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The Guardian, in early September 2017, released a report that microplastic contamination has been found in tap water in countries around the world. What this means for the seven billion people on earth, no one yet knows. All the experts can agree on is that, given the warning signs being given by life in the oceans, the need to find out is urgent.
Scores of tap water samples from more than a dozen nations were analysed by scientists for an investigation by Orb Media . Overall, 83% of the samples were contaminated with plastic fibres. Bottled water may not provide a microplastic-free alternative to tapwater, as the as it was also found in a few samples of commercial bottled water tested in the United States for Orb.
The US had the highest contamination rate, at 94%, with plastic fibres found in tap water sampled at sites including Congress buildings, the US Environmental Protection Agency’s headquarters, and Trump Tower in New York. Lebanon and India had the next highest rates.
Why should you care? Microplastics have been shown to absorb toxic chemicals linked to cancer and other illnesses, and then release them when consumed by fish and mammals. If fibers are in your water, experts say they’re surely in your food as well – baby formula, pasta, soups and sauces whether from the kitchen or the grocery. It gets worse. Plastic is all but indestructible, meaning plastic waste doesn’t biodegrade; rather it only breaks down into smaller pieces of itself, even down to particles in nanometer scale. Studies show that particles of that size can migrate through the intestinal wall and travel to the lymph nodes and other bodily organs.
The new analyses indicate the ubiquitous extent of microplastic contamination in the global environment. Previous work has been largely focused on plastic pollution in the oceans, which suggests people are eating microplastics via contaminated seafood. But the wholesale pollution of the land was hidden. Tap water is gathered from hills, rivers, lakes and wells, sampling the environment as it goes. It turns out that tiny fibres of plastic are everywhere.
“We have enough data from looking at wildlife, and the impacts that it’s having on wildlife, to be concerned,” said Dr Sherri Mason, a microplastic expert at the State University of New York in Fredonia, who supervised the analyses for Orb. “If it’s impacting [wildlife], then how do we think that it’s not going to somehow impact us?”
Plastics often contain a wide range of chemicals to change their properties or color and many are toxic or are hormone disruptors. Plastics can attract other pollutants too, including dioxins, metals and some pesticides. Microplastics have also been shown to attract microbial pathogens. Research on wild animals shows conditions in animal guts are also known to enhance the release of pollutants from plastics. “Further,” as the review puts is, “there is evidence that particles may even cross the gut wall and be translocated to other body tissues, with unknown consequences”. Prof Richard Thompson, at Plymouth University, UK, told Orb: “It became clear very early on that the plastic would release those chemicals and that actually, the conditions in the gut would facilitate really quite rapid release.” His research has shown microplastics are found in a third of fish caught in the UK.
Does any of this affect people? The only land animals in which the consumption of microplastic has been closely studied are two species of earthworm and a nematode.
The scale of global microplastic contamination is only starting to become clear, with studies in Germany finding fibers in all of 24 beer brands tested , as well as in honey and sugar . A study revealed a rain of microplastics falling on Paris from the air, dumping between 3 and 10 tons a year on the city. The same team found microplastics in an apartment and hotel room. “We really think that the lakes [and other water bodies] can be contaminated by cumulative atmospheric inputs,” said Johnny Gasperi, at the University Paris-Est Créteil, who did the Paris studies. “What we observed in Paris tends to demonstrate that a huge amount of fibres are present in atmospheric fallout.”
This research led Frank Kelly, professor of environmental health at King’s College London, to tell a UK parliamentary inquiry in 2016: “If we breathe them in they could potentially deliver chemicals to the lower parts of our lungs and maybe even across into our circulation.” Having seen the Orb data, Kelly told the Guardian that research is urgently needed to determine whether ingesting plastic particles is a health risk.
Another huge unanswered question is how microplastics get into our water and food. A report from the UK’s Chartered Institution of Water and Environmental Management says the biggest proportion are fibers shed by synthetic textiles and tire dust from roads, with more from the breakdown of waste plastics. It suggests the plastic being dumped on land in Europe alone each year is between four and 23 times the amount dumped into all the world’s oceans.
A lot of the microplastic debris is washed into wastewater treatment plants, where the filtering process does capture many of the plastic fragments. But about half the resulting sludge is ploughed back on to farmland across Europe and the US, according to recent research published in the Journal Environmental Science & Technology. That study estimates that up to 430,000 tons of microplastics could be being added to European fields each year, and 300,000 tons in North America. “It is striking that transfers of microplastics – and the hazardous substances bound to them – from urban wastewater to farmland has not previously been considered by scientists and regulators,” the scientists concluded. “This calls for urgent investigation if we are to safeguard food production,” they say in a related publication.
Plastic fibres may also be flushed into water systems, with a recent study finding that each cycle of a washing machine could release 700,000 fibers into the environment. Tumble dryers are another potential source, with almost 80% of US households having dryers that usually vent to the open air. Rains could also sweep up microplastic pollution, which could explain why the household wells used in Indonesia were found to be contaminated.
In Beirut, Lebanon, the water supply comes from natural springs but 94% of the samples were contaminated. “This research only scratches the surface, but it seems to be a very itchy one,” said Hussam Hawwa, at the environmental consultancy Difaf, which collected samples for Orb.
Like so many environmental problems – climate change, pesticides, air pollution – the impacts only become clear years after damage has been done. If we are lucky, the plastic planet we have created will not turn out to be too toxic to life. If not, cleaning it up will be a mighty task. Dealing properly with all waste plastic will be tricky: stopping the unintentional loss of microplastics from clothes and roads even more so.
But above all we need to know if we are all drinking, eating and breathing microplastic every day and what that is doing to us, and we need to know urgently. | https://oecotextiles.blog/2017/09/21/microplastics-found-in-tap-water/ |
4-H Afterschool is a special focused effort within the 4-H Youth Development Program that helps 4-H and other youth-serving organizations create and improve after-school programs in urban, suburban, and rural communities across the United States.
4-H Youth Development Program
The 4-H Youth Development Program is the only national organization that is federally mandated to conduct positive youth development programs. The program works to improve knowledge and skills of young people (their Heads, Hearts, Hands, and Health) and the quality of life in the communities in which they live.
Cooperative Extension System
The CES, administered by over 130 land grant universities and anchored in all 3,150 counties across the country, is a network of academically trained university faculty and staff who provide a broad array of staff training, curriculum, community collaboration building, evaluation, resource development, and other expertise and resources to out-of-school time programs.
National Network for Child Care
NNCC unites the expertise of many of the nation's leading universities through the outreach system of Cooperative Extension. Our goal is to share knowledge about children and child care from the vast resources of the land grant universities with parents, professionals, practitioners, and the general public.
You For Youth
This site helps youth professionals connect and share resources with colleagues, provide professional development and technical assistance opportunities, and offer tools for program improvement. The site provides information focused on afterschool programs.
America's Children: Key National Indicators of Well-Being
Youth Indicators is a statistical compilation of data on the distribution of youth, their family structure, economic factors, school and extracurricular activities, health factors, and other elements that constitute the world of young people between the ages of 0-17 years. This report is created and published by Child Stats, a division of the Federal Interagency Forum on Child and Family Statistics. | https://youth.gov/federal-resources?f%5B0%5D=federal_resources_agencies%3A105&f%5B1%5D=federal_resources_agencies%3A164&f%5B2%5D=federal_resources_agencies%3A177&f%5B3%5D=federal_resources_agencies%3A223&f%5B4%5D=federal_resources_agencies%3A233&f%5B5%5D=federal_resources_topic%3A2 |
1. Mission summaryThe ISO mission resulted from a proposal made to ESA in 1979. After a number of studies ISO was selected in 1983 as the next new start in the ESA Scientific Programme. Following a Call for Experiment and Mission Scientist Proposals, the scientific instruments were selected in mid 1985. The two spectrometers (SWS, LWS), a camera (ISOCAM) and an imaging photo-polarimeter (ISOPHOT) jointly covered wavelengths from 2.5 to around 240 microns with spatial resolutions ranging from 1.5 arcseconds (at the shortest wavelengths) to 90 arcseconds (at the longer wavelengths). The satellite design and main development phases started in 1986 and 1988, respectively. ISO was launched perfectly in November 1995 by an Ariane 44P vehicle. Routine scientific operations commenced in February 1996 and continued until depletion of the liquid helium (LHe) in April 1998, with limited operations continuing through May. The first homogeneous ISO data archive opened to the community in December 1998 and, by August 1999, all data had entered the public domain. Work on supporting the community in their exploitation of ISO data and on bringing the legacy archive into its final shape continued until the end of 2006, in the Post Operations Phase (1998-2001) and Active Archive Phase (2002-2006), as outlined below. Maintenance of the historical archive is now carried out by the core archive team at ESAC.
2. Operations Phase (1995-1998)In orbit, ISO was an outstanding technical, operational and scientific success. Due to excellent engineering and a somewhat fortunate combination of circumstances at launch, the liquid helium supply lasted over 10 months longer than the specified 18 months. The extra lifetime not only led to many more observations but also made it possible to observe the scientifically-important Taurus/Orion region - inaccessible in the nominal mission. By a combination of very good in-orbit performance, detailed analysis on the ground and a variety of tune-ups, the accuracy of the pointing system was improved to the arc second level. The absolute pointing error was reduced to around 1 arcsec - ten times better than specified - and the short-term jitter was about five times better than the specification of 2.7 arcsec (2 sigma, half cone, over a 30 second period of time). The optical performance of the telescope and baffle system was excellent, with stray light being too low to measure. All elements of the ground segment also performed excellently, leading to an overall availability of the system during routine phase of 98.3% of the time scheduled for science. Taking into account all possible reasons for failure, only 4% of observations were lost. Over 98% of the highest-priority observations were successfully executed. All the scientific instruments, including many delicate cryogenic mechanisms, performed extremely well. At a wavelength of 12 microns, ISO was one thousand times more sensitive and had one hundred times better angular resolution than IRAS.
3. Post Operations Phase (1998 - 2001)The goal of the post operations phase was to maximise the scientific return of ISO by facilitating effective and widespread exploitation of data. This was accomplished by:
- deepening the understanding of the performance of the instruments and satellite in orbit;
- improving the data processing, both pipeline products and interactive analysis software;
- supporting the general astronomical community to use ISO data;
- providing a homogeneous archive.
It was a collaborative effort between the ESA ISO Data Centre (IDC) in Villafranca Madrid, five specialist National Data Centres (NDCs) built around the teams that had provided the instruments, and the US ISO Support Center at IPAC.
At the start of the Post Operation Phase, all data were re-processed with the end-of-mission calibration to populate the first homogeneous ISO Data Archive, which opened to the community in December 1998. Some 10 versions of the pipeline were released, grouped under three major overall ISO pipeline versions, from Version 8 to Version 10. The improved products were made available to the community via on-the-fly reprocessing in the archive. Users then selected, from the archive, data sets of interest and used the provided (and evolving) interactive analysis tools for deeper study. ISO's Legacy Archive, containing the reference product set from the final pipeline processing, was released just after the end of this phase.
A major effort was made on calibration and cross-calibration, using topic-oriented Working Groups, each addressing one specific calibration topic but with many links between them and fluid exchange of useful information. These Working Groups were formed by members from the IDC and from the different NDCs and reported on: Beam Profiles/Pointing; Glitches; Line profiles; Photometric calibration; Polarisation; Spectral Matching; Transients; and Interactive Analysis. Cross-calibration specialists maintained an overview of the work of the Working Groups and cooperated with instrument-specific calibration manpower in efforts to understand inconsistencies of calibration relevant to more than one instrument. Every six months an overall cross-calibration report was compiled. The final Cross-Calibration Final Report was issued in January 2001.
A mid-term review was held in February 2000 to review progress and make recommendations re future directions. All data centres provided direct support to users and welcomed visitors. Eight general conferences and specific small "hands-on" data reduction workshops were organised with the proceedings being made widely available via the ESA SP publications series.
4. Active Archive Phase (2002 - 2006)The main goal of the Active Archive Phase was "to bring the archive into its final shape, while further facilitating the direct and easy access of the world-wide community to the ISO data products, especially for the preparation and exploitation of upcoming missions". The main thrusts of the active archive phase were to continue the support of the community in their use of ISO data and to capture back into the archive as much as possible of the user knowledge so as to maximize the long-term value and usability of the archive. One specific direction set by the post-operations mid-term review was "scientifically focused interactive data processing by users with the aim of including the results in the archive".
The responsibilities of the ESA ISO Data Centre in the active archive phase included:
- archive maintenance and improvements,
- support in data usage,
- supply of general information,
- promotion of awareness of ISO data
- overall co-ordination of managerially- and financially-independent data centres.
The responsibilities of the National Data Centres included:
- maintenance and improvement of software packages for interactive data reduction,
- including making available new algorithms and calibration files
- further work on instrument-specific calibration;
- focused reduction of specific data sets to be ingested back into the archive.
This phase continued most of the collaborations between the centres involved in the previous phase. In general, the effort was concentrated at the start of the phase, allowing a smooth transfer of expertise to other missions.
5. Science Highlights and PublicationsISO has delivered important results in nearly all fields of astronomical research, almost literally from comets to cosmology. Some are already being followed up with existing telescopes; others have to await future facilities, such as the Herschel Space Observatory. Highlights include:
- the discovery of crystalline silicates outside our own solar system, in the atmospheres of young and old stars as well as in comet Hale-Bopp giving a link between interplanetary and interstellar dust; showing that water is ubiquitous in the cosmos. A wealth of water vapour transitions were measured in objects such as Mars, Titan, the giant planets, comets including Hale-Bopp, in shocks, in the cold interstellar medium, in circumstellar envelopes and in the ultra-luminous galaxy Arp220;
- the first detections of the lowest pure rotational lines of H2 (giving access to gas at temperatures less than a few hundred K) in many sources such as young massive stars, HH-objects, PDR's, the diffuse ISM, outer parts of edge-on galaxies; detailed investigations of interstellar solid state features, e.g. CO2 ices, leading to a very detailed interplay between observations and laboratory spectroscopy.
- obtaining spectral energy distributions of extragalactic objects, which serve as templates for cosmological studies, helped to consolidate the unified scheme or to develop quasar evolutionary scenarios.
- making deep cosmological surveys at near- and far-infrared wavelengths the results from which show: early star formation hidden by dust; the need for evolutionary models; resolution of part of the cosmic infrared background (CIB) into discrete sources; and detection of fluctuations in the CIB.
The results produced until late 2004 were reviewed in a special issue of Space Science Reviews (vol 119, 2005). This issue was reprinted into a 450-page book entitled "ISO Science Legacy - a compact review of ISO major achievements", consisting of 4 general articles reviewing four major themes investigated by ISO (crystalline silicates, molecular hydrogen, water in the universe, deep surveys), followed by 13 papers reviewing ISO science from the Solar System to the distant Universe.
Recent papers continue to develop these themes and address a number of important questions in all areas of astronomy, either based on the study of a particular object or, mostly, on samples of targets extracted from the ISO archive and often in combination with data from other facilities. ISO data are also resulting in feedback into modelling and laboratory research activities.
Nearly 1400 papers have been published in the refereed literature on ISO results. Note that the ISO Data Archive contains links from the individual observations to the papers that use them. On the other hand, ISO observations are linked from the associated papers in ADS.
6. ISO Data Archive (IDA)ISO performed around 30,000 science observations. If account is taken of observations made in the parallel and serendipity modes of the instruments (observational modes in which an instrument could observe while another instrument was prime) almost 150000 data sets were recorded with ISO. Since ISO was operated as an observatory with four complex instruments, the resulting data is very heterogeneous. The data underwent sophisticated processing, including validation and accuracy analysis before products were made available via the archive.
The ISO Data Archive (IDA) opened to the external world on December 9, 1998, six months after the end of the operations. Around 400 GBytes of data are stored on magnetic disks. In addition to the observational data products, the archive also contains satellite housekeeping data, software tools, documentation, and externally derived products.
Users of the ISO Data Archive see a self-contained, fast and powerful interface to all ISO data products. Complex queries can be made against hundreds of database parameters using friendly and modular query panels. The user is helped in selection of observations by a clear and configurable results display that includes quick-look data browsing, access to auxiliary and ancillary files, access to related observations in the ISO catalogue, on-line help and access to other archives.
The IDA is based on an open and flexible 3-tier architecture comprising the data products and database, the business logic and the user interface. An important consideration was to separate the stored data from their final presentation to the user. The business logic and the user interface have been developed entirely in JAVA and XML. This has facilitated its re-use for other ESA science archives (such XMM-Newton, INTEGRAL and Planetary Missions).
In addition to the 'standard' data products generated for every ISO observation by an automatic data-analysis pipeline, the ISO archive contains so-called "Highly Processed Data Products (HPDP)". These are the result of further processing beyond the pipeline and/or use of new, refined algorithms mainly contributed by ISO instrument experts. They include processed images and spectra, object catalogs, and spectral and image atlases. A number of instrument-mode or object-type specific projects have been carried out, fulfilling the goal set at the start of the Phase to populate 30% of the scientific content of the archive with more readily usable products. Thirty sets of HPDPs are available. The total number of observations associated with one or more HPDP sets is 9607, i.e. 32% of its scientific content.
The ISO Data Centre has also fostered the ISO presence in the Virtual Observatory. The initial ad-hoc implementation of elements of interoperability between archives (e.g. with CDS/VizieR, SIMBAD, ADS and NASA's IRSA) evolved into a system complying with the new standards set by the Virtual Observatory international community. The IDA was one of the first archives to be part of the European Virtual Observatory prototypes, as demonstrated in January 2004 and 2005. ISO has played a key role in the definition of standards for interoperability within the International Virtual Observatory Alliance (IVOA). Access to ISO spectral and image data is provided, respectively, via the IVOA Simple Spectrum Access Protocol (SSAP) and the IVOA Simple Image Access Protocol (SIAP). ISO has also been a pioneer in Europe by implementing Basic SkyNode (another IVOA standard) access to the ISO products.
7. Support and information to the community and beyondInteractive analysis tools - software packages offered to the community for reduction and analysis of ISO data - have been further refined and are available from the ISO Web site. These include: ISOCAM Interactive Analysis (CIA); ISOPHOT Interactive Analysis (PIA); Observers' SWS Interactive Analysis (OSIA); LWS Interactive Analysis (LIA); and ISO Spectroscopic Analysis Package (ISAP).
Extensive explanatory and technical support documentation is archived. This includes the five volumes of the ISO Handbook (released in their final form as ESA SP-1262 in 2003), gathering all the information needed to make efficient use of ISO data, and extensive technical documentation, tracing and explaining the experience of the instrument teams as they worked to understand the calibration of their instruments. Together with the ISO data products, the body of explanatory and support documentation is called the ISO Explanatory Library. About 200 major documents are archived in an organised and uniform fashion for the satellite and the four instruments.
