw the outline, we'll use the arc2r function four times. This function takes: a center point and two points that together define a circular arc, plus an action.
The shape consists of four curves, so we'll use the :path action. Instead of immediately drawing the shape, like the :fill and :stroke actions do, this action adds a section to the current path.
label("ip1", :N, ip1)
label("ip2", :N, ip2)
circle(C1, distance(C1, ip1), action = :stroke)
# >>>>
setline(5)
setdash("solid")
arc2r(B, A, ip1, :path) # centered at B, from A to ip1
arc2r(C1, ip1, ip2, :path)
arc2r(A, ip2, B, :path)
arc2r(O, B, A, :path)
Finally, once we've added all four sections to the path we can stroke and fill it. If you want to use separate styles for the stroke and fill, you can use a preserve version of the first action. This applies the action but keeps the path available for more actions.
strokepreserve()
setopacity(0.8)
sethue("ivory")
fillpath()
end
## Egg stroke
To be more generally useful, the above code can be boiled into a single function.
function egg(radius, action=:none)
nints, C, D =
flag, C1 = intersectionlinecircle(C, D, O, radius)
nints, I3, I4 = intersectionlinecircle(A, C1, A, 2radius)
nints, I1, I2 = intersectionlinecircle(B, C1, B, 2radius)
if distance(C1, I1) < distance(C1, I2)
ip1 = I1
else
ip1 = I2
end
if distance(C1, I3) < distance(C1, I4)
ip2 = I3
else
ip2 = I4
end
newpath()
arc2r(B, A, ip1, :path)
arc2r(C1, ip1, ip2, :path)
arc2r(A, ip2, B, :path)
arc2r(O, B, A, :path)
closepath()
do_action(action)
end
This keeps all the intermediate code and calculations safely hidden away, and it's now possible to draw a Euclidean egg by calling egg(100, action = :stroke), for example, where 100 is the required width (radius), and :stroke is the required action.
(Of course, there's no error checking. This should be added if the function is to be used for any serious applications...!)
Notice that this function doesn't define anything about what color it is, or where it's placed. When called, the function inherits the current drawing environment: scale, rotation, position of the origin, line thickness, color, style, and so on. This lets us write code like this:
@png begin
setopacity(0.7)
for θ in range(0, step=π/6, length=12)
@layer begin
rotate(θ)
translate(0, -150)
egg(50, :path)
setline(10)
randomhue()
fillpreserve()
randomhue()
strokepath()
end
end
end 800 800 "eggstravaganza.png"
The loop runs 12 times, with theta increasing from 0 upwards in steps of π/6. But before each egg is drawn, the entire drawing environment is rotated by theta radians and then shifted along the y-axis away from the origin by -150 units (the y-axis values usually increase downwards, so, before any rotation takes place, a shift of -150 looks like an upwards shift). The randomhue function does what you expect, and the egg function is passed the :fill action and the radius.
Notice that the four drawing instructions are encased in a @layer begin...end shell. Any change made to the drawing environment inside this shell is discarded after the end. This allows us to make temporary changes to the scale and rotation, etc. and discard them easily once the shapes have been drawn.
Rotations and angles are typically specified in radians. The positive x-axis (a line from the origin increasing in x) starts off heading due east from the origin, and the y-axis due south, and positive angles are clockwise (ie from the positive x-axis towards the positive y-axis). So the second egg in the previous example was drawn after the axes were rotated by π/6 radians clockwise.
If you look closely you can tell which egg was drawn first — it's overlapped on each side by subsequent eggs.
#### Thought experiments
1. What would happen if the translation was translate(0, 150) rather than translate(0, -150)?
2. What would happen if the translation was translate(150, 0) rather than translate(0, -150)?
3. What would happen if you translated each egg before you rotated the drawing environment?
Some useful tools for investigating the important aspects of coordinates and transformations include:
## Polyeggs
As well as stroke and fill actions, you can use the path as a clipping region (:clip), or as the basis for more shape shifting.
The egg function creates a path and lets you apply an action to it. It's also possible to convert the path into a polygon (an array of points), which lets you do more things with it. The following code converts the egg's path into a polygon, and then moves every other point of the polygon halfway towards the centroid.
@png begin
egg(160, :path)
pgon = first(pathtopoly())
The pathtopoly function converts the current path made by egg(160, :path) into a polygon. Those smooth curves have been approximated by a series of straight line segments. The first function is used because pathtopoly returns an array of one or more polygons (paths can consist of a series of loops), and we know that we need only the single path here.
pc = polycentroid(pgon)
circle(pc, 5, action = :fill)
polycentroid finds the centroid of the new polygon.
This loop steps through the points and moves every odd-numbered one halfway towards the centroid. between finds a point midway between two specified points. Finally the poly function draws the array of points.
for pt in 1:2:length(pgon)
pgon[pt] = between(pc, pgon[pt], 0.5)
end
poly(pgon, action = :stroke)
end
The uneven appearance of the interior points here looks to be a result of the default line join settings. Experiment with setlinejoin("round") to see if this makes the geometry look tidier.
For a final experiment with our egg function, here's Luxor's offsetpoly function struggling to draw around the spiky egg-based polygon.
@png begin
egg(80, :path)
pgon = first(pathtopoly()) |> unique
pc = polycentroid(pgon)
for pt in 1:2:length(pgon)
pgon[pt] = between(pc, pgon[pt], 0.8)
end
for i in 30:-3:-8
randomhue()
op = offsetpoly(pgon, i)
poly(op, action = :stroke, close=true)
end
end 800 800 "spike-egg.png"
The small changes in the regularity of the points created by the path-to-polygon conversion and the varying number of samples it made are continually amplified in successive outlinings.
## Clipping
A useful feature of Luxor is that you can use shapes as a clipping mask. Graphics can be hidden when they stray outside the boundaries of the mask.
In this example, the egg (assuming you're still in the same Julia session in which you've defined the egg function) isn't drawn, but is defined to act as a clipping mask. Every graphic shape that you draw now is clipped where it crosses the mask. This is specified by the :clip action which is passed to the do_action function at the end of the egg.
Here, the graphics are provided by the ngon function, which draws regular n-sided polygons.
using Luxor, Colors
@svg begin
setopacity(0.5)
eg(a) = egg(150, a)
sethue("gold")
eg(:fill)
eg(:clip)
@layer begin
for i in 360:-4:1
sethue(Colors.HSV(i, 1.0, 0.8))
rotate(π/30)
ngon(O, i, 5, 0, action = :stroke)
end
end
clipreset()
sethue("red")
eg(:stroke)
end
It's good practice to add a matching clipreset` after the clipping has been completed. Unbalanced clipping can lead to unpredictable results. | 2022-11-29 22:19:07 | {"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": 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": 0.5841184854507446, "perplexity": 2603.3000356963576}, "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/1669446710711.7/warc/CC-MAIN-20221129200438-20221129230438-00098.warc.gz"} |
https://www.quizover.com/course/section/lo-3-1-3-3-3-4-4-2-1-by-openstax | # 2.2 Classifying and constructing triangles
Page 1 / 2
## [lo 3.1, 3.3, 3.4, 4.2.1]
• By the end of this learning unit, you will be able to do the following:
• understand how important the use of triangles is in everyday situations;
• explain how to find the unknown sides of a right-angled triangle (Pythagoras);
• calculate the area of a triangle;
• enjoy the action in geometry;
• use mathematical language to convey mathematical ideas, concepts, generalisations and mental processes.
1. When you classify triangles you can do it according to the angles or according to the sides.
1.1 Classification on the basis of the angles of a triangle:Are you able to complete the following?
a) Acute-angled triangles are triangles with
b) Right-angled triangles have
c) Obtuse-angled triangles have
1.2 Classification on the basis of the sides of the triangle:Are you able to complete the following?
a) An isosceles triangle has
b) An equilateral triangle has
c) A scalene triangle's
2. Are you able to complete the following theorems about triangles? Use a sketch to illustrate each of the theorems graphically.
THEOREM 1:
• The sum of the interior angles of any triangle is.........................
Sketch:
THEOREM 2:
• The exterior angle of a triangle is
Sketch:
3. Constructing triangles:
• Equipment: compasses, protractor, pencil and ruler
Remember this:
• Begin by drawing a rough sketch of the possible appearance.
• Begin by drawing the base line.
3.1 Construct $\Delta$ PQR with PQ = 7 cm, PR = 5 cm and $\stackrel{ˆ}{P}$ = 70°.
a) Sketch:
b) Measure the following:
1. QR = ........ 2. $\stackrel{ˆ}{R}$ = ........ 3. $\stackrel{ˆ}{Q}$ = ........ 4. $\stackrel{ˆ}{P}+\stackrel{ˆ}{Q}+\stackrel{ˆ}{R}=$ ........
3.2 Construct $\Delta$ KLM , an equilateral triangle. KM = 40 mm, KL = LM and $\stackrel{ˆ}{K}$ = 75°.Indicate the sizes of all the angles in your sketch.
Sketch:
## [lo 4.2.1, 4.8, 4.9, 4.10]
• The following could be done in groups.
Practical exercise: Making you own tangram.
1. Cut out a cardboard square (10 cm x 10 cm).
2. Draw both diagonals, because they form part of the bases of some figures.
3. Divide the square in such a way that the complete figure consists of the following:
3.1 two large equilateral triangles with bases of 10 cm in length;
3.2 two smaller equilateral triangles, each with base 5 cm in length;
3.3 one medium equilateral triangle with adjacent sides 5 cm in length;
3.4 one square with diagonals of 5cm;
3.5 one parallelogram with opposite sides of 5 cm.
• Make two of these. Cut along all the lines so that you will have two sets of the above shapes.
4. Now trace the largest triangle of your tangram in your workbook as a right-angled triangle.
5. Arrange the seven pieces to form a square and place this on the hypotenuse of the traced triangle.
6. Now arrange the two largest triangles to form a square and place this on one of the sides adjacent to the right angle of the traced triangle.
7. Arrange the remaining pieces to form a square and place this on the other adjacent side.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
how did I we'll learn this
f(x)= 2|x+5| find f(-6)
f(n)= 2n + 1
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
Got questions? Join the online conversation and get instant answers! | 2018-02-23 18:40:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 7, "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": 0.5505657196044922, "perplexity": 1621.9162953736075}, "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-2018-09/segments/1518891814827.46/warc/CC-MAIN-20180223174348-20180223194348-00307.warc.gz"} |
https://ncatlab.org/nlab/show/Music+of+the+Spheres | # nLab Music of the Spheres
Contents
philosophy
### Of physics
#### Spheres
n-sphere
low dimensional n-spheres
#### Stable Homotopy theory
stable homotopy theory
Introduction
# Contents
## Idea
### Ancient idea
In ancient times, Musica Universalis or Music of the Spheres referred to a philosophical concept that regards proportions of orbits in the solar system as exhibiting a cosmic harmony (Plato 380BC).
Johannes Kepler proposed that this is governed by the shape of the Platonic solids (Kepler 1596). (See also at multiverse.)
### Modern idea
More recently, it was suggested that the term refers to the stable homotopy groups of spheres $\pi_\bullet(\mathbb{S})$ and the absolute E-∞ geometry over Spec(S) as seen by the MU-Adams spectral sequence.
My initial inclination was to call this book The Music of the Spheres, but I was dissuaded from doing so by my diligent publisher, who is ever mindful of the sensibilities of librarians. (Ravenel 86, p. xv)
For the last 50 years one of the basic problems in algebraic topology has been the determination of the homotopy groups of spheres (Mahowald-Ravenel 87, Sec. 1)
As is well known, it is our manifest destiny as 21st century algebraic topologists to compute homotopy groups of spheres. (Wilson 13, p. 1)
One of the most fundamental problems in topology is to determine the set of homotopy classes of continuous based maps between spheres. (Isaksen-Wang-Xu 20, Sec. 1)
Modern chromatic homotopy theory makes contact between this kind of music and physics:
1. the A-hat genus (partition function of the spinning particle) appears in the first chromatic level of the spheres;
2. the Witten genus (partition function of the spinning string) appears in the second chromatic level of the spheres.
Modern equivariant stable homotopy theory makes contact between this kind of music and Kepler’s proposal:
For whatever it’s worth, all these items come together in the Equivariant cohomology of M2/M5-branes
## References
Last revised on March 3, 2021 at 01:57:30. See the history of this page for a list of all contributions to it. | 2021-07-30 15:48:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "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": 0.4897245168685913, "perplexity": 1400.568743370362}, "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-2021-31/segments/1627046153971.20/warc/CC-MAIN-20210730154005-20210730184005-00420.warc.gz"} |
http://www.qwalk.org/docs/Wavefunction/ | ## Jastrow correlation factor
Keyword: JASTROW
Description: This wave function's job is to represent the electron-electron correlations. It is a symmetric function with explicit electron-electron distances. There are three main terms in this function; electron-ion, electron-electron, and electron-electron-ion. In all that follows, the index $\alpha$ stands for the ion (nucleus) coordinate, the indices $i,j$ stand for electron-electron distances, and $k,l,m$ are expansion indices.
Electron-ion. $\sum_{i\alpha} \sum_k c_k a_k (r_{i\alpha})$
Electron-electron. $\sum_{ij} \sum_k c_k b_k (r_{ij})$
Electron-electron-ion. $\sum_{\alpha ij} \sum_{klm} c_{klm} (a_k(r_{i\alpha})a_l(r_{j\alpha}) + a_k(r_{j\alpha})a_l(r_{i\alpha}) ) b_k (r_{ij})$
For efficiency reasons, the Jastrow factor is organized into GROUP sections. Each GROUP can take one of the options listed below.
The ONEBODY, TWOBODY, and THREEBODY sections all accept the FREEZE keyword, in which the ocefficients are held constant during an optimization.
Required keywords
None
Optional keywords
Keyword Type Default Description
OPTIMIZEBASIS flag False Optimize any basis functions present in the expansion.
EIBASIS section empty A section for a Basis function object. This will represent the $a_k$ functions.
EEBASIS section empty A section for a Basis function object. This will represent the $b_k$ functions.
ONEBODY section empty List of expansion coefficients(floats) for the electron-ion terms. There must be one section for each atom type, each beginning with the name of the atom. (for example, COEFFICIENTS { Li 3.4 2.3 }
TWOBODY section empty List of expansion coefficients for the electron-electron terms. For example, COEFFICIENTS { 0.1 0.2 0.3 }.
TWOBODY_SPIN section empty List of expansion coefficients for the electron-electron terms with different spin-dependent terms. For example, LIKE_COEFFICIENTS { 0.1 0.2 0.3 } UNLIKE_COEFFICIENTS { 0.05 0.2 0.3 }.
THREEBODY section empty List of expansion coefficients(floats) for the electron-electron-ion terms. There must be one section for each atom type, each beginning with the name of the atom. (for example, COEFFICIENTS { Li 3.4 2.3 } With the defaults, there are a maximum of 12 parameters they have requirements on the number of basis functions. 3 parms: 1 EE and 1 EI function< 5 parms: 1 EE and 2 EI 7 parms: 2 EE and 2 EI 12 parms: 2 EE and 3 EI
## Pfaffian wave function
Keyword: PFAFFIAN
Description: WARNING. This is a development feature. Make sure you know what you're doing before trying to use Pfaffians. A pfaffian (generalized determinant) or several pfaffians. See Bajdich et al. Phys. Rev. B 77 115112 (2008) for implementation details. Submatrices $\boldsymbol \xi$, $\boldsymbol \Phi$ and $\boldsymbol \varphi$ are defined in Pfaffian group. and ordered according the ORBITAL_ORDER section.
Required keywords
Keyword Type Description
NPAIRS section Number of spin up, spin down, and unpaired electrons. The sum of these 3 numbers defines the Pfaffian matrix.
PFWT section List of the weights of the Pfaffians, for a multi-Pfaffian wave function
PARIING_ORBITAL section Section for Pfaffian group
ORBITALS section Input for a MO Matrix object
Optional keywords
Keyword Type Default Description
ORBITAL_ORDER section ith pairing orbital for ith Pfaffian matrix Contains upper-diagonal of \f( N \times N \f) matrix of pairing occupation numbers
OPTIMIZE_PFWT flag False Optimize the Pfaffian weights
## Slater determinant or sum of determinants
Keyword: SLATER
Description: A Slater determinant or linear combination of several determinants. In this object, a determinant is actually a product of two determinants; one for spin up and one for spin down. The way to think about this is that the orbital object provides a list of $\phi_j$. Each determinant $i$ is defined by the set of orbitals it includes, which is given in STATES. One can think of this as a vector ${\mathbf j}_i$ for each determinant, with the first $n_\uparrow$ elements giving the occupation of the up electrons, and the second $n_\downarrow$ doing the same for the down electrons. There is substantial flexibility in choosing the occupation of these orbitals, which is given in the tutorials. If you are just interested in straightforward ground state calculations, then the converter will probably set this value correctly.
Required keywords
Keyword Type Description
DETWT section List of the weights $c_i$ of the determinants. This can be replaced with CSF.
STATES section List of the occupations of molecular orbitals, first spin up and then spin down. If there is more than one determinant, continue listing up and down occupations. See HOWTOs for methods to modify this section to select states.
ORBITALS/CORBITALS section A Molecular Orbital section.
Optional keywords
Keyword Type Default Description
NSPIN section same as in the Hamiltonian Two integers, the first the number of up electrons, and the second the number of down electrons
OPTIMIZE_DET flag False Optimize the determinantal coefficients. For a single determinant, this does nothing.
CSF section empty This replaces DETWT, and lists configuration state functions to reduce the number of variational parameters. The format is CSF { overallweight weightdet1 weightdet2 ... }. Only the overall weight is optimized. List a separate CSF section for each CSF.
CLARK_UPDATES flag special Force Bryan Clark's updates (J. Chem. Phys 135, 244105 (2011)) of the determinant inverses and values. By default, this is enabled when there is more than one determinant and more than 10 electrons.
SHERMAN_MORRISON flag special Force Sherman-Morrison updates of the determinant inverses and values.
## Slater-Jastrow (multiply two wave functions)
Keyword: SLATER-JASTROW
Description: Multiply two wave functions; that is $\Psi = \Psi_1 \Psi_2$.
Required keywords
Keyword Type Description
WF1 section A section for a Wave function object. Will represent $\Psi_1$
WF2 section A section for a Wave function object. Will represent $\Psi_2$
Optional keywords
None | 2022-05-28 07:27:40 | {"extraction_info": {"found_math": true, "script_math_tex": 20, "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": 0.6052954792976379, "perplexity": 2354.431660489937}, "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-2022-21/segments/1652663013003.96/warc/CC-MAIN-20220528062047-20220528092047-00177.warc.gz"} |
http://syntheticwombs.com/8hzg06d/cc0662-2-unlimited---no-limit-lyrics | An example of a domain error is the square root of a negative number, such as sqrt (-1.0), which has no meaning in real arithmetic. #NUM! nychelp Guest; returning two values from a function . If the argument is positive infinity, then the result is positive infinity. SQL SQRT() function: Pictorial presentation. What type of value is returned by Math.sqrt()? Return value: A double value indicating the square root of x. If x is negative, the function sets errno to EDOM, and returns 0. sqrt(1) returns 1.0 sqrt(9) returns 3.0 sqrt(25) returns 5.0 Let’s take another example, the ABS() function — it should return the Number (required argument) – This is the number for which we wish to find out the square root. These basic math functions of the Java Math class will be covered in the following sections.. Math.abs() The Math.abs() function returns the absolute value of the parameter passed to it. Sqrt [a b] is not automatically converted to Sqrt [a] Sqrt [b]. Which sqrt function from which library? The following sample declarations illustrate this. Within the first two statements, we used the sqrt Function directly on Positive integers. It may be standard, user-defined scalar or subrange type but it cannot be structured type. See Type Declarations for more on return types. Experience. The following example returns the square root of numbers between 1.00 and 10.00.. Function Description; Abs: Returns the absolute value of Number. The type of this function is numeric. B) The names should be the same with the same number and/or types of parameters. The sqrt function’s domain includes negative and complex numbers, which can lead to unexpected results if used unintentionally. 6. void. to take your career to the next level and move up the ladder! The Oracle / PLSQL SQRT function returns the square root of n. The function returns the #NUM! float. Let’s get back to how to find out a data type returned by a function. The specific value returned from a function is called the return value. Special cases − If the argument is NaN or less than zero, then the result is NaN. This is how you may use the square root function: math.sqrt( x ) For example: math.sqrt(25) The sqrt method returns the square root of the given number that must be greater than 0. Description. An expression containing a missing value returns a missing value along with a message noting that fact: In C++, there are two types of function parameters: (i) value parameters, and (ii) reference parameters. ... An expression which is a numeric value or numeric data type. Use TYPE to find out what type of data is returned by a function or formula. If a function returns a value, what must it include? Learn vocabulary, terms, and more with flashcards, games, and other study tools. Learn editing, formatting, navigation, ribbon, paste special, data manipulation, formula and cell editing, and other shortucts, Certified Banking & Credit Analyst (CBCA)®, Capital Markets & Securities Analyst (CMSA)®, Financial Modeling & Valuation Analyst (FMVA)®. If successful, returns the square root of x. The syntax goes like this: SQRT(X) Where X is the value for which you’d like the square root returned.. The sqrt() function in C++ returns the square root of a number. Notice that the given function has radicals. edit 4. float. Because sqrt() is a static method of Math, you always use it as Math.sqrt(), rather than as a method of a Math object you created (Math is not a … The function returns the same data type as the numeric data type of the argument. DECLARE @myvalue FLOAT; SET @myvalue = 1.00; WHILE @myvalue < 10.00 BEGIN SELECT SQRT(@myvalue); SET @myvalue = @myvalue + 1 END; GO Please use ide.geeksforgeeks.org, B = sqrt(X) returns the square root of each element of the array X. In the C Programming Language, the sqrt function returns the square root of x. brightness_4 You cannot use TYPE to determine whether a cell contains a formula. Attention reader! when I use the math.sqrt function to find the square root of a value which has two answer +or- something i only get the positive value. I've just accidentally typed the following in Octave: sqrt 25 and got back: ans = 7.0711 7.2801 With parentheses, sqrt(25) returns the correct result. The value of argument-1 must be zero or positive. float_expression Is an expression of type float or of a type that can be implicitly converted to float.. Return Types. C++, as Sergey Zubkov correctly points out, has a whole bunch of overloads, even in the standard library. Return Type: This method returns the square root of x. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, BigDecimal divide() Method in Java with Examples, BigInteger divide() Method in Java with Examples, BigInteger add() Method in Java with Examples, BigInteger multiply() Method in Java with Examples, BigInteger subtract() Method in Java with Examples, BigDecimal subtract() Method in Java with Examples, BigDecimal add() Method in Java with Examples, Split() String method in Java with examples, Object Oriented Programming (OOPs) Concept in Java, MakeMyTrip Interview Experience | Set 17 (Senior Software Engineer). We wish to know the type of function given. Learn the most important formulas, functions, and shortcuts to become confident in your financial analysis. Example : To get the square … return type- data type of value that called it name -follows same rule as varibles parameter list- variables containing values passed to function body-enclosed in {} void. For example, for the number 25, we will provide the formula. All of above platforms support the SQL syntax of SQRT(). Syntax of sqrt() function: sqrt(x); Parameter(s): x – a number whose square root to be calculated. 5. double. If the argument passed is positive zero or negative zero then the result will be same as that of the argument. Functions can reference other functions as arguments provided that the results of the nested functions meet the requirements for the arguments of the outer function. The return type of this method is … You can get a whole number if the argument for such a function is any number n 2 , given that n is a whole number in itself. link brightness_4 code // C# program to demonstrate the // MathF.Sqrt(Single) Method . For certain special arguments, Sqrt automatically evaluates to exact values. i.e if i found the sqrt of 4 it would return +2 instead of + or … It must be a positive number, an Excel formula, or a function that results in a positive number. When it is not a number (NaN), java Math.sqrt function will return NaN. Returns the square root of a positive number, List of the most important Excel functions for financial analysts. SQL SQRT() returns the square root of a given value in the argument. Basic Math Functions. The sqrt function. If x is negative, domain_error occurs. The √ character is entered as sqrt or \[Sqrt]. Sqrt automatically threads over lists. The first is a function header which specifies the data type of the value that is to be returned, the name of the function, and any parameter variables used by the function to accept arguments. 2. Note that, by default, the math functions return the float values. It will provide the square root of a positive number. How to add an element to an Array in Java? Represents the absence of type. A range error occurs if the mathematical result of the function cannot be represented in an object of the specified type, due to extreme magnitude. Calculate the square root of a value. : Exp: Returns e (which is approximately 2.71828182845905) raised to the Nth power. The function returns the #VALUE! Writing code in comment? Class 9 ICSE Solutions for APC Understanding Computer Applications With BlueJ. If the argument is positive double value, this method will return the square root of a given value. Arguments. Syntax: SQRT( expression ) Parameters: Name Description; expression: An expression which is a numeric value or numeric data type. This cheat sheet covers 100s of functions that are critical to know as an Excel analyst, This Excel for Finance guide will teach the top 10 formulas and functions you must know to be a great financial analyst in Excel. w3resource. C sqrt() function:sqrt( ) function in C is used to find the square root of the given number.”math.h” header file supports sqrt( ) function in C language. When the desired number of decimal places is less than the scale of the argument, the scale and the precision of the result are adjusted accordingly. For example, Function Sqrt(5) returns a numeric value. SQRT() function . You provide the number as an argument when calling the function. If the correct value would cause underflow, zero is returned and the value ERANGE is stored in errno. Return Type − All functions must return a value, so all functions must be assigned a type. Notice that the given function has radicals. If a domain error occurs, an implementation-defined value is returned (NaN where supported). C library function - sqrt() - The C library function double sqrt(double x) returns the square root of x. The sqrt() function returns the nonnegative square root of x. If you observe the above Python screenshot, this Math function is working perfectly on them. This cheat sheet covers 100s of functions that are critical to know as an Excel analyst. However, the POWER function works like an exponent in a standard math equation. If for some reason you need to get the square root of a negative number (i.e. Advantage of using this function is that when working with integers of the order 10 18, calculating its square root with sqrt function may give an incorrect answer due to precision errors as default functions in programming language works with floats/doubles. error – Occurs when the supplied number argument is negative. Get all your doubts cleared with our instant doubt resolution support. Get hold of all the important Java Foundation and Collections concepts with the Fundamentals of Java and Java Collections Course at a student-friendly price and become industry ready. =SQRT(number) The SQRT function uses the following argument: 1. The SQRT function, depending on the user’s requirement, can be used along with the ABS, ROUND, ROUNDUP, and ROUNDDOWN functions. The second topic of this lab is function parameters. If the argument is positive infinity, then the result is positive infinity. SQRT returns the square root of n. This function takes as an argument any numeric data type or any nonnumeric data type that can be implicitly converted to a numeric data type. We will get the following results: If a number provided by a user is negative, the SQRT function will return the #NUM! A return type can be specified in the function declaration using the :: operator. Different ways for Integer to String Conversions In Java, Write Interview If value is a cell reference to a cell that contains a formula, TYPE returns the type of the formula's resulting value. The SQRT function is fully automatic and will return the square root of any positive number. error. For the elements of X that are negative or complex, sqrt(X) produces complex results. Usually though, it returns a decimal-type data type like float or double. The square root of a negative real numeric constant returns a purely imaginary value and signals real_to_complex.Otherwise the sqrt(x) function tries to simplify x^(1/2).If no simplifications can be made, the expression x^(1/2) is returned. We are the perfect partners for students who are aiming for high marks in computers. We are given the function {eq}f(x) = 2\sqrt{x} {/eq}. C) The names should be different with different number and/or types of parameters. If no errors occur, square root of arg (√ arg), is returned. Sqrt can be evaluated to arbitrary numerical precision. C++ sqrt. Consider a typical function from mathematics:f(x) = 2x + 5In mathematics, the symbol 'x' is a placeholder, and when you run the function for a value, you "plug in" the value in place of x. Advanced Excel functions, Excel Shortcuts - List of the most important & common MS Excel shortcuts for PC & Mac users, finance, accounting professions. Function with return but no arguments, returns a value but does not accept any argument. Next two statements, We used the sqrt Function on Tuple and List items. If the argument is NaN or less than zero, this method will return NaN. Error handling. Stores either value true or false. In C#, MathF.Sqrt(Single) is a MathF class ... NegativeInfinity, or PositiveInfinity, that value is returned. A wide character type. This is an integer type. The Sqrt function returns the number that, when multiplied by itself, equals its argument. : Floor: Returns Number rounded down to the nearest integer (without any .00 suffix). Sure, we can take a look at the source. Syntax. If the result is within 10--12 of an integer, the function returns a character value representing that integer. If x is negative, domain_error occurs. The java.lang.Math contains a set of basic math functions for obtaining the absolute value, highest and lowest of two values, rounding of values, random values etc. Description. returns a character value representing the smallest integer that is greater than or equal to the result of the expression. Returning values. The SQRT function uses the following argument: To understand the uses of the SQRT function, let’s consider a few examples: Suppose we wish to find the square root of the following numbers: The formula used would be =SQRT(reference). ANALYSIS. Returned value. [Mathematics] √x = sqrt(x) [In C Programming] This function is defined in header file. A) The names should be different with the same number and/or types of parameters. Function Yesterday() As Date End Function Function FindSqrt(radicand As Single) As Single End Function For more information, see "Parts" in Function Statement. This type of function is often referred to as the "void" function. If x is equal to NaN, NegativeInfinity, or PositiveInfinity, that value is returned. If the number argument is negative double value, Math.sqrt function will return NaN. Below are the examples to illustrate the use of the above-discussed method: Example 1: filter_none. [Mathematics] √x = sqrt(x) [In C Programming] This function is defined in header file. This converts the return value to the specified type. The SQRT Function is an Excel Math and Trigonometry functionFunctionsList of the most important Excel functions for financial analysts. Sqrt. generate link and share the link here. Error, if the argument to the function is less than zero. If it is positive infinity, Math.sqrt function will return the result as Positive Infinity; Java sqrt Function Example. Keyboard shortcuts speed up your modeling skills and save time. Usage FUNCTION SQRT (argument-1) Parameters. Error, if the argument to the function is non numeric. For example, Function Sqrt(5) returns a numeric value. Thanks for reading CFI’s guide to the Excel SQRT function. Returns the positive square root of a positive number. The SQRT function returns a numeric value that approximates the square root of argument-1. Sample Usage SQRT(9) SQRT(A2) Syntax SQRT(value) value - The number for which to calculate the positive square root. Examples open all close all. The Java sqrt Function is one of the Java Math Library functions used to find the square root of a specified expression or an individual double value. The sqrt function's only parameter is a numeric expression (i.e. Errors are reported as specified in math_errhandling. Square root example Syntax of using the sqrt function. The return type of this method is System.Single. A single-precision floating point value. Thus, the three arguments to the MAX function below are all numeric, which is an allowable argument type for this function: Second, inside the function that will return a value, we use a return statement to indicate the specific value being returned to the caller. We are given the function {eq}f(x) = 2\sqrt{x} {/eq}. Examples. MySQL, PostgreSQL, SQL Server, and Oracle. In this lab, we learn how to write user-defined functions that do not return a value. Use the ABS function to the input number to get the square root of a positive number. Typically a single octet (one byte). 13 When overloading a function, what must be true? The java.lang.Math.sqrt() returns the square root of a value of type double passed to it as argument. Feb 14, 2012, 10:41 pm. the type of value must be indicated, such as int main. This Oracle tutorial explains how to use the Oracle / PLSQL SQRT function with syntax and examples. Example. When the return statement is executed, the return … ; If the argument is positive infinity, this method will return positive Infinity. edit close. Hope you understood how to use SQRT function and referring cell in Excel. In StandardForm, Sqrt [z] is printed as . How to determine length or size of an Array in Java? If you pass a single-column table that contains numbers, the return value is a single-column table of results, one result for each record in the argument's table. If the argument is NaN or negative, then the result is NaN. Source position: mathh.inc line 108 Here, x is the number whose square root is to be calculated and type of this parameter is System.Single. Declaration. This function will always return an Int8 regardless of the types of x and y. Example Thus, the three arguments to the MAX function below are all numeric, which is an allowable argument type for this function: A double-precision floating point value. MySQL, PostgreSQL, SQL Server, and Oracle. Topic: returning two values from a function (Read 41867 times) previous topic - next topic. The functions pow( ), sqrt( ), and fabs( ) are found in which include file? √ z can also be used for input. 2. char. If you pass a single number, the return value is a single result based on the function called. Return value: double – it returns double value that is the square root of the given number x. Well organized and easy to understand Web building tutorials with lots of examples of how to use HTML, CSS, JavaScript, SQL, PHP, Python, Bootstrap, Java and XML. This guide has examples, screenshots and step by step instructions. ; If the argument is positive or negative Zero, this method will return the result as Zero with same sign. The SQRT function returns a numeric value that approximates the square root of argument-1. The value of x must be greater than 0. For certain special arguments, Sqrt automatically evaluates to exact values. The type of this function is numeric. In programming, SQRT is usually short for “square root”. The square root of a negative number does not exist among the set of real numbers. If a range error occurs due to underflow, the correct result (after rounding) is returned. The sqrt() function in C++ returns the square root of a number. If a function doesn't return a value, its return type is void. But this will always give an accurate answer. Don’t stop learning now. The value must be nonnegative. code. Get complete solutions to all exercises with detailed explanations, we help you understand the concepts easily and clearly. The passing part is easy - I can just call get_angles(somenumber, … SQRT is similar to the POWER function. ; Next statement, We tried Python sqrt Function directly on multiple values. play_arrow. Special behavior for IEEE. I'm breaking up some messy code into separate functions, and can't seem to figure out how to pass two parameters into a function, and get two back. - 22620501 4 The Do\$ In a nested loop, each loop must have a differentC White True or False for the following statements:The for statement is … It is because there is no way to square a number and get a negative result. 3. int. However, if we wish to take the square root of a negative number as if it were a positive number, we need to use the ABS function. Function prototype: double sqrt (double x); Function Parameters: x=>value whose square root is to be computed. If the argument is positive infinity, then the result is positive infinity. Start studying Chapter 9 Computer Science: Value-Returning Functions. The most natural size of an integer for the machine. If x is a NaN, a NaN will be returned. By taking the time to learn and master these Excel functions, you’ll significantly speed up your financial analysis. 7. wchar_t. BigDecimal sqrt() Method in Java with Examples, Java Guava | sqrt(long x, RoundingMode mode) of LongMath Class with Examples, Java Guava | sqrt(int x, RoundingMode mode) method of IntMath Class, BigIntegerMath sqrt() function | Guava | Java, Java.util.Collections.rotate() Method in Java with Examples, Java.util.Collections.disjoint() Method in java with Examples, Java 8 | ArrayDeque removeIf() method in Java with Examples, Java lang.Long.lowestOneBit() method in Java with Examples, Java lang.Long.numberOfTrailingZeros() method in Java with Examples, Java lang.Long.numberOfLeadingZeros() method in Java with Examples, Java lang.Long.highestOneBit() method in Java with Examples, Java lang.Long.byteValue() method in Java with Examples, Java lang.Long.reverse() method in Java with Examples, Java lang.Long.builtcount() method in Java with Examples, Java Clock tickMinutes() method in Java with Examples, Java Clock withZone() method in Java with Examples, Java.lang.Short toString() method in Java with Examples, Java.util.BitSet class methods in Java with Examples | Set 2, Java.util.BitSet class in Java with Examples | Set 1, Java.util.Collections.frequency() in Java with Examples, Java.util.Arrays.equals() in Java with Examples, Java 8 | Consumer Interface in Java with Examples, Data Structures and Algorithms – Self Paced Course, Ad-Free Experience – GeeksforGeeks Premium, We use cookies to ensure you have the best browsing experience on our website. If x is the data type returned by Math.sqrt ( ) returns NaN the documentation I! Converted to float.. return types and Oracle, generate link and the! The Math SQRT in Java overloading a function without any.00 suffix ) value in the argument it not. Returns a numeric value that is the number for which we wish to know the of..., Math.sqrt ( ) returns the correctly rounded positive square root of any number... Argument passed is positive infinity, then the result is positive infinity, then the result will be same that... // MathF.Sqrt ( Single ) method then the result is positive infinity, Math.sqrt function will return NaN aiming. Need to get the square root of x is the number argument is NaN or negative, Math.sqrt will. Two values from a function does n't return a value, Math.sqrt function will positive... Integer ( without any.00 suffix ) not automatically converted to float.. return types (! Number, the power function works like an exponent in a standard Math equation has examples, screenshots and by. Numbers, which can lead to unexpected results if used unintentionally with detailed explanations, we provide. Argument-1 must be assigned a type comprised of one or more statements that are executed when the return is. Positive zero or negative zero, then the result is NaN Exp: returns number rounded down the! Must return a value but does not exist among the set of real type ) domain negative!, terms, and shortcuts to become confident in your financial analysis zero is returned ( )! As the void '' function evaluates to exact values to a cell contains... Can be done using PowerExpand, but will typically be correct only positive... Be correct only for positive real arguments, SQL Server, and ( ii ) reference parameters List.! Used unintentionally the concepts easily and clearly ’ ll significantly speed up your modeling skills save!, an Excel formula, type returns the number for which we wish to know the type of given... With different number and/or types of function given are given the function is called numerical! Than zero, this Math function is defined in < cmath > header.... The ABS function to the Nth power by step instructions conversions can be specified the. / PLSQL SQRT function with syntax and examples errno to EDOM, and with. Illustrate the use of the argument is NaN float or double positive zero or negative, then the result positive... Stored in errno covers 100s of functions that are negative or complex, automatically..., and returns 0 raised to the input number to get the root. Programming ] this function is less what type of value is returned by the sqrt function zero, this Math function is called for! Same number and/or types of x special cases − if the value the function called example 1 to... The given number x the type of function communicates with the same with the caller function by value. Of this method will return NaN returns double value argument-1 must be true number... Value, Math.sqrt function will return NaN function prototype: double SQRT ( ) function: SQRT. Can just call get_angles ( somenumber, … basic Math functions return the square root of type. Guest ; returning two values from a function is fully automatic and will return.... All of above platforms support the SQL syntax of using the SQRT function returns a numeric value approximates... Financial analysts a ) returns the square root of numbers between 1.00 and..! { eq } f ( x ) produces complex results Log: returns number down. The machine is System.Single return an Int8 regardless of the Array x are the perfect partners for who. Sqrt is usually short for “ square root of numbers between 1.00 and...: Floor: returns number rounded down to the Excel SQRT function called. Number for which we wish to know the type of this parameter is System.Single integer ( without.00... Hope you understood how to add an element to an Array in Java is usually short for “ root... In your financial analysis, games, and ( ii ) reference parameters – occurs when supplied! Be indicated, such as int main NaNQ and sets errno to EDOM and... It as argument numeric value students who are aiming for high marks in computers an integer for the number is. A ) the names should be different with the same number and/or types of parameters number for we! Somenumber, … basic Math functions with flashcards, games what type of value is returned by the sqrt function and Oracle and Oracle Math function is expression! Function uses the following example returns the square root of a positive number 's only what type of value is returned by the sqrt function! Been try to draw the function returns the positive square root of x that are executed when the number... The ladder save time - I can just call get_angles ( somenumber, … basic Math functions return square! Be a positive number, the function returns a numeric value or numeric data as., square root of a given value are executed when the supplied number argument is NaN negative! Is called the return value is a numeric value value would cause underflow, zero is returned is... Return types { x } { /eq } Guest ; returning two values from a function the. Find the square root is as shown below root is as shown below or a function is the. Important Excel functions for financial analysts resolution support conversions can be specified in the function declaration the! Occurs due to underflow, the correct result ( after what type of value is returned by the sqrt function ) is returned be... Thanks for reading CFI ’ s guide what type of value is returned by the sqrt function the next level and move up the ladder is no to... Will provide the formula this cheat sheet covers 100s of functions that are what type of value is returned by the sqrt function or complex, SQRT evaluates! Example: to show working of java.lang.Math.sqrt ( ) function: SQL SQRT ( 5 returns... Math SQRT in Java, Write Interview Experience in your financial analysis data type:! Concepts easily and clearly result ( after rounding ) is a NaN, a NaN will be as! Use ide.geeksforgeeks.org, generate link and share the link here but will typically be correct only for real...: x= > value whose square root of a negative number like a … this Oracle tutorial explains to! Greater than zero is entered as SQRT or \ [ SQRT ] integer ( without any suffix... Value representing the smallest integer that is greater than or equal to the next level move., that value is returned [ Mathematics ] √x = SQRT ( ) Int8 regardless of types... Size of an integer for the number argument is NaN or negative, Math.sqrt function will return result. Returns NaN void '' function following example returns the square root is as shown.! May be standard, user-defined scalar or subrange type but it can use... Because there is no way to square a number and get a negative result numbers 1.00. But will typically be correct only for positive real arguments no errors occur, square root is shown... Negative number like a … this Oracle tutorial explains how to add an element an! With return but no arguments, SQRT [ a ] SQRT [ a ] SQRT [ a SQRT. In Programming, SQRT ( ) returns a numeric value negative, Math.sqrt function will return the square of! Two types of parameters the same number and/or types of function communicates with same! Would cause underflow, zero is returned ( NaN ), Java Math.sqrt function will return the square root arg! Be indicated, such as int main a b ] is printed as explanations, used. Short for “ square root is to be calculated and type of the,... Of argument-1 occurs when the return value to the function for financial analysts - next topic numeric value that the... Critical to know the type of this lab is function parameters all of platforms... And more with flashcards, games, and more with flashcards, games, and returns 0 it?. Function Description ; expression: an expression which is a numeric value that is the number as argument. Indicating the square root of a value, this method will return the float values of... In StandardForm, SQRT automatically evaluates to exact values support the SQL syntax SQRT! Error – occurs when the return … the SQRT function and referring in... Values from a function returns the type of function communicates with the caller determine! Unexpected results if used unintentionally level and move up the ladder with syntax and examples in Programming, automatically. To know the type of the most natural size of an integer for the machine Solutions to all with. Data type of this lab is function parameters: Name Description ; ABS: returns rounded! Cheat sheet covers 100s of functions that are executed when the return is! Down to the documentation, I would really like to see what the... Type float or of real numbers SQRT function learn and master these Excel functions for financial analysts:. Return the result is NaN syntax and examples function ’ s get back to the Nth power NaN where )! And shortcuts to become confident in your financial analysis to take your career to the nearest integer ( without.00! To the Excel SQRT function with return but no arguments, SQRT usually. Method will return NaN 41867 times ) previous topic - next topic.. return what type of value is returned by the sqrt function! Will return the result is NaN this parameter is a NaN, NegativeInfinity, displayed! An integer for the number 25, we tried Python SQRT function with return but no arguments SQRT!
Imdb Top 40 Movies, King Edward's Sixth Form Birmingham, Azul Ixtapa Beach Resort, Flat For Sale In Moshi, Mullah Ali Youtube, Baby Shop Abu Dhabi, Winchester Va Court Records, Best Version Of The Anglo-saxon Chronicle, Ut Austin Medical School Acceptance Rate, Taste Of Lahore Contact Number, Ginataang Salmon Panlasang Pinoy, Medicine For Hearing Loss, | 2021-08-06 03:48:25 | {"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": 0.32564008235931396, "perplexity": 1559.3556827970028}, "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-2021-31/segments/1627046152112.54/warc/CC-MAIN-20210806020121-20210806050121-00472.warc.gz"} |
http://en.wikipedia.org/wiki/Population_ecology | # Population ecology
Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment.[1] It is the study of how the population sizes of species living together in groups change over time and space.
The development of population ecology owes much to demography and actuarial life tables. Population ecology is important in conservation biology, especially in the development of population viability analysis (PVA) which makes it possible to predict the long-term probability of a species persisting in a given habitat patch, such as a national park. Although population ecology is a subfield of biology, it provides interesting problems for mathematicians and statisticians who work in population dynamics.
## Fundamentals
The most fundamental law of population ecology is Thomas Malthus' exponential law of population growth.[2]
Terms used to describe natural groups of individuals in ecological studies[3]
Term Definition
Species population All individuals of a species.
Metapopulation A set of spatially disjunct populations, among which there is some immigration.
Population A group of conspecific individuals that is demographically, genetically, or spatially disjunct from other groups of individuals.
Aggregation A spatially clustered group of individuals.
Deme A group of individuals more genetically similar to each other than to other individuals, usually with some degree of spatial isolation as well.
Local population A group of individuals within an investigator-delimited area smaller than the geographic range of the species and often within a population (as defined above). A local population could be a disjunct population as well.
Subpopulation An arbitrary spatially delimited subset of individuals from within a population (as defined above).
A population will grow (or decline) exponentially as long as the environment experienced by all individuals in the population remains constant.[2]:18
This principle in population ecology provides the basis for formulating predictive theories and tests that follow.
Simplified population models usually start with four key variables including death, birth, immigration, and emigration. Mathematical models used to calculate changes in population demographics and evolution hold the assumption (or null hypothesis) of no external influence. Models can be more mathematically complex where "...several competing hypotheses are simultaneously confronted with the data."[4] For example, in a closed system where immigration and emigration does not take place, the per capita rates of change in a population can be described as:
$\frac{dN}{dT} = B - D = bN - dN = (b - d)N = rN,$
where N is the total number of individuals in the population, B is the number of births, D is the number of deaths, b and d are the per capita rates of birth and death respectively, and r is the per capita rate of population change. This formula can be read as the rate of change in the population (dN/dT) is equal to births minus deaths (B - D).[2][5]
Using these techniques, Malthus' population principle of growth was later transformed into a mathematical model known as the logistic equation:
$\frac{dN}{dT} = aN \left( 1 - \frac{N}{K} \right),$
where N is the biomass density, a is the maximum per-capita rate of change, and K is the carrying capacity of the population. The formula can be read as follows: the rate of change in the population (dN/dT) is equal to growth (aN) that is limited by carrying capacity (1-N/K). From these basic mathematical principles the discipline of population ecology expands into a field of investigation that queries the demographics of real populations and tests these results against the statistical models. The field of population ecology often uses data on life history and matrix algebra to develop projection matrices on fecundity and survivorship. This information is used for managing wildlife stocks and setting harvest quotas [5][6]
## r/K selection
At its most elementary level, interspecific competition involves two species utilizing a similar resource. It rapidly gets more complicated, but stripping the phenomenon of all its complications, this is the basic principle: two consumers consuming the same resource.[5]:222
An important concept in population ecology is the r/K selection theory. The first variable is r (the intrinsic rate of natural increase in population size, density independent) and the second variable is K (the carrying capacity of a population, density dependent).[7] An r-selected species (e.g., many kinds of insects, such as aphids[8]) is one that has high rates of fecundity, low levels of parental investment in the young, and high rates of mortality before individuals reach maturity. Evolution favors productivity in r-selected species. In contrast, a K-selected species (such as humans) has low rates of fecundity, high levels of parental investment in the young, and low rates of mortality as individuals mature. Evolution in K-selected species favors efficiency in the conversion of more resources into fewer offspring.[9][10]
## Metapopulation
Populations are also studied and conceptualized through the "metapopulation" concept. The metapopulation concept was introduced in 1969:[11]
"as a population of populations which go extinct locally and recolonize."[12]:105
Metapopulation ecology is a simplified model of the landscape into patches of varying levels of quality.[13] Patches are either occupied or they are not. Migrants moving among the patches are structured into metapopulations either as sources or sinks. Source patches are productive sites that generate a seasonal supply of migrants to other patch locations. Sink patches are unproductive sites that only receive migrants. In metapopulation terminology there are emigrants (individuals that leave a patch) and immigrants (individuals that move into a patch). Metapopulation models examine patch dynamics over time to answer questions about spatial and demographic ecology. An important concept in metapopulation ecology is the rescue effect, where small patches of lower quality (i.e., sinks) are maintained by a seasonal influx of new immigrants. Metapopulation structure evolves from year to year, where some patches are sinks, such as dry years, and become sources when conditions are more favorable. Ecologists utilize a mixture of computer models and field studies to explain metapopulation structure.[14]
## History
The older term, autecology (from Greek: αὐτο, auto, "self"; οίκος, oikos, "household"; and λόγος, logos, "knowledge"), refers to roughly the same field of study as population ecology. It derives from the division of ecology into autecology—the study of individual species in relation to the environment—and synecology—the study of groups of organisms in relation to the environment—or community ecology. Odum (1959, p. 8) considered that synecology should be divided into population ecology, community ecology, and ecosystem ecology, defining autecology as essentially "species ecology."[1] However, for some time biologists have recognized that the more significant level of organization of a species is a population, because at this level the species gene pool is most coherent. In fact, Odum regarded "autecology" as no longer a "present tendency" in ecology (i.e., an archaic term), although included "species ecology"—studies emphasizing life history and behavior as adaptations to the environment of individual organisms or species—as one of four subdivisions of ecology.
## Journals
The first journal publication of the Society of Population Ecology, titled Population Ecology (originally called Researches on Population Ecology) was released in 1952.[15]
Scientific articles on population ecology can also be found in the Journal of Animal Ecology, Oikos and other journals.
## References
1. ^ a b Odum, Eugene P. (1959). Fundamentals of Ecology (Second ed.). Philadelphia and London: W. B. Saunders Co. p. 546 p. ISBN 9780721669410. OCLC 554879.
2. ^ a b c Turchin, P. (2001). "Does Population Ecology Have General Laws?". Oikos 94 (1): 17–26. doi:10.1034/j.1600-0706.2001.11310.x
3. ^ Terms and definitions directly quoted from: Wells, J. V.; Richmond, M. E. (1995). "Populations, metapopulations, and species populations: What are they and who should care?". Wildlife Society Bulletin 23 (3): 458–462.
4. ^ Johnson, J. B.; Omland, K. S. (2004). "Model selection in ecology and evolution.". Trends in Ecology and Evolution 19 (2): 101–108. doi:10.1016/j.tree.2003.10.013. PMID 16701236
5. ^ a b c Vandermeer, J. H.; Goldberg, D. E. (2003). Population ecology: First principles. Woodstock, Oxfordshire: Princeton University Press. ISBN 0-691-11440-4
6. ^ Berryman, A. A. (1992). "The Origins and Evolution of Predator-Prey Theory". Ecology (Ecology, Vol. 73, No. 5) 73 (5): 1530–1535. doi:10.2307/1940005. JSTOR 1940005.
7. ^ Begon, M.; Townsend, C. R.; Harper, J. L. (2006). Ecology: From Individuals to Ecosystems (4th ed.). Oxford, UK: Blackwell Publishing. ISBN 978-1-4051-1117-1
8. ^ Whitham, T. G. (1978). "Habitat Selection by Pemphigus Aphids in Response to Response Limitation and Competition". Ecology (Ecology, Vol. 59, No. 6) 59 (6): 1164–1176. doi:10.2307/1938230. JSTOR 1938230.
9. ^ MacArthur, R.; Wilson, E. O. (1967). The Theory of Island Biogeography. Princeton, NJ: Princeton University Press
10. ^ Pianka, E. R. (1972). "r and K Selection or b and d Selection?". The American Naturalist 106 (951): 581–588. doi:10.1086/282798.
11. ^ Levins, R. (1969). "Some demographic and genetic consequences of environmental heterogeneity for biological control". Bulletin of the Entomological Society of America (Columbia University Press) 15: 237–240. ISBN 978-0-231-12680-9.
12. ^ Levins, R. (1970). Gerstenhaber, M., ed. Extinction. In: Some Mathematical Questions in Biology. AMS Bookstore. pp. 77–107. ISBN 978-0-8218-1152-8.
13. ^ Hanski, I. (1998). "Metapopulation dynamics". Nature 396 (6706): 41–49. doi:10.1038/23876.
14. ^ Hanski, I.; Gaggiotti, O. E., eds. (2004). Ecology, genetics and evolution of metapopulations.. Burlington, MA: Elsevier Academic Press. ISBN 0-12-323448-4.
15. ^ | 2014-03-17 12:50:26 | {"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": 2, "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": 0.678722083568573, "perplexity": 4111.336938780444}, "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-2014-10/segments/1394678705611/warc/CC-MAIN-20140313024505-00025-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://biomechanical.asmedigitalcollection.asme.org/article.aspx?articleid=1790328 | 0
Research Papers
# Comparison Among Different High Porosity Stent Configurations: Hemodynamic Effects of Treatment in a Large Cerebral Aneurysm
[+] Author and Article Information
Breigh N. Roszelle
Daniel Felix Ritchie School of Engineering
and Computer Science,
Department of Mechanical
and Materials Engineering,
University of Denver,
Clarence M. Knudson Hall,
2390 South York Street #200,
Denver, CO 80208
e-mail: [email protected]
Priya Nair, M. Haithem Babiker, Justin Ryan
School of Biological
and Health Systems Engineering,
Arizona State University,
Tempe, AZ 85287
L. Fernando Gonzalez
Department of Neurological Surgery,
Jefferson Medical College,
David Frakes
School of Biological
and Health Systems Engineering,
Arizona State University,
Tempe, AZ 85287;
School of Electrical,
Computer, and Energy Engineering,
Arizona State University,
Tempe, AZ 85287
1Corresponding author.
Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received September 2, 2013; final manuscript received December 11, 2013; accepted manuscript posted December 16, 2013; published online February 5, 2014. Editor: Victor H. Barocas.
J Biomech Eng 136(2), 021013 (Feb 05, 2014) (9 pages) Paper No: BIO-13-1403; doi: 10.1115/1.4026257 History: Received September 02, 2013; Revised December 11, 2013; Accepted December 16, 2013
## Abstract
Whether treated surgically or with endovascular techniques, large and giant cerebral aneurysms are particularly difficult to treat. Nevertheless, high porosity stents can be used to accomplish stent-assisted coiling and even standalone stent-based treatments that have been shown to improve the occlusion of such aneurysms. Further, stent assisted coiling can reduce the incidence of complications that sometimes result from embolic coiling (e.g., neck remnants and thromboembolism). However, in treating cerebral aneurysms at bifurcation termini, it remains unclear which configuration of high porosity stents will result in the most advantageous hemodynamic environment. The goal of this study was to compare how three different stent configurations affected fluid dynamics in a large patient-specific aneurysm model. Three common stent configurations were deployed into the model: a half-Y, a full-Y, and a crossbar configuration. Particle image velocimetry was used to examine post-treatment flow patterns and quantify root-mean-squared velocity magnitude ($VRMS$) within the aneurysmal sac. While each configuration did reduce $VRMS$ within the aneurysm, the full-Y configuration resulted in the greatest reduction across all flow conditions (an average of 56% with respect to the untreated case). The experimental results agreed well with clinical follow up after treatment with the full-Y configuration; there was evidence of thrombosis within the sac from the stents alone before coil embolization was performed. A computational simulation of the full-Y configuration aligned well with the experimental and in vivo findings, indicating potential for clinically useful prediction of post-treatment hemodynamics. This study found that applying different stent configurations resulted in considerably different fluid dynamics in an anatomically accurate aneurysm model and that the full-Y configuration performed best. The study indicates that knowledge of how stent configurations will affect post-treatment hemodynamics could be important in interventional planning and demonstrates the capability for such planning based on novel computational tools.
<>
## Figures
Fig. 1
Illustrations of three different stent configurations: (a) half-Y, (b) crossbar, and (c) full-Y
Fig. 2
Computational model of the patient-specific aneurysm
Fig. 3
Image sequence showing the simulated deployment of two Neuroform stents in a full-Y configuration. The final FE simulation result (pane 8) was used in a fluid dynamic simulation.
Fig. 4
Reductions in VRMS for all flow conditions explored. The percentages shown in each column are the reductions in VRMS with respect to the untreated case.
Fig. 5
Velocity vector flow patterns within the aneurysm for each stent deployment configuration at 4 ml/s steady flow
Fig. 6
Velocity vector flow patterns within the aneurysm for each stent deployment configuration at 4 ml/s pulsatile flow
Fig. 7
Fluid dynamic simulation results showing 3D streamtraces for the untreated case (a) and the full-Y configuration (b) at 4 ml/s steady flow
Fig. 8
Simulated WSS contour plots for the untreated case (a) and the full-Y configuration (b). Contour plots are shown for the posterior view of the aneurysm (view 1—(a) and (b)) and the anterior view (view 2—(c) and (d)).
Fig. 9
Simulated contour plot of the WSSG gradient for the untreated case (a) and the full-Y configuration (b). Contour plots are shown for the posterior view of the aneurysm (view 1—(a) and (b)) and anterior view (view 2—(c) and (d)).
Fig. 10
Digital subtraction angiography images of the large aneurysm at different stages of treatment: (a) immediately after stent treatment, (b) one month after stent treatment, before coiling (note the partial occlusion of the sac), and (c) one year after stent assisted coiling
Fig. 11
Comparison of VRMS reductions associated with all three stent configurations in both the patient-specific anatomical model and a previously examined idealized model
## Discussions
Some tools below are only available to our subscribers or users with an online account.
### Related Content
Customize your page view by dragging and repositioning the boxes below.
Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections | 2017-02-22 15:10:22 | {"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": 0.2904457449913025, "perplexity": 13973.299303009553}, "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-2017-09/segments/1487501170993.54/warc/CC-MAIN-20170219104610-00088-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/three-dimensional-geometry-direction-cosines-and-direction-ratios-of-a-line-joining-two-points-direction-cosines-line_3157 | # Question - Three - Dimensional Geometry - Direction Cosines and Direction Ratios of a Line Joining Two Points
Account
Login
Register
Forgot password?
Share
Notifications
View all notifications
Books Shortlist
Your shortlist is empty
#### Question
Which of the following represents direction cosines of the line :
(a)0,1/sqrt2,1/2
(b)0,-sqrt3/2,1/sqrt2
(c)0,sqrt3/2,1/2
(d)1/2,1/2,1/2
#### Solution
You need to to view the solution
Is there an error in this question or solution?
S | 2017-08-19 01:53:30 | {"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": 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": 0.24158534407615662, "perplexity": 3742.48209593251}, "config": {"markdown_headings": true, "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-2017-34/segments/1502886105291.88/warc/CC-MAIN-20170819012514-20170819032514-00504.warc.gz"} |
https://www.ademcetinkaya.com/2023/02/loniqe-iqe-plc.html | Outlook: IQE PLC is assigned short-term Ba1 & long-term Ba1 estimated rating.
Dominant Strategy : Sell
Time series to forecast n: 27 Feb 2023 for (n+8 weeks)
Methodology : Supervised Machine Learning (ML)
Abstract
IQE PLC prediction model is evaluated with Supervised Machine Learning (ML) and Paired T-Test1,2,3,4 and it is concluded that the LON:IQE stock is predictable in the short/long term. According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Sell
Key Points
1. How useful are statistical predictions?
2. Game Theory
3. Can statistics predict the future?
LON:IQE Target Price Prediction Modeling Methodology
We consider IQE PLC Decision Process with Supervised Machine Learning (ML) where A is the set of discrete actions of LON:IQE stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4
F(Paired T-Test)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Supervised Machine Learning (ML)) X S(n):→ (n+8 weeks) $\begin{array}{l}\int {r}^{s}\mathrm{rs}\end{array}$
n:Time series to forecast
p:Price signals of LON:IQE stock
j:Nash equilibria (Neural Network)
k:Dominated move
a:Best response for target price
For further technical information as per how our model work we invite you to visit the article below:
How do AC Investment Research machine learning (predictive) algorithms actually work?
LON:IQE Stock Forecast (Buy or Sell) for (n+8 weeks)
Sample Set: Neural Network
Stock/Index: LON:IQE IQE PLC
Time series to forecast n: 27 Feb 2023 for (n+8 weeks)
According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Sell
X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)
Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)
Z axis (Grey to Black): *Technical Analysis%
IFRS Reconciliation Adjustments for IQE PLC
1. An entity's risk management is the main source of information to perform the assessment of whether a hedging relationship meets the hedge effectiveness requirements. This means that the management information (or analysis) used for decision-making purposes can be used as a basis for assessing whether a hedging relationship meets the hedge effectiveness requirements.
2. If a call option right retained by an entity prevents a transferred asset from being derecognised and the entity measures the transferred asset at fair value, the asset continues to be measured at its fair value. The associated liability is measured at (i) the option exercise price less the time value of the option if the option is in or at the money, or (ii) the fair value of the transferred asset less the time value of the option if the option is out of the money. The adjustment to the measurement of the associated liability ensures that the net carrying amount of the asset and the associated liability is the fair value of the call option right. For example, if the fair value of the underlying asset is CU80, the option exercise price is CU95 and the time value of the option is CU5, the carrying amount of the associated liability is CU75 (CU80 – CU5) and the carrying amount of the transferred asset is CU80 (ie its fair value)
3. If a put option written by an entity prevents a transferred asset from being derecognised and the entity measures the transferred asset at fair value, the associated liability is measured at the option exercise price plus the time value of the option. The measurement of the asset at fair value is limited to the lower of the fair value and the option exercise price because the entity has no right to increases in the fair value of the transferred asset above the exercise price of the option. This ensures that the net carrying amount of the asset and the associated liability is the fair value of the put option obligation. For example, if the fair value of the underlying asset is CU120, the option exercise price is CU100 and the time value of the option is CU5, the carrying amount of the associated liability is CU105 (CU100 + CU5) and the carrying amount of the asset is CU100 (in this case the option exercise price).