ISO Data Centres
The Data Centres responsible for ISO User Support were as follows (Centres which continued to operate into the Active Archive Phase are marked with a (#) :
ISO Data Centre at ESA, ESAC in Spain (#)
Five Specialist National Data Centres (NDCs) :
French ISO Centres, SAp/Saclay and IAS/Orsay, France;
ISOPHOT Data Centre at MPIA, Heidelberg, in Germany (#);
Dutch ISO Data Analysis Centre - DIDAC) (now part of the HIFI Operations Centre) at SRON, Groningen, in the Netherlands (#);
ISO Spectrometer Data Centre at MPE in Garching, Germany (#);
UK ISO Data Centre at RAL, Didcot, in the United Kingdom (#)
Plus, in the USA, :
The ISO Support Center at NASA's Infrared Processing and Analysis Centre (IPAC).
Alberto Salama,
ISO Project Scientist. | https://www.cosmos.esa.int/web/iso/mission-overview |
The invention discloses a vehicle ad hoc network road connectivity real-time repair mechanism method based on unmanned aerial vehicle nodes, and relates to the technical field of Internet of Vehiclesand ad hoc networks. The method mainly comprises: obtaining data such as the real-time position and the free flow speed of a current road vehicle based on an unmanned aerial vehicle; calculating the position of the vehicle at each moment in the next period according to the obtained information, and predicting the road multi-hop network communication condition between two intersections according tothe positions; and if the regional network on the road is disconnected in the future period, enabling the unmanned aerial vehicle to calculate an optimal periodic movement strategy according to the current condition to perform bridging repair. According to the mechanism method, only a single unmanned aerial vehicle needs to be configured on a single road to collect vehicle information by means ofa vehicle ad hoc network, calculate the future motion trail of the vehicle to predict the position of the network disconnection area; the optimal real-time moving strategy is calculated in combination the current position, direction and speed of the unmanned aerial vehicle, the possible disconnection area in the future period is repaired to the maximum extent, and the mechanism method provides stable and effective network connectivity support for road vehicle communication when the vehicle flow is small, namely the number of vehicle nodes is small. | |
Pima County, Ariz., has reduced the number of miles traveled by the county fleet by 21% and reduced carbon intensity of its fleet operations by nearly 6%, according to its Sustainable Action Plan Report Card. The report card details progress made in improving the sustainability of Pima County operations during fiscal year 2014-15.
The county reduced its fleet carbon intensity — greenhouse gases emitted per square foot — by increasing the number of miles traveled by passenger vehicles and reducing those of trucks and SUVs, a result of county right-sizing efforts. It used a FY-2013-14 baseline.
In its goal to reduce the ratio of carbon emissions produced by county fleet vehicles (excluding Sheriff’s vehicles, off-road vehicles, and heavy equipment) per service population, the county has improved by 25%. This was achieved by reducing vehicle miles traveled by 21% and reducing fuel use per vehicle mile traveled by 4%. Fleet-wide fuel economy improved from 16.17 PMG to 16.88 MPG, a 4.4% improvement. The county replaced 45 conventional fuel vehicles with alternative-fuel vehicles in FY 2014-15.
Additionally, the county completed construction of the new Fleet Services building, which was submitted for LEED Gold Certification, a green building certification.
For the full report, click here. | https://www.government-fleet.com/134486/right-sizing-helps-ariz-county-reduce-fleet-emissions |
In recent years, there has been a growing recognition among scholars and international development institutions of the necessity for approaches to community-development that not only increase capacity for self-help but also fundamentally increase the rights of poor and marginalized people within national and international governing structures. At a practical level, community organizing can be thought of as the process or a set of tools with which communities can accomplish this goal and strategically build the power necessary to influence local, national, or international policy and discourse.
Taking a practical “hands-on” perspective, this course will explore the theories, tools, styles and challenges of community-based organizing. It will discuss practical strategies for developing community leadership and working with marginalized communities, exploring the ideas and examples from Evo Morales, Paulo Freire, Saul Alinsky, Sup-Comandante Marcos, the Bridge Immigrant Rights experiment and Martin Heidegger. By diving into the depths of organizing with intentionality, we will discover the impact that ordinary individuals can and have had on the world.
Upon completion of this course participants will be able to:
• Understand the history and basic principles of community organizing
• Apply basic organizing techniques, such as popular education and direct action
• Support current organizing efforts in the student’s field or situation
• Understand the role of privilege, race, gender and class in struggles for change
Noncredit courses do not produce academic credit nor appear on a Colorado State University academic transcript. | https://villageearth.org/class/gsll-1517-community-based-organizing/ |
In a changing climate, land use planning for the urban billions
Large Chinese cities such as Beijing are already bursting at their seams. Imagine the daily commute for one of Beijing’s 21.7 million residents. Most people live in the outskirts of the city, where there is housing, but have to commute to the city center for jobs. Although public transportation is available, average commutes still can be upwards of an hour and a half. And more people are driving too – rush hour traffic in the urban core increased by 50%, even though average travel distance is only about 6 miles.
Because of the way Beijing is expanding both vertically and horizontally, with increasing physical distances between housing and jobs, carbon pollution from transportation has also increased. If measures aren’t implemented to reduce these emissions, China may not be able to meet their carbon pollution targets.
When discussing climate change mitigation strategies, the global conversation tends to focus on energy – the switch to renewables or increasing energy efficiency. Urban land use is an underrepresented part of the climate dialogue – how cities are designed and how people move within them – even though land use has long-term consequences for a city to mitigate and adapt to climate change.
The upcoming UN Habitat III Conference presents an opportunity to create a ‘New Urban Agenda’ policy that includes the climate consequences of land use planning.
Because land use decisions are relatively permanent, Beijing’s urban policies also have consequences for the city’s ability to adapt to a changing climate. According to the Intergovernmental Panel on Climate Change, Beijing residents will have reduced access to potable water, increased respiratory illness due to higher prevalence of dust storms, and increased incidence of heat stroke from heat waves. The city has already planted rows of trees along the north rim of the city to halt desertification – will this be sufficient, especially if urban infrastructure expands beyond the existing greenbelts?
The Habitat III conference will focus on ways that cities can be built for the challenges of the 21st century. Chief among these challenges is climate change. Land use planning emerges as a potential bridge between the New Urban Agenda and last year’s Paris Agreement to reduce carbon pollution.
Land use planning is commonly developed across governance scales, and often has a good deal of local control. The leverage to use land use planning to mitigate carbon emissions and to employ best practices to reduce transport-related emissions rests with a suite of officials across different governance scales. This includes creating integrated public transportation systems, access to multimodal transportation options, and the co-location of housing and jobs to reduce commutes. Coordination among different levels of government, including local, state, and federal, to ensure that best practices are employed allows for effective land use planning.
The way that cities are built in the next 10-20 years will have long-term impacts for climate change. If cities and their leaders are given effective tools to do urban planning, understanding how it impacts climate mitigation and adaptation, cities can begin the transition to reduce urban carbon pollution. For urbanizing cities, particularly in developing countries, building infrastructure that will allow communities to be resilient to climate change represents a critical aspect of climate change planning.
However, the ‘Urban and Spatial Planning and Design’ issue paper developed in advance of Habitat III by the United Nations Task Team draws only limited connections between urban form and climate change. The transformation to dense, connected cities needs to be made more explicit in the issue papers and policy positions.
The New Urban Agenda can help frame the tradeoffs and opportunities to better plan urban land use in low carbon cities. It can identify best practices, successful case studies, and provide sustainable models to set cities on a low-carbon trajectory. It can demonstrate how to integrate climate adaptation and resilience into land use decisions. This type of foresight in urban land use planning, combined with climate projections, would help maximize the relevance of the New Urban Agenda and Habitat III to a rapidly changing world.
Beijing has built a world-class subway system and high speed train. The city’s approach integrates many different best practices into their regional planning and economic development. Even with the long commutes, Beijing is an example of new urbanization in the 21st century – and Habitat III should take note. | https://environment.yale.edu/blog/2016/05/urban-land-use-planning-climate/ |
Q. Do you still have a museum?
Answer
The space where the Reuel B. Pritchett Museum was housed for many years was converted into the Bridgewater College Campus Store. There is no longer a permanent museum gallery. Museum artifacts central to the educational mission are in preservation storage and are experiencing a revival as material culture teaching artifacts. 176 Bridgewater College students used Special Collections in classes during the 2019-2020 year. Museum artifacts are also shown in rotating exhibits and serve as a hands-on learning tool for Bridgewater College student assistants, interns, and volunteers. Museum artifacts are available to view by appointment.
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Welcome to our Special Collections Frequently Asked Questions page! Visit our Library Services and Interlibrary Loan FAQ pages as well. Feel free to contact us at any time! | https://libanswers.bridgewater.edu/specialcollections/faq/336161 |
From Methyl Radical to Polyacetylene: Size-Dependent Structural Properties of Linear Polyenes
Hydrocarbons and nanostructures, consisting of trigonally coordinated C-atoms, represent a huge family of functional materials. Depending on the configuration and the size, they may be highreactivity intermediates, raw materials or catalyzers of organic reactions, or semiconducting polymers with variable bandgap. Small molecules have been intensively studied by chemists, and crystalline polymers by physicist, but the knowledge on the medium-size oligomers is rather incomplete. For a better understanding of such materials, the size-dependence of several structural properties of linear polyenes and infinite polymers were calculated at the same level of density functional theory. Linear polyenes are the simplest derivatives of trigonal carbon and their study is instructive for the understanding of more complicated series. The analysis of heats of formation and bondlength distributions reveals a singlet-triplet transition in the trans-cisoid polyenes at the carbon number of n = 28. An efficient method is suggested for the common treatment of the molecular orbitals of polyenes and the energy bands of polyacetylene: the mapping of the energy levels of polyenes to the bands of polyacetylene. The excellent agreement of the levels of molecular orbitals and the polymer bands makes possible the reconstruction of the bands in the knowledge of molecular orbitals and vice versa. A future extension of the suggested mapping to 2 dimensions may be suitable for a uniform treatment of trigonal carbon systems from methyl radical through polycyclic aromatic hydrocarbons to graphene.
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Keywords: DFT Calculation; Electronic Structure; Linear Polyenes; Polyacetylene
Document Type: Research Article
Affiliations: Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, H-1525 Budapest, P.O. Box 49, Hungary; Faculty of Light Industry and Environmental Engineering, Óbuda University, Doberdó út 6, H-1034 Budapest, Hungary
Publication date: January 1, 2019
More about this publication?
- Journal for Nanoscience and Nanotechnology (JNN) is an international and multidisciplinary peer-reviewed journal with a wide-ranging coverage, consolidating research activities in all areas of nanoscience and nanotechnology into a single and unique reference source. JNN is the first cross-disciplinary journal to publish original full research articles, rapid communications of important new scientific and technological findings, timely state-of-the-art reviews with author's photo and short biography, and current research news encompassing the fundamental and applied research in all disciplines of science, engineering and medicine. | https://www.ingentaconnect.com/contentone/asp/jnn/2019/00000019/00000001/art00052 |
TECHNICAL FIELD
BACKGROUND
SUMMARY
BRIEF DESCRIPTION OF THE DRAWINGS
DETAILED DESCRIPTION
Null Control Signal And Examples of Imaging Signals That Can Be Used to Generate The Null Control Signal
Focal Distance-Based Null Control Signals
Field of View-Based Null Control Signals
Zoom Control-Based Null Control Signals
Proximity-Based Null Control Signals
STEERING ANGULAR LOCATION OF FRONT-SIDE NULLS TO CONTROL STEREO IMAGING OF SUBJECT(S) BEING ACQUIRED
STEERING ANGULAR LOCATIONS OF REAR-SIDE NULLS TO CANCEL REAR-SIDE SOUND SOURCES
The present invention generally relates to electronic devices, and more particularly to electronic devices having the capability to selectively acquire stereo spatial audio information.
Conventional multimedia audio/video recording devices, such as camcorders, commonly employ relatively expensive directional microphones for stereo recording of audio events. Such directional microphones have directional beamform patterns with respect to an axis, and the orientation or directionality of the microphones' beamforms can be changed or steered so that the beamform points or is oriented toward a particular direction where the user wants to record sound events.
Notwithstanding these advances in audio/video recording devices, it can be impractical to implement directional microphones in other types of portable electronic devices that include audio and video recording functionality. Examples of such portable electronic devices include, for example, digital wireless cellular phones and other types of wireless communication devices, personal digital assistants, digital cameras, video recorders, etc.
These portable electronic devices include one or more microphones that can be used to acquire and/or record audio information from a subject or subjects that is/are being recorded. In some cases, two microphones are provided on opposite ends of the device (e.g., located near the right-side and left-side of the device) so that when the device is used for audio/video acquisition the microphones are positioned for recording one or more subject(s).
The number of microphones that can be included in such devices can be limited due to the physical structure and relatively small size of such devices. Cost is another constraint that can make it impractical to integrate additional microphones in such devices for the sole purpose of multimedia acquisition and/or recording. This is particularly true with regard to directional microphones because they tend to be more expensive and more difficult to package than omnidirectional microphones. Additionally, the microphones in these types of devices have to serve multiple use cases such as private voice calls, speakerphone calls, environmental noise pickup, multimedia recording, etc. As a result, device manufacturers will often implement less expensive omnidirectional microphones. In short, the space and/or cost of adding additional microphone elements is a factor that weighs against inclusion of more than two microphones in a device.
At the same time, it is desirable to provide stereo recording features that can be used with such portable electronics devices so that an operator can record sound events with stereo characteristics.
GB 2418332
UK patent application publication no. describes a sound system which uses steerable (phased) array techniques to generate a strong sound at a first location and a weak or null sound at a second location. The sound signal is split into a plurality of frequency bands and each frequency band is directed independently such that a trough in sound pressure level exists at a common location in space. Two such sound signals may be reproduced simultaneously, the first generating a strong sound at the first location and a null at the second location while the second generates a strong sound at the second location and a null at the first location. The two signals may be the left and right channels of a stereo signal, providing excellent cross-talk cancellation. Alternatively, the two signals may be different audio programmes, directed at two different listeners at the first and second locations.
In accordance with the present invention, there is provided an apparatus and a method for recording one or more subjects by a camera operator as recited in the accompanying claims.
Accordingly, there is an opportunity to provide portable electronic devices having the capability to acquire stereo audio information using two microphones that are located at or near different ends/sides of the portable electronic device. It is also desirable to provide methods and systems within such devices to enable stereo acquisition or recording of audio sources consistent with a video frame being acquired regardless of the distance between those audio sources and the device. Furthermore, other desirable features and characteristics of the present invention will become apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and the foregoing technical field and background.
FIG. 1A
is a front perspective view of an electronic apparatus in accordance with one exemplary implementation of the disclosed embodiments;
FIG. 1B
FIG. 1A
is a rear perspective view of the electronic apparatus of ;
FIG. 2A
FIG. 1A
is a front view of the electronic apparatus of ;
FIG. 2B
FIG. 1A
is a rear view of the electronic apparatus of ;
FIG. 3
is a schematic of a microphone and video camera configuration of an electronic apparatus in accordance with some of the disclosed embodiments;
FIG. 4
is a block diagram of an exemplary system for delay and sum beamform processing of microphone output signals;
FIG. 5
is a block diagram of an audio processing system of an electronic apparatus in accordance with some of the disclosed embodiments;
FIG. 6
is a diagram that illustrates an exemplary polar graph of a right beamformed audio signal and an exemplary polar graph of a left beamformed audio signal with respect to an electronic apparatus and an angular field of view being acquired in accordance with one implementation of some of the disclosed embodiments;
FIG. 7
is a diagram that illustrates an exemplary polar graph of a right beamformed audio signal and an exemplary polar graph of a left beamformed audio signal that are generated by an electronic apparatus in accordance with another implementation of some of the disclosed embodiments;
FIG. 8A
is an exemplary polar graph of a left-side-oriented beamformed signal generated by the audio processing system in accordance with one implementation of some of the disclosed embodiments;
FIG. 8B
is an exemplary polar graph of a right-side-oriented beamformed signal generated by the audio processing system in accordance with one implementation of some of the disclosed embodiments;
FIG. 8C
is an exemplary polar graph of a right-side-oriented beamformed signal generated by the audio processing system in accordance with another implementation of some of the disclosed embodiments;
FIG. 9A
is an exemplary polar graph of a right-side-oriented beamformed audio signal and a left-side-oriented beamformed audio signal generated by the audio processing system in accordance with one implementation of some of the disclosed embodiments;
FIG. 9B
is an exemplary polar graph of a right-side-oriented beamformed audio signal and a left-side-oriented beamformed audio signal generated by the audio processing system in accordance with another implementation of some of the disclosed embodiments;
FIG. 9C
is an exemplary polar graph of a right-side-oriented beamformed audio signal and a left-side-oriented beamformed audio signal generated by the audio processing system in accordance with yet another implementation of some of the disclosed embodiments; and
FIG. 10
is a block diagram of an electronic apparatus that can be used in an implementation of the disclosed embodiments.
A more complete understanding of the present invention may be derived by referring to the detailed description and claims when considered in conjunction with the following figures, wherein like reference numbers refer to similar elements throughout the figures.
As used herein, the word "exemplary" means "serving as an example, instance, or illustration." The following detailed description is merely exemplary in nature and is not intended to limit the invention or the application and uses of the invention. Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. All of the embodiments described in this Detailed Description are exemplary embodiments provided to enable persons skilled in the art to make or use the invention and not to limit the scope of the invention which is defined by the claims. Furthermore, there is no intention to be bound by any expressed or implied theory presented in the preceding technical field, background, or the following detailed description.
Before describing in detail embodiments that are in accordance with the present invention, it should be observed that the embodiments reside primarily in an electronic apparatus that has a front side and a rear side oriented in opposite directions along a first axis, and a right-side and a left-side oriented in opposite directions along a second axis that is perpendicular to the first axis. The electronic apparatus also includes a first microphone located near the right-side of an electronic apparatus that generates a first signal, and a second microphone located near the left-side of the electronic apparatus that generates a second signal. In addition, a null control signal can be generated based on an imaging signal. The first and second signals are processed, based on the null control signal, to generate a right beamformed audio signal having a first directional pattern with at least one first null, and a left beamformed audio signal having a second directional pattern with at least one second null. As used herein, the term "null" refers to a portion of a beamform where the magnitude is near-zero. Theoretically, a null exhibits no sensitivity to sound waves that emanate from angular directions incident on the angular location of the null. In reality, a perfect null with zero sensitivity is rarely (if ever) achieved, so an alternate definition of a null would be "a minimum portion or portions of a beamform with significant (e.g., 12 db) attenuation of the incoming signal". A first angular location (α) of the at least one first null and a second angular location (P) of the at least one second null are steered based on the null control signal. As such the outputs of the microphones can be processed to create opposing, virtual microphones with beamforms that have steerable nulls. This way, the first and second directional patterns can remain diametrically opposed, but the angular locations of their respective nulls can be steered to a desired location for improved stereo imaging and/or for cancellation of an audio source at the rear-side of the electronic apparatus.
FIGS. 3-10
FIGS. 1A-2B
FIG. 1A
FIG. 1B
FIGS. 1A
1B
FIG. 2A
FIG. 2B
Prior to describing the electronic apparatus with reference to , one example of an electronic apparatus and an operating environment will be described with reference to . is a front perspective view of an electronic apparatus 100 in accordance with one exemplary implementation of the disclosed embodiments. is a rear perspective view of the electronic apparatus 100. The perspective view in and are illustrated with reference to an operator 140 of the electronic apparatus 100 that is recording one or more subjects 150, 160. is a front view of the electronic apparatus 100 and is a rear view of the electronic apparatus 100.
The electronic apparatus 100 can be any type of electronic apparatus having multimedia recording capability. For example, the electronic apparatus 100 can be any type of portable electronic device with audio/video recording capability including a camcorder, a still camera, a personal media recorder and player, or a portable wireless computing device. As used herein, the term "wireless computing device" refers to any portable computer or other hardware designed to communicate with an infrastructure device over an air interface through a wireless channel. A wireless computing device is "portable" and potentially mobile or "nomadic" meaning that the wireless computing device can physically move around, but at any given time may be mobile or stationary. A wireless computing device can be one of any of a number of types of mobile computing devices, which include without limitation, mobile stations (e.g. cellular telephone handsets, mobile radios, mobile computers, hand-held or laptop devices and personal computers, personal digital assistants (PDAs), or the like), access terminals, subscriber stations, user equipment, or any other devices configured to communicate via wireless communications.
FIG. 2A
FIG. 2B
The electronic apparatus 100 has a housing 102, 104, a left-side portion 101, and a right-side portion 103 opposite the left-side portion 101. The housing 102, 104 has a width dimension extending in a y-direction, a length dimension extending in an x-direction, and a thickness dimension extending in a z-direction (into and out of the page). The electronic apparatus 100 has a front-side (illustrated in ) and a rear-side (illustrated in ) oriented in opposite directions along a first axis. The rear-side is oriented in a +z-direction and the front-side oriented in a -z-direction. The left-side portion 101 and the right-side portion 103 are oriented in opposite directions along a y-axis that is perpendicular to the z-axis. Of course, as the electronic apparatus is re-oriented, the designations of "right", "left", "width", and "length" may be changed. The current designations are given for the sake of convenience.
More specifically, the housing includes a rear housing 102 on the operator-side or rear-side of the apparatus 100, and a front housing 104 on the subject-side or front-side of the apparatus 100. The rear housing 102 and front housing 104 are assembled to form an enclosure for various components including a circuit board (not illustrated), a speaker (not illustrated), an antenna (not illustrated), a video camera 110, and a user interface including microphones 120, 130 that are coupled to the circuit board. Microphone 120 is located nearer the left-side 101, and microphone 130 is located nearer the right-side 103.
The housing includes a plurality of ports for the video camera 110 and the microphones 120, 130. Specifically, the front housing 104 has ports for the front-side video camera 110 and other ports for the front-side microphones 120, 130. The microphones 120, 130 are disposed at/near these ports, and in some implementations the y-axis goes through the two microphone port openings.
The video camera 110 is positioned on the front-side and thus oriented in the same direction as the front housing 104, opposite the operator, to allow for images of the subject(s) to be acquired or captured during recording by the video camera 110.
The left-side portion 101 is defined by and shared between the rear housing 102 and the front housing 104, and oriented in a +y-direction that is substantially perpendicular with respect to the rear housing 102 and the front housing 104. The right-side portion 103 is opposite the left-side portion 101, and is defined by and shared between the rear housing 102 and the front housing 104. The right-side portion 103 is oriented in a -y-direction that is substantially perpendicular with respect to the rear housing 102 and the front housing 104.
FIG. 3
is a schematic of a microphone and video camera configuration 300 of the electronic apparatus in accordance with some of the disclosed embodiments. The configuration 300 is illustrated with reference to a Cartesian coordinate system and includes the relative locations of a left-side microphone 320 with respect to a right-side microphone 330 and video camera 310. Both physical microphone elements 320, 330 are shown on the subject or front-side of the electronic apparatus 100, but could reside on left and right sides 101, 103 respectively. The left-side microphone 320 is disposed near the left-side of the electronic apparatus and the right-side microphone 330 is disposed near a right-side of the electronic apparatus 100. As described above, the video camera 310 is shown positioned on a front-side of the electronic apparatus 100 and disposed near the left-side of the electronic apparatus 100, but could be disposed anywhere on the front side of the electronic apparatus 100. Alternatively, the video camera 310 could be disposed on the rear-side of the electronic apparatus 100 or a second camera (not shown) could be disposed on the rear-side of the electronic apparatus 100 to capture images or video of the operator 140 of the electronic apparatus 100 (e.g., in a webcam configuration).
The left-side and right-side microphones 320, 330 are located or oriented opposite each other along a common y-axis, which is oriented along a line at zero and 180 degrees. The z-axis is oriented along a line at 90 and 270 degrees and the x-axis is oriented perpendicular to the y-axis and the z-axis in an upward direction. The left-side and right-side microphones 320, 330 are separated by 180 degrees along the y-axis or diametrically opposed with respect to each other. The camera 310 is also located along the y-axis and points into the page in the -z-direction towards the subject(s) who are located in front of the apparatus 100. This way the left-side and right-side microphones 320, 330 are oriented such that they can capture audio signals or sound from the operator taking the video and as well as from the subjects being recorded by the video camera 310.
FIG. 4
The left-side and right-side microphones 320, 330 can be any known type of microphone elements including omnidirectional microphones and directional microphones, pressure microphones, pressure gradient microphones or any other equivalent acoustic-to-electric transducer or sensor that converts sound into an electrical audio signal, etc. In one embodiment, where the left-side and right-side microphones 320, 330 are pressure microphone elements, they will have omnidirectional polar patterns that sense/capture incoming sound more or less equally from all directions. In one implementation, the left-side and right-side microphones 320, 330 can be part of a microphone array that is processed using beamforming techniques, such as delaying and summing (or delaying and differencing), to establish directional patterns based on electrical audio signals generated by the left-side and right-side microphones 320, 330. The delay can either be a phase delay distinct at every frequency implemented via a filter, or a fixed time delay. One example of delay and sum beamform processing will now be described with reference to .
FIG. 4
is a block diagram of an exemplary system 400 for delay and sum beamform processing of microphone output signals 422, 412. Concepts illustrated in this system can be used in accordance with some of the disclosed embodiments.
The system 400 includes a microphone array that includes left and right microphones 320, 330 and a beamformer module 450. Each of the microphones 330, 320 generates an electrical audio signal 412, 422 in response to incoming sound. These electrical audio signals 412, 422 are generally a voltage signal that corresponds to sound captured at the left and right microphones 330, 320.
The beamformer module 450 is designed to generate right and left beamformed signals 452, 454. In this embodiment, the beamformer module 450 includes a first correction filter 414, a second correction filter 424, a first summer module 428, and a second summer module 429.
The first correction filter 414 adds phase delay to the first electrical audio signal 412 to generate a first delayed signal 416, and the second correction filter 424 adds phase delay to the second electrical audio signal 422 to generate a second delayed signal 426. For instance, in one implementation, the correction filters 414, 424 add a phase delay to the corresponding electrical audio signals 412, 422 to generate the corresponding delayed signals 416, 426.
The first summer module 428 sums the first signal 412 and the second delayed signal 426 to generate a first beamformed signal 452. Similarly, the second summer module 429 sums the second signal 422 and the first delayed signal 416 to generate a second beamformed signal 454.
FIG. 4
In one implementation illustrated in , the first beamformed signal 452 is a right-facing first-order directional signal (e.g., supercardioid or hypercardioid) that corresponds to a right channel stereo output with a beampattern that is oriented to the right-side or in the -y-direction. The second beamformed signal 454 is a left-facing first-order directional signal (e.g., supercardioid or hypercardioid) that corresponds to a left channel stereo output with a beampattern that is oriented to the left-side or in the +y-direction. The left channel stereo output is spatially distinct from the right channel stereo output.
FIG. 4
Thus, in the embodiment of , the first beamformed signal 452 corresponds to a right-facing virtual directional microphone with a main lobe having a maximum located along the 0 degree axis, and the second beamformed signal 454 corresponds to a left-facing virtual directional microphone with a main lobe having a maximum located along the 180 degree axis.
Although each of the beamformed audio signals 452, 454 is shown as separate right and left output channels, in some embodiments, these signals 452, 454 can be combined into a single audio output data-stream that can be transmitted and/or recorded as a single file containing separate stereo coded signals, but do not necessarily have to be combined.
FIG. 4
Although the beamformed signals 452, 454 shown in are both beamformed first order hypercardioid directional beamform patterns that are either right-side-oriented or left-side-oriented, those skilled in the art will appreciate that the beamformed signals 452, 454 are not necessarily limited to having these particular types of first order hypercardioid directional patterns and that they are shown to illustrate one exemplary implementation. In other words, although the directional patterns are hypercardioid-shaped, this does not necessarily imply the beamformed signals are limited to having a hypercardioid shape, and may have any other shape that is associated with first order directional beamform patterns such as a cardioid, dipole, supercardioid, etc. Alternatively a higher order directional beamform could be used in place of the first order directional beamform. Moreover, although the beamformed signals 452, 454 are illustrated as having hypercardioid directional patterns, it will be appreciated by those skilled in the art, that these are mathematically ideal examples only and that, in some practical implementations, these idealized beamform patterns will not necessarily be achieved.
<mrow><mfenced separators=""><mi mathvariant="normal">A</mi><mo>+</mo><mi mathvariant="normal">Bcosθ</mi></mfenced><mo>/</mo><mfenced separators=""><mi mathvariant="normal">A</mi><mo>+</mo><mi mathvariant="normal">B</mi></mfenced></mrow>
As will be appreciated by those skilled in the art, the first order beamforms are those which follow the form A+Bcos(θ) in their directional characteristics. To explain further, all first order directional microphones have a polar response described by equation (1): where A is a constant that represents the omnidirectional component of the directional pattern of the beamformed signal, where B is a constant that represents the bidirectional component of the directional pattern of the beamformed signal, and where θ is the angle of incidence of the acoustic wave. Using the omnidirectional and bidirectional elements, any first order element can be created oriented along the axis of the bidirectional element. The directional patterns that can be produced by beamforming can range from a nearly cardioid beamform to a nearly bidirectional beamform, or from a nearly cardioid beamform to a nearly omnidirectional beamform. For an omnidirectional microphone B is 0; and for a bidirectional microphone A is zero. Other well known configurations are a cardioid where A=B=1; a hypercardioid where A=1, B=3, and a supercardioid where A=0.37, B=0.63.
In general, first order directional patterns where A<B result in patterns with higher directivity, and two nulls symmetric about the axis of the microphone wherein the axis of the microphone is defined as the angle of the peak of the main lobe of the beampattern through its 180-degree opposite. When the A=B the nulls are collocated as one single null which is at an angle of 0 degrees to the axis (and opposite the peak). The larger B is than A, the closer the angle gets to +/- 90 degrees off the axis of the microphone (and opposite the peak). This will be described in more detail later.
A linear combination of properly phased omnidirectional and bidirectional microphone signals will produce the desired first order directional microphone pattern. Omnidirectional and bidirectional elements can be extracted by simple weighted addition and subtraction. For example, a virtual cardioid microphone with its lobe pointed to the right would be equals parts omnidirectional and bidirectional added together. A virtual cardioid microphone pointed in the opposite direction would be the difference between equal parts omnidirectional and bidirectional. For instance, opposing cardioids would have A=B for one direction and A= -B for the other. So the sum of signals from opposing cardioids would be an omnidirectional signal of twice the maximum amplitude of the individual cardioids, and the difference of the signals would be a bidirectional of twice the maximum amplitude of the individual cardioids.
FIG. 5
is a block diagram of an audio processing system 500 of an electronic apparatus 100 in accordance with some of the disclosed embodiments. The audio processing system 500 includes a microphone array that includes a first or left microphone 520 that generates a first signal 521 in response to incoming sound, and a second or right microphone 530 that generates a second signal 531 in response to the incoming sound. These electrical signals are generally a voltage signal that corresponds to a sound pressure captured at the microphones.
A first filtering module 522 is designed to filter the first signal 521 to generate a first phase-delayed audio signal 525 (e.g., a phase delayed version of the first signal 521), and a second filtering module 532 is designed to filter the second signal 531 to generate a second phase-delayed audio signal 535. Although the first filtering module 522 and the second filtering module 532 are illustrated as being separate from processor 550, it is noted that in other implementations the first filtering module 522 and the second filtering module 532 can be implemented within the processor 550 as indicated by the dashed-line rectangle 540.
The automated null controller 560 generates a null control signal 565 based on an imaging signal 585. Depending on the implementation, the imaging signal 585 can be provided from any one of number of different sources, as will be described in greater detail below. The sources that can provide the imaging signal can include a video camera, a controller for the video camera, or proximity sensors.
The processor 550 is coupled to the first microphone 520, the second microphone 530, and the automated null controller 560, and receives a plurality of input signals including the first signal 521, the first phase-delayed audio signal 525, the second signal 531, the second phase-delayed audio signal 535, and the null control signal 565.
FIG. 4
The processor 550 performs beamform processing. The beamform processing performed by the processor 550 can generally include delay and sum processing (as described above with reference to , for example), delay and difference processing, or any other known beamform processing technique for generating directional patterns based on microphone input signals. Techniques for generating such first order beamforms are well-known in the art, and will not be described further herein.
In accordance with the disclosed embodiments, the null control signal 565 can be used by the processor 550 to control or steer nulls of the right-side-oriented beamformed audio signal 552 and the left-side-oriented beamformed audio signal 554 during beamform processing.
FIG. 4
In one implementation, the processor 550 processes the input signals 521, 525, 531, 535, based on the null control signal 565, to generate a right (or "right-side-oriented") beamformed audio signal 552 that has a first directional pattern having at least one "first" null, and a left (or "left-side-oriented") beamformed audio signal 554 that has a second directional pattern having at least one "second" null, where a first angular location (α) of the at least one first null and a second angular location (β) of the at least one second null is steered based on the null control signal 565. The first angular location (α) is at a first angle with respect to the +y-axis, and the second angular location (β) is at a second angle with respect to the -y-axis. Depending on the implementation, the values of the first and second angular locations can be the same or different. The directional patterns can be first-order directional patterns as described above with reference to . As will be described below, during beamform processing, the null control signal 565 can be used to control or "steer" the first angular location (α) of the first null of the right-side-oriented beamformed audio signal 552 and the second angular location (β) of the second null of the left-side-oriented beamformed audio signal 554. As will be explained further below, this allows for control of the sensitivity of subject-oriented virtual microphones as well as for steering of the nulls of those virtual microphones.
FIGS. 6-9C
Depending on the implementation, as will be described below with reference to , the nulls of the beamformed audio signals 552, 554 may include more than one null point. For instance, in one implementation, the right beamformed audio signal 552 can include a first null point oriented towards the front-side 104 at an angular location +α and a second null point oriented toward the rear-side 102 at an angular location -α, and the left beamformed audio signal 554 can include a third null point oriented towards the front-side 104 at an angular location +β and a fourth null point oriented toward the rear-side 102 at an angular location -β, respectively.
In one implementation, the processor 550 can include a look up table (LUT) that receives the input signals and the null control signal 565, and generates the right beamformed audio signal 552 and the left beamformed audio signal 554. The LUT is table of values that generates different signals 552, 554 depending on the value of the null control signal 565.
In another implementation, the processor 550 is designed to process a set of equations based on the input signals 521, 525, 531, 535 and the null control signal 565 to generate the right beamformed audio signal 552 and the left beamformed audio signal 554. The equations include coefficients for the first signal 521, the first phase-delayed audio signal 525, the second signal 531, and the second phase-delayed audio signal 535; and the values of these coefficients can be adjusted or controlled based on the null control signal 565 to generate the right beamformed audio signal 552 and/or the left beamformed audio signal 554 with nulls steered to the desired angular locations (+α,-α,+β,-β).
Examples of imaging signals 585 that can be used to generate the null control signal 565 will now be described in greater detail for various implementations.
The imaging signal 585 used to determine or generate the null control signal 565, can vary depending on the implementation. For instance, in some embodiments, the automated null controller 560 can be coupled to the video camera 310 that provides the imaging signal 585. In other embodiments, the automated null controller 560 is coupled to a video controller that is coupled to the video camera 310 and provides the imaging signal 585 to the automated null controller 560. The imaging signal 585 that is used by the automated null controller 560 to generate the null control signal 565 can be (or can be determined based on) one or more of (a) an angular field of view of a video frame of the video camera 310, (b) a focal distance for the video camera 310, or (c) a zoom control signal for the video camera 310. Any of these parameters can be used alone or in combination with the others to generate a null control signal 565. The video controller that generates the imaging signal 585 can be implemented in hardware or software. It may be an automated controller or one driven by user input such as a button, slider, navigation control, any other touch controller, or a graphical user interface (GUI).
In one embodiment, the imaging signal 585 is based on focal distance for the video camera 310. For instance, in one implementation, focal distance information from the camera 310 to the subjects 150, 160 can be obtained from the camera 310, a video controller for the video camera 310, or any other distance determination circuitry in the device. In some implementations, focal distance of the video camera 310 can be used by the automated null controller 560 to generate the null control signal 565. In one implementation, the null control signal 565 can be a calculated focal distance of the video camera 110 that is sent to the automated null controller 560 by a video controller. The first angular location (α) and the second angular location (β) increase relative to the y-axis as the focal distance is increased. The first angular location (α) and the second angular location (β) decrease relative to the y-axis as the focal distance is decreased.
In one implementation, the first angular location (α) and the second angular location (β) can be determined from a lookup table for a particular value of the focal distance. In another implementation, the first angular location (α) and the second angular location (β) can be determined from a function relating the focal distance to the null angles.
In another embodiment, the imaging signal 585 can be based on an angular field of view (FOV) of a video frame of the video camera 310. For instance, in some implementations, the angular field of view of the video frame of the video camera 310 can be calculated and sent to the automated null controller 560, which can then use that information to generate the null control signal 565. The first angular location (α) and the second angular location (β) increase relative to the y-axis as the angular field of view is narrowed or decreased. The first angular location (α) and the second angular location (β) decrease relative to the y-axis as the angular field of view is widened or increased.