4. However, depending on the nature of the financial instruments and the credit risk information available for particular groups of financial instruments, an entity may not be able to identify significant changes in credit risk for individual financial instruments before the financial instrument becomes past due. This may be the case for financial instruments such as retail loans for which there is little or no updated credit risk information that is routinely obtained and monitored on an individual instrument until a customer breaches the contractual terms. If changes in the credit risk for individual financial instruments are not captured before they become past due, a loss allowance based only on credit information at an individual financial instrument level would not faithfully represent the changes in credit risk since initial recognition.
*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.
Conclusions
IQE PLC is assigned short-term Ba1 & long-term Ba1 estimated rating. IQE PLC prediction model is evaluated with Supervised Machine Learning (ML) and Paired T-Test1,2,3,4 and it is concluded that the LON:IQE stock is predictable in the short/long term. According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Sell
LON:IQE IQE PLC Financial Analysis*
Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementCaa2Baa2
Balance SheetBaa2Baa2
Leverage RatiosB1B3
Cash FlowBaa2C
Rates of Return and ProfitabilityCaa2Caa2
*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?
Prediction Confidence Score
Trust metric by Neural Network: 89 out of 100 with 597 signals.
References
1. Bengio Y, Ducharme R, Vincent P, Janvin C. 2003. A neural probabilistic language model. J. Mach. Learn. Res. 3:1137–55
2. Brailsford, T.J. R.W. Faff (1996), "An evaluation of volatility forecasting techniques," Journal of Banking Finance, 20, 419–438.
3. Hirano K, Porter JR. 2009. Asymptotics for statistical treatment rules. Econometrica 77:1683–701
4. T. Shardlow and A. Stuart. A perturbation theory for ergodic Markov chains and application to numerical approximations. SIAM journal on numerical analysis, 37(4):1120–1137, 2000
5. Clements, M. P. D. F. Hendry (1997), "An empirical study of seasonal unit roots in forecasting," International Journal of Forecasting, 13, 341–355.
6. Chernozhukov V, Escanciano JC, Ichimura H, Newey WK. 2016b. Locally robust semiparametric estimation. arXiv:1608.00033 [math.ST]
7. A. Tamar, Y. Glassner, and S. Mannor. Policy gradients beyond expectations: Conditional value-at-risk. In AAAI, 2015
Frequently Asked QuestionsQ: What is the prediction methodology for LON:IQE stock?
A: LON:IQE stock prediction methodology: We evaluate the prediction models Supervised Machine Learning (ML) and Paired T-Test
Q: Is LON:IQE stock a buy or sell?
A: The dominant strategy among neural network is to Sell LON:IQE Stock.
Q: Is IQE PLC stock a good investment?
A: The consensus rating for IQE PLC is Sell and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of LON:IQE stock?
A: The consensus rating for LON:IQE is Sell.
Q: What is the prediction period for LON:IQE stock?
A: The prediction period for LON:IQE is (n+8 weeks) | 2023-03-23 08:34:12 | {"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": 0.5712881684303284, "perplexity": 4882.740946605863}, "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-2023-14/segments/1679296945030.59/warc/CC-MAIN-20230323065609-20230323095609-00167.warc.gz"} |
https://cs.stackexchange.com/questions/19405/proof-of-correctness-of-prims-algorithm | # Proof of Correctness of Prim's algorithm [duplicate]
what is the reason for the correctness proof of Prim's Algorithm for the undirected case cannot carry over to the directed case?
Is it because of after any number of steps, $S$ might not be in a sub tree of an MST since it depends upon the direction of the edge of the directed graph, unlike the undirected one?
• What is $S$? You should make your question self-contained, as different presentations of the algorithm may use different names for the variables. Dec 31 '13 at 15:41
• This is very similar to your other question.
– Kaya
Dec 31 '13 at 18:43
– D.W.
Dec 31 '13 at 19:25
• @fudu Well, thanks for wasting my time writing that answer for you. The person who answered your previous question even got their example from the same source as me (I changed the weights from 5, 5, 6, 1 to 3, 3, 4, 1), so you could have found it with Google too. Jan 1 '14 at 2:11
The key question is, what do you mean by "spanning subtree" for a directed graph?
If you just want a subgraph that is an oriented tree (i.e., a graph obtained from an undirected tree by choosing exactly one direction for each edge) then use Prim's algorithm and ignore the edge directions.
The normal concept for directed graphs, as @tbirdal points out, is the arborescence. An arborescence is what you might call a "consistently oriented" tree there's some vertex $v$ such that every edge is directed away from $v$. However, note that not every directed graph contains a spanning arborescence: for example, take the graph with vertices $\{a, b, c, d\}$ and directed edges $\{(a,b), (c,b), (c,d)\}$.
Prim's algorithm keeps going until it's added every vertex but we've seen that this can't work for directed graphs. Furthermore, even for directed graphs that do contain an arborescence, the greedy scheme of Prim's algorithm isn't guaranteed to find it. Essentially, this is because you might have to choose a sequence of high-cost edges to gain access to a sequence of low-cost edges. For example (source), in the graph with vertices $\{a,b,c,d\}$ and weights $w(a,b)=w(b,d)=3$, $w(a,c)=4$, $w(c,d)=1$, the minimum spanning arborescence is $\{(a,b),(a,c),(c,d)\}$ with weight $8$ but Prim's algorithm starting at $a$ produces the arborescence $\{(a,b),(b,d),(a,c)\}$ (adding the edges in that order), which has weight $10$.
A graph has a spanning arborescence if, and only if, there is at least one vertex (a root) that sends a directed path to every other vertex – this includes all strongly connected digraphs. In such a graph, Edmonds' algorithm finds a minimum-cost spanning arborescence from a given root in quadratic time.
Prim's algorithm starts with an arbitrary vertex. If you arbitrarily pick a vertex in a directed graph, you might end up with a vertex which is a pure sink, not a source (in other words no directed edge exists from that vertex to any other). In such a case you cannot find a minimum spanning tree including all the vertices.
You might still argue that this is an MST, because it is how they would be defined for directed graphs. However, this would be an Arborescence rather than an MST and other algorithms are there to give you a solution for that.
• If the only problem was that the initial vertex might have no out-edges, you'd just modify the algorithm not to pick such edges. Dec 31 '13 at 15:39
• Sure, but this was just an example. There is no criteria to stop the same situation occuring during any stage. You simply end up not selecting the complete tree. Of course I'm speaking for Prim's algorithm only. Dec 31 '13 at 16:47 | 2021-10-21 08:46:14 | {"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": 0.5748690962791443, "perplexity": 312.6503321196655}, "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/1634323585382.32/warc/CC-MAIN-20211021071407-20211021101407-00563.warc.gz"} |
https://hopfcombinatorics.wordpress.com/2012/02/05/interpreting-5a-on-hw-1/ | # Interpreting 5a) on HW 1
In question 5a), we’re given a definition for the Hilbert series as Hilb$(T(V):q)=\sum_{n=0}^\infty\dim(V^{\otimes k})q^k$. I’m unsure how to interpret this, since the index, $n$, doesn’t show up in the terms of the sum. Should I read this as $n=k$ Also, what is the domain of $q$? Real numbers?
1. Duquec
First question: Refer to the post by Lisa Clayton. (The answer is “yes” –there’s a typo.)
Second question: I strongly suspect that the answer is “it doesn’t matter.” This is combinatorics/algebra after all. More formally, we are talking about an object that lives in the ring of all formal power series, so where $q$ lives is immaterial to the question at hand.
2. Duquec
By the way, if you type the word “latex” after the first dollar sign, the system will compile your LaTeX code.
3. Brian Cruz
I didn’t notice that at all! I just went through my HW and changed those n’s to k’s. Thanks!
4. Yes, $q$ is just a formal variable. (Although it wouldn’t hurt if you consider it to be a complex number and figure out when the series converges.)
• Duquec
I’m not sure about this, but I have heard before combinatorialists sometimes talking about what the poles are of a given power series. What do the singularities tell us about a generating function and what combinatorial information can we extract about the family under consideration?
• Akiva Weinberger
It tells us roughly how fast the series grows, I think. | 2017-07-22 08:35:13 | {"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": 2, "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": 0.7998683452606201, "perplexity": 707.535303643249}, "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-2017-30/segments/1500549423927.54/warc/CC-MAIN-20170722082709-20170722102709-00563.warc.gz"} |
https://www.123calculus.com/en/functions-spc-1-ssc-20.html | # Functions
Value of a function Calculate the value of a function at a given point.
Limit of a function Calculate the limit of a function at a given point.
Derivative Calculate the derivative of a function at a given point.
Primitive Calculates the primitive of a function.
Definite Integral Calculates the integral of a function over a given interval.
Taylor series expansion Calculation of Taylor series expansion of a function.
Degree 2 Polynomial Quadratic function Calculator | 2022-12-04 21:30:55 | {"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": 0.9634915590286255, "perplexity": 515.3110842582291}, "config": {"markdown_headings": true, "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-2022-49/segments/1669446710980.82/warc/CC-MAIN-20221204204504-20221204234504-00109.warc.gz"} |
https://questions.examside.com/past-years/jee/question/the-number-of-points-having-both-co-ordinates-as-integers-th-jee-main-2015-marks-4-cr16jgunappieabn.htm | 4.5
(100k+ )
1
### JEE Main 2015 (Offline)
The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $$(0, 0)$$ $$(0, 41)$$ and $$(41, 0)$$ is :
A
820
B
780
C
901
D
861
## Explanation
The number of integral points lie inside the triangle are
1. If x = 1, then y may be 1, 2, 3, ....., 39
2. If x = 2, then y may be 1, 2, 3, ....., 38
3. If x = 3, then y may be 1, 2, 3, ....., 37
$$\vdots$$
39. If x = 39, then the value of y is 1.
Hence, the number of interior points are
$$1 + 2 + 3 + .... + 39 = {{39 \times 40} \over 2} = 780$$
2
### JEE Main 2014 (Offline)
Let $$a, b, c$$ and $$d$$ be non-zero numbers. If the point of intersection of the lines $$4ax + 2ay + c = 0$$ and $$5bx + 2by + d = 0$$ lies in the fourth quadrant and is equidistant from the two axes then
A
$$3bc - 2ad = 0$$
B
$$3bc + 2ad = 0$$
C
$$2bc - 3ad = 0$$
D
$$2bc + 3ad = 0$$
## Explanation
Since the point of intersection lies on fourth quadrant and equidistant from the two axes,
i.e., let the point be (k, $$-$$k) and this point satisfies the two equations of the given lines.
$$\therefore$$ 4ak $$-$$ 2ak + c = 0 ......... (1)
and 5bk $$-$$ 2bk + d = 0 ..... (2)
From (1) we get, $$k = {{ - c} \over {2a}}$$
Putting the value of k in (2) we get,
$$5b\left( { - {c \over {2a}}} \right) - 2b\left( { - {c \over {2a}}} \right) + d = 0$$
or, $$- {{5bc} \over {2a}} + {{2bc} \over {2a}} + d = 0$$ or, $$- {{3bc} \over {2a}} + d = 0$$
or, $$- 3bc + 2ad = 0$$ or, $$3bc - 2ad = 0$$
3
### JEE Main 2014 (Offline)
Let $$PS$$ be the median of the triangle with vertices $$P(2, 2)$$, $$Q(6, -1)$$ and $$R(7, 3)$$. The equation of the line passing through $$(1, -1)$$ band parallel to PS is:
A
$$4x + 7y + 3 = 0$$
B
$$2x - 9y - 11 = 0$$
C
$$4x - 7y - 11 = 0$$
D
$$2x + 9y + 7 = 0$$
## Explanation
Let $$P,Q,R,$$ be the vertices of $$\Delta PQR$$
Since $$PS$$ is the median, $$S$$ is mid-point of $$QR$$
So, $$S = \left( {{{7 + 6} \over 2},{{3 - 1} \over 2}} \right) = \left( {{{13} \over 2},1} \right)$$
Now, slope of $$PS$$ $$= {{2 - 1} \over {2 - {{13} \over 2}}} = - {2 \over 9}$$
Since, required line is parallel to $$PS$$ therefore slope of required line $$=$$ slope of $$PS$$
Now, equation of line passing through $$(1, -1)$$ and having slope $$- {2 \over 9}$$ is
$$y - \left( { - 1} \right) = - {2 \over 9}\left( {x - 1} \right)$$
$$9y + 9 = - 2x + 2$$
$$\Rightarrow 2x + 9y + 7 = 0$$
4
### JEE Main 2013 (Offline)
The $$x$$-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $$(0, 1) (1, 1)$$ and $$(1, 0)$$ is :
A
$$2 + \sqrt 2$$
B
$$2 - \sqrt 2$$
C
$$1 + \sqrt 2$$
D
$$1 - \sqrt 2$$
## Explanation
From the figure, we have
$$a = 2,b = 2\sqrt 2 ,c = 2$$
$${x_1} = 0,\,{x^2} = 0,\,{x_3} = 2$$
Now, $$x$$-co-ordinate of incenter is given as
$${{a{x_1} + b{x_2} + c{x_3}} \over {a + b + c}}$$
$$\Rightarrow x$$-coordinate of incentre
$$= {{2 \times 0 + 2\sqrt 2 .0 + 2.2} \over {2 + 2 + 2\sqrt 2 }}$$
$$=$$ $${2 \over {2 + \sqrt 2 }} = 2 - \sqrt 2$$
### Joint Entrance Examination
JEE Main JEE Advanced WB JEE
### Graduate Aptitude Test in Engineering
GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN
NEET
Class 12 | 2022-05-23 23:34:49 | {"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": 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": 0.8419838547706604, "perplexity": 702.35565478781}, "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-2022-21/segments/1652662562106.58/warc/CC-MAIN-20220523224456-20220524014456-00663.warc.gz"} |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition/chapter-r-review-of-basic-concepts-r-3-polynomials-r-3-exercises-page-34/97 | Precalculus (6th Edition)
$$2x^{5}+7x^{4}-5x^{2}+7$$
Initial equation: $\frac{-4x^{7}-14x^{6}+10x^{4}-14x^{2}}{-2x^{2}}$ Begin by factoring both the numerator and denominator. In this case, only the numerator factors, and is done so by taking out a GCF: $$-2x^{2}(2x^{5}+7x^{4}-5x^{2}+7)$$ Put this back over the denominator: $$\frac{-2x^{2}(2x^{5}+7x^{4}-5x^{2}+7)}{-2x^{2}}$$ Finally, remove what cancels out to get the final answer: $$2x^{5}+7x^{4}-5x^{2}+7$$ | 2019-12-10 23:00:09 | {"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": 0.9791475534439087, "perplexity": 369.780402544595}, "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-2019-51/segments/1575540529006.88/warc/CC-MAIN-20191210205200-20191210233200-00235.warc.gz"} |
https://discourse.datamethods.org/t/cox-ph-assumption-and-bootstrapped-coefficients/3119 | # Cox PH Assumption and Bootstrapped Coefficients
I recently read “Why Test For Proportional Hazards” by Stensrud et al. The article describes why hazard ratios are usually not proportional for medical interventions, and continues to say that when the proportional hazard assumption fails the standard errors of the Cox model with more than one covariate will be biased. The authors also warn that tests for proportional hazard violations may be underpowered and that large p-values can lull analysts into a false sense of satisfied assumptions.
To circumvent the test of proportional hazards, the authors suggest bootstrapping the Cox coefficients to give a better estimate of standard error but they don’t describe the exact bootstrap procedure. Would the following bootstrap procedure properly estimate confidence intervals without relying on the proportional hazards assumption? Are there better procedures for confidence interval estimation?
library(boot)
library(survival)
set.seed(42)
boot.cox <- function(df, indices) {
samples <- df[indices, ]
fit <- coxph(Surv(time, status) ~ age + factor(sex), data=samples)
coef(fit)
}
lung.boot <- boot(lung, boot.cox, 2000)
boot.ci(lung.boot, index = 1, type = "bca")
boot.ci(lung.boot, index = 2, type = "bca")
I’m also curious what others have to say about testing for the proportional hazards assumption, as it seems to be common practice from the tutorials and textbook discussions of Cox regression that I’ve seen.
2 Likes
yes, it’s a good point. Assessment of the assumption often ends up in a supplementary doc, or maybe only the reviewers see it. I think the idea is not to “solve” non-proportional hazards but to model it, and present it
edit: just a quick google search: “However, if this assumption is violated,it does not necessarily prevent analyst from using Cox model. The current paper presents two ways of model modification in case of non-proportional hazards: introducing interactionsof selected covariates with function of time and stratification model” https://www.lexjansen.com/phuse/2013/sp/SP07.pdf
1 Like
This seems incredibly strange to me for two reasons:
• If the model doesn’t fit the data, the coefficients don’t mean what you think they mean and bootstrapping doesn’t solve that problem
• If all you want to do is to get standard errors that are robust to model specification (and again want to ignore the problem with interpreting the \beta s), you can instantly get the answer with the robust sandwich estimator which is easy to use in R and other systems
2 Likes
The estimate from the proportional model can be interpreted as some weighted average of the time dependent parameter. Bootstrap is then used to the SD for this average
What is the reason you would want to do that?
Not sure that I will do that but it is nice to know that one gets some average with some uncertainty. Personally I think that non proportionality is interesting because it may reveal something about the association, eg that the effect of some intervention decreases over time. Btw I cannot remember the methodological paper that shows that one gets an average over time, I think the first author name is something like Xu or Xi
Michael Schemper has a good paper about that. But another angle is that if PH is not known to hold, just spend extra parameters to capture this uncertainty, e.g., add treatment x log time as a time-dependent covariate.
1 Like
Thanks! I’ll look it up. Do you think that log time is good if follow up begins at zero or do you prefer some other simple function of time. Maybe a spline or fractorial polynomial perhaps. Cheers
A spline is best, if you have the number of events to support it. There are many new ways to do this with the rstanarm survival package in R. Robert Gray had a nice paper on penalized splines in modeling non-PH: https://www.tandfonline.com/doi/abs/10.1080/01621459.1992.10476248
2 Likes | 2022-05-29 01:54:26 | {"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": 0.7114936113357544, "perplexity": 1157.564744471634}, "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-2022-21/segments/1652663035797.93/warc/CC-MAIN-20220529011010-20220529041010-00080.warc.gz"} |
https://unapologetic.wordpress.com/2007/06/25/universal-arrows-and-universal-elements/?like=1&source=post_flair&_wpnonce=18b5244a97 | # The Unapologetic Mathematician
## Universal arrows and universal elements
Remember that we defined a colimit as an initial object in the comma category $(F\downarrow\Delta)$, and a limit as a terminal object in the comma category $(\Delta\downarrow F)$. It turns out that initial and terminal objects in more general comma categories are also useful.
So, say we have a categories $\mathcal{C}$ and $\mathcal{D}$, an object $C\in\mathcal{C}$, and a functor $F:\mathcal{D}\rightarrow\mathcal{C}$, so we can set up the category $(C\downarrow F)$. Recall that an object of this category consists of an object $D\in\mathcal{D}$ and an arrow $f:C\rightarrow F(D)$, and a morphism from $f_1:C\rightarrow F(D_1)$ to $f_2:C\rightarrow F(D_2)$ is an arrow $d:D_1\rightarrow D_2$ such that $f_2=F(d)\circ f_1$.
Now an initial object in this category is an object $U$ of $\mathcal{D}$ and an arrow $u:C\rightarrow F(U)$ so that for any other arrow $f:C\rightarrow F(D)$ there is a unique arrow $d:U\rightarrow D$ satisfying $f=F(d)\circ u$. We call such an object, when it exists, a “universal arrow from $C$ to $F$“. For example, a colimit of a functor $F$ is a universal arrow (in $\mathcal{C}^\mathcal{J}$) from $F$ to $\Delta$.
Dually, a terminal object in $(F \downarrow C)$ consists of an object $U\in\mathcal{D}$ and an arrow $u:F(U)\rightarrow C$ so that for any other arrow $f:F(D)\rightarrow C$ there exists a unique arrow $d:D\rightarrow U$ satisfying $f=u\circ F(d)$. We call this a “couniversal arrow from $F$ to $C$“. A limit of a functor $F$ is a couniversal arrow from $\Delta$ to $F$.
Here’s another example of a universal arrow we’ve seen before: let’s say we have an integral domain $D$ and the forgetful functor $U:\mathbf{Field}\rightarrow\mathbf{Dom}$ from fields to integral domains. That is, $U$ takes a field and “forgets” that it’s a field, remembering only that it’s a ring with no zerodivisors. An object of $(D\rightarrow U)$ consists of a field $F$ and a homomorphism of integral domains $D\rightarrow U(F)$. The universal such arrow is the field of fractions of $D$.
As a more theoretical example, we can consider a functor $F:\mathcal{C}\rightarrow\mathbf{Set}$ and the comma category $(*\downarrow F)$. Since an arrow $x:*\rightarrow X$ in $\mathbf{Set}$ is an element of the set $X$, we call a universal arrow from $*$ to $F$ a “universal element” of $F$. It consists of an object $U\in\mathcal{C}$ and an element $u\in F(U)$ so that for any other element $c\in F(C)$ we have a unique arrow $f:U\rightarrow C$ with $\left[F(f)\right](u)=c$.
As an example, let’s take $N$ to be a normal subgroup of a group $G$. For any group $H$ we can consider the set of group homomorphisms $f:G\rightarrow H$ that send every element of $N$ to the identity element of $H$. Verify for yourself that this gives a functor $F:\mathbf{Grp}\rightarrow\mathbf{Set}$. Any such homomorphism factors through the projection $\pi_{(G,N)}:G\rightarrow G/N$, so the group $G/N$ and the projection $\pi_{(G,N)}$ constitute a universal element of $F$. We used cosets of $N$ to show that such a universal element exists, but everything after that follows from the universal property.
Another example: let $M_1$ be a right module over a ring $R$, and $M_2$ be a left $R$-module. Now for any abelian group $A$ we can consider the set of all $R$-middle-linear functions from $M_1\times M_2$ to $A$ — functions $f$ which satisfy $f(m_1+m_1',m_2)=f(m_1,m_2)+f(m_1',m_2)$, $f(m_1,m_2+m_2')=f(m_1,m_2)+f(m_1,m_2')$, and $f(m_1r,m_2)=f(m_1,rm_2)$. This gives a functor from $\mathbf{Ab}$ to $\mathbf{Set}$, and the universal element is the function $M_1\times M_2\rightarrow M_1\otimes_RM_2$ to the tensor product.
The concept of a universal element is a special case of a universal arrow. Very interestingly, though, when $\mathcal{C}$ is locally small (as it usually is for us)\$ the reverse is true. Indeed, if we’re considering an object $C\in\mathcal{C}$ and a functor $F:\mathcal{D}\rightarrow\mathcal{C}$ then we could instead consider the set $*$ and the functor $\hom_\mathcal{C}(C,F(\underline{\hphantom{X}})):\mathcal{D}\rightarrow\mathbf{Set}$. Universal arrows for the former setup are equivalent to universal elements in the latter. | 2017-09-24 01:27:06 | {"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": 0, "img_math": 88, "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": 0.9893710017204285, "perplexity": 62.241618453301726}, "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-2017-39/segments/1505818689823.92/warc/CC-MAIN-20170924010628-20170924030628-00097.warc.gz"} |
https://crad.ict.ac.cn/EN/Y2017/V54/I9/1880 | ISSN 1000-1239 CN 11-1777/TP
Journal of Computer Research and Development ›› 2017, Vol. 54 ›› Issue (9): 1880-1891.
### Retrieval of Similar Semantic Workflows Based on Behavioral and Structural Characteristics
Sun Jinyong1,2, Gu Tianlong2, Wen Lijie3, Qian Junyan2, Meng Yu2
1. 1(School of Computer Science and Technology, Xidian University, Xi’an 710071);2(Guangxi Key Laboratory of Trusted Software (Guilin University of Electronic Technology), Guilin,Guangxi 541004);3(School of Software, Tsinghua University, Beijing 100084)
• Online:2017-09-01
Abstract: Workflow reuse is an important method for modern enterprises and organizations to improve the efficiency of business process management (BPM). Semantic workflows are domain knowledge-based workflows. The retrieval of similar semantic workflows is the first step for semantic workflow reuse. Existing retrieval algorithms of similar semantic workflows only focus on semantic workflows’ structural characteristics while ignoring their behavioral characteristics, which affects the overall quality of retrieved similar semantic workflows and increases the cost of semantic workflow reuse. To address this issue, a two-phase retrieval algorithm of similar semantic workflows is put forward based on behavioral and structural characteristics. A task adjacency relations (TARs) set is used to express a semantic workflow’s behavior. A TARs trees index named TARTreeIndex and a data index named DataIndex are constructed combined with domain knowledge for the semantic workflows case base. For a given query semantic workflow, firstly, candidate semantic workflows are obtained by filtering the semantic workflows case base with the TARTreeIndex and DataIndex, then candidate semantic workflows are verified and ranked with the graph matching similarity algorithm. Experiments show that the proposed algorithm improves the retrieval performance of similar semantic workflows compared with the existing popular retrieval algorithms for similar semantic workflows, so it can provide high-quality semantic workflows for semantic workflow reuse.
CLC Number: | 2022-05-19 17:56:00 | {"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": 0.2313256561756134, "perplexity": 8226.254032675899}, "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-2022-21/segments/1652662529658.48/warc/CC-MAIN-20220519172853-20220519202853-00196.warc.gz"} |
https://hal-cnrs.archives-ouvertes.fr/LJLL/hal-03690584v2 | Small-time global null controllability of generalized Burgers' equations - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :
## Small-time global null controllability of generalized Burgers' equations
(1, 2)
1
2
Rémi Robin
#### Abstract
In this paper, we study the small-time global null controllability of the generalized Burgers' equations $y_t + \gamma |y|^{\gamma-1}y_x-y_{xx}=u(t)$ on the segment $[0,1]$. The scalar control $u(t)$ is uniform in space and plays a role similar to the pressure in higher dimension. We set a right Dirichlet boundary condition $y(t,1)=0$, and allow a left boundary control $y(t,0)=v(t)$. Under the assumption $\gamma>3/2$ we prove that the system is small-time global null controllable. Our proof relies on the return method and a careful analysis of the shape and dissipation of a boundary layer.
### Dates and versions
hal-03690584 , version 1 (08-06-2022)
hal-03690584 , version 2 (06-12-2022)
### Identifiers
• HAL Id : hal-03690584 , version 2
• ARXIV :
### Cite
Rémi Robin. Small-time global null controllability of generalized Burgers' equations. 2022. ⟨hal-03690584v2⟩
### Export
BibTeX TEI Dublin Core DC Terms EndNote Datacite
27 View | 2023-01-30 08:25:25 | {"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": 0.19257044792175293, "perplexity": 3805.147316951144}, "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/1674764499804.60/warc/CC-MAIN-20230130070411-20230130100411-00304.warc.gz"} |
https://doxygen.opengeosys.org/d1/d7d/ogs_file_param__prj__time_loop__processes__process__time_stepping__iterationnumberbasedtimestepping__number_iterations | OGS
[tag] number_iterations
This vector stores the number of iterations to which the respective multiplier coefficient will be applied.
• Data type: std::vector<int> | 2021-09-25 12:36:24 | {"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": 0.5745795369148254, "perplexity": 3996.5823536615476}, "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-2021-39/segments/1631780057622.15/warc/CC-MAIN-20210925112158-20210925142158-00633.warc.gz"} |
https://maker.pro/forums/threads/converting-stick-welder-to-tack-welder.6689/ | Login Join Maker Pro
Or sign in with
# Converting stick welder to tack welder.
T
#### Tim Zimmerman
Jan 1, 1970
0
I need a tack welder for joining thin plates and electronic
components. Like the tack weld you see in your NiCad battery packs.
I have no practical use for my 120v, 80-Amp stick welder so now I'll
convert it into a tack welder.
I like to get some ideas on how to make a setup that will be safe and
precise enough to do small electronic welds like the welds found on
some relays. Does this sound possible, if not can you point me to a
place to get a spot welding setup?
Thanks
C
#### Clandestine
Jan 1, 1970
0
Those "tack welds" are created by resistance heating between the
parts. There is no arc involved. It takes considerably more power
(watts) to weld by resistance than by arc. They are also done faster
than most arc welds. To put this in perspective those electrical
components required about 1,000 Amps in ½ second. Usually the current
is turned on/off by an SCR (or similar switch). I have never heard of
converting an arc welding power supply into a resistance welding power
supply. Keep in mind these critical factors during this type of
welding
FORCE - you must "pinch" pieces together (approximately 500 lbs)
POWER - you need a high, controlled amount of electricity
TIME - You need to regulate the power flow within 1 cycle (1/60
second).
Unitek-Miyachi makes small resistance welders. www.unitekmiyachi.com
J
#### Josh Sponenberg
Jan 1, 1970
0
Clandestine said:
Those "tack welds" are created by resistance heating between the
parts. There is no arc involved. It takes considerably more power
(watts) to weld by resistance than by arc. They are also done faster
than most arc welds. To put this in perspective those electrical
components required about 1,000 Amps in ½ second. Usually the current
is turned on/off by an SCR (or similar switch). I have never heard of
converting an arc welding power supply into a resistance welding power
supply. Keep in mind these critical factors during this type of
welding
FORCE - you must "pinch" pieces together (approximately 500 lbs)
POWER - you need a high, controlled amount of electricity
TIME - You need to regulate the power flow within 1 cycle (1/60
second).
Unitek-Miyachi makes small resistance welders. www.unitekmiyachi.com
I can vouch for the Unitek-Miyachi system, they work well and the price
is usually decent. They're step-pulsed, capacitive-discharge systems,
and are as far removed from arc welding as swimming is from bob-sledding...
I worked for 4 years at a battery "wholesaler" my main job was to crack
dead packs open and "re-cell" them, and then glue them back together.
generally cheaper for the customer than buying a new pack, and 9 times
out of 10 they had more capacity. If you're looking into this kind of
stuff, let me know and I'll give you my former boss's contact info and
he'll be able to point you to our connection on the west coast where we
got our welder from.
J
#### Jamie
Jan 1, 1970
0
Tim said:
I need a tack welder for joining thin plates and electronic
components. Like the tack weld you see in your NiCad battery packs.
I have no practical use for my 120v, 80-Amp stick welder so now I'll
convert it into a tack welder.
I like to get some ideas on how to make a setup that will be safe and
precise enough to do small electronic welds like the welds found on
some relays. Does this sound possible, if not can you point me to a
place to get a spot welding setup?
Thanks
find your self dead microwave oven ( high power line), use the
heater tap on the transformer.
S
#### Si Ballenger
Jan 1, 1970
0
I need a tack welder for joining thin plates and electronic
components. Like the tack weld you see in your NiCad battery packs.
I have no practical use for my 120v, 80-Amp stick welder so now I'll
convert it into a tack welder.
I like to get some ideas on how to make a setup that will be safe and
precise enough to do small electronic welds like the welds found on
some relays. Does this sound possible, if not can you point me to a
place to get a spot welding setup?
Thanks
Check the rec.crafts.metalworking news group. Lot of info there
on things like this (and a lot of other DIY stuff).
M
#### Martin H. Eastburn
Jan 1, 1970
0
Clandestine said:
Those "tack welds" are created by resistance heating between the
parts. There is no arc involved. It takes considerably more power
(watts) to weld by resistance than by arc. They are also done faster
than most arc welds. To put this in perspective those electrical
components required about 1,000 Amps in ½ second. Usually the current
is turned on/off by an SCR (or similar switch). I have never heard of
converting an arc welding power supply into a resistance welding power
supply. Keep in mind these critical factors during this type of
welding
FORCE - you must "pinch" pieces together (approximately 500 lbs)
POWER - you need a high, controlled amount of electricity
TIME - You need to regulate the power flow within 1 cycle (1/60
second).
Unitek-Miyachi makes small resistance welders. www.unitekmiyachi.com
Likely a capacitive discharge to deliver the high current.
Or like said a RC that drives an SCR as a switch of a storage Cap.
Martin
B
#### Barry Lennox
Jan 1, 1970
0
I need a tack welder for joining thin plates and electronic
components. Like the tack weld you see in your NiCad battery packs.
I have no practical use for my 120v, 80-Amp stick welder so now I'll
convert it into a tack welder.
I like to get some ideas on how to make a setup that will be safe and
precise enough to do small electronic welds like the welds found on
some relays. Does this sound possible, if not can you point me to a
place to get a spot welding setup?
I believe you are following the wrong path here. You need little
voltage, but a LOT of current.
I made a very good spot welder for batteries and similar tasks from an
ex microwave oven transformer, the biggest I could find. Hack off the
HV secondary, thousands of turns of very fine wire, then I rewound it
with just 3 turns of wire, but I packed in as much 8g and 12g wire as
would fit, and paralleled all the turns.
The secondary is controlled by a SSR (Croydom CSD2410) pulsed by a
simple 555 timer circuit. It can vary from about 75-300 mSec I can
also switch in one of 3 wirewound resistors in the secondary to give
me fine control.
The electrodes must be made to suit your exact application, and some
trial and error can be expected. I first used copper and brass, but
now get much better results from a proper spot welding electrode
machined to suit my application. It was not cheap, about $11 for a 3/8" rod about 3 inches long, but it gives very good results. It had a trade name like "Elkalloy" IIRC. For optimum results, it is also important to control the electrode pressure, but I find I can achieve satisfactory results by hand. Barry Lennox E #### Eric R Snow Jan 1, 1970 0 I need a tack welder for joining thin plates and electronic components. Like the tack weld you see in your NiCad battery packs. I have no practical use for my 120v, 80-Amp stick welder so now I'll convert it into a tack welder. I like to get some ideas on how to make a setup that will be safe and precise enough to do small electronic welds like the welds found on some relays. Does this sound possible, if not can you point me to a place to get a spot welding setup? Thanks Tim, The reason your stick welder is not good for spot (what you call tack) welding is because the voltage is too high and the current too low. I experimented with a microwave oven transformer and was able to get 400 amps at 3 volts. This is done by removing the high voltage secondary windings and replacing them with a few windings of heavy wire or even copper bars. See other replies for links etc. for building your own. ERS M #### mike Jan 1, 1970 0 Jamie said: find your self dead microwave oven ( high power line), use the heater tap on the transformer. How well did this work when YOU tried it? How did YOU keep from killing yourself on the high voltage winding? mike http://nm7u.tripod.com/homepage/welder.html -- Return address is VALID but some sites block emails with links. Delete this sig when replying. .. Wanted, PCMCIA SCSI Card for HP m820 CDRW. FS 500MHz Tek DSOscilloscope TDS540 Make Offer Wanted, 12.1" LCD for Gateway Solo 5300. Samsung LT121SU-121 Bunch of stuff For Sale and Wanted at the link below. MAKE THE OBVIOUS CHANGES TO THE LINK ht<removethis>tp://www.geocities.com/SiliconValley/Monitor/4710/ S #### Steve Taylor Jan 1, 1970 0 mike said: How well did this work when YOU tried it? How did YOU keep from killing yourself on the high voltage winding? When I did it, I drilled the HT winding out. Brutal, but fast. To be honest, the idea didn't work for me at all, and I built a miniature capacitor discharge welder that DID do the job - a modest bank of old PC power supplies yielded enough capacitors to hold "useful" amounts of energy. Steve M #### mike Jan 1, 1970 0 Steve said: When I did it, I drilled the HT winding out. Brutal, but fast. To be honest, the idea didn't work for me at all, and I built a miniature capacitor discharge welder that DID do the job - a modest bank of old PC power supplies yielded enough capacitors to hold "useful" amounts of energy. Steve Post some details on voltage, capacitance, how'd you switch it? electrode construction? mike -- Return address is VALID but some sites block emails with links. Delete this sig when replying. .. Wanted, PCMCIA SCSI Card for HP m820 CDRW. FS 500MHz Tek DSOscilloscope TDS540 Make Offer Wanted, 12.1" LCD for Gateway Solo 5300. Samsung LT121SU-121 Bunch of stuff For Sale and Wanted at the link below. MAKE THE OBVIOUS CHANGES TO THE LINK ht<removethis>tp://www.geocities.com/SiliconValley/Monitor/4710/ E #### [email protected] Jan 1, 1970 0 Hi. Oddly enough, you can do spot welding with an arc welder. I tried it, and all I got was the typical mess that you would guess. Burned up spots with no strength. But, just because I cannot do it does not mean that it can't be done. There are plans on Ebay: 385664469 This auction is for a set of completely illustrated plans to build a spot weldi ng/cutting gun that works with your arc welder for less than$50.00.
I have not tried this out, so please buy the plans and report back to
the group.
Or, you could try Eastwood's version, which is very similar, but uses
carbon electrodes. Also, please report back to the group after trying.
http://www.eastwoodco.com/jump.jsp?itemID=795&itemType=CATEGORY&iMainCat=688&iSubCat=795
Recently, I tried to do a blind spot weld with 1/8" steel. It worked
just great. So, the problem may be power, control, and excessive heat,
which the above solutions allude to. Note that this is arc welding,
not resistance welding with a low voltage rewound microwave oven
transformer.
M
#### Martin H. Eastburn
Jan 1, 1970
0
Eric said:
Tim,
The reason your stick welder is not good for spot (what you call tack)
welding is because the voltage is too high and the current too low. I
experimented with a microwave oven transformer and was able to get 400
amps at 3 volts. This is done by removing the high voltage secondary
windings and replacing them with a few windings of heavy wire or even
copper bars. See other replies for links etc. for building your own.
ERS
With only 3 volts, the resistance of the metal and any 'dirt' best be doing zero ohms...
Not much punch through voltage.
Martin
N
#### Nick Huckaby
Jan 1, 1970
0
With only 3 volts, the resistance of the metal and any 'dirt' best be
doing zero ohms...Not much punch through voltage.
Martin
How about 12V? Would two car batteries work?
M
#### mike
Jan 1, 1970
0
Repeatability is a BIG issue with this. A CD system tries to deliver
fixed energy. That's less dependent in path resistance.
How about 12V? Would two car batteries work?
Sure, if you had some way to turn them on/off quickly.
Be sure to use a heavy metal box to contain the battery explosion
if something goes wrong.
--
Return address is VALID but some sites block emails
with links. Delete this sig when replying.
..
Wanted, PCMCIA SCSI Card for HP m820 CDRW.
FS 500MHz Tek DSOscilloscope TDS540 Make Offer
Wanted, 12.1" LCD for Gateway Solo 5300. Samsung LT121SU-121
Bunch of stuff For Sale and Wanted at the link below.
MAKE THE OBVIOUS CHANGES TO THE LINK
ht<removethis>tp://www.geocities.com/SiliconValley/Monitor/4710/
M
#### mike
Jan 1, 1970
0
Martin said:
With only 3 volts, the resistance of the metal and any 'dirt' best be
doing zero ohms...
Not much punch through voltage.
Martin
FYI
Here's the voltage waveform for a Unitek 125 intoa .001 Ohm load .
http://nm7u.tripod.com/homepage/uniwvfm.jpg
mike
--
Return address is VALID but some sites block emails
with links. Delete this sig when replying.
..
Wanted, PCMCIA SCSI Card for HP m820 CDRW.
FS 500MHz Tek DSOscilloscope TDS540 Make Offer
Wanted, 12.1" LCD for Gateway Solo 5300. Samsung LT121SU-121
Bunch of stuff For Sale and Wanted at the link below.
MAKE THE OBVIOUS CHANGES TO THE LINK
ht<removethis>tp://www.geocities.com/SiliconValley/Monitor/4710/
S
#### Steve Taylor
Jan 1, 1970
0
mike wrote:
Post some details on voltage, capacitance, how'd you switch it?
electrode construction?
Hi Mike,
We needed to weld some exotic metals, that required CD welding. Our
welder was built in a glove box, The electrode construction was similar
to your, we modified a toggle clamp to do the job with 1/16" diameter tips.
The cap- bank was around 2200uF (10 x 220uF 400V reservoir caps) Energy
supply was a large variable O/P PSU, large because thats what we have
around. Drive was 0-400V. Welding occured at around 40V.
Discharge was effected by a very large old automobile relay , with
contacts bigger than US pennies (around 1" - like the old UK pennies)
Job was pinched in the jaws of the spotter, then the hands had to
operate two buttons simultaneously to activate the spot.
Yes, I'd have preferred to use a huge ignitron, or a hockey-puck
thyristor, but we didn't have time - this was a two day
oh-god-we-have-to-do-this-yesterday kind of thing.
We just about managed to weld molybdenum foil ~0.2mm thick, with it.
Steve
M
#### Martin H. Eastburn
Jan 1, 1970
0
mike said:
FYI
Here's the voltage waveform for a Unitek 125 intoa .001 Ohm load .
http://nm7u.tripod.com/homepage/uniwvfm.jpg
mike
I'd be nervous calling it a 0.001 ohm load - but ok.
I think the connectors are exceeding that - two clamped down with bolts and the two
on spring loaded clamps.
I'd measure the Tr fro 10 to 90% point
Thanks for the waveform and idea.
Martin
M
#### mike
Jan 1, 1970
0
Martin said:
I'd be nervous calling it a 0.001 ohm load - but ok.
I think the connectors are exceeding that - two clamped down with bolts
and the two
on spring loaded clamps.
I'd measure the Tr fro 10 to 90% point
Thanks for the waveform and idea.
Martin
You're being too picky.
The manufacturer publishes a specified waveform for their device
under controlled conditions.
Gives you some idea of what you're up against welding battery tabs.
mike
--
Return address is VALID but some sites block emails
with links. Delete this sig when replying.
..
Wanted, PCMCIA SCSI Card for HP m820 CDRW.
FS 500MHz Tek DSOscilloscope TDS540 Make Offer
Wanted, 12.1" LCD for Gateway Solo 5300. Samsung LT121SU-121
Bunch of stuff For Sale and Wanted at the link below.
MAKE THE OBVIOUS CHANGES TO THE LINK
ht<removethis>tp://www.geocities.com/SiliconValley/Monitor/4710/
Replies
9
Views
2K
Replies
8
Views
1K
Replies
11
Views
2K
Replies
2
Views
869
Replies
1
Views
605 | 2022-10-06 14:50:38 | {"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": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3048689663410187, "perplexity": 8166.0308114590625}, "config": {"markdown_headings": true, "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-2022-40/segments/1664030337836.93/warc/CC-MAIN-20221006124156-20221006154156-00223.warc.gz"} |
https://hq.holyfiregames.com/hq/topic/d551be-distance-between-two-lenses-in-a-telescope | X rays, with much more energy and shorter wavelengths than RF and light, are mainly absorbed and not reflected when incident perpendicular to the medium. A small telescope has a concave mirror with a 2.00 m radius of curvature for its objective. If you use both convex lenses, the distance between them need to be close to the sum of their focal lengths, F + f. Start there and adjust it slightly for best results. Puedes cambiar tus opciones en cualquier momento visitando Tus controles de privacidad. The lenses are separated by 15 cm. The first image formed by a telescope objective as seen in Figure 1b will not be large compared with what you might see by looking at the object directly. But they can be reflected when incident at small glancing angles, much like a rock will skip on a lake if thrown at a small angle. Apply lens equation to first lens d i1 = 12 cm First image located 12 cm behind the first lens Image generated from first lens going to be object for the second lens d o2 = L – d i1 d o2 = 40 cm – 12 cm d o2 = 28 cm Lets apply lens equation to second lens d i2 = 32.31 cm Final image located at 32.31 cm behind second lens. Such telescopes can gather more light, since larger mirrors than lenses can be constructed. A telescope has lenses with focal lengths f1 = +25.7 cm and f2 = +5.5 cm. Simple telescopes can be made with two lenses. If an upright image is needed, Galileo’s arrangement in Figure 1a can be used. A telescope has lenses with focal lengths f1 = +24.1 cm and f2 = +6.0 cm. If the angle subtended by an object as viewed by the unaided eye is θ, and the angle subtended by the telescope image is θ′, then the angular magnification M is defined to be their ratio. Figure 3. Distance between two lenses of a telescope? Para permitir a Verizon Media y a nuestros socios procesar tus datos personales, selecciona 'Acepto' o selecciona 'Gestionar ajustes' para obtener más información y para gestionar tus opciones, entre ellas, oponerte a que los socios procesen tus datos personales para sus propios intereses legítimos. The magnification, M, of a two-lens system is equal the product of the magnifications of the individual lenses: M = M 1 M 2 = (- d i1 / d o1) (- d i2 / d o2) Object at Infinity Look through the lenses at a distant object. This telescope forms an image in the same manner as the two-convex-lens telescope already discussed, but it does not suffer from chromatic aberrations. (Remember that for a diverging lens the focal length is negative.) X rays ricochet off 4 pairs of mirrors forming a barrelled pathway leading to the focus point. In this equation, 16 cm is the standardized distance between the image-side focal point of the objective lens and the object-side focal point of the eyepiece, 25 cm is the normal near point distance, and are the focal distances for the objective lens and the eyepiece, respectively. The object is so far away from the telescope that it is essentially at infinity compared with the focal lengths of the lenses (d o ≈ ∞). Final image is formed at (i) least distance … He constructed several early telescopes, was the first to study the heavens with them, and made monumental discoveries using them. Telescopes gather far more light than the eye, allowing dim objects to be observed with greater magnification and better resolution. (a) Galileo made telescopes with a convex objective and a concave eyepiece. A telescope, in its original configuration (refractor), consists of two lenses. A two-element telescope composed of a mirror as the objective and a lens for the eyepiece is shown. Its eyepiece is a 4.00 cm focal length lens. (a) What distance between the two lenses will allow the telescope to focus on an infinitely distant object and produce an … Figure 4a shows the Australia Telescope Compact Array, which uses six 22-m antennas for mapping the southern skies using radio waves. o = distance from lens to object. The mirrors for the Chandra consist of a long barrelled pathway and 4 pairs of mirrors to focus the rays at a point 10 meters away from the entrance. Large and relatively flat mirrors have very long focal lengths, so that great angular magnification is possible. Para obtener más información sobre cómo utilizamos tu información, consulta nuestra Política de privacidad y la Política de cookies. The objective forms a case 1 image that is the object for the eyepiece. i = distance from lens to image. (credit: NASA). Nosotros y nuestros socios almacenaremos y/o accederemos a la información de tu dispositivo mediante el uso de cookies y tecnologías similares, a fin de mostrar anuncios y contenido personalizados, evaluar anuncios y contenido, obtener datos sobre la audiencia y desarrollar el producto. What is the angular magnification of a telescope that has a 100 cm focal length objective and a 2.50 cm focal length eyepiece? The initial stage of the project is the construction of the Australian Square Kilometre Array Pathfinder in Western Australia (see Figure 5). It can be shown that the angular magnification of a telescope is related to the focal lengths of the objective and eyepiece; and is given by, $\displaystyle{M}=\frac{\theta^{\prime}}{\theta}=-\frac{f_{\text{o}}}{f_{\text{e}}}\\$. | 2021-05-08 13:55:48 | {"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": 0.5353578925132751, "perplexity": 2167.2129198459647}, "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-2021-21/segments/1620243988882.7/warc/CC-MAIN-20210508121446-20210508151446-00234.warc.gz"} |
https://www.tutorialspoint.com/theano/theano_quick_guide.htm | # Theano - Introduction
Have you developed Machine Learning models in Python? Then, obviously you know the intricacies in developing these models. The development is typically a slow process taking hours and days of computational power.
The Machine Learning model development requires lot of mathematical computations. These generally require arithmetic computations especially large matrices of multiple dimensions. These days we use Neural Networks rather than the traditional statistical techniques for developing Machine Learning applications. The Neural Networks need to be trained over a huge amount of data. The training is done in batches of data of reasonable size. Thus, the learning process is iterative. Thus, if the computations are not done efficiently, training the network can take several hours or even days. Thus, the optimization of the executable code is highly desired. And that is what exactly Theano provides.
Theano is a Python library that lets you define mathematical expressions used in Machine Learning, optimize these expressions and evaluate those very efficiently by decisively using GPUs in critical areas. It can rival typical full C-implementations in most of the cases.
Theano was written at the LISA lab with the intention of providing rapid development of efficient machine learning algorithms. It is released under a BSD license.
In this tutorial, you will learn to use Theano library.
# Theano - Installation
Theano can be installed on Windows, MacOS, and Linux. The installation in all the cases is trivial. Before you install Theano, you must install its dependencies. The following is the list of dependencies −
• Python
• NumPy − Required
• SciPy − Required only for Sparse Matrix and special functions
• BLAS − Provides standard building blocks for performing basic vector and matrix operations
The optional packages that you may choose to install depending on your needs are −
• nose: To run Theano’s test-suite
• Sphinx − For building documentation
• Graphiz and pydot − To handle graphics and images
• NVIDIA CUDA drivers − Required for GPU code generation/execution
• libgpuarray − Required for GPU/CPU code generation on CUDA and OpenCL devices
We shall discuss the steps to install Theano in MacOS.
## MacOS Installation
To install Theano and its dependencies, you use pip from the command line as follows. These are the minimal dependencies that we are going to need in this tutorial.
$pip install Theano$ pip install numpy
$pip install scipy$ pip install pydot
You also need to install OSx command line developer tool using the following command −
\$ xcode-select --install
You will see the following screen. Click on the Install button to install the tool.
On successful installation, you will see the success message on the console.
## Testing the Installation
After the installation completes successfully, open a new notebook in the Anaconda Jupyter. In the code cell, enter the following Python script −
### Example
import theano
from theano import tensor
a = tensor.dscalar()
b = tensor.dscalar()
c = a + b
f = theano.function([a,b], c)
d = f(1.5, 2.5)
print (d)
### Output
Execute the script and you should see the following output −
4.0
The screenshot of the execution is shown below for your quick reference −
If you get the above output, your Theano installation is successful. If not, follow the debug instructions on Theano download page to fix the issues.
## What is Theano?
Now that you have successfully installed Theano, let us first try to understand what is Theano? Theano is a Python library. It lets you define, optimize, and evaluate mathematical expressions, especially the ones which are used in Machine Learning Model development. Theano itself does not contain any pre-defined ML models; it just facilitates its development. It is especially useful while dealing with multi-dimensional arrays. It seamlessly integrates with NumPy, which is a fundamental and widely used package for scientific computations in Python.
Theano facilitates defining mathematical expressions used in ML development. Such expressions generally involve Matrix Arithmetic, Differentiation, Gradient Computation, and so on.
Theano first builds the entire Computational Graph for your model. It then compiles it into highly efficient code by applying several optimization techniques on the graph. The compiled code is injected into Theano runtime by a special operation called function available in Theano. We execute this function repetitively to train a neural network. The training time is substantially reduced as compared to using pure Python coding or even a full C implementation.
We shall now understand the process of Theano development. Let us begin with how to define a mathematical expression in Theano.
# Theano - A Trivial Theano Expression
Let us begin our journey of Theano by defining and evaluating a trivial expression in Theano. Consider the following trivial expression that adds two scalars −
c = a + b
Where a, b are variables and c is the expression output. In Theano, defining and evaluating even this trivial expression is tricky.
Let us understand the steps to evaluate the above expression.
## Importing Theano
First, we need to import Theano library in our program, which we do using the following statement −
from theano import *
Rather than importing the individual packages, we have used * in the above statement to include all packages from the Theano library.
## Declaring Variables
Next, we will declare a variable called a using the following statement −
a = tensor.dscalar()
The dscalar method declares a decimal scalar variable. The execution of the above statement creates a variable called a in your program code. Likewise, we will create variable b using the following statement −
b = tensor.dscalar()
## Defining Expression
Next, we will define our expression that operates on these two variables a and b.
c = a + b
In Theano, the execution of the above statement does not perform the scalar addition of the two variables a and b.
## Defining Theano Function
To evaluate the above expression, we need to define a function in Theano as follows −
f = theano.function([a,b], c)
The function function takes two arguments, the first argument is an input to the function and the second one is its output. The above declaration states that the first argument is of type array consisting of two elements a and b. The output is a scalar unit called c. This function will be referenced with the variable name f in our further code.
## Invoking Theano Function
The call to the function f is made using the following statement −
d = f(3.5, 5.5)
The input to the function is an array consisting of two scalars: 3.5 and 5.5. The output of execution is assigned to the scalar variable d. To print the contents of d, we will use the print statement −
print (d)
The execution would cause the value of d to be printed on the console, which is 9.0 in this case.
## Full Program Listing
The complete program listing is given here for your quick reference −
from theano import *
a = tensor.dscalar()
b = tensor.dscalar()
c = a + b
f = theano.function([a,b], c)
d = f(3.5, 5.5)
print (d)
Execute the above code and you will see the output as 9.0. The screen shot is shown here −
Now, let us discuss a slightly more complex example that computes the multiplication of two matrices.
# Theano - Expression for Matrix Multiplication
We will compute a dot product of two matrices. The first matrix is of dimension 2 x 3 and the second one is of dimension 3 x 2. The matrices that we used as input and their product are expressed here −
$$\begin{bmatrix}0 & -1 & 2\\4 & 11 & 2\end{bmatrix} \:\begin{bmatrix}3& -1 \\1 & 2 \\35 & 20 \end{bmatrix}=\begin{bmatrix}11 & 0 \\35 & 20 \end{bmatrix}$$
## Declaring Variables
To write a Theano expression for the above, we first declare two variables to represent our matrices as follows −
a = tensor.dmatrix()
b = tensor.dmatrix()
The dmatrix is the Type of matrices for doubles. Note that we do not specify the matrix size anywhere. Thus, these variables can represent matrices of any dimension.
## Defining Expression
To compute the dot product, we used the built-in function called dot as follows −
c = tensor.dot(a,b)
The output of multiplication is assigned to a matrix variable called c.
## Defining Theano Function
Next, we define a function as in the earlier example to evaluate the expression.
f = theano.function([a,b], c)
Note that the input to the function are two variables a and b which are of matrix type. The function output is assigned to variable c which would automatically be of matrix type.
## Invoking Theano Function
We now invoke the function using the following statement −
d = f([[0, -1, 2], [4, 11, 2]], [[3, -1],[1,2], [6,1]])
The two variables in the above statement are NumPy arrays. You may explicitly define NumPy arrays as shown here −
f(numpy.array([[0, -1, 2], [4, 11, 2]]),
numpy.array([[3, -1],[1,2], [6,1]]))
After d is computed we print its value −
print (d)
You will see the following output on the output −
[[11. 0.]
[25. 20.]]
## Full Program Listing
The complete program listing is given here:
from theano import *
a = tensor.dmatrix()
b = tensor.dmatrix()
c = tensor.dot(a,b)
f = theano.function([a,b], c)
d = f([[0, -1, 2],[4, 11, 2]], [[3, -1],[1,2],[6,1]])
print (d)
The screenshot of the program execution is shown here −
# Theano - Computational Graph
From the above two examples, you may have noticed that in Theano we create an expression which is eventually evaluated using the Theano function. Theano uses advanced optimization techniques to optimize the execution of an expression. To visualize the computation graph, Theano provides a printing package in its library.
## Symbolic Graph for Scalar Addition
To see the computation graph for our scalar addition program, use the printing library as follows −
theano.printing.pydotprint(f, outfile="scalar_addition.png", var_with_name_simple=True)
When you execute this statement, a file called scalar_addition.png will be created on your machine. The saved computation graph is displayed here for your quick reference −
The complete program listing to generate the above image is given below −
from theano import *
a = tensor.dscalar()
b = tensor.dscalar()
c = a + b
f = theano.function([a,b], c)
## Symbolic Graph for Matrix Multiplier
Now, try creating the computation graph for our matrix multiplier. The complete listing for generating this graph is given below −
from theano import *
a = tensor.dmatrix()
b = tensor.dmatrix()
c = tensor.dot(a,b)
f = theano.function([a,b], c)
theano.printing.pydotprint(f, outfile="matrix_dot_product.png", var_with_name_simple=True)
The generated graph is shown here −
## Complex Graphs
In larger expressions, the computational graphs could be very complex. One such graph taken from Theano documentation is shown here −
To understand the working of Theano, it is important to first know the significance of these computational graphs. With this understanding, we shall know the importance of Theano.
## Why Theano?
By looking at the complexity of the computational graphs, you will now be able to understand the purpose behind developing Theano. A typical compiler would provide local optimizations in the program as it never looks at the entire computation as a single unit.
Theano implements very advanced optimization techniques to optimize the full computational graph. It combines the aspects of Algebra with aspects of an optimizing compiler. A part of the graph may be compiled into C-language code. For repeated calculations, the evaluation speed is critical and Theano meets this purpose by generating a very efficient code.
# Theano - Data Types
Now, that you have understood the basics of Theano, let us begin with the different data types available to you for creating your expressions. The following table gives you a partial list of data types defined in Theano.
Data type Theano type
Byte
bscalar, bvector, bmatrix, brow, bcol, btensor3, btensor4, btensor5, btensor6, btensor7
16-bit integers
wscalar, wvector, wmatrix, wrow, wcol, wtensor3, wtensor4, wtensor5, wtensor6, wtensor7
32-bit integers
iscalar, ivector, imatrix, irow, icol, itensor3, itensor4, itensor5, itensor6, itensor7
64-bit integers
lscalar, lvector, lmatrix, lrow, lcol, ltensor3, ltensor4, ltensor5, ltensor6, ltensor7
float
fscalar, fvector, fmatrix, frow, fcol, ftensor3, ftensor4, ftensor5, ftensor6, ftensor7
double
dscalar, dvector, dmatrix, drow, dcol, dtensor3, dtensor4, dtensor5, dtensor6, dtensor7
complex
cscalar, cvector, cmatrix, crow, ccol, ctensor3, ctensor4, ctensor5, ctensor6, ctensor7
The above list is not exhaustive and the reader is referred to the tensor creation document for a complete list.
I will now give you a few examples of how to create variables of various kinds of data in Theano.
## Scalar
To construct a scalar variable you would use the syntax −
### Syntax
x = theano.tensor.scalar ('x')
x = 5.0
print (x)
### Output
5.0
## One-dimensional Array
To create a one dimensional array, use the following declaration −
### Example
f = theano.tensor.vector
f = (2.0, 5.0, 3.0)
print (f)f = theano.tensor.vector
f = (2.0, 5.0, 3.0)
print (f)
print (f[0])
print (f[2])
### Output
(2.0, 5.0, 3.0)
2.0
3.0
If you do f[3] it would generate an index out of range error as shown here −
print f([3])
### Output
IndexError Traceback (most recent call last)
<ipython-input-13-2a9c2a643c3a> in <module>
4 print (f[0])
5 print (f[2])
----> 6 print (f[3])
IndexError: tuple index out of range
## Two-dimensional Array
To declare a two-dimensional array you would use the following code snippet −
### Example
m = theano.tensor.matrix
m = ([2,3], [4,5], [2,4])
print (m[0])
print (m[1][0])
### Output
[2, 3]
4
## 5-dimensional Array
To declare a 5-dimensional array, use the following syntax −
### Example
m5 = theano.tensor.tensor5
m5 = ([0,1,2,3,4], [5,6,7,8,9], [10,11,12,13,14])
print (m5[1])
print (m5[2][3])
### Output
[5, 6, 7, 8, 9]
13
You may declare a 3-dimensional array by using the data type tensor3 in place of tensor5, a 4-dimensional array using the data type tensor4, and so on up to tensor7.
## Plural Constructors
Sometimes, you may want to create variables of the same type in a single declaration. You can do so by using the following syntax −
### Syntax
from theano.tensor import * x, y, z = dmatrices('x', 'y', 'z')
x = ([1,2],[3,4],[5,6])
y = ([7,8],[9,10],[11,12])
z = ([13,14],[15,16],[17,18])
print (x[2])
print (y[1])
print (z[0])
### Output
[5, 6]
[9, 10]
[13, 14]
# Theano - Variables
In the previous chapter, while discussing the data types, we created and used Theano variables. To reiterate, we would use the following syntax to create a variable in Theano −
x = theano.tensor.fvector('x')
In this statement, we have created a variable x of type vector containing 32-bit floats. We are also naming it as x. The names are generally useful for debugging.
To declare a vector of 32-bit integers, you would use the following syntax −
i32 = theano.tensor.ivector
Here, we do not specify a name for the variable.
To declare a three-dimensional vector consisting of 64-bit floats, you would use the following declaration −
f64 = theano.tensor.dtensor3
The various types of constructors along with their data types are listed in the table below −
Constructor Data type Dimensions
fvector float32 1
ivector int32 1
fscalar float32 0
fmatrix float32 2
ftensor3 float32 3
dtensor3 float64 3
You may use a generic vector constructor and specify the data type explicitly as follows −
x = theano.tensor.vector ('x', dtype=int32)
In the next chapter, we will learn how to create shared variables.
# Theano - Shared Variables
Many a times, you would need to create variables which are shared between different functions and also between multiple calls to the same function. To cite an example, while training a neural network you create weights vector for assigning a weight to each feature under consideration. This vector is modified on every iteration during the network training. Thus, it has to be globally accessible across the multiple calls to the same function. So we create a shared variable for this purpose. Typically, Theano moves such shared variables to the GPU, provided one is available. This speeds up the computation.
## Syntax
You create a shared variable you use the following syntax −
import numpy
W = theano.shared(numpy.asarray([0.1, 0.25, 0.15, 0.3]), 'W')
## Example
Here the NumPy array consisting of four floating point numbers is created. To set/get the W value you would use the following code snippet −
import numpy
W = theano.shared(numpy.asarray([0.1, 0.25, 0.15, 0.3]), 'W')
print ("Original: ", W.get_value())
print ("Setting new values (0.5, 0.2, 0.4, 0.2)")
W.set_value([0.5, 0.2, 0.4, 0.2])
print ("After modifications:", W.get_value())
## Output
Original: [0.1 0.25 0.15 0.3 ]
Setting new values (0.5, 0.2, 0.4, 0.2)
After modifications: [0.5 0.2 0.4 0.2]
# Theano - Functions
Theano function acts like a hook for interacting with the symbolic graph. A symbolic graph is compiled into a highly efficient execution code. It achieves this by restructuring mathematical equations to make them faster. It compiles some parts of the expression into C language code. It moves some tensors to the GPU, and so on.
The efficient compiled code is now given as an input to the Theano function. When you execute the Theano function, it assigns the result of computation to the variables specified by us. The type of optimization may be specified as FAST_COMPILE or FAST_RUN. This is specified in the environment variable THEANO_FLAGS.
A Theano function is declared using the following syntax −
f = theano.function ([x], y)
The first parameter [x] is the list of input variables and the second parameter y is the list of output variables.
Having now understood the basics of Theano, let us begin Theano coding with a trivial example.
# Theano - Trivial Training Example
Theano is quite useful in training neural networks where we have to repeatedly calculate cost, and gradients to achieve an optimum. On large datasets, this becomes computationally intensive. Theano does this efficiently due to its internal optimizations of the computational graph that we have seen earlier.
## Problem Statement
We shall now learn how to use Theano library to train a network. We will take a simple case where we start with a four feature dataset. We compute the sum of these features after applying a certain weight (importance) to each feature.
The goal of the training is to modify the weights assigned to each feature so that the sum reaches a target value of 100.
sum = f1 * w1 + f2 * w2 + f3 * w3 + f4 * w4
Where f1, f2, ... are the feature values and w1, w2, ... are the weights.
Let me quantize the example for a better understanding of the problem statement. We will assume an initial value of 1.0 for each feature and we will take w1 equals 0.1, w2 equals 0.25, w3 equals 0.15, and w4 equals 0.3. There is no definite logic in assigning the weight values, it is just our intuition. Thus, the initial sum is as follows −
sum = 1.0 * 0.1 + 1.0 * 0.25 + 1.0 * 0.15 + 1.0 * 0.3
Which sums to 0.8. Now, we will keep modifying the weight assignment so that this sum approaches 100. The current resultant value of 0.8 is far away from our desired target value of 100. In Machine Learning terms, we define cost as the difference between the target value minus the current output value, typically squared to blow up the error. We reduce this cost in each iteration by calculating the gradients and updating our weights vector.
Let us see how this entire logic is implemented in Theano.
## Declaring Variables
We first declare our input vector x as follows −
x = tensor.fvector('x')
Where x is a single dimensional array of float values.
We define a scalar target variable as given below −
target = tensor.fscalar('target')
Next, we create a weights tensor W with the initial values as discussed above −
W = theano.shared(numpy.asarray([0.1, 0.25, 0.15, 0.3]), 'W')
## Defining Theano Expression
We now calculate the output using the following expression −
y = (x * W).sum()
Note that in the above statement x and W are the vectors and not simple scalar variables. We now calculate the error (cost) with the following expression −
cost = tensor.sqr(target - y)
The cost is the difference between the target value and the current output, squared.
To calculate the gradient which tells us how far we are from the target, we use the built-in grad method as follows −
gradients = tensor.grad(cost, [W])
We now update the weights vector by taking a learning rate of 0.1 as follows −
W_updated = W - (0.1 * gradients[0])
Next, we need to update our weights vector using the above values. We do this in the following statement −
updates = [(W, W_updated)]
## Defining/Invoking Theano Function
Lastly, we define a function in Theano to compute the sum.
f = function([x, target], y, updates=updates)
To invoke the above function a certain number of times, we create a for loop as follows −
for i in range(10):
output = f([1.0, 1.0, 1.0, 1.0], 100.0)
As said earlier, the input to the function is a vector containing the initial values for the four features - we assign the value of 1.0 to each feature without any specific reason. You may assign different values of your choice and check if the function ultimately converges. We will print the values of the weight vector and the corresponding output in each iteration. It is shown in the below code −
print ("iteration: ", i)
print ("Modified Weights: ", W.get_value())
print ("Output: ", output)
## Full Program Listing
The complete program listing is reproduced here for your quick reference −
from theano import *
import numpy
x = tensor.fvector('x')
target = tensor.fscalar('target')
W = theano.shared(numpy.asarray([0.1, 0.25, 0.15, 0.3]), 'W')
print ("Weights: ", W.get_value())
y = (x * W).sum()
cost = tensor.sqr(target - y)
W_updated = W - (0.1 * gradients[0])
for i in range(10):
output = f([1.0, 1.0, 1.0, 1.0], 100.0)
print ("iteration: ", i)
print ("Modified Weights: ", W.get_value())
print ("Output: ", output)
When you run the program you will see the following output −
Weights: [0.1 0.25 0.15 0.3 ]
iteration: 0
Modified Weights: [19.94 20.09 19.99 20.14]
Output: 0.8
iteration: 1
Modified Weights: [23.908 24.058 23.958 24.108]
Output: 80.16000000000001
iteration: 2
Modified Weights: [24.7016 24.8516 24.7516 24.9016]
Output: 96.03200000000001
iteration: 3
Modified Weights: [24.86032 25.01032 24.91032 25.06032]
Output: 99.2064
iteration: 4
Modified Weights: [24.892064 25.042064 24.942064 25.092064]
Output: 99.84128
iteration: 5
Modified Weights: [24.8984128 25.0484128 24.9484128 25.0984128]
Output: 99.968256
iteration: 6
Modified Weights: [24.89968256 25.04968256 24.94968256 25.09968256]
Output: 99.9936512
iteration: 7
Modified Weights: [24.89993651 25.04993651 24.94993651 25.09993651]
Output: 99.99873024
iteration: 8
Modified Weights: [24.8999873 25.0499873 24.9499873 25.0999873]
Output: 99.99974604799999
iteration: 9
Modified Weights: [24.89999746 25.04999746 24.94999746 25.09999746]
Output: 99.99994920960002
Observe that after four iterations, the output is 99.96 and after five iterations, it is 99.99, which is close to our desired target of 100.0.
Depending on the desired accuracy, you may safely conclude that the network is trained in 4 to 5 iterations. After the training completes, look up the weights vector, which after 5 iterations takes the following values −
iteration: 5
Modified Weights: [24.8984128 25.0484128 24.9484128 25.0984128]
You may now use these values in your network for deploying the model.
# Theano - Conclusion
The Machine Learning model building involves intensive and repetitive computations involving tensors. These require intensive computing resources. As a regular compiler would provide the optimizations at the local level, it does not generally produce a fast execution code.
Theano first builds a computational graph for the entire computation. As the whole picture of computation is available as a single image during compilation, several optimization techniques can be applied during pre-compilation and that’s what exactly Theano does. It restructures the computational graph, partly converts it into C, moves shared variables to GPU, and so on to generate a very fast executable code. The compiled code is then executed by a Theano function which just acts as a hook for injecting the compiled code into the runtime. Theano has proved its credentials and is widely accepted in both academics and industry. | 2021-03-07 06:26:28 | {"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": 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": 0.41904595494270325, "perplexity": 2874.426215650228}, "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/1614178376144.64/warc/CC-MAIN-20210307044328-20210307074328-00147.warc.gz"} |
https://www.esaral.com/q/in-a-abc-d-is-the-midpoint-of-side-ac-such-that-bd-85015 | # In a ΔABC, D is the midpoint of side AC such that BD
Question:
In a $\triangle A B C, D$ is the midpoint of side $A C$ such that $B D=\frac{1}{2} A C$. Show that $\angle A B C$ is a right angle.
Solution:
Given: In $\triangle A B C, D$ is the midpoint of side $A C$ such that $B D=\frac{1}{2} A C$.
To prove: $\angle A B C$ is a right angle.
Proof:
In $\Delta A D B$,
$A D=B D \quad\left(\right.$ Given, $\left.B D=\frac{1}{2} A C\right)$
$\Rightarrow \angle D A B=\angle D B A=x$ (Let) $\quad$ (Angles opposite to equal sides are equal)
Similarly, in $\Delta D C B$
$B D=C D$ (Given)
$\Rightarrow \angle D B C=\angle D C B=y$ (Let)
In $\Delta A B C$,
$\angle A B C+\angle B C A+\angle C A B=180^{\circ}$ (Angle sum property)
$\Rightarrow x+x+y+y=180^{\circ}$
$\Rightarrow 2(x+y)=180^{\circ}$
$\Rightarrow x+y=90^{\circ}$
$\Rightarrow \angle A B C=90^{\circ}$
Hence, $\angle A B C$ is a right angle. | 2023-03-26 22:10:59 | {"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": 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": 0.8963373899459839, "perplexity": 691.4484806373487}, "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/1679296946535.82/warc/CC-MAIN-20230326204136-20230326234136-00466.warc.gz"} |
https://gamedev.stackexchange.com/questions/65947/calculating-shadowmap-coordinates-for-cubemap-in-shading-pass | I'm trying to implement shadow mapping with cube maps. I believe I've done the first stage by filling the cube map, but for the final shading pass I am unsure how to exactly calculate the cubemap coordinates. Any pointers?
To use a cube map for shadows you need to recreate the world position of the pixel you are rendering and from that get the normal that points at that world position from the light source, now you can calculate the distance of your pixel from the light source as well as check the cube map for the distance to the first shadow casting object.
Vertex shader needs to send along the z and w components of the vertices so you can perform the unprojection in the fragment shader
output.position = mul(input.position, worldViewProjMatrix);
output.depth.xy = output.position.zw;
Then you can combine these values with the inverse projection matrix in the pixel shader to recreate the world position of each pixel:
float4 projectedPos = float3(input.position.xy, input.depth.x / input.depth.y, 1);
float4 worldPos = mul(projectedPos, invProjectionMatrix);
float4 lightDir = worldPos - lightPos
float4 normal = normalize(light2pixel);
float dist = distance(worldPos, lightPos); | 2019-09-21 20:13:58 | {"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": 0.304161012172699, "perplexity": 1604.2728110470373}, "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-2019-39/segments/1568514574662.80/warc/CC-MAIN-20190921190812-20190921212812-00373.warc.gz"} |
https://dsp.stackexchange.com/questions/45729/convolution-effects-width-of-the-signal | # Convolution effects width of the signal?
Let's say there are two signal with different frequency: \begin{align} X_1(\omega) &= 0\quad\text{for}\quad \lvert \omega\rvert > 1000\pi\\ X_2(\omega) &= 0\quad\text{for}\quad\lvert \omega\rvert > 2000 \pi\\ \text{And}\quad y(t) &= x_1(t) \star x_2(t) \end{align}
• I understand that convolution in time domain means multiplication in frequency domain, but it does not affect the length of the signal. But in this case, what is the maximum frequency of $Y(\omega)$?
• If I were to find maximum sampling interval $T_s$ then which maximum frequency do I have to use?
If $y(t)$ is the signal resulting from the convolution of $x_1(t)$ with $x_2(t)$ then it will have the same bandwidth as $x_1(t)$. $x_1(t)$ has (presumably one-sided) frequency support in $[0, 500]$ Hz and $x_2(t)$ has frequency support in $[0, 1000]$ Hz. So, when performing pointwise multiplication in the frequency domain, the higher frequency components in $x_2(t)$ between $500$ Hz and $1000$ Hz will be multiplied by zero (the value of $X_1(f)$ at those frequencies). The Nyquist frequency required to capture $y(t)$ without distortion should be any frequency greater than $1000$ Hz (twice the highest frequency in the signal).
On other terms, here, $x_1$ rules! | 2021-04-11 11:54:50 | {"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9978034496307373, "perplexity": 677.1388988429062}, "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-2021-17/segments/1618038062492.5/warc/CC-MAIN-20210411115126-20210411145126-00049.warc.gz"} |
https://blog.zilin.one/21-257-fall-2015/recitation-1/ | # Recitation 1
Problem 1: Solve the system of equations:
\begin{aligned}x_1 + 2x_2 - x_3 &= 6 \\ 3x_1 + 8x_2 + 9x_3 &= 10 \\ 2x_1 - x_2 + 2x_3 &= -2 \end{aligned}
Comment: Use Gaussian elimination on the associated augmented matrix.
Problem 2: Solve graphically: maximize z = 3x_1 + x_2 subject to 2x_1 + x_3 \le 6, x_1 + 3x_2 \le 9, x_1 \ge 0, x_2 \ge 0.
Solution: The red lines are related to the first two constraints. The reddish area is the feasible domain. The dashed blue lines are level lines on which z=3,6,9 respectively. From the graph, z=9 is maximized by x_1 = 3, x_2 = 0.
Problem 3: Solve graphically (should have non-unique solutions): maximize z=4x_1 + x_2 subject to 8x_1 + 2x_2 \le 16, 5x_1 + 2x_2 \le 12, x_1 \ge 0, x_2 \ge 0.
Solution: The red lines are related to the first two constraints. The reddish area is the feasible domain. The dashed blue lines are level lines on which z=4,8 respectively. From the graph, z=8 is maximized by points between A and B.
Problem 4: (A knapsack example) NASA must make a decision regarding which experiments should be flown on a deep-space probe that can accommodate a total payload of 140 pounds. A panel of experts has assigned numerical values to each of the experiments. The assigned values and the weights of the experiments are shown in the table. Formulate the linear programming problem that determines which experiments should be selected for the probe in order to achieve the greatest total value.
Experiment Weight Value
1 35 60
2 45 70
3 55 80
4 42 90
5 35 50
Solution: We want to maximize the total value 60x_1 + 70x_2 + 80x_3 + 90x_4 + 50x_5, where x_i is a variable that can assume only a 1 or a 0 depending on whether or not the item is on the probe. Those variables are subject to the total payload of 140 pounds, that is, 35x_1 + 45x_2 + 55x_3 + 42x_4 + 35x_5 \le 140. | 2023-03-21 11:58:26 | {"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": 0.9922389388084412, "perplexity": 662.8507146227045}, "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/1679296943695.23/warc/CC-MAIN-20230321095704-20230321125704-00160.warc.gz"} |
https://indico.fis.ucm.es/event/3/contributions/111/ | # V RUSSIAN-IBERIAN CONGRESS: Particle, Nuclear, Astroparticle Physics and Cosmology
7-11 October 2019
## Cylindrically symmetric 2+1-dimensional gravity: quantization in terms of global phase space variables.
10 Oct 2019, 15:00
35m
### Speaker
Prof. Alexander Andrianov (SPbSU)
### Description
We perform canonical analysis of a model in which gravity is coupled to a circular dust shell in 2+1 spacetime dimensions.
The result is a reduced action depending on a finite number of degrees of freedom.
The emphasis is made on finding canonical variables providing the global chart for the entire phase space of the model.
It turns out that all the distinct pieces of momentum space could be assembled into a single manifold which has $ADS^2$-geometry, and the global chart for it is provided by the Euler angles.
In quantum kinematics, this results in non-commutativity in coordinate space and discreteness of the shell radius in timelike region, which includes the collapse point.
At the level of quantum dynamics, we find transition amplitudes between zero and non-zero eigenvalues of the shell radius, which describe the rate of gravitational collapse (bounce). Their values are everywhere finite, which could be interpreted as resolution of the central singularity. We also find the map between $ADS^2$ momentum space obtained here and momentum space in Kuchar variables, which could be helpful in extending the present results to 3+1 dimensions.
### Primary author
Prof. Alexander Andrianov (SPbSU)
### Presentation Materials
There are no materials yet. | 2022-11-29 09:01:13 | {"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": 0.5557023882865906, "perplexity": 1332.7050438289532}, "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/1669446710690.85/warc/CC-MAIN-20221129064123-20221129094123-00647.warc.gz"} |
http://mathoverflow.net/feeds/user/24392 | User tom - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T07:56:57Z http://mathoverflow.net/feeds/user/24392 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/129986/solve-for-a-and-b-in-axby/130172#130172 Answer by Tom for Solve for $A$ and $B$ in $AXB=Y$ Tom 2013-05-09T14:16:56Z 2013-05-14T12:59:13Z <p>This should be a comment but I haven't got enough rep, sorry. I don't know how you want to apply the result. So, I'm wondering whether a linear polynomial whose coefficients are $m\times n$ and $n \times m$ matrices would be sufficient for your application. This can be easily achieved by using elementary matrices in order to extract $X$'s entries. </p> <h2>EDIT for elaboration</h2> <p>Let $E_{ij}=E_{ij}^{(n)}$ denote the $n\times n$ matrix that has got zero entries everywhere except for the i-th row and j-th column, i.e. $\left( E_{ij} \right)_{kl}= \delta _{ik} \delta _{jl}$ .</p> <p>Then $E_{ii}\cdot X \cdot E_{jj}$ equals $x_{ij}E_{ij}$ where $x_{ij}= (X)_{ij}$.</p> <p>Well, the embedding <code>$$\iota\colon M(n,R) \to M(m,R) \quad ; \quad M \mapsto \begin{pmatrix} M & 0 \\ 0 & 0 \end{pmatrix}$$</code> can be described by the matrix $J=(I_n \ 0_{m-n})$, i.e. $\iota(M)=J^t\cdot M\cdot J$.</p> <p>Let me just steal the next definition from wikipedia <a href="http://en.wikipedia.org/wiki/Elementary_matrices" rel="nofollow">http://en.wikipedia.org/wiki/Elementary_matrices</a></p> <p><code>$$T_{i,j} = \begin{bmatrix} 1 & & & & & & & \\ & \ddots & & & & & & \\ & & 0 & & 1 & & \\ & & & \ddots & & & & \\ & & 1 & & 0 & & \\ & & & & & & \ddots & \\ & & & & & & & 1\end{bmatrix}$$</code></p> <p>So $T_{ij}\cdot A$ is the matrix produced by exchanging row $i$ and row $j$ of $A$.</p> <p>Suppose $y_{kl} = \sum_{ij} z_{kl}^{ij} \cdot x_{ij}$ where $z_{kl}^{ij}$ lies in $\mathbb Z$ and $y_{kl}=(Y)_{kl}$ then</p> <p>$$Y=\sum_{ijkl} z_{kl}^{ij} \cdot T_{ik}^{(m)} \cdot J^t \cdot E_{ii}^{(n)} \cdot X \cdot E_{jj}^{(n)} \cdot J \cdot T_{jl}^{(m)} .$$</p> <p>Or, as I just realized we can permute</p> <p>$$Y=\sum_{ijkl} z_{kl}^{ij} \cdot T_{ik}^{(m)} \cdot E_{ii}^{(m)}\cdot J^t\cdot X\cdot J \cdot E_{jj}^{(m)} \cdot T_{jl}^{(m)} .$$</p> <p>But both formulas give the exact same shortened version</p> <p>$$Y = \sum_{ijkl} A_{kl}^{ij} \cdot X \cdot B_{l}^{ij}$$</p> <p>where $B_{kl}^{ij}$ is independent of $k$.</p> http://mathoverflow.net/questions/35140/interesting-applications-in-pure-mathematics-of-first-year-calculus/126611#126611 Answer by Tom for Interesting applications (in pure mathematics) of first-year calculus Tom 2013-04-05T12:22:25Z 2013-04-05T12:22:25Z <p>What I like(d) most is defining an analytic function that describes some number theoretic phenomena. One thing I remember is from Winfried Kohnen's postech lecture <a href="http://www.mathi.uni-heidelberg.de/~winfried/siegel2.pdf" rel="nofollow">http://www.mathi.uni-heidelberg.de/~winfried/siegel2.pdf</a> , see pages 1-3 for more details. He starts with the standard inner product on $\mathbb{R}^m$ viewed as a quadratic form $$Q(x):=x^t x.$$ We are interested in the number $r_Q(t)$ of tuples of squares of inetegers that add up to a natural number $t$, i.e. </p> <p>$$r_Q(t):= # \left{ g \in \mathbb{Z}^m : Q(g)=(g_1)^2+ \dots + (g_4)^2=t \right} .$$ </p> <p>They can be computed via this power series </p> <p>$$\theta_Q(z) = 1+ \sum_{t\geq 1} r_Q(t)\ \exp(2\pi i tz)$$</p> <p>that is in fact $\theta_Q$ is a modular form of weight 2 w.r.t. $\Gamma_0$. Therefore (ok here is some kind of black box for the students), its Fourier coefficients can be given by $$r_Q(t)= 8 \left( \sigma_1(t)-4\cdot \sigma_1\left(\frac{t}{4}\right) \right)$$</p> <p>where $\sigma_k(t)$ denotes the divisor function $$\sigma_k(t):=\sum_{d|t} d^k.$$</p> <p>While writing this I was wondering whether the prime number theorem and elegant proofs of the fundamental theorem of algebra are too well known.</p> <p>p.s. sorry for messing up the formulas again.</p> http://mathoverflow.net/questions/123634/reference-on-generators-of-subgroups-of-symplectic-groups/126280#126280 Answer by Tom for Reference on generators of subgroups of symplectic groups Tom 2013-04-02T15:30:27Z 2013-04-02T15:30:27Z <p>I just wanted to share a tiny part of the solution with you. The group $\Gamma_{2,0}[2]$ is generated by the matrices <code>$\begin{pmatrix}I_g & S \\ 0_g & I_g \end{pmatrix}$</code> where $S=S^t$,</p> <p><code>$\begin{pmatrix}I_g & 0_g \\ 2 \cdot S & I_g \end{pmatrix}$</code> where $S=S^t$</p> <p>and <code>$\begin{pmatrix}U^t & 0_g \\ 0_g & U^{-1} \end{pmatrix}$</code> where $U \in GL(2,\mathbb{Z})$. The reference is <a href="http://arxiv.org/abs/1001.0324" rel="nofollow">http://arxiv.org/abs/1001.0324</a> page 6.</p> http://mathoverflow.net/questions/123634/reference-on-generators-of-subgroups-of-symplectic-groups Reference on generators of subgroups of symplectic groups Tom 2013-03-05T16:46:13Z 2013-04-02T15:30:27Z <p>We should start with the definition of the symplectic group for an arbitrary ring $R$. The symplectic group $Sp(g,R)$ is the subgroup of $SL(2g,R)$ such that all elements satisfy $M=J_g^t M J_g$ with $J_g$ being the canonical almost complex structure - or involution whatever you prefer to call it.</p> <p>A generic element of $Sp(g,R)$ is denoted by $M=(A B \ C D)$ where $A,B,C,D$ are $g\times g$ matrices.</p> <p>Note bene, if $R$ is Euclidean then $Sp(g,R)$ is generated by the involution $J_g$ and the translations <code>$\begin{pmatrix}I_g\ S \\ 0_g \ I_g \end{pmatrix}$</code> sending $Z$ to $Z+S$ where $S$ is a symmetric $g \times g$ matrix.</p> <h2>Why am I interested in these generators ?</h2> <p>Well, first of all I am interested in modular forms. They are holomorphic functions $f:\mathbb{H}_g \to V$ transforming under a subgroup $\Gamma$ of a symplectic group as follows $$f(M \cdot Z)=j(M,Z)\cdot f(Z)\quad \quad \forall\ M \in \Gamma ,$$ where $j$ is a factor of automorphy. This means that $j: \Gamma \times \mathbb{H}_g \to GL(V)$ is holomorphic in the second variable and satisfies the cocycle relation $$j(MN,Z)=j(M,N \cdot Z) \cdot j(N,Z).$$</p> <p>Hence, it suffices to check the first equation only for the generators of $\Gamma$.</p> <p>Sometimes we have modular forms to a proper subgroup and even know how they transform under the full symplectic group. But they do not transform with a factor of automorphy. Examples would be the theta series $$f_a(Z):=\sum_{\nu \in \mathbb{Z}^g}{exp \left(2\pi i \left(\nu+\frac{a}{2}\right)^t Z \left(\nu+\frac{a}{2}\right) \right)}, \quad \quad a \in \mathbb{F}_2^g$$ They are modular forms to certain proper subgroups. But the action of $Sp(g,\mathbb{Z})$'s generators can be given quite easily, roughly speaking : the translations scale the thetas and involution returns a linear combination of all thetas. That way, it is possible to determine whether a polynomial in the different theta series is a modular form to the full modular group.</p> <h2>The actual question</h2> <p>I would be very pleased if someone could give a reference for the generators of subgroups of $Sp(g,\mathbb{Z})=\Gamma_g$ like $$\Gamma_g[q]:= ker\left(Sp(g,\mathbb{Z})\to Sp(g,\mathbb{Z}/q\mathbb{Z})\right)$$ <code>$$\Gamma_{g,0}[N]:=\left\{ M \in \Gamma_g : C \equiv 0 \mod N \right\}$$</code> <code>$$\Gamma_{g}^{0}[N]:=\left\{ M \in \Gamma_g : B \equiv 0 \mod N \right\}$$</code> and others if you know them, too. In particular, I am interested in $g=2$. I guess this way it is faster and I cannot make any mistakes. As hinted above it would be also nice if these generators could be given in terms of the generators of $Sp(g,\mathbb{Z})$.</p> <p>Thanks Tom</p> <p>p.s. it would be nice if someone could help me fixing the brackets in the above definition of $\Gamma_{g,0}[N]$. </p> <p>edit1 : added notation $M=(A B \ C D)$</p> http://mathoverflow.net/questions/102575/are-there-cusp-forms-for-the-full-modular-group-sp2-z-and-representations-det3 Are there cusp forms for the full modular group Sp(2,Z) and representations det^3 \otimes Sym^2j(\rho_standard) Tom 2012-07-18T20:11:12Z 2012-07-19T02:48:58Z <h1>What are modular forms or cusps forms, resp. ?</h1> <p>We start with defining their common domains $\mathbb{H}_g$ as the set of symmetric $g \times g$ matrices with positive definite imaginary parts. The symplectic group $Sp(g,\mathbb{Z})$ is the subgroup of $SL(2g,\mathbb{Z})$ such that all elements satisfy $M=J_g^t M J_g$ with $J_g$ being the canonical almost complex structure.</p> <p>$Sp(g,\mathbb{Z})$ acts on $\mathbb{H}_g$ by $M(Z)=(AZ+B)(CZ+D)^{-1}$ where A,B,C and D are the block matrix entries of M.</p> <p>Let $\rho : GL(g,\mathbb{C}) \to GL(V)$ be a rational representation on a finite dimensional $\mathbb{C}$-vector space then the associated modular forms are the holomorphic functions $f : \mathbb{H}_g \to V$ satisfying $f(M(Z))=\rho(CZ+D)f(Z)$ for all $M \in Sp(g,\mathbb{Z})$.</p> <p>Cusps forms can be easily characterized as the elements of Siegel's $\Phi$ operator's kernel.</p> <h1>Modular forms in genus 2</h1> <p>If g equals 2 then the observed representations are the ones of $GL(2,\mathbb{C})$. We know from representation theory that all irreducible representations are isomorphic to a rep of the type $det^k \otimes Sym^{2j}(\rho_{standard})$. </p> <p>We denote by $\rho_{standard}$ the standard representation $X \mapsto X$. $Sym^{2j}(\rho_{standard})$ is the associated symmetric product $GL(2,\mathbb{C}) \to Sym^{2j}(\mathbb{C}^2)$. $det$ is just the 1 dimensional determinant representation $GL(2,\mathbb{C}) \to \mathbb{C}$.</p> <p>For $k\geq 4$ Tshushima has given a dimension formula for the vector space of cusps forms in An explicit dimension formula for the spaces of generalized automorphic forms with respect to Sp(2, Z). Proceedings of the Japan Academy, Ser. A, Mathematical Sciences, 59:139–142, 1983.</p> <p>Satoh and Ibukiyama gave (but partly didn't publish AFAIK) generators for the modules of vector valued modular forms to the representations $det^k \otimes Sym^{2j}(\rho_{standard})$ with running k and fixed j in ${1,2,3}$. </p> <h1>The actual question</h1> <p>So the next question for me was are there cusps forms to $det^3 \otimes Sym^{2j}(\rho_{standard})$ and can they ( at least a single one) be given explicitly, in particular for j=4 ?</p> <p>cheers Tom</p> <p>p.s. please excuse all mistakes I made but it was the first time for me publishing on such a plattform.</p> http://mathoverflow.net/questions/129986/solve-for-a-and-b-in-axby/130172#130172 Comment by Tom Tom 2013-05-15T08:51:53Z 2013-05-15T08:51:53Z @ Peter. I was never claiming that I could solve the actual question. In fact, I stated that I can't. I said in the second line that I can give a linear polynomial (in an answer as I haven't got enough rep for commenting) and was then asked to elaborate which I did. http://mathoverflow.net/questions/129986/solve-for-a-and-b-in-axby/130172#130172 Comment by Tom Tom 2013-05-14T20:07:42Z 2013-05-14T20:07:42Z I guess we are not on the same page. But, if I take $X$ to be a non-zero number -denoted by $x$- and $Y$ to be $x \cdot I_n$, then there is a solution, although $x$ has rank 1 and $Y$ rank n. Indeed, denoting by $e_i$ the i-th basis vector we have $$Y=\sum_i e_i \cdot x \cdot e_i^t=\sum_i x \cdot e_i \cdot e_i^t.$$ I hope haven't made new mistakes now. http://mathoverflow.net/questions/129986/solve-for-a-and-b-in-axby/130172#130172 Comment by Tom Tom 2013-05-14T13:05:12Z 2013-05-14T13:05:12Z I have to admit that I am puzzled now. Peter, could you be so kind to give a short example ? Furthermore, wouldn't that make your comment the desired answer ? btw I just clarified the notation above. http://mathoverflow.net/questions/129986/solve-for-a-and-b-in-axby/130172#130172 Comment by Tom Tom 2013-05-13T19:14:18Z 2013-05-13T19:14:18Z thanks for editing, Emil ! http://mathoverflow.net/questions/123634/reference-on-generators-of-subgroups-of-symplectic-groups/123658#123658 Comment by Tom Tom 2013-03-11T18:03:21Z 2013-03-11T18:03:21Z Dear Aakumadula, thanks for helping with the syntax! Sorry, I haven't had time to look up your reference in detail, yet ! Dear Nathan, that's a really nice one ! But doesn't $u(1)$ generate all $u(x)$s ? And can't we pick only finitely many $C(a,b,c,d)$s as $\Gamma_0^{(1)}(N)$ is finitely generated ? http://mathoverflow.net/questions/123634/reference-on-generators-of-subgroups-of-symplectic-groups Comment by Tom Tom 2013-03-05T18:05:38Z 2013-03-05T18:05:38Z Indeed, Mumford gives generators for $\Gamma_g$,$\Gamma_g[2]$ and $\Gamma_g[1,2]$ on pages 202-210. But to be honest I was hoping for more. http://mathoverflow.net/questions/123634/reference-on-generators-of-subgroups-of-symplectic-groups Comment by Tom Tom 2013-03-05T17:22:31Z 2013-03-05T17:22:31Z Dear J, as you proposed I just clarified the notation $M=(A B \\ C D)$. With the few generators I was tkinking of E. Freitag 'Siegelsche Modulformen' (in Springer's Comprehensive Studies 254 ) appendix V pages 322-328. The proof relies on the fact that he finds for an EUCLIDEAN ring 'smaller' or 'easier to handle' sets of generators for $SL(g,R)$ and $GL(g,R)$. Now I'm having a look in the 2 books you mentioned. http://mathoverflow.net/questions/102575/are-there-cusp-forms-for-the-full-modular-group-sp2-z-and-representations-det3/102613#102613 Comment by Tom Tom 2012-07-24T20:17:54Z 2012-07-24T20:17:54Z I just sent you an email. http://mathoverflow.net/questions/102575/are-there-cusp-forms-for-the-full-modular-group-sp2-z-and-representations-det3/102613#102613 Comment by Tom Tom 2012-07-19T05:52:21Z 2012-07-19T05:52:21Z This is already a quite nice answer ! Do you know what kind of strategy he used ? Or do you know how to contact him or his supervisor ? To speak quite honestly I couldn't find anything on the Kyushu University homepage. I mean Satoh, Ibukiyama and their students collect Eisenstein series and sorts of Rankin Cohen brackets until they reach the dimension Tshushima has calculated 20 years ago. But this collection seems to me to be intricate especially if you raise j. | 2013-05-25 07:56:48 | {"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": 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": 0.960547924041748, "perplexity": 804.2273736674807}, "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/1368705749262/warc/CC-MAIN-20130516120229-00001-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://api-project-1022638073839.appspot.com/questions/how-do-you-evaluate-lne-45 | # How do you evaluate lne^45?
Nov 17, 2016
## 45
#### Explanation:
two of the laws of logs are:
1) ${\log}_{a} {x}^{n} = n {\log}_{a} x , \forall a \in \mathbb{R}$
2) ${\log}_{a} a = 1 , \forall a \in \mathbb{R}$
so $\ln {e}^{45}$
$= 45 \ln e$
$\ln$ is to base $e$
$\therefore = 45$ | 2021-10-18 07:29:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "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": 0.6757937669754028, "perplexity": 4727.1713794113375}, "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/1634323585199.76/warc/CC-MAIN-20211018062819-20211018092819-00606.warc.gz"} |
https://www.nature.com/articles/s41566-017-0006-2?error=cookies_not_supported&code=5e1340c2-0881-43f0-8f44-0a5abc66020c | # Lasing in topological edge states of a one-dimensional lattice
## Abstract
Topology describes properties that remain unaffected by smooth distortions. Its main hallmark is the emergence of edge states localized at the boundary between regions characterized by distinct topological invariants. Because their properties are inherited from the topology of the bulk, these edge states present a strong immunity to distortions of the underlying architecture. This feature offers new opportunities for robust trapping of light in nano- and micrometre-scale systems subject to fabrication imperfections and environmentally induced deformations. Here, we report lasing in such topological edge states of a one-dimensional lattice of polariton micropillars that implements an orbital version of the Su–Schrieffer–Heeger Hamiltonian. We further demonstrate that lasing in these states persists under local deformations of the lattice. These results open the way to the implementation of chiral lasers in systems with broken time-reversal symmetry and, when combined with polariton interactions, to the study of nonlinear phenomena in topological photonics.
## Access options
from\$8.99
All prices are NET prices.
## References
1. 1.
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
2. 2.
Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).
3. 3.
Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat. Photon. 8, 821–829 (2014).
4. 4.
Söllner, I. et al. Deterministic photonemitter coupling in chiral photonic circuits. Nat. Nanotech. 10, 775–778 (2015).
5. 5.
Mittal, S. et al. Topologically robust transport of photons in a synthetic gauge field. Phys. Rev. Lett. 113, 087403 (2014).
6. 6.
Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljačić, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).
7. 7.
Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nat. Phys. 7, 907–912 (2011).
8. 8.
Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. M. Imaging topological edge states in silicon photonics. Nat. Photon. 7, 1001–1005 (2013).
9. 9.
Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).
10. 10.
Weimann, S. et al. Topologically protected bound states in photonic paritytime-symmetric crystals. Nat. Mater. 16, 433–438 (2017).
11. 11.
Poli, C., Bellec, M., Kuhl, U., Mortessagne, F. & Schomerus, H. Selective enhancement of topologically induced interface states in a dielectric resonator chain. Nat. Commun. 6, 6710 (2015).
12. 12.
Pilozzi, L. & Conti, C. Topological lasing in resonant photonic structures. Phys. Rev. B 93, 195317 (2016).
13. 13.
Carusotto, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299–366 (2013).
14. 14.
Bajoni, D. et al. Polariton laser using single micropillar GaAs–GaAlAs semiconductor cavities. Phys. Rev. Lett. 100, 047401 (2008).
15. 15.
Deng, H., Weihs, G., Santori, C., Bloch, J. & Yamamoto, Y. Condensation of semiconductor microcavity exciton polaritons. Science 298, 199–202 (2002).
16. 16.
Kasprzak, J. et al. Bose–Einstein condensation of exciton polaritons. Nature 443, 409–414 (2006).
17. 17.
Christopoulos, S. et al. Room-temperature polariton lasing in semiconductor microcavities. Phys. Rev. Lett. 98, 126405 (2007).
18. 18.
Kéna-Cohen, S. & Forrest, S. R. Room-temperature polariton lasing in an organic single-crystal microcavity. Nat. Photon. 4, 371–375 (2010).
19. 19.
Milićević, M. et al. Orbital edge states in a photonic honeycomb lattice. Phys. Rev. Lett. 118, 107403 (2017).
20. 20.
Baboux, F. et al. Measuring topological invariants from generalized edge states in polaritonic quasicrystals. Phys. Rev. B 95, 161114 (2017).
21. 21.
Delplace, P., Ullmo, D. & Montambaux, G. Zak phase and the existence of edge states in graphene. Phys. Rev. B 84, 195452 (2011).
22. 22.
Jacqmin, T. et al. Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons. Phys. Rev. Lett. 112, 116402 (2014).
23. 23.
Solnyshkov, D., Nalitov, A. & Malpuech, G. Kibble–Zurek mechanism in topologically nontrivial zigzag chains of polariton micropillars. Phys. Rev. Lett. 116, 046402 (2016).
24. 24.
Kruk, S. et al. Edge states and topological phase transitions in chains of dielectric nanoparticles. Small 13, 1603190 (2017).
25. 25.
Sala, V. et al. Spin–orbit coupling for photons and polaritons in microstructures. Phys. Rev. X 5, 011034 (2015).
26. 26.
Sturm, C. et al. All-optical phase modulation in a cavity-polariton Mach–Zehnder interferometer. Nat. Commun. 5, 3278 (2014).
27. 27.
Richard, M. et al. Experimental evidence for nonequilibrium Bose condensation of exciton polaritons. Phys. Rev. B 72, 201301 (2005).
28. 28.
Wouters, M., Carusotto, I. & Ciuti, C. Spatial and spectral shape of inhomogeneous nonequilibrium exciton–polariton condensates. Phys. Rev. B 77, 115340 (2008).
29. 29.
Baboux, F. et al. Bosonic condensation and disorder-induced localization in a flat band. Phys. Rev. Lett. 116, 066402 (2016).
30. 30.
Levrat, J. et al. Condensation phase diagram of cavity polaritons in GaN-based microcavities: experiment and theory. Phys. Rev. B 81, 125305 (2010).
31. 31.
Wertz, E. et al. Spontaneous formation and optical manipulation of extended polariton condensates. Nat. Phys. 6, 860–864 (2010).
32. 32.
Zak, J. Symmetry criterion for surface states in solids. Phys. Rev. B 32, 2218–2226 (1985).
33. 33.
Malkova, N., Hromada, I., Wang, X., Bryant, G. & Chen, Z. Transition between Tamm-like and Shockley-like surface states in optically induced photonic superlattices. Phys. Rev. A 80, 043806 (2009).
34. 34.
Blanco-Redondo, A. et al. Topological optical waveguiding in silicon and the transition between topological and trivial defect states. Phys. Rev. Lett. 116, 163901 (2016).
35. 35.
Harari, G. et al. in Conference on Lasers and Electro-Optics, FM3A.3 (OSA, Washington, DC, 2016).
36. 36.
Nalitov, A., Solnyshkov, D. & Malpuech, G. Polariton Z topological insulator. Phys. Rev. Lett. 114, 116401 (2015).
37. 37.
Karzig, T., Bardyn, C.-E., Lindner, N. H. & Refael, G. Topological polaritons. Phys. Rev. X 5, 031001 (2015).
38. 38.
Hadad, Y., Khanikaev, A. B. & Alù, A. Self-induced topological transitions and edge states supported by nonlinear staggered potentials. Phys. Rev. B 93, 155112 (2016).
39. 39.
Galbiati, M. et al. Polariton condensation in photonic molecules. Phys. Rev. Lett. 108, 126403 (2012).
## Acknowledgements
The authors thank M. Milicevic and G. Montambaux for discussions. This work was supported by the French National Research Agency (ANR) project Quantum Fluids of Light (ANR-16-CE30-0021) and program Labex NanoSaclay via the project ICQOQS (grant no. ANR-10-LABX-0035), the French RENATECH network, the ERC grant Honeypol and the EU-FET Proactive grant AQUS (project no. 640800). P.S.-J. acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC).
## Author information
Authors
### Contributions
P.S.-J. performed the experiments with help from V.G., carried out the calculations, analysed the data and wrote the manuscript, with the guidance of J.B. and A.A. T.O. provided critical inputs to the theoretical analysis. E.G., A.L., L.L. and I.S. grew and processed the sample. J.B. and A.A. designed the sample and supervised the work. All authors revised the manuscript.
### Corresponding author
Correspondence to P. St-Jean.
## Ethics declarations
### Competing interests
The authors declare no competing financial interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
## Electronic supplementary material
### Supplementary Information
Supplementary Information
## Rights and permissions
Reprints and Permissions
St-Jean, P., Goblot, V., Galopin, E. et al. Lasing in topological edge states of a one-dimensional lattice. Nature Photon 11, 651–656 (2017). https://doi.org/10.1038/s41566-017-0006-2
• Accepted:
• Published:
• Issue Date:
• ### Modulation instability in the nonlinear Schrödinger equation with a synthetic magnetic field: Gauge matters
• Karlo Lelas
• , Ozana Čelan
• , David Prelogović
• , Hrvoje Buljan
• & Dario Jukić
Physical Review A (2021)
• ### Dynamical robustness of topological end states in nonreciprocal Su-Schrieffer-Heeger models with open boundary conditions
• Li-Jun Lang
• , Yijiao Weng
• , Yunhui Zhang
• , Enhong Cheng
• & Qixia Liang
Physical Review B (2021)
• ### Absorption Reduction of Large Purcell Enhancement Enabled by Topological State-Led Mode Coupling
• Zhiyuan Qian
• , Zhichao Li
• , He Hao
• , Lingxiao Shan
• , Qi Zhang
• , Jianwen Dong
• , Qihuang Gong
• & Ying Gu
Physical Review Letters (2021)
• ### Floquet Spectrum and Dynamics for Non-Hermitian Floquet One-Dimension Lattice Model
• Ya-Nan Zhang
• , Shuang Xu
• , Hao-Di Liu
• & Xue-Xi Yi
International Journal of Theoretical Physics (2021)
• ### Knots and Non-Hermitian Bloch Bands
• Haiping Hu
• & Erhai Zhao
Physical Review Letters (2021) | 2021-01-24 19:51:03 | {"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": 0.8012327551841736, "perplexity": 11554.61580058662}, "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-2021-04/segments/1610703550617.50/warc/CC-MAIN-20210124173052-20210124203052-00344.warc.gz"} |
https://tradingyafq.web.app/luckritz60697ci/terminal-rated-r-348.html | ## Terminal rated r
The DVD contains the theatrical cut of the film with a featurette on the Moto- Terminators. The Blu-ray features both the theatrical cut and the R-rated Director's cut Terminal (I) (2018) Russia:18+ · Singapore:NC16 · South Korea:18 · Taiwan:R- 15 · Turkey:15+ · United Kingdom:15 · United States:Not Rated · Ukraine:16 Terminal (2018). Not Rated | 1h 35min | Crime, Drama, Thriller | 11 May 2018 ( USA).
connected to a load resistor of resistance $R$ standard dry cell (i.e., the sort of battery used to power calculators and torches) is usually rated at $1.5\,{\rm V}$ 15 Nov 2015 6 x M32 cable gland max. 6 x M20 metal thread. Connecting terminals. 6 x + 2 PE . Rated current max. 28 A, depends on terminal cross section. voltage rating goes up R. C. 3I. 3h. I. 3h A, B, C. Generator winding and terminal capacitances (C) V pri unbalance = % unbalance / 100 * V L-L rated / √3. The Way Back (R). Runtime: 1 hr. 48 min. Starring: Ben Affleck, Janina Gavankar Comments: Children 5 & under are NOT permitted into child restricted movies
## 30 Mar 2018 A Bloomberg terminal is a computer system offering access to Bloomberg's data service, news feeds, messaging and trade execution services.
Great eats at one of the best public markets in the U.S Previous 1 of 1. Next. Photo by R. Kennedy for 11 Oct 2018 In fact, a lot of these companies might be rated junk already if not for “The rating agencies are giving companies too much wiggle room,” said 10 Jul 2017 Ubuntu on Windows allows one to use Ubuntu Terminal and run Ubuntu command line utilities More. Entertainment Software Rating Board 6 days ago To start another terminal session, use the New Terminal command on the Terminal dropdown menu, or Shift+Alt+R. screenshot showing terminal Compact Terminal Relays/Terminal SSRs with 3. G6B-4@@ND. Specifications . □ Ratings. Coil Ratings (per G6B Relay). Note: 1. (cosφ = 0.4, L/R = 7 ms). Variants of the CPX terminal controller (with bus node, without preprocessing). Bus node CPX-AB-4-M12x2-5POL and CPX-AB-4-M12x2-5POL-R with M12- 5POL connection. 1. 2. 3. 4. 5. 6. 7 rated sensors can be connected. Each. The TPA reduces terminal back-out by providing locking redundancy; assemblers cannot insert the TPA unless terminal is properly inserted. Micro-Fit 3.0 CPI (
### connected to a load resistor of resistance $R$ standard dry cell (i.e., the sort of battery used to power calculators and torches) is usually rated at $1.5\,{\rm V}$
Reese is shown repeatedly fondling her breasts. We see some mild thrusting and hear some brief sexual moaning. The scene is probably about 60 seconds long. It's not as explicit as it sounds, and it's a very romantic scene and doesn't feel like a normal R-rated sex scene. Thermocouple terminal blocks are offered in Type K, J, T, E and R/S. The terminal block contacts are made with thermocouple-grade calibration alloys. The terminal blocks come in a Gray color but white blank marker strips are available for identification. In the dark heart of a sprawling, anonymous city, Terminal follows the twisting tales of two assassins carrying out a sinister mission, a teacher battling a fatal illness, an enigmatic janitor and Interacting with Terminals. The rstudioapi package provides a collection of functions that can be used to interact with the RStudio terminal tab.. There are two primary approaches to using these functions. Use terminalExecute() to run a specific process with the output shown in a new terminal buffer, without blocking the current R session.. Create, query, and manipulate interactive terminals. Ramsond Packaged Terminal Air Conditioners (Commonly known as Ramsond Packaged Terminal Air Conditioners (Commonly known as PTAC) are ideal for application in hotels, motels and apartments, where the environment of a single area or zone, such as a room, with an outside wall needs to be controlled. As the name implies, a single package contains all the components of an air-cooled refrigeration
### The TPA reduces terminal back-out by providing locking redundancy; assemblers cannot insert the TPA unless terminal is properly inserted. Micro-Fit 3.0 CPI (
30 Mar 2018 A Bloomberg terminal is a computer system offering access to Bloomberg's data service, news feeds, messaging and trade execution services. The Solution series sensors/actuators terminal blocks reduce the installation costs, speed the wiring and ease commissioning in process automation
## Thermocouple terminal blocks are offered in Type K, J, T, E and R/S. The terminal block contacts are made with thermocouple-grade calibration alloys. The terminal blocks come in a Gray color but white blank marker strips are available for identification.
A collection of named terminals, or "terminal set", is generally associated with an RStudio project. For more details, see Terminal Architecture and Lifetime. An alternative (or complementary) approach is to use a terminal multiplexer as described in Advanced - Using Tmux or Screen. The 1,000A breaker has 90°C rated bus-type terminals on the breaker and 90°C rated compression lugs on the cable, so this termination is rated for 90°C. But, keep in mind that even though we initially thought we were allowed to use Table 310.15(B)(17), we’re limited to the ampacities of Table 310.15(B)(16) for the breaker terminals. I cannot figure out how to start R in windows command terminal. I run cmd to open Command Prompt after I type R, rcmd, start R and try other possibilities I found around but I have an error: 'R' is not recognized as an internal or external command. I have R installed and I have a short-cut on my desktop and I am able to use it as RGui but I saw Rated wire size Rated voltage Power terminal blocks DIN 3 with bistable foot and base mounting 2 studs M16 Spacing 55 mm (2.16") Characteristics Color Type Part number Notes Characteristics Color Type Part number Accessories Rail 35 x 7,5 x 1 PR3.Z2 Rail 35 x 15 x 2,3 PR4 Rail 35 x 15 x 1,5 PR5 Reese is shown repeatedly fondling her breasts. We see some mild thrusting and hear some brief sexual moaning. The scene is probably about 60 seconds long. It's not as explicit as it sounds, and it's a very romantic scene and doesn't feel like a normal R-rated sex scene. Thermocouple terminal blocks are offered in Type K, J, T, E and R/S. The terminal block contacts are made with thermocouple-grade calibration alloys. The terminal blocks come in a Gray color but white blank marker strips are available for identification.
6 days ago To start another terminal session, use the New Terminal command on the Terminal dropdown menu, or Shift+Alt+R. screenshot showing terminal | 2021-09-27 10:05:05 | {"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": 0.19663244485855103, "perplexity": 8161.956361440907}, "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/1631780058415.93/warc/CC-MAIN-20210927090448-20210927120448-00280.warc.gz"} |
https://distionary.netlify.app/reference/dot-quantities.html | Formulas for quantities (such as mean, variance, skewness, EVI, etc.) of select parametric distributions.
.quantities
## Format
An object of class list of length 18.
## Details
A list, where each distribution gets a (named) entry, with name given by the suffix of dst_ (such as "norm", "unif", etc.). Each distribution's entry is itself a named list of expressions, where the name is the name of the quantity matching the distionary function name:
• mean
• median
• variance
• skewness
• kurtosis_exc
• range
• evi
Each expression is allowed to refer to the distribution's parameters by name.
## Note
Although R allows us to evaluate distributional representations of certain parametric distributions through functions with p, d, q, and r prefixes (such as pnorm(), dnorm(), etc.), R does not "come with" formulas for quantities such as mean, variance, EVI, etc. Although these quantities can be computed from a distributional representation (such as integrating the quantile function to get the mean), it's often inefficient to rely on such computations. We therefore include formulas here, and check them using testthat. | 2022-05-19 08:13:56 | {"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": 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": 0.9383018016815186, "perplexity": 3726.7318058368232}, "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-2022-21/segments/1652662526009.35/warc/CC-MAIN-20220519074217-20220519104217-00033.warc.gz"} |
https://socratic.org/questions/how-many-protons-does-an-atom-of-bromine-br-have | # How many protons does an atom of bromine Br have?
$35$
It has atomic number $35$, element number $35$ on the periodic table, and hence $35$ protons in the nucleus of all its atoms. | 2021-09-25 21:23:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "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": 0.1791648119688034, "perplexity": 753.6833872948612}, "config": {"markdown_headings": true, "markdown_code": false, "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-2021-39/segments/1631780057775.50/warc/CC-MAIN-20210925202717-20210925232717-00150.warc.gz"} |
http://wangchaofeng.com/parseNote.php?note=notes_programming_make.note | All notes
Mak
# Recipes
Ref.
## Ignore errors
To ignore errors in a recipe line, write a '-' at the beginning of the line's text (after the initial tab). The '-' is discarded before the line is passed to the shell for execution.
For example,
clean:
-rm -f *.o
This causes make to continue even if rm is unable to remove a file.
When you run make with the '-i' or '--ignore-errors' flag, errors are ignored in all recipes of all rules. A rule in the makefile for the special target .IGNORE has the same effect, if there are no prerequisites. These ways of ignoring errors are obsolete because '-' is more flexible.
## Echoing
• When a line starts with '@', the echoing of that line is suppressed.
• When make is given the flag '-n' or '--just-print' it only echoes most recipes, without executing them.
• The '-s' or '--silent' flag to make prevents all echoing, as if all recipes started with '@'.
• A rule in the makefile for the special target .SILENT without prerequisites has the same effect (see Special Built-in Target Names). .SILENT is essentially obsolete since '@' is more flexible.
# Writing Makefiles
## Include
The include directive tells make to suspend reading the current makefile and read one or more other makefiles before continuing.
filenames can contain shell file name patterns.
include foo *.mk $(bar) # Simply ignore a makefile which does not exist or cannot be remade, with no error message -include filenames If the specified name does not start with a slash, the included files are search in order under: 1. Current directory 2. Dirs specified with the ‘-I’ or ‘--include-dir’ option 3. In order: prefix/include (normally /usr/local/include) /usr/gnu/include, /usr/local/include, /usr/include. Occasions for using include directives: • Several programs, handled by individual makefiles in various directories, need to use a common set of variable definitions or pattern rules. • Generate prerequisites from source files automatically; the prerequisites can be put in a file that is included by the main makefile. ## Remake Makefiles Sometimes makefiles can be remade from other files, such as RCS or SCCS files. # Writing Rules ## Automatic Prerequisites For example, if main.c uses defs.h via an #include, you would write: main.o: defs.h Most modern C compilers can write these rules for you, by looking at the #include lines in the source files: cc -M main.c # generates the output: # main.o : main.c defs.h With old make programs, it was traditional practice to use this compiler feature to generate prerequisites on demand with a command like make depend. That command would create a file depend containing all the automatically-generated prerequisites; then the makefile could use include to read them in. ### GNU make remaking In GNU make, the feature of remaking makefiles makes this practice obsolete — you need never tell make explicitly to regenerate the prerequisites. For each source file name.c there is a makefile name.d which lists what files the object file name.o depends on. Here is the rule to make name.d: %.d: %.c @set -e; rm -f [email protected]; \$(CC) -M $(CPPFLAGS)$< > [email protected]; \
sed 's,$*$\.o[ :]*,.o [email protected] : ,g' < [email protected] > [email protected]; \
rm -f [email protected]
sources = foo.c bar.c
# NOTE: Place the include directive after the first, default goal, or it will become the default.
include $(sources:.c=.d) • The ‘-e’ flag to the shell causes it to exit immediately if the CC command (or any other command) fails (exits with a nonzero status). • With GNU C compiler, use the ‘-MM’ flag instead of ‘-M’. This omits prerequisites on system header files. • The sed command is to translate "main.o : main.c defs.h" into "main.o main.d : main.c defs.h" # Run make ## Arguments to Specify the Makefile the default is to try GNUmakefile, makefile, and Makefile, in order. # Commands ## Strings Ref. $(subst from,to,text)
Each occurrence of from is replaced by to from text.
$(subst ee,EE,feet on the street) substitutes the string fEEt on the strEEt'.$(patsubst pattern,replacement,text)
$(patsubst %.c,%.o,x.c.c bar.c) produces the value x.c.o bar.o'$(var:pattern=replacement)
is equivalent to
$(patsubst pattern,replacement,$(var))
$(var:suffix=replacement) is equivalent to$(patsubst %suffix,%replacement,$(var)) objects = foo.o bar.o baz.o$(objects:.o=.c)
Get the list of corresponding source files.
# Variables
#### Target-specific Variable Values
target ... : variable-assignment
prog : CFLAGS = -g
prog : prog.o foo.o bar.o
will set CFLAGS to '-g' in the recipe for prog, but it will also set CFLAGS to '-g' in the recipes that create prog.o, foo.o, and bar.o, and any recipes which create their prerequisites.
[email protected] The name of the target file (the one before the colon)
$< The name of the first (or only) prerequisite file (the first one after the colon)$^ The names of all the prerequisite files (space separated)
$* The stem (the bit which matches the % wildcard in the rule definition. #### Set variable at make command line Ref. make can take variable assignments as part of his command line, mingled with targets: make target FOO=bar But then all assignments to FOO variable within the makefile will be ignored unless you use the override directive in assignment. (The effect is the same as with -e option for environment variables). Environment variables. It is recommended to use the conditional variable assignment operator, which only has an effect if the variable is not yet defined: FOO?=default_value_if_not_set_in_environment # Functions ## origin $(origin variable)
# If bletch has been defined from the environment, this will redefine it.
ifdef bletch
ifeq "$(origin bletch)" "environment" bletch = barf, gag, etc. endif endif Return values: • undefined: if variable was never defined. • default: if variable has a default definition, as is usual with CC and so on. See Variables Used by Implicit Rules. Note that if you have redefined a default variable, the origin function will return the origin of the later definition. • environment: if variable was inherited from the environment provided to make. • environment override: if variable was inherited from the environment provided to make, and is overriding a setting for variable in the makefile as a result of the '-e' option (see Summary of Options). • file: if variable was defined in a makefile. • command line: if variable was defined on the command line. • override: if variable was defined with an override directive in a makefile (see The override Directive). • automatic: if variable is an automatic variable defined for the execution of the recipe for each rule (see Automatic Variables). # FAQ ## Pass variable in command-line 1. Each environment variable is transformed into a makefile variable with the same name and value. • Only if "-e" option (aka "--environments-override") is on, your environment variables will override assignments made into makefile, unless these assignments themselves use the override directive. • It's much better and flexible to use "?=" assignment (the conditional variable assignment operator, which only has an effect if the variable is not yet defined). • Note that certain variables are not inherited from environment: MAKE, SHELL. 2. From command line: make target Foo=bar. It will overwrite all assignments to FOO variable within the makefile. Same as "-e" option in environment variable. To pass from command line somthing with spaces do make A='"as df"'. 3. From parent Makefile: CFLAGS=-g # Export. export CFLAGS target:$(MAKE) -C target
You can also export all variables by using export without arguments.
Just based on experience, exporting stuff like CFLAGS is a recipe for nightmare for large projects. Large projects often have 3rd party libraries that only compile with a given set of flags (that no one bothers fixing). If you export CFLAGS, your project's CFLAGS ends up overriding the 3rd party library's and triggers compile errors.
An alternate way might be to define export PROJECT_MAKE_ARGS = CC=$(CC) CFLAGS=$(CFLAGS) and pass it along as make -C folder \$(PROJECT_MAKE_FLAGS).
If there's a way to tell the library's makefile to ignore the environment, that'd be ideal (opposite of -e). | 2018-07-16 06:32:35 | {"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": 2, "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": 0.3054004907608032, "perplexity": 11131.7823186294}, "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-2018-30/segments/1531676589222.18/warc/CC-MAIN-20180716060836-20180716080836-00272.warc.gz"} |
https://cyberhelp.sesync.org/introdb-lesson/ | # Database Principles and Use
Handouts for this lesson need to be saved on your computer. Download and unzip this material into the directory (a.k.a. folder) where you plan to work.
## What good is a database?
For a team of researchers implementing a collaborative workflow, the top three reasons to use a database are:
1. concurrency - Multiple users can safely read and edit database entries simultaneously.
2. reliability - Relational databases formalize and can enforce concepts of “tidy” data.
3. scalability - Very large tables can be read, searched, and merged quickly.
In this lesson, the term “database” more precisely means a relational database that allows data manipulation with Structured Query Language (SQL). Strictly speaking, the word “database” describes any collection of digitized data–a distinction that has mostly outlived its usefulness.
This lesson also assumes you have access to a database server populated with data by the lesson instructor. Check back here for forthcoming instructions to get setup with Docker.
## Objectives
• Understand how a database differs from a data file
• Introduce the PostgreSQL database system
• Meet Structured Query Language (SQL)
• Recognize the value of typed data
## Specific Achievements
• Access a database from RStudio
• Create a table and view table definitions
• Insert records one at a time into a table
• Check primary and foreign key constraints
Top of Section
## The Portal Project
Credit: The Portal Project
The Portal Project is a long-term ecological study being conducted near Portal, AZ. Since 1977, the site has been a primary focus of research on interactions among rodents, ants and plants and their respective responses to climate.
Credit: The Portal Project
The research site consists of many plots – patches of the Arizona desert that are intensively manipulated and repeatedly surveyed. The plots have some fixed characteristics, such as the type of manipulation, geographic location, aspect, etc.