In one implementation, the first angular location (α) and the second angular location (β) can be determined from a lookup table for a particular value of the field of view. In another implementation, the first angular location (α) and the second angular location (β) can be determined from a function relating the field of view to the null angles.
In other embodiments, the imaging signal 585 is based on a zoom control signal for the video camera 310. In one embodiment, the physical video zoom of the video camera 310 is used to generate the null control signal 565. In these embodiments, a narrow zoom can also be called a high zoom value, whereas a wide zoom can also be called a low zoom value. As the zoom control signal is increased to narrow the angular field of view, this will cause the first angular location (α) and the second angular location (β) to increase relative to the y-axis which goes through the left and right microphones 320, 330. By contrast, as the zoom control signal is decreased to widen or expand the angular field of view, this will cause the first angular location (α) and the second angular location (β) to decrease relative to the y-axis which goes through the left and right microphones 320, 330.
In some embodiments, the null control signal 565 can be a zoom control signal for the video camera 310, whereas in other embodiments the null control signal 565 can be derived based on a zoom control signal for the video camera 310. In some implementations, the zoom control signal for the video camera 310 can be a digital zoom control signal that controls an apparent angle of view of the video camera, whereas in other implementations the zoom control signal for the video camera 310 can be an optical/analog zoom control signal that controls position of lenses in the camera. In one implementation, preset null angle values can be assigned for particular values (or ranges of values) of the zoom control signal.
In some embodiments, the zoom control signal for the video camera can be controlled by a user interface (UI). Any known video zoom UI methodology can be used to generate a zoom control signal. For example, in some embodiments, the video zoom can be controlled by the operator via a pair of buttons, a rocker control, virtual controls on the display of the device including a dragged selection of an area, by eye tracking of the operator, etc.
In one implementation, the first angular location (α) and the second angular location (β) can be determined from a lookup table for a particular value of the zoom control signal. In another implementation, the first angular location (α) and the second angular location (β) can be determined from a function relating the value of a zoom control signal to field of view.
Additionally these embodiments allow for a stereo image to zoom in or out in accordance with a video image zooming in or out.
In some embodiments, when the electronic apparatus 100 includes proximity sensor(s) (infrared, ultrasonic, etc.), proximity detection circuits, and/or other types of distance measurement device(s) (not shown), the imaging signal 585 can include proximity information generated by the proximity detector or sensor. For example, in some embodiments, the apparatus 100 can include a rear-side proximity sensor that is coupled to the automated null controller 560. The rear-side proximity sensor generates a rear-side proximity sensor signal that corresponds to a distance between the camera operator 140 and the apparatus 100. The rear-side proximity sensor signal can then be sent to the automated null controller 560, which can use the rear-side proximity sensor signal to generate the null control signal 565.
In one embodiment, the rear-side proximity sensor signal corresponds to a distance between the camera operator 140 and the apparatus 100. Depending on the implementation, the rear-side proximity sensor signal can be based on estimated, measured, or sensed distance between the camera operator 140 and the electronic apparatus 100.
In another embodiment, the rear-side proximity sensor signal corresponds to a predetermined distance between the camera operator 140 and the apparatus 100. For instance, in one implementation, the predetermined distance can be set as a fixed distance at which an operator of the camera 110 is normally located (e.g., based on an average human holding the device in a predicted usage mode). In such an embodiment, the automated null controller 560 presumes that the camera operator is a predetermined distance away from the apparatus and generates a null control signal 565 to reflect that predetermined distance.
FIG. 7
In yet another embodiment, the rear-side proximity sensor signal corresponds to a distance between the camera operator and the apparatus 100, and the second null point (of the right beamformed audio signal 552) and the fourth null point (of the left beamformed audio signal 554) are oriented to cancel sound that originates from the rear-side at the distance. As will be described further below with reference to , this allows the coverage angle of the nulls to be oriented such that a sound source behind the apparatus 100 (e.g., such as the operator) can be suppressed.
FIG. 6
An example of how the angular locations α, β of the nulls relate to a video frame or angular field of view being acquired will now be provided with reference to .
FIG. 6
FIG. 6
FIG. 6
is a diagram that illustrates an exemplary polar graph of a right beamformed audio signal 652 and an exemplary polar graph of a left beamformed audio signal 654 with respect to an electronic apparatus 600 and an angular field of view being acquired in accordance with one implementation of some of the disclosed embodiments. In , the electronic apparatus 600 is not drawn to scale, and is exaggerated in size to illustrate its relationship to a field of view 650 being acquired or recorded by a video camera (not shown) of the electronic apparatus 600. In most implementations, the field of view 650 being acquired or recorded by the video camera (not shown) is much larger than the apparatus 600 such that the apparatus is effectively a point receptor with respect to the field of view 650. For example, in , where an orchestra is being recorded, the desired recording would be for (a) the audio from the right side of the stage to be recorded on the right channel, (b) the audio from the left side of the stage recorded to the left channel, and (c) to have objects in the middle appear on both channels to give a center audio image for those objects.
FIGS. 8A
8B
Output signals 521, 531 generated by the physical microphones 520, 530 are processed using the beamforming techniques described above to generate the right beamformed audio signal 652 that has a first super-cardioid directional pattern that is oriented to the right in the direction of the -y-axis, and the left beamformed audio signal 654 that has a second super-cardioid directional pattern that is oriented to the left in the direction of the +y-axis. The major lobes of the first super-cardioid directional pattern and the second super-cardioid directional pattern are oriented diametrically opposite each other to the right and left, respectively. Further details regarding the 654 and 652 will be described below with reference to and , respectively.
The field of view 650 of the video frame is split into a left-side portion and a right-side portion via a center line 651. The left-side portion contributes to a desired left audio image 625, and the right-side portion contributes to a desired right audio image 645. The first super-cardioid directional pattern of the right beamformed audio signal 652 produces a right channel null region 635, and the second super-cardioid directional pattern of the left beamformed audio signal 654 produces a left channel null region 655.
δ
To explain further, the desired left audio image 625 overlaps the right channel null region 635 (as illustrated by a rectangular shaded region) that is associated with the right beamformed audio signal 652 but does not include the left channel null region 655 (as illustrated by a rectangular shaded region), and the desired right audio image 645 overlaps the left channel null region 655 that is associated with the left beamformed audio signal 654 but does not include the right channel null region 635. In addition, the first angular location (α) of the first null is defined between two null lines 636, 638 that diverge from a common origin to define a right channel null region 635. A first null center line 637 is defined between the null region boundaries 636, 638, and has a first angular location (α) with respect to the +y-axis. The right channel null region 635 is a null region that is centered around the first null center line 637 and bounded by the null region boundaries 636, 638. The angle that the null region 635 spans is a first number of degrees equal to 2γ. As used herein, the term "null center line" refers to a line going through a null of a beamform at a point where the magnitude of the beamform is at its minimum. As the first angular location (α) changes, the angle of the two null region boundaries 636, 638 also changes along with the right channel null region 635. Similarly, the second angular location (β) of the second null is defined between two null region boundaries 656, 658 that diverge from a common origin to define a left channel null region 655. The left channel null region 655 also spans a second number of degrees equal to 2, which may be equal to the first number of degrees 2γ. A null center line 657 is defined between the null region boundaries 656, 658, and has the second angular location (β) with respect to the -y-axis. The left channel null region 655 is a null region that is centered around the second null center line 657. As the second angular location (β) changes, the angle of the two null region boundaries 656, 658 also changes along with the left channel null region 655.
γ
δ
FIG. 6
Thus, with respect to the first angular location (α), the right channel null region 635 is illustrated as covering a portion of the field of view 650 that is ± degrees with respect to α, and the second angular location (β) of the left channel null region 655 is illustrated as covering another portion of the field of view 650 that is ± degrees with respect to β. In the particular implementation illustrated in , each channel's null regions are located approximately three-quarters of the way across the image field from a desired edge of field for that channel, and at approximately the center of the opposite side of the field being acquired.
The directional pattern of the right beamformed audio signal 652 will have stronger sensitivity to sound waves originating from the region that corresponds to the desired right audio image 645, but significantly lessened sensitivity to sound waves originating from the region that corresponds to the desired left audio image 625. The right channel null region 635 coincides with the desired left audio image 625 and allows some of sound originating from the desired left audio image 625 to be reduced. As such, the virtual microphone corresponding to the right beamformed audio signal 652 can be used to acquire/record a desired right audio image 645, with minimal signal being acquired from the left audio image 625 due to the right channel null region 635.
In this specific non-limiting implementation, the right channel null of the beamform is centered on the left side of the stage. The signal that will be recorded on the right channel will include a full audio level for the subjects furthest to the right, with a general decline in audio level moving towards center, and with a significant suppression of the audio at the center of the left side of the stage where the shaded rectangle is shown.
Similarly, the directional pattern of the left beamformed audio signal 654 will have stronger sensitivity to sound waves originating from the region that corresponds to the desired left audio image 625, but significantly lessened sensitivity to sound waves originating from the region that corresponds to the desired right audio image 645. The left channel null region 655 coincides with the desired right audio image 645 and allows some of sound originating from the desired right audio image 645 to be reduced. As such, the virtual microphone corresponding to the left beamformed audio signal 654 can be used to acquire/record a desired left audio channel 625, with minimal signal being acquired from the right audio image 645 due to the left channel null region 655.
In this specific non-limiting implementation, the left channel null of the beamform is centered on the right-side. The signal that will be recorded on the left channel will include a full audio level for the subjects furthest to the left, with a general decline in audio level moving towards center, and with a significant suppression of the audio at the center of the right side of the stage where the shaded rectangle is shown.
The right beamformed audio signal 652 and the left beamformed audio signal 654 can ultimately be combined to produce a stereo signal with appropriate imaging contributions from the desired left audio channel 625 and the desired right audio channel 645 of the subject(s) being acquired.
As described above, the first angular location (α) of the right channel null region 635 and the second angular location (β) of the left channel null region 655 can be steered based on the null control signal 565 during beamform processing. In other words, the null control signal 565 can be used to control or "steer" the first angular location (α) of the right channel null region 635 of the right-side-oriented beamformed audio signal 652 and the second angular location (β) of the left channel null region 655 of the left-side-oriented beamformed audio signal 654.
This allows the angular locations (α, β) of the right channel null region 635 and the left channel null region 655 to be steered based on an angular field of view, a focal distance, or a zoom control signal, for example, to vary the stereo imaging and make the stereo signal coincide with the video frame that is being acquired/captured by the operator. The angles or angular locations (α, β) of the right channel null region 635 and the left channel null region 655 can be steered to deemphasize sound waves that originate from directions corresponding to different null regions with respect to the field of view 650 being acquired by the electronic apparatus 600. Thus, although the right channel null region 635 and the left channel null region 655 are aligned with the center of the opposite side of field of view 650 being acquired, the positions of the right channel null region 635 and the left channel null region 655 can be changed or controlled via the null control signal. For example, as the first angular location (α) of the right channel null region 635 decreases (e.g., by decreasing a zoom control signal), the right channel null region 635 will move further away from the center line 651 and the audio field of view will widen.
FIGS. 8A
8B
Other characteristics of the left beamformed audio signal 654 and the right beamformed audio signal 652 will be described below with reference to and , respectively.
FIG. 7
is a diagram that illustrates an exemplary polar graph of a right beamformed audio signal 752 and an exemplary polar graph of a left beamformed audio signal 754 that are generated by an electronic apparatus 700 in accordance with another implementation of some of the disclosed embodiments.
FIG. 6
This view differs from that in in that it shows the angular locations (-α, -β) of the right channel null region 735 and the left channel null region 755 with respect to an operator 740 of the electronic apparatus 700, where the angular locations (-α, -β) of the right channel null region 735 and the left channel null region 755 of virtual microphones have been steered for cancellation of sound waves that originate from the rear-side of the electronic apparatus 700 (e.g., from the operator 740).
As described above, the nulls of the beamformed audio signals 752, 754 may include more than one null region. For instance, in one implementation, the right beamformed audio signal 752 can include a first null point (corresponding to line 737) oriented towards the front-side 704 and a second null point (corresponding to line 741) oriented toward the rear-side 702, and the left beamformed audio signal 754 can include a third null point (corresponding to line 757) oriented towards the front-side 704 and a fourth null point (corresponding to line 760) oriented toward the rear-side 702, respectively.
For example, in one implementation, a rear-side proximity sensor, coupled to the automated null controller, generates a rear-side proximity sensor signal that corresponds to a predetermined distance between a camera operator and the apparatus. The imaging signal is also based on the rear-side proximity sensor signal. For example, the nulls on the operator side of the apparatus 700 can be computed such that a ratio of A and B (in equation (1)) are selected such that the null from each side is pointed at the operator controlling the apparatus 700. This can be accomplished in a number of different non-limiting ways. For example, in one embodiment, the angle can be computed based on the average position that is it assumed the operator is going to be behind the device based on human factors studies or user testing. In another embodiment, the angle can be computed from half the distance between the microphones and the measured distance to the operator. The angle would be computed using a function such as ARCTAN ( (micspacing/2)/ distance).
In another implementation, a rear-side proximity sensor (not shown) can generate a rear-side proximity sensor signal that corresponds to a distance between a camera operator 740 and the apparatus 700. The automated null controller can use the rear-side proximity sensor signal to generate a null control signal such that the second null point (corresponding to line 741) and the fourth null point (corresponding to line 760) are steered such that they are oriented to cancel sound that originates from the rear-side 702 at the proximity-sensed distance of the operator thus reducing or canceling sound that originates from the camera operator 740 or other proximity-sensed rear-side sound source.
This also allows for the cancellation of sound arising from directly behind the recording device, such as sounds made by the operator. Rear-side cancellation is a separate mode and is not based on the optical frame being acquired.
FIGS. 8A-9C
FIGS. 8A-9C
FIGS. 1A
1B
FIG. 3
FIG. 3
FIGS. 8A-9C
Examples of beamformed signals generated by the processor 550 and null steering of those signals will be described below with reference to polar graphs illustrated in . Preliminarily, it is noted that in any of the polar graphs described below, signal magnitudes are plotted linearly to show the directional or angular response of a particular signal. Further, in the examples that follow, for purposes of illustration of one example, it can be assumed that the subject is generally centered at approximately 90° while the operator is located at approximately 270°. The directional patterns shown in are slices through the directional response forming a plane as would be observed by a viewer who, located above the electronic apparatus 100 of and , is looking downward, where the z-axis in corresponds to the 90°- 270° line, and the y-axis in corresponds to the 0°-180° line through the microphone port openings. As a person of ordinary skill is aware, the complete directional patterns are three-dimensional and planar slices are provided here for the sake of simplicity. Moreover, for sake of clarity in the polar graphs that are illustrated in , a particular null region is represented here only by its corresponding null center line.
FIG. 8A
FIG. 8A
FIGS. 6
7
is an exemplary polar graph of a left-side-oriented beamformed signal 854 generated by the audio processing system 500 in accordance with one implementation of some of the disclosed embodiments. The left-side-oriented beamformed signal 854 of is representative of the left-side-oriented beamformed signals 654, 754 shown in and .
FIG. 8A
As illustrated in , the left-side-oriented beamformed signal 854 has a first-order directional pattern that points or is oriented towards the +y-direction, and has a main lobe 854-A having a maximum at 180 degrees and a minor lobe 854-B that is oriented in the -y-direction. This directional pattern indicates that there is a stronger directional sensitivity to sound waves traveling towards the left-side of the apparatus 100. The left-side-oriented beamformed signal 854 also has a pair of nulls that are centered at null center lines 857-A, 857-B.
FIG. 6
FIG. 7
The null center line 857-A of one null points at an angular location (β) towards the front right-side of the apparatus 100 and corresponds to a front-left channel null region (see ). The other null center line 857-B of the other null points at an angle or angular location (-β) towards the rear right-side of the apparatus 100 and corresponds to a rear-left channel null region (see ). In this particular example, the angular location (β) of the null center line 857-A is at approximately 75 degrees with respect to the -y-axis, and the angular location (-β) of the null center line 857-B is at approximately -75 degrees with respect to the -y-axis.
FIG. 8B
FIG. 8B
FIGS. 6
7
is an exemplary polar graph of a right-side-oriented beamformed signal 852 generated by the audio processing system 500 in accordance with one implementation of some of the disclosed embodiments. The right-side-oriented beamformed signal 852 of is representative of the right-side-oriented beamformed signals 652, 752 shown in and .
FIG. 8B
As illustrated in , the right-side-oriented beamformed signal 852 has a first-order directional pattern that points or is oriented towards the right in the-y-direction, and has a main lobe 852-A having a maximum at zero degrees and a minor lobe 852-B that is oriented in the +y-direction. This directional pattern indicates that there is a stronger directional sensitivity to sound waves traveling towards the right-side of the apparatus 100. The right-side-oriented beamformed signal 852 also has a pair of nulls that are centered at null center lines 837-A, 837-B.
FIG. 6
FIG. 7
The null center line 837-A of one null points at an angular location (α) towards the front left-side of the apparatus 100 and corresponds to a front-right channel null region (see ). The other null center line 837-B of the other null points at an angular location (-α) towards the rear left-side of the apparatus 100 and corresponds to a rear-right channel null region (see ). In this particular example, the angular location (α) of the null center line 837-A is at approximately -75 degrees with respect to the +y-axis, and the angular location (-α) of the null center line 837-B is at approximately +75 degrees with respect to the +y-axis.
FIG. 5
As described above with reference to , the automated null controller 560 generates a null control signal 565 that can be used by the processor 550 to control or steer nulls of the right-side-oriented beamformed audio signal 552 and the left-side-oriented beamformed audio signal 554 during beamform processing to change the angular locations of the nulls. For example, when the magnitude of the angular location (α) of the null center line 837-A increases, this has the effect of increasing a ratio of B:A in equation (1) described above, and when the magnitude of the angular location (α) of the null center line 837-A decreases this has the effect of decreasing a ratio of B:A in equation (1) described above.
FIG. 8C
As the recorded field of view goes from a wide (un-zoomed) angular field of view to a narrow (high-zoomed) angular field of view, the ratio of B/A in equation (1) that describes the first order beamform and the angular location α would increase. As the zoom value goes from a narrow (high-zoomed) angular field of view to a wide (un-zoomed) angular field of view, the ratio of B/A in equation (1) and angular location α would become smaller. One example will now be illustrated with reference to .