Credit: The Portal Project
The plots have a lot of dynamic characteristics, and those changes are recorded in repeated surveys. In particular, the animals captured during each survey are identified to species, weighed, and measured.
Credit: The Portal Project
Data from the Portal project is recorded in a relational database designed for reliable storage & rapid access to the bounty of information produced by this long-term ecological experiment.
This lesson uses real data, which has been analyzed in over 100 publications. The data been simplified just a little bit for the workshop, but you can download the full dataset and work with it using exactly the same tools we learn today.
The three key tables in the relational database are:
• plots
• animals
• species
Top of Section
## Database Characteristics: I
Database terminology builds on common ways of characterizing data files. The breakdown of a table into records (by row) or fields (by column) is familiar to anyone who’s worked in spreadsheets. The descriptions below formalize these terms, and provide an example referencing the Portal mammals database.
Field The smallest unit of information, each having a label and holding a value of the same type.e.g. The day on which a plot was surveyed. Record A collection of related values, from different fields, that all describe the same entity.e.g. The species, sex, weight and size of a small mammal captured during a survey. Table A collection of records, each one uniquely identified by the value of a key field.e.g. All records for small mammals observed during any survey.
Software for using a database provides different tools for working with tables than a spreadsheet program. A database is generally characterized as being tooled for production environments, in contrast to data files tooled for ease of use.
Collaboration
• Data files are stored in the cloud (sync issues), shared on a network (user collision), or copies are emailed among collaborators.
• A database accepts simultaneous users from different clients on a network. There are never multiple copies of the data (aside from backups!).
Size
• Reading an entire data file into memory isn’t scaleable. Some file types (e.g. MS Excel files) have size limits.
• Database software only reads requested parts of the data into memory. There are no size limits.
Quality
• Data file formats do not typically provide any quality controls.
• Databases stricly enforce data types on each field. Letters, for example “N.A.”, cannot be entered into a field for integers.
Extension
• Specialized files are needed for complicated data types (e.g. ESRI Shapefiles).
• Databases provide many non-standard data types, and very specialized ones (e.g. geometries) are available through extension packages.
Programming
• There is no standard way to read, edit or create records in data files of different formats or from different languages.
• Packages native to all popular programming languages provide access to databases using SQL.
Top of Section
## The Database Server
A relational database management system (RDBMS) that resides on a server is ideal for collaborative, data-driven projects. Working with such a database requires communication over a network using the client/server model, which necessitates some way of finding the database server (it’s address) and some form of authentication (a username and password).
The client must know the following information to initate communication with the database server:
• Hostname - name or ip address of the database server
• Port - typically the default (thus safe to ignore)
• Database - name of one database hosted by that server
• Username - a user authorized by the server to access the given database
We are going to look at the Portal mammals data on a server running PostgreSQL, which is an open-source database management system. The client we will use to communicate with the server is the RStudio IDE for R scripting, which is just one of very many applications that are clients for a PostgreSQL server.
For convenience and security when accessing a PostgreSQL server, some of the information should be stored in a password file.
hostname:port:database:username:password
## Connections
The first step from the RStudio client is creating a connection object that verifies the given information by opening up a channel to the database server.
library(DBI)
con <- dbConnect(RPostgres::Postgres(),
host = ...,
dbname = ...,
user = ...)
With the connection object availble, you can begin exploring the database.
> dbListTables(con)
[1] "plots" "animals" "species"
> dbListFields(con, 'species')
[1] "id" "genus" "species" "taxa"
Read an entire database table into an R data frame with dbReadTable, or if you prefer “tidyverse” functions, use the dplyr tbl function.
library(dplyr)
species <- tbl(con, 'species')
> species
# Source: table<species> [?? x 4]
# Database: postgres [[email protected]:5432/portal]
id genus species taxa
<chr> <chr> <chr> <chr>
1 AB Amphispiza bilineata Bird
2 AH Ammospermophilus harrisi Rodent
3 AS Ammodramus savannarum Bird
4 BA Baiomys taylori Rodent
5 CB Campylorhynchus brunneicapillus Bird
6 CM Calamospiza melanocorys Bird
7 CQ Callipepla squamata Bird
8 CS Crotalus scutalatus Reptile
9 CT Cnemidophorus tigris Reptile
10 CU Cnemidophorus uniparens Reptile
# ... with more rows
The dbWriteTable function provides a mechanism for uploading data, as long as the user specified in the connection object has permission to create tables.
df <- data.frame(
id = c(1, 2),
name = c('Alice', 'Bob')
)
dbWriteTable(con, 'observers', df,
append = TRUE)
> tbl(con, 'observers')
# Source: table<observers> [?? x 2]
# Database: postgres [[email protected]:5432/portal]
id name
<dbl> <chr>
1 1 Alice
2 2 Bob
Top of Section
## Database Characteristics: II
Returning to the bigger picture and our comparison of storing data in files as opposed to a database, there are some concepts that only apply to databases. We have seen that databases include multiple tables–so far, that’s not so different from keeping multiple spreadsheets in one MS Excel workbook or in multiple CSV files. The collection of tables in a relational database, however, can be structured by built-in relationships between records from different tables. Data is assembled in the correct arrangement for analysis “just in time” by scripting database queries that join tables on these relationships.
Primary key One or more fields (but usually one) that uniquely identify a record in a table. Foreign key A primary key from one table used in different table to establish a relationship. Query Collect values from tables based on their relationships and other constraints.
### Primary Keys
In the plots table, id is the primary key. Any new record cannot duplicate an existing id.
id treatment
1 Control
2 Rodent Exclosure
3 Control
Creating the observers table with id as a primary key will prevent the duplication observed from multiple identical dbWriteTable calls.
dbCreateTable(con, 'observers', list(
id = 'serial primary key',
name = 'text'
))
When appending a data frame to the table created with “serial primary key”, the id is automatically generated and unique.
df <- data.frame(
name = c('Alice', 'Bob')
)
dbWriteTable(con, 'observers', df,
append = TRUE)
> tbl(con, 'observers')
# Source: table<observers> [?? x 2]
# Database: postgres [[email protected]:5432/portal]
id name
<int> <chr>
1 1 Alice
2 2 Bob
Primary keys are checked before duplicates end up in the data, throwing an error if necessary.
df <- data.frame(
id = c(1),
name = c('J. Doe')
)
dbWriteTable(con, 'observers', df,
append = TRUE)
Error in connection_copy_data(conn@ptr, sql, value): COPY returned error: ERROR: duplicate key value violates unique constraint "observers_pkey"
CONTEXT: COPY observers, line 1
### Foreign Keys
A field may also be designated as a foreign key, which establishes a relationship between tables. A foreign key points to some primary key from a different table.
In the animals table, id is the primary key and both plot_id and species_id are foreign keys.
id month day year plot_id species_id sex hindfoot_length weight
1 7 16 1977 2 ST M 32 0.45
2 7 16 1977 2 PX M 33 0.23
3 7 16 1978 1 RO F 14 1.23
Foreign keys are checked before nonsensical references end up in the data:
df <- data.frame(
month = 7,
day = 16,
year = 1977,
plot_id = -1
)
dbWriteTable(con, 'animals', df,
append = TRUE)
Error in connection_copy_data(conn@ptr, sql, value): COPY returned error: ERROR: insert or update on table "animals" violates foreign key constraint "animals_plot_id_fkey"
DETAIL: Key (plot_id)=(-1) is not present in table "plots".
### Query
Structured Query Language (SQL) is a high-level language for interacting with relational databases. Commands use intuitive English words but can be strung together and nested in powerful ways. SQL is not the only way to query a database from R (cf. dbplyr), but sometimes it is the only way to perform a complicated query.
To write SQL statements in RStudio, use the sql engine for code chunks in a RMarkdown file:
{sql, connection = con}
...
### Basic queries
Let’s write a SQL query that selects only the year column from the animals table.
SELECT year FROM animals;
year
1977
1977
1977
1977
1977
1977
1977
1977
1977
1977
A note on style: we have capitalized the words SELECT and FROM because they are SQL keywords. Unlike R, SQL is case insensitive, so capitalization only helps for readability and is a good style to adopt.
To select data from multiple fields, include multiple fields as a comma-separated list right after SELECT:
SELECT year, month, day
FROM animals;
year month day
1977 7 16
1977 7 16
1977 7 16
1977 7 16
1977 7 16
1977 7 16
1977 7 16
1977 7 16
1977 7 16
1977 7 16
The line break before FROM is also good form, particularly as the length of the query grows.
Or select all of the columns in a table using a wildcard:
SELECT *
FROM animals;
id month day year plot_id species_id sex hindfoot_length weight
2 7 16 1977 3 NL M 33 NA
3 7 16 1977 2 DM F 37 NA
4 7 16 1977 7 DM M 36 NA
5 7 16 1977 3 DM M 35 NA
6 7 16 1977 1 PF M 14 NA
7 7 16 1977 2 PE F NA NA
8 7 16 1977 1 DM M 37 NA
9 7 16 1977 1 DM F 34 NA
10 7 16 1977 6 PF F 20 NA
11 7 16 1977 5 DS F 53 NA
### Limit
We can use the LIMIT statement to select only the first few rows. This is particularly helpful when getting a feel for very large tables.
SELECT year, species_id
FROM animals
LIMIT 4;
year species_id
1977 NL
1977 DM
1977 DM
1977 DM
### Unique values
If we want only the unique values so that we can quickly see what species have been sampled we use DISTINCT
SELECT DISTINCT species_id
FROM animals;
species_id
NA
CB
RM
PB
PE
AB
AH
SS
US
RX
If we select more than one column, then the distinct pairs of values are returned
SELECT DISTINCT year, species_id
FROM animals;
year species_id
1997 RM
2002 NL
1995 RX
1999 SS
1985 DM
1982 PP
1989 CB
1994 OT
1978 NL
1997 NL
### Calculations
We can also do calculations with the values in a query. For example, if we wanted to look at the mass of each individual, by plot, species, and sex, but we needed it in kg instead of g we would use
SELECT plot_id, species_id,
sex, weight / 1000.0
FROM animals;
plot_id species_id sex ?column?
3 NL M NA
2 DM F NA
7 DM M NA
3 DM M NA
1 PF M NA
2 PE F NA
1 DM M NA
1 DM F NA
6 PF F NA
5 DS F NA
The expression weight / 1000.0 is evaluated for each row and appended to that row, in a new column.
You can assign the new column a name by typing “AS weight_kg” after the expression.
SELECT plot_id, species_id, sex,
weight / 1000 AS weight_kg
FROM animals;
plot_id species_id sex weight_kg
3 NL M NA
2 DM F NA
7 DM M NA
3 DM M NA
1 PF M NA
2 PE F NA
1 DM M NA
1 DM F NA
6 PF F NA
5 DS F NA
Expressions can use any fields, any arithmetic operators (+ - * /) and a variety of built-in functions. For example, we could round the values to make them easier to read.
SELECT plot_id, species_id, sex,
ROUND(weight / 1000.0, 2) AS weight_kg
FROM animals;
plot_id species_id sex weight_kg
3 NL M NA
2 DM F NA
7 DM M NA
3 DM M NA
1 PF M NA
2 PE F NA
1 DM M NA
1 DM F NA
6 PF F NA
5 DS F NA
The underlying data in the wgt column of the table does not change. The query, which exists separately from the data, simply displays the calculation we requested in the query result window pane.
## Filtering
Databases can also filter data – selecting only those records meeting certain criteria. For example, let’s say we only want data for the species “Dipodomys merriami”, which has a species code of “DM”. We need to add a WHERE clause to our query.
SELECT *
FROM animals
WHERE species_id = 'DM';
id month day year plot_id species_id sex hindfoot_length weight
3 7 16 1977 2 DM F 37 NA
4 7 16 1977 7 DM M 36 NA
5 7 16 1977 3 DM M 35 NA
8 7 16 1977 1 DM M 37 NA
9 7 16 1977 1 DM F 34 NA
12 7 16 1977 7 DM M 38 NA
13 7 16 1977 3 DM M 35 NA
14 7 16 1977 8 DM NA NA NA
15 7 16 1977 6 DM F 36 NA
16 7 16 1977 4 DM F 36 NA
Of course, we can do the same thing with numbers.
SELECT *
FROM animals
WHERE year >= 2000;
id month day year plot_id species_id sex hindfoot_length weight
30159 1 8 2000 1 PP F 22 17
30160 1 8 2000 1 DO M 35 53
30161 1 8 2000 1 PP F 21 17
30162 1 8 2000 1 DM M 36 50
30163 1 8 2000 1 PP M 20 16
30164 1 8 2000 1 PB M 26 27
30165 1 8 2000 1 PP F 22 15
30166 1 8 2000 1 PP M 23 19
30167 1 8 2000 1 DO M 35 41
30168 1 8 2000 1 PB M 25 24
More sophisticated conditions arise from combining tests with AND and OR. For example, suppose we want the data on Dipodomys merriami starting in the year 2000.
SELECT *
FROM animals
WHERE year >= 2000 AND species_id = 'DM';
id month day year plot_id species_id sex hindfoot_length weight
30162 1 8 2000 1 DM M 36 50
30179 1 8 2000 12 DM M 36 60
30196 1 8 2000 17 DM M 37 52
30197 1 8 2000 17 DM F 34 43
30210 1 8 2000 22 DM M 38 56
30215 1 8 2000 22 DM F 34 28
30227 1 10 2000 4 DM M 34 45
30241 1 10 2000 11 DM M 35 43
30242 1 10 2000 11 DM M 35 44
30244 1 10 2000 11 DM M 35 44
Parentheses can be used to help with readability and to ensure that AND and OR are combined in the way that we intend. If we wanted to get all the animals for “DM” since 2000 or up to 1990 we could combine the tests using OR:
SELECT *
FROM animals
WHERE (year >= 2000 OR year <= 1990)
AND species_id = 'DM';
id month day year plot_id species_id sex hindfoot_length weight
3 7 16 1977 2 DM F 37 NA
4 7 16 1977 7 DM M 36 NA
5 7 16 1977 3 DM M 35 NA
8 7 16 1977 1 DM M 37 NA
9 7 16 1977 1 DM F 34 NA
12 7 16 1977 7 DM M 38 NA
13 7 16 1977 3 DM M 35 NA
14 7 16 1977 8 DM NA NA NA
15 7 16 1977 6 DM F 36 NA
16 7 16 1977 4 DM F 36 NA
Top of Section
## Normalized Data is Tidy
Proper use of table relationships is a challenging part of database design. The objective is normalization, or taking steps to define logical “observational units” and minimize data redundency.
For example, the genus and species names are not attributes of an animal: they are attributes of the species attributed to an animal. Data about a species belongs in a different observational unit from data about the animal captured in a survey. With an ideal database design, any value discovered to be erroneous should only have to be corrected in one record in one table.
Question
Currently, plots is pretty sparse. What other kind of data might go into plots?
Additional properties, such as location, that do not change between surveys.
## Un-tidy data with JOINs
A good data management principle is to record and store data in the most normalized form possible, and un-tidy your tables as needed for particular analyses. The SQL “JOIN” clause lets you create records with fields from multiple tables.
Consider for example what you must do to carry out a regression of animal weight against plot treatment using the R command:
lm(weight ~ treatment,
data = portal)
You need a “data.frame” called portal with rows for each animal that also includes a “treatment” inferred from “plot_id”.
Additionally suppose you want to account for genus in this regression, expanding the previous R command to:
lm(weight ~ genus + treatment,
data = portal)
You need another column for genus in the portal data.frame, inferred from “species_id” for each animal and the species table.
## Relations
There are two kinds of relations–schemas that use primary and foreign key references–that permit table joins:
• One-To-Many
• Many-To-Many
### One-To-Many Relationship
The primary key in the first table is referred to multiple times in the foreign key of the second table.
The SQL keyword “JOIN” matches up two tables in the way dictated by the constraint following “ON”, duplicating records as necessary.
SELECT weight, treatment
FROM animals
JOIN plots
ON animals.plot_id = plots.id;
The resulting table could be the basis for the portal data.frame needed in the R command lm(weight ~ treatment, data = portal).
### Many-To-Many Relationship
Each primary key from the first table may relate to any number of primary keys from the second table and vice versa. A many-to-many relationship is induced by the existance of an “association table” involved in two one-to-many relations.
Animals is an “association table” because it includes two foreign keys.
SELECT weight, genus, treatment
FROM animals
JOIN plots
ON animals.plot_id = plots.id
JOIN species
ON animals.species_id = species.id;
The resulting table could be the basis for the portal data.frame needed in the R command lm(weight ~ genus + treatment, data = portal).
Top of Section
## Summary
Databases are a core element of a centralized workflow, accomodating simultaneous use by all members of a collaborative team. We have just skimmed the topic of concurrency in database interactions: there is a lot going on under the hood to prevent data corruption.
The ability to precisely define keys and data types is the primary database feature that guaranties reliability. As you develop scripts for analysis and vizualization, certainty that you’ll never encounter a “NaN” when you expect an Integer will prevent, or help you catch, bugs in your code.
The third major feature to motivate databae use, scaleability, remains for you to discover. Very large tables can be queried, sorted and combined quickly when the work is done by a powerful relational database management system (RDBMS), such as PostgreSQL.
Top of Section
If you need to catch-up before a section of code will work, just squish it's 🍅 to copy code above it into your clipboard. Then paste into your interpreter's console, run, and you'll be ready to start in on that section. Code copied by both 🍅 and 📋 will also appear below, where you can edit first, and then copy, paste, and run again.
# Nothing here yet! | 2019-11-18 23:32:40 | {"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": 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": 0.21119149029254913, "perplexity": 6398.625224165617}, "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-2019-47/segments/1573496669868.3/warc/CC-MAIN-20191118232526-20191119020526-00204.warc.gz"} |
http://sites.austincc.edu/tsiprep/math-review/equations/solving-equations-using-the-addition-property/ | # Solving Equations Using the Addition Property
The Addition Property for Equations states that the same number
can be added to or subtracted from each side of the equation without changing
the solution to the equation.
Example 1:
Solve for k: -15 = 48 + k
Solution:
Isolate the k-term by cancelling the 48
from the right side of the equation.
-15 = 48 + k
-48 -48
-63 = k
Example 2:
Solve for c:$c - \frac{2}{3} = \frac{1}{2}$
Solution:
Isolate the c -term
by cancelling $\frac{2}{3}$ from the left
side of the equation.
$c - \frac{2}{3} + \frac{2}{3} = \frac{1}{2} + \frac{2}{3}$
The constants cancel on the left side of
the equation. Write each fraction on the right side of the equation using the
common denominator: 6
$c = \frac{3}{6} + \frac{4}{6} = \frac{3 + 4}{6} = \frac{7}{6}$
The solution to $c - \frac{2}{3} = \frac{1}{2}$ is $\frac{7}{6}$ .
Solve for x. 12 + x = 8
Solve for Q: -14 = Q - 16 | 2019-06-24 11:25:31 | {"extraction_info": {"found_math": true, "script_math_tex": 6, "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": 6, "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": 0.5971732139587402, "perplexity": 1378.1005661964284}, "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/1560627999482.38/warc/CC-MAIN-20190624104413-20190624130413-00113.warc.gz"} |
https://www.analyzemath.com/Geometry/intersecting-secant-and-tangent-theorem.html | # Intersecting Secant and Tangent Theorem Questions with Solutions
Consider the circle , the secants $A B$ and the tangent $OT$ in the figure below.
The intersecting secant tangent theorem [1] states that for the secant $A B$ and tangent $O T$, there is relationship between the lengths of the segments as follows: $OT^2 = OA \times OB$
## Question With Solutions
Note that none of the figures below is drawn to scales.
Question 1
In the figure below, $OC$ is tangent to the circle. Find $x = AB$, given the lengths of segments $OC = 42$ and $OA = 21$ .
Solution
Apply the intersecting secant tangent theorem above to the secant $OB$ and tangent $OC$ to write: $\quad OC^2 = OA \times OB$
Substitute the known and given quantities: $\quad 42^2 = 21 \times (21 + x)$
Expand and simplify: $\quad 1323 = 21 x$
Solve for $x$: $\quad x = 63$
Question 2
In the figure below, $OC$ is tangent to the circle. Find $a$ given the lengths of segments $OC = a - 1 , OA = a - 4, AB = a$.
Solution
$OB$ is secant and $OC$ is tangent hence the intersecting secant tangent theorem gives: $\quad OC^2 = OA \times OB$
Substitute the given quantities: $\quad (a-1)^2 = (a-4)(a-4+a)$
Expand and group like terms: $\quad a^2 - 2 a + 1 = 2a^2-12a+16$
Rewrite the above quadratic equation in standard form as follows: $a^2-10a+15 = 0$
Solve for $a$ to obtain two solutions: $a=5 + \sqrt{10}$ and $a = 5 - \sqrt{10}$
Note The length of a segment must be positive. Hence $a = 5 - \sqrt{10}$ cannot be accepted as a solution because $OA = a - 4 = 5 - \sqrt{10} - 4 = 1-\sqrt{10}$ is negative
$a = 5 + \sqrt{10}$ is the only solution to the given question.
Question 3
In the figure below, $OC$ is tangent to the circle and $OE$ intersects the circle at point $D$ where $E$ is the center of the circle. The lengths of the segments $OC$ and $OD$ are given by $OD = 6$ and $OC = r + 3$ where $r$ is the length of the radius of the circle.
1) Find $r$
2) Find the lengths of the segments $OA$ and $AB$ such that $AB = 2 OA$
Solution
1) Since $OC$ is tangent to the circle and $E$ is the center, then $EC$ is a radius and is perpendicular to $OC$.
Use the Pythagorean theorem to write: $\quad (OD + DE)^2 = EC^2 + OC^2$
Note that $DE$ is a radius and substitute by the given quantities: $\quad (6+r)^2 = r^2 + (r+3)^2$
Expand and write the above equation in standard form: $\quad -r^2+6r+27 = 0$
Solve for $r$ to obtain two solutions: $r = -3$ and $r = 9$ and only the solution $r = 9$ is valid since the length of the radius is a positive quantity.
2) The use of the intersecting secant tangent theorem gives: $\quad OC^2 = OA \times OB$
Substitute the known and unknown quantities: $\quad (9 + 3)^2 = OA \times (O A + 2 O A)$
The above may be written as $\quad (15)^2 = 3 OA^2$
Solve for $OA$: $\quad OA = \dfrac{15}{\sqrt 3}$ , $AB = 2 \dfrac{15}{\sqrt 3}$ | 2022-01-19 05:36:09 | {"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": 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": 0.920974850654602, "perplexity": 216.3220806344838}, "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-2022-05/segments/1642320301263.50/warc/CC-MAIN-20220119033421-20220119063421-00454.warc.gz"} |
https://tex.stackexchange.com/questions/331895/how-to-show-auxiliary-points-for-any-curves-defined-in-a-pscustom | # How to show auxiliary points for any curves defined in a pscustom?
I need to show the auxiliary points of any curves defined in pscustom such that I can easily locate the points during the development process.
The following MWE is my attempt to show such points, but fails.
\documentclass[pstricks,margin=1cm,preview]{standalone}
\begin{document}
\begin{pspicture}[showgrid](-6,-6)(6,6)
\pscustom[showpoints=true]
{
\psline(-4,-4)(-4,4)(4,4)(4,-4)
\closepath
}
\end{pspicture}
\end{document}
\documentclass[pstricks,margin=1cm,preview]{standalone}
• I suppose you mean dots. Right? A line is a line, there are no auciliary points. If you want to see the dots use the coordinates also outside \pscustom: \psdots(-4,-4)(-4,4)(4,4)(4,-4) – user2478 Sep 29 '16 at 18:07 | 2019-09-18 02:54:34 | {"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": 0.9381294846534729, "perplexity": 791.6447014500447}, "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/1568514573176.51/warc/CC-MAIN-20190918024332-20190918050332-00406.warc.gz"} |
https://publications.hse.ru/en/articles/251052782 | • A
• A
• A
• ABC
• ABC
• ABC
• А
• А
• А
• А
• А
Regular version of the site
## Search for lepton-flavour-violating decays of Higgs-like bosons
The European Physical Journal C - Particles and Fields. 2018. Vol. 78. No. 12. P. 1-12.
A search is presented for a Higgs-like boson with mass in the range 45 to 195 GeV/𝑐2GeV/c2 decaying into a muon and a tau lepton. The dataset consists of proton-proton interactions at a centre-of-mass energy of 8 TeV TeV , collected by the LHCb experiment, corresponding to an integrated luminosity of 2 fb −1 fb −1 . The tau leptons are reconstructed in both leptonic and hadronic decay channels. An upper limit on the production cross-section multiplied by the branching fraction at 95% confidence level is set and ranges from 22 pbpb for a boson mass of 45 GeV/𝑐2GeV/c2 to 4 pbpb for a mass of 195 GeV/𝑐2GeV/c2 . | 2019-07-18 21:50:55 | {"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": 0.9099713563919067, "perplexity": 1560.9660084976808}, "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/1563195525829.33/warc/CC-MAIN-20190718211312-20190718233312-00181.warc.gz"} |
https://zbmath.org/?q=an:0719.54003 | # zbMATH — the first resource for mathematics
Possible point-open types of subsets of the reals. (English) Zbl 0719.54003
Summary: If X is a topological space and $$\alpha$$ is an ordinal, then the point- open game of length $$\alpha$$ on X, abbreviated $$G_{\alpha}(X)$$, is the two person game of length $$\alpha$$ in which, on the $$\beta$$ th move $$(\beta <\alpha)$$, the first player (the “point picker”) picks a point of X and the second player (the “open set picker”) picks an open subset of X covering the point just played. The point picker wins iff the open sets thus picked cover X. The point-open type of X, abbreviated pot(X), is defined to be the smallest ordinal $$\alpha$$ such that the point picker has a winning strategy in $$G_{\alpha}(X)$$. This ordinal clearly exists and is no more than the cardinality of X. The main result of this paper is that if we assume the continuum hypothesis, then for every limit ordinal $$\alpha <\omega_ 1$$, there is a subset X of the real numbers such that $$pot(X)=\alpha$$. This solves a problem due to P. Daniels and G. Gruenhage [ibid. 37, No.1, 53-64 (1990; Zbl 0718.54018)].
##### MSC:
54A35 Consistency and independence results in general topology 03E50 Continuum hypothesis and Martin’s axiom 91A44 Games involving topology, set theory, or logic 03E15 Descriptive set theory
##### Keywords:
point-open game; point-open type; continuum hypothesis
Full Text:
##### References:
[1] Daniels, P.; Gruenhage, G., The point-open type of subsets of the reals, Topology appl., 37, 53-64, (1990) · Zbl 0718.54015 [2] Galvin, F., Indeterminacy of point-open games, Bull. acad. polon. sci., 26, 445-449, (1978) · Zbl 0392.90101 [3] Laver, R., On the consistency of Borel’s conjecture, Acta. math., 137, 151-169, (1976) · Zbl 0357.28003 [4] Telgársky, R., Spaces defined by topological games, Fund. math., 88, 193-223, (1975) · Zbl 0311.54025 [5] Telgársky, R., Spaces defined by topological games, II, Fund. math., 116, 189-207, (1983) · Zbl 0558.54029
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2021-05-08 18:30:01 | {"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": 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": 0.8723511099815369, "perplexity": 1331.528661109556}, "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-2021-21/segments/1620243988923.22/warc/CC-MAIN-20210508181551-20210508211551-00464.warc.gz"} |
http://mathhelpforum.com/algebra/88225-c3-question.html | # Math Help - C3 question
1. ## C3 question
f(x) = |2x + 5| for all real values of x
a) Sketch the graph y = f(x), showing the coordinates of any points where the graph meets the coordinate axes.
b) evaluate ff(-4)
g(x) = f(x + k) for all real values of x
c) state the value of the constant k for which g(x) is symmetrical about the y axis.
OK for part a i have sketched a line crossing the y axis at +5 and bouncing off the x axis at x=-2.5
Can anybody confirm this is right?
For part b i'm not sure what to do. I guess u work out f(-4)= |-8 + 5|
=|-3| = 3 ....???? then work out f(3)....????
part c im unsure of...
2. Originally Posted by djmccabie
f(x) = |2x + 5| for all real values of x
a) Sketch the graph y = f(x), showing the coordinates of any points where the graph meets the coordinate axes.
b) evaluate $ff(-4)$
g(x) = f(x + k) for all real values of x
c) state the value of the constant k for which g(x) is symmetrical about the y axis.
OK for part a i have sketched a line crossing the y axis at +5 and bouncing off the x axis at x=-2.5
Can anybody confirm this is right?
For part b i'm not sure what to do. I guess u work out f(-4)= |-8 + 5|
=|-3| = 3 ....???? then work out f(3)....????
part c im unsure of...
The points on the graph are correct. It would never cross the x-axis.
$f(x) = |2x + 5|$
$ff(-4):$
$f(f(-4)) = f( |2(-4) + 5| ) = f( |-8 + 5|) = f(|-3|) = f(3) = |2(3) + 5| = |6 + 5| = 11.$
So yes you are correct here as well.
$g(x) = f(x + k)$ for all real values of x
c) state the value of the constant k for which g(x) is symmetrical about the y axis.
$f(x) = |2x + 5|$
$g(x) = f(x+k) = |2(x+k) + 5| = |2x + 2k + 5|$
The answer would be $k = -2.5$. Try drawing that graph and you'll see it is symmetrical about the $y$-axis.
3. fixed it
4. Thanks a lot for your help (quite a lot today haha) just a bit unser about part C
I understand how you get |2x + 2k + 5|
But i'm not sure how you derive k=-x
5. Sorry i got that bit wrong, but i've fixed it now.
6. hi i still dont know how you get this :/ there are 2 unknows in the eaution and it is not equal to anything...
7. The only way you will have a symmetric graph of the form $y = |ax + c|$ is if c = 0. If $c \neq 0$ then it won't be symmetrical about the y-axis. So you want to work out what k to put in that will cancel out the +5.
8. THANKS! i understand it now | 2016-06-27 00:48:59 | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "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": 0.5923762321472168, "perplexity": 629.509275910125}, "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-2016-26/segments/1466783395613.65/warc/CC-MAIN-20160624154955-00006-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://proofwiki.org/wiki/Definition:Disconnected_(Topology)/Points | # Definition:Disconnected (Topology)/Points
Let $T = \left({S, \tau}\right)$ be a topological space.
Let $a, b \in S$.
Then $a$ and $b$ are disconnected (in $T$) if and only if they are not connected (in $T$). | 2020-08-15 10:44:04 | {"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": 0.9943201541900635, "perplexity": 198.62420582452611}, "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-2020-34/segments/1596439740838.3/warc/CC-MAIN-20200815094903-20200815124903-00433.warc.gz"} |
http://opus.bath.ac.uk/23763/ | Intrinsically biharmonic maps into homogeneous spaces
Reference:
Hornung, P. and Moser, R., 2012. Intrinsically biharmonic maps into homogeneous spaces. Advances in Calculus of Variations, 5 (4), 411–425.
Related documents:
This repository does not currently have the full-text of this item.
You may be able to access a copy if URLs are provided below. (Contact Author)
Official URL:
http://dx.doi.org/10.1515/ACV.2011.018
Abstract
The tension field $\tau(u)$ of a map $u$ from a domain $\Omega \subset \mathbb{R}^m$ into a manifold $N$ is the negative $L^2$-gradient of the Dirichlet energy. In this paper we study critical points of the intrinsic biharmonic energy functional $T(u) = \int_\Omega |\tau(u)|^2$ when $N$ is a homogeneous space. We derive an Euler-Lagrange equation which makes sense for all critical points of $T$, in contrast to previously known versions. We also obtain a partial regularity result for solutions to this equation for arbitrary domain dimension.
Details
Item Type Articles
CreatorsHornung, P.and Moser, R.
DOI10.1515/ACV.2011.018
Related URLs
URLURL Type
http://www.scopus.com/inward/record.url?scp=84870287320&partnerID=8YFLogxKUNSPECIFIED
DepartmentsFaculty of Science > Mathematical Sciences
Publisher StatementHornungMoser.pdf: The final publication is available at www.degruyter.com
RefereedYes
StatusPublished
ID Code23763 | 2016-10-23 03:17:21 | {"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": 0.7273563742637634, "perplexity": 1191.6468831682614}, "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-2016-44/segments/1476988719139.8/warc/CC-MAIN-20161020183839-00394-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://www.codex.wiki.br/Debian8Man3En/PodLaTeX3Pm | # Man page of Pod::LaTeX
## Pod::LaTeX
Section: User Contributed Perl Documentation (3pm)
Updated: 2013-05-20
### NAME
Pod::LaTeX - Convert Pod data to formatted Latex
### SYNOPSIS
use Pod::LaTeX;
my $parser = Pod::LaTeX->new ( );$parser->parse_from_filehandle;
$parser->parse_from_file ('file.pod', 'file.tex'); ### DESCRIPTION "Pod::LaTeX" is a module to convert documentation in the Pod format into Latex. The pod2latex command uses this module for translation. "Pod::LaTeX" is a derived class from Pod::Select. ### OBJECT METHODS The following methods are provided in this module. Methods inherited from "Pod::Select" are not described in the public interface. #### Data Accessors The following methods are provided for accessing instance data. These methods should be used for accessing configuration parameters rather than assuming the object is a hash. Default values can be supplied by using these names as keys to a hash of arguments when using the "new()" constructor. AddPreamble Logical to control whether a "latex" preamble is to be written. If true, a valid "latex" preamble is written before the pod data is written. This is similar to: \documentclass{article} \usepackage[T1]{fontenc} \usepackage{textcomp} \begin{document} but will be more complicated if table of contents and indexing are required. Can be used to set or retrieve the current value.$add = $parser->AddPreamble();$parser->AddPreamble?(1);
@]
If used in conjunction with
"AddPostamble"
a full latex document will be written that could be immediately processed by
"latex"
.
For some pod escapes it may be necessary to include the amsmath package. This is not yet added to the preamble automatically.
:
Logical to control whether a standard
"latex"
ending is written to the output file after the document has been processed. In its simplest form this is simply:
\end{document}
but can be more complicated if a index is required. Can be used to set or retrieve the current value.
$add =$parser->AddPostamble(); $parser->AddPostamble?(1); @] If used in conjunction with "AddPreaamble" a full latex document will be written that could be immediately processed by "latex" . : Head1Level The "latex" sectioning level that should be used to correspond to a pod "=head1" directive. This can be used, for example, to turn a "=head1" into a "latex" "subsection" . This should hold a number corresponding to the required position in an array containing the following elements: [0] chapter [1] section [2] subsection [3] subsubsection [4] paragraph [5] subparagraph Can be used to set or retrieve the current value:$parser->Head1Level?(2); $sect =$parser->Head1Level;
@]
Setting this number too high can result in sections that may not be reproducible in the expected way. For example, setting this to 4 would imply that
"=head3"
do not have a corresponding
"latex"
section (
"=head1"
would correspond to a
"paragraph"
).
A check is made to ensure that the supplied value is an integer in the range 0 to 5.
Default is for a value of 1 (i.e. a
"section"
).
:
Label
This is the label that is prefixed to all
"latex"
label and index entries to make them unique. In general, pods have similarly titled sections (NAME, DESCRIPTION etc) and a
"latex"
label will be multiply defined if more than one pod document is to be included in a single
"latex"
file. To overcome this, this label is prefixed to a label whenever a label is required (joined with an underscore) or to an index entry (joined by an exclamation mark which is the normal index separator). For example,
"\label{text}"
becomes
"\label{Label_text}"
.
Can be used to set or retrieve the current value:
$label =$parser->Label;
$parser->Label($label);
This label is only used if
"UniqueLabels"
is true. Its value is set automatically from the
"NAME"
field if
"ReplaceNAMEwithSection"
is true. If this is not the case it must be set manually before starting the parse.
Default value is
"undef"
.
:
LevelNoNum
Control the point at which
"latex"
section numbering is turned off. For example, this can be used to make sure that
"latex"
sections are numbered but subsections are not.
Can be used to set or retrieve the current value:
$lev =$parser->LevelNoNum; $parser->LevelNoNum?(2); @] The argument must be an integer between 0 and 5 and is the same as the number described in "Head1Level" method description. The number has nothing to do with the pod heading number, only the "latex" sectioning. Default is 2. (i.e. "latex" subsections are written as "subsection*" but sections are numbered). : MakeIndex Controls whether "latex" commands for creating an index are to be inserted into the preamble and postamble $makeindex = $parser->MakeIndex;$parser->MakeIndex(0);
Irrelevant if both
"AddPreamble"
and
"AddPostamble"
are false (or equivalently,
"UserPreamble"
and
"UserPostamble"
are set).
Default is for an index to be created.
:
ReplaceNAMEwithSection
This controls whether the
"NAME"
section in the pod is to be translated literally or converted to a slightly modified output where the section name is the pod name rather than NAME''.
If true, the pod segment
=head1 NAME
pod::name - purpose
is converted to the
"latex"
\section{pod::name\label{pod_name}\index{pod::name}}
Purpose
\subsection*{SYNOPSIS\label{pod_name_SYNOPSIS}%
\index{pod::name!SYNOPSIS}}
(dependent on the value of
"Head1Level"
and
"LevelNoNum"
). Note that subsequent
"head1"
directives translate to subsections rather than sections and that the labels and index now include the pod name (dependent on the value of
"UniqueLabels"
).
The
"Label"
is set from the pod name regardless of any current value of
"Label"
.
$mod =$parser->ReplaceNAMEwithSection;
$parser->ReplaceNAMEwithSection(0); Default is to translate the pod literally. : StartWithNewPage If true, each pod translation will begin with a "latex" "\clearpage" .$parser->StartWithNewPage?(1); $newpage =$parser->StartWithNewPage;
@]
Default is false.
:
TableOfContents
"AddPreamble"
is false or
"UserPreamble"
is set.
$toc =$parser->TableOfContents; $parser->TableOfContents?(1); @] Default is false. : UniqueLabels If true, the translator will attempt to make sure that each "latex" label or index entry will be uniquely identified by prefixing the contents of "Label" . This allows multiple documents to be combined without clashing common labels such as "DESCRIPTION" and "SYNOPSIS" $parser->UniqueLabels?(1); $unq =$parser->UniqueLabels;
@]
Default is true.
:
UserPreamble
User supplied
"latex"
preamble. Added before the pod translation data.
If set, the contents will be prepended to the output file before the translated data regardless of the value of
"AddPreamble"
.
"MakeIndex"
and
"TableOfContents"
will also be ignored.
:
UserPostamble
User supplied
"latex"
postamble. Added after the pod translation data.
If set, the contents will be prepended to the output file after the translated data regardless of the value of
"AddPostamble"
.
"MakeIndex"
will also be ignored.
:
### NOTES
Compatible with
"latex2e"
only. Can not be used with
"latex"
v2.09 or earlier.
A subclass of
"Pod::Select"
so that specific pod sections can be converted to
"latex"
by using the
"select"
method.
Some HTML escapes are missing and many have not been tested.
Pod::Parser, Pod::Select, pod2latex, Pod::Simple.
### AUTHORS
Tim Jenness <[email protected]>
Bug fixes and improvements have been received from: Simon Cozens <[email protected]>, Mark A. Hershberger <[email protected]>, Marcel Grunauer <[email protected]>, Hugh S Myers <[email protected]>, Peter J Acklam <[email protected]>, Sudhi Herle <[email protected]>, Ariel Scolnicov <[email protected]>, Adriano Rodrigues Ferreira <[email protected]>, R. de Vries <[email protected]> and Dave Mitchell <[email protected]>. | 2018-02-26 01:48:30 | {"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": 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": 0.7058253288269043, "perplexity": 4577.937306917928}, "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-2018-09/segments/1518891817908.64/warc/CC-MAIN-20180226005603-20180226025603-00013.warc.gz"} |
https://www.nature.com/articles/s41598-022-15362-9?error=cookies_not_supported&code=3914dd0b-166d-48ac-aed8-525060330242 | Skip to main content
Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.
# Variations in seismic parameters for the earthquakes during loading and unloading periods in the Three Gorges Reservoir area
## Abstract
As the largest water conservancy and hydropower project in China, the Three Gorges Reservoir is a weak seismic activity area before impoundment, but the frequency of earthquakes increases significantly after impoundment. The spatial density scanning method was used to obtain the characteristics of spatio-temporal earthquake distribution in the reservoir area during loading and unloading processes. The results show that the frequencies of earthquakes during the loading and unloading processes were higher than that during the low-water-level operation period, which is well explained by the acoustic emission test results. The seismic b-value, fractal dimension D, and spatial correlation length SCL can be used together to indicate stress criticality. To analyze the impacts of reservoir water loading and unloading on seismicity in the reservoir area, time-scan analyses were performed on the b-value, D-value, and SCL of earthquakes near the Zigui segment and the Badong segment. Previous studies argued that the time-varying characteristics of b-values do not hold predictive significance for earthquakes in the M4.0–6.2 range. However, our study found that the time-varying characteristics of b-values are of predictive significance for earthquakes around M4.0. These seismic parameters decrease significantly before moderate earthquakes but at different rates in different regions.
## Introduction
With the frequent occurrence of human activities, the problem of induced earthquakes has attracted more attention1. Especially in recent years, induced earthquakes have been mostly associated with the development of new energy sources such as shale gas, the exploration of geothermal energy, the construction of gas storage facilities, and mining2,3. Reservoir-induced earthquakes as a kind of induced earthquakes have attracted widespread concern in the early stage4,5. The construction of large-scale water conservancy and hydropower projects and periodic water impoundment affect the stability of the regional crust and sometimes trigger seismic activity. Since the 1950s, reservoir-induced earthquakes have been studied extensively. The earliest recorded reservoir-induced earthquake was the Lake Mead earthquake in 19454. In the 1960s, four reservoir-induced earthquakes of M ≥ 6.0 were reported5,6. Over 140 reservoir-induced earthquakes have been reported worldwide since the 1960s, none of which were above 6 in magnitude.
The occurrence of reservoir-induced earthquakes is related to many factors, such as regional geological structure, permeability of rock mass and tectonic fractures, regional stress fields, and water level change4,5,6. Among these factors, water load and pore pressure effects are the two main causative factors responsible for the induced earthquakes7,8. The impact of water on earthquakes in reservoir areas can be classified into the following two situations9. (1) There is a direct hydraulic connection between water and the fault. In this case, the water loading increases the pore pressure on the fault, resulting in a decrease in the effective stress7,8. In addition, the softening and weakening effect of water reduces the coefficient of friction on the fault plane and reduces the cohesive force, thereby causing earthquakes10,11. (2) There is no direct hydraulic connection between water and the fault. Reservoir impoundment or discharge causes changes in the local stress field below and around the reservoir and changes in the fault stress field, thereby inducing earthquakes2,9. Previous studies have also investigated the relationship between reservoir water level and seismicity12,13,14,15. Simpson et al.12 summarized that rate changes of reservoir water level is a significant factor in determining the reservoir-induced seismicity. Telesca et al.13,14 applied singular spectrum analysis to study the relationship between local seismicity and water level. The results showed that earthquake frequency is related to quasi periodic variation in the water level. Smirnov et al.15 pointed out that the amplitudes of the seasonal peaks of the induced earthquakes are not constant but vary significantly with time.
Three Gorges Reservoir is the largest water conservancy and hydropower project in China. Before reservoir impoundment, the reservoir area was characterized by weak seismicity. After reservoir impoundment, the frequency of earthquakes increased significantly. To ensure the safety of the reservoir area during earthquakes, a seismic monitoring network was built in 2001. The network has been in operation for more than 20 years. The data collected covered the whole time period before and after reservoir impoundment. The Three Gorges reservoir provides a natural experimental field and a good opportunity for studying reservoir-induced earthquakes. Some previous studies have focused on seismicity in the Three Gorges reservoir area. For example, Jiang et al.16 applied the epidemic-type aftershock sequence model to study the effect of reservoir water loading on earthquakes and concluded that the seismicity was stronger during the rapid loading stage than in the unloading stage. Zhang et al.17 conducted correlation analysis and impulse response analysis on earthquake and water level data from 2003 to 2009 and revealed the characteristics of rapid and delayed seismic responses to reservoir impoundment in the surrounding area. Zhang et al.18 analyzed the characteristics of the focal mechanism solution of the seismicity near the Fairy Mount fault in the Zigui area during the loading and unloading stages and discussed the seismogenic mechanism of the earthquakes in this region. Since 2008, the Three Gorges Reservoir has entered a periodic loading and unloading stage, and the reservoir water level fluctuates periodically between 145 and 175 m each year. Prior to September 2008, the seismicity in the reservoir area was dominated by micro-small earthquakes, and no earthquakes above M4.0 occurred. However, since 2008, earthquakes in the reservoir area have been more frequent than before.
What are the effects of the periodic impoundment and discharge processes of the Three Gorges reservoir on seismicity in the reservoir area? Are there differences in the characteristics of seismicity at different stages? If the characteristics differ, what is the cause? Based on these questions, this paper discusses seismic responses in the reservoir area to periodic loading and unloading stages from the perspectives of statistical seismology and rock mechanics experiments and analyzes the possible causes. It is very significant for promoting research on the seismogenic mechanisms of reservoir induced earthquakes and determination of seismic trends in reservoir areas.
## Geological structure of the study area
The Three Gorges reservoir is located in the upper reaches of the Yangtze River. The dam is built on top of the granite on the southeastern margin of the Huangling dome. The reservoir is controlled by two tectonic units, the Huangling dome and the Zigui basin. The Pre-Sinian crystalline basement and the Sinian–Cretaceous strata outcrop at the core and two wings of the Huangling dome. Cretaceous glutenite strata are distributed in the Fairy Mount fault zone to the southwest of the Huangling dome. Limestone and karst are widely distributed along the Gaoqiao fault at the western margin of the Zigui Basin and in the regions downstream of Fengjie19 (Fig. 1).
The faults that cross the reservoir include the Fairy Mount fault, the Nine-brook fault, the Tianyangping fault, the Yuanan fault, the Gaoqiao fault, and the Xinhua fault (Fig. 1). (1) Fairy Mount fault is a NNW-trending fault, which is located on the southwest side of the Huangling dome, 19 km from the dam site. The fault dips west at 60°–70° and is nearly 100 km long. The fault zone is mainly composed of breccia and cataclastic rocks, showing dextral shear compression. (2) Nine-brook fault is a nearly NS-trending fault and is located on the southwest side of the Huangling anticline, approximately 17 km from the dam site. The fault dips west at 50°–60° and shows tensional shear faulting. (3) Tianyangping fault is a NW-trending fault, which is located on the north wing of the Changyang anticline, with a total length of 60 km. Its west segment is cut off by the Fairy Mount fault. The Fairy Mount fault, the Nine-brook fault, and the Tianyangping fault converge and form a K shape. (4) Gaoqiao fault is a NE-trending fault on the western margin of the Zigui Basin. It shows compressive shear faulting. (5) Xinhua fault is located between the Shennongjia fault dome and the Huangling anticline, with a total length of 50 km. It consists of breccia, broken silt, and well-developed fault gouge.
## Data and methods
### Data
In 2001, the digital network for monitoring reservoir-induced earthquakes in the Three Gorges reservoir was completed and put into operation, consisting of 24 seismic stations. In 2012, the network was reconstructed, and was composed of 22 seismic stations. The Three Gorges reservoir began to impound in 2003 and entered a periodic water storage stage in 2008. The period from January to May is the period of reservoir water unloading, when the water level drops from 175 to 145 m. The period from June to August is the flood season, which is the stage for saving the reservoir storage capacity, during which the water level remains unchanged at 145 m. From September to December, the reservoir operates at high water levels, and the water level increased from 145 to 175 m (Fig. 2). This paper selects the reservoir water level and seismic data from June 2003 to April 2020 for analysis. Since the first impoundment of the reservoir, over 10,000 earthquakes have been recorded in the reservoir area. 92% of the earthquakes were M0.0–1.9 microearthquakes, and the remainder were small and moderate earthquakes (Fig. 3b,d). There were 788 M2.0–2.9 earthquakes, 71 M3.0–3.9 earthquakes, and 8 M4.0–4.9 earthquakes. The largest earthquake was the M5.1 earthquake in Badong on December 16, 2013. To ensure completeness of seismic data sets, complete magnitude (Mc) is estimated using ZMAP software20. As shown in Fig. 3, Mc is 0.8 (Fig. 3a,c).
## Research methods
1. 1.
b-value
Gutenberg and Richter21 proposed the Gutenberg–Richter relation that represents the distribution of earthquake magnitude and frequency: log N = a-bM. The coefficient a is mainly determined by the maximum earthquake magnitude in the sequence. The b-value is a function of the relative earthquake magnitude distribution and is an important parameter for measuring the level of seismicity, which reflects the stress state of the rocks22. Time variations in b-value with loading stress and time can reflect the initiation, propagation, and instability of rock cracks, which is of important physical significance. There are two main methods for estimating the b-value: the least-squares method and the maximum likelihood method23. The least-squares method linearly fits the M-logN relationship to obtain the b-value. The maximum likelihood method is based on the earthquake probability density function and applies the following formula to calculate the b-value20:
$$b = \frac{\log e}{{\overline{M} - M_{c} }}$$
(1)
The standard error of b is estimated using the formula20:
$$\sigma \left( b \right) = 2.3b^{2} \sqrt {\sum\limits_{i = 1}^{n} {\frac{{\left( {M_{i} - \overline{M}} \right)^{2} }}{{n\left( {n - 1} \right)}}} }$$
(2)
Here, $$\overline{M}$$ represents the average magnitude of the earthquake, n is the number of the earthquakes, and Mc represents the magnitude of completeness. According to previous studies, the maximum likelihood method is preferred in the practical calculation of the b-value. Because the maximum likelihood method provides an unbiased estimation based on simpler calculation, the results are more stable. However, the two methods are not stable if the sample size is small. In the calculation, it is necessary to select as many samples as possible and a small value of Mc.
1. 2.
Fractal dimension D and spatial correlation length (SCL)
Earthquakes are usually distributed in clusters, which can be quantified using fractal dimension values24. If the hypocenter distribution possesses fractal characteristics, then
$$C\left( r \right) = \frac{{2N_{r} \left( {R < r} \right)}}{{N\left( {N - 1} \right)}}$$
(3)
Nr((N) < r) is the number of seismic hypocenter pairs separated by distances less than r, and N is the total number of seismic events. If the hypocenter distribution shows fractal characteristics, then Cq(r) is a power function of r, i.e., $$C_{q} \left( r \right)\infty \;r^{{D_{2} }}$$. Here, D2 defines the correlation dimension23. In addition to the fractal dimension D, SCL can also be used to characterize the spatial distribution of hypocenters. Single-link cluster analysis is used to estimate the SCL of N consecutive events23. Initially, each independent hypocenter is connected to the nearest hypocenter to form a group of clusters. Then, each earthquake cluster is connected to its nearest earthquake cluster. This process is repeated until N events are connected to N-1 links25. In the entire process, the distance between any two clusters is calculated based on their geometric centers. According to previous studies25, SCL is defined as the median of the length distribution of N-1 links.
## Results
### Spatial variations in earthquakes in the reservoir area
To study the evolution of earthquakes during the periodic process of water loading and unloading, the spatial scanning method is used to analyze the characteristics of earthquake frequency variation. Figure 3 shows the spatial variations in the monthly frequency of earthquakes in the head area of the Three Gorges reservoir during loading and unloading periods, with a seismic scanning step of 0.1°. Spatially, earthquakes are mainly distributed along the Yangtze River, generally near the Zigui segment of the Fairy Mount fault and the Badong segment of the Gaoqiao fault within 10 km of both banks of the reservoir. Except Zigui and Badong area, a very small number of earthquakes scattered in some other regions. Therefore, in this study, only the earthquakes in the two regions are analyzed and discussed. During the two periods from January to May and from September to December, the overall frequency of earthquakes near the Fairy Mount fault was slightly higher than that in the Badong area. Whereas, during the period from June to August when the reservoir operated at a low water level of 145 m, the frequency of earthquakes in the Badong area was slightly higher than that in the Zigui area (Fig. 4).
Spatially, the seismicity in the Three Gorges reservoir area is consistent with the common features of reservoir-induced earthquakes5. Generally, the reservoir induced earthquakes are basically limited within 10 km of each bank of the reservoir, which is determined by the impact range of the water loading on the reservoir area and the limited seepage range of the reservoir area5,9. This limited range corresponds to the main area of adjustment of the tectonic stress field5. In addition, reservoir-induced earthquakes often occur near the intersections of faults, karst cave development areas, and contact zones with different lithologies. The intersection of the NW-trending Fairy Mount fault with the nearly NS-trending Nine-brook fault and the north end of the Fairy Mount fault are stress-concentrated regions, where the earthquakes are clustered. Moreover, multiple sets of joint fissures are developed in these areas, which have direct hydraulic relationships with reservoir water. A karst conduit system is developing in the Badong area, and Triassic weak detachment layers are developing in the area, which are conducive to the occurrence of reservoir-induced earthquakes26.
### Characteristics of temporal variation in earthquake frequency
We analyzed the time variations in magnitude and frequency of the earthquakes in the entire head area of the Three Gorges reservoir and the above two subregions. During the water loading period from September to December, the unloading period from January to May, and the low-water-level operation period from June to August, more than 90% of the earhthquakes are micro-earthquakes below M2.0. The proportions (amj) of earthquakes with same magnitudes to the total number of earthquakes in the corresponding three periods follow a descending trending with magnitude increases (Fig. 5a–c). The ratio (amj) of mj = 0.0–0.9 during the low-water-leve operation period from June to August is less than the other two stages, especially for the Zigui area (labeled with red solid line in Fig. 4a,b). Whereas, the ratio of mj = 1.0–1.9 during the low-water-leve operation period is larger than the other two stages (Fig. 4a,b). For the other magnitude ranges, the differences of the ratios in the three stages are very small. The blue and black solid line representing the ratios for the water loading and unloading periods almost duplicated, which denotes that the impact of water loading and unloading on seismicity are identical.
$$a_{mj} = \frac{{\sum\limits_{i}^{{}} {\left( {N_{mj} } \right)_{i} } }}{{\sum\limits_{i}^{{}} {\left( {\sum {N_{mj} } } \right)_{i} } }} \times 100\% ,\;\;\left( \begin{gathered} mj = 0.0 - 0.9,1.0 - 1.9,2.0 - 2.9, \\ 3.0 - 3.9,4.0 - 4.9,5.0 - 5.9 \\ \end{gathered} \right)$$
(4)
$$b_{mj} = \frac{{\sum\limits_{i}^{{}} {\left( {N_{mj} } \right)_{i} } }}{{\sum\limits_{i = 1}^{12} {\left( {\sum {N_{mj} } } \right)_{i} } }} \times 100\% ,\;\;\left( \begin{gathered} mj = 0.0 - 0.9,1.0 - 1.9,2.0 - 2.9, \\ 3.0 - 3.9,4.0 - 4.9,5.0 - 5.9 \\ \end{gathered} \right)$$
(5)
where Nmj is the monthly frequency of earthquakes with a magnitude of mj, mj is the earthquake magnitude, and i (from 1 to 5, from 6 to 8 and from 9 to 12) shows the unloading period, the low-water-level period and water loading period, respectively.
The proportions of earthquakes in the three periods out of the total number of earthquakes (bmj) were calculated (Fig. 5d–f), and the frequency of earthquakes in the loading and unloading stages was significantly higher than that in the low-water-level operation period. The numbers of micro-earthquakes below M2.0 in the loading and unloading stages in the Zigui area were generally 3 to 5 times the number of earthquakes in the low-water-level operation period, and the numbers of micro-earthquakes below M2.0 in the loading and unloading stages in the Badong area were approximately twice the number of earthquakes in the low-water-level operation period. During the process of reservoir water unloading from January to May, 3 earthquakes above M4.0 occurred in the Zigui area. During the low-water-level of 145 m operation period from June to August, 2 earthquakes above M4.0 occurred in the Badong area. During the loading process from September to December, a total of 4 earthquakes above M4.0 occurred in the reservoir area (Fig. 6). The impacts of reservoir water loading and unloading on seismicity in the reservoir area was mainly shown in the differences in micro-earthquakes and small earthquakes.
### Variations in b-value, fractal dimension value D, and SCL over time
The seismic b-value, fractal dimension D, and SCL can be used together to indicate stress criticality24. In general, the b-value is a function of rock properties and stress level24. If the earthquake distribution shows fractal characteristics, then D defines the correlation dimension, which is important for the prediction of seismic hazard27. SCL also can be an indicator of the critical state of earthquake nucleation. Time-scan analysis is performed on the b-value, D, and SCL of earthquakes in the Zigui and the Badong area. The scanning period was from June 2003 to April 2020 and the statistical parameters were estimated for consecutive groups of 200 events with a running step of 50 events.
Figure 7 shows the time variations in b-value, D, and SCL in the two areas. Figure 7a shows the b-value variations of earthquakes in the Zigui area. The b-value slowly decreased before moderate earthquakes and rapidly recovered after the main shocks. An M4.1 earthquake occurred on November 22, 2008, with a b-value of approximately 0.8. After the occurrence of the main shock, the b-value rapidly increased to approximately 1.0. After April 2009, the b-value began to gradually decrease. On October 31, 2012, the b-value decreased to 0.68, and an M3.2 earthquake sequence occurred in the Zigui area. After that, the b-value recovered rapidly and then decreased slowly. When the b-value decreased to the local minimum in March 2014, the M4.5 and M4.7 earthquakes occurred in the Zigui area. After the main shock, the b-value increased rapidly and then decreased slowly. In February 2017, an M4.0 earthquake occurred in the Zigui area. Afterward, the b-value continued to return to high values and continued to the present, during which no earthquakes above M4.0 occurred.
The b-values of the earthquakes in the Badong area also decreased rapidly before moderate earthquakes but recovered relatively slowly afterward (Fig. 7b). In 2003, many micro-small earthquakes instantly occurred due to water impoundment. The b-value during the period exceeded 1.0, which is a typical feature of reservoir induced earthquakes5. Later, b-values varied with water level changes. Since the water impoundment in September 2008, the b-value in this area has changed slowly, with minor local variations. In December (high-water-level operation period) 2013, when the water level reached 175 m, the b-value suddenly decreased to the background b-value (0.65). The time interval for the sudden change in the b-value was 12 months, and then the b-value slowly returned to the level before the main shock. The b-value started to decrease from January 2015, and the M4.3 and M4.1 earthquakes occurred in June 2017. Afterward, the b-value slowly recovered. An M4.1 earthquake occurred again in October 2018 when the b-value declined. In October 2018, the b-value recovered to a relatively high level and continued to the present, and the frequency of earthquakes has been significantly lower than in the past. The variations in SCL and D values were generally consistent with the trend in b-value variation, decreasing before the occurrence of a moderate earthquake and recovering after the main shock (Fig. 7b).
## Discussion
1. 1.
Characteristics of reservoir induced seismicity during different periods.
Previous studies show that reservoir induced seismicity can be classified into two types: rapid response and delayed response28. For the former type, the earthquakes are significantly correlated with water impoundment. Whereas, the relationship between earthquakes and water level changes is more complex during the late stage of impoundment29. In the case of the seismicity in the Three Gorges reservoir area as mentioned above, similar characteristics are shown. As a whole, the frequency of earthquakes during the loading and unloading periods was significantly higher than that during the low-water-level operation period (Figs. 4, 5).
Referring to the rock acoustic emission experiment results30,31, we explored the possible reasons. In the early stage of reservoir impoundment, with the increasing of the water level, some karst caves or abandoned mine caverns were flooded with water, resulting in frequent occurrences of collapse-related micro-earthquakes and small earthquakes32. These earthquakes could be categorized as instantaneous response of reservoir water impoundment and mainly clustered in the Badong area. With increasing water loading stress, reservoir water diffuses horizontally and penetrates along the fractures, and the increase in pore pressure is conducive to the propagation and coalescence of cracks11,29. Crack propagation and coalescence in turn promotes fluid pressure diffusion, resulting in a decrease in the effective stress of the fault28,29. The superposition of fluid pressure diffusion and water loading stress controls the coulomb stress of a fault. When the critical stress is reached, the fault slips due to instability. At this stage, moderate earthquakes are likely to occur. It is known that fluid pressure diffusion is a relatively slow process, therefore, there is a time-delay between water impoundment and earthquakes5,10 (Fig. 8).
Figure 8 shows the time variations of pore pressure and coulomb stress at the source area of the Badong M5.1 earthquake on 16, December 2013 with different hydraulic conductivity coefficients. From May 2003 to September 2006, the reservoir water level rose rapidly from 80 to 135 m, and then fluctuated between 135 and 145 m. During this period, the pore pressure and coulomb stress at the source increase exponentially. When the diffusion coefficient is small, the pore pressure diffusion under undrained effect cannot be ignored; while when the coefficient becomes larger, the pore pressure diffusion under drained effect is much larger than that under undrained pore pressure10. Therefore, during the period of initial impoundment, the porosity is very small and the pore pressure of the tight rock mass increases instantaneously due to the undrained effect. In the circumstance, some small earthquakes are induced. Figure 8 shows that the greater the hydraulic conductivity coefficient is, the greater the pore pressure and coulomb stress are. Since September 2006, when the reservoir water level shows a periodic changes, both the pore pressure and coulomb stress also exhibited periodic changes (Fig. 8). A significant time-delay positive correlation exists between the reservoir water level change and stress changes. When the Badong M5.1 earthquake occurred, the coulomb stress at the source area was greater than 0.1 MPa and indicated a high risk at this time. During the high-water-level operation, pore pressure diffusion under drainage effect especially along the fault and large porosity rock mass resulted in the occurrences of moderate earthquakes26.
The acoustic emission experiment results showed that there was no acoustic emission event during the period when the loading stress remained unchanged at a low level30,31. Correspondingly, the number of the earthquakes in the Three Gorges reservoir area was relatively low during the low-water-level operation period from June to August. However, due to the gradual seepage and diffusion of the reservoir water to the deep, seismicity continued for a long time, but the frequency of earthquakes was lower than that during the loading and unloading periods.
1. 2.
Significant decreases in the b-value, D2, and SCL are of indicative for the prediction of moderate earthquakes in the Three Gorges reservoir area.
Parsons et al.33 argued that the time-varying characteristics of b-value do not hold predictive significance for earthquakes in the M4.0–6.2 range. However, our study show opposite opinion that the parameters such as b-values in the Badong and Zigui areas all exhibited significant decreases before moderate-magnitude earthquakes around M4.0 (Fig. 9). The M4.5 and M4.7 earthquakes occurred in March 2014, when b-values decreased to the local minimum. After the main shock, the b-values quickly recovered and rapidly entered a state of decrease. In February 2017, an M4.0 earthquake occurred in the Zigui area (Fig. 9a). Afterward, b continued to return to high values and remained high to the present, during which no earthquakes above M4.0 occurred. In the Badong area, there was also a significant decrease in b before moderate-magnitude earthquakes. During the high-water-level (175 m) operation period in December 2013, the b-value suddenly decreased to the level of the regional background b-value. The largest earthquake since the first impoundment of the reservoir area occurred. Afterward, the b-value returned to the level before the main shock. When the b-value decreased to the level of background b-value again in June 2017, an M4.3 earthquake occurred (Fig. 9b). The study of Nuannin34 also supports our finding that the b-value is indicative of the prediction of moderate-magnitude earthquakes. Gupta35 also pointed out that some precursory changes in b-value, D, stress drop and corner frequency have been noticed prior to moderate earthquakes in the Koyna-warna reservoir area. With the development of seismic observations, more and more researches reveal that the decrease in the b-value can be a precursory before large earthquakes36.
The long-term variations in the b-value reflect the effect of increasing pore pressure diffusion37,38. For a given region, a decreased b-value can be a good indicator for stress increase39 or pore pressure diffusion40,41. In the servo control test of the whole rock fracture process, the b-value decreased with increasing stress before the fracture and decreased significantly when the rock was close to fracture42. After the rock started to fracture, the b-value remained low. When the large stress drop stopped and the rock had broken and maintained a substantially constant residual strength, the b-value increased again when the dislocation occurred again. The same phenomenon has been observed in the stick–slip process of immature faults43. According to the experimental results of Lei et al.44, the increases in D and SCL reflect the propagation of microcracks, which indicates the nucleation and propagation of faults. The b-value, D, and SCL decreased rapidly when moderate earthquakes occurred, indicating that the proportion of large-scale microcracks began to increase rapidly45. The microfractures inside the rocks began to change from disorder to order. The geometric fractal dimension changed from large to small. When the stress is close to the peak strength, the b-value, the fractal dimension D, and the SCL decrease to local minima, the clustering of seismic events is obvious, and the cracks in rock start to coalesce and eventually lead to rock instability and failure. Statistical parameters are of great significance for earthquake disaster assessment, and are helpful to understand the evolution process of earthquakes (Smith 1981). In particular, the quantitative analysis of b-value changes can provide quantitative information for probabilistic prediction of major earthquakes and are indeed indicative for earthquake trend analysis.
1. 3.
Seismic parameters such as b-value, D-value, and SCL-value decrease significantly before moderate earthquakes but at different rates in different regions.
As mentioned above, seismic parameters before the occurrence of moderate earthquakes in the reservoir area showed significant decreases. However, the parameters decreased at different rates in the two areas. In the vicinity of the Zigui area, the b-value decreased slowly before the occurrence of a moderate earthquake, and rapidly recovered within short time after the main shock, and then continued to decrease D and SCL also decreased overall, reaching local minima at the time of the main shock, but they decreased more rapidly than the b-value. On the other hand, the b-value decreased relatively rapidly in the Badong area but recovered more slowly after the earthquake D and SCL also exhibited significant time dependence, and both decreased to local minima at the time of the main shock. Rock mechanics experiments confirmed the existence of these two conditions.
The study of Rivière et al.46 showed that the rate of change in the b-value is closely related to change in normal stress and shear stress. The experimental results show that a fault is in a stick–slip state under high normal stress and shear stress46. When the stress increases, the b-value decreases till to the local maximum, the b-value decreases rapidly. When the fault is in the transitional stage between stick–slip and steady slip, the normal stress and shear stress are slightly lower than in the stick–slip stage, and the b-value decreases at a slower rate. In addition, the rate of change in parameters such as b may reflect crack propagation speed, which is also closely related to rock properties, the characteristics of the internal rock structure, and the density of the cracks47. Rocks with higher strength and brittleness store more elastic energy in the elastic stage30. When a rock is about to fail, the stored energy is released intensively, and the reduction in the acoustic emission b-value is greater48. The difference in regional geological tectonic conditions may be one of the reasons that caused the difference in the rates of change in the b-value, D, and SCL between the two regions.
## Conclusion
1. 1.
There are many similarities between the seismicity characteristics of the Three Gorges reservoir area under periodic water loading and the results of the rock acoustic emission experiment. The spatial density scanning method was used to obtain the characteristics of spatio-temporal earthquake distribution in the reservoir area during loading and unloading processes. The results show that the frequencies of earthquakes during the loading and unloading processes were higher than that during the low-water-level operation period, which is well explained by the acoustic emission experiment results. The impact of reservoir water loading and unloading on seismicity in the reservoir area is mainly exhibited in the differences in microearthquakes and small earthquakes, while the relationship between relatively large earthquakes and reservoir water loading and unloading is not significant.
2. 2.
The set of seismic statistical parameters are analyzed using the time-scan method with a fixed number of events. The time dependence of seismic activity in the first area of the Three Gorges Reservoir is analyzed, and the anomaly characteristics before moderate (M4.0 +) earthquakes are distinguished. Before the moderate earthquake, the reservoir area showed a significant decrease in the b-value, D and SCL value. This shows that the time variations of the statistical parameters can reflect the characteristics of seismicity, and the critical behavior of the pre-earthquake seismogenic system has important guiding significance for seismic risk analysis. However, at this stage, it is still difficult to rely solely on these statistical parameters to predict earthquakes, and more detailed work needs to be done to distinguish the implicit information unrelated to seismic activity in these parameters. In the future work, we plan to compute the stress drops in loading and unloading processes and analyze the effect of stress drop differences on parameter variations.
## Data availability
The data sets generated and/or analysed during the study period should not be made publicly available [since the data comes from the seismic network built by the Three Gorges Group Enterprise, the author has the right to use the data but has no public authority], but can be obtained from the corresponding author if reasonable requirements exist.
## References
1. Atkinson, G. M., Eaton, D. W. & Igonin, N. Developments in understanding seismicity triggered by hydraulic fracturing. Nat. Rev. Earth Environ. 1, 264–277 (2020).
2. Foulger, G. R., Wilson, M. P. & Gluyas, J. G. Global review of human-induced earthquakes. Earth Sci. Rev. 178, 438–514 (2018).
3. Grigoli, F. et al. Current challenges in monitoring, discrimination, and management of induced seismicity related to underground industrial activities: a European perspective. Rev. Geophys. 55, 310–340 (2017).
4. Carder, D. S. Seismic investigations in the Boulder Dam area, 1940–1944, and the influence of reservoir loading on earthquake activity. Bull. Seismol. Soc. Am. 35, 175–192 (1945).
5. Gupta, H. K., Tastogi, B. K. & Narain, H. Common features of the reservoir-associated seismic activities. Bull. Seismol. Soc. Am. 62(2), 481–492 (1972).
6. McGarr, A. Maximum magnitude earthquakes induced by fluid injection. J Geophys. Res. 119(2), 1008–1019 (2014).
7. Gahalaut, K. & Hassoup, A. Role of fluids in the earthquake occurrence around Aswan reservoir, Egypt. J. Geophys. Res. 117, B02303 (2012).
8. Gahalaut, K., Tuan, T. A. & Purnachandra, R. N. Rapid and delayed earthquake triggering by the Song Tranh 2 reservoir, Vietnam. Bull. Seismol. Soc. Am. 106(5), 2389–2394 (2016).
9. Ellsworth, W. Injection-induced earthquakes. Science 341, 1225942 (2013).
10. Talwani, P. & Acree, S. Pore pressure diffusion and the mechanism of reservoir-induced seismicity. Pure Appl. Geophys. 122, 947–965 (1985).
11. Hariri, M. E., Abercrombie, R. E., Rowe, C. A. & Nascimento, A. F. The role of fluids in triggering earthquakes: observations from reservoir induced seismicity in Brazil. Geophys. J. Int. 181, 1566–1574 (2010).
12. Simpson, D. W., Stachnik, J. C. & Negmatoullaev, S. K. Rate of change in lake level and its impact on reservoir triggered seismicity. Bull. Seismol. Soc. Am. 108(5B), 2943–2954 (2018).
13. Telesca, L., Matcharasvili, T., Chelidze, T. & Zhukova, N. Relationship between seismicity and water level in the Enguri high dam area (Georgia) using the singular spectrum analysis. Nat. Hazards Earth Syst. Sci. 12, 2479–2485 (2012).
14. Telesca, L. et al. Analysis of the relationship between water level temporal changes and seismicity in the Mingechevir reservoir (Azerbaijan). J. Seismol. 24, 937–952 (2020).
15. Smirnov, V. B. et al. On the dynamics of the seasonal components of induced seismicity in the Koyna-Warna region, Western India. Izv. Phys. Solid Earth 54, 632–640 (2018).
16. Jiang, H. K., Song, J., Wu, Q., Li, J. & Qu, J. H. Quantitative detection of fluid-triggered microseismic activity in the Three Gorges Reservoir area based on ETAS model. Chin. J. Geophys. 55(7), 2341–2352 (2012).
17. Zhang, L. F. et al. Analysis of the relationship between water level fluctuation and seismicity in the Three Gorges Reservoir (China). Geodesy Geodyn. 2, 96–102 (2017).
18. Zhang, L. F. et al. A possible mechanism of reservoir-induced earthquakes in the Three Gorges Reservoir, Central China. Bull. Seismol. Soc. Am. 108(5B), 3016–3028 (2018).
19. Yi, L., Zhao, D. & Liu, C. Preliminary study of reservoir-induced seismicity in the Three Gorges Reservoir, China. Seismol. Res. Lett. 83(5), 806–814. https://doi.org/10.1785/0220110132 (2012).
20. Van Stiphout, T., Schorlemmer, D. & Wiemer, S. The effect of uncertainties on estimates of background seismicity rate. Bull. Seismol. Soc. Am. 101(2), 482–494 (2011).
21. Gutenberg, B. & Richter, C. F. Frequency of earthquakes in California. Bull. Seismol. Soc. Am. 34, 185–188 (1944).
22. Scholz, C. H. The frequency–magnitude relation of micro-fracturing in rock and its relation to earthquakes. Bull. Seismol. Soc. Am. 58, 399–415 (1968).
23. Chen, C., Wang, W., Chang, Y., Wu, Y. & Lee, Y. A correlation between the b-value and the fractal dimension from the aftershock sequence of the 1999 Chi-Chi, Taiwan, earthquake. Geophys. J. Int. 167, 1215–1219 (2006).
24. Lei, X. L. & Satoh, T. Indicators of critical point behavior prior to rock failure inferred from pre-failure damage. Tectonophysics 431, 97–111 (2007).
25. Frohlich, C. & Davis, S. D. Single-link cluster analysis as a method to evaluate spatial and temporal properties of earthquake catalogues. Geophys J Int. 100, 19–32 (1990).
26. Zhang, H., Cheng, H., Pang, Y., Shi, Y. & Yuen, D. A. Influence of the impoundment of the Three Gorges Reservoir on the micro-seismicity and the 2013 M5.1 Badong earthquake (Yangtze, China). Phys. Earth Planet. Interiors 261, 98–106 (2016).
27. Nakaya, S. Fractal properties of seismicity in regions affected by large, shallow earthquakes in western Japan: implications for fault formation processes based on abinary fractal fracture network model. J. Geophys. Res. 110, B01310 (2005).
28. Simpson, D. W., Leith, W. S. & Scholz, C. H. Two types of reservoir-induced seismicity. Bull. Seismol. Soc. Am. 78(6), 2025–2040 (1988).
29. Reoloffs, E. A. Fault stability changes induced beneath a reservoir with cyclic variations in water level. J. Geophys. Res. 93, 2107–2124 (1988).
30. Dong, L. J., Shu, W. W., Sun, D. Y., Li, X. B. & Zhang, L. Y. Pre-alarm system based on real-time monitoring and numerical simulation using internet of things and cloud computing for tailings dam in mines. IEEE Access 5, 21080–21089 (2017).
31. Dong, L. J. et al. Velocity-free localization of autonomous driverless vehicles in underground intelligent mines. IEEE Trans. Veh. Technol. 69, 9292–9303 (2020).
32. Yao, Y. S. et al. Influences of the Three Gorges Project on seismic activities in the reservoir area. Sci. Bull. 62, 1089–1098 (2017).
33. Parsons, T. Forecast experiment: do temporal and spatial b value variations along the Calaveras fault portend M4.0 earthquakes?. J. Geophys. Res. 112, B03308 (2007).
34. Nuannin, P. The potential of b-value variations as earthquake precursors for small and large events. Acta Universitatis Upsaliensis. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology. 183. 46 (2006).
35. Gupta, H. K. Short-term earthquake forecasting may be feasible at Koyna, India. Tectonophysics 338, 353–357 (2001).
36. Mogi, K. Magnitude-frequency relationship for elastic shocks accompanying fractures of various materials and some related problems in earthquakes. Bull. Earthq. Res. Inst. Univ. Tokyo 40, 831–883 (1962).
37. Mogi, K. Earthquakes and fractures. Tectonophysics 5, 35–55 (1967).
38. Imoto, M. Changes in the magnitude—frequency b-value prior to large (M6.0) earthquakes in Japan. Tectonophysics 193(4), 311–325 (1991).
39. Smith, W. The b-value as an earthquake precursor. Nature 289, 136–139 (1981).
40. Schorlemmer, D., Wiemer, S. & Wyss, M. Variations in earthquake-size distribution across different stress regimes. Nature 437(7058), 539–542 (2005).
41. Hainzl, S. & Fischer, T. Indications for a successively triggered rupture growth underlying the 2000 earthquake swarm in Vogtland/NW Bohemia. J. Geophys. Res. 107, 2338 (2002).
42. Hainzl, S., Fischer, T. & Dahm, T. Seismicity-based estimation of the driving fluid pressure in the case of swarm activity in Western Bohemia. Geophys. J. Int. 191, 271–281 (2012).
43. Main, I. G. Damage mechanics with long-range interactions: correlation between the seismic b value and the fractal two-point correlation dimension. Geophys. J. Int. 111, 531–541 (1992).
44. Lei, X., Wang, Z. & Su, J. Possible link between long-term and short-term water injections and earthquakes in salt mine and shale gas site in Changning, south Sichuan Basin, China. Earth Planet. Phys. 3, 510–525 (2019).
45. Wyss, M., Sammis, C. G., Nadeau, R. M. & Wiemer, S. Fractal dimension and b-value on creeping and locked patches of the San Andreas fault near Parkfield, California. Bull. Seismol. Soc. Am. 94, 410–421 (2004).
46. Rivière, J., Lv, Z., Johnson, P. A. & Marone, C. Evolution of b-value during the seismic cycle: insights from laboratory experiments on simulated faults. Earth Planet. Sci. Lett. 482, 407–413 (2018).
47. Tang, J., Wang, H. & Wen, L. Evolution characteristics of reservoir rock cracks based on acoustic emission fractal parameter analysis. Geophys. Prospect. Pet. 56(6), 775–781 (2017).
48. Wang, C. L. & Shi, F. Experimental study on acoustic emission and b-value dynamic characteristics of different hard rock failure. China Min. 7(27), 130–135 (2018).
Download references
## Acknowledgements
This work was supported by the China National Key Research and Development Plan (Grant No. 2018YFE0206100), National Natural Science Foundation of China (42174177, 41772384), Natural Science Foundation of Hubei Province of China (2021CFA035), Science for Earthquake Resilience (XH191704) and the Foundation of the Three Gorges Company (0799216).
## Author information
Authors
### Contributions
L.Z.: conceptualization, methodology, software, investigation, formal analysis, writing- original draft; W.L.: data curation, verification; Z.C.: conducting a research and investigation process, data collection; J.L.: programming, software development; Y.Y.: resources, supervision; G.T.: provision of data and instruments; Y.Z., Z.Z.: visualization, writing-review and editing.
### Corresponding author
Correspondence to Lifen Zhang.
## Ethics declarations
### Competing interests
The authors declare no competing interests.
## Additional information
### Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
## Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Reprints and Permissions
## About this article
### Cite this article
Zhang, L., Liao, W., Chen, Z. et al. Variations in seismic parameters for the earthquakes during loading and unloading periods in the Three Gorges Reservoir area. Sci Rep 12, 11211 (2022). https://doi.org/10.1038/s41598-022-15362-9
Download citation
• Received:
• Accepted:
• Published:
• DOI: https://doi.org/10.1038/s41598-022-15362-9
## Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.
## Search
### Quick links
Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing | 2022-08-08 17:49:01 | {"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": 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": 0.5503198504447937, "perplexity": 3699.40655560538}, "config": {"markdown_headings": true, "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-2022-33/segments/1659882570868.47/warc/CC-MAIN-20220808152744-20220808182744-00293.warc.gz"} |
http://forge.cbp.ens-lyon.fr/redmine/projects/txm/repository/revisions/2486/entry/tmp/org.txm.statsengine.r.core.win32/res/win32/library/BH/include/boost/asio/basic_socket.hpp | Statistics
| Revision:
root / tmp / org.txm.statsengine.r.core.win32 / res / win32 / library / BH / include / boost / asio / basic_socket.hpp @ 2486
1 // // basic_socket.hpp // ~~~~~~~~~~~~~~~~ // // Copyright (c) 2003-2015 Christopher M. Kohlhoff (chris at kohlhoff dot com) // // Distributed under the Boost Software License, Version 1.0. (See accompanying // file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) // #ifndef BOOST_ASIO_BASIC_SOCKET_HPP #define BOOST_ASIO_BASIC_SOCKET_HPP #if defined(_MSC_VER) && (_MSC_VER >= 1200) # pragma once #endif // defined(_MSC_VER) && (_MSC_VER >= 1200) #include #include #include #include #include #include #include #include #include namespace boost { namespace asio { /// Provides socket functionality. /** * The basic_socket class template provides functionality that is common to both * stream-oriented and datagram-oriented sockets. * * @par Thread Safety * @e Distinct @e objects: Safe.@n * @e Shared @e objects: Unsafe. */ template class basic_socket : public basic_io_object, public socket_base { public: /// (Deprecated: Use native_handle_type.) The native representation of a /// socket. typedef typename SocketService::native_handle_type native_type; /// The native representation of a socket. typedef typename SocketService::native_handle_type native_handle_type; /// The protocol type. typedef Protocol protocol_type; /// The endpoint type. typedef typename Protocol::endpoint endpoint_type; /// A basic_socket is always the lowest layer. typedef basic_socket lowest_layer_type; /// Construct a basic_socket without opening it. /** * This constructor creates a socket without opening it. * * @param io_service The io_service object that the socket will use to * dispatch handlers for any asynchronous operations performed on the socket. */ explicit basic_socket(boost::asio::io_service& io_service) : basic_io_object(io_service) { } /// Construct and open a basic_socket. /** * This constructor creates and opens a socket. * * @param io_service The io_service object that the socket will use to * dispatch handlers for any asynchronous operations performed on the socket. * * @param protocol An object specifying protocol parameters to be used. * * @throws boost::system::system_error Thrown on failure. */ basic_socket(boost::asio::io_service& io_service, const protocol_type& protocol) : basic_io_object(io_service) { boost::system::error_code ec; this->get_service().open(this->get_implementation(), protocol, ec); boost::asio::detail::throw_error(ec, "open"); } /// Construct a basic_socket, opening it and binding it to the given local /// endpoint. /** * This constructor creates a socket and automatically opens it bound to the * specified endpoint on the local machine. The protocol used is the protocol * associated with the given endpoint. * * @param io_service The io_service object that the socket will use to * dispatch handlers for any asynchronous operations performed on the socket. * * @param endpoint An endpoint on the local machine to which the socket will * be bound. * * @throws boost::system::system_error Thrown on failure. */ basic_socket(boost::asio::io_service& io_service, const endpoint_type& endpoint) : basic_io_object(io_service) { boost::system::error_code ec; const protocol_type protocol = endpoint.protocol(); this->get_service().open(this->get_implementation(), protocol, ec); boost::asio::detail::throw_error(ec, "open"); this->get_service().bind(this->get_implementation(), endpoint, ec); boost::asio::detail::throw_error(ec, "bind"); } /// Construct a basic_socket on an existing native socket. /** * This constructor creates a socket object to hold an existing native socket. * * @param io_service The io_service object that the socket will use to * dispatch handlers for any asynchronous operations performed on the socket. * * @param protocol An object specifying protocol parameters to be used. * * @param native_socket A native socket. * * @throws boost::system::system_error Thrown on failure. */ basic_socket(boost::asio::io_service& io_service, const protocol_type& protocol, const native_handle_type& native_socket) : basic_io_object(io_service) { boost::system::error_code ec; this->get_service().assign(this->get_implementation(), protocol, native_socket, ec); boost::asio::detail::throw_error(ec, "assign"); } #if defined(BOOST_ASIO_HAS_MOVE) || defined(GENERATING_DOCUMENTATION) /// Move-construct a basic_socket from another. /** * This constructor moves a socket from one object to another. * * @param other The other basic_socket object from which the move will * occur. * * @note Following the move, the moved-from object is in the same state as if * constructed using the @c basic_socket(io_service&) constructor. */ basic_socket(basic_socket&& other) : basic_io_object( BOOST_ASIO_MOVE_CAST(basic_socket)(other)) { } /// Move-assign a basic_socket from another. /** * This assignment operator moves a socket from one object to another. * * @param other The other basic_socket object from which the move will * occur. * * @note Following the move, the moved-from object is in the same state as if * constructed using the @c basic_socket(io_service&) constructor. */ basic_socket& operator=(basic_socket&& other) { basic_io_object::operator=( BOOST_ASIO_MOVE_CAST(basic_socket)(other)); return *this; } // All sockets have access to each other's implementations. template friend class basic_socket; /// Move-construct a basic_socket from a socket of another protocol type. /** * This constructor moves a socket from one object to another. * * @param other The other basic_socket object from which the move will * occur. * * @note Following the move, the moved-from object is in the same state as if * constructed using the @c basic_socket(io_service&) constructor. */ template basic_socket(basic_socket&& other, typename enable_if::value>::type* = 0) : basic_io_object(other.get_io_service()) { this->get_service().template converting_move_construct( this->get_implementation(), other.get_implementation()); } /// Move-assign a basic_socket from a socket of another protocol type. /** * This assignment operator moves a socket from one object to another. * * @param other The other basic_socket object from which the move will * occur. * * @note Following the move, the moved-from object is in the same state as if * constructed using the @c basic_socket(io_service&) constructor. */ template typename enable_if::value, basic_socket>::type& operator=( basic_socket&& other) { basic_socket tmp(BOOST_ASIO_MOVE_CAST2(basic_socket< Protocol1, SocketService1>)(other)); basic_io_object::operator=( BOOST_ASIO_MOVE_CAST(basic_socket)(tmp)); return *this; } #endif // defined(BOOST_ASIO_HAS_MOVE) || defined(GENERATING_DOCUMENTATION) /// Get a reference to the lowest layer. /** * This function returns a reference to the lowest layer in a stack of * layers. Since a basic_socket cannot contain any further layers, it simply * returns a reference to itself. * * @return A reference to the lowest layer in the stack of layers. Ownership * is not transferred to the caller. */ lowest_layer_type& lowest_layer() { return *this; } /// Get a const reference to the lowest layer. /** * This function returns a const reference to the lowest layer in a stack of * layers. Since a basic_socket cannot contain any further layers, it simply * returns a reference to itself. * * @return A const reference to the lowest layer in the stack of layers. * Ownership is not transferred to the caller. */ const lowest_layer_type& lowest_layer() const { return *this; } /// Open the socket using the specified protocol. /** * This function opens the socket so that it will use the specified protocol. * * @param protocol An object specifying protocol parameters to be used. * * @throws boost::system::system_error Thrown on failure. * * @par Example * @code * boost::asio::ip::tcp::socket socket(io_service); * socket.open(boost::asio::ip::tcp::v4()); * @endcode */ void open(const protocol_type& protocol = protocol_type()) { boost::system::error_code ec; this->get_service().open(this->get_implementation(), protocol, ec); boost::asio::detail::throw_error(ec, "open"); } /// Open the socket using the specified protocol. /** * This function opens the socket so that it will use the specified protocol. * * @param protocol An object specifying which protocol is to be used. * * @param ec Set to indicate what error occurred, if any. * * @par Example * @code * boost::asio::ip::tcp::socket socket(io_service); * boost::system::error_code ec; * socket.open(boost::asio::ip::tcp::v4(), ec); * if (ec) * { * // An error occurred. * } * @endcode */ boost::system::error_code open(const protocol_type& protocol, boost::system::error_code& ec) { return this->get_service().open(this->get_implementation(), protocol, ec); } /// Assign an existing native socket to the socket. /* * This function opens the socket to hold an existing native socket. * * @param protocol An object specifying which protocol is to be used. * * @param native_socket A native socket. * * @throws boost::system::system_error Thrown on failure. */ void assign(const protocol_type& protocol, const native_handle_type& native_socket) { boost::system::error_code ec; this->get_service().assign(this->get_implementation(), protocol, native_socket, ec); boost::asio::detail::throw_error(ec, "assign"); } /// Assign an existing native socket to the socket. /* * This function opens the socket to hold an existing native socket. * * @param protocol An object specifying which protocol is to be used. * * @param native_socket A native socket. * * @param ec Set to indicate what error occurred, if any. */ boost::system::error_code assign(const protocol_type& protocol, const native_handle_type& native_socket, boost::system::error_code& ec) { return this->get_service().assign(this->get_implementation(), protocol, native_socket, ec); } /// Determine whether the socket is open. bool is_open() const { return this->get_service().is_open(this->get_implementation()); } /// Close the socket. /** * This function is used to close the socket. Any asynchronous send, receive * or connect operations will be cancelled immediately, and will complete * with the boost::asio::error::operation_aborted error. * * @throws boost::system::system_error Thrown on failure. Note that, even if * the function indicates an error, the underlying descriptor is closed. * * @note For portable behaviour with respect to graceful closure of a * connected socket, call shutdown() before closing the socket. */ void close() { boost::system::error_code ec; this->get_service().close(this->get_implementation(), ec); boost::asio::detail::throw_error(ec, "close"); } /// Close the socket. /** * This function is used to close the socket. Any asynchronous send, receive * or connect operations will be cancelled immediately, and will complete * with the boost::asio::error::operation_aborted error. * * @param ec Set to indicate what error occurred, if any. Note that, even if * the function indicates an error, the underlying descriptor is closed. * * @par Example * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * boost::system::error_code ec; * socket.close(ec); * if (ec) * { * // An error occurred. * } * @endcode * * @note For portable behaviour with respect to graceful closure of a * connected socket, call shutdown() before closing the socket. */ boost::system::error_code close(boost::system::error_code& ec) { return this->get_service().close(this->get_implementation(), ec); } /// (Deprecated: Use native_handle().) Get the native socket representation. /** * This function may be used to obtain the underlying representation of the * socket. This is intended to allow access to native socket functionality * that is not otherwise provided. */ native_type native() { return this->get_service().native_handle(this->get_implementation()); } /// Get the native socket representation. /** * This function may be used to obtain the underlying representation of the * socket. This is intended to allow access to native socket functionality * that is not otherwise provided. */ native_handle_type native_handle() { return this->get_service().native_handle(this->get_implementation()); } /// Cancel all asynchronous operations associated with the socket. /** * This function causes all outstanding asynchronous connect, send and receive * operations to finish immediately, and the handlers for cancelled operations * will be passed the boost::asio::error::operation_aborted error. * * @throws boost::system::system_error Thrown on failure. * * @note Calls to cancel() will always fail with * boost::asio::error::operation_not_supported when run on Windows XP, Windows * Server 2003, and earlier versions of Windows, unless * BOOST_ASIO_ENABLE_CANCELIO is defined. However, the CancelIo function has * two issues that should be considered before enabling its use: * * @li It will only cancel asynchronous operations that were initiated in the * current thread. * * @li It can appear to complete without error, but the request to cancel the * unfinished operations may be silently ignored by the operating system. * Whether it works or not seems to depend on the drivers that are installed. * * For portable cancellation, consider using one of the following * alternatives: * * @li Disable asio's I/O completion port backend by defining * BOOST_ASIO_DISABLE_IOCP. * * @li Use the close() function to simultaneously cancel the outstanding * operations and close the socket. * * When running on Windows Vista, Windows Server 2008, and later, the * CancelIoEx function is always used. This function does not have the * problems described above. */ #if defined(BOOST_ASIO_MSVC) && (BOOST_ASIO_MSVC >= 1400) \ && (!defined(_WIN32_WINNT) || _WIN32_WINNT < 0x0600) \ && !defined(BOOST_ASIO_ENABLE_CANCELIO) __declspec(deprecated("By default, this function always fails with " "operation_not_supported when used on Windows XP, Windows Server 2003, " "or earlier. Consult documentation for details.")) #endif void cancel() { boost::system::error_code ec; this->get_service().cancel(this->get_implementation(), ec); boost::asio::detail::throw_error(ec, "cancel"); } /// Cancel all asynchronous operations associated with the socket. /** * This function causes all outstanding asynchronous connect, send and receive * operations to finish immediately, and the handlers for cancelled operations * will be passed the boost::asio::error::operation_aborted error. * * @param ec Set to indicate what error occurred, if any. * * @note Calls to cancel() will always fail with * boost::asio::error::operation_not_supported when run on Windows XP, Windows * Server 2003, and earlier versions of Windows, unless * BOOST_ASIO_ENABLE_CANCELIO is defined. However, the CancelIo function has * two issues that should be considered before enabling its use: * * @li It will only cancel asynchronous operations that were initiated in the * current thread. * * @li It can appear to complete without error, but the request to cancel the * unfinished operations may be silently ignored by the operating system. * Whether it works or not seems to depend on the drivers that are installed. * * For portable cancellation, consider using one of the following * alternatives: * * @li Disable asio's I/O completion port backend by defining * BOOST_ASIO_DISABLE_IOCP. * * @li Use the close() function to simultaneously cancel the outstanding * operations and close the socket. * * When running on Windows Vista, Windows Server 2008, and later, the * CancelIoEx function is always used. This function does not have the * problems described above. */ #if defined(BOOST_ASIO_MSVC) && (BOOST_ASIO_MSVC >= 1400) \ && (!defined(_WIN32_WINNT) || _WIN32_WINNT < 0x0600) \ && !defined(BOOST_ASIO_ENABLE_CANCELIO) __declspec(deprecated("By default, this function always fails with " "operation_not_supported when used on Windows XP, Windows Server 2003, " "or earlier. Consult documentation for details.")) #endif boost::system::error_code cancel(boost::system::error_code& ec) { return this->get_service().cancel(this->get_implementation(), ec); } /// Determine whether the socket is at the out-of-band data mark. /** * This function is used to check whether the socket input is currently * positioned at the out-of-band data mark. * * @return A bool indicating whether the socket is at the out-of-band data * mark. * * @throws boost::system::system_error Thrown on failure. */ bool at_mark() const { boost::system::error_code ec; bool b = this->get_service().at_mark(this->get_implementation(), ec); boost::asio::detail::throw_error(ec, "at_mark"); return b; } /// Determine whether the socket is at the out-of-band data mark. /** * This function is used to check whether the socket input is currently * positioned at the out-of-band data mark. * * @param ec Set to indicate what error occurred, if any. * * @return A bool indicating whether the socket is at the out-of-band data * mark. */ bool at_mark(boost::system::error_code& ec) const { return this->get_service().at_mark(this->get_implementation(), ec); } /// Determine the number of bytes available for reading. /** * This function is used to determine the number of bytes that may be read * without blocking. * * @return The number of bytes that may be read without blocking, or 0 if an * error occurs. * * @throws boost::system::system_error Thrown on failure. */ std::size_t available() const { boost::system::error_code ec; std::size_t s = this->get_service().available( this->get_implementation(), ec); boost::asio::detail::throw_error(ec, "available"); return s; } /// Determine the number of bytes available for reading. /** * This function is used to determine the number of bytes that may be read * without blocking. * * @param ec Set to indicate what error occurred, if any. * * @return The number of bytes that may be read without blocking, or 0 if an * error occurs. */ std::size_t available(boost::system::error_code& ec) const { return this->get_service().available(this->get_implementation(), ec); } /// Bind the socket to the given local endpoint. /** * This function binds the socket to the specified endpoint on the local * machine. * * @param endpoint An endpoint on the local machine to which the socket will * be bound. * * @throws boost::system::system_error Thrown on failure. * * @par Example * @code * boost::asio::ip::tcp::socket socket(io_service); * socket.open(boost::asio::ip::tcp::v4()); * socket.bind(boost::asio::ip::tcp::endpoint( * boost::asio::ip::tcp::v4(), 12345)); * @endcode */ void bind(const endpoint_type& endpoint) { boost::system::error_code ec; this->get_service().bind(this->get_implementation(), endpoint, ec); boost::asio::detail::throw_error(ec, "bind"); } /// Bind the socket to the given local endpoint. /** * This function binds the socket to the specified endpoint on the local * machine. * * @param endpoint An endpoint on the local machine to which the socket will * be bound. * * @param ec Set to indicate what error occurred, if any. * * @par Example * @code * boost::asio::ip::tcp::socket socket(io_service); * socket.open(boost::asio::ip::tcp::v4()); * boost::system::error_code ec; * socket.bind(boost::asio::ip::tcp::endpoint( * boost::asio::ip::tcp::v4(), 12345), ec); * if (ec) * { * // An error occurred. * } * @endcode */ boost::system::error_code bind(const endpoint_type& endpoint, boost::system::error_code& ec) { return this->get_service().bind(this->get_implementation(), endpoint, ec); } /// Connect the socket to the specified endpoint. /** * This function is used to connect a socket to the specified remote endpoint. * The function call will block until the connection is successfully made or * an error occurs. * * The socket is automatically opened if it is not already open. If the * connect fails, and the socket was automatically opened, the socket is * not returned to the closed state. * * @param peer_endpoint The remote endpoint to which the socket will be * connected. * * @throws boost::system::system_error Thrown on failure. * * @par Example * @code * boost::asio::ip::tcp::socket socket(io_service); * boost::asio::ip::tcp::endpoint endpoint( * boost::asio::ip::address::from_string("1.2.3.4"), 12345); * socket.connect(endpoint); * @endcode */ void connect(const endpoint_type& peer_endpoint) { boost::system::error_code ec; if (!is_open()) { this->get_service().open(this->get_implementation(), peer_endpoint.protocol(), ec); boost::asio::detail::throw_error(ec, "connect"); } this->get_service().connect(this->get_implementation(), peer_endpoint, ec); boost::asio::detail::throw_error(ec, "connect"); } /// Connect the socket to the specified endpoint. /** * This function is used to connect a socket to the specified remote endpoint. * The function call will block until the connection is successfully made or * an error occurs. * * The socket is automatically opened if it is not already open. If the * connect fails, and the socket was automatically opened, the socket is * not returned to the closed state. * * @param peer_endpoint The remote endpoint to which the socket will be * connected. * * @param ec Set to indicate what error occurred, if any. * * @par Example * @code * boost::asio::ip::tcp::socket socket(io_service); * boost::asio::ip::tcp::endpoint endpoint( * boost::asio::ip::address::from_string("1.2.3.4"), 12345); * boost::system::error_code ec; * socket.connect(endpoint, ec); * if (ec) * { * // An error occurred. * } * @endcode */ boost::system::error_code connect(const endpoint_type& peer_endpoint, boost::system::error_code& ec) { if (!is_open()) { if (this->get_service().open(this->get_implementation(), peer_endpoint.protocol(), ec)) { return ec; } } return this->get_service().connect( this->get_implementation(), peer_endpoint, ec); } /// Start an asynchronous connect. /** * This function is used to asynchronously connect a socket to the specified * remote endpoint. The function call always returns immediately. * * The socket is automatically opened if it is not already open. If the * connect fails, and the socket was automatically opened, the socket is * not returned to the closed state. * * @param peer_endpoint The remote endpoint to which the socket will be * connected. Copies will be made of the endpoint object as required. * * @param handler The handler to be called when the connection operation * completes. Copies will be made of the handler as required. The function * signature of the handler must be: * @code void handler( * const boost::system::error_code& error // Result of operation * ); @endcode * Regardless of whether the asynchronous operation completes immediately or * not, the handler will not be invoked from within this function. Invocation * of the handler will be performed in a manner equivalent to using * boost::asio::io_service::post(). * * @par Example * @code * void connect_handler(const boost::system::error_code& error) * { * if (!error) * { * // Connect succeeded. * } * } * * ... * * boost::asio::ip::tcp::socket socket(io_service); * boost::asio::ip::tcp::endpoint endpoint( * boost::asio::ip::address::from_string("1.2.3.4"), 12345); * socket.async_connect(endpoint, connect_handler); * @endcode */ template BOOST_ASIO_INITFN_RESULT_TYPE(ConnectHandler, void (boost::system::error_code)) async_connect(const endpoint_type& peer_endpoint, BOOST_ASIO_MOVE_ARG(ConnectHandler) handler) { // If you get an error on the following line it means that your handler does // not meet the documented type requirements for a ConnectHandler. BOOST_ASIO_CONNECT_HANDLER_CHECK(ConnectHandler, handler) type_check; if (!is_open()) { boost::system::error_code ec; const protocol_type protocol = peer_endpoint.protocol(); if (this->get_service().open(this->get_implementation(), protocol, ec)) { detail::async_result_init< ConnectHandler, void (boost::system::error_code)> init( BOOST_ASIO_MOVE_CAST(ConnectHandler)(handler)); this->get_io_service().post( boost::asio::detail::bind_handler( BOOST_ASIO_MOVE_CAST(BOOST_ASIO_HANDLER_TYPE( ConnectHandler, void (boost::system::error_code)))( init.handler), ec)); return init.result.get(); } } return this->get_service().async_connect(this->get_implementation(), peer_endpoint, BOOST_ASIO_MOVE_CAST(ConnectHandler)(handler)); } /// Set an option on the socket. /** * This function is used to set an option on the socket. * * @param option The new option value to be set on the socket. * * @throws boost::system::system_error Thrown on failure. * * @sa SettableSocketOption @n * boost::asio::socket_base::broadcast @n * boost::asio::socket_base::do_not_route @n * boost::asio::socket_base::keep_alive @n * boost::asio::socket_base::linger @n * boost::asio::socket_base::receive_buffer_size @n * boost::asio::socket_base::receive_low_watermark @n * boost::asio::socket_base::reuse_address @n * boost::asio::socket_base::send_buffer_size @n * boost::asio::socket_base::send_low_watermark @n * boost::asio::ip::multicast::join_group @n * boost::asio::ip::multicast::leave_group @n * boost::asio::ip::multicast::enable_loopback @n * boost::asio::ip::multicast::outbound_interface @n * boost::asio::ip::multicast::hops @n * boost::asio::ip::tcp::no_delay * * @par Example * Setting the IPPROTO_TCP/TCP_NODELAY option: * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * boost::asio::ip::tcp::no_delay option(true); * socket.set_option(option); * @endcode */ template void set_option(const SettableSocketOption& option) { boost::system::error_code ec; this->get_service().set_option(this->get_implementation(), option, ec); boost::asio::detail::throw_error(ec, "set_option"); } /// Set an option on the socket. /** * This function is used to set an option on the socket. * * @param option The new option value to be set on the socket. * * @param ec Set to indicate what error occurred, if any. * * @sa SettableSocketOption @n * boost::asio::socket_base::broadcast @n * boost::asio::socket_base::do_not_route @n * boost::asio::socket_base::keep_alive @n * boost::asio::socket_base::linger @n * boost::asio::socket_base::receive_buffer_size @n * boost::asio::socket_base::receive_low_watermark @n * boost::asio::socket_base::reuse_address @n * boost::asio::socket_base::send_buffer_size @n * boost::asio::socket_base::send_low_watermark @n * boost::asio::ip::multicast::join_group @n * boost::asio::ip::multicast::leave_group @n * boost::asio::ip::multicast::enable_loopback @n * boost::asio::ip::multicast::outbound_interface @n * boost::asio::ip::multicast::hops @n * boost::asio::ip::tcp::no_delay * * @par Example * Setting the IPPROTO_TCP/TCP_NODELAY option: * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * boost::asio::ip::tcp::no_delay option(true); * boost::system::error_code ec; * socket.set_option(option, ec); * if (ec) * { * // An error occurred. * } * @endcode */ template boost::system::error_code set_option(const SettableSocketOption& option, boost::system::error_code& ec) { return this->get_service().set_option( this->get_implementation(), option, ec); } /// Get an option from the socket. /** * This function is used to get the current value of an option on the socket. * * @param option The option value to be obtained from the socket. * * @throws boost::system::system_error Thrown on failure. * * @sa GettableSocketOption @n * boost::asio::socket_base::broadcast @n * boost::asio::socket_base::do_not_route @n * boost::asio::socket_base::keep_alive @n * boost::asio::socket_base::linger @n * boost::asio::socket_base::receive_buffer_size @n * boost::asio::socket_base::receive_low_watermark @n * boost::asio::socket_base::reuse_address @n * boost::asio::socket_base::send_buffer_size @n * boost::asio::socket_base::send_low_watermark @n * boost::asio::ip::multicast::join_group @n * boost::asio::ip::multicast::leave_group @n * boost::asio::ip::multicast::enable_loopback @n * boost::asio::ip::multicast::outbound_interface @n * boost::asio::ip::multicast::hops @n * boost::asio::ip::tcp::no_delay * * @par Example * Getting the value of the SOL_SOCKET/SO_KEEPALIVE option: * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * boost::asio::ip::tcp::socket::keep_alive option; * socket.get_option(option); * bool is_set = option.value(); * @endcode */ template void get_option(GettableSocketOption& option) const { boost::system::error_code ec; this->get_service().get_option(this->get_implementation(), option, ec); boost::asio::detail::throw_error(ec, "get_option"); } /// Get an option from the socket. /** * This function is used to get the current value of an option on the socket. * * @param option The option value to be obtained from the socket. * * @param ec Set to indicate what error occurred, if any. * * @sa GettableSocketOption @n * boost::asio::socket_base::broadcast @n * boost::asio::socket_base::do_not_route @n * boost::asio::socket_base::keep_alive @n * boost::asio::socket_base::linger @n * boost::asio::socket_base::receive_buffer_size @n * boost::asio::socket_base::receive_low_watermark @n * boost::asio::socket_base::reuse_address @n * boost::asio::socket_base::send_buffer_size @n * boost::asio::socket_base::send_low_watermark @n * boost::asio::ip::multicast::join_group @n * boost::asio::ip::multicast::leave_group @n * boost::asio::ip::multicast::enable_loopback @n * boost::asio::ip::multicast::outbound_interface @n * boost::asio::ip::multicast::hops @n * boost::asio::ip::tcp::no_delay * * @par Example * Getting the value of the SOL_SOCKET/SO_KEEPALIVE option: * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * boost::asio::ip::tcp::socket::keep_alive option; * boost::system::error_code ec; * socket.get_option(option, ec); * if (ec) * { * // An error occurred. * } * bool is_set = option.value(); * @endcode */ template boost::system::error_code get_option(GettableSocketOption& option, boost::system::error_code& ec) const { return this->get_service().get_option( this->get_implementation(), option, ec); } /// Perform an IO control command on the socket. /** * This function is used to execute an IO control command on the socket. * * @param command The IO control command to be performed on the socket. * * @throws boost::system::system_error Thrown on failure. * * @sa IoControlCommand @n * boost::asio::socket_base::bytes_readable @n * boost::asio::socket_base::non_blocking_io * * @par Example * Getting the number of bytes ready to read: * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * boost::asio::ip::tcp::socket::bytes_readable command; * socket.io_control(command); * std::size_t bytes_readable = command.get(); * @endcode */ template void io_control(IoControlCommand& command) { boost::system::error_code ec; this->get_service().io_control(this->get_implementation(), command, ec); boost::asio::detail::throw_error(ec, "io_control"); } /// Perform an IO control command on the socket. /** * This function is used to execute an IO control command on the socket. * * @param command The IO control command to be performed on the socket. * * @param ec Set to indicate what error occurred, if any. * * @sa IoControlCommand @n * boost::asio::socket_base::bytes_readable @n * boost::asio::socket_base::non_blocking_io * * @par Example * Getting the number of bytes ready to read: * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * boost::asio::ip::tcp::socket::bytes_readable command; * boost::system::error_code ec; * socket.io_control(command, ec); * if (ec) * { * // An error occurred. * } * std::size_t bytes_readable = command.get(); * @endcode */ template boost::system::error_code io_control(IoControlCommand& command, boost::system::error_code& ec) { return this->get_service().io_control( this->get_implementation(), command, ec); } /// Gets the non-blocking mode of the socket. /** * @returns @c true if the socket's synchronous operations will fail with * boost::asio::error::would_block if they are unable to perform the requested * operation immediately. If @c false, synchronous operations will block * until complete. * * @note The non-blocking mode has no effect on the behaviour of asynchronous * operations. Asynchronous operations will never fail with the error * boost::asio::error::would_block. */ bool non_blocking() const { return this->get_service().non_blocking(this->get_implementation()); } /// Sets the non-blocking mode of the socket. /** * @param mode If @c true, the socket's synchronous operations will fail with * boost::asio::error::would_block if they are unable to perform the requested * operation immediately. If @c false, synchronous operations will block * until complete. * * @throws boost::system::system_error Thrown on failure. * * @note The non-blocking mode has no effect on the behaviour of asynchronous * operations. Asynchronous operations will never fail with the error * boost::asio::error::would_block. */ void non_blocking(bool mode) { boost::system::error_code ec; this->get_service().non_blocking(this->get_implementation(), mode, ec); boost::asio::detail::throw_error(ec, "non_blocking"); } /// Sets the non-blocking mode of the socket. /** * @param mode If @c true, the socket's synchronous operations will fail with * boost::asio::error::would_block if they are unable to perform the requested * operation immediately. If @c false, synchronous operations will block * until complete. * * @param ec Set to indicate what error occurred, if any. * * @note The non-blocking mode has no effect on the behaviour of asynchronous * operations. Asynchronous operations will never fail with the error * boost::asio::error::would_block. */ boost::system::error_code non_blocking( bool mode, boost::system::error_code& ec) { return this->get_service().non_blocking( this->get_implementation(), mode, ec); } /// Gets the non-blocking mode of the native socket implementation. /** * This function is used to retrieve the non-blocking mode of the underlying * native socket. This mode has no effect on the behaviour of the socket * object's synchronous operations. * * @returns @c true if the underlying socket is in non-blocking mode and * direct system calls may fail with boost::asio::error::would_block (or the * equivalent system error). * * @note The current non-blocking mode is cached by the socket object. * Consequently, the return value may be incorrect if the non-blocking mode * was set directly on the native socket. * * @par Example * This function is intended to allow the encapsulation of arbitrary * non-blocking system calls as asynchronous operations, in a way that is * transparent to the user of the socket object. The following example * illustrates how Linux's @c sendfile system call might be encapsulated: * @code template * struct sendfile_op * { * tcp::socket& sock_; * int fd_; * Handler handler_; * off_t offset_; * std::size_t total_bytes_transferred_; * * // Function call operator meeting WriteHandler requirements. * // Used as the handler for the async_write_some operation. * void operator()(boost::system::error_code ec, std::size_t) * { * // Put the underlying socket into non-blocking mode. * if (!ec) * if (!sock_.native_non_blocking()) * sock_.native_non_blocking(true, ec); * * if (!ec) * { * for (;;) * { * // Try the system call. * errno = 0; * int n = ::sendfile(sock_.native_handle(), fd_, &offset_, 65536); * ec = boost::system::error_code(n < 0 ? errno : 0, * boost::asio::error::get_system_category()); * total_bytes_transferred_ += ec ? 0 : n; * * // Retry operation immediately if interrupted by signal. * if (ec == boost::asio::error::interrupted) * continue; * * // Check if we need to run the operation again. * if (ec == boost::asio::error::would_block * || ec == boost::asio::error::try_again) * { * // We have to wait for the socket to become ready again. * sock_.async_write_some(boost::asio::null_buffers(), *this); * return; * } * * if (ec || n == 0) * { * // An error occurred, or we have reached the end of the file. * // Either way we must exit the loop so we can call the handler. * break; * } * * // Loop around to try calling sendfile again. * } * } * * // Pass result back to user's handler. * handler_(ec, total_bytes_transferred_); * } * }; * * template * void async_sendfile(tcp::socket& sock, int fd, Handler h) * { * sendfile_op op = { sock, fd, h, 0, 0 }; * sock.async_write_some(boost::asio::null_buffers(), op); * } @endcode */ bool native_non_blocking() const { return this->get_service().native_non_blocking(this->get_implementation()); } /// Sets the non-blocking mode of the native socket implementation. /** * This function is used to modify the non-blocking mode of the underlying * native socket. It has no effect on the behaviour of the socket object's * synchronous operations. * * @param mode If @c true, the underlying socket is put into non-blocking * mode and direct system calls may fail with boost::asio::error::would_block * (or the equivalent system error). * * @throws boost::system::system_error Thrown on failure. If the @c mode is * @c false, but the current value of @c non_blocking() is @c true, this * function fails with boost::asio::error::invalid_argument, as the * combination does not make sense. * * @par Example * This function is intended to allow the encapsulation of arbitrary * non-blocking system calls as asynchronous operations, in a way that is * transparent to the user of the socket object. The following example * illustrates how Linux's @c sendfile system call might be encapsulated: * @code template * struct sendfile_op * { * tcp::socket& sock_; * int fd_; * Handler handler_; * off_t offset_; * std::size_t total_bytes_transferred_; * * // Function call operator meeting WriteHandler requirements. * // Used as the handler for the async_write_some operation. * void operator()(boost::system::error_code ec, std::size_t) * { * // Put the underlying socket into non-blocking mode. * if (!ec) * if (!sock_.native_non_blocking()) * sock_.native_non_blocking(true, ec); * * if (!ec) * { * for (;;) * { * // Try the system call. * errno = 0; * int n = ::sendfile(sock_.native_handle(), fd_, &offset_, 65536); * ec = boost::system::error_code(n < 0 ? errno : 0, * boost::asio::error::get_system_category()); * total_bytes_transferred_ += ec ? 0 : n; * * // Retry operation immediately if interrupted by signal. * if (ec == boost::asio::error::interrupted) * continue; * * // Check if we need to run the operation again. * if (ec == boost::asio::error::would_block * || ec == boost::asio::error::try_again) * { * // We have to wait for the socket to become ready again. * sock_.async_write_some(boost::asio::null_buffers(), *this); * return; * } * * if (ec || n == 0) * { * // An error occurred, or we have reached the end of the file. * // Either way we must exit the loop so we can call the handler. * break; * } * * // Loop around to try calling sendfile again. * } * } * * // Pass result back to user's handler. * handler_(ec, total_bytes_transferred_); * } * }; * * template * void async_sendfile(tcp::socket& sock, int fd, Handler h) * { * sendfile_op op = { sock, fd, h, 0, 0 }; * sock.async_write_some(boost::asio::null_buffers(), op); * } @endcode */ void native_non_blocking(bool mode) { boost::system::error_code ec; this->get_service().native_non_blocking( this->get_implementation(), mode, ec); boost::asio::detail::throw_error(ec, "native_non_blocking"); } /// Sets the non-blocking mode of the native socket implementation. /** * This function is used to modify the non-blocking mode of the underlying * native socket. It has no effect on the behaviour of the socket object's * synchronous operations. * * @param mode If @c true, the underlying socket is put into non-blocking * mode and direct system calls may fail with boost::asio::error::would_block * (or the equivalent system error). * * @param ec Set to indicate what error occurred, if any. If the @c mode is * @c false, but the current value of @c non_blocking() is @c true, this * function fails with boost::asio::error::invalid_argument, as the * combination does not make sense. * * @par Example * This function is intended to allow the encapsulation of arbitrary * non-blocking system calls as asynchronous operations, in a way that is * transparent to the user of the socket object. The following example * illustrates how Linux's @c sendfile system call might be encapsulated: * @code template * struct sendfile_op * { * tcp::socket& sock_; * int fd_; * Handler handler_; * off_t offset_; * std::size_t total_bytes_transferred_; * * // Function call operator meeting WriteHandler requirements. * // Used as the handler for the async_write_some operation. * void operator()(boost::system::error_code ec, std::size_t) * { * // Put the underlying socket into non-blocking mode. * if (!ec) * if (!sock_.native_non_blocking()) * sock_.native_non_blocking(true, ec); * * if (!ec) * { * for (;;) * { * // Try the system call. * errno = 0; * int n = ::sendfile(sock_.native_handle(), fd_, &offset_, 65536); * ec = boost::system::error_code(n < 0 ? errno : 0, * boost::asio::error::get_system_category()); * total_bytes_transferred_ += ec ? 0 : n; * * // Retry operation immediately if interrupted by signal. * if (ec == boost::asio::error::interrupted) * continue; * * // Check if we need to run the operation again. * if (ec == boost::asio::error::would_block * || ec == boost::asio::error::try_again) * { * // We have to wait for the socket to become ready again. * sock_.async_write_some(boost::asio::null_buffers(), *this); * return; * } * * if (ec || n == 0) * { * // An error occurred, or we have reached the end of the file. * // Either way we must exit the loop so we can call the handler. * break; * } * * // Loop around to try calling sendfile again. * } * } * * // Pass result back to user's handler. * handler_(ec, total_bytes_transferred_); * } * }; * * template * void async_sendfile(tcp::socket& sock, int fd, Handler h) * { * sendfile_op op = { sock, fd, h, 0, 0 }; * sock.async_write_some(boost::asio::null_buffers(), op); * } @endcode */ boost::system::error_code native_non_blocking( bool mode, boost::system::error_code& ec) { return this->get_service().native_non_blocking( this->get_implementation(), mode, ec); } /// Get the local endpoint of the socket. /** * This function is used to obtain the locally bound endpoint of the socket. * * @returns An object that represents the local endpoint of the socket. * * @throws boost::system::system_error Thrown on failure. * * @par Example * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * boost::asio::ip::tcp::endpoint endpoint = socket.local_endpoint(); * @endcode */ endpoint_type local_endpoint() const { boost::system::error_code ec; endpoint_type ep = this->get_service().local_endpoint( this->get_implementation(), ec); boost::asio::detail::throw_error(ec, "local_endpoint"); return ep; } /// Get the local endpoint of the socket. /** * This function is used to obtain the locally bound endpoint of the socket. * * @param ec Set to indicate what error occurred, if any. * * @returns An object that represents the local endpoint of the socket. * Returns a default-constructed endpoint object if an error occurred. * * @par Example * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * boost::system::error_code ec; * boost::asio::ip::tcp::endpoint endpoint = socket.local_endpoint(ec); * if (ec) * { * // An error occurred. * } * @endcode */ endpoint_type local_endpoint(boost::system::error_code& ec) const { return this->get_service().local_endpoint(this->get_implementation(), ec); } /// Get the remote endpoint of the socket. /** * This function is used to obtain the remote endpoint of the socket. * * @returns An object that represents the remote endpoint of the socket. * * @throws boost::system::system_error Thrown on failure. * * @par Example * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * boost::asio::ip::tcp::endpoint endpoint = socket.remote_endpoint(); * @endcode */ endpoint_type remote_endpoint() const { boost::system::error_code ec; endpoint_type ep = this->get_service().remote_endpoint( this->get_implementation(), ec); boost::asio::detail::throw_error(ec, "remote_endpoint"); return ep; } /// Get the remote endpoint of the socket. /** * This function is used to obtain the remote endpoint of the socket. * * @param ec Set to indicate what error occurred, if any. * * @returns An object that represents the remote endpoint of the socket. * Returns a default-constructed endpoint object if an error occurred. * * @par Example * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * boost::system::error_code ec; * boost::asio::ip::tcp::endpoint endpoint = socket.remote_endpoint(ec); * if (ec) * { * // An error occurred. * } * @endcode */ endpoint_type remote_endpoint(boost::system::error_code& ec) const { return this->get_service().remote_endpoint(this->get_implementation(), ec); } /// Disable sends or receives on the socket. /** * This function is used to disable send operations, receive operations, or * both. * * @param what Determines what types of operation will no longer be allowed. * * @throws boost::system::system_error Thrown on failure. * * @par Example * Shutting down the send side of the socket: * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * socket.shutdown(boost::asio::ip::tcp::socket::shutdown_send); * @endcode */ void shutdown(shutdown_type what) { boost::system::error_code ec; this->get_service().shutdown(this->get_implementation(), what, ec); boost::asio::detail::throw_error(ec, "shutdown"); } /// Disable sends or receives on the socket. /** * This function is used to disable send operations, receive operations, or * both. * * @param what Determines what types of operation will no longer be allowed. * * @param ec Set to indicate what error occurred, if any. * * @par Example * Shutting down the send side of the socket: * @code * boost::asio::ip::tcp::socket socket(io_service); * ... * boost::system::error_code ec; * socket.shutdown(boost::asio::ip::tcp::socket::shutdown_send, ec); * if (ec) * { * // An error occurred. * } * @endcode */ boost::system::error_code shutdown(shutdown_type what, boost::system::error_code& ec) { return this->get_service().shutdown(this->get_implementation(), what, ec); } protected: /// Protected destructor to prevent deletion through this type. ~basic_socket() { } }; } // namespace asio } // namespace boost #include #endif // BOOST_ASIO_BASIC_SOCKET_HPP | 2020-09-24 19:01:50 | {"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": 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": 0.5332813858985901, "perplexity": 14513.66702978533}, "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/1600400219691.59/warc/CC-MAIN-20200924163714-20200924193714-00060.warc.gz"} |
http://thesmallbusinessmarketingblog.com/how-to-jodrp/a9e3db-what-is-a-target-function | SuperUser reader Vishnu Vivek is curious about MAC addresses and their function: I understand that IP addresses are hierarchical, so that routers throughout the internet know which direction to forward a packet. This will also help determine what the function … Frames are deprecated in HTML5. Now I know what you're asking. The simplest example is shown below. The launch function has had a few additional options added recently, and even though they are apparently still in preview they are worth it to have a look at. Function of Beauty to Launch Its Customizable Haircare Range at Target Along with its #hairgoal booster shots that help achieve specific hair needs. _parent: Opens the link in the parent frame. The Launch function in Power Apps helps you to open links in your browser from your app. The Oxytocin Function Explained. In the context of a "gene knockout", a "target gene" may be the gene that a "targeting vector" is designed to knock out (make non-functional, non-stable, or non-expressable). Risk assessment is the identification of hazards that could negatively impact an organization's ability to conduct business. Hormones influence the development and function of human skin which also produces and releases hormones. Definition: Target market is the end consumer to which the company wants to sell its end products too. To perform these roles, there is a great variety of astrocytes. But it doesn't hurt to introduce function notations because it makes it very clear that the function takes an input, takes my x-- in this definition it munches on it. A route target takes the form of an extended BGP community with a structure similar to that of a route distinguisher (which is probably why the two are so easily confused). You gain the most benefits when you exercise in your ''target heart rate zone.'' Well organized and easy to understand Web building tutorials with lots of examples of how to use HTML, CSS, JavaScript, SQL, PHP, Python, Bootstrap, Java and XML. The target pin you're seeing is in essence the this pointer. Function of Beauty’s 8-ounce and 16-ounce shampoo and conditioner sets costs $39.99 and$49.99, respectively, on its DTC channel, Target is retailing the products for \$28.95. It is different from Event.currentTarget when the event handler is called during the bubbling or capturing phase of the event. and twice in 14.2.16: An ArrowFunction does not define local bindings for arguments, super, this, or new.target. There are three major versions: 1.x, 2.x, and 3.x. Recommended Articles. A Key Performance Indicator (KPI) is a measurable value that demonstrates how effectively a company is achieving key business objectives. Learn more. Engineering: IMCONJUGATE: IMCONJUGATE(number) Returns the complex conjugate of a number. This will show you where to start and let you know if your intervention has actually been helpful. Launch Function. And then it produces 1 more than it. In addition, selling is a fundamental function of marketing. All right. The target property of the Event interface is a reference to the object onto which the event was dispatched. Usually, this is a heart rate (pulse) of 60%-80% of your maximum heart rate. Serotonin (also known as 5-hydroxytryptamine or 5-HT) is a naturally occurring substance that functions as a neurotransmitter to carry signals between nerve cells (called neurons) throughout your body. This article explains how to configure a function app in Azure to run on the version you choose. By default, function apps are created in version 3.x of the runtime. Oxytocin And Reproduction. Baseline data is data you take before you start an intervention. Generally speaking, a function is a "subprogram" that can be called by code external (or internal in the case of recursion) to the function. Values can be passed to a function, and the function … The same is roughly true in blueprints. One or more route targets can be affixed to routes within a VRF using the VRF configuration command route-target export: Microsoft Windows Defender: Windows Defender is Microsoft's antimalware software. So here, whatever the input is, the output is 1 more than that original function. VNFs move individual network functions out of dedicated hardware devices into software that runs on commodity hardware. Oxytocin has multiple functions in the human body, both physical and psychological. You can also go through our other suggested articles – VBA Loops; VBA Web Scraping What Is an S-Function? Here we discuss how to use Excel VBA Intersect Function along with some practical examples and downloadable excel template. Part of the Function. These assessments help identify these inherent business risks and provide measures, processes and controls to reduce the impact of these risks to business operations. Other essential functions of marketing outside of the four P’s include financing marketing activities and conducting market research about the target audience. Known for its customizable beauty products, Function of Beauty is set to release its haircare range exclusively at Target later this month. Normally, Contains does not look inside most function forms However, Contains is used to detect new.target, this, and super usage within an ArrowFunction. And once you're inside that function this is implicitly the context of the function. The target operating model is the "to be" model. In general, women tend to have higher levels of oxytocin in the body than men. Target operating model (TOM) is a blueprint of a firm’s business vision that aligns operating capacities and strategic objectives and provides an overview of the core business capabilities, internal factors, and external drivers, strategic and operational levers, organizational and functional structure, technology, and information resources of a company. In fact the Domain is an essential part of the function. The IMARGUMENT function returns the angle (also known as the argument or \theta) of the given complex number in radians. Make sure that the relation is a function. Now, what comes out (the Range) depends on what we put in (the Domain)..... but WE can define the Domain! I am trying to pass the clicked event (event.target) to a function inside a function that is being called when clicked how would i do this? So in C++ terms when you call a function on an instance of an object you can do GetOwner() (which implies this->GetOwner()) or MyActor->GetOwner(). A function app runs on a specific version of the Azure Functions runtime. While all humans use oxytocin, it is particularly important for females due to its role in reproduction. Cite. Change the Domain and we have a different function. Target marketing involves breaking down the entire market into various segments and planning marketing strategies accordingly for each segment to increase the market share. An S-function is a computer language description of a Simulink block written in MATLAB ®, C, C++, or Fortran.C, C++, and Fortran S-functions are compiled as MEX files using the mex utility (see Build C MEX Function). Learn more: Engineering: IMCOS: IMCOS(number) The IMCOS function returns the cosine of the given complex number. Like the program itself, a function is composed of a sequence of statements called the function body. Virtual network functions (VNFs) are virtualized tasks formerly carried out by proprietary, dedicated hardware. Most commonly, people are aware of serotonin's role in the central nervous system (CNS). It is possible to produce a target operating model for a business or a function within a business or a government department or a charity. For a relation to be a function, every time you put in one number of an x coordinate, the y coordinate has to be the same. S-functions (system-functions) provide a powerful mechanism for extending the capabilities of the Simulink ® environment. This is a guide to VBA Intersect. Open a site using Launch. In this review, we sum … Astrocytes are the most numerous cell type within the central nervous system (CNS) and perform a variety of tasks, from axon guidance and synaptic support, to the control of the blood brain barrier and blood flow. There are many different frameworks identifying the components of a target operating model. test function: it is plus test function: it is minus test function: it is the function f test function: it is the function g [] See als Using Target Range as shown in example-2 is useful in specifying the area to hit. The function object can be copied and moved around, and can be used to directly invoke the callable object with the specified call signature (see member operator() ). You have your target behavior and definition – now you need to take some baseline data. The term Target Operating Model (or TOM) has been used a lot in many of the organizations that I have worked for all around the world, from London, to Mexico City, to Moscow, to New York, to Sydney, to Johannesburg, to Singapore, to Shanghai and Hong Kong, and in Sao Paulo too.Many 100s of millions of dollars in business change budgets has been invested in TOM projects all over the world. The specific type of this target callable object is not needed in order to instantiate the function wrapper class; only its call signature. It says, OK, x plus 1. Value Name Notes; _blank: Opens the linked document in a new tab or window. Organizations use KPIs to evaluate their success at reaching targets. Functions of marketing set to release its Haircare Range exclusively at target along with its # hairgoal booster that... Extending the capabilities of the function end consumer to which the event handler is called during the or! Let you know if your intervention has actually been helpful passed to a function is composed of a.! Complex number than that original function phase of the given complex number ) are virtualized tasks formerly carried out proprietary... -80 % of your maximum heart rate ( pulse ) of 60 % -80 % of your maximum heart zone. To conduct business commodity hardware Intersect function along with some practical examples and downloadable template. You know if your intervention has actually been helpful your target heart rate the bubbling capturing... Commonly, people are aware of serotonin 's role in reproduction function of Beauty to its! Its # hairgoal booster shots that help achieve specific hair needs take some baseline data \theta ) of given... Returns the complex conjugate of a number influence the development and function of outside! In version 3.x of the function body configure a function, and the function wrapper class ; only its signature! Booster shots that help achieve specific hair needs system-functions ) provide a powerful for! Of the function that function this is implicitly the context of the event interface is reference... End consumer to which the company wants to sell its end products too market research the... While all humans use oxytocin, it is particularly important for females due to its role reproduction! In order to instantiate the function body mechanism for extending the capabilities of the function … of... The identification of hazards that could negatively impact an organization 's ability to conduct business function, and 3.x at! Tab or window set to release its Haircare Range exclusively at target along with its # hairgoal shots... Marketing activities and conducting market research about the target property of the given complex number in radians function. Function Apps are created in version 3.x of the given complex number in radians out of hardware... From your app, people are aware of serotonin 's role in reproduction company wants sell. End consumer to which the event interface is a heart rate zone. number in.! S-Functions ( system-functions ) provide a powerful mechanism for extending the capabilities of the four ’! ) returns the angle ( also known as the argument or \theta ) 60. Body, both physical and psychological version you choose you exercise in your browser from your.! The entire market into various segments and planning marketing strategies accordingly for each segment to the! ( also known as the argument or \theta ) of the Simulink ® environment 's antimalware software to... All humans use oxytocin, it is different from Event.currentTarget when the event was dispatched onto which the wants. The Domain and we have a different function by proprietary, dedicated hardware or new.target ( ). Segment to increase the market share IMCOS ( number ) returns the (... Mechanism for extending the capabilities of the four P ’ s include financing marketing and. The company wants to sell its end products too target heart rate known for its Customizable products. You need to take some baseline data out by proprietary, dedicated hardware devices into software that on! Need to take some baseline data is data you take before you start an intervention given complex number in.... The runtime ( CNS ) context of the event interface is a great variety of.. Tasks formerly carried out by proprietary, dedicated hardware devices into software that what is a target function on a specific version the... Your target behavior and definition – now you need to take some baseline data is data take. To evaluate their success at reaching targets market share and we have a different function and we have a function. Consumer to which the company wants to sell its end products too ; its. To Launch its Customizable Haircare Range at target later this month end products too needed in order to the. So here, whatever the input is, the output is 1 more than original... Launch its Customizable Haircare Range at target later this month ( pulse ) of 60 -80. Specific type of this target callable object is not needed in order to instantiate the function this! Range at target later this month usually, this is implicitly the context the!: target market is the identification of hazards that could negatively impact an organization 's ability to conduct business their. About the target audience a specific version of the four P ’ s include financing activities... Into various segments and planning marketing strategies accordingly for each segment to increase the market share target.... Due to its role in the central nervous system ( CNS ) segment to increase the market share and –... Target callable object is not needed in order to instantiate the function marketing involves breaking down entire... The runtime their success at reaching targets planning marketing strategies accordingly for each to! Document in a new tab or window research about the target audience, super, this is a variety! ( pulse ) of 60 % -80 % of your maximum heart what is a target function! Helps you to open links in your browser from your app ( pulse of! Take some baseline data is data you take before you start an intervention due its! In general, women tend to have higher levels of oxytocin in the central nervous system ( ). Of this target callable object is not needed in order to instantiate the function benefits when exercise. There is a heart rate ( pulse ) of 60 % -80 % of your maximum heart zone. Operating model you gain the most benefits when you exercise in your browser from your app aware... A number event interface is a great variety of astrocytes ( also known as the or... Reference to the object onto which the company wants to sell its products. Program itself, a function, and 3.x definition: target market the... Instantiate the function body into various segments and planning marketing strategies accordingly for each segment increase. To its role in the parent frame before you start an intervention variety of astrocytes explains how to configure function... Launch its Customizable Beauty products, function of Beauty to Launch its Beauty!, dedicated hardware function Apps are created in version 3.x of the event handler is called the... Hardware devices into software that runs on a specific version of the given complex number humans oxytocin. And planning marketing strategies accordingly for each segment to increase the market share while all humans use oxytocin, is. Of hazards that could negatively impact an organization 's ability to conduct business have. The company wants to sell its end products too risk assessment is the of. Entire market into various segments and planning marketing strategies accordingly for each segment to increase the share., it is particularly important for females due to its role in reproduction capabilities of event. ’ s include financing marketing activities and conducting market research about the target audience phase the... Angle ( also known as the argument or \theta ) of the event interface is a fundamental of... Original function ( CNS ) functions out of dedicated hardware in Power Apps helps to... Tend to have higher levels of oxytocin in the body than men skin also! A heart rate zone. a target operating model Range at target later this month inside function! People are aware of serotonin 's role in the parent frame know if your has... An organization 's ability to conduct business in Azure to run on version. Number in radians on the version you choose functions runtime to start and let you if. Use oxytocin, it is particularly important for females due to its role the. The most benefits when you exercise in your target heart rate have your target behavior definition! The context of the four P ’ s include financing marketing activities conducting! S-Functions ( system-functions ) provide a powerful mechanism for extending the capabilities of the Simulink ® environment some data... System ( CNS ) important for females due to its role in the body. Handler is called during the bubbling or capturing phase of the four P ’ s include marketing... Handler is called during the bubbling or capturing phase of the function wrapper class ; only its call signature the! To configure a function app in Azure to run on the version you choose, or new.target specific! Discuss how to use Excel VBA Intersect function along with some practical examples and downloadable Excel template input. Body, both physical and psychological in order to instantiate the function body you need to take some data... Essential Part of the event handler is called during the bubbling or capturing phase of given. Known as the argument or \theta what is a target function of 60 % -80 % your... Sell its end products too start an intervention the function of dedicated hardware devices into software that runs on specific..., a function app in Azure to run on the version you choose where to start and you. You choose input is, the output is 1 more than that function. The parent frame Defender is microsoft 's antimalware software system-functions ) provide a powerful mechanism for extending capabilities. This will show you where to start and let you know if your intervention has been! Input is, the output is 1 more than that original function which also produces and releases hormones reference the... The Launch function in Power Apps helps you to open links in your from! Will show you where to start and let you know if your intervention actually!: IMCOS: IMCOS: IMCOS: IMCOS: IMCOS ( number the...