FIG. 8C
FIG. 8C
FIG. 8B
FIG. 8B
FIG. 8C
is an exemplary polar graph of a right-side-oriented beamformed signal 852 generated by the audio processing system 500 in accordance with another implementation of some of the disclosed embodiments. As illustrated in , the right-side-oriented beamformed signal 852 has a first-order directional pattern similar to that illustrated in . However, in this implementation, an angular location of the nulls of the right-side-oriented beamformed signal 852 has changed. Specifically, the null center line 837-1A now has an angular location α of approximately -60 degrees with respect to the +y-axis, and the null center line 837-1B now has an angular location -α of approximately +60 degrees) with respect to the +y-axis. Thus, in comparison to , the angular location of the nulls (as represented by their respective null center lines 837-1A, 837-1B) have been steered to point at different angular locations in (even though the null center lines still remain oriented at angles towards the front left-side and the rear left-side of the apparatus 100, respectively, and the main lobe still has its maximum located at 0 degrees). As such, the relative locations of the front-right channel null region (not illustrated) and the rear-right channel null region (not illustrated) will also change the location of the right audio image further to the right. In addition, it is also noted that the magnitude of the main lobe 852-1A has increased relative to the magnitude of the minor lobe 852-1B resulting in the audio image shifting further to the right. As mentioned previously, the angular location of the main lobe 852-1A remains fixed at zero degrees.
FIGS. 9A-9C
Further details regarding the effects that can be achieved by implementing such null steering techniques will now be described below with reference to .
FIGS. 8A-8C
FIGS. 9A-9C
FIGS. 9A-9C
Preliminarily, it is noted that although not illustrated in , in some embodiments, the beamformed audio signals 852, 854 can be combined into a single audio output data stream that can be transmitted and/or recorded as a file containing separate stereo coded signals. will illustrate some examples of such a combination by describing different examples of beamformed signals 552, 554 that can be generated by the processor 550 in different scenarios. In , both the responses of a right-side-oriented beamformed audio signal 952 and a left-side-oriented beamformed audio signal 954 will be shown together to illustrate that the signals may be combined in some implementations to achieve stereo effect.
FIG. 9A
is an exemplary polar graph of a right-side-oriented beamformed audio signal 952 and a left-side-oriented beamformed audio signal 954 generated by the audio processing system 500 in accordance with one implementation of some of the disclosed embodiments.
FIG. 9A
As illustrated in , the right-side-oriented beamformed audio signal 952 has a first-order directional pattern with a major lobe 952-A that is oriented towards or points in the -y-direction. This first-order directional pattern has a maximum at 0 degrees and has a relatively strong directional sensitivity to sound waves traveling towards the right-side of the apparatus 100. The right-side-oriented beamformed audio signal 952 also has a first null with a null center line 937 at approximately 150 degrees, or at an angle of approximately 30 degrees with respect to the +y-axis. The first null points towards the left-front-side of the apparatus 100, which indicates that there is little or no directional sensitivity to sound waves traveling towards the apparatus 100 that originate from the front-left of the apparatus 100. The first angular location (α) of the first null corresponds to the first null center line 937 that corresponds to a right channel null region.
The left-side-oriented beamformed audio signal 954 also has a first-order directional pattern with a major lobe 954-A that is oriented in the +y-axis, and has a maximum at 180 degrees. This indicates that there is strong directional sensitivity to sound waves traveling towards the left-side of the apparatus 100. The left-side-oriented beamformed audio signal 954 also has a second null with a null center line at approximately 30 degrees. The second null center line 957 is at an angle of approximately 30 degrees with respect to the -y-axis. The second null points towards the front-right-side of the apparatus 100, which indicates that there is little or no directional sensitivity to sound waves traveling towards the apparatus 100 that originate from the front-right of the apparatus 100. The second angular location (β) of the second null corresponds to the second null center line 957 that corresponds to a left channel null region. The sum of the first angular location (α) and the second angular location (β) will be equal to the difference between 180 degrees and a spacing or separation angle (ϕ) that represents the angular spacing between the second null center line 957 and the first null center line 937. The spacing angle (ϕ) can range between 0 and 180 degrees. In some implementations α= β, meaning that both are equal to 90 degrees minus ½ (ϕ).
FIGS. 9B
9C
FIG. 9A
To illustrate examples with reference to and , it can be assumed that the null settings in could be used, for example, when a relatively wide the field of view is desired by decreasing a zoom control signal to steer the nulls to the specified locations.
FIG. 9B
is an exemplary polar graph of a right-side-oriented beamformed audio signal 952-1 and a left-side-oriented beamformed audio signal 954-1 generated by the audio processing system 500 in accordance with another implementation of some of the disclosed embodiments.
FIG. 9B
As illustrated in , the right-side-oriented beamformed audio signal 952-1 has a first-order directional pattern with a major lobe 952-1A that is oriented towards or points in the -y-direction. This first-order directional pattern has a maximum at 0 degrees and has a relatively strong directional sensitivity to sound waves traveling towards the right-side of the apparatus 100. The right-side-oriented beamformed audio signal 952-1 also has a first null with a null center line 937-1 at approximately 120 degrees. The first null center line 937-1 is thus at an angle of approximately 60 degrees with respect to the +y-axis. The first null points towards the left-front-side of the apparatus 100, which indicates that there is little or no directional sensitivity to sound waves traveling towards the apparatus 100 that originate from the front-left of the apparatus 100. The first angular location (α) of the first null corresponds to the first null center line 937-1 that corresponds to a right channel null region.
The left-side-oriented beamformed audio signal 954-1 also has a first-order directional pattern with a major lobe 954-1A that is oriented in the +y-axis, and has a maximum at 180 degrees. This indicates that there is strong directional sensitivity to sound waves traveling towards the left-side of the apparatus 100. The left-side-oriented beamformed audio signal 954-1 also has a second null with a null center line 957-1 at approximately 60 degrees. Thus, the second null center line 957-1 is at an angle of approximately 60 degrees with respect to the -y-axis. The second null points towards the front-right-side of the apparatus 100, which indicates that there is little or no directional sensitivity to sound waves traveling towards the apparatus 100 that originate from the front-right of the apparatus 100. The second angular location (β) of the second null corresponds to the second null center line 957-1 that corresponds to a left channel null region.
FIG. 9A
FIG. 9B
FIG. 9B
In comparison to , the α and β values are increased in . This could be accomplished, for example, by increasing the zoom control signal to narrow the angular field of view. The zoom control signal or the angular field of view could then be used as the imaging signal at the automated null controller to generate a null control signal that would set the α and β values that are shown in .
FIG. 9C
is an exemplary polar graph of a right-side-oriented beamformed audio signal 952-2 and a left-side-oriented beamformed audio signal 954-2 generated by the audio processing system 500 in accordance with one implementation of some of the disclosed embodiments.
FIG. 9C
As illustrated in , the right-side-oriented beamformed audio signal 952-2 has a first-order directional pattern with a major lobe 952-2A that is oriented towards or points in the -y-direction. This first-order directional pattern has a maximum at 0 degrees and has a relatively strong directional sensitivity to sound waves traveling towards the right-side of the apparatus 100. The right-side-oriented beamformed audio signal 952-2 also has a first null with a null center line 937-2 at approximately 105 degrees. The first null center line 937-2 is thus at an angle of approximately 75 degrees with respect to the +y-axis. The first null points towards the left-front-side of the apparatus 100, which indicates that there is little or no directional sensitivity to sound waves traveling towards the apparatus 100 that originate from the front-left of the apparatus 100. The first angular location (α) of the first null corresponds to the first null center line 937-2 that corresponds to a right channel null region.
The left-side-oriented beamformed audio signal 954-2 also has a first-order directional pattern with a major lobe 954-2A that is oriented in the +y-axis, and has a maximum at 180 degrees. This indicates that there is strong directional sensitivity to sound waves traveling towards the left-side of the apparatus 100. The left-side-oriented beamformed audio signal 954-2 also has a second null with a null center line 957-2 at approximately 75 degrees. Thus, the second null center line 957-2 is at an angle of approximately 75 degrees with respect to the -y-axis. The second null points towards the front-right-side of the apparatus 100, which indicates that there is little or no directional sensitivity to sound waves traveling towards the apparatus 100 that originate from the front-right of the apparatus 100. The second angular location (β) of the second null corresponds to the second null center line 957-2 that corresponds to a left channel null region.
FIG. 9B
FIG. 9C
FIG. 9B
In comparison to , the α and β values have been increased further in . This could be accomplished, for example, by increasing the zoom control signal to further narrow the angular field of view even more than in .
FIGS. 9A-9C
Thus, generally illustrate that angular locations of the nulls can be steered (i.e., controlled or adjusted) during beamform processing based on the null control signal 965. This way the angular locations of the nulls of the beamformed audio signals 952, 954 can be controlled to enable a concert mode stereo recording to be acquired that corresponds to the video frame being viewed by the camera operator.
FIG. 9A-9C
Although the beamformed audio signals 952, 954 shown in are both beamformed first order supercardioid directional beamform patterns that are either right-side-oriented or left-side-oriented, those skilled in the art will appreciate that the beamformed audio signals 952, 954 are not necessarily limited to having these particular types of first order directional patterns and that they are shown to illustrate one exemplary implementation. In other words, although the directional patterns are supercardioid-shaped (i.e., have a directivity index between that of a bidirectional pattern and a cardioid), this does not necessarily imply the beamformed audio signals are limited to having that shape, and may have any other shape that is associated with first order directional beamform patterns such as a supercardioid, dipole, hypercardioid, etc. Depending on the null control signal 565, the directional patterns can range from a nearly cardioid beamform to a nearly bidirectional beamform, or from a nearly cardioid beamform to a nearly omnidirectional beamform. Alternatively a higher order directional beamform could be used in place of the first order directional beamform.
Moreover, although the beamformed audio signals 952, 954 are illustrated as having ideal directional patterns, it will be appreciated by those skilled in the art, that these are mathematically ideal examples only and that, in some practical implementations, these idealized beamform patterns will not necessarily be achieved.
In addition, the angular locations of the null center lines are exemplary only and can generally be steered to any angular locations in the yz-plane to allow for stereo recordings to be recorded or to allow for rear-side sound sources (e.g., operator narration) to be cancelled when desired. In other implementations in which nulls are not steered to cancel rear-side sound sources, the rear-side oriented portions of the beamformed audio signals 952, 954 can be used to acquire rear-side stereo sound sources.
FIG. 5
Although not explicitly described above, any of the embodiments or implementations of the null control signals that were described above with reference to can be applied equally in all of the embodiments illustrated and described herein.
FIG. 10
FIG. 10
is a block diagram of an electronic apparatus 1000 that can be used in one implementation of the disclosed embodiments. In the particular example illustrated in , the electronic apparatus is implemented as a wireless computing device, such as a mobile telephone, that is capable of communicating over the air via a radio frequency (RF) channel.
FIG. 10
FIG. 10
The wireless computing device 1000 comprises a processor 1001, a memory 1003 (including program memory for storing operating instructions that are executed by the processor 1001, a buffer memory, and/or a removable storage unit), a baseband processor (BBP) 1005, an RF front end module 1007, an antenna 1008, a video camera 1010, a video controller 1012, an audio processor 1014, front and/or rear proximity sensors 1015, audio coders/decoders (CODECs) 1016, a display 1017, a user interface 1018 that includes input devices (keyboards, touch screens, etc.), a speaker 1019 (i.e., a speaker used for listening by a user of the device 1000) and two or more microphones 1020, 1030. The various blocks can couple to one another as illustrated in via a bus or other connection. The wireless computing device 1000 can also contain a power source such as a battery (not shown) or wired transformer. The wireless computing device 1000 can be an integrated unit containing at least all the elements depicted in , as well as any other elements necessary for the wireless computing device 1000 to perform its particular functions.
As described above, the microphones 1020, 1030 can operate in conjunction with the audio processor 1014 to enable acquisition of audio information that originates on the front-side of the wireless computing device 1000, and/or to cancel audio information that originates on the rear-side of the wireless computing device 1000. The automated null controller 1060 that is described above can be implemented at the audio processor 1014 or external to the audio processor 1014. The automated null controller 1060 can use an imaging signal provided from one or more of the processor 1001, the camera 1010, the video controller 1012, the proximity sensors 1015, and the user interface 1018 to generate a null control signal that is provided to the beamformer 1050. The beamformer 1050 processes the output signals from the microphones 1020, 1030 to generate one or more beamformed audio signals, and controls or "steers" the angular locations of one or more nulls of each of beamformed audio signals during processing based on the null control signal.
FIG. 10
The other blocks in are conventional features in this one exemplary operating environment, and therefore for sake of brevity will not be described in detail herein.
As such, a directional stereo acquisition and recording system can be implemented. One of the benefits of this system are improved stereo separation effect by constructing directional microphone patterns and the ability to null out noise and sound from unwanted directions while using only two microphones. In addition, the variable pattern forming aspects of the invention can be coupled to a variable zoom video camera to make the sound pickup field proportionate to the video angle of view by manipulation of the microphone pattern null points. In some embodiments, operator cancellation inherently results in a specific subject-side null configuration.
FIG. 1-10
FIGS. 1-10
It should be appreciated that the exemplary embodiments described with reference to are not limiting and that other variations exist. It should also be understood that various changes can be made without departing from the scope of the invention as set forth in the appended claims and the legal equivalents thereof. The embodiments described with reference to can be implemented a wide variety of different implementations and different types of portable electronic devices.
The methods shown here use omnidirectional pressure microphones, but those skilled in the art would appreciate the same results could be obtained with opposing unidirectional microphones oriented along the y-axis, or with a single omnidirectional microphone and a single gradient microphone oriented along the y-axis. A unidirectional microphone here is any pressure gradient microphones, not including bidirectional, such as a cardioid, supercardioid, hypercardioid, etc. The use of these other microphone capsules would only require the use of a different beamforming algorithm in the processing module 450, 550, 1014.
Those of skill will appreciate that the various illustrative logical blocks, modules, circuits, and steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. Some of the embodiments and implementations are described above in terms of functional and/or logical block components (or modules) and various processing steps. However, it should be appreciated that such block components (or modules) may be realized by any number of hardware, software, and/or firmware components configured to perform the specified functions. As used herein the term "module" refers to a device, a circuit, an electrical component, and/or a software based component for performing a task. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention. For example, an embodiment of a system or a component may employ various integrated circuit components, e.g., memory elements, digital signal processing elements, logic elements, look-up tables, or the like, which may carry out a variety of functions under the control of one or more microprocessors or other control devices. In addition, those skilled in the art will appreciate that embodiments described herein are merely exemplary implementations
The various illustrative logical blocks, modules, and circuits described in connection with the embodiments disclosed herein may be implemented or performed with a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In the alternative, the processor and the storage medium may reside as discrete components in a user terminal.
Furthermore, the connecting lines or arrows shown in the various figures contained herein are intended to represent example functional relationships and/or couplings between the various elements. Many alternative or additional functional relationships or couplings may be present in a practical embodiment.
In this document, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Numerical ordinals such as "first," "second," "third," etc. simply denote different singles of a plurality and do not imply any order or sequence unless specifically defined by the claim language. The sequence of the text in any of the claims does not imply that process steps must be performed in a temporal or logical order according to such sequence unless it is specifically defined by the language of the claim. The process steps may be interchanged in any order without departing from the scope of the invention as long as such an interchange does not contradict the claim language and is not logically nonsensical.
Furthermore, depending on the context, words such as "connect" or "coupled to" used in describing a relationship between different elements do not imply that a direct physical connection must be made between these elements. For example, two elements may be connected to each other physically, electronically, logically, or in any other manner, through one or more additional elements.
While at least one exemplary embodiment has been presented in the foregoing detailed description, it should be appreciated that a vast number of variations exist. It should also be appreciated that the exemplary embodiment or exemplary embodiments are only examples, and are not intended to limit the scope, applicability, or configuration of the invention in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient road map for implementing the exemplary embodiment or exemplary embodiments. It should be understood that various changes can be made in the function and arrangement of elements without departing from the scope of the invention as set forth in the appended claims thereof. | |
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Learn to Cook South Indian Cuisine
With so few Indian restaurants in town, it's worth it to learn to cook your own. Balarama Chandra and Emma Kate Veader from Bend Ayurveda are offering a plant-based South Indian cooking class that, they say, "will awaken your inner chef and leave your senses wanting more." A few things you will learn to make: idli, steamed savory cakes similar to dumplings; masala dosa, a fermented crepe filled with curried potato; uttapam, a thick savory pancake with toppings cooked into the batter; and a sweet variation of dosa with homemade chocolate hazelnut spread. Pre-registration is required. | |
The qualitative characteristics of the immune responses are regulated by T cell subsets through their production of distinctive cytokines. Well-characterised T cell subsets are T helper (Th) cells, of which two different subsets are recognised. Th1 cells, which through the production of IFN-γ, promote cell-mediated responses, and Th2 cells which, by producing IL-4, IL-5, IL-13, induce antibody synthesis, as well as mast cell and eosinephil responses. Both subsets originate from a naive T cell precursor, whose differentiation is influenced by both the modes of activation and the environment. A number of variables known to influence the development of T cell subsets includes the interaction of the T cell receptor (TCR) with antigen, the presence of antigen presenting cells (APC) and the presence of certain cytokines during activation of the T cells.
A third subset of T cells, so-called regulatory CD4+ cells or regulatory T cells, is described that predominantly produces interleukin-10 (IL-10)1. IL-10 inhibits a broad array of immune parameters, including activation and effector function of T cells, monocytes and dendritic cells (DCs), limiting and ultimately terminating inflammatory responses2, 3. These IL-10 producing T cells are named regulatory T cells type 1 (Tr1), because of their immunosuppressive effects both in vitro4 and in experimental colitis1. Tr1 cells produce little IL-2, no IL-4 and the production rate of IL-5, IFN-γ and transforming growth factor beta (TGF-β) is similar to those of naïve T cell clones. The mechanisms by which regulatory T cells mediate immunosuppressive activities in vivo are still unknown, but some regulatory T cell populations are known to be dependent on IL-10 for their function5, 6.
Studies of IL-10 deficient (IL-10−/−) and IL-10 receptor-2 deficient mice7, 8, which show that these mice develop a T helper (Th)-1 mediated intestinal inflammation in the absence of IL-10 or IL-10 mediated signalling indicate that IL-10 is an important regulatory cytokine within the mucosal immune system. The activity of IL-10 in counter regulating mucosal inflammation is likely to be multifactorial. IL-10 is a potent down regulator of IL-12 production and thus acts at the level of Th1 cell induction.9 In addition, IL-10 suppresses production of other proinflammatory cytokines and chemokines including TNF-α, IL-1, IL-6 and IL-8.3 Finally, there is substantial evidence that IL-10 acts both to promote the differentiation and augment the activity of regulatory T cells.1, 6, 10, 11
The observations in IL-10−/− mice have laid the foundation for therapeutic trials of IL-10 in several other models of colitis. These studies have shown that systemic IL-10 administration is able to prevent intestinal inflammation by down-regulating the intestinal proinflammatory Th1 response.7, 12, 13 Based on these successful experimental findings, recombinant (r)IL-10 was administered by subcutaneous injection to patients with either mild/moderate or steroid refractory Crohn's disease, as well as in patients undergoing ileal resection to prevent postoperative recurrence.14-16 Although the data indicated that systemic rIL-10 therapy is safe and well tolerated, this therapy did not result in significantly higher remission rates or clinical improvement compared to placebo. Explanations for this lack of efficacy include the short half-life of rIL-10,17 local delivery of insufficient amounts of rIL-10 to inhibit mucosal Th1 responses and the side effects associated with high dose rIL-10.18
Sustained IL-10 delivery may prove more effective than daily systemic injections.
These limitations of systemic rIL-10 therapy might be overcome by the infusion of in vitro generated regulatory T cells to patients with T cell-mediated inflammatory diseases. However, the low proliferation rate of regulatory T cells and the high cost of rIL-10, required for their generation in vitro, seriously hamper the production in vitro of therapeutically effective quantities of regulatory T cells.
In an experiment to overcome the anti-proliferative properties of IL-10, antigen-specific murine T cells transduced with IL-10 have been employed (Setoguchi et al., 2000, J. Immunol. 165: 5980-5986). Splenic T cells from mice transgenic for an ovalbumin-specific TCR were transduced with a retroviral plasmid containing the murine IL-10 gene. The IL-10-transduced ovalbumin-specific T cells were subsequently infused into mice with antigen (ovalbumin) induced arthritis. The transduced T cells migrated to the inflamed joint and ameliorated the arthritis symptoms of the joint. However, this use of IL-10 transduced T cells is strictly limited to T cells that are specific for a predetermined antigen. As for most (if not all) inflammatory diseases the relevant antigens are not known, this antigen-specific application of IL-10-expressing T cells currently has no practical therapeutic value.
In experimental autoimmune encephalomyelitis (EAE), a Th1 mediated disease, efficient delivery to the site of inflammation of either therapeutic19 or exacerbating factors20 by genetically modified T cells has been reported. Encouraging results were obtained from a study showing that antigen specific T-cell clones transfected with IL-10 cDNA were able to inhibit EAE19 However, because of the antigen specificity of the transfected T cell clones these results again have no practical therapeutic value.
Thus, it is an object of the invention to provide for IL-10 producing regulatory T cells for use in the therapy of inflammatory diseases in an antigen-independent manner, as well as to provide for methods of obtaining such regulatory T cells. In general, it is an object of the invention to provide for mononuclear cell populations that are derived from peripheral blood mononuclear cells (PBMCs) and that are transgenic for IL-10. Such IL-10 transgenic mononuclear cell populations or specific subfractions thereof may be used as therapeutic agents in a variety of inflammatory diseases, in particular in Th1-mediated inflammatory diseases.
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At Smyrna First United Methodist Church, we believe that prayer is a vital part of your relationship with God. When we pray, we are offered the opportunity to be in conversation with Jesus.
There are special times of prayer in every worship service at Smyrna First for prayer requests of our members and guests to be offered up to God. Our vibrant prayer ministry also includes a team dedicated to praying individually over each and every request we receive. It is our privilege to pray for and with you.
LJ
Praying for Gods protection, favor and miracle blessings upon Leland. Praying for a positive breakthrough in his life. Praying he knows he is loved and cared about and will contact and reconnect with his family and friends for support and encouragement. God is Able! | https://smyrnafumc.org/prayer-wall/?enmpe=1&enmpe_i=89 |
The structure and dynamics of intertidal rockpool, or tidepool, fish assemblages were studied along the south coast of New South Wales (NSW), Australia. This work aimed to fulfil a number of objectives that contribute to three key components in fish ecology. These are: 1) the structure and patterns of variation in rockpool fish assemblages, 2) role of fish movements (recruitment, relocation and homing) in influencing fish population dynamics and 3) the role of structural heterogeneity in structuring fish assemblages.
Since sampling rockpool fishes is difficult owing to the variable-sized rockpools, and their small secretive fishes, the effectiveness of three sampling methods was assessed. Emptying water from rockpools with a battery-powered bilge pump proved the best method, which accounted for significantly more species and individuals than a fish anaesthetic (clove oil) and visual census. Despite being more time consuming and cumbersome, bilge-pumping provides access to crevices and under rocks, thus results in a more accurate census than the other methods trialled.
The rockpool fish assemblages of the NSW south coast comprised 50 species, mainly permanent residents endemic to Australian waters. The main families represented were: Blenniidae, Clinidae, Tripterygiidae, Gobiidae and Gobiesocidae. At the level of family, NSW rockpools fish assemblages were different from those in the United States, Spain, France and Portugal, but similar to Chile and New Zealand. They were surprisingly similar to those in South Africa, to the extent of sharing species. At a regional scale, south coast NSW fish assemblages differed from those to the north in having different relative abundance of the species common in each region. Some species of economic and conservation importance were caught, such as Girella elevata and the protected black rockcod, Epinephelus daemelii. Their presence exclusively as juveniles indicates that rockpools may be possible nursery areas for such species that live their adult lives subtidally.
The rockpool fish assemblages were dynamic across various spatial and temporal scales. Horizontal spatial variability across scales of kilometres to hundreds of kilometres may be due to barriers to larval dispersal (e.g. local currents or upwelling events) or barriers to fish migration (e.g. sandy beaches between headlands). Across scales of metres to kilometres, the presence of different microhabitats within and among locations favours species having specific requirements for a particular habitat. In contrast, vertical spatial variability may be controlled by differences in fish physiology, which appears to broadly separate species by their intertidal residential status. Highly adapted resident species generally occupy rockpools of highest elevations where the environment can be harsh and variable, whereas opportunists and transients possessing few or no adaptations for intertidal life occupy lower rockpools where water chemistry is similar to the adjacent ocean.
Temporal variability in rockpool fish assemblages across scales of months to years was due to seasonal recruitment that occurs from summer to autumn (February to April) for most species studied. During recruitment pulses the abundance of each species varies but the relative change is minimal, resulting in highly stable and persistent assemblages. In the short-term (weeks to months), fish assemblages are resilient to perturbations and recolonise rockpools within weeks. This process was primarily due to sub-adult and adult fishes moving in from nearby rockpools, although many fishes displaced up to 20 m have the ability to home. This homing ability m a y be facilitated by identification of specific topographic cues learned by swimming over a limited geographic range at high tide. Juveniles appear only to be a major contributor to the recolonisation process if perturbations coincide with recruitment periods. The high stability of rockpool fish assemblages both in the long and short term may be a result of only fishes with specialised adaptations being able to utilise vacant habitats in the highly variable rockpool environment. Despite occupying a highly variable environment, the high resilience and stability detected indicates that NSW rockpool fish assemblages are probably regulated by deterministic, rather than stochastic, processes. However, a longer study period is needed to determine the effects of natural stochastic elements these fish assemblages.
Manipulation experiments explored the effects of varying structural complexity of two major habitat types (suspended algae and substratum cover) on rockpool fish assemblages. Fish did not discriminate between different habitat types so long as some shelter was available. The amount of substrate rock cover afforded the most attractive shelter to fish, since most rockpool fishes are benthic. However, increased habitat complexity only increased the numbers of species and fish in a rockpool to a threshold where other factors (possibly food) probably become limiting. Alternatively, the lack habitat specificity of fishes indicates fish may only utilise rockpools as temporary refuges before moving throughout the intertidal zone during high tide. Since rockpool fishes may be still vulnerable to predation at low tide (i.e. terrestrial predators), appear to select rockpools with shelter where predators may have difficulty of access.
By undertaking experiments that manipulated both fish assemblages and habitats in rockpools, the dynamics of rockpool fish populations can be better understood. Establishing a link between regulation processes allowed the development of the "Nearest Neighbour Model", which describes the dynamics of rockpool fish assemblages being primarily dependent upon fish populations and habitats in neighbouring rockpools. This model opposes population regulation of reef and estuarine fish assemblages, which are primarily controlled by recruitment processes, and stochastic availability of resources.
The paucity of data on rockpool fishes in Australia and the increasing potential of anthropogenic impacts on coastal ecosystems highlight an urgent need to document, protect and manage its biological integrity. The most appropriate means of managing intertidal fishes may be the use of intertidal protected areas (IPA) where human activity is restricted. The limited movements and larval dispersal of intertidal fishes and the small scale patchiness of assemblage structure indicate that several small reserves be better than a single large reserve. However, there are many socio-economic issues that need to be carefully addressed before implementation of IPAs. | https://ro.uow.edu.au/theses/1381/ |
This invention relates to TV stereo sound and more particularly to apparatus for generating control signals for controlling a spectral expander.
BACKGROUND OF THE INVENTION
On the recommendation of the Broadcast Television Systems Committee (BTSC), the audio signal standard adopted for Multichannel Television Sound incorporates compression/expansion of the stereophonic difference signal and the secondary audio program (SAP) signal. At the transmitter the stereophonic difference signal and the SAP signal are compressed to enhance signal to noise ratio. Receivers adapted to faithfully reproduce these signals include expander circuitry which operate on the stereophonic difference and SAP signals with a transfer function which is the inverse of the compression function. The expander transfer function, T(f,b), according to the BTSC standard is defined by the equation ##EQU1## where j is the conventional imaginary operator, f is the signal frequency and b is the root mean square value of the signal to be expanded.
The transfer function T(f,b) requires a number of division operations which, in general, require relatively complex circuitry to implement. This is particularly so if the audio signal is to be processed in digital format. It has been determined that a digital transfer function H(Z,k) which closely approximates the transfer function T(f,b) is defined by ##EQU2## where Z is the conventional Z transform variable, A is a mapping constant equal to 2&pgr;(20.1 KHz)/26(f.sub.s) and k is related to the root mean square variable "b" by the equation ##EQU3## The factor f.sub.s in the mapping constant A is the sample rate of the digital audio samples.
The transfer function H(Z,k) may be realized without using any variable divider circuits, thus, simplifying the expander circuitry. However, such an expander system requires apparatus to derive the variable, k, from the root mean square value, b, of the signal to be expanded. This invention is directed toward deriving the control variable, k, from the variable b.
From the function defining the variable k it will be seen that a straight forward generation of the variable k from the variable b requires division. Division in real time processing is undesirable because of circuit complexity. It is therefore an object of this invention to derive the variable, k, with a minimum of circuitry hardware.
SUMMARY OF THE INVENTION
The present invention is directed toward circuitry for approximating the function
k=R(b+1)/(b+51)
where R is a constant and b is a variable in the form of a sampled data signal. The sampled data signal b is scaled by a first constant and applied to a combining circuit. Samples corresponding to the square of the sampled data signal b are scaled by a second constant and applied to the combining circuit. The combining circuitry algebraically combines a third constant, the scaled sample corresponding to the square of the sampled data signal, b, and the scaled sampled data signal, b, to produce the variable k(b) approximating R(b+1)/(b+51).
BRIEF DESCRIPTION OF THE DRAWING
FIG. 1 is a block diagram of a signal expander including circuitry exhibiting the transfer function H(Z,k).
FIGS. 2 and 3 are block diagrams of circuitry, embodying the present invention, for generating a variable k(b) which approximates the function R(b+1)/(b+51).
FIGS. 4-6 are block diagrams of alternative serial bit digital circuits, embodying the present invention, for generating the variable k(b) approximating the function R(b+1)/(b+51).
DETAILED DESCRIPTION
FIG. 1 illustrates circuitry which may be utilized in a multichannel TV sound receiver for performing spectral expansion of the audio stereo difference signal (L-R) and wherein the invention may be advantageously implemented. The stereo difference signal (L-R), which may be derived from a synchronous AM demodulator (not shown) and assumed for illustrative purposes to be in digital sampled data format, is applied to input terminal 10. This signal is coupled to a fixed de- emphasis circuit 15 which attenuates higher frequency signal components. The output of the fixed de-emphasis circuit 15 is coupled to the input terminal of the spectral expander 22 which amplifies/attenuates higher frequency signal components as a function of the RMS signal value. In this example, control of the expander is provided by the control signal, k, which is functionally related to the RMS value b of the (L-R) signal according to the equation
k=R(b+1)/(b+51) (4)
Circuit analysis of expander 22 will reveal its transfer function to be ##EQU4##
In expander 22, the control signal, k, and the signal being processed are scaled by the factor 1/m and/or the factor 2.sup.-6. This is done in the illustrated example to maintain the processed signal amplitude within a range of values to prevent overflows. The effect of scaling by 1/m is ultimately counteracted by scaling the processed signal by m (in the scaler designated 2.sup.-5 m). If the scale factor m is made equal to 1/2A, equation (5) reduces to equation (2), with the exception that it is scaled by (1/64) and it is delayed by one sample period.
The expander 22 is comprised of only delay elements designated Z. sup.- 1, adders, subtracters, constant scalers, and one variable multiplier, and, thus, is relatively straight forward to implement. If the circuit elements are provided with sufficient bit capacity that value overflows are not a consideration, then the scaling elements designated 1/m, 2.sup.- 6, and 2.sup.-5 m may be eliminated from the expander.
To generate the control signal, the stereo difference signal at input terminal 10 is coupled to a multiplier 11 wherein the signal is scaled by a constant C0. The factor C0 is user adjustable and provides some user control over the expander by virtue of effecting changes to the control signal k. The output signal from multiplier 11 is coupled to a high-pass filter 12. High-pass filter 12, has a lower 3 dB roll-off point at a frequency of 7 KHz, to limit the energy sensed by the RMS detector to the high frequency energy spectra of most program material. The signal provided by the highpass filter 12 is coupled to the RMS detector 13 including the cascade connection of a squaring circuit, 14, an averaging circuit, 16, and a square root circuit, 18. Squaring circuit 14 may be a multiplier having both its multiplier and multiplicand input terminals coupled to the bandpass filter 12. Averaging circuit 16 is typically realized with a low-pass filter having a weighting interval of 11.4 msec. An example of a square root circuit which may be implemented for element 18 is disclosed in U.S. Pat. No. 4, 757,467, filed May 15, 1986, entitled "Apparatus For Estimating The Square Root Of Digital Samples", assigned to the same assignee as the present invention.
The output of the square root circuit 13 is coupled to the RMS- to- control signal converter 20.
The function k=R(b+1)/(b+51) may be realized without performing variable division by implementation of a series expansion of the function, such as a Taylor series expansion. It has been found, however, that in order to obtain a relatively accurate approximation by the series expansion, that a significant number of the series terms are required resulting in polynomials in "b" to at least the 4th power. Generating high order polynomials in hardware undesirably tends to require relatively complex circuitry. The present inventors found that the function k(b) could be closely approximated by forming a polynomial comprised of the first few terms P.sub.i (x) of Legendre polynomials and fitting coefficients, g.sub.i, to the contributing Legendre polynomials. In particular, the first three polynomials P.sub.0 (x), P.sub.1 (x) and P. sub.2 (x), which are defined as
P.sub.0 (x)=1
P.sub.1 (x)=x
P.sub.2 (x)=(3x.sup.2 -1)/2
are summed in the proportions
Q(x)=g.sub.oi P.sub.0 (x)+g.sub.1 P.sub.1 (x)+g.sub.2 P.sub.2 (x) (7)
Using a least square error approach to the difference k(x)-Q(x) the coefficients g.sub.i are resolved and then the coefficients, Ci, for the powers of the variable x in the expanded polynomial are determined.
Substituting b for x, an expanded polynomial which closely approximates the function k(b) is given by
k(b)=0.509784+0.4961900b-0.0072318b.sup.2. (8)
The coefficients in equation (8) are valid provided the variable b is constrained to the range of.+-.1. If the variable b is expected to exceed this range, the system may be rearranged to process x=b/C4 (C4 being a constant). In this instance, equation (8) takes the form
k(x)=0.509784+0.4961900(C4)x-0.0072318(C4).sup.2 x.sup.2 (9)
FIG. 2 illustrates the control signal converter 20 in general schematic form. In FIG. 2, the RMS value, b, is coupled to a squaring circuit 24 and to a scaling circuit 25. Squaring circuit 24 squares the input values, b, and applies the squared values to a second scaling circuit 26. Scaling circuit 26 scales the squared values by a constant factor C3 and applies the scaled values to one input terminal of adder 27.
Scaling circuit 25 scales the input values, b, by a constant factor C2 and applies the scaled values to one input terminal of a second adder 28. A constant value C1, from terminal 29, is applied to a second input terminal of adder 28, the output of which equals C1+C2b. The output sums from adder 28 are applied to a second input terminal of adder 27, the output of which is the control signal, k, given by
k=C1+C2b+C3b.sup.2. (10)
The scale factors C1, C2 and C3 as exemplified in equation (8) are
C1=0.509784 (11)
C2=0.4961900 (12)
C3=-0.0072318 (13)
or close approximations thereof to facilitate digital processing. As indicated above, if the value of b is expected to exceed.+- .1, it may be necessary to scale the input to the RMS detector, which scaling will scale the RMS value by a like amount. For example, if the input to the RMS detector is scaled by 1/C4, the value b will be scaled by 1/C4. Designating the input to the RMS detector x, the internal values x.sup.- 2 and {square root}x.sup.2 of the RMS detector correspond to (b/C4).sup.2 and b/C4 respectively. The factor C4 may be incorporated in the scale factor C0 applied to multiplier 11. In this instance, the constant scale factors in equation (10) are changed to accommodate the scaling of the input signal. For the input signal x, equation (10) becomes
k'=C1'+xC2'+x.sup.2 C3' (15)
where C2'=C2C4 and C3'=C3C4.sup.2. In the serial bit implementations to be discussed, it has been found to be advantageous to scale the RMS value, b, by the factor 1/32 in which case the scale factors C1', C2' and C3' are
C1'=0.509784 (15)
C2'=15.8780814 (16)
C3'=-7.4053632 (17)
The expander circuit illustrated in FIG. 1 incorporates a scaling circuit for scaling the control signal by the factor 1/m where m was chosen to equal 32.391911. The system of FIG. 1 may be simplified by incorporating this scale factor in the RMS-to-k converter per se. In this case, the output, k", of the RMS-to-k converter is equal to k'/m and
k"=k'/m=C1"+xC"2+x.sup.2 C"3 (18)
wherein the coefficients are equal to
C1"=(C1)/m=0.015738 (19)
C2"=(C2C4)m=0.49018662 (20)
C3"=(C3C4.sub.2)/m=-0.22861634 (21)
To facilitate implementation in digital form, the coefficients will nominally be approximated to be equal to values corresponding to sums of reciprocal powers of two, i.e. &Sgr;.sub.i a.sub.i 2.sup.-i where the coefficients a.sub.i equal 0 or.+-.1. The RMS signal x and the signal x. sup.2 are both available from the RMS circuit 13. This simplifies the construction of the RMS-to-k converter as illustrated in FIG. 3. In this example, the signal x.sup.2 from averaging circuit 16 is coupled to the scaling circuit 26 and the RMS signal x from square root circuit 18 is coupled to scaling circuit 25. Scaled signals C2"x and C3"x.sup.2 are summed in adder 30. The constant C1" is then added to these sums in adder 31. It will be appreciated that the set of coefficients C1, C2 and C3 may be chosen to equal any of the aforedescribed sets of coefficients C1, C2, C3; C1', C2', C3' or C1", C2", C3".