Calandra's Mediterranean Grill Menu, What Are The Benefits Of Cooperative And Collaborative Learning, Westringia Blue Gem Bunnings, Mochi Uk Supermarket, Irish Guinness Stew, Mantra To Silence Enemies, | 2022-05-28 23:11:28 | {"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": 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": 0.1853783279657364, "perplexity": 2444.574884313388}, "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-2022-21/segments/1652663021405.92/warc/CC-MAIN-20220528220030-20220529010030-00337.warc.gz"} |
https://socratic.org/questions/the-perimeter-of-a-rectangle-is-158-the-length-is-7-more-than-the-width-what-is- | # The perimeter of a rectangle is 158. The length is 7 more than the width. What is the length and the width?
Apr 8, 2018
Width is 36, length is 43
#### Explanation:
Let the width be $x$ so the length would be $x + 7$.
The perimeter is the distance around the shape so
$x + \left(x + 7\right) + x + \left(x + 7\right) = 158$
$4 x + 14 = 158$
$4 x = 144$
$x = 36$ | 2019-11-15 13:50:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "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": 0.9385712742805481, "perplexity": 570.0266842231144}, "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-2019-47/segments/1573496668644.10/warc/CC-MAIN-20191115120854-20191115144854-00122.warc.gz"} |
https://socratic.org/questions/how-do-you-simplify-5-3i-4-2i | # How do you simplify 5-[(-3i+4)-2i]?
Jun 23, 2016
$5 - \left[\left(- 3 i + 4\right) - 2 i\right] = 1 + 5 i$
#### Explanation:
$5 - \left[\left(- 3 i + 4\right) - 2 i\right]$
= $5 - \left[- 3 i + 4 - 2 i\right]$
= $5 - \left[- 5 i + 4\right]$
Now we have a negative sign outside brackets.
How do we interpret it?
There are two ways
(i) it is as if we are multiplying by $- 1$ and hence
$- \left[- 5 i + 4\right] = - 1 \times \left[- 5 i + 4\right]$
= $\left(- 1\right) \times \left(- 5 i\right) + \left(- 1\right) \times 4 = 5 i - 4$ or
(ii) using simple properties of negative numbers i.e. negative of a negative is positive and negative of a positive is negative and hence again $- \left\{- 5 i + 4\right] = 5 i - 4$.
In any case, it means we change all the signs inside the brackets and above is equal to
$5 + 5 i - 4$
= $1 + 5 i$ | 2019-03-25 11:35:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 10, "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": 0.9601497054100037, "perplexity": 568.4210377020855}, "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/1552912203947.59/warc/CC-MAIN-20190325112917-20190325134917-00203.warc.gz"} |
http://www.math.columbia.edu/~woit/wordpress/?p=9509 | # QCD at $\theta=\pi$
Earlier this week Zohar Komargodski (who is now at the Simons Center) visited Columbia, and gave a wonderful talk on recent work he has been involved in that provides some new insight into a very old question about QCD. Simplifying the problem by ignoring fermions, QCD is a pure SU(3) Yang-Mills gauge theory, a simple to define QFT which has been highly resistant to decades of effort to better understand it.
One aspect of the theory is that it can be studied as a function of an angular parameter, the so-called $\theta$-angle. Most information about the theory comes from simplifying by taking $\theta=0$, which seems to be the physically relevant value, one at which the theory is time reversal invariant. There is however another value for which the theory is time reversal invariant, $\theta=\pi$, and what happens there has always been rather mysterious.
The new ideas about this question that Komargodski talked about are in the paper Theta, Time Reversal and Temperature from earlier this year, joint work with Gaiotto, Kapustin and Seiberg. Much of the talk was taken up with going over the details of the toy model described in Appendix D of this paper. This is an extremely simple quantum mechanical model, that of a particle moving on a circle, where you add to the Lagrangian a term proportional to the velocity, which is where the angle $\theta$ appears. You can also think of this as a coupling to an electromagnetic field describing flux through the circle.
Even if you’re put off by the difficulty of questions about quantum field theories such as QCD, I strongly recommend reading their Appendix. It’s a simple and straightforward quantum mechanics story, with the new feature of a beautiful interpretation of the model in terms of a projective representation of the group O(2), or equivalently, a representation of Pin(2), a central extension of O(2). In the analogy to SU(N) Yang-Mills, it is the $\mathbf Z_N$ symmetry of the theory that gets realized projectively.
Komargodski himself commented at the beginning of the talk on the reasons that people are returning to look again at old, difficult problems about QCD. The new ideas he described are closely related to ones that are part of the recent hot topic of symmetry protected phases in condensed matter theory. It’s great to see that this QFT research may not just have condensed matter applications, but seems to be leading to a renewal of interest in long-standing problems about QCD itself.
Besides the paper mentioned above, there are now quite a few others. One notable one is very recent work of Komargodski and collaborators, Time-Reversal Breaking in QCD4, Walls and Dualities in 2+1 Dimensions.
This entry was posted in Uncategorized. Bookmark the permalink.
### 11 Responses to QCD at $\theta=\pi$
1. Arun Debray says:
> a projective representation of the group O(2), or equivalently, a representation of Pin(2), a central extension of O(2)
There are two nontrivial central extensions of O(2), called Pin^+(2) and Pin^-(2). The paper didn’t seem to mention which Pin group is appearing here; do you know which one it is?
2. Anon says:
Thanks for posting on this. I tried looking through their paper. Will take more time to read it. But I was wondering if in the talk at Columbia whether the speaker mentioned how their works fits in with the strong CP phase or strong CP problem. Their paper doesn’t explicitly mention the strong CP phase/problem.
3. P says:
Interesting post, thanks.
Do you have any opinion on Arkani-Hamed’s latest paper? Judging from the title it sounds pretty spectacular. Unfortunately I don’t have the technical skill sett to judge the impact of the paper.
https://arxiv.org/abs/1709.04891
4. Peter Woit says:
Arun Debray,
No, I don’t (since I don’t know the difference between those two versions of Pin), but I’d think it’s quite explicit and should be easy to figure out.
Anon,
No mention of the strong CP problem (other than the standard fact that it disappears for a massless fermion), no claim to have something new to say about that.
P.
Looks quite interesting, and I’ll look at it more closely, especially since I’m quite interested in how much reps of the Poincare group tell you about QFT. Some of the claims in the abstract look much stronger than plausible, so very interesting. But, this really is off-topic, and I don’t want to host a discussion of this paper here and now.
Like the paper discussed here, another quite encouraging example of some of the best theorists around working on new ideas about 4d qft close to the Standard Model.
5. BCnrd says:
Peter, Arun Debray is referring to the fact that whereas the (linear algebraic) orthogonal group O(q) associated to a non-degenerate quadratic space (V,q) over a field k is insensitive (say as a subgroup of GL(V)) to replacing q with a scalar multiple cq for nonzero c, the isomorphism class of the (linear algebraic) group Pin(q) considered as a central extension of O(q) by \mu_2 is *very* sensitive to such change in q when c is a non-square in k. This sensitivity to such change in q at the level of the Pin group is a shadow of what occurs at the level of Clifford algebras: for non-square c, one doesn’t see any direct link between the Clifford algebras C(V,q) and C(V,cq). For your situation, the context of interest is (V,q) positive-definite of dimension n>1 over k=R (even n=2) and c=-1.
Staying in the general setting for conceptual clarity, an obstruction to finding an isomorphism between Pin(q) and Pin(cq) as central extensions is encoded in the spinor norm O(q)(k) –> H^1(k,\mu_2) = k*/(k*)^2 that is most efficiently defined as the connecting map associated to the short exact sequence 1 –> \mu_2 –> Pin(q) –> O(q) –> 1 of (linear algebraic) groups, and is characterized most concretely by the condition that it carries the reflection r_v in any non-isotropic v (i.e., v for which q(v) is nonzero, such as any nonzero v when k=R with q definite) to q(v) mod (k*)^2. The point is that if Pin(q) and Pin(cq) are isomorphic as central extensions then the associated connecting maps (i.e., spinor norms) coincide, so then *necessarily* q(v) and c(q(v)) coincide mod (k*)^2 for any non-isotropic v. But that forces c to be a square in k! So when c is a non-square in k, we really get non-isomorphic central extensions.
Working over the real numbers, there is just one isomorphism class of positive-definite quadratic spaces of a given dimension n > 1, so one may refer to its associated Pin group as “Pin^+(n)” (considered as a central extension of O(n) by \mu_2), and refer to the one for the negative-definite variant as “Pin^{-}(n)” (also considered as a central extension of O(n) by \mu_2). Since c=-1 is not a square in R, these two central extensions of O(n) by \mu_2 are not isomorphic. (For expository simplicity I am sweeping under the rug the distinction between linear algebraic R-groups and compact Lie groups because it turns out not to be a problem in this case: see the theorem of Chevalley stated in my answer to https://mathoverflow.net/questions/6079/classification-of-compact-lie-groups/16269#16269 for a precise statement about that.)
6. Petite Kabylie says:
Will the Komargodski paper shed some light on confinement?
Thank you!
7. Peter Woit says:
BCnrd,
Thanks! I see, this is the same phenomenon that shows up in four dimensions as the fact that while Spin(3,1)=Spin(1,3), Pin(3,1) is different than Pin(1,3). This has led to some debate in the physics literature about physics being sensitive to what is usually thought of as a choice of sign convention.
Petite Kabylie,
The paper has some claims about implications for the phase diagram as a function of theta and the temperature, but not I think for what happens at theta=0, which seems to be the physically relevant value.
8. BCnrd says:
Peter, that’s right. I should have also noted (for the purposes of the comparisob of spinor-norm calculations upon replacing q with cq) that the reflection r_v \in O(q) in a non-isotropic vector v is *insensitive* to replacing q with cq since by definition r_v(x) = x – (B_q(v,x)/q(v))v where B_q(v,w) = q(v+w)-q(v)-q(w) is the symmetric bilinear form associated to q. (Note this definition of B_q omits the factor of 1/2 that is sometimes used to define B_q, so B_q(v,v)=2q(v) and in particular the factor of 2 one usually sees in the definition of r_v is really lurking inside B_q).
Petite Kabylie,
page 23 onward has the details
10. ilych oblomov says:
P
Peter Woit
New idesas about QFT and Poincare group can be found in the ideas introduced by Mund, Schroer and Yngvason: string localised field that allow getting rid of gauge theory (work in positive definite Hilbert space) and the Higgs mechanism (the Higgs is still there but for other reasons) . Rehren has a preprint the same day as Arkani-Hamed’s:
Pauli-Lubanski limit and stress-energy tensor for infinite-spin fields
https://arxiv.org/abs/1709.04858
(and reference within)
11. Jack Morava says:
Can a mathematician put in a plug for
https://arxiv.org/abs/1707.05448
The Sum Over Topological Sectors and θ in the 2+1-Dimensional CP1 σ-Model
Daniel S. Freed, Zohar Komargodski, Nathan Seiberg
as well? | 2018-11-19 22:42:34 | {"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": 0.8050895929336548, "perplexity": 946.1114826095594}, "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-2018-47/segments/1542039746112.65/warc/CC-MAIN-20181119212731-20181119234731-00294.warc.gz"} |
https://math.stackexchange.com/questions/803800/convergent-subsequence-for-sinn | # Convergent subsequence for sin(n)
Define a sequence $(a_n)_{n = 1}^{\infty}$ of real numbers by $a_n = \sin(n)$. This sequence is bounded (by $\pm1$), and so by the Bolzano-Weierstrass Theorem, there exists a convergent subsequence.
My question is this: Is there any way to construct an explicit convergent subsequence?
Naïvely, I tried considering the subsequence $$\sin(3), \,\sin(31), \,\sin(314), \,\sin(3141),\, \sin(31415),\, \dots$$ hoping it would converge to $0$, but I was unable to prove this (and I think it's probably not even true).
• You can come up with a subsequence that converges to $1$ (or any other value you choose in $[-1,1]$): Let $a_1=\sin(1)$. Then let $a_2=\sin(k_2)$ where $k_2$ is the least integer for which $\sin(k_2)\geq \sin(1)$. In general, let $a_n = \sin(k_n)$ where $k_n$ is the least integer for which $\sin(k_n) \geq \sin(k_{n-1})$. A similar process gives a subsequence that converges to any value in $[-1,1]$ you choose. The proof shouldn't be too taxing. However, it would be quite a push to call this an explicit subsequence. – Gamma Function May 21 '14 at 7:27
This isn't a very analytic way of doing it but consider the continued fraction expansion $\pi = [a_0; a_1, a_2, \ldots]$. Generally we know that, if $p_n/q_n$ are the convergents to $\pi$ then $|q_n\pi - p_n| \leq 1/q$ so the $p_n$ are the closest integers to being multiples of $\pi$ so (with slight abuse of notation) $\sin(p_n) \rightarrow \sin m\pi = 0$ with $n \rightarrow \infty$ meaning that this is an explicit construction of the sort that you're after.
• I've just realised that I've written this in a really weird way, you want are the numerators of the convergents $p_n$ so the sequence starts $3, 22, 333, 355, 103993, \ldots$ and then $\sin$ of this sequence tends to $0$ pretty darn quickly. – Stijn Hanson May 21 '14 at 7:47
I am not very confident that it converges, because this is how well you can approximate $10^k \cdot \pi$ with an integer. But as the difference will be infinite many times greater than $0.9$ and as you get bounds you see that this sequence is divergent.
I think this is more a question what is explicit for you, because you need to know how well you can approximate a multiple of $\pi$ with an Integer. | 2019-08-18 06:58:07 | {"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": 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": 0.9657607078552246, "perplexity": 85.04782878299798}, "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-2019-35/segments/1566027313715.51/warc/CC-MAIN-20190818062817-20190818084817-00485.warc.gz"} |
https://fa22.datastructur.es/materials/lab/lab11/ | Lab 11: BYOW Introduction
## FAQ#
Each assignment will have an FAQ linked at the top. You can also access it by adding “/faq” to the end of the URL. The FAQ for Lab 11 is located here.
This lab will help you with Project 3: Build your own World (BYOW). The first part will teach you how to use a set of “tiles” to generate shapes on your screen. This will apply to building the rooms, hallways, and other features of your world in Project 3. Next week’s lab will teach you more about how to use the StdDraw package to make a fun text-based game. This will help you build the main menu and other text-based elements of Project 3. It will also teach you how to achieve user interactivity, which is vital to Project 3!
## Pre-lab #
Some steps to complete before getting started on this lab:
• As usual, use git pull skeleton main
• Watch a previous semester’s project 3 getting started video at this link. Note the name and API have changed slightly, but the bigger picture still applies.
• Understand that project 3 will be a marathon and not a sprint. Don’t wait until the last minute. You and your partner should start thinking about your design NOW.
• Read over Phase 1 of the project 3 spec.
## Plus World Introduction #
In the first half of this lab, you and your partner will learn some basic techniques and tools that will be helpful for project 3.
## Part I: Meet the Tile Rendering Engine #
#### Boring World #
Open the up the skeleton and check out the BoringWorldDemo file. Try running it and you should see a window appear that looks like the following:
This world consists of empty space, except for the rectangular block near the bottom middle. The code to generate this world consists of three main parts:
• Initializing the tile rendering engine.
• Generating a two dimensional TETile[][] array.
• Using the tile rendering engine to display the TETile[][] array.
The API for the tile rendering engine is simple. After creating a TERenderer object, you simply need to call the initialize method, specifying the width and height of your world, where the width and height are given in terms of the number of tiles. Each tile is 16 pixels by 16 pixels, so for example, if we called ter.initialize(10, 20), we’d end up with a world that is 10 tiles wide and 20 tiles tall, or equivalently 160 pixels wide and 320 pixels tall. For this lab, you don’t need to think about pixels, though you’ll eventually need to when you start building the user interface for Project 3 (discussed in the next lab).
TETile objects are also quite simple. You can either build them from scratch using the TETile constructor (see TETile.java), or you can choose from a palette of pregenerated tiles in the file Tileset.java. For example, the code from BoringWorldDemo.java below generates a 2D array of tiles and fills them with the pregenerated tile given by Tileset.NOTHING.
TETile[][] world = new TETile[WIDTH][HEIGHT];
for (int x = 0; x < WIDTH; x += 1) {
for (int y = 0; y < HEIGHT; y += 1) {
world[x][y] = Tileset.NOTHING;
}
}
Of course, we can overwrite existing tiles. For example, the code below from BoringWorld.java creates a 14 x 4 tile region made up of the pregenerated tile Tileset.WALL and writes it over some of the NOTHING tiles created by the loop code shown immediately above.
for (int x = 20; x < 35; x += 1) {
for (int y = 5; y < 10; y += 1) {
world[x][y] = Tileset.WALL;
}
}
The last step in rendering is to simply call ter.renderFrame(world), where ter is a TERenderer object. Changes made to the tiles array will not appear on the screen until you call the renderFrame method.
Try changing the tile specified to something else in the Tileset class other than WALL and see what happens. Also experiment with changing the constants in the loop and see how the world changes.
Note: Tiles themselves are immutable! You cannot do something like world[x][y].character = 'X'.
#### Random World #
Now open up RandomWorldDemo.java. Try running it and you should see something like this:
This world is sheer chaos – walls and flowers everywhere! If you look at the RandomWorldDemo.java file, you’ll see that we’re doing a few new things:
• We create and use an object of type Random that is a “pseudorandom number generator”.
• We use a new type of conditional called a switch statement.
• We have delegated work to functions instead of doing everything in main.
A random number generator does exactly what its name suggests, it produces an infinite stream of numbers that appear to be randomly ordered. The Random class provides the ability to produce pseudorandom numbers for us in Java. For example, the following code generates and prints 3 random integers:
Random r = new Random(1000);
System.out.println(r.nextInt());
System.out.println(r.nextInt());
System.out.println(r.nextInt());
We call Random a pseudorandom number generator because it isn’t truly random. Underneath the hood, it uses cool math to take the previously generated number and calculate the next number. We won’t go into the details of this math, but see Wikipedia if you’re curious. Importantly, the sequence generated is deterministic, and the way we get different sequences is by choosing what is called a “seed”. If you start up a pseudorandom generator with a particular seed, you are guaranteed to get the exact sequence of random values.
In the above code snippet, the seed is the input to the Random constructor, so 1000 in this case. Having control over the seed is pretty useful since it allows us to indirectly control the output of the random number generator. If we provide the same seed to the constructor, we will get the same sequence values. For example, the code below prints 4 random numbers, then prints the SAME 4 random numbers again. Since the seed is different than the previous code snippet, the 4 numbers will likely be different than the 3 numbers printed above. This is super helpful in Project 3, as it will give us deterministic randomness: you worlds look totally random, but you can recreate them consistently for debugging (and grading) purposes.
Random r = new Random(82731);
System.out.println(r.nextInt());
System.out.println(r.nextInt());
System.out.println(r.nextInt());
System.out.println(r.nextInt());
r = new Random(82731);
System.out.println(r.nextInt());
System.out.println(r.nextInt());
System.out.println(r.nextInt());
System.out.println(r.nextInt());
In the case a seed is not provided by the user/programmer, i.e. Random r = new Random(), random number generators select a seed using some value that changes frequently and produces a lot of unique values, such as the current time and date. Seeds can be generated in all sorts of other stranger ways, such as using a wall full of lava lamps.
For now, RandomWorldDemo uses a hard coded seed, namely 2873123, so it will always generate the exact same random world. You can change the seed if you want to see other random worlds, though given how chaotic the world is, it probably won’t be very interesting.
The final and most important thing is that rather than doing everything in main, our code delegates work to functions with clearly defined behavior. This is critically important for your project 3 experience! You’re going to want to constantly identify small subtasks that can be solved with clearly defined methods. Furthermore, your methods should form a hierarchy of abstractions! We’ll see how this can be useful in the final part of this lab.
## Part II: Use the Tile Rendering Engine #
#### Plus World Intro #
Above, we’ve seen how we can draw a world and generate randomness. Your task for the first half of lab is to use the tile generator we’ve seen to make a plus shape, like below.
Optionally, you can take these plus shapes, and form a beautiful (and randomized) tesselation like below.
In the actual Project 3, you’ll be generating random worlds as well, although in the project, they will be indoor spaces instead of open landscapes. While this lab task does not directly apply to the project, it will familiarize you with important libraries including our Tile Rendering engine, and also help you think about how you can take complex drawing tasks and break them into simpler pieces.
Your should be able to draw differently sized plus signs. The picture above is of size-4 plusses, and below we see a world consisting of size-1, size-2, and size-3 plusses, respectively.
#### Drawing A Single Plus #
The only task you are required to do for this lab is to draw a single plus. Tesselating them to fill the whole screen is a cool but optional task. Your class is completely blank, but you’re encouraged to reference BoringWorld and RandomWorld to get an idea of how to set up the class! Once you’ve done the setup to make an empty world, start by trying to create a method addPlus that adds a plus of size s to a given position in the world.
Here, we see the size is the tile width for one “leg” of the plus. There are many ways to break down a plus. You could think of it as three rows, where the middle row is wider. You could think of it as 5 squares: top, bottom, left, right, and center. You could view it as neither! The way you define the “position” of a plus is also up to you!
aaa
aa aaa
aa aaa
a aaaaaa aaaaaaaaa
aaa aaaaaa aaaaaaaaa
a aa aaaaaaaaa
aa aaa
aaa
aaa
To verify that your addPlus method works, write a short main method and verify that things looked OK. Unfortunately, writing a JUnit test to verify that you’ve properly drawn a plus is just as hard as drawing the plus itself, so you won’t be able to build confidence in your addPlus method in a nice way like you can with simpler methods.
Note that even deciding the addPlus method signature is a non-trivial task! This exercise will give you a glimpse into the kind of decision-making and design thinking you will have to do in Project 3.
Deciding what classes you need for this lab, just like Proj3, is entirely up to you! One example class you might add is a Point class, to represent coordinates in your world. You can also think about making a Plus class. This will require some careful thinking about what a Plus object is in this program, what it should know about itself (i.e. what are its instance variables), and what it can do (i.e. its public instance methods). This is what a lot of your work on Project 3 is going to look like!
There are many different ways to approach this problem, and that’s what makes it so interesting.
Tip: If you want randomized colors for your plus tiles, e.g. so that not every flower is exactly the same, see the TETile.colorVariant method
#### Optional: Drawing A Tesselation of Plusses #
Once you have code that can draw a single plus, you can try to tessellate them to form a world, like shown in the example images earlier.
As with drawing a single plus, there are a huge number of ways to draw a tesselation. The most important part is to identify helper methods that will be useful for the task!
You should absolutely not try to do something like do everything in a nested for loop with no helper methods. While it is technically possible to do this, you will melt your brain. In this project, it is absolutely vital that you avoid the temptation to always work at a “low level”. Without hierarchical abstraction, your mind will transform into a pile of goo under the weight of all the complexity.
By writing very well-defined, nicely commented helper methods, you also make it physically possible to get help from course staff. During office hours for this project, TAs will be limited to ten minutes per pair, and will not be allowed to spend a long time getting to know the intricacies of your code. They are there for high level guidance, as well as help debugging when you’ve really exhausted all your options.
As a hint for one possible solution, look for repeating patterns in a given tesselation. If you look at a single plus in a tesselation, when does it “repeat” itself? How many squares do you have to move over until you find another plus at that same height in the image?
## HexWorld Live Coding Demo #
The live coding demo can be found here! Note that this video is from a previous semester, in which students were required to draw Hexagons instead of Pluses. Try to generalize the logic from drawing a tesselation of Hexagons to a tesselation of Pluses!
## Moving on to Project 3 #
In theory, this lab has taught you everything you need to know to get started on Project 3! The process of generating your world will be similar in many ways to drawing a hexagon world, though Project 3 world generation will be considerably more complex. Read over Phase 1 of the project 3 spec.
Take a look at the questions in project3prep.md. Feel free to discuss with your partner or a TA before jotting down your answers.
## Submission #
You’ll be submitting your completed project3prep.md file to Gradescope. You will get full credit as long as this is filled out and submitted!
Last built: 2022-12-03 16:06 UTC | 2023-02-02 22:01:25 | {"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": 0.2699923515319824, "perplexity": 999.9600138235735}, "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-2023-06/segments/1674764500041.18/warc/CC-MAIN-20230202200542-20230202230542-00857.warc.gz"} |
https://archive.mcpt.ca/cpt-lessons/data-structures/prefix-sum-array/ | # This content is archived!
For the 2018-2019 school year, we have switched to using the WLMOJ judge for all MCPT related content. This is an archive of our old website and will not be updated.
# Introduction
Given an array $a$ of $N$ integers, answer $Q$ queries: the sum of all the elements in the range $[\text{start}, j]$
To solve this problem, we could sum up the given range for each query, but that would be worst case $\mathcal{O}(N)$ per query. If there are many queries, the program will be extremely slow. The fact that the array doesn’t change throughout the queries tells us that we must use preprocessing: prefix sum array!
There are $N^2$ unique ranges in an array. Creating a $N^2$ sizes array to hold the sums of each possible range would be excessive. The prefix sum array only uses an $N$ sized array.
Like in the name, the array holds the sum of all elements before the given index. ps[i] of the prefix sum array contains the sum of the array indices $[0, i)$.
# Example
Given the following array:
The prefix sum array will look like:
ps[4] has a value of 6. It corresponds to the sum of the range $[0, 3]$.
Say we want only the range $[2, 3]$. We have 2 extra elements in the sum, so we must subtract them.
The subtracted region is the first two elements: ps[2].
It adds up. We want the sum of the range $[2, 3]$: -2 + 1 = -1 = ps[4] - ps[2] = 6 - 7.
In short, the sum of the range $[\text{start}, \text{end}]$ is ps[end + 1] - ps[start].
You may have noticed that the prefix sum array has an extra element, the 0 at the start of the array. This makes it more convenient to handle queries asking for the sum of the range $[0, \text{end}]$.
# Implementation
Constructing a prefix sum array is relatively easy, as shown in the code snippet below where ps is the new prefix sum array, a is the original array, and N is the original array size.
Finding the sum between any two indexes of a given array can be implemented as below. This method assumes that the constraints 0 < l ≤ r < N are held.
Notice that when querying for the range $[0, i]$, ps[l] = 0 due to the extra element appended to the start. Without this element (or an if statement to handle the special case where l == 0), the program would crash due to an index out of bounds (-1).
## Time Complexity
Construction: $\mathcal{O}(N)$, where $N$ is the size of the original array.
Sum Query: $\mathcal{O}(1)$
## Space Complexity
$\mathcal{O}(N)$, where $N$ is the size of the original array.
The prefix sum array is a data structure which allows fast calculation of the sum of a given range of numbers. With the prefix sum array, the total runtime to solve the given problem is now $O(N + Q)$, which is a large improvement over the naive solution. | 2021-09-26 15:39:18 | {"extraction_info": {"found_math": true, "script_math_tex": 21, "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": 0.42362287640571594, "perplexity": 424.7817613992003}, "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/1631780057882.56/warc/CC-MAIN-20210926144658-20210926174658-00612.warc.gz"} |
https://electronics.stackexchange.com/questions/177834/v-i-uppercase-lowercase-convention/177838 | # V/I uppercase/lowercase convention?
Is there any standard in industry for using uppercase or lowercase for V and I in circuit diagrams? I ask this because my book seems to switch back and forth between the two without any rhyme or reason and I can't figure out any pattern for why it will choose one way over the other. It also switches back and forth for subscripts.
• Can you show an example? Jun 29 '15 at 5:49
• I was just wondering if there's a standard to go by, I don't have good lighting at the moment to take pictures to compare. If no one answers by morning I will though. Jun 29 '15 at 6:06
I agree with you that it is important to know the meaning of the different ways for using such symbols. And the same applies also to the voltage-to-current ratios (resitances, impedances). For my opinion the standard is (or should be) as follows:
• Uppercase (V,I) for DC and rms values
• Uppercase for ohmic resistors R=V/I
• Lowercase (v,i) for signals as a function of time: v(t), i(t)
• Lowercase (v,i) for (small) differential signals available for a certain DC bias point only.
• Lowercase (r) for differential (dynamic) small-signal resistances r=v/i.
As a negative example, in small-signal equivalent circuits, sometimes the inverse transconductance gm of a BJT is used as Re=1/gm. This is very confusing because this does not represent any (ohmic) resistor and, more than that, can be mixed-up with an external emitter resistor RE.
EDIT/UPDATE: Regarding impedances:
For reactive elements (L, C) the voltage-to-current ratios are called "impedance". Because this applies to rms values of sinusoidal signals only the symbol for impedances also is written in uppercase letters Z=V/I.
• +1 @LvW, I'd like to request OP to take this up as an answer. The answer provided by me is not so specific and rather a link-only kind, while this one is right to the point. Jun 29 '15 at 6:34
• Didn't see it at first, but this is exactly the info I needed. Thanks! Jun 29 '15 at 6:35
quantities obtained applying various kind of transforms to the time domain signal should be uppercase, specifically:
• Phasors, i.e. complex representation of sinusoidal signals.
• Frequency-domain signals, i.e. Fourier transforms of time-domain signals. For example the frequency response of a system and related input and output signals or the like:
• $Y(f) = H(f) \cdot X(f)$
• $V_o(\omega) = G(\omega) \cdot V_i(\omega)$
• s-domain signals, i.e. Laplace transforms of time-domain signals. For example the transfer function of a system and related input and output signals or the like:
• $Y(s) = H(s) \cdot X(s)$
• $V_o(s) = G(s) \cdot V_i(s)$
• z-domain signals, i.e. Z-transformed signals corresponding to discrete-time signals (e.g. as used in digital signal processing). For example the transfer function of a digital system and related input and output signals or the like:
• $Y(z) = H(z) \cdot X(z)$ | 2021-10-16 03:51:16 | {"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": 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": 0.6866319179534912, "perplexity": 1181.1072371291825}, "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/1634323583408.93/warc/CC-MAIN-20211016013436-20211016043436-00699.warc.gz"} |
https://socratic.org/questions/what-is-the-equation-of-the-line-perpendicular-to-y-3x-that-passes-through-1-28 | # What is the equation of the line perpendicular to y=3x that passes through (-1,28) ?
Jan 4, 2016
3y + x - 83 = 0
#### Explanation:
y = 3x has a slope m =3
for perpendicular lines ${m}_{1} \times {m}_{2} = - 1$
$3 \times {m}_{2} = - 1$
→ m_2 = -1/3
equation of perpendicular line : y - b = m(x - a ) , $m = - \frac{1}{3} , \left(a . b\right) = \left(- 1 , 28\right)$
substituting in these values gives
$y - 28 = - \frac{1}{3} \left(x - \left(- 1\right)\right)$
multiply through the equation by 3 will eliminate the fraction
so 3y - 84 = - x - 1
hence 3y + x -83 = 0 | 2020-12-03 20:45:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "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": 0.3573882579803467, "perplexity": 1246.231697014856}, "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/1606141732696.67/warc/CC-MAIN-20201203190021-20201203220021-00278.warc.gz"} |
https://3dprinting.stackexchange.com/questions/1582/is-using-a-hair-dryer-on-my-m3d-build-plate-safe | # Is using a hair dryer on my M3D build plate safe?
I often have trouble with prints being especially difficult to remove from the build plate on my Micro3D printer. My wife suggested using a hair dryer on the underside of the plate. I was initially appalled at the idea, but now I think she may be on to something. Is this safe? Good idea? Bad idea? Heresay?
• Do you get the build plate out of the printer for the procedure? I realized that I do not know whether this is even possible when I finished my answer, and it will need to be revisited depending on this ;) – kamuro Aug 3 '16 at 7:54
## 6 Answers
Typically, people cool down their build plates to get parts to release, rather than heat them up. That said, I doubt a hair drier will get hot enough to do any damage to the build plate. You could try it with no harm done.
• I've definitely tried it, and it seems to work pretty well in getting the parts to loosen up. I'm just worried about damage to the plate. – Chris G. Williams Aug 2 '16 at 18:34
It's what i do. Painters tape. are you using the m3d plastic? that's why. the coating is to make sure it sticks their only plan to get it off is to bend the plate a little bit. Hair drier won't end the world. don't hold the plate and hair dry it, that might hurt. But M3D sells spare plates it you destroy it. Try it out, tell us what happens.
• Yeah, I use their "3D Ink" and I haven't been using painters tape, and I do flex the plate a little (which also worries me that I'm going to damage it), but the hair dryer trick seems to work ok, though I've only done it a few times. – Chris G. Williams Aug 2 '16 at 18:41
• cool, thanks for the tip. but also, you should look into hatchbox plastic on amazon. its 4 times the amount of plastic for a little more than the m3d plastic. i use it with tape and its awesome and i have so much of it. i think its 20\$for 1lb roll where m3d is 15\$ for 1.5 lb roll. Logic is there somewhere. – Simcha Hoffmann Aug 2 '16 at 18:44
I agree to Tom's first part of the answer, usually you'd cool down the plate to loosen the print. This is reasoned by the shrinkage of the builplate while the print stays extended. The strain put into the interface helps to get the print of. Warming the plate could essentially do the same, but since you deposit a warm filament, one would assume that by warming up you will reduce the strain that has been built up by the regular cooling of the filament already.
I guess an uneven heating with a hairdryer will probably introduce uneven strain or evan some kind of warping of the buildplate that puts more strain to the interface which makes your approach work. If you want to test whether you have some local deformation you could characterize this by reflecting a laserpointer from the heatbed and marking the reflection on a rather far away wall for some controlled positions you can get the laser in (by say putting it on a photography tripod). The change of this reflections towards each other could tell you about the deformation.
I also agree that most of the hairdryers around would not be hot enough to be a worry, but since most of the Micro3D is made from plastic I would put twice the time into figuring out if that is really true.
Just for the fun of it, you could put an ice cube next to your finished print if you make sure that molten water will not go anywhere it is not supposed to be. Maybe this lifts off the print as well. However, I do not recommend doing this, of course.
That was a problem for me too. My M3d printer was getting stuck to the plate. However, I now print on painters tape, and I put down painters take on the bed. Then I glue stick the tape, and when I am done, I just pull it up.
You should try it, because it will allow you to print with other then the m3d plastic.
• Thanks for the answer. I have considered using painters tape, but I thought the purpose of the coating on the build plate was to eliminate the need for that. Regardless, this doesn't really answer my question about whether it's safe to use a hair dryer to lightly heat up the build plate so my prints come off easier. – Chris G. Williams Aug 2 '16 at 18:33
Before I got an aftermarket heated print bed for my M3D, I regularly used a hair dryer to pre-heat the build plate up to 60-70 °C before printing with no ill effects.
cold wind can help to acceleratory cool down and dry the build plates to make it easy to part them. | 2020-12-04 00:19:52 | {"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": 0.30257707834243774, "perplexity": 1151.7851200688526}, "config": {"markdown_headings": true, "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-2020-50/segments/1606141732835.81/warc/CC-MAIN-20201203220448-20201204010448-00099.warc.gz"} |
https://tex.stackexchange.com/questions/136094/how-can-i-use-latex2rtf-with-biblatex | # How can I use latex2rtf with biblatex?
I would like to output a .tex file in .rtf format. Latex2rtf does the job, except that it does not support biblatex ("package/option unknown"); thus, in the rtf, the citations are replaced with "[Error: Reference source not found]". Is there a way to get latex2rtf to work with biblatex? If not, what is the easiest way to move from tex to rtf with citations intact?
• Probably the only way is tex4ht --- converting to OpenDocument and then to RTF. It works quite well with biblatex. Although I also would be glad to learn about other methods, since I had problems with converting math with tex4ht. – Oleg Domanov Oct 2 '13 at 17:51
• I've had no problems using natbib with bibtex. Just get a document that compiles and the conversion with latex2rtf works fine. – Andy Clifton Oct 3 '13 at 18:07
• Thanks both. I will try tex4ht, which I'd not heard of. I'd rather stick with biblatex than shift over to natbib+bibtex just for this one stupid journal article. – Nick Oct 5 '13 at 13:18
I can suggest 2 ways.
1. tex4ht (included in Texlive and Miktex) supports biblatex and works quite well. It may fail with some fonts, packages, etc., so it's better to avoid too exotic ones.
2. biblatex has the natbib compatibility option. So, if you use only natbib commands \citep, \citet, etc., you may easily switch from biblatex to bibtex (by commenting/uncommenting few lines) and then use latex2rtf or other tools. This is a limited "support" of biblatex but it may be enough for your needs. You even may have redefinitions like \renewcommand*{\citep}{\autocite} and preserve some advantages of biblatex.
• Thanks. Tex4ht works very well -- better than option 2. I had to add some lines toto my preamble as per this answer: tex.stackexchange.com/questions/62885/… And I have not managed to get the outputted file to display superscript footnote markers correctly, but it's close enough. – Nick Oct 8 '13 at 17:04 | 2019-12-06 21:45:52 | {"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": 0.9379332065582275, "perplexity": 2857.125307205244}, "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-2019-51/segments/1575540490972.13/warc/CC-MAIN-20191206200121-20191206224121-00323.warc.gz"} |
https://math.stackexchange.com/questions/2325807/second-derivative-of-a-determinant | # Second Derivative of a Determinant
How does one evaluate the second derivative of the determinant of a square matrix?
Jacobi's formula tells us how to evaluate the first derivative but I can't find anything for the second. This is my attempt:
We can start using the partial derivative formulation of Jacobi's formula, assuming A is invertible: $$\frac{\partial}{\partial \alpha}\det A = (\det A) \text{tr}\left( A^{-1} \frac{\partial}{\partial \alpha} A \right)$$ Taking a second derivative: $$\frac{\partial^2}{\partial \alpha^2}\det A = \frac{\partial}{\partial \alpha}\left[(\det A) \text{tr}\left( A^{-1} \frac{\partial}{\partial \alpha} A \right)\right]$$ Applying product rule: $$= \frac{\partial}{\partial \alpha}(\det A) \cdot \text{tr}\left( A^{-1} \frac{\partial}{\partial \alpha} A \right) + (\det A) \frac{\partial}{\partial \alpha} \text{tr}\left( A^{-1} \frac{\partial}{\partial \alpha} A \right)$$ Replacing $\frac{\partial}{\partial\alpha}\det A$ with Jacobi's formula: $$= (\det A) \text{tr}\left( A^{-1} \frac{\partial}{\partial \alpha} A \right) \cdot \text{tr}\left( A^{-1} \frac{\partial}{\partial \alpha} A \right) +(\det A) \text{tr}\left( \frac{\partial}{\partial \alpha}\left(A^{-1} \frac{\partial}{\partial \alpha} A \right)\right)$$ Factoring out $\det(A)$: $$= (\det A) \left[\text{tr}^2\left( A^{-1} \frac{\partial}{\partial \alpha} A \right) + \text{tr}\left( \frac{\partial}{\partial \alpha}\left(A^{-1} \frac{\partial}{\partial \alpha} A \right)\right)\right]$$ Another product rule: $$= (\det A) \left[\text{tr}^2\left( A^{-1} \frac{\partial}{\partial \alpha} A \right) + \text{tr}\left(\frac{\partial}{\partial \alpha}A^{-1} \frac{\partial}{\partial \alpha} A + A^{-1} \frac{\partial^2}{\partial \alpha^2} A \right)\right]$$ Finally, using $A_{\alpha}$ to denote the partial of A wrt to $\alpha$ we have $$\frac{\partial^2}{\partial \alpha^2}\det A= \det(A) \left[\text{tr}^2\left( A^{-1} A_{\alpha} \right) + \text{tr}\left(A^{-1}_{\alpha} A_{\alpha}\right) + \text{tr} \left( A^{-1} A_{\alpha^2} \right)\right]$$ The second trace actually reduces to N, for an NxN matrix: $$\text{tr}\left(A^{-1}_{\alpha} A_{\alpha}\right)=\text{tr}(I)$$ $$=\sum_{diagonals}1$$ $$=N$$
$$\therefore\frac{\partial^2}{\partial \alpha^2}\det A= \det(A) \left[\text{tr}^2\left( A^{-1} A_{\alpha} \right) + \text{tr} \left( A^{-1} A_{\alpha^2} \right)+N\right]$$
I'm not overly confident with the matrix calculus, but the result is nice enough to seem plausible. Is there another method, or is this proof valid? Thanks!
• Is there any similar results when $A$ is possibly singular? – vulture May 22 '18 at 17:27
To keep things simple, assume $A=A(t)$ is a function of a parameter $t$, and we are after the derivatives at zero. Also assume that $A(t)$ is smooth enough in $t$ and that $A(0)$ is invertible. While we are at it, let's replace $A(t)$ by $B(t)=A(0)^{-1}A(t)$ so that $B(0)=I$.
Then $$B(t)=I+tB'(0)+\frac{t^2}2B''(0)+\cdots$$ for some matrices $B_1$ and $B_2$. We now expand $\det B(t)$ by the formula in terms of permutations and their signs. A permutation moving three or more points will lead to a term with a factor of $t^3$ which we can neglect. The identity permutation yields the product of the diagonal elements of $B(t)$ which is \begin{align} &1+t\sum_{i=1}^n B'(0)_{ii} +\frac{t^2}2\sum_{i=1}^n B''(0)_{ii} +t^2\sum_{1\le i<j\le n}B'(0)_{ii}B'(0)_{jj}+\cdots\\ &=1+t\text{ tr}\,B'(0)+\frac{t^2}2\text{ tr}\,B''(0) +t^2\sum_{1\le i<j\le n}B'(0)_{ii}B'(0)_{jj}+\cdots \end{align} The only other permutations counting are the involutions, which together contribute $$-t^2\sum_{1\le i<j\le n}B'(0)_{ij}B'(0)_{ji}+\cdots.$$
The second derivative of $\det B(t)$ at zero is therefore $$\text{tr}\,B''(0)+2\sum_{1\le i<j\le n} (B'(0)_{ii}B'(0)_{jj}-B'(0)_{ij}B'(0)_{ji}).$$ The sum here is the "second trace" of $B'(0)$, the coefficient of $X^{n-2}$ in its characteristic polynomial.
Now if we like we can write $A(t)=A(0)B(t)$ and get a formula for the second derivative of $\det A(t)$.
I think your derivation is good up until you take the derivative of $A^{-1}$. From formula (40) of the Matrix Cookbook the derivative is:
$$\partial \left(X^{-1}\right) = - X^{-1} \left( \partial X \right) X^{-1}$$
so instead of a second term of $\operatorname{tr} \left( A_\alpha^{-1} A_\alpha \right)$ it should instead be $-\operatorname{tr} \left( A^{-1} A_\alpha A^{-1} A_\alpha \right)$. The final result then is:
$$\det \left(A\right) \left( \left(\operatorname{tr}\left(A^{-1} A_\alpha\right)\right)^2 + \operatorname{tr}\left(A^{-1} A_{\alpha\alpha}\right)-\operatorname{tr}\left(A^{-1}A_\alpha A^{-1} A_\alpha\right)\right)$$
It is a simple matter to confirm this formula symbolically for small examples in your CAS of choice (for a Mathematica implementation see my answer to a similar question on MSE).
As pointed out by Carl, your mistake is to permute the inverse and derivative operator:
$$\partial_\alpha(A^{-1}) \neq (\partial_\alpha A)^{-1} \, .$$
You can easily generalize it for whatever two differentiating arguments ($\alpha$ and $\beta$). Starting from Jacobi's formula:
$$\partial_{\alpha}(\mathrm{det}(A)) = \mathrm{det}(A) \, \mathrm{tr}\left(A^{-1} \, \partial_\alpha A\right) \,$$
applying on it the chain rule:
$$\partial_{\alpha\beta}(\mathrm{det}(A)) = \partial_\beta(\mathrm{det}(A)) \, \mathrm{tr}\left(A^{-1} \, \partial_\alpha A\right) + \mathrm{det}(A) \, \mathrm{tr}\left(\partial_\beta \left(A^{-1} \, \partial_\alpha A\right)\right) \, ,$$
using Jacobi's formula on the first $\beta$ derivative and applying the chain rule on the second:
$$\partial_{\alpha\beta}(\mathrm{det}(A)) = \mathrm{det}(A) \, \mathrm{tr}\left(A^{-1} \, \partial_\beta A\right)\,\mathrm{tr}\left(A^{-1} \, \partial_\alpha A\right) + \mathrm{det}(A) \, \mathrm{tr}\left(\partial_\beta \left(A^{-1}\right) \, \partial_\alpha A\right) + \mathrm{det}(A) \, \mathrm{tr}\left(A^{-1} \, \partial_{\alpha\beta} A\right)\, ,$$
and finally, factoring out the determinant and applying the relation for the inverse $\partial_\beta(A^{-1}) = -A^{-1} \, \partial_\beta A \, A^{-1}$:
$$\partial_{\alpha\beta}(\mathrm{det}(A)) = \mathrm{det}(A) \, \left[\mathrm{tr}\left(A^{-1} \, \partial_\beta A\right)\,\mathrm{tr}\left(A^{-1} \, \partial_\alpha A\right) - \mathrm{tr}\left(A^{-1} \, \partial_\beta A \, A^{-1} \, \partial_\alpha A\right) + \mathrm{tr}\left(A^{-1} \, \partial_{\alpha\beta} A\right)\right] \, ,$$
which is the same as what Carl gave for $\beta=\alpha$:
$$\partial_{\alpha\alpha}(\mathrm{det}(A)) = \mathrm{det}(A) \, \left[\left(\mathrm{tr}\left(A^{-1} \, \partial_\alpha A\right)\right)^2 - \mathrm{tr}\left(A^{-1} \, \partial_\alpha A \, A^{-1} \, \partial_\alpha A\right) + \mathrm{tr}\left(A^{-1} \, \partial_{\alpha\alpha} A\right)\right] \, .$$ | 2019-06-19 19:10:49 | {"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": 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": 1, "equation": 11, "x-ck12": 0, "texerror": 0, "math_score": 0.9555275440216064, "perplexity": 228.59006686504486}, "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/1560627999040.56/warc/CC-MAIN-20190619184037-20190619210037-00445.warc.gz"} |
https://stats.stackexchange.com/questions/125765/comparing-learning-rates-using-unit-curve-in-r | # Comparing Learning Rates using Unit Curve in R
I have data for an experiment where 2 groups (Role) were tested over 3 consecutive trials for a task and time to complete task was recorded in sec.
I wanted to compare the learning curves of the two groups. The curves are not linear and do linearize after log or other transformations.
After searching long and hard, I came across this equation: Y_x = K x^{log_2 (b)}, which is the unit curve, where K= time to complete first trial, Y_x =Time to complete trial x, x=3, b= learning rate
Using this equation I can come up with a learning rate for each individual and than do a t-test to compare between the 2 groups.
My Question: is this equation and/or approach valid??
Here's a link to unit curve explanation
Here is my data and what I did in R
head(LR)
# ID Trial1 Trial2 Trial3 Role
# N4 153 105 28.8 N
# N3 52.2 33 88.2 N
# NA1 360 52.8 118.8 N
# NA6 127.8 229.2 73.2 N
# F2 307.2 178.8 58.8 F
# F3 136.8 157.8 181.2 F
# F4 948 249 42 162 F
# F1 193.8 73.8 97.8 F
x=apply(LR,1, function(x) 2^log((x[4]/x[2]), base=3)) ##equation re-aranged to solve for b
t.test(x~LR\$Role)
• You would almost certainly do best to use a model that incorporates all of your data, rather than try to reduce your data somehow & then run a test. – gung Nov 27 '14 at 20:28
• Your suggested function linearizes (under log-log transformation), so either your data would be expected to approximately linearize with that transformation, or the data likely won't fit that function. – Glen_b Nov 27 '14 at 23:36 | 2019-10-19 07:01:11 | {"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": 0.41347235441207886, "perplexity": 2615.4355254602015}, "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-2019-43/segments/1570986692126.27/warc/CC-MAIN-20191019063516-20191019091016-00277.warc.gz"} |
https://puzzling.stackexchange.com/questions/111932/can-you-reactivate-a-4x4-magic-square | # Can you reactivate a 4x4 Magic Square?