In a given sample period the signal x and the signal x.sup.2 may not correspond to the same sample since the square root circuit 18 may have a processing delay of several sample periods. This, however, is of no consequence for several reasons. First, the signal may be oversampled to the extent that there is very little value change over several samples. Second, the averaging circuit 16 tends to remove sample to sample changes, and third, a compensating delay may be interposed between the averaging circuit 16 and the scaling circuit 26.
Because audio signals have a relatively low bandwidth, they lend themselves to bit-serial digital processing which tends to be significantly more parts efficient than parallel bit processing. Thus, several bit-serial RMS-to-k converter circuits will be described. The converter will be assumed to be in a gated-clock bit-serial system wherein (a) the samples are in two's complement format; (b) the samples occur bit seriatim with the least significant bit occurring first and sign bit last; (c) the samples are properly justified at the beginning of each sample period; and (d) the samples are n bits long, but the sample period exceeds n bit periods.
Relative to a given datum, a bit-serial sample may be multiplied or divided by integer powers of two, by delaying or advancing (shifting) the sample by the number of bit periods equal to such power of two. For example, a sample delayed by one bit period relative to the nondelayed sample assumes a value of twice the nondelayed sample and a sample advanced in time by one bit period assumes a value of one-half the nonadvanced sample.
Adding and/or subtracting delayed and/or advanced versions of a sample produces a scaled version of the sample. For example, adding a sample to a one-bit delayed (times 2) version of the sample and subtracting the sample advanced by two-bit periods (divided by 4) produces the sample scaled by 23/4. This principal is used to perform scaling of the signals x and x.sup.2 by fixed constants.
FIG. 4 illustrates a first bit-serial implementation which incorporates parallel delay circuits to perform bit shifting to implement sample scaling. In FIG. 4, the RMS samples x are applied to delay circuits D1-D4 which delay the sample x by 13, 7, 6 and 2 sample bit periods respectively. The sample x is relatively multiplied by the factors 2.sup.13, 2.sup.7, 2.sup.6 and 2.sup.2 by the delay circuits D1- D4.
The output samples from delay circuits D1-D4 are coupled to input terminals of subtracter circuits A1-A3. The subtracter circuits (and subsequent adder circuits) are each presumed to have a one bit- period inherent processing delay which effects a multiplication by two, of the difference or sum produced. Subtracter A1, coupled to delay circuits D1 and D2 produces the difference 2(2.sup.13 -2.sup.7)x. This value and the output of delay circuit D3 are applied to subtracter A2 which produces the difference 2(2(2.sup.13 -2.sup.7)x-2.sup.6 x). The output of subtracter A2 and the output of delay circuit D4 are applied as inputs to subtracter A3 which produces the differences 2(2(2(2.sup.13 -2. sup. 7)x-2. sup.6 x)-2.sup.2 x). This output reduces to (2.sup.16 -2. sup. 10 -2. sup. 8 -2.sup.3)x which is coupled to adder A4 wherein it is summed with the coefficient C10/4. The output of adder A4 is 2(2.sup.16 - 2.sup.10 -2. sup.8 -2.sup.3)x+2(C10)/4 and is applied to adder A11 wherein it is summed with the x.sup.2 terms 2.sup.18 (C3x.sup.2) to produce the sums A11S given by
A11S=4(2.sup.16 -2.sup.10 -2.sup.8 -2.sup.3)x+4(C10)/4+2(2.sup. 18 (C3x.sup.2). (22) (C3x.sup. 2). (22)
The output signal A11S is loaded bit seriatim into the N-bit serial shift register, SXSR, by a clock having (n+19) pulses per sample period. The extra 19 clock pulses effectively advances the bit positions of the signal A11S relative to the system datum, thereby dividing the signal samples A11S by 2.sup.19. The first term on the right hand side of equation (22), as resident in register SXSR, is ##EQU5## The numerical coefficient of x in equation 23 approximates the coefficient C2" within 0. 003%.
The value (C10)/4 stored in register 40 and applied to adder A4 is equal to 2.sup.19 times the coefficient C1 divided by four or 2.sup. 17 times the coefficient C1 if the system is arranged to begin clocking the coefficient out of register 40 in consonance with the clocking in of the samples x and x.sup.2. Alternatively, the value (C10)/4 may equal the coefficient (C1)/4 if the clocking of register 40 is not started until the 20th bit of the sample.
The scaling of the samples x.sup.2 is accomplished in a similar manner, by delay circuits D5-D9 adders/subtracters A5-A11 and the clocking of register SXSR. The value corresponding to the last term on the right hand side of equation (22) when resident in register SXSR can be shown to be
2(2.sup.18 C3"x.sup.2)2.sup.-19 =-0.228614807x.sup.2.
The coefficient of x.sup.2 developed by the FIG. 4 circuit is within 0. 0007 percent of the desired value C3".
FIG. 5 is a more parts efficient embodiment of the control signal converter in that it requires fewer delay stages. In FIG. 5, the scaler for signal x consists of the cascade connection of delay circuits D10- D13 with interposed adder/subtracters A20-A24. As in FIG. 4, the adder/subtracters are assumed to have a one bit-period internal processing delay.
The input signal x is applied directly to one input of subtracter A20 and delayed by six-bit periods by delay circuit D10 (multiplied by 2. sup. 6) and applied to the second input of subtracter A20. The difference provided by subtracter A20 is equal to 2(2.sup.6 x- x) or 2.sup.7 x-2x. This difference is delayed one bit period by delay circuit D11 (multiplied by 2) and applied to one input of subtracter A21. The signal x is coupled directly to a second input of subtracter A21 which develops the difference 2(2(2.sup.7 x-2x)-x) or (2.sup.9 -2.sup.3 - 2)x. The output of subtracter A21 is delayed four bit periods in delay circuit D12 (multiplied by 2.sup.4) and coupled to subtracter A22. The signal x is couple directly to a second input of subtracter A22 which develops the difference 2(2.sup.4 (2.sup.9 -2.sup.3 -2)x-x) or (2.sup.14 - 2.sup.8 -2. sup.6 -2x. This value is coupled to the register SXSR through the two- bit-period delay circuit D13, adder A23 and subtracter A24. The added delays of elements D13, A23 and A24 multiplies the output of subtracter A22 by 2.sup.4 resulting in sample values applied to register SXSR equal to (2.sup.18 -2.sup.12 -2.sup.10 -2.sup.5)x. This value is clocked into register SXSR with a clock having n+19 pulses so that the value in the register is equal to the output of subtracter A24 divided by 2.sup.19 or x(2.sup.-1 -2.sup.-7 -2.sup.-9 -2.sup.-14)=0. 490173340x. The scaling coefficient for the signal x is the same as the scaling coefficient developed in the FIG. 4 circuitry. A similar analysis of the circuit elements disposed in the signal path of the signal x.sup.2 will show that the signal x.sup.2 is scaled by the coefficient-0.228614807. The constant component of the control signal k is provided from register and combined with the x and x.sup.2 via adder A23.
A still more parts efficient scaling circuit may be realized by the apparatus illustrated in FIG. 6 which comprises a bit-serial merged- multiplier. From either the FIG. 4 or FIG. 5 circuitry, it may be seen that the coefficient of x is developed by summing and/or differencing the signal x multiplied by powers of two (specifically (2.sup.18 -2.sup. 12 - 2.sup.10 -2.sup.5)x) and dividing the result by 2.sup.19. Similarly, the coefficient of x.sup.2 is developed by summing and/or differencing the signal x.sup.2 multiplied by powers of two (specifically (-2.sup.17 + 2. sup.13 +2.sup.11 +2.sup.10 -2.sup.6 +2.sup.3 +2.sup.2)x.sup.2) and dividing the result by 2.sup.19. The sums of products &Sgr;A.sub.i x2. sup.i and &Sgr;.sub.j A.sub.j x.sup.2 2.sup.j are internally added (in adder A11 in FIG. 4) before division in the register SXSR. Ignoring the constant C1, the expanded sum, ES, that is input to the register SXSR is thus
ES=2.sup.18 x-2.sup.17 x.sup.2 +2.sup.13 x.sup.2 -2.sup.12 x+2. sup.11 x.sup.2 -2.sup.10 (x-x.sup.2)-2.sup.6 x.sup.2 -2.sup.5 x+2.sup.3 x. sup.2 + 2.sup.2 x.sup.2. (24)
Only the terms -2.sup.10 x and 2.sup.10 x.sup.2 share the same 2. sup. 10 scaler, therefore, all of the other terms may be combined in a single cascade connection of adder/subtracter circuits and delay circuits. The x and x.sup.2 signals may be differenced external to the cascade connected circuit and then added into the cascade circuitry with appropriate delay and sign. This arrangement tends to eliminate a number of delay circuits relative to the FIG. 5 embodiment, and is illustrated in FIG. 6.
In FIG. 6, the adder/subtracter circuits A30-A39 have a processing delay of one bit-period. The subtracter A40 for illustrative purposes is presumed not to have a processing delay, however, in practice A40 would nominally have delay. This delay would be compensated by splitting the delay element D32 into two delay circuits having delays of one and two bit-periods and moving subtracter A34 rightward between the split delay circuit. The input connections to the adder/subtracter circuits have designations e(i) where the index (i) indicates the number of delays incurred by the applied signals x and x.sup.2 between their respective input terminals and the output of adder A39. With the methodology used in analysing the circuitry illustrated in FIG. 6, it can be shown that the output, OA39, of adder A39 is given by
OA39=2C10'+2.sup.18 x-2.sup.17 x.sup.2 +2.sup.13 x.sup.2 -2.sup. 12 x+ 2.sup.11 x.sup.2 -2.sup.10 (x-x.sup.2)-2.sup.6 x.sup.2 -2.sup.5 x+ 2. sup. 3 x.sup.2 +2.sup.2 x.sup.2. (25)
This output is loaded into the register SXSR with a clock of (n+ 19) pulses effectively dividing the output OA39 by 2.sup.19 to produce the desired control signal. The constant term C10' is added to the summed x and x.sup.2 terms at the output end of the cascade connection. The term C10' provided by register 40' is equal to 2.sup.18 C1. It should be appreciated, however, that the constant term, if appropriately scaled, can be added into the cascade connection at any convenient locations. | |
Foes of a controversial copyright measure have gained some high-profile allies: Google, Facebook, Twitter, Zynga, and other Web companies have joined the ranks of the bill's opponents.
They sent a letter (PDF) last night to key members of the U.S. Senate and House of Representatives, saying the Stop Online Piracy Act, or SOPA, "pose[s] a serious risk to our industry's continued track record of innovation and job creation, as well as to our nation's cybersecurity."
U.S. House of Representatives
The protest was designed to raise objections in advance of a hearing before the full House Judiciary committee tomorrow at 10 a.m. ET (7 a.m. PT). The letter, also signed by eBay, Mozilla, Yahoo, AOL, and LinkedIn, asks politicians to "consider more targeted ways to combat foreign 'rogue' Web sites."
SOPA, which was introduced last month in the House to the applause of lobbyists for Hollywood and other large content holders, is designed to make allegedly copyright-infringing Web sites, sometimes called "rogue" Web sites, virtually disappear from the Internet.
An announcement of tomorrow's hearing leaves little doubt about where House Judiciary Chairman Lamar Smith, a Texas Republican, stands. It says SOPA reflects a bipartisan "commitment toward ensuring that law enforcement and job creators have the necessary tools to protect American intellectual property from counterfeiting and piracy."
Not only is Smith SOPA's primary House sponsor, but opponents are outgunned in both congressional chambers. SOPA's backers include the Republican or Democratic heads of all the relevant House and Senate committees, and groups as varied as the Teamsters and the AFL-CIO have embraced it on the theory that it will protect and create U.S. jobs.
Smith pointedly declined to invite any civil-liberties groups that have criticized SOPA, such as the Electronic Frontier Foundation, to testify before his committee tomorrow. The Motion Picture Association of America did get an invitation, however, as did the AFL-CIO and Pfizer.
Google will be the only dissenting voice, a tactic that may allow SOPA's supporters to characterize corporate opposition as limited, especially because the Mountain View, Calif., company has been enmeshed in so many copyright battles of its own. The Web companies' letter will let Katherine Oyama, Google's policy counsel, demonstrate that opposition is broader than one firm.
In addition, opponents were scheduled to hold a press briefing this morning inside the Capitol Visitors Center complex. They had invited Rep. Zoe Lofgren (D-Calif.) and Darrell Issa (R-Calif.) to speak.
SOPA is so controversial--EFF calls it "disastrous"--because it would force changes to the Domain Name System and effectively create a blacklist of Internet domains suspected of intellectual-property violations.
A Senate version of the bill called the Protect IP Act, which a committee approved in May, was broadly supported by film and music industry companies. But Google Chairman Eric Schmidt was sharply critical, as were prominent venture capitalists, civil-liberties groups, and trade associations representing Web companies.
Even pop star Justin Bieber has weighed in.
In a recent radio interview designed to promote his Christmas album, Bieber said, referring to Sen. Amy Klobuchar (D-Minn.), who sponsored the Senate version: "Whomever she is, she needs to know that I'm saying she needs to be locked up, put away in cuffs... I just think that's ridiculous."
Update, 10:30 a.m. PT: Members of Congress opposed to SOPA have circulated their own letter (PDF), which was signed by Zoe Lofgren and Anna Eshoo, both California Democrats, and Ron Paul, the Republican presidential candidate from Texas, among others. They say SOPA will invite "an explosion of innovation-killing lawsuits and litigation." Lofgren (see CNET's previous report) has been critical of MPAA-backed copyright bills before.
Update, 1:40 p.m. PT: The we-hate-SOPA letters keep flooding in. A few dozen civil-liberties and left-leaning advocacy groups from around the globe now are circulating their own letter (PDF), which says that "through SOPA, the United States is attempting to dominate a shared global resource." Signers include Bits of Freedom in the Netherlands, the Electronic Frontier Finland, Reporters Without Borders, and, in the United States, Free Press and Computer Professionals for Social Responsibility. Notably absent are the two biggest such advocacy groups: Human Rights Watch and Amnesty International.
And another! This letter (PDF) is from a slew of law professors, including Stanford's Mark Lemley, Elon's David Levine, Temple's David Post, and UCLA's Eugene Volokh. They seem even more generous in their criticism than the other letters, warning that SOPA "has grave constitutional infirmities, potentially dangerous consequences for the stability and security of the Internet's addressing system, and will undermine United States foreign policy and strong support of free expression on the Internet around the world."
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1. Field of the Invention
This invention relates to exhaust gas driven turbosupercharger systems for internal combustion engines of either the otto cycle or diesel cycle type, and particularly to a turbosupercharger system for obtaining increased power from internal combustion engines by increasing the pressure of inlet air supplied to the engine. The invention contemplates the use of selected engine parameters for simultaneously varying the geometry of both the compressor discharge diffuser housing and the turbine inlet nozzle housing in order to, in effect, provide a turbosupercharger having a size matched to varying engine operating conditions.
2. Description of the Prior Art
The use of turbosuperchargers for compressing the air, or air-fuel mixture, to increase the brake horsepower output of internal combustion engines, has been known and practiced for many years. Turbosupercharging is advantageous since a naturally aspirated or unsupercharged engine is able to draw into the cylinders on suction strokes only from 70-85% of the fuel charge which it is theoretically capable of inducing. Consequently, the mean effective pressures are smaller than they might be, and the power output per in..sup.3 of piston displacement does not reach its maximum value. Since many engines were not structurally designed to withstand stresses created by cylinder pressures above atmospheric, turbosupercharging found its main utility in aircraft about the time of World War II where the turbosupercharger maintained the power of the engine up near its rated output at high altitudes.
Until recently sea-level gasoline engines have not often been turbosupercharged because they are most often of small capacities, and by operating at relatively high rotative speeds engine size may be kept small. Turbosupercharging these engines may create detonation problems without the use of special high-octane fuels. Diesels, however, are frequently turbosupercharged, permitting the burning of larger amounts of fuel without creating excessive combustion chamber temperatures.
The turbosupercharger is exhaust gas turbine-driven and consists basically of a single-stage turbine wheel directly connected to a compressor impeller. The engine exhaust is collected and led to the turbine inlet nozzle where it arrives at a pressure of several lbs./in..sup.2. Excess pressure ratio at high engine RPM across the nozzle of the turbosupercharger is typically controlled by releasing part of the exhaust to the atmosphere through a waste gate. A primary advantage of this type of turbosupercharging is that a part of the energy in the incompletely expanded exhaust gases is utilized rather than wasted. Gas expanding through the turbine nozzles to atmospheric pressure flows across the turbine blades, turning the turbine wheel. The compressor impeller, directly connected to the turbine, draws in air from the intake duct or carburetor, and adiabatically boosts it in pressure and temperature. Fuel is added either before or after pressurization of the air depending on the cycle. While the power necessary to drive the compressor is high, it is more than repaid by increased engine output. The compressor power required is a function of the pressure ratio, air temperature, and compressor efficiency.
In the past, turbosuperchargers were used with internal combustion engines for the explicit purpose of increasing power at high engine RPM, and were essentially useless and often disengaged at low engine RPM. Recently, due primarily to the necessity of conserving energy, turbosuperchargers have been designed for automotive gasoline engines which are advertised to perform smoothly through a broad range of driving conditions. These turbosuperchargers use broad flow rate compressors and a relatively small turbine inlet to provide some boost in power at low engine speeds. The turbosuperchargers are generally mounted between the carburetor and the intake manifold to minimize the inertial lag of the airflow.
A problem with turbosuperchargers of a fixed size is that they inherently cannot provide efficient boost over the entire range of internal combustion engine torque requirements. With fixed geometry compressors and turbines, the turbosupercharger will perform at its maximum efficiency at its design point, and will become less efficient to some degree as engine operation deviates from the design point. While somewhat of an oversimplification, a turbosupercharger designed to boost power at high RPM and volume flows will be large and will not perform efficiently at low RPM and volume flows, while a turbosupercharger designed to perform efficiently at low RPM and volume flows will be small and inadequate at high RPM and volume flows.