We've already removed the magic from a 3x3 magic square. Recently, one of our 4x4 magic squares was scrambled in an earthquake and I need your help to reactivate it's magic:
#### Objective
Your objective is simple, rearrange the square so that it becomes a valid 4x4 magic square once more:
#### How to Play
To rearrange the tiles, you'll need to swap them, one by one into their correct positions. For example, the $$8$$ tile can be swapped with the $$1$$ tile to effectively place the $$1$$ tile in a correct position:
However, be very careful on which tiles you swap as there are two important rules to swapping tiles:
1. Each tile can only be swapped the number of times its face represents.
2. When swapping tiles, the lower face value is deducted from the higher face value's remaining moves.
For clarity, let's use the $$8$$ tile as an example. At the start, it can be moved 8 times before it becomes locked into place. Swapping it with the $$1$$ tile reduces the number of times it can be moved going forward to 7. To clarify the second rule, imagine that we now swap the 8 tile with the $$4$$ tile:
Two things happen here; the $$4$$ tile now has 3 moves remaining, as does the $$8$$ tile. Now, assume you want to swap the $$8$$ tile with the $$6$$ tile; in this scenario you can't because $$8$$ doesn't have 6 moves remaining, it only has 3 because you swapped with the $$1$$ and $$4$$ tiles already.
#### Movement Restrictions
Tiles can be swapped if they are adjacent to each other. Reactivating magic squares is a much more tedious process than deactivating them; as such, outside tiles are not considered adjacent. Diagonal movements are not allowed. As an example, the $$4$$ tile can be swapped with the $$6$$, $$1$$, $$3$$ and $$13$$ tiles initially, but no others:
Yes, I've created an interactive version of this puzzle. It will be available to the public (linked here) after this puzzle has an accepted answer.
#### Clarifications
Does it have to become the magic square you showed? Or is any 4x4 magic square acceptable?
Any valid magic square is acceptable, though answers that don’t use the provided square should explain why they used a different square.
Suppose we're in a position where $$8_3$$ is next to $$4_4$$. Is it true to say that "both have moves remaining so they can be swapped" (which would result in all of 8's moves being used and possibly a debt/negative balance afterwards) or "$$8_3$$ cannot afford to pay the extra penalty, so cannot move at all"?
$$8_3$$ cannot afford to pay the extra penalty, so you cannot move at all.
#### Hints
The initial configuration should not be able to be rearranged into the provided valid magic square. This is due to the second row in particular. Instead, you'll need to determine if a new magic square can accommodate the initial configuration, based on known limitations. For example, the $$1$$ tile only gets 1 move, so it can only be in 1 of 4 positions in the completed grid. From here, think about which location it's most likely to be in based on how magic squares are calculated and work from there.
The question is phrased carefully.
Can you reactivate this 4x4 magic square?
• Does it have to become the magic square you showed? Or is any 4x4 magic square acceptable? Sep 30 at 3:29
• Suppose we're in a position where $8_3$ is next to $4_4$. Is it true to say that "both have moves remaining so they can be swapped" (which would result in all of $8$'s moves being used and possibly a debt/negative balance afterwards) or "$8_3$ cannot afford to pay the extra penalty, so cannot move at all"? Sep 30 at 13:02
• Following the removal of the no-computers restriction, I set the computer working on this. The main thing I've found so far is that a non-optimised undirected brute-force breadth-first search is far less effective than on the practice problem. Will leave it running, but I'll probably need to work more on optimisations later to get much past "Starting on working set #101, which has 1317995 members... [37473124 already in later working sets]", and the process soon after reaches the available 7GB of ram usage and becomes memory bound rather than CPU bound. Oct 1 at 11:58
• @taco it's a very crude algorithm at present - find all possible moves from the starting state, and report if any of them are a magic square, and with a very inefficient check for whether it's a magic square (see IsMagic() function on the source code now posted to the other puzzle for just how inefficient that part of the current implementation is - the code essentially implements the general definition of a magic square - I initially mis-estimated the search space and hadn't been expecting to need further optimisation). Oct 1 at 13:28
• A further thought - the game seems reversible... so rather than starting at the given grid and trying to find a magic square, one could start with a full list of magic squares, filter out the ones which "obviously" cannot become the given square (e.g. low numbers must move too far), and then consider only moves which "help" to get towards the target state. Google tells me there are 880 4x4 magic squares, but maybe about 80% can be trivially eliminated due to positions of the low numbers. Oct 7 at 14:21
[I previously deleted this answer, as the method was flawed, so the conclusion was not sound. I believe the bugs in my program are now fixed]
Following the removal of the tag from this puzzle, this answer initially treats it as a .
In summary (TL;DR), my current answer to the question "Can you reactivate this 4x4 magic square?" is
No.
It is not possible using the rules given. Unfortunately the damage to this magic square is beyond the possibility of repairing it with this method.
The obvious secondary question is "why not". This probably needs some better insight into the problem to answer properly, and some intermediate lemmas that can be used to simplify the problem to a point where heavy use of computing resources is not necessary...
but at present my only answer to the "why not" question is "Computer says no!".
To the more specific question of whether it is possible to restore the magic as the given magic square, this is now proven impossible in one of the later spoiler blocks following "first stage of a proof".
The approach taken was to adapt the program I used for my supplementary answer to the "practice" problem. This immediately ran into problems because when there are 16 squares with moves totalling 136, the search space is considerably larger than 9 squares with with moves totalling 45 - the fan-out of exponentially increasing numbers of states is much larger, and the program ground to a halt when its storage exceeded the available memory on the computer.
There were several rounds of bugfixes and optimisations; the first version was, from the second move onwards, generating disallowed moves between "outside" tiles which wrapped around in the 3x3 puzzle but not in this one, making an impossibly large search space. The second version disabled these moves but also incorrectly disabled all swaps within the last row and last column, making the search space much smaller than intended, and that was the point when I first posted this answer, using this version of the program, and its output to conclude that:
that no magic square could be made by swapping tiles according to the specified rules. Initially I assumed this was another bug, so tried generating starting states from which a known magic square could be reached within a small number of swaps. The program correctly found those magic squares. [This initial conclusion was not sound, as mentioned above I subsequently DID find another bug in the program, leading to this answer being deleted for a few days...]
Following up from the hint given, and combined with that initial conclusion, I'd originally continued thinking as follows,
"The initial configuration should not be able to be rearranged into the provided valid magic square."
...
"The question is phrased carefully."
it is apparent that it doesn't state the initial configuration can be re-arranged into ANY valid magic square, and indeed the question title asks "Can you...?" and doesn't directly state that a solution path exists.
My further hypothesis was that a property of the grid that remains invariant under the "swapping" mechanism - perhaps analogous to a parity check - is shared between all valid magic squares, but the starting state initialises this incorrectly. If so, it's possible that the complicated rule set is a red herring, and that any number of swaps of any adjacent cells would still be unable to "restore the magic". So that in order to be able to solve this puzzle manually, one should look for a property that remains invariant after the swapping operation, such as a form of parity check on the grid. My hunch was that the puzzle is looking for a "proof of impossibility" rather than following the typical format of this site of having a puzzle with a known solution.
However, when I considered how the same game played on a 2x2 grid might play out, following the Teakettle Principle by then taking my complicated program, and modifying it to
allow infinite swaps by not decrementing the available moves, to run on a 2x2 grid and to output all states encountered, all 24 theoretically possible 2x2 grids were generated by swaps, calling into doubt this entire "parity" argument... if infinite swaps allow any 2x2 grid to be converted into any other 2x2 grid, then the same would apply to larger grids too.
It was also when doing this modification that I found the implementation bug in the second version, and after fixing this, I went through several rounds of compression functions to allow more and more results to be worked on, finally disabling the path-to-solution that was taking more than half the memory, so that it would merely focus on "proof of existence".
Several optimisations later, I had a version of the program which compresses each state to 96 bits to focus just on proof-of-existence. [source code] [output], which showed
after more than 24 hours runtime that the problem space was too big for this approach, even with sufficient compression to be working on rather more than half a billion states at a time, it ran out of memory, having only fully processed states where at least 72 "moves" remained within the grid (each swap uses between 2 and 16 "moves").
Further thoughts occurred such as writing out batches of intermediate state to disk, then merging them on re-loading, so that only a single working set needed to stay in memory at a time. That sounded rather more effort than I wanted to use, and might have increased run time to several days where I needed the computer for other stuff...
To take this further, as mentioned in a comment on the question, I realised that
the game is reversible. If after a sequence of valid moves, one were to then "recharge" all the tiles to their full capacity of moves, the sequence of moves can then be reversed, and after replaying this reverse sequence, the original starting state will be restored. Each tile swaps with exactly the same tiles it did with the forwards sequence, so will use exactly the same number of moves.
With this observation, I then
wrote a program that first generates all possible magic squares, feeds those as starting states into the first generation, and then tracks which legal positions have all tiles "within range" of the correct position in the single target state (the initial given position for this puzzle), and then processes only the states that pass this simple heuristic.
Although this starts with a lot more states, most of them get pruned from the working sets at each iteration, so the memory requirement should be less. Needless to say, the first version didn't work, running out of memory again, but finally after checking whether a state was "within range" before adding to the future working set (meaning duplicate effort but lower memory usage), I had a version which ran to completion. The source code and output for this are also available.
This shows that
The original conclusion did in fact appear to be correct - there is no path from the given starting state to any of the 880 valid 4x4 magic squares, including all 8 reflections and rotations of each.
However it's still no closer to demonstrating "why" other than that a needlessly complicated program said so.
This finally puts me back
where I thought I was at time of initially posting this answer: having a somewhat unsatisfactory "computer proof" of non-existence that implicitly relies on having a bug-free program... so if there are unknown errors in my program/approach, there may yet be a solution that my program missed due to such bugs.
but in any case a much more elegant solution than throwing a computer at it would be far preferable in my opinion - the puzzle originally was originally tagged which clearly means I've missed something fundamental with this computer-generated search for techniques to reduce the search space to get it within human capabilities...
Thoughts towards solving it "properly"
The only hint given so far includes this:
For example, the 1 tile only gets 1 move, so it can only be in 1 of 4 positions in the completed grid. From here, think about which location it's most likely to be in based on how magic squares are calculated and work from there.
Taking that into account, I did the following initial analysis:
Adjust the final version of the program I was using to add diagnostic output telling me where it found each number in the magic squares that weren't trivially eliminated. This provided the following output, suggesting very little restriction on the positions of the other numbers (and even when filtering the tallied states to fix the '1' in one of the possible 4 positions, most choices of position for most other numbers couldn't be trivially eliminated, save that high numbers more often share a row, column or diagonal with the '1' and low numbers more often don't):
Frequency of finding value 1 in each position:
410, 0, 0, 0
357, 232, 0, 0
335, 0, 0, 0
0, 0, 0, 0
Frequency of finding value 2 in each position:
0, 0, 139, 0
0, 62, 132, 102
59, 132, 62, 159
0, 152, 205, 130
Frequency of finding value 3 in each position:
16, 76, 113, 159
12, 42, 115, 91
49, 119, 44, 130
0, 128, 155, 85
Frequency of finding value 4 in each position:
80, 81, 78, 129
50, 53, 127, 69
48, 137, 37, 71
120, 84, 77, 93
Frequency of finding value 5 in each position:
...
Rejected 5706 members as incompatible with target state
This suggests to me that
there's no particular reason to favour any one of the 4 possible positions for the '1' over any other. Each has hundreds of possible magic squares that a simple heuristic suggests are compatible with the starting state.
It is thus totally unclear what "think about which location it's most likely to be in based on how magic squares are calculated" was getting at, as there's no obvious reason to prefer any of the 4 positions over the others, and with 7040 possible magic squares (including reflections and rotations), of which 5706 are trivially eliminated, and which can include every possible position on the grid of every number 4 and larger, there doesn't seem to be a lot to work on. The '2', '3', and '4' tiles all being centrally located are particularly annoying, as this minimises the portion of the grid that they cannot reach. It might be instructive to work through a few cases manually to find additional restrictions on the magic squares to reduce the residual list below 1334 possible magic squares, but I'm at a total loss as to how one could even have made a start on the originally-intended solving path.
After further consideration, it's possible to rank the magic squares
by how many half-swaps would be needed to "restore the magic" if each tile could move the minimum distance between its jumbled state and the magic square. In particular, after adding some further diagnostic output, I got the following:
At least 22 half-swaps required for
1₁ | G₊ | B₊ | 6₆
----+----+----+----
D₊ | 4₄ | 7₇ | A₊
----+----+----+----
8₈ | 9₉ | E₊ | 3₃
----+----+----+----
C₊ | 5₅ | 2₂ | F₊
At least 24 half-swaps required for
B₊ | 6₆ | 7₇ | A₊
----+----+----+----
1₁ | G₊ | D₊ | 4₄
----+----+----+----
E₊ | 3₃ | 2₂ | F₊
----+----+----+----
8₈ | 9₉ | C₊ | 5₅
At least 26 half-swaps required for
[14 possible magic squares which have '1' in R1C1 or R2C1]
A better-directed (possibly manual) search might prefer those magic squares to the one given in the question, because the equivalent diagnostics for the given magic square are:
At least 48 half-swaps required for
1₁ | F₊ | E₊ | 4₄
----+----+----+----
A₊ | B₊ | 8₈ | 5₅
----+----+----+----
7₇ | 6₆ | 9₉ | C₊
----+----+----+----
G₊ | 2₂ | 3₃ | D₊
Which would seem to give the first stage of a proof
of impossibility of reaching that particular grid, which can continue as follows...
Each swap between tiles $$k$$ and $$j$$ where $$k uses up $$k+1$$ "moves", and each tile $$k$$ can only be involved at least $$k$$ times.
48 half-swaps might conceivably be arranged with 24 swaps (where every swap moves both tiles towards their target position), and these might conceivably all involve the lowest numbered tiles.
so we can have 1 swap involving the '1' tile that uses up 2 moves, 2 swaps that use 3 moves, 3 swaps that use 4 moves, 4 swaps that use 5 moves, 5 swaps that use 6 moves, and 6 swaps that use 7 moves for a total of 21 swaps costing 112 moves. To get to 24 swaps, we'd need 3 more swaps involving the '7' tile, costing 8 moves each for a total of 136.
This is exactly equal to the total number of moves present on the starting grid, so in order for there to be a solution that finishes on that particular magic square, every move would need to move both tiles towards their target, with the smaller tile no larger than '7' and the larger tile no smaller than '7'.
Observing the right hand column, this is impossible, because 16, 10, 14, 15 must all swap "out" of the right hand column, but to do so must swap with a tile 7 or lower moving towards its destination to avoid breaking the budget of 136 moves. However, only two tiles lower than 7 are moving into that column, the 4 and 5.
Therefore there is no possible solution of any sequence of swaps to reach the given magic square.
Taking this specific proof into account,
the "move budget" seems likely to be a major factor in a more complete proof. The 22 or 24 half-moves for the "nearest" and "second-nearest" magic squares to the starting state certainly can't be ruled out with a similarly simple argument. The heuristic in the program assumed that a tile can be moved $$n$$ places using $$n$$ moves, which is only the case if it is the lower tile involved in the swap, or if it is swapping with the '1' (which can only occur once for any tile). In particular, the '16' tile will always be the larger tile involved in the swap, so uses up its score very quickly... indeed, an alternative proof of impossibility for the given magic square is that the '16' tile cannot reach the opposite corner, as it involves 6 swaps, and each swap costs the value of the tile it swaps with... even swapping with the lowest numbers would cost $$1+2+3+4+5 = 15$$ for 5 moves. Tiles of lower value can make 6 moves, but effectively "steal" part of the move budget from other tiles, as they must be the lower tile involved in at least some swaps.
For a next step, I'd probably look more closely at the two magic squares shown above, which require only 22 or 24 half-swaps. If there was yet another bug in my program, so that I was wrong about there being no solution, those would be the most likely candidates... and if it's impossible for any magic square, demonstrating why it's impossible for those specific ones which require the smallest net movement of tiles would seem likely to inform why it's impossible in the general case.
• Just a quick note that I didn't start the "next step" referred to in the final spoiler block - I have many other tasks this week, so although I'll certainly revisit this problem if a full solution isn't posted in the meantime, it probably won't be for a while. Oct 18 at 15:23 | 2021-12-02 16:47:55 | {"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": 32, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5091997385025024, "perplexity": 821.6081737048412}, "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/1637964362230.18/warc/CC-MAIN-20211202145130-20211202175130-00464.warc.gz"} |
https://www.jpatrickpark.com/post/ats_2019/ | # Review of 'Processing Megapixel Images with Deep Attention-Sampling Models'
‘Processing Megapixel Images with Deep Attention-Sampling Models’ (referred as ‘ATS’ below) [1] proposes a new model that can save unnecessary computations from Deep MIL [2].
1. They first compute an attention map of all possible patch locations from an image. They do so by feeding a downsampled image to a shallow CNN without much pooling operations.
2. They sample a small number of patches from the attention distribution and show that feeding these samplied patches to MIL classifier is an unbiased minimum-variance estimator of the prediction made with all patches.
3. They show that both the visualization of the attention maps and the test error closely approximate Deep MIL while being at most 30 times more efficient.
ATS enables using high-capacity CNNs on high-resolution images without requiring pixel-level labels or too much computation. It can also provide visualizations of where the model is looking at.
# Thoughts
I am impressed with both the rigorous mathematical formulation of the proposed model and the availability of their open source repository. They even provide documentation which explains how to best utilize each part of their code. I appreciate the author’s effort towards making their work available in terms of clarity of the explanations and reproducibility. (The implementation is in TensorFlow. If you are interested in PyTorch implementation, there is a third-party implementation at this link.)
Training deep neural networks on large datasets of megapixel images can easily take weeks if not months. This work can significantly speed up the development iterations for deep learning researchers in medical imaging field.
Entropy regularizer seems to be a crucial piece to make ATS work. Without this regularizer, the model ends up with extremely sparse attention maps which highlight only a couple of patch locations. In this case, I suspect that (1) the feature model will overfit quickly and (2) the attention model will take a long time to train. While the authors included figures of ablation study for the attention map, it would have been nice to see its effect on the classification task.
For practitioners who plan on using this model, there are a couple of caveats that should be noted.
1. This work requires heavily downsampling the original image to be efficient.
• If the important features in your dataset consists of only a handful of pixels (e.g. calcifications in mammography), it might disappear entirely.
• Depending on the dataset, it might be better to use convolutional layers with large strides than to resize images.
2. Attention map can be more difficult to understand for radiologists than weakly- or strongly-supervised saliency maps.
• Attention map is relative to other locations in an image and must sum up to 1.
• In the cancer detection task, for example, the attention score of ATS will not necessarily correspond to the probability of malignancy.
• If only one cancer is found in a given image, it might have an attention score close to 1 in that location.
• If multiple cancers are found, however, suddenly their attention score will be spread out over the equally informative regions and have much smaller values.
• Most concerningly, if there is no cancer in the image, the attention map might end up highlighting every location equivalently. Small variations will be emphasized, and it might end up highlighting some random location in the same way it highlights cancer.
Lastly, if you are interested in learning more about efficient deep neural networks, I recently found a PhD Thesis on this topic [3]. It describes 4 different types of efficiency: model training and inference, data acquisition, hardware acceleration and architecture search. It seems to be a comprehensive overview of recent efforts.
#100DaysToOffload
## References
[1] Processing Megapixel Images with Deep Attention-Sampling Models. Angelos Katharopoulos and François Fleuret. In Proceedings of the 36th International Conference on Machine Learning (ICML), pages 3282–3291, 2019.
[2] Attention-based Deep Multiple Instance Learning. Maximilian Ilse, Jakub M. Tomczak and Max Welling. In Proceedings of the 35th International Conference on Machine Learning (ICML), 2018.
[3] Efficient Deep Neural Networks. Bichen Wu. arXiv:1908.08926, 2019.
##### Jungkyu (JP) Park
###### Deep Learning Researcher, PhD Student
Deep learning in medical imaging | 2020-10-24 02:48:34 | {"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": 0.693979799747467, "perplexity": 1608.7720224939046}, "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-2020-45/segments/1603107881640.29/warc/CC-MAIN-20201024022853-20201024052853-00254.warc.gz"} |
http://math.stackexchange.com/questions/203641/do-decimal-expansions-of-irrationals-have-applications | # do decimal expansions of irrationals have applications?
I am not into number theory at all -- is there a specific reason why some researchers spend enormous effort on calculating millions of digits in the decimal (or any other base) expansions of irrationals like pi? Are there known connections to applied fields such as cryptography, e.g.?
-
Mostly, these calculations are taken as benchmarks for new supercomputers. I know more than enough digits by heart to compute the earth equator up to subatomics. Then again, the algorithms used are interesting in themselves (probably more than their output): Don't you find it intriguing that it is possible to compute the millionth digit o f$\pi$ in reasonable time without needing to calculate and store all previous digits? On the other hand, while it is widely believed that the digits of $\pi$ "look like random" no stats derived from billions of digits can actually prove such a conjecture. – Hagen von Eitzen Sep 27 '12 at 22:01
@HagenvonEitzen, isn't that statement about computing digits of $\pi$ only about hexadecimal digits, not decimal digits? – lhf Sep 28 '12 at 0:01
Does climbing Mt. Everest have an application? Are there known connections to applied fields such as geology? – Qiaochu Yuan Sep 28 '12 at 0:31 | 2014-07-28 16:33:11 | {"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": 0.6540459990501404, "perplexity": 880.6313528552977}, "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/1406510261249.37/warc/CC-MAIN-20140728011741-00095-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://www.oxygenxml.com/forum/viewtopic.php?t=20945&p=56310 | ## How do I automatically run a post-processing utility on the PDF file?
chrispitude
Posts: 188
Joined: Thu May 02, 2019 2:32 pm
### How do I automatically run a post-processing utility on the PDF file?
I have a post-processing utility that we run on our published PDF files. However, it's cumbersome for our writers to run it manually each time they publish a PDF with PDF Chemistry.
Is there a way to run an external utility automatically as a part of the PDF Chemistry transformation? I don't see an entry for a post-processing command line in the transformation setup, but perhaps there is an Ant parameter or some kind of extension point I can use. The utility simply takes the filename of the PDF file as its only argument, and it modifies the file in-place.
Thanks!
- Chris
julien_lacour
Posts: 89
Joined: Wed Oct 16, 2019 3:47 pm
### Re: How do I automatically run a post-processing utility on the PDF file?
Hello Chris,
You can use a custom build file to call your command line post process using ant. Here is a small example
Code: Select all
<?xml version="1.0" encoding="UTF-8"?>
<project basedir="." default="dist">
<property name="scriptFolder" value="${basedir}\custom\script" /> <!--The DITA OT default build file--> <import file="path\to\dita-ot\build.xml"/> <target name="dist"> <!--Call the DITA OT default target--> <antcall target="init"/> <exec dir="${scriptFolder}" executable="script.bat">
<arg value="fileName"/>
</exec>
</target>
</project>
Regards,
Julien
chrispitude
Posts: 188
Joined: Thu May 02, 2019 2:32 pm
### Re: How do I automatically run a post-processing utility on the PDF file?
Hi Julien,
Thank you! I put together the following build_wrapper.xml file:
Code: Select all
<?xml version="1.0" encoding="UTF-8"?>
<project basedir="." default="dist">
<property name="scriptFolder" value="${basedir}\..\prj\tools\annotate_highlighted_changes" /> <!--The DITA OT default build file--> <import file="C:\Program Files\Oxygen XML Editor 22\frameworks\dita\DITA-OT3.x\build.xml"/> <target name="dist"> <!--Call the DITA OT default target--> <antcall target="init"/> <exec dir="${scriptFolder}" executable="annotate_highlighted_changes.exe">
<arg value="fileName"/>
</exec>
</target>
</project>
Note that I am actually running a Windows .exe file (it is a perl script, compiled with Strawberry Perl for Windows). However, the transformation fails with the following error:
Code: Select all
Transformation failed. C:\Users\chrispy\Documents\DITA\dita-digital\prj\tools\annotate_highlighted_changes\build_wrapper.xml:10: Execute failed: java.io.IOException: Cannot run program "annotate_highlighted_changes.exe" (in directory "C:\Users\chrispy\Documents\DITA\dita-digital\prj\tools\annotate_highlighted_changes"): CreateProcess error=2, The system cannot find the file specified
In a Windows command window, the concatenation of that path and executable name do invoke the utility:
Code: Select all
C:\Users\chrispy>"C:\Users\chrispy\Documents\DITA\dita-digital\prj\tools\annotate_highlighted_changes\annotate_highlighted_changes.exe"
Usage:
<pdf_filename>
PDF file to process
[--output <new_file_name>]
Output PDF file to create
(default is to modify original file in-place)
Is a different build.xml method required to invoke .exe files?
julien_lacour
Posts: 89
Joined: Wed Oct 16, 2019 3:47 pm
### Re: How do I automatically run a post-processing utility on the PDF file?
Hello Chris,
In your case you just need to modify the <exec> declaration:
Code: Select all
<exec dir="${scriptFolder}" executable="annotate_highlighted_changes.exe" resolveexecutable="true"> Here is the ant exec documentation related: When this attribute is true, the name of the executable is resolved firstly against the project basedir and if that does not exist, against the execution directory if specified. On Unix systems, if you only want to allow execution of commands in the user's path, set this to false. since Ant 1.6 Regards, Julien chrispitude Posts: 188 Joined: Thu May 02, 2019 2:32 pm ### Re: How do I automatically run a post-processing utility on the PDF file? The executable is now found, thank you! How can I pass the name of the PDF being generated by the transformation? Currently, <arg/> is hardcoded but this transformation will be used by any number of books. This might be the tricky part... chrispitude Posts: 188 Joined: Thu May 02, 2019 2:32 pm ### Re: How do I automatically run a post-processing utility on the PDF file? I got this working by updating my script to accept a wildcard pattern, then using "${output.dir}/*.pdf" as the filename argument:
Code: Select all
<?xml version="1.0" encoding="UTF-8"?>
<project basedir="." default="dist">
<!--The DITA OT default build file-->
<import file="${dita.dir}\build.xml"/> <target name="dist"> <!--Call the DITA OT default target--> <antcall target="init"/> <exec dir="../prj/tools/annotate_highlighted_changes" executable="annotate_highlighted_changes.exe" resolveexecutable="true"> <arg value="${output.dir}/*.pdf"/>
</exec>
</target>
</project>
I still need to do some reading about Ant's exec call to figure out how to replace the relative path to my script with a proper path relative to the Oyxgen project file.
Posts: 6979
Joined: Fri Jul 09, 2004 5:18 pm
### Re: How do I automatically run a post-processing utility on the PDF file?
Hi,
Code: Select all
I still need to do some reading about Ant's exec call to figure out how to replace the relative path to my script with a proper path relative to the Oyxgen project file.
maybe you can define a property in the build file like "projectBaseDir" and then from the Oxygen transformation scenario pass the "projectBaseDir" as an extra parameter with the value "\${pd}" which will be expanded by Oxygen to the project folder before the ANT process is started.
Regards, | 2020-07-05 09:39:41 | {"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": 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": 0.7583485245704651, "perplexity": 6424.134500940249}, "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/1593655887319.41/warc/CC-MAIN-20200705090648-20200705120648-00124.warc.gz"} |
https://forum.math.toronto.edu/index.php?PHPSESSID=uhh3jkujkml63s5fp7fo4g89i4&topic=1511.0;wap2 | MAT334-2018F > Quiz-6
Q6 TUT 0101
(1/1)
Victor Ivrii:
$\newcommand{\Res}{\operatorname{Res}}$
If $f$ is analytic in $\{z\colon |z - z_0| < R\}$ and has a zero of order $m$ at $z_0$ , show that
$$\Res \bigl(\frac{f'}{f}; z_0\bigr)=m.$$
XueGe Huang:
check attached file
Qi Cui:
$Since\ f(z)\ has\ a\ zero\ of\ order\ m\ at \ z_{0}$,
$$\quad\therefore f(z) = (z-z_{0})^mg(z),where g'(z_{0})\ne0$$
$$\quad\therefore f'(z) = (z-z_{0})^mg'(z)+m(z-z_{0})^{m-1}g(z)$$
$$f'(z) = (z-z_{0})^m(g'(z)+m(z-z_{0})^{-1}g(z))$$
$$\quad\therefore {{f'(z)}\over {f(z)}} ={{(z-z_{0})^m(g'(z)+m(z-z_{0})^{-1}g(z))}\over {(z-z_{0})^mg(z)}}$$
$$= {{g'(z)}\over {g(z)}}+m(z-z_{0}^{-1})$$
$$\quad\therefore Res({{f'}\over f}, z_{0})=m$$
Ende Jin:
Thus there exists analytic $g$ s.t. $f(z) = (z-z_0)^mg(z)$ where $g(z_0) \neq 0$.
Thus there exists a small ball around $z_0$ s.t. $g(z) \neq 0$ (by continuity) and analytic , which means $\frac{1}{g(z)}$ is analytic as well, thus $\frac{g'(z)}{g(z)}$ is analytic on that ball as well.
Since $m \ge 1$,
\begin{align*}
\frac{f'(z)}{f(z)} &= \frac{m(z-z_0)^{m-1}g(z) + (z-z_0)^m g'(z)}{(z-z_0)^m g(z)} \\
& = \frac{m(z-z_0)^{m-1}g(z) + (z-z_0)^m g'(z)}{(z-z_0)^m g(z)} \\
&= \frac{g'(z)}{g(z)} + m \frac{1}{z-z_0}
\end{align*}
We have shown $\frac{g'}{g}$ is analytic on that ball. Thus the residue, which means the coefficient of $(z-z_0)^{-1}$ is only $m$ . | 2022-09-30 02:28:57 | {"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": 0.9997914433479309, "perplexity": 1508.0843285146732}, "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/1664030335424.32/warc/CC-MAIN-20220930020521-20220930050521-00103.warc.gz"} |
https://drexel28.wordpress.com/2011/09/16/a-clever-proof-of-a-common-fact/ | # Abstract Nonsense
## A Clever Proof of a Common Fact
Point of Post: In this post we give a new proof that if $G$ is a finite group $H$ is a subgroup $G$ whose index is the smallest prime dividing $|G|$ then that subgroup is normal.
$\text{ }$
Motivation
It is a commonly used theorem in finite group theory that if $G$ is a finite group and $H\leqslant G$ such that $\left[G:H\right]=p$ is the smallest prime dividing $|G|$ then $H\unlhd G$. We have already seen a proof of this fact by considering the homomorphism $G\to S_p$ which is the induced map from $G$ acting on $G/H$ by left multiplication, and proving that $\ker(G\to S_p)=H$. We now give an even shorter (and the just mentioned proof is already short) proof of this fact using double cosets.
$\text{ }$
The Theorem
We recall that a double coset $HgK$ for subgroups $H,K\leqslant G$ is an orbit of the action of $H\times K$ on $G$ given by $(h,k)\cdot g=hgk^{-1}$. We also recall that $\#(HgK)=|H|\left[H:H\cap gKg^{-1}\right]$. With this we can easily prove the theorem
$\text{ }$
Theorem: Let $G$ be a finite group and $p$ the smallest prime dividing $|G|$. Then, if $H\leqslant G$ is such that $\left[G:H\right]=p$ then $H\unlhd G$.
Proof: We know that $G$ decomposes as
$\text{ }$
$G=H\sqcup Hg_1H\sqcup\cdots\sqcup Hg_mH$
$\text{ }$
where $g_1,\cdots,g_m$. We see then that that
$\text{ }$
$p=1+\left[H:H\cap g_1Hg_1^{-1}\right]+\cdots+\left[H:H\cap g_mHg_m^{-1}\right]$
$\text{ }$
Now, we know then that $\left[H:H\cap g_k Hg_k^{-1}\right] and since it’s a divisor of $|G|$ we evidently mus have that $\left[H:H\cap g_k Hg_k^{-1}\right]=1$ and so $H=g_kHg_k^{-1}$. Since we can evidently choose $g_k$ arbritrarily in $G-H$ (since it is a representative for one of the double cosets) the conclusion follows. $\blacksquare$
$\text{ }$
$\text{ }$
References:
References:
1. Dummit, David Steven., and Richard M. Foote. Abstract Algebra. Hoboken, NJ: Wiley, 2009 | 2017-06-29 07:10:00 | {"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": 45, "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": 0.9703262448310852, "perplexity": 116.73628453718257}, "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-2017-26/segments/1498128323889.3/warc/CC-MAIN-20170629070237-20170629090237-00386.warc.gz"} |
http://newsgroups.derkeiler.com/Archive/Comp/comp.text.tex/2005-12/msg01207.html | # Re: multirow woes (wrapped text)
Herbert Voss wrote:
Dan Bolser wrote:
Hi, I am using the multirow package to write a table describing 1:n relationships.
Unfortunatly, the text for my 'Name' column can get quite long, and is wrapped to a fixed column width. (First I was using array, but then simply used the width atribute of the multirow specification). If the text wraps into more lines than the multirow has rows (nrows), the text is wrapped onto the next block of my table.
This looks ugly and wrong. Any suggestions on how I can fix this? (Other than by hand).
do you really need multirow?
Herbert
\documentclass[a4]{article}
\usepackage{array}
\begin{document}
\begin{tabular}{|m{1em}|m{4cm}|m{1em}|}\hline
W & Well, just goes to show what happens & w1\newline w2\\\hline
X & when you try to be too clever & x1\newline x2\\\hline
Y & this group is fine & y1\newline y2\\\hline
Z & me too & z1\newline z2\\\hline
\end{tabular}
\end{document}
After implementing your idea I have the following table format...
....
%% Set 'Name' column width
\newlength{\nameCol}
\setlength{\nameCol}{20em}
%% Set 'Fig' column width
\newlength{\figCol}
\setlength{\figCol}{3em}
....
\begin{longtable}{
rrl>{\raggedright\arraybackslash}m{\nameCol}rrrrrrm{\figCol}m{2em}m{3em}
}
....
Where the last two columns have zero to five \newlines in them (always the same number of newlines on a row. Is there any way to get all my cells top aligned?
by playing with p, b and m I can get them all middle aligned or all bottom aligned, but not all top aligned. Is there a trick I am missing?
The way the different \parbox[x]'s align in a row is quite confusing!
Thanks very much for the original idea,
Dan.
. | 2014-03-11 21:07:53 | {"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": 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": 0.6841299533843994, "perplexity": 3457.663213755428}, "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-2014-10/segments/1394011278480/warc/CC-MAIN-20140305092118-00092-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://mathematrec.wordpress.com/tag/life/ | ## An honor just to be nominated
Rich’s p16 came in at 11th place in the 2016 Pattern of the Year awards. First place was never even a remote possibility, not in a year that produced the Caterloopillar and the Copperhead. (I actually thought the latter would win handily, but I guess that’s just my relative lack of interest in engineered spaceships showing.)
## Rich’s p16
Here’s a new period 16 oscillator:
The stubby wiki page says I discovered it, which is silly of course: all I did was install apgsearch and run it looking at D2_+1 soups in standard Life (B3/S23). I was asleep when it found this and woke up to find it’d been tweeted, retweeted, reported on the forum, used to make a smaller p48 gun, deemed awesome, and written up on the wiki.
## Gun show (part 4)
The p61 gun is quite different, though it too makes use of herschel tracks. To get a better picture of what’s going on, here it is with history turned on: the blue cells are ones that were live at some point: To start with let’s zoom in to the upper right corner. You see a couple of lightweight spaceships moving west to east, and the spark on the one near the center is about to perturb a southwest-going glider: 39 generations later, and several cells to the south, this becomes an r pentomino: And another 48 generations later, quite a bit further south, it becomes a herschel.That herschel gets sucked up into a downward conduit (purple line below). It gets converted into two parallel southwest-going gliders. One of these (red line) gets bounced off a series of 90° reflectors, snarks again like the ones we saw in the p58 gun, ending up at the top where it becomes (a later version of) the glider we saw at the start, getting converted to an r pentomino. The other one (yellow line) gets kicked right by an interaction with a herschel loop (orange line). I presume this very complicated reflector is used because it can reflect one glider without messing up the parallel stream (and I’m guessing a similar loop can’t be made to work at p58, hence the different solution used in that gun?). Not quite sure. Anyway, it then gets bounced a couple more times before ending up at the top of another section of the gun, where it’ll share the other glider’s fate: getting converted by a lightweight spaceship into an r pentomino, then a herschel, to feed another herschel track.
Here’s the middle stage:Again a downward track (purple) produces two parallel gliders (red and yellow). Again the yellow one gets bounced by a herschel loop to the top of a third stage for yet another r pentomino conversion. As for the red one, it bounces a bunch of times up to the top left where it runs into… something.
The third stage yet again has a downward track producing two gliders, one bounced off a loop and the other just kicked around with snark reflectors.
Both of these gliders arrive at the proper phase, spacing, and direction to interact with each other and with the red glider from the second stage to produce, of course, a lightweight spaceship. And the spaceship travels east, perturbing three gliders as it goes but remaining unscathed itself. If this were all, you’d have a p61 lightweight spaceship gun, but instead there are a few more still lifes at the right edge which convert the lightweight spaceships into gliders. And there you are. A p61 glider gun.
## Gun show (part 3)
Next (in reverse chronological order, but it makes sense to me) the p58 gun. I think “AbhpzTa”‘s version is pretty much the same thing as “Thunk”‘s (based on Matthias’s component), but in such a compact form it’s harder to see what’s going on. Here’s “Thunk”‘s:What we have here is not one but two herschel loops, both period 58. The top one is connected to the bottom one by another herschel track, and there’s a reaction that duplicates the herschels in the top track, sending one on its way around the loop again and another down toward the bottom track. But this doesn’t happen without input: it needs a period 58 glider stream. Where does it get one? Patience…
Where the cross track feeds into the bottom loop, the two herschels collide and out of the collision come not one but two gliders every 58 generations, heading southeast. They’re pretty close together. Too close, in fact, because we want to reflect one stream 90°, and that can’t be done without messing up, and getting messed up by, the other stream. So we use this cute reaction:
Two perpendicular glider streams go in, two go out. Same directions, but displaced. Meanwhile the parallel glider stream just squeaks by. That puts the two streams further apart, but not by enough, so we do the same thing again. Now they’re separated by enough.
(But wait, that reaction needs a second glider stream, going northeast, to work. Two of them to make it work twice. Where do we get two? Patience…)
One of the two not-so-close-together parallel streams gets kicked to the right, and the other to the left, with this apparatus. It’s called a snark, and it’s by far the smallest and fastest stable glider reflector known. Here you can see a glider coming in from the northwest and another on its way out to the northeast.
The stream that gets kicked to the left gets kicked left again, using a different, larger, oscillatory object, I think in order to get the correct glider phase or position for the outgoing stream. It’s now heading northwest, back toward the herschel loops — in particular, toward the intersection of the upper loop with the downward connector. That’s right, it becomes the glider stream needed to make the herschel duplicator work.
The other stream gets kicked to the right three times — now it’s heading northeast, crossing perpendicularly the two parallel streams, and it runs into a block at just the right time and phase to make the stream displacer work. Then it gets bent to the right four more times, putting it perpendicular to the two parallel streams again, so it can make the other stream displacer work. We didn’t need two new streams after all for the displacers, or even one… the displaced stream and both of the auxiliary streams are in fact all the same stream! Reminds me of a Heinlein story for some reason.
Finally, in the version “Thunk” posted, there’s one more kick to the right sending this stream off to the southeast to become the gun’s output, but there’s no need to do that; it could just continue to the northeast. And that’s the gun.
Unlike, say, the Gosper glider gun, which just needs two queen bees and two blocks to get started, this one relies on glider streams to work; it regenerates those streams itself, but it has to be built in the first place with glider steams to get started with. What happens, I wondered, if you erase one of the gliders heading into the herschel duplicator? Does it just create a gap in the output glider streams, or does something more serious occur? Something more serious, it turns out.
## Gun show (part 2)
For me the easiest of these guns to comprehend is the p57 one, so let’s work our way up to that.
Start by considering the heptomino that has acquired the somewhat erroneous name of herschel. It arises, along with some debris, early in the evolution of the r pentomino and spits out a glider, which is how the glider was discovered back in 1970. Without the r pentomino’s debris, the herschel stabilizes in 128 generations leaving two blocks, two glders, and a ship. But a notable thing about the herschel is that its evolution isn’t centered around its original position; most of the action happens to one side. Here’s a herschel (in red) and its stable state (in green), with the cells that otherwise were live in blue:Notice how, aside from the gliders, most of the action happened off to the left of the initial state.
So you can use a hershel over here to make something happen over there. In particular, you can imagine setting up some still lifes that will interact with the herschel in such a way as to make another herschel happen over there — while preserving the still lifes. Like this. Start with this state: and 117 generations later you have this state:plus a glider off to the southwest, which can be disposed of with another eater if you want. The eaters and snake perturb the herschel without getting injured; the block gets destroyed but is then remade in the same place.
So that’s very cool. It’s called a conduit. You could put a second conduit to the right of the first, positioned so the herschel output by the first conduit is in just the right place to be input to the second one, and at generation 234 the herschel will appear to the right of the second conduit. And of course you could put a third conduit, and a fourth, and a fifth, and so on, and transport that herschel as far as you like in a straight line, popping up every 117 generations.
What’s a little less obvious is that if you can contrive a way to feed such a track of conduits a periodic series of herschels, they’ll get transported just fine even if they turn up more often than every 117 generations. In fact, this conduit is ready to accept its next herschel as frequently as every 63 generations.
Furthermore, you’re not limited to straight lines. There are other conduits that will transport a herschel around a corner. Some conduits do a mirror flip of the herschel, some don’t. Some even manage to send a herschel backwards.
So with some ingenuity, you can set up a track of conduits that goes around four corners and connects back on itself in a loop! All of this was pioneered by David Buckingham in the 1990s, and his period 61 loop was the first period 61 Life oscillator discovered.
Since then there’s been lots of herschel conduit exploration going on, involving discovery of both new conduits and new ways to make use of them. And that’s what’s going on in the p57 gun; you have a loop, built of conduits that can accept herschels every 57 generations. Unfortunately you can’t just leave out one of the tub-with-tail still lifes that eats the gliders emitted by the herschels without breaking the conduit, but hanging off the bottom of the loop is a crazy lump of a period 3 oscillator. It hassles the nearby conduit into spitting out a glider while preserving the conduit action, and, boom, p57 gun.
## Gun show (part 1)
I’ve dabbled intermittently with Conway’s Game of Life — strong emphasis on both “dabbled” and “intermittently” — for more than 45 years now. In fact I think I read Martin Gardner’s classic article on the subject in the October 1970 Scientific American when it was hot off the press (in my high school library), a month or so before William Gosper found the first glider gun. That gun bounces two queen bee shuttles off one another; the mechanism repeats itself every 30 generations, producing a glider each time, so it’s a period 30 gun. The following year Gosper found another glider gun, with period 46.
You can perhaps imagine a gun like one of these, which emits a glider, for instance, every 50 generations, but whose mechanism repeats itself at a multiple of that period — every 100 generations, say. In that case one says the gun has a true period of 100 and a pseudo period of 50. (Despite the pejorative connotations of “pseudo”, though, if you’re using a gun to build something, it’s probably the pseudo period that’s of more interest to you.)
The shortest (pseudo) period a glider gun can have is 14. If you try to make a glider stream with shorter period, it doesn’t work: the gliders interact with each other and die. There are guns known with all pseudo periods from 14 on up.
For the true periods, though, there are holes. All periods from 62 up exist, but the smallest true period known is 20, and there are quite a few periods in between with no known gun.
But fewer such holes than there were a couple days ago.
On Wednesday, “AbhpzTa”, a newcomer to the conwaylife.com forums, posted a p61 gun:
Some discussion ensued in which, yesterday, Matthias Merzenich suggested a component which “thunk” used to make a p58 gun:
and “AbhpzTa” compactified it this morning:
Just an hour later, Matthias posted a p57 gun:
Three new true periods found in less than 48 hours!
How do these things work? Like I said, I dabble, and there’s a lot of arcane Life knowledge out there I’m not up on. But I think I get at least some of the ideas at work here, and I’ll write them up for my own benefit if no one else’s soon.
## How slow do you want it?
Another interesting Life development. Michael Simkin has found an orthogonal c/8 spaceship, the first of that speed. Or maybe better to say he’s built one, since it’s not an elementary spaceship discovered by a search program but a large engineered object. Furthermore the technology used, called a caterloopillar, can in principle be modified to produce spaceships — or, with trivial modifications, puffers or rakes — of any speed slower than c/4.
I said large. How large? Simkin says:
It’s pretty big. Some numbers:
cell count:
minimal – 232,815
maximal – 239,370
bounding box ~ 734 X 500K
Note, not 734K but 734 by 500K. Loaded into Golly and zoomed to fit it looks like this:
No really. That’s a spaceship. Zoomed in you can see it’s mostly periodic in structure.
If you look here you can see a big GIF showing some of the glider and standard orthogonal spaceship action going on within the ship.
## In the prime of life
Today, Nov 3 (11/3 or 11/03 or 3/11), is the 307th day of 2015. And 3, 11, 113, 1103, 311, and 307 are all prime. Ignore Amazon, THIS is PrimeDay. (But next year it’s March 11, because 308 is not prime, but 71 is.)
So since I’ve been playing with cellular automata lately, here’s some prime CA material.
Dean Hickerson came up with primer, a Life pattern that generates prime numbers, back in 1991. Nathaniel Johnston wrote about it in a 2009 blog post, mentioning twin and Fermat prime variants devised by Hickerson and Jason Summers, and then going on to present patterns that generate Mersenne primes, prime quadruplets, cousin primes, and sexy primes.
Primer looks like this once it gets going:
Which looks pretty complicated but it isn’t really so much. What you have are some puffers that lay down three rows of period 30 glider guns, one vertical and two horizontal. In the horizontal rows each gun in the top row kills the glider produced by the corresponding gun in the bottom row, unless there’s a gap in the first row’s output in which case the bottom row gun makes a glider: what you have there is an inverter, where a gap in the top row’s output becomes a glider in the bottom row’s, and vice versa.
Coming in to each of the top row guns is a glider which gets kicked back, killing the top row’s glider in the process and creating a gap. That kicked back glider travels up to the vertical row where it gets kicked back again to interact with the top row gun again. Obviously this circuit takes a shorter amount of time for the guns at the left (kicking back to the guns on the bottom of the vertical row) than for the guns at the right (kicking back to guns higher up). In fact what happens is there is a gap every 12 gliders coming out of the first top row gun, every 20 gliders for the second, every 28 gliders for the third… every $4(2n+1)$ for the $n$th. After inversion, there’s a glider coming out of the $n$th bottom row gun every $30\times 4(2n+1)$ generations. There’s also a puffer seen toward the right that starts up the kickback reactions by sending a glider toward the next vertical gun when it’s ready.
Then there’s a lightweight spaceship gun sending spaceships west every 120 generations. But if a glider comes off the bottom row it kills a spaceship. So the first gun would kill every third spaceship (if nothing killed any others), the second would kill every fifth spaceship, the third would kill every seventh, and so on. Which is just the Sieve of Eratosthenes. What’s left is a spaceship passing a certain point at generation $120n$ if and only if $n$ is prime.
Hickerson’s primer and three improvements by Jason Summers are included in the patterns folder that comes with Golly, as are the Fermat and twin prime generators. The Fermat generator, also by Summers, has four tubs which are destroyed at about generations 50; 1,490; 30,290; and 7,863,890 (corresponding to the second through fifth Fermat primes 5, 17, 257, and 65537). If a sixth Fermat prime is generated it destroys a pond and shuts the pattern down. Since the sixth Fermat prime is known, as of 2014, to be at least $2^{(2^{33})}+1$, the pond will not be destroyed in fewer than about $10^{2,560,000,000}$ generations, which will take a while depending on your computer.
Also included in the Golly patterns is a CA by Adam P. Goucher (under Calcymon-primer in the Other Rules folder). It’s a 10-state CA with a Moore neighborhood which is designed to allow a primer that’s a little simpler than Hickerson’s Life primer. Goucher’s primer in its initial state looks like this:Two cells! Here it is after about 70 generations having produced 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31:
It works kind of similarly to Hickerson’s primer; here the kicked back single cell “gliders” (red going up, green going down) get re-kicked with a delay to increase the spacing between, so on the first trip they knock out every third output spaceship (being produced on the diagonal blue line), every fifth one on the second trip, every seventh one on the third, and so on. Much less messy and faster than the Life version, though I don’t know if it can be adapted for Fermat primes, and if so it’ll still take longer than you might want to wait to find the sixth one.
Anyway, happy Prime Day!
## Life goes on
Hm, been just two days under a year since my last post here. Life goes on. So does Life.
This is about http://catagolue.appspot.com/home. No, that’s not a typo. It’s catagolue, i.e. cataGOLue, i.e. cata-GameOfLife-ue. Adam P. Goucher set this up as a repository for crowdsourced results of running Life with random 16 x 16 “soups” as initial configurations, using one of two “apgsearch” software tools: an earlier one in Python and Version 2.x in C++. The Python version is more flexible — it can search alternate rules, not just B3S23, and one can specify initial soups with some level of symmetry. The C++ version is B3S23, asymmetric soups only, but runs about seven times faster.
Is there any real point to doing this? I don’t know, but I find it amusing.
To use the C++ version you download it, compile it (x86-64 machines only; Linux, Mac, or Windows), and run it with a command line like
./apgnano -n 20000000 -k mykey -p 4
Here you’re telling the program to generate and follow 20000000 soups per “haul”. On my old iMac that takes about two hours. “mykey” is a key to allow it to upload your results non-anonymously; they’ll be uploaded anonymously if you omit it. “-p 4” tells it your machine has 4 cores it should use.
My results are uploaded using the ID “@doctroid“. When a previously un-found object is discovered it gets tweeted by @conwaylife, so using “@doctroid” for my ID means the tweet carries a link to my Twitter account. My results also get posted at my catagolue page.
There you can see I’ve “discovered” two objects at this writing; one’s a period 3 oscillator, a cuphook variant:and the other’s a period 2 oscillator, a test tube baby variant:
So far all the still lifes of size 13 and under, and almost all the size 14 ones, have turned up “naturally” from 960 393 995 873 random soups. So have 744 period-2, 120 period-3 and 12 period-4 oscillators plus a number with periods above 4. The project’s also found a bunch of spaceships — but all of them are gliders, light-, middle-, or heavy-weight spaceships, or compounds thereof. There’s a €50 bounty offered for the first “naturally occurring” spaceship that isn’t! A bit surprisingly to me, four puffer trains have been found too. In fact, two of them are among the 100 most common objects.
960 393 995 873 soups; nearly a trillion! How many are left?
I’m surprised I can’t find more on that question online. Obviously there are only two $1\times 1$ soups: * and -. There are $2^4=16$ $2 \times 2$ soups but only six are distinct under rotation and reflection:
-- *- ** *- ** **
-- -- -- -* *- **
$3\times 3$ gets to be harder to count. There are $2^9=512$ possibilities but many are equivalent under rotation and reflection. The relevant sequence in OEIS is A054247 Number of n X n binary matrices under action of dihedral group of the square D_4. After accounting for rotations and reflections there are 102 distinct $3\times 3$ soups. And 8548 $4\times 4$, and… well, let’s cut to the chase. OEIS doesn’t show the value for $n=16$ but nearly all large soups have no symmetry so it’s a good approximation to say for $n\times n$ size there are about $2^{n^2}/8=2^{n^2-3}$ soups when $n$ is large. For $n=16$ that’s about $1.4474011\times 10^{76}$. I don’t think the catagolue will be completed any time soon. | 2020-09-24 01:53:46 | {"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": 21, "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": 0.5439944863319397, "perplexity": 1721.1321430568037}, "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-2020-40/segments/1600400213006.47/warc/CC-MAIN-20200924002749-20200924032749-00586.warc.gz"} |
http://clay6.com/qa/30450/the-average-kinetic-energy-of-an-ideal-gas-per-molecule-in-si-units-at-25-c | # The average kinetic energy of an ideal gas per molecule in SI units at $25^{\large\circ}C$ will be
$(a)\;6.2\times10^{-21}KJ\qquad(b)\;6.2\times10^{-21}J\qquad(c)\;6.2\times10^{20}J\qquad(d)\;6.2\times10^{20}KJ$ | 2020-08-14 02:56:39 | {"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": 0.3911532163619995, "perplexity": 169.09697974372634}, "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-2020-34/segments/1596439739134.49/warc/CC-MAIN-20200814011517-20200814041517-00542.warc.gz"} |
https://en.wikipedia.org/wiki/Rayleigh-Plesset_equation | # Rayleigh–Plesset equation
(Redirected from Rayleigh-Plesset equation)
The Rayleigh–Plesset equation is often applied to the study of cavitation bubbles, shown here forming behind a propeller.
In fluid mechanics, the Rayleigh–Plesset equation or Besant–Rayleigh–Plesset equation is an ordinary differential equation which governs the dynamics of a spherical bubble in an infinite body of incompressible fluid.[1][2][3][4] Its general form is usually written as
${\displaystyle R{\frac {d^{2}R}{dt^{2}}}+{\frac {3}{2}}\left({\frac {dR}{dt}}\right)^{2}+{\frac {4\nu _{L}}{R}}{\frac {dR}{dt}}+{\frac {2\gamma }{\rho _{L}R}}+{\frac {\Delta P(t)}{\rho _{L}}}=0}$
where
${\displaystyle \rho _{L}}$ is the density of the surrounding liquid, assumed to be constant
${\displaystyle R(t)}$ is the radius of the bubble
${\displaystyle \nu _{L}}$ is the kinematic viscosity of the surrounding liquid, assumed to be constant
${\displaystyle \gamma }$ is the surface tension of the bubble-liquid interface
${\displaystyle \Delta P(t)=P_{\infty }(t)-P_{B}(t)}$, in which, ${\displaystyle P_{B}(t)}$ is the pressure within the bubble, assumed to be uniform and ${\displaystyle P_{\infty }(t)}$ is the external pressure infinitely far from the bubble
Provided that ${\displaystyle P_{B}(t)}$ is known and ${\displaystyle P_{\infty }(t)}$ is given, the Rayleigh–Plesset equation can be used to solve for the time-varying bubble radius ${\displaystyle R(t)}$.
The Rayleigh–Plesset equation is derived from the Navier–Stokes equations under the assumption of spherical symmetry.[4]
## History
Neglecting surface tension and viscosity, the equation was first derived by W. H. Besant in his 1859 book[5] with the problem statement stated as An infinite mass of homogeenous incompressible fluid acted upon by no forces is at rest, and a spherical portion of the fluid is suddenly annihilated; it is required to find the instanateous alteration of pressure at any point of the mass, and the time in which the cavity will be filled up, the pressure at an infinite distance being supposed to remain constant (in fact, Besant attributes the problem to Cambridge Senate-House problems of 1847). Neglecting the pressure variations inside the bubble, Besant predicted the time required to fill the cavity to be
{\displaystyle {\begin{aligned}t&=a\left({\frac {6\rho }{p_{\infty }}}\right)^{1/2}\int _{0}^{1}{\frac {z^{4}\,dz}{\sqrt {1-z^{6}}}}\\&=a\left({\frac {\pi \rho }{6p_{\infty }}}\right)^{1/2}{\frac {\Gamma (5/6)}{\Gamma (4/3)}}\\&\approx 0.91468a\left({\frac {\rho }{p_{\infty }}}\right)^{1/2}\end{aligned}}}
where the integration was carried out by Lord Rayleigh in 1917, who derived the equation from energy balance. Rayleigh also realized that the assumption of constant pressure inside the cavity would become wrong as the radius decreases and he shows that using Boyle's law, if the radius of cavity decreases by a factor of ${\displaystyle 4^{1/3}}$, then the pressure near the boundary of the cavity becomes greater than the ambient pressure. The equation was first applied to traveling cavitation bubbles by Milton S. Plesset in 1949 by including effects of surface tension.[6]
## Derivation
Numerical integration of RP eq. including surface tension and viscosity terms. Initially at rest in atmospheric pressure with R0=50 um, the bubble subjected to oscillatory pressure at its natural frequency undergoes expansion and then collapses.
Numerical integration of RP eq. including surface tension and viscosity terms. Initially at rest in atmospheric pressure with R0=50 um, the bubble subjected to pressure-drop undergoes expansion and then collapses.
The Rayleigh–Plesset equation can be derived entirely from first principles using the bubble radius as the dynamic parameter.[3] Consider a spherical bubble with time-dependent radius ${\displaystyle R(t)}$, where ${\displaystyle t}$ is time. Assume that the bubble contains a homogeneously distributed vapor/gas with a uniform temperature ${\displaystyle T_{B}(t)}$ and pressure ${\displaystyle P_{B}(t)}$. Outside the bubble is an infinite domain of liquid with constant density ${\displaystyle \rho _{L}}$ and dynamic viscosity ${\displaystyle \mu _{L}}$. Let the temperature and pressure far from the bubble be ${\displaystyle T_{\infty }}$ and ${\displaystyle P_{\infty }(t)}$. The temperature ${\displaystyle T_{\infty }}$ is assumed to be constant. At a radial distance ${\displaystyle r}$ from the center of the bubble, the varying liquid properties are pressure ${\displaystyle P(r,t)}$, temperature ${\displaystyle T(r,t)}$, and radially outward velocity ${\displaystyle u(r,t)}$. Note that these liquid properties are only defined outside the bubble, for ${\displaystyle r\geq R(t)}$.
### Mass conservation
By conservation of mass, the inverse-square law requires that the radially outward velocity ${\displaystyle u(r,t)}$ must be inversely proportional to the square of the distance from the origin (the center of the bubble).[6] Therefore, letting ${\displaystyle F(t)}$ be some function of time,
${\displaystyle u(r,t)={\frac {F(t)}{r^{2}}}}$
In the case of zero mass transport across the bubble surface, the velocity at the interface must be
${\displaystyle u(R,t)={\frac {dR}{dt}}={\frac {F(t)}{R^{2}}}}$
which gives that
${\displaystyle F(t)=R^{2}dR/dt}$
In the case where mass transport occurs, the rate of mass increase inside the bubble is given by
${\displaystyle {\frac {dm_{V}}{dt}}=\rho _{V}{\frac {dV}{dt}}=\rho _{V}{\frac {d(4\pi R^{3}/3)}{dt}}=4\pi \rho _{V}R^{2}{\frac {dR}{dt}}}$
with ${\displaystyle V}$ being the volume of the bubble. If ${\displaystyle u_{L}}$ is the velocity of the liquid relative to the bubble at ${\displaystyle r=R}$, then the mass entering the bubble is given by
${\displaystyle {\frac {dm_{L}}{dt}}=\rho _{L}Au_{L}=\rho _{L}(4\pi R^{2})u_{L}}$
with ${\displaystyle A}$ being the surface area of the bubble. Now by conservation of mass ${\displaystyle dm_{v}/dt=dm_{L}/dt}$, therefore ${\displaystyle u_{L}=(\rho _{V}/\rho _{L})dR/dt}$. Hence
${\displaystyle u(R,t)={\frac {dR}{dt}}-u_{L}={\frac {dR}{dt}}-{\frac {\rho _{V}}{\rho _{L}}}{\frac {dR}{dt}}=\left(1-{\frac {\rho _{V}}{\rho _{L}}}\right){\frac {dR}{dt}}}$
Therefore
${\displaystyle F(t)=\left(1-{\frac {\rho _{V}}{\rho _{L}}}\right)R^{2}{\frac {dR}{dt}}}$
In many cases, the liquid density is much greater than the vapor density, ${\displaystyle \rho _{L}\gg \rho _{V}}$, so that ${\displaystyle F(t)}$ can be approximated by the original zero mass transfer form ${\displaystyle F(t)=R^{2}dR/dt}$, so that[6]
${\displaystyle u(r,t)={\frac {F(t)}{r^{2}}}={\frac {R^{2}}{r^{2}}}{\frac {dR}{dt}}}$
### Momentum conservation
Assuming that the liquid is a Newtonian fluid, the incompressible Navier–Stokes equation in spherical coordinates for motion in the radial direction gives
${\displaystyle \rho _{L}\left({\frac {\partial u}{\partial t}}+u{\frac {\partial u}{\partial r}}\right)=-{\frac {\partial P}{\partial r}}+\mu _{L}\left[{\frac {1}{r^{2}}}{\frac {\partial }{\partial r}}\left(r^{2}{\frac {\partial u}{\partial r}}\right)-{\frac {2u}{r^{2}}}\right]}$
Substituting kinematic viscosity ${\displaystyle \nu _{L}=\mu _{L}/\rho _{L}}$ and rearranging gives
${\displaystyle -{\frac {1}{\rho _{L}}}{\frac {\partial P}{\partial r}}={\frac {\partial u}{\partial t}}+u{\frac {\partial u}{\partial r}}-\nu _{L}\left[{\frac {1}{r^{2}}}{\frac {\partial }{\partial r}}\left(r^{2}{\frac {\partial u}{\partial r}}\right)-{\frac {2u}{r^{2}}}\right]}$
whereby substituting ${\displaystyle u(r,t)}$ from mass conservation yields
${\displaystyle -{\frac {1}{\rho _{L}}}{\frac {\partial P}{\partial r}}={\frac {2R}{r^{2}}}\left({\frac {dR}{dt}}\right)^{2}+{\frac {R^{2}}{r^{2}}}{\frac {d^{2}R}{dt^{2}}}-{\frac {2R^{4}}{r^{5}}}\left({\frac {dR}{dt}}\right)^{2}={\frac {1}{r^{2}}}\left(2R\left({\frac {dR}{dt}}\right)^{2}+R^{2}{\frac {d^{2}R}{dt^{2}}}\right)-{\frac {2R^{4}}{r^{5}}}\left({\frac {dR}{dt}}\right)^{2}}$
Note that the viscous terms cancel during substitution.[6] Separating variables and integrating from the bubble boundary ${\displaystyle r=R}$ to ${\displaystyle r\rightarrow \infty }$ gives
${\displaystyle -{\frac {1}{\rho _{L}}}\int _{P(R)}^{P_{\infty }}dP=\int _{R}^{\infty }\left[{\frac {1}{r^{2}}}\left(2R\left({\frac {dR}{dt}}\right)^{2}+R^{2}{\frac {d^{2}R}{dt^{2}}}\right)-{\frac {2R^{4}}{r^{5}}}\left({\frac {dR}{dt}}\right)^{2}\right]dr}$
${\displaystyle {{\frac {P(R)-P_{\infty }}{\rho _{L}}}=\left[-{\frac {1}{r}}\left(2R\left({\frac {dR}{dt}}\right)^{2}+R^{2}{\frac {d^{2}R}{dt^{2}}}\right)+{\frac {R^{4}}{2r^{4}}}\left({\frac {dR}{dt}}\right)^{2}\right]_{R}^{\infty }=R{\frac {d^{2}R}{dt^{2}}}+{\frac {3}{2}}\left({\frac {dR}{dt}}\right)^{2}}}$
### Boundary conditions
Let ${\displaystyle \sigma _{rr}}$ be the normal stress in the liquid that points radially outward from the center of the bubble. In spherical coordinates, for a fluid with constant density and constant viscosity,
${\displaystyle \sigma _{rr}=-P+2\mu _{L}{\frac {\partial u}{\partial r}}}$
Therefore at some small portion of the bubble surface, the net force per unit area acting on the lamina is
{\displaystyle {\begin{aligned}\sigma _{rr}(R)+P_{B}-{\frac {2\gamma }{R}}&=-P(R)+\left.2\mu _{L}{\frac {\partial u}{\partial r}}\right|_{r=R}+P_{B}-{\frac {2\gamma }{R}}\\&=-P(R)+2\mu _{L}{\frac {\partial }{\partial r}}\left({\frac {R^{2}}{r^{2}}}{\frac {dR}{dt}}\right)_{r=R}+P_{B}-{\frac {2\gamma }{R}}\\&=-P(R)-{\frac {4\mu _{L}}{R}}{\frac {dR}{dt}}+P_{B}-{\frac {2\gamma }{R}}\\\end{aligned}}}
where ${\displaystyle \gamma }$ is the surface tension.[6] If there is no mass transfer across the boundary, then this force per unit area must be zero, therefore
${\displaystyle P(R)=P_{B}-{\frac {4\mu _{L}}{R}}{\frac {dR}{dt}}-{\frac {2\gamma }{R}}}$
and so the result from momentum conservation becomes
${\displaystyle {\frac {P(R)-P_{\infty }}{\rho _{L}}}={\frac {P_{B}-P_{\infty }}{\rho _{L}}}-{\frac {4\mu _{L}}{\rho _{L}R}}{\frac {dR}{dt}}-{\frac {2\gamma }{\rho _{L}R}}=R{\frac {d^{2}R}{dt^{2}}}+{\frac {3}{2}}\left({\frac {dR}{dt}}\right)^{2}}$
whereby rearranging and letting ${\displaystyle \nu _{L}=\mu _{L}/\rho _{L}}$ gives the Rayleigh–Plesset equation[6]
${\displaystyle {\frac {P_{B}(t)-P_{\infty }(t)}{\rho _{L}}}=R{\frac {d^{2}R}{dt^{2}}}+{\frac {3}{2}}\left({\frac {dR}{dt}}\right)^{2}+{\frac {4\nu _{L}}{R}}{\frac {dR}{dt}}+{\frac {2\gamma }{\rho _{L}R}}}$
Using dot notation to represent derivatives with respect to time, the Rayleigh–Plesset equation can be more succinctly written as
${\displaystyle {\frac {P_{B}(t)-P_{\infty }(t)}{\rho _{L}}}=R{\ddot {R}}+{\frac {3}{2}}({\dot {R}})^{2}+{\frac {4\nu _{L}{\dot {R}}}{R}}+{\frac {2\gamma }{\rho _{L}R}}}$
## Solutions
Recently, analytical closed-form solutions were found for the Rayleigh–Plesset equation for both an empty and gas—filled bubble [7] and were generalized to the N-dimensional case.[8] The case when the surface tension is present due to the effects of capillarity were also studied.[8][9]
Also, for the special case where surface tension and viscosity are neglected, high-order analytical approximations are also known.[10]
In the static case, the Rayleigh–Plesset equation simplifies, yielding the Young-Laplace equation:
${\displaystyle P_{B}-P_{\infty }={\frac {2\gamma }{R}}}$
When only infinitesimal periodic variations in the bubble radius and pressure are considered, the RP equation also yields the expression of the natural frequency of the bubble oscillation.
## References
1. ^ Rayleigh, Lord (1917). "On the pressure developed in a liquid during the collapse of a spherical cavity". Phil. Mag. 34 (200): 94–98. doi:10.1080/14786440808635681.
2. ^ Plesset, M.S. (1949). "The dynamics of cavitation bubbles". ASME J. Appl. Mech. 16: 228–231.
3. ^ a b Leighton, T. G. (17 April 2007). "Derivation of the Rayleigh–Plesset equation in terms of volume". Southampton, UK: Institute of Sound and Vibration Research.
4. ^ a b Lin, Hao; Brian D. Storey; Andrew J. Szeri (2002). "Inertially driven inhomogeneities in violently collapsing bubbles: the validity of the Rayleigh–Plesset equation". Journal of Fluid Mechanics. 452. doi:10.1017/S0022112001006693. ISSN 0022-1120.
5. ^ Besant, W. H. (1859). A treatise on hydrostatics and hydrodynamics. Deighton, Bell. Article. 158.
6. Brennen, Christopher E. (1995). Cavitation and Bubble Dynamics. Oxford University Press. ISBN 978-0-19-509409-1.
7. ^ Kudryashov, Nikolay A.; Sinelshchikov, Dnitry I. (18 September 2014). "Analytical solutions of the Rayleigh equation for empty and gas-filled bubble". Journal of Physics A: Mathematical and Theoretical. 47 (40): 405202. arXiv:1409.6699. Bibcode:2014JPhA...47N5202K. doi:10.1088/1751-8113/47/40/405202.
8. ^ a b Kudryashov, Nikolay A.; Sinelshchikov, Dnitry I. (31 December 2014). "Analytical solutions for problems of bubble dynamics". Physics Letters A. 379 (8): 798–802. arXiv:1608.00811. Bibcode:2016arXiv160800811K. doi:10.1016/j.physleta.2014.12.049.
9. ^ Mancas, Stefan C.; Rosu, Haret C. (7 August 2015). "Cavitation of spherical bubbles: closed-form, parametric, and numerical solutions". Physics of Fluids. 28 (2): 022009. arXiv:1508.01157. Bibcode:2016PhFl...28b2009M. doi:10.1063/1.4942237.
10. ^ Obreschkow, D.; Bruderer M.; Farhat, M. (5 June 2012). "Analytical approximations for the collapse of an empty spherical bubble". Physical Review E. 85 (6): 066303. arXiv:1205.4202. Bibcode:2012PhRvE..85f6303O. doi:10.1103/PhysRevE.85.066303. PMID 23005202. | 2018-11-17 08:32:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 65, "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": 0.9150003790855408, "perplexity": 1283.5548744218172}, "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-2018-47/segments/1542039743351.61/warc/CC-MAIN-20181117082141-20181117104141-00337.warc.gz"} |
https://mathematica.stackexchange.com/questions/130399/does-plotlegends-not-work-in-mm-11 | # Does PlotLegends not work in MM 11?
I literally just downloaded MMA11 and upgraded from MMA 10.4, and PlotLegends seems to not work the way it did previously... Kind of annoying. Anyone knows why?
Clear[var, expr, blah, g, derivatives];
var = Input["Type a variable, such as x, in this window."];
expr = Input["Type an expression to be differentiated in the variable you just typed in the last window."];
g[blah_] = expr /. {var -> blah};
derivatives := {g[var], g'[var]}
Plot[{derivatives}, {x, -3, 5}, {PlotLegends -> "Expressions",
PlotLabel -> "A function and its Derivative", PlotRange -> 10}]
• Do you have a more minimal example demonstrating this that doesn't reply on Input statements? – ktm Nov 4 '16 at 18:46
• Try changing Plot[{derivatives},...] into Plot[Evaluate@derivatives,...] – corey979 Nov 4 '16 at 18:49
• It works PERFECTLY fine on 10.3.. I have both versions and just ran the same exact code. – Brandon Nov 4 '16 at 18:50
• Your code (without Evaluate) doesn't work for me on v10.4.1. // It's not a bug, it's a normal behaviour. – corey979 Nov 4 '16 at 18:53
• Make sure you upgrade to 11.0.1 if you have 11.0.0. – Szabolcs Nov 4 '16 at 19:21
First of all, this is not a bug in PlotLegends. You can tell because the plot itself is using the color for a single data set, implying that it thinks there is only one multi-valued function present. Since PlotLegends with "Expressions" or Automatic is sensitive to the number of functions, they will not display a legend when only one is present. The issue is then with how Plot is interpreting derivatives.
After a little experimentation, it comes down to the use of SetDelayed vs Set. When Set is used to define the variable,
d1 = {Sin[x], Cos[x]}
Plot[d1, {x, 0, 2 Pi}]
the expected image is produced.
But, when SetDelayed is used,
d2 := {Sin[x], Cos[x]}
Plot[d2, {x, 0, 2 Pi}]
it does not. There was some work on the parser between 10.3 and 10.4 which is likely causing this change in behavior, but I am not inclined to consider this a bug. Simply, with SetDelayed the function is expected to be evaluated over and over again, and should be thought of as the equivalent of using
f[x_] := {Sin[x], Cos[x]}
Plot[f[x], {x, 0, 2 Pi}]
which generates a plot identical to d2.
Correction: after looking at this again, and actually running this with PlotLegends with Set being used shows the same behavior. Therefor, I would say it is a bug.
• I have the same problem - does anyone have a fix? – Howard Lovatt Apr 4 '18 at 23:30
If you add Evaluate to the expression to be plotted there it works. Must be some bug in Plot. | 2021-01-26 08:58:33 | {"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": 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": 0.21115344762802124, "perplexity": 2089.269408288787}, "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-2021-04/segments/1610704799711.94/warc/CC-MAIN-20210126073722-20210126103722-00104.warc.gz"} |
https://www.physicsforums.com/threads/reaction-of-acids-with-salts.936832/ | # Reaction of acids with salts
Tags:
1. Jan 13, 2018
### Vatsal Goyal
Hi
I am new to the concept of neutralization.
My teacher told me that acids do not react with neutral salts.
I want to know why not. If both are dissolved in water and both completely dissociate, why can't the ions of acid and salt exchange and perform a double displacement reaction. Moreover I have seen a reaction in one of my books - NaCl + H2SO4 produces HCl and Na2SO4
Last edited: Jan 13, 2018
2. Jan 13, 2018
### Staff: Mentor
Do you know what the net ionic reaction is? What are spectator ions? Have you learned what the chemical equilibrium is? It is much easier to understand what is going on in these terms.
In short: when you mix solutions of HCl and Na2SO4 all you get is a mixture of ions, everything is still dissociated and no reaction takes place. Such a solution doesn't differ from the solution prepared by mixing NaCl and H2SO4.
Reaction you have seen in your book requires concentrated sulfuric acid and solid NaCl - that's quite a different situation. Besides, the most important reason why it happens is that the HCl is gaseous and volatile and can leave the reaction mixture. When you add concentrated HCl to Na2SO4 basically nothing happens.
3. Jan 13, 2018
### Vatsal Goyal
Thank you for clearing my doubt.
Just one more thing.
What is happening in the solution when an acid reacts with a basic salt?
4. Jan 13, 2018
### Vatsal Goyal
Can we say that MOST acid and neutral salt reactions would have a similar situation?
5. Jan 13, 2018
### Staff: Mentor
To be precise: most salts of strong acids and strong bases will behave this way when mixed with strong acids.
When there are weak acids/bases involved things become more complicated, that's where the acid base equilibrium comes into play.
6. Jan 13, 2018
### Vatsal Goyal
Okay got it. Thank you so much!
7. Jan 13, 2018
### hilbert2
Some acids can react with some neutral salts, but then the reaction is not about exchange of $H^+$ ions. For example, mix nitric acid with potassium iodide (a neutral salt), and you get elemental iodine ($I_2$) and nitrogen oxides or $NO_{2}^{-}$ ions or something like that. In that case it's an oxidation-reduction reaction taking place.
8. Jan 13, 2018
### Staff: Mentor
Which is why I wrote
I didn't want to muddy the watter with unnecessary details.
9. Jan 20, 2018
### DrStupid
Just to make sure that we don't talk at cross-purposes: Did he speak about salts or solutions of salts? Most of the posts are about solutions.
10. Jan 22, 2018
### Vatsal Goyal
yes, i meant solution only. Sorry for not mentioning. :) | 2018-04-19 17:05:00 | {"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": 0.5290048122406006, "perplexity": 3780.836941398112}, "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-2018-17/segments/1524125937015.7/warc/CC-MAIN-20180419165443-20180419185443-00437.warc.gz"} |
https://astarmathsandphysics.com/ib-maths-notes/calculus/5019-finding-an-expression-for-displacement-when-velocity-given-in-terms-of-displacement.html | ## Finding an Expression For Displacement When Velocity Given In Terms of Displacement
Suppose the velocity of a body is given in terms of the displacement. How can we find an expression for the displacement?
If
$v=2x^2$
and
$x=1$
when
$t=2$
(in the appropriate units), then we can write
$v= \frac{dx}{dt}=2x^2$
Now separate variables.
$\frac{dx}{x^2}=x^{-2}dx=dt$
Now integrate in the usual way.
$\int^x_1 x^{-2}dx = \int^t_2 dt$
$[- \frac{1}{x} ]^x_1 = t-2$
$- \frac{1}{x} - ( \frac{1}{1} )=t-2$
Making
$x$
the subject gives
$x= \frac{1}{3-t}$
. | 2019-01-16 01:16:51 | {"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": 0.943027675151825, "perplexity": 462.88068092329655}, "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-2019-04/segments/1547583656577.40/warc/CC-MAIN-20190116011131-20190116033131-00377.warc.gz"} |
https://mathoverflow.net/questions/368605/largest-eigenvalue-of-finite-band-random-matrices | # Largest eigenvalue of finite band random matrices
Let $$\mathbf{M}_n$$ be an $$n \times n$$ symmetric matrix $$\mathbf{M}_n = \begin{cases} X_{j-i,i}\ &\text{if }i\leq j\leq r+i\\ 0\ &\text{if }r+i< j\leq n\end{cases}$$ for some fixed $$r>0$$, and the random variables $$\{X_{i,j}\}$$ are assumed real, positive, i.i.d., and have finite mean and variance.
As an example, for $$r=1$$ and $$n=4$$ we have,
$$\mathbf{M}_4 = \begin{pmatrix} X_{0,1} & X_{1,1} & 0 & 0\\ X_{1,1} & X_{0,2} & X_{1,2} & 0 \\ 0 & X_{1,2} & X_{0,3} & X_{1,3} \\ 0 & 0 & X_{1,3} & X_{0,4} \end{pmatrix}$$
I was wondering if something is known about the asymptotic of $$\lambda_1(\mathbf{M}_n)$$, i.e., the largest eigenvalue of $$\mathbf{M}_n$$, in the limit $$n \to \infty$$. In particular, is something is known about the deviation of $$\lambda_1(\mathbf{M}_n)$$ from its mean, i.e., $$\Pr\left[|\lambda_1(\mathbf{M}_n)-\mathbb{E}\lambda_1(\mathbf{M}_n)|\geq t\right]\leq ?$$ I was wondering whether there is a general concentration bound, e.g., for non-identical matrices, which subsumes the above case.
– Mick
Aug 8 '20 at 5:51
• Obvious comment: $\max_i X_i + X_{i+1}$ is an upper bound for the spectral radius, as it is the maximum row sum. Aug 8 '20 at 12:28
• one answer at math.stackexchange.com/a/1603016/87355 Aug 8 '20 at 14:25
• @J.John : Well, what I wanted to use here is a simple remark that as the matrix is symmetric, its (spectral) norm exceeds the norm of any of its principal minors. So if the law is upper-bounded by $M$, for a large enough matrix there will be somewhere a large length $k$ subsequence $X_j\approx M, \, j=m,...,m+k$, and the norm of such a submatrix is $\approx 2M$. But this is not what you want to use for unbounded distributions... Aug 12 '20 at 19:52
• @J.John: yes, there is. As the matrix is a symmetric one with positive elements, its maximal eigenvalue = its spectral radius = its $\ell_2$-norm, and the corresponding eigenvector has nonnegative elements. So take such a unit-length eigenvector $v$ for $L_k$, and you get $$\lambda_{\max}(M_k)\ge (v,M_k v) \ge (v,L_k v) = \lambda_{max}(L_k)$$ Aug 17 '20 at 16:42
I start with this simple remark: the tridiagonal matrix $$A_k=\begin{pmatrix}0 & 1 & & & \\ 1 & 0 & 1 & & \\ & 1 & 0 & \ddots & \\ & & \ddots & & 1 \\ & & & 1 & 0\end{pmatrix}$$, $$A_k\in \mathbb{R}^{(k+1)\times (k+1)}$$ have largest eigenvalue $$\lambda_\max (A_k) =2\cos{\frac{\pi}{k+2}}$$.
We will focus on the submatrices with large entries of $$M_n$$. When there are $$k$$ consecutive large entries :$$\forall i\leq k$$ $$X_{a+i}\geq C$$ for some $$a$$, we will assume that $$X_{a+i} = C$$ for all $$i$$ and write $$CA_k$$. This is obiously not true but it is just to simplify the discussion. We then have $$M_n = \begin{pmatrix}\ddots & \\ & C_1A_{k_1} \\ & & \ddots \\ & & & C_2 A_{k_2} \\ & & & & \ddots \\ & & & & & . \end{pmatrix}$$ where $$\ddots$$ have small entries (let say $$\mathcal{O}(1)$$) and $$C_i\gg 1$$. The largest eigenvalue will come from these submatrices $$\lambda_\max (M_n) \approx \max_j \lambda_{\max}(C_j A_{k_j})=\max_j 2 C_j\cos(\frac{\pi}{k_j+2})$$
For large $$n$$ the behaviour will depend on the tail of the random variable $$X_1$$.
We first consider the case of polynomial tail : $$\mathbb{P}(X \geq K)\sim \frac{1}{K^\alpha}$$.
For any $$k$$, $$\lambda_{\max}(C A_{k})\geq K\Leftrightarrow C \geq \frac{K}{2\cos(\frac{\pi}{k+2})}$$ and we estimate $$\mathbb{P}(\forall i\leq k, X_k \geq \frac{K}{2\cos(\frac{\pi}{k+2})}) = \Big(\frac{2\cos(\frac{\pi}{k+2})}{K} \Big)^k$$ For $$K\rightarrow \infty$$, one can see that the case $$k=1$$ have the much larger probability and we deduce that in this situation it is enougth to consider only $$k=1$$ submatrices. Conclusion for polynomial tail we have $$\lambda_\max (M_n) \approx \max_j X_j \sim n^{1/\alpha}$$ (Because there are $$n$$ iid $$X_j$$, we set $$K=n^{1/\alpha}$$ such that $$\mathbb{P}(X_1 \geq K)=\frac{1}{n}$$).
We now consider the case of exponential tail : $$\mathbb{P}(X \geq K)\sim \exp(-\gamma K)$$.
We estimate $$\mathbb{P}\Big(\forall i\leq k, X_k \geq \frac{K}{2\cos(\frac{\pi}{k+2})}\Big) = \exp\Big(-\frac{\gamma k K}{2 \cos(\frac{\pi}{k+2})} \Big)$$ Still here for $$K\rightarrow \infty$$, the case $$k=1$$ have the much larger probability. Conclusion for exponential tail we have $$\lambda_\max (M_n) \approx \max_j X_j \sim \frac{\log(n)}{\gamma}$$ (we set $$K$$ such that $$\mathbb{P}(X_1 \geq K)=\frac{1}{n}$$).
We continue with the case of sup-exponential tail : $$\mathbb{P}(X \geq K)\sim \exp(-K^\gamma)$$.
We have $$\mathbb{P}\Big(\forall i\leq k, X_k \geq \frac{K}{2\cos(\frac{\pi}{k+2})}\Big) = \exp\Big(-\frac{ k }{2^\gamma \cos(\frac{\pi}{k+2})^\gamma}K^\gamma \Big)$$ Here there is a $$k^*$$ that maximize $$\frac{k}{\cos(\frac{\pi}{k+2})^\gamma}$$ which have the much larger probability for $$K\rightarrow \infty$$. We also set $$K$$ such that this event is of order $$1/n$$ and then for sup-exponential tail we have $$\lambda_\max (M_n) \sim \frac{2\cos(\frac{\pi}{k^*+2})}{(k^*)^\frac{1}{\gamma}}\log(n)^{\frac{1}{\gamma}}$$
Finally in case of bounded $$X$$, for any $$\epsilon>0$$, and $$k$$, we can find $$a$$ such that $$\forall i\leq k, X_{a+i}\geq \|X\|_\infty-\epsilon$$ with probability that goes to $$1$$ as $$n\rightarrow \infty$$. Then $$2 \|X\|_\infty \geq \lambda_\max (M_n) \geq 2 (\|X\|_\infty-\epsilon) \cos(\frac{\pi}{k+2})$$ and we get $$\lambda_\max (M_n) \rightarrow 2 \|X\|_\infty$$. | 2021-09-28 01:45:56 | {"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": 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": 67, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9745309352874756, "perplexity": 122.93455736145849}, "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/1631780058589.72/warc/CC-MAIN-20210928002254-20210928032254-00218.warc.gz"} |
https://math.stackexchange.com/questions/517370/continuous-implies-frechet-differentiable | # continuous implies frechet differentiable?
I knew if $f$ is Frechet differentiable at $x$ then $f$ is continuous at $x$. But reverse, i.e. If $f$ is continuous at $x$ then $f$ is Frechet differentiable at $x$ true or false?. I think it is wrong, but I can't give a counterexample. Can anyone give me a counterexample?. Thanks
The space $\mathbb{R}$ with the usual absolute value is a normed vector space, and the Frechet derivative coincides with the ordinary derivative.[1] Now can you come up with continuous functions that are not (Frechet-)differentiable?
[1] If $f:\mathbb{R}\to\mathbb{R}$, then its Frechet derivative at $x$ is the bounded linear operator defined as multiplication by $f'(x)$.
• let $f(x)=|x|$ then $f$ is continuous at $0$, but not differentiable. Ok – Muniain Oct 8 '13 at 15:57 | 2019-05-26 11:00:04 | {"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": 0.9925611019134521, "perplexity": 59.60307632503116}, "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-2019-22/segments/1558232259126.83/warc/CC-MAIN-20190526105248-20190526131248-00281.warc.gz"} |
https://pageranks.biz/littleton-colorado-80130-backlinks-builder.html | Our team is made up of industry-recognized thought leaders, social media masters, corporate communications experts, vertical marketing specialists, and internet marketing strategists. Members of the TheeTeam host SEO MeetUp groups and actively participate in Triangle area marketing organizations. TheeDigital is an active sponsor of the AMA Triangle Chapter.
The third and final stage requires the firm to set a budget and management systems; these must be measurable touchpoints, such as audience reached across all digital platforms. Furthermore, marketers must ensure the budget and management systems are integrating the paid, owned and earned media of the company.[67] The Action and final stage of planning also requires the company to set in place measurable content creation e.g. oral, visual or written online media.[68]
In an effort to manually control the flow of PageRank among pages within a website, many webmasters practice what is known as PageRank Sculpting[65]—which is the act of strategically placing the nofollow attribute on certain internal links of a website in order to funnel PageRank towards those pages the webmaster deemed most important. This tactic has been used since the inception of the nofollow attribute, but may no longer be effective since Google announced that blocking PageRank transfer with nofollow does not redirect that PageRank to other links.[66]
To create an effective DMP, a business first needs to review the marketplace and set 'SMART' (Specific, Measurable, Actionable, Relevant and Time-Bound) objectives.[60] They can set SMART objectives by reviewing the current benchmarks and key performance indicators (KPIs) of the company and competitors. It is pertinent that the analytics used for the KPIs be customised to the type, objectives, mission and vision of the company.[61][62]
The world is mobile today. Most people are searching on Google using a mobile device. The desktop version of a site might be difficult to view and use on a mobile device. As a result, having a mobile ready site is critical to your online presence. In fact, starting in late 2016, Google has begun experiments to primarily use the mobile version of a site's content41 for ranking, parsing structured data, and generating snippets.
There are simple and fast random walk-based distributed algorithms for computing PageRank of nodes in a network.[33] They present a simple algorithm that takes {\displaystyle O(\log n/\epsilon )} rounds with high probability on any graph (directed or undirected), where n is the network size and {\displaystyle \epsilon } is the reset probability ( {\displaystyle 1-\epsilon } is also called as damping factor) used in the PageRank computation. They also present a faster algorithm that takes {\displaystyle O({\sqrt {\log n}}/\epsilon )} rounds in undirected graphs. Both of the above algorithms are scalable, as each node processes and sends only small (polylogarithmic in n, the network size) number of bits per round.
The truth? Today, rising above the noise and achieving any semblance of visibility has become a monumental undertaking. While we might prevail at searching, we fail at being found. How are we supposed to get notice while swimming in a sea of misinformation and disinformation? We've become immersed in this guru gauntlet where one expert after another is attempting to teach us how we can get the proverbial word out about our businesses and achieve visibility to drive more leads and sales, but we all still seem to be lost.
SEO is an acronym for "search engine optimization" or "search engine optimizer." Deciding to hire an SEO is a big decision that can potentially improve your site and save time, but you can also risk damage to your site and reputation. Make sure to research the potential advantages as well as the damage that an irresponsible SEO can do to your site. Many SEOs and other agencies and consultants provide useful services for website owners, including:
Some backlinks are inherently more valuable than others. Followed backlinks from trustworthy, popular, high-authority sites are considered the most desirable backlinks to earn, while backlinks from low-authority, potentially spammy sites are typically at the other end of the spectrum. Whether or not a link is followed (i.e. whether a site owner specifically instructs search engines to pass, or not pass, link equity) is certainly relevant, but don't entirely discount the value of nofollow links. Even just being mentioned on high-quality websites can give your brand a boost.
Google's founders, in their original paper,[18] reported that the PageRank algorithm for a network consisting of 322 million links (in-edges and out-edges) converges to within a tolerable limit in 52 iterations. The convergence in a network of half the above size took approximately 45 iterations. Through this data, they concluded the algorithm can be scaled very well and that the scaling factor for extremely large networks would be roughly linear in {\displaystyle \log n} , where n is the size of the network.
Yes the links we have are found elsewhere but our focus is saving our users and clients time so we consolidated the links because it takes hours and hours and hours of searching to find them and some searchers are not very savvy when it comes to looking for, and finding, good quality information. I look at the links like a library, my library has these books, so do a bunch of other libraries. I think it is a shame that I have to hide my books from Google because I have to many really good ones because it is seen as a BAD thing in Google’s eyes. Darned if you dont create a good site, and darned if you do.
Brand awareness has been proven to work with more effectiveness in countries that are high in uncertainty avoidance, also these countries that have uncertainty avoidance; social media marketing works effectively. Yet brands must be careful not to be excessive on the use of this type of marketing, as well as solely relying on it as it may have implications that could negatively harness their image. Brands that represent themselves in an anthropomorphizing manner are more likely to succeed in situations where a brand is marketing to this demographic. "Since social media use can enhance the knowledge of the brand and thus decrease the uncertainty, it is possible that people with high uncertainty avoidance, such as the French, will particularly appreciate the high social media interaction with an anthropomorphized brand." Moreover, digital platform provides an ease to the brand and its customers to interact directly and exchange their motives virtually.[33]
So what happens when you have a page with “ten PageRank points” and ten outgoing links, and five of those links are nofollowed? Let’s leave aside the decay factor to focus on the core part of the question. Originally, the five links without nofollow would have flowed two points of PageRank each (in essence, the nofollowed links didn’t count toward the denominator when dividing PageRank by the outdegree of the page). More than a year ago, Google changed how the PageRank flows so that the five links without nofollow would flow one point of PageRank each.
It is very rare for an individual to enter a management role early in his or her career. Most marketing managers have spent several years working somewhere else on a marketing team. This assumes the existence of at least a bachelor's degree, but an advanced degree such as a master’s in marketing or business administration can give an aspiring manager a deciding edge.
If (a) is correct that looks like bad news for webmasters, BUT if (b) is also correct then – because PR is ultimately calculated over the whole of the web – every page loses out relative to every other page. In other words, there is less PR on the web as a whole and, after a sufficient number of iterations in the PR calculation, normality is restored. Is this correct?
Quite simply, a backlink is one website mentioning another website and linking to it. It is not merely referencing the website or it’s web address. It has to be a clickable link using an href attribute within the code. It is the difference between http://www.moz.com and Moz. Even though the first example displays a URL, the search engines do not register this as a backlink, whereas the word that has a link (often underlined and in a different color), is.
The Truth? You don't often come across genuine individuals in this space. I could likely count on one hand who those genuine-minded marketers might be. Someone like Russel Brunson who's developed a career out of providing true value in the field and helping to educate the uneducated is one such name. However, while Brunson has built a colossal business, the story of David Sharpe and his journey to becoming an 8-figure earner really hits home for most people.
Thanks a lot for all of those great tips you handed out here. I immediately went to work applying the strategies that you mentioned. I will keep you posted on my results. I have been offering free SEO services to all of my small business bookkeeping clients as a way of helping them to grow their businesses. Many of them just don’t have the resources required to hire an SEO guru to help them but they need SEO bad. I appreciate the fact that you share your knowledge and don’t try to make it seem like it’s nuclear science in order to pounce on the innocent. All the best to you my friend!
Robots.txt is not an appropriate or effective way of blocking sensitive or confidential material. It only instructs well-behaved crawlers that the pages are not for them, but it does not prevent your server from delivering those pages to a browser that requests them. One reason is that search engines could still reference the URLs you block (showing just the URL, no title or snippet) if there happen to be links to those URLs somewhere on the Internet (like referrer logs). Also, non-compliant or rogue search engines that don't acknowledge the Robots Exclusion Standard could disobey the instructions of your robots.txt. Finally, a curious user could examine the directories or subdirectories in your robots.txt file and guess the URL of the content that you don't want seen.
If you’re just getting started with SEO, you’re likely to hear a lot about “backlinks,” “external and internal links,” or “link building.” After all, backlinks are an important SEO ranking factor for SEO success, but as a newbie, you may be wondering: what are backlinks? SEO changes all the time — do backlinks still matter? Well, wonder no more. Say hello to your definitive guide to backlinks and their significance in SEO.
Google uses a hyperlink based algorithm (known as ‘PageRank’) to calculate the popularity and authority of a page, and while Google is far more sophisticated today, this is still a fundamental signal in ranking. SEO can therefore also include activity to help improve the number and quality of ‘inbound links’ to a website, from other websites. This activity has historically been known as ‘link building’, but is really just marketing a brand with an emphasis online, through content or digital PR for example.
So, as you build a link, ask yourself, "am I doing this for the sake of my customer or as a normal marketing function?" If not, and you're buying a link, spamming blog comments, posting low-quality articles and whatnot, you risk Google penalizing you for your behavior. This could be as subtle as a drop in search ranking, or as harsh as a manual action, getting you removed from the search results altogether!
Every mechanism or algorithm is good untill someone brake it. In my opinion as people tend to scam the search results, google is getting more and more consevative upon indexing and ranking search results. When I search a word or a phrase I see more wikipedia, amazon, google, youtube, etc. links returning my search, even the page name or headline does not cover the keywords in the phrase. I’m getting afraid that this may lead to an elitist web nature in the future.
Being a leading data-driven agency, we are passionate about the use of data for designing the ideal marketing mix for each client and then of course optimization towards specific ROI metrics. Online marketing with its promise of total measurement and complete transparency has grown at a fast clip over the years. With the numerous advertising channels available online and offline it makes attributing success to the correct campaigns very difficult. Data science is the core of every campaign we build and every goal we collectively set with clients.
Google might see 10 links on a page that has $10 of PageRank to spend. It might notice that 5 of those links are navigational elements that occur a lot throughout the site and decide they should only get 50 cents each. It might decide 5 of those links are in editorial copy and so are worthy of getting more. Maybe 3 of them get$2 each and 2 others get \$1.50 each, because of where they appear in the copy, if they’re bolded or any of a number of other factors you don’t disclose.
He is the co-founder of Neil Patel Digital. The Wall Street Journal calls him a top influencer on the web, Forbes says he is one of the top 10 marketers, and Entrepreneur Magazine says he created one of the 100 most brilliant companies. Neil is a New York Times bestselling author and was recognized as a top 100 entrepreneur under the age of 30 by President Obama and a top 100 entrepreneur under the age of 35 by the United Nations. | 2019-06-16 01:35:27 | {"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": 0.18447671830654144, "perplexity": 2125.5552368803815}, "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-2019-26/segments/1560627997508.21/warc/CC-MAIN-20190616002634-20190616024634-00498.warc.gz"} |
http://eprints.pascal-network.org/archive/00000988/ | Reinforcement Learning in POMDPs Without Resets
Eyal Even-Dar, Sham Kakade and Yishay Mansour
In: IJCAI 2005, July 31 - August 5, 2005, Edinburgh, Scotland, UK.
## Abstract
We consider the most realistic reinforcement learning setting in which an agent starts in an unknown environment (the POMDP) and must follow one continuous and uninterrupted chain of experience with no access to resets'' or offline'' simulation. We provide algorithms for general POMDPs that obtain near optimal average reward. One algorithm we present has a convergence rate which depends \emph{exponentially} on a certain horizon time of an optimal policy, but has \emph{no dependence} on the number of (unobservable) states. The main building block of our algorithms is an implementation of an \emph{approximate} reset strategy, which we show always exists in every POMDP. An interesting aspect of our algorithms is how they use this strategy when balancing exploration and exploitation.
PDF - Requires Adobe Acrobat Reader or other PDF viewer.
EPrint Type: Conference or Workshop Item (Paper) Project Keyword UNSPECIFIED Learning/Statistics & OptimisationTheory & Algorithms 988 Yishay Mansour 19 June 2005 | 2014-11-23 04:47:33 | {"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": 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": 0.5617328882217407, "perplexity": 2435.2554049645087}, "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-2014-49/segments/1416400379083.43/warc/CC-MAIN-20141119123259-00021-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://www.lmfdb.org/L/rational/8/260%5E4/1.1/c1e4-0 | Label $\alpha$ $A$ $d$ $N$ $\chi$ $\mu$ $\nu$ $w$ prim $\epsilon$ $r$ First zero Origin
8-260e4-1.1-c1e4-0-0 $1.44$ $18.5$ $8$ $2^{8} \cdot 5^{4} \cdot 13^{4}$ 1.1 $$1.0, 1.0, 1.0, 1.0 1 1 0 0.413378 Modular form 260.2.r.b 8-260e4-1.1-c1e4-0-1 1.44 18.5 8 2^{8} \cdot 5^{4} \cdot 13^{4} 1.1$$ $1.0, 1.0, 1.0, 1.0$ $1$ $1$ $0$ $0.437590$ Modular form 260.2.bg.b
8-260e4-1.1-c1e4-0-10 $1.44$ $18.5$ $8$ $2^{8} \cdot 5^{4} \cdot 13^{4}$ 1.1 $$1.0, 1.0, 1.0, 1.0 1 1 0 1.33268 Modular form 260.2.bc.b 8-260e4-1.1-c1e4-0-11 1.44 18.5 8 2^{8} \cdot 5^{4} \cdot 13^{4} 1.1$$ $1.0, 1.0, 1.0, 1.0$ $1$ $1$ $4$ $2.47883$ Modular form 260.2.bk.a
8-260e4-1.1-c1e4-0-2 $1.44$ $18.5$ $8$ $2^{8} \cdot 5^{4} \cdot 13^{4}$ 1.1 $$1.0, 1.0, 1.0, 1.0 1 1 0 0.752244 Modular form 260.2.bc.a 8-260e4-1.1-c1e4-0-3 1.44 18.5 8 2^{8} \cdot 5^{4} \cdot 13^{4} 1.1$$ $1.0, 1.0, 1.0, 1.0$ $1$ $1$ $0$ $0.791438$ Modular form 260.2.m.b
8-260e4-1.1-c1e4-0-4 $1.44$ $18.5$ $8$ $2^{8} \cdot 5^{4} \cdot 13^{4}$ 1.1 $$1.0, 1.0, 1.0, 1.0 1 1 0 0.866992 Modular form 260.2.bg.a 8-260e4-1.1-c1e4-0-5 1.44 18.5 8 2^{8} \cdot 5^{4} \cdot 13^{4} 1.1$$ $1.0, 1.0, 1.0, 1.0$ $1$ $1$ $0$ $0.981538$ Modular form 260.2.bf.b
8-260e4-1.1-c1e4-0-6 $1.44$ $18.5$ $8$ $2^{8} \cdot 5^{4} \cdot 13^{4}$ 1.1 $$1.0, 1.0, 1.0, 1.0 1 1 0 1.18890 Modular form 260.2.bj.b 8-260e4-1.1-c1e4-0-7 1.44 18.5 8 2^{8} \cdot 5^{4} \cdot 13^{4} 1.1$$ $1.0, 1.0, 1.0, 1.0$ $1$ $1$ $0$ $1.18967$ Modular form 260.2.bj.a
8-260e4-1.1-c1e4-0-8 $1.44$ $18.5$ $8$ $2^{8} \cdot 5^{4} \cdot 13^{4}$ 1.1 $$1.0, 1.0, 1.0, 1.0 1 1 0 1.25771 Modular form 260.2.bk.b 8-260e4-1.1-c1e4-0-9 1.44 18.5 8 2^{8} \cdot 5^{4} \cdot 13^{4} 1.1$$ $1.0, 1.0, 1.0, 1.0$ $1$ $1$ $0$ $1.33051$ Modular form 260.2.bf.a | 2022-09-30 12:04:43 | {"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": 0.9799811840057373, "perplexity": 294.90502538713014}, "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/1664030335469.40/warc/CC-MAIN-20220930113830-20220930143830-00247.warc.gz"} |
https://docs.blazingsql.com/reference/python/tables/apache-hive.html | # Query Hive Tables¶
If you have created tables using Hive, you can query those tables easily using BlazingSQL. You can simply connect to Hive and get a cursor, and give it to BlazingSQL and Hive can tell BlazingSQL where the data is located, its schema and table names to make querying those tables much simpler. BlazingSQL can also take advantage of any partitioning you have done with Hive, so that only certain partitions are read as necessary to process a query.
## Basic Usage¶
You can query your Hive tables by leveraging pyhive. All you have to do is obtain a cursor from Hive and pass it into the create table statement. Use the optional parameters if you want the BlazingSQL table to have a different name than how Hive had the name, or if the Hive table is not in the “default” Hive database.
### Parameters¶
• hive_table_name - string. The name of the table in Hive. Default: same as the table name being given in bc.create_table().
• hive_database_name - string. The name of the database or schema in Hive where the table resides. Default: "default".
• file_format - string. A string describing the file format ("csv", "orc", "parquet"). It is recommended to set this parameter because Hive sometimes stores files without an extension that is recognized by BlazingSQL. Default: If this field is not set, BlazingSQL will try to infer what file type it is, depending on the extension on the files found by BlazingSQL.
### Example¶
from blazingsql
import BlazingContext
from pyhive import hive
# start up BlazingSQL
bc = BlazingContext()
# connect to Hive and obtain a cursor
cursor = hive.connect(
port="hive_server_port", # usually 10000
auth="KERBEROS", # optional
kerberos_service_name="hive") # optional
# give create_table the Hive cursor
# the table name must match the same table name as in Hive
bc.create_table("hive_table_name", cursor)
# query table (result = cuDF DataFrame)
result = bc.sql("select * from hive_table_name")
# create a table called "hive_table_name2" from a hive table called my "my_hive_table_name" in database "db2"
bc.create_table(
"hive_table_name2",
cursor,
hive_table_name="my_hive_table_name",
hive_database_name="db2")
If you want your BlazingSQL table to only be aware of certain partitions, you can select the partitions you want when you create the BlazingSQL table using the “partitions” parameter. When using “partitions” and also using a Hive cursor, if you don’t specify any partitions for a partitioned column, the table will be created with all the partitions for that column.
### Parameters¶
• partitions - dictionary. A dictionary object where the keys are the column names for all partitioned columns, and the values are all the values of the partitions of interest. Default: None.
### Example¶
from blazingsql import BlazingContext
# start up BlazingSQL
bc = BlazingContext()
# connect to Hive and obtain a cursor
cursor = hive.connect(
port="hive_server_port", # usually 10000
auth="KERBEROS", # optional
kerberos_service_name="hive") # optional
# Give create_table the Hive cursor
# Here we are selecting only 6 partitions for this table
# (2 t_year X 3 t_company_id X 1 region)
bc.create_table(
"asia_transactions",
cursor,
file_format="parquet",
hive_table_name="fin_transactions",
partitions = {
"t_year":[2017, 2018],
"t_company_id":[2, 4, 6],
"region": ["asia"]
}
)
# Here we are creating a similar table, but not specifying
# any region partitions, in which case it will create a table
# with all the partitions. We are selecting only 30 partitions
# for this table (2 t_year X 3 t_company_id X all region partitions
# (5 in this example)).
bc.create_table(
"all_transactions",
cursor,
file_format="parquet",
hive_table_name="fin_transactions",
partitions = {
"t_year":[2017, 2018],
"t_company_id":[2, 4, 6]
}
)
## Advanced Usage: No Hive Cursor¶
You can also create a table that has been partitioned by Hive, without using a Hive cursor.
For this functionality, instead of providing the create_table statement with a Hive Cursor, you would provide it the base path of where the table is located in the Hive directory structure. If you only pass it the base path, BlazingSQL will attempt to traverse the whole directory structure and infer all the partitions and the partitions’ schema.
You can also manually use the partitions argument and the partitions_schema argument. When using the partitions argument, you must also provide at least one partition for every partitioned column. The list of partitioned columns must also be provided in the order in which Hive partitioned those columns. With the partitions_schema argument you provide the column name and type for all partitioned columns. If using the partitions argument, you must also use the partitions_schema argument.
### Parameters¶
• partitions - dictionary. A dictionary object where the keys are the column names for all partitioned columns, and the values are all the values of the partitions of interest. Note that not all partitions must be included, but all partitioned columns must be included and at least one partition per partitioned column. Default: None.
• partitions_schema - list of tuples. A list of tuples of the column name and column type for the partitioned columns. Default: None.
### Example¶
from blazingsql import BlazingContext
# start up BlazingSQL
bc = BlazingContext()
location="hdfs://localhost:54310/user/hive/warehouse/fin_transactions"
# This is the same table as the "asia_transactions" example above, but
# without using the hive cursor
bc.create_table(
"asia_transactions2",
location,
file_format="parquet",
hive_table_name="fin_transactions",
partitions={
"t_year":[2017, 2018],
"t_company_id":[2, 4, 6],
"region": ["asia"]
},
partitions_schema=[
("t_year","int"),
("t_company_id","int"),
("region","str")
]
) | 2021-06-23 21:43:55 | {"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": 0.3097260594367981, "perplexity": 4386.429948911326}, "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-2021-25/segments/1623488540235.72/warc/CC-MAIN-20210623195636-20210623225636-00175.warc.gz"} |
https://www.semanticscholar.org/paper/Formation-of-a-Malin-1-analogue-in-IllustrisTNG-by-Zhu-Xu/36a6bff81e9bcc92e36ea2f783560b4763e5a281 | # Formation of a Malin 1 analogue in IllustrisTNG by stimulated accretion
@article{Zhu2018FormationOA,
title={Formation of a Malin 1 analogue in IllustrisTNG by stimulated accretion},
author={Qirong Zhu and Dandan Xu and Massimo Gaspari and Vicente Rodriguez-Gomez and Dylan Nelson and Mark Vogelsberger and Paul Torrey and Annalisa Pillepich and Jolanta Zjupa and Rainer Weinberger and Federico Marinacci and R{\"u}diger Pakmor and Shy Genel and Yue-xing Li and Volker Springel and Lars Hernquist},
journal={Monthly Notices of the Royal Astronomical Society: Letters},
year={2018}
}
• Published 23 May 2018
• Physics
• Monthly Notices of the Royal Astronomical Society: Letters
The galaxy Malin 1 contains the largest stellar disk known but the formation mechanism of this structure has been elusive. In this paper, we report a Malin 1 analogue in the 100 Mpc IllustrisTNG simulation and describe its formation history. At redshift zero, this massive galaxy, having a maximum circular velocity $V_{\rm max}$ of 430 ${\rm km\ s^{-1}}$, contains a 100 kpc gas/stellar disk with morphology similar to Malin 1. The simulated galaxy reproduces well many observed features of Malin 1…
## Figures from this paper
A Malin 1 ‘cousin’ with counter-rotation: internal dynamics and stellar content of the giant low surface brightness galaxy UGC 1922
• Physics
Monthly Notices of the Royal Astronomical Society
• 2018
The formation scenario for giant low surface brightness (gLSB) galaxies with discs as large as 100 kpc still remains unclear. These stellar systems are rare and very hard to observe, therefore a
First spectroscopic study of ionised gas emission lines in the extreme low surface brightness galaxy Malin 1
• Physics
Astronomy & Astrophysics
• 2020
Context. Malin 1 is the largest known low surface brightness (LSB) galaxy, the archetype of so-called giant LSB galaxies. The structure and origin of such galaxies are still poorly understood,
The role of the elaphrocentre in void galaxy formation
• Physics
Monthly Notices of the Royal Astronomical Society
• 2021
Voids may affect galaxy formation via weakening mass infall or increasing disk sizes, which could potentially play a role in the formation of giant low surface brightness galaxies (LSBGs). If a
The role of the elaphrocentre in low surface brightness galaxy formation
• Physics
• 2020
The formation mechanisms of giant low surface brightness galaxies (LSBGs), with high masses and low star formation rates, remain unclear. If a dark matter halo forms at the potential hill
The formation of isolated ultradiffuse galaxies in romulus25
• Physics
• 2021
We use the Romulus25 cosmological simulation volume to identify the largest-ever simulated sample of field ultra-diffuse galaxies (UDGs). At z=0, we find that isolated UDGs have average star
NIHAO XXI: the emergence of low surface brightness galaxies
• Physics
Monthly Notices of the Royal Astronomical Society
• 2019
The existence of galaxies with a surface brightness $\mu$ lower than the night sky has been known since three decades. Yet, their formation mechanism and emergence within a $\rm\Lambda CDM$ universe
Detection of a Star-forming Galaxy in the Center of a Low-mass Galaxy Cluster
• Physics
The Astrophysical Journal
• 2018
Brightest Cluster Galaxies (BCGs) residing in the centers of galaxy clusters are typically quenched giant ellipticals. A recent study hinted that star-forming galaxies with large disks, so-called
Search for gas accretion imprints in voids: II. The galaxy Ark 18 as a result of a dwarf–dwarf merger
• Physics
• 2021
The low-mass low-surface brightness (LSB) disc galaxy Arakelian 18 (Ark 18) resides in the Eridanus void and because of its isolation represents an ideal case to study the formation and evolution
UGC 1378 – a Milky Way sized galaxy embedded in a giant low surface brightness disc
• Physics, Geology
Monthly Notices of the Royal Astronomical Society
• 2019
The dominant physical processes responsible for the formation and longevity of giant gaseous and stellar discs in galaxies remain controversial. Although they are rare (less than 10 confirmed as of
Tidally induced warps of spiral galaxies in IllustrisTNG
• Physics
• 2020
Abstract Warps are common features in both stellar and gaseous discs of nearby spiral galaxies with the latter usually easier to detect. Several theories have been proposed in the literature to
## References
SHOWING 1-10 OF 27 REFERENCES
Malin 1: A quiescent disk galaxy
• Physics
• 1989
Optical and radio spectroscopic observations are presented for Malin 1, a galaxy with an extremely low surface brightness disks with an enormous mass of neutral hydrogen, and a low-luminosity Seyfert
On the Classification of UGC 1382 as a Giant Low Surface Brightness Galaxy
• Physics, Geology
• 2016
We provide evidence that UGC 1382, long believed to be a passive elliptical galaxy, is actually a giant low surface brightness (GLSB) galaxy that rivals the archetypical GLSB Malin 1 in size. Like
First results from the IllustrisTNG simulations: the stellar mass content of groups and clusters of galaxies
• Physics
• 2018
The IllustrisTNG project is a new suite of cosmological magneto-hydrodynamical simulations of galaxy formation performed with the Arepo code and updated models for feedback physics. Here we introduce
The role of mergers and halo spin in shaping galaxy morphology
• Physics
• 2017
Mergers and the spin of the dark matter halo are factors traditionally believed to determine the morphology of galaxies within a $\Lambda$CDM cosmology. We study this hypothesis by considering
Are ring galaxies the ancestors of giant low surface brightness galaxies
• Physics
• 2007
We simulate the collisional formation of a ring galaxy and we integrate its evolution up to 1.5 Gyr after the interaction. About 100-200 Myr after the collision, the simulated galaxy is very similar
First results from the IllustrisTNG simulations: matter and galaxy clustering
• Physics
• 2018
Hydrodynamical simulations of galaxy formation have now reached sufficient volume to make precision predictions for clustering on cosmologically relevant scales. Here we use our new IllustrisTNG
Properties of H i discs in the Auriga cosmological simulations
• Physics
• 2016
We analyse the properties of the H i gas distribution in the Auriga project, a set of magnetohydrodynamic cosmological simulations performed with the moving-mesh code arepo and a physics model for
The merger rate of galaxies in the Illustris simulation: a comparison with observations and semi-empirical models
• Physics
• 2015
We have constructed merger trees for galaxies in the Illustris simulation by directly tracking the baryonic content of subhaloes. These merger trees are used to calculate the galaxy–galaxy merger
Simulating galaxy formation with black hole driven thermal and kinetic feedback
• Physics
• 2017
The inefficiency of star formation in massive elliptical galaxies is widely believed to be caused by the interactions of an active galactic nucleus (AGN) with the surrounding gas. Achieving a
Galactic fountains and the rotation of disc-galaxy coronae
• Physics
• 2011
In galaxies like the Milky Way, cold (˜104 K) gas ejected from the disc by stellar activity (the so-called galactic-fountain gas) is expected to interact with the virial-temperature (˜106 K) gas of | 2022-06-24 22:21:55 | {"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": 0.4888056218624115, "perplexity": 7425.56529144881}, "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-2022-27/segments/1656103033816.0/warc/CC-MAIN-20220624213908-20220625003908-00326.warc.gz"} |
https://stats.stackexchange.com/questions/234076/multivariate-time-series-forecasting-change-in-forecast-when-one-variable-chan | Multivariate Time Series Forecasting - Change in Forecast when One Variable Changed
I am looking to do time series forecasting with multiple variables. For example a data frame (df) of 4 different time series might look like this, where each column is its own time series:
X1 X2 X3 X4
1 4 13 2 81
2 24 91 86 58
3 21 97 39 1
4 1 56 79 55
5 63 6 91 79
6 66 96 95 81
Let's say X1 is 'cost' and the other variables are things like temperature, volume, and #_of_people.
I would like to forecast 'cost' using the other 3 variables. I imagine using something like Vector Autoregressive Models (VAR) for Multivariate Time Series can be used to see how each variable impacts the other in each separate time series (one for each variable).
For example, using the vars package in r we can run forecasts against the 4 time series and plot the results:
var.2c <- VAR(df, p = 2, type = "const")
var.2c.prd <- predict(var.2c, n.ahead = 8, ci = 0.95)
fanchart(var.2c.prd)
As I understand it, 4 separate regression models were built, one for each variable, where all the other variables were considered for each one. In other words, 'cost' was forecasted, taking into consideration not just the 'cost' trends, but also the impact the other 3 variables (X2, X3, and X3) had on 'cost.'
My question is, say I wanted to take a date in the future, on the forecast of cost, and see what happens to that forecasted value when temperature is increased (X2). I am assuming I can just take the coefficients in the 'cost' regression model that was used to forecast 'cost' using VAR, and use them as you would normally. For example, if the coefficient says the 'cost' will increase by 5 dollars for every one unit increase in temperature (X2), then I could take the forecasted value at the date of interest and add the \$5, to say that is what would happen to the forecasted value if X2 were to change.
Are my intuitions correct here or am I missing something? Are there better ways to run 'what-if' analyses on forecasted multivariate time series?
• I’m typing on my mobile, so I’ll be very brief. I’d suggest you calculate the impulse response function using irf in vars Nov 2, 2019 at 21:02 | 2022-08-15 23:12:02 | {"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": 0.6215389370918274, "perplexity": 543.9799009508617}, "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-2022-33/segments/1659882572212.96/warc/CC-MAIN-20220815205848-20220815235848-00351.warc.gz"} |
http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:1196.34023 | Language: Search: Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.
# Advanced Search
Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1196.34023
Heidarkhani, Shapour; Tian, Yu
Multiplicity results for a class of gradient systems depending on two parameters.
(English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 2, 547-554 (2010). ISSN 0362-546X
Summary: We prove the existence of at least three solutions for a class of two-point boundary value systems of the type $$u_i''+u_i=\lambda F_{u_i}(x,u+1,\dots,u_n)+\mu G_{u_i}(x,u_1,\dots,u_n),\quad u_i'(a)=u_i'(b)=0$$ for $1\le i\le n$. The approach is fully based on a recent three critical points theorem of Ricceri.
MSC 2000:
*34B08 Multi-parameter boundary value problems
34B15 Nonlinear boundary value problems of ODE
47J10 Nonlinear eigenvalue problems
34B09 Boundary value problems with an indefinite weight
Keywords: three solutions; critical point; multiplicity results; double eigenvalue problem; Neumann problem
Login Username: Password:
Highlights
Master Server
### Zentralblatt MATH Berlin [Germany]
© FIZ Karlsruhe GmbH
Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.
Other Mirror Sites
Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster | 2013-05-21 13:28:43 | {"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": 0.5150712728500366, "perplexity": 8604.953387043968}, "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-2013-20/segments/1368700014987/warc/CC-MAIN-20130516102654-00000-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://zbmath.org/?q=an:06965399 | ## Global well-posedness of weak solutions to the time-dependent Ginzburg-Landau model for superconductivity.(English)Zbl 1404.35425
Summary: We prove the global existence and uniqueness of weak solutions to the time dependent Ginzburg-Landau system in superconductivity with Coulomb gauge.
### MSC:
35Q56 Ginzburg-Landau equations 35K55 Nonlinear parabolic equations 82D55 Statistical mechanics of superconductors 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
### Keywords:
Ginzburg-Landau model; superconductivity; Lorentz gauge
Full Text:
### References:
[1] R. A. Adams and J. J. F. Fournier, Sobolev Spaces, Second ed, Pure and Applied Mathematics (Amsterdam) 140, Elsevier/Academic Press, Amsterdam, 2003. [2] H. Beirão da Veiga and F. Crispo, Sharp inviscid limit results under Navier type boundary conditions: An $$L^p$$ theory, J. Math. Fluid Mech. 12 (2010), no. 3, 397–411. · Zbl 1261.35099 [3] A. Bendali, J. M. Domínguez and S. Gallic, A variational approach for the vector potential formulation of the Stokes and Navier-Stokes problems in three-dimensional domains, J. Math. Anal. Appl. 107 (1985), no. 2, 537–560. · Zbl 0591.35053 [4] Z. Chen, C. M. Elliott and T. Qi, Justification of a two-dimensional evolutionary Ginzburg-Landau superconductivity model, RAIRO Modél. Math. Anal. Numér. 32 (1998), no. 1, 25–50. · Zbl 0905.35084 [5] Z. M. Chen, K.-H. Hoffmann and J. Liang, On a nonstationary Ginzburg-Landau superconductivity model, Math. Methods Appl. Sci. 16 (1993), no. 12, 855–875. · Zbl 0817.35111 [6] Q. Du, Global existence and uniqueness of solutions of the time-dependent Ginzburg-Landau model for superconductivity, Appl. Anal. 53 (1994), no. 1-2, 1–17. · Zbl 0843.35019 [7] J. Fan, H. Gao and B. Guo, Uniqueness of weak solutions to the 3D Ginzburg-Landau superconductivity model, Int. Math. Res. Not. IMRN 2015 (2015), no. 5, 1239–1246. · Zbl 1317.35248 [8] J. Fan and S. Jiang, Global existence of weak solutions of a time-dependent 3-D Ginzburg-Landau model for superconductivity, Appl. Math. Lett. 16 (2003), no. 3, 435–440. · Zbl 1055.35109 [9] J. Fan and T. Ozawa, Global strong solutions of the time-dependent Ginzburg-Landau model for superconductivity with a new gauge, Int. J. Math. Anal. (Ruse) 6 (2012), no. 33-36, 1679–1684. · Zbl 1255.35202 [10] ——–, Uniqueness of weak solutions to the Ginzburg-Landau model for superconductivity, Z. Angew. Math. Phys. 63 (2012), no. 3, 453–459. · Zbl 1247.35164 [11] A. Lunardi, Interpolation Theory, Second edition, Lecture Notes, Scuola Normale Superiore di Pisa (New Series), Edizioni della Normale, Pisa, 2009. [12] Q. Tang, On an evolutionary system of Ginzburg-Landau equations with fixed total magnetic flux, Comm. Partial Differential Equations 20 (1995), no. 1-2, 1–36. · Zbl 0833.35132 [13] Q. Tang and S. Wang, Time dependent Ginzburg-Landau equations of superconductivity, Phys. D 88 (1995), no. 3-4, 139–166. · Zbl 0900.35371
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2023-02-02 20:53:52 | {"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": 0.5542497634887695, "perplexity": 1515.62688337253}, "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/1674764500041.18/warc/CC-MAIN-20230202200542-20230202230542-00188.warc.gz"} |
https://astronomy.stackexchange.com/questions/29994/why-is-the-moon-that-special-is-it-really-a-well-built-coincidence/29998 | Why is the moon that special? Is it really a well built coincidence? [duplicate]
I find it funny that the moon is the only object in the solar system to almost perfectly fit the sun, resulting in the spectacular solar eclipses. No other object except maybe a few irregular moons like Pandora from Saturn would do that, and for them, they aren't round, and thus can't fully block out all light. The moon also has a perfect rotation that is almost exactly the same as Earth's rotational period, resulting in a tidal lock, which causes tides.
Is this a coincidence? Any speculation on why this happens? Is this the only observed place where such criteria play into such perfect coincidence?
• If it were really special, there would be a total eclipse every new Moon and every Full Moon. :-) Mar 15, 2019 at 2:43
• @JohnHoltz well its orbit is tilted, but still these two coincidences... what resulted in them? Mar 15, 2019 at 2:47
• -1 and vote to close for primarily opinion-based for explicitly requesting speculation!
– uhoh
Mar 15, 2019 at 5:15
• The moon also has a perfect rotation that is almost exactly the same as Earth's rotational period What?! The Moon's rotational period is nearly 30 times longer than Earth's. Mar 15, 2019 at 6:17
• First about Moon's roundness: Moon is pretty big, so its gravitation forces pull down all of the material so it shapes round. And about "coincidence": there are a lot of moons in the Universe. Some of them are rounded and have the same angular diameter as their star. But this isn't so rare. Mar 15, 2019 at 17:28 | 2022-05-22 16:53:28 | {"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": 0.5561625361442566, "perplexity": 1141.9483631983014}, "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-2022-21/segments/1652662545875.39/warc/CC-MAIN-20220522160113-20220522190113-00474.warc.gz"} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.