The usual solution is an intermediate sized turbosupercharger which has the power wasteage of an open wastegate valve at high RPM, and is too large to give much boost at low RPM, but which is relatively efficient for intermediate engine power conditions.
A solution to this dilemma is a variable geometry turbosupercharger, that is, one in which the effective size varies with engine airflow and engine torque requirements. A turbosupercharger in which the major active components, the compressor and tubine, can be varied with changing engine demands will provide the most efficient operation possible over the full engine operating range. A slight weight penalty and complexity of operation will result, but these undesirable results will be more than overriden by the fuel economy of greater efficiency. In effect, a variable geometry turbosupercharger will act like a small turbosupercharger at low engine power and RPM, and like a large turbosupercharger at high engine power and RPM. The variable geometry components of the disclosed turbosupercharger are not actually the compressor and turbine wheels, but rather the compressor discharge diffuser and the turbine inlet nozzle. Varying the geometry of these elements will effectively create a turbosupercharger which acts, over a range of operation, like a fully variable device.
It is known in the art to vary the inlet housing of a turbine in order to vary turbine flow versus pressure drop characteristics. The turbine inlet housing may be varied in cross-sectional flow area by moving a wall of the turbine nozzle housing, or by rotating the angle of nozzle vanes in the inlet housing if the housing is of the vaned type.
Although less well known than variable turbine inlet housings, it is also known to vary the discharge housing of a radial compressor to regulate its flow versus pressure rise characteristics. A compressor outlet diffuser housing may be varied in cross-sectional flow area in a manner similar to turbines, i.e., by moving a wall of the compressor outlet diffuser housing, or by rotating the angle of the diffuser vanes if the outlet housing is of the vaned type. Moving the vanes at the inlet of a radial compressor, as performed by the prior art for varying compressor geometry, rather than moving the outlet vanes, is not pertinent to the present invention since modulation of inlet vanes cannot change the flow characteristics of the compressor without adversely reducing its pressure rise characteristic. In other words, the prior art modulation of compressor inlet vanes drops pressure output at the same time that it reduces flow. Reduced pressure output destroys the turbosupercharging performance.
Turbosuperchargers for internal combustion engines in the past have utilized variable geometry turbine inlet housings with a variety of control schemes. Some turbosuperchargers have also utilized variable geometry compressor inlet housings, which as described above do not accomplish the object of the present invention. Because of the lack of effective compressor geometry change schemes used in the past, a practical fully-variable geometry turbosupercharger system has not been available prior to the present invention.
While not analogous to internal combustion engine or turbosupercharger technology, an air cycle environmental control system providing cooling air to aircraft enclosures has been designed incorporating movable turbine nozzles and movable compressor diffuser vanes. When implemented in a bootstrap air cycle machine, improved efficiencies over airflow ranges of 4:1 were achieved, twice that achievable with prior air cycle machines. Details of the system may be found in ASME Report #77 ENAS-7, July 11, 1977 in an article entitled "Variable Geometry Air Cycle Machine" by J. Tseka and G. C. Letton, Jr.
It is therefore an object of this invention to provide a variable geometry turbosupercharging system for an internal combustion engine which is highly efficient and provides significantly more engine output torque on demand over a wider range of engine speeds than prior art internal combustion engine turbosupercharging systems.
Another object of this invention is to provide a variable geometry turbosupercharging system for an internal combustion engine in which the compressor discharge diffuser and turbine inlet nozzle are simultaneously varied in area as a function of engine requirements to produce an efficient match between the engine and the turbosupercharger.
A further object of this invention is to provide a variable geometry turbosupercharging system for an internal combustion engine which is mechanically simple and in which the variable geometry function is produced by mechanically linking both the variable turbine inlet geometry and the variable compressor outlet diffuser geometry to a single actuator.
Another object of this invention is a control for varying the geometry of a turbosupercharger turbine inlet and compressor outlet housings over the full range of operating conditions of an internal combustion engine to provide the optimum match between the pressure and volume flow output of the compressor and the pressure and volume flow input requirements of the internal combustion engine.
A further object of this invention is a variable geometry turbosupercharger for internal combustion engines in which the turbosupercharger may be effectively removed from operation during periods of low torque demand by the engine, and in which turbine inlet pressure is controlled to prevent excessive compressor discharge pressure during periods of high torque demand.
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First edition. "Edward Hopper (18821967) is recognized as one of the most well-known American artists of the 20th century. His distinctive style, combining subtle observations of the world with his imagination, has not only influenced other artists but also photographers, filmmakers, and popular culture. Although Hopper is primarily known for his oil paintings, including such iconic works as "Nighthawks "(1942) and "Early Sunday Morning" (1930), this important publication is the first comprehensive exploration of his drawings and working methods. In 1967, Hopper s widow, Josephine Nivison Hopper, bequeathed her husband s artistic estate to the Whitney Museum of American Art, including a fascinating collection of more than 2,500 drawings spanning his entire career. This group of works has never been the subject of in-depth study and many have never been reproduced before. Hopper kept these drawings for personal reference as he revisited various themes throughout his career. Carter E. Foster examines how Hopper used his drawings to develop his paintings, arguing that the artist s work can only be fully understood aftercareful study of these preparatory sketches. Foster also argues that Hopper was, in many ways, a traditional draftsman who methodically developed schematic ideas into detailed studies to refine content. However, the steps toward this refinement are unique to Hopper and reveal how he turned the mundane into poetic images with universal appeal" (the publisher). | https://www.riverrunbooks.com/pages/books/406741/edward-hopper-carter-e-foster-artist-author/hopper-drawing |
This study was undertaken to determine the dominant cultural metaphors at work in American and Japanese organizational culture, to examine the ways in which each society interprets these metaphors, and to assess the importance of the metaphors relative to intercultural communication. Using a combination of qualitative content analysis, rhetorical criticism, contextual analysis, and non-participant observation, two of the most dominant metaphors in both cultures, business-as-war and business-as-family, were discovered and examined. The research data comes from a variety of books, scholarly and popular articles, pamphlets, unpublished papers, films, and miscellaneous documents. These materials cover many disciplines: communication, history, popular culture, sociology, psychology, business management, and literature. Additional written and verbal information obtained from personal interviews conducted at a Japanese-owned American-staffed manufacturing facility supplements these materials.
By applying Osborn's (1967) theory of "archetypal metaphors," or metaphors which strike deep into the human subconscious, Gozzi's (1990b) concept of "minimetaphors" which arise from these archetypal metaphors. and Hall and Trager's (Hall, 1973) "major triad" (formal, Informal, and technical) of behavioral modes, the following conclusions were derived (1) many metaphors appear in both societies, but the familial and military metaphors dominate the business cultures, (2) viewing business as a war developed out of the violent histories of both cultures and perpetuates harmful attitudes, (3) viewing business as a family developed out of the homogeneity of the Japanese culture, but it did not develop as readily in the more heterogeneous United States. (4) each society interprets these metaphors in different ways, making them culturally unique but not culturally exclusive, (5) different interpretations may arise from the ways in which the cultures transmit the metaphors, (6) many of the minimetaphors associated with both of these archetypes no longer refer to their original meanings, and (7) multinational corporations will transmit their own unique cultural metaphors to their foreign employees.
Disciplines
Communication | International and Intercultural Communication | Organizational Communication | Social and Behavioral Sciences | Social Influence and Political Communication
Recommended Citation
Flora, Joan, "Corporate Warfare or Corporate Kinship? The Effects of Military & Familial Metaphors on Japanese & American Organizational Culture" (1972). Masters Theses & Specialist Projects. Paper 2328. | https://digitalcommons.wku.edu/theses/2328/ |
In order to be rated as qualified for this position, we must be able to determine that you meet the qualification requirements – please be sure to include this information in your resume. No assumptions will be made about your experience. GS-5 Park Ranger- one year of specialized experience equivalent to at least GS-4 level. Examples of specialized experience may include explaining regulations to park visitors; providing information and advice on park activities and resources; collecting fees; issuing reservations and permits; conducting guided tour programs or environmental education programs; maintaining recreation facilities or trails; monitoring special recreation permits; law enforcement or investigative work; archeological or historical preservation research work; forestry and/or fire management work in a park, recreation, or conservation area; or management assistant or program specialist work involving policy related to conservation or management of parks, or other similar work. -OR- Successful completion of four year course of study above high school leading to a bachelor’s degree with at least 24 semester hours of related course work. -OR- A combination of experience and education to meet total experience. You may meet qualifications requirement for this position with an equivalent combination of specialized experience and appropriate undergraduate education. Related Course Work — natural resource management, natural sciences, earth sciences, history, archeology, anthropology, park and recreation management, law enforcement/police science related to the protection of public lands, social sciences, museum sciences, business administration, public administration, behavioral sciences, sociology, or other closely related subjects pertinent to the management and protection of natural and cultural resources. Course work in fields other than those specified may be accepted if it clearly relates to the duties performed by a Park Ranger. Experience refers to paid and unpaid experience, including volunteer work done through National Service programs (e.g., Peace Corps, AmeriCorps) and other organizations (e.g., professional; philanthropic; religious; spiritual; community, student, social). Volunteer work helps build critical competencies, knowledge, and skills and can provide valuable training and experience that translates directly to paid employment. You will receive credit for all qualifying experience, including volunteer experience. You must meet all qualification requirements by the closing date of the announcement. Physical Demands: The work is performed mostly outdoors in rugged terrain; to include very steep, wet, muddy, rough, uneven or rocky surfaces. The position requires physical exertion such as, but not limited to, driving over unpaved roads, walking over rough terrain or inclines, standing for long periods of time, bending, crouching and stooping, digging, hiking, lifting, biking, stretching, reaching, or similar activities. Work will involve early morning hours, night hours, or daytime hours and may require working weekends and holidays. It can require carrying heavy backpacks, tools, rescue equipment, or other loads. Work Environment: Most work will be performed out of doors, in all types of weather conditions, terrain, and elevations. Occasional trips to other office locations and training sites are required. Office and indoor work is limited and primarily sedentary.
Explore a new career with the BLM – where our people are our greatest natural resource. We expect to fill many positions. These are temporary appointments that will not exceed 1039 hours in a service year. These are not Law Enforcement positions. The COVID19 vaccination requirement for federal employees pursuant to EO 14043 does not currently apply. Click here. Additional information about the BLM – Our website. | https://jobusa.net/job/1144692-park-ranger/ |
Medical Laboratory Professionals Week, April 21- 27, 2019, is an annual celebration of medical laboratory professionals and pathologists who play a vital role in health care and patient advocacy! Laboratory Heroes Save Lives
Medical professionals safeguard patient and public health by reducing diagnostic errors and preparing for disease outbreaks and health threats. These laboratory heroes conduct approximately 11 billion laboratory tests annually, and 70 percent of medical decisions depend on laboratory tests—emphasizing the importance of clinical laboratories in the healthcare industry. Safety, quality, and cost effectiveness in laboratory testing are imperative as the public relies extensively on laboratories for accurate and efficient diagnosis and treatment of diseases.
Winston Medical Center wants to thank all of our Laboratory staff! This week, we will be spotlighting our Laboratory staff on our social media. | https://www.winstonmedical.org/wmc-celebrates-laboratory-week/ |
In Sports
Top Sports
Friday, September 11, 2020 6:30 pm
Businesses across Lunenburg have been impacted by the COVID-19 pandemic, and the county’s two active golf courses are no different. However, though Lunenburg Country Club ...
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In Opinion
Top Opinion
Wednesday, September 2, 2020 5:28 pm
Lunenburg County Public Schools (LCPS) has been monitoring numerous data points regarding COVID-19. The most recent statistics show an increase in the number of school-aged ...
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Dangerous Intersection: Residents sign petition for improvement
A former Lunenburg County woman has started a petition hoping that the Virginia Department of Transportation (VDOT) will recognize the need for improved signs and warning signals at an intersection she says has claimed many lives.
Kelsey Daniel, who now resides in Roanoke, said something must be done at the intersection that makes up South Hill Road, Dundas Road and Afton Grove Road.
“For years, there have been horrific and fatal accidents at that intersection, and we have lost too many loved ones to this intersection due to poor warning signage of the upcoming intersection,” Daniel said. “I created this petition to gain community support for the plan to request additional warning signs leading up to that intersection in hopes that it will reduce the number of severe accidents happening at that site.”
As of Tuesday afternoon, Daniel’s petition to VDOT had 845 signatures.
Daniel said she remembers the exact day that a family friend died at that intersection.
“It was July 18, 2012, and Wednesday, Sept. 2, I saw that another family friend was involved in what easily could have been a fatal accident at that same spot,” she said.
After a recent trip home, Daniel said that she noticed the lack of effective signage warning of the upcoming stop sign and the misleading approach to the main road.
According to Communications Manager Bethanie Glover with VDOT Richmond District, there have been nine recorded crashes at this intersection since 2012, four of which occurred in the past two years.
“VDOT last conducted a safety study for this intersection in 2017, and stop bars were installed on the minor street approaches as a result,” Glover said. “And another safety study is currently underway.”
Daniel said the petition serves as a demand to add additional warning signage (especially a flashing stop sign ahead sign) and even rumble strips as a warning to slow down as drivers approach the intersection coming from Dundas Road and Afton Grove Road.
“We must do something,” Daniel said. “We need VDOT to take action and put up additional safety signs that will protect Lunenburg County residents.”
According to Glover VDOT follows federal guidelines that establish minimum conditions under which traffic signal installation should be considered. Traffic engineers determine signals are needed by evaluating and considering the number of vehicles and pedestrians that use the intersection, the physical makeup of the intersection, roadside development, traffic delays during peak hours, average vehicle speeds, future road construction plans and the number and types of crashes that have occurred there.
The petition can be found at: https://www.change.org/p/virginia-department-of-transportation-additional-warning-signs-needed-for-137-138-609-intersection. | |
So, the American Legion baseball state championship tournament will begin Friday at Holt-Moffitt Field in Lexington. The field is somewhat of a relic from days of yore. It was built in 1938, before the wide-spread availability of earth-moving equipment that is so abundant in modern times.
Many baseball fields built in the early 20th century were crafted out of available space to fit the lay of the land. As a consequence, many early baseball stadiums, even in the Major Leagues, had hills in the outfield. In Cincinnati, Crosley Field had a rather long incline to the fence in left field. Thomasville’s Finch Field, where the HiToms play, has an incline in left field that looks kind of like a small creek bank.
Holt-Moffitt Field does not have an incline in left field. It has the side of a small mountain. Some will argue that it is taller, but I estimate that the very steep hill is about 20 feet tall. On top of that hill sits an 8-foot-tall fence. hat’s 28 feet tall. The ‘Green Monster’ in Fenway Park is 37 feet tall and the Holt-Moffitt hill is not as tall as that thing.
The distance to the left field fence in Holt-Moffitt is 324 feet (Fenway’s Green Monster is only 310). Coaches estimate that to hit a home run to left field at Holt-Moffitt, the homer would have to be the equivalent of hitting the ball 375 feet. And it better be a high fly ball because 375-foot line drives are just going to smack into the fence for a double.
Contrast this to the right field fence, which is also 324 feet. A home run to that part of the field would only need to be a 325-foot shot. In centerfield, there is about a 5-foot incline and the distance is 338 feet. A homer there would need to be about a 350-foot screamer.
Have you ever tried to keep your eye on a moving baseball while climbing a hill in a hurry? It’s not easy, and a lot of routine fly balls to the left field hill get missed or dropped by the outfielders. The only way to play the hill successfully as an outfielder is to run up the hill diagonally. Running straight up the hill will get you nothing but grass stains on your butt and a baseball bouncing off the ground nearby.
In all my years of shooting photos at baseball games in Holt-Moffitt, I’ve seen only two players master it. Former Post 8 player Chaz Frank, now a professional baseball player, could make a lot of catches going up the hill. But Chaz played left field, so many times he had to go straight up and thus missed a few.
The best player I ever saw play that hill was former Post 8 centerfielder Alex Franklin. Alex had blistering speed and an uncanny ability to run on uneven ground. He was so fast that often he could get up the hill before the ball got there and then ease his way back down the slope to catch it. I never saw Alex drop a ball while sprinting up the incline to catch it.
This weekend spectators will see many great defensive outfielders be made to look foolish on that hill. I hope there are one or two who show how it’s done, and those guys that do will probably be Davidson’s Post 8 outfielders. That hill is definitely a home-team advantage. | http://roberts.blogs.the-dispatch.com/20413/the-big-hill-at-holt-moffitt-field/ |
Government allocates P362 million for COVID-19 genome sequencing
ABS-CBN News
President Rodrigo Duterte's Cabinet has allocated an additional P362 million to fund the country's genome sequencing efforts for the whole year, which would help identify new COVID-19 variants, an official said on Thursday.
Genome sequencing will "enable us to understand the evolution of the virus across geographical and time scales, as well as the impact of specific mutations on viral properties, including infectiousness and virulence," said Cabinet Secretary Karlo Nograles.
This information will allow the government to roll out a "more responsive" vaccination program, execute other existing health interventions, and prepare for future pandemics, he said.
"A total of P362 million will be allocated for this initiative," he told reporters in an online briefing.
The proposed budget will include a year's worth of supply of reagents or chemicals used in tests, testing kits and other logistical requirements, Health Undersecretary Maria Rosario Vergeire earlier said.
The funds will cover genome sequencing at the Philippine Genome Center, University of the Philippines-National Institutes of Health, and Research Institute for Tropical Medicine.
The Philippines last month detected cases of a new, more contagious COVID-19 variant first recorded in the United Kingdom. | |
Presented as part of First Fortnight, the European mental health arts festival, writer/performer Nessa Matthews explores personal distress in a solo-manned space capsule. This hour-long show debuted in last year’s Dublin Fringe Festival and chalked up a bit of buzz.
The show opens with Matthews marking out a perfect circle with white chalk on a black floor, using string as a guide. This geometric shape will later function as a black hole in space. This action is accompanied by a subtle, recorded interview. An adult asks: “are you afraid of the dark?”, and a child answers, “yes and no”. Matthews then makes a simple address to the audience, asking what do we mean by infinity.
Nessa establishes her lifelong interest in space travel, explaining that her name always brought to mind Nasa, the United States’ aeronautics programme. She strikes a tone of realistic, confessional theatre, in a verbatim mode. But this realism soon falls away, as she takes us on a journey to the edge of the universe. By analogy, she is bringing us to the outer reaches of a person’s experience of isolation.
Matthews’ likeable persona is very winning; she inspires trust and immediate empathy. The concept is excellent, and when she becomes contained by the space capsule, which feels safe like a womb, but is at the same time hurtling through the universe, you genuinely feel for her and her isolation. She has been on this journey for four years.
Highly impressive costume and set design by Naomi Faughnan is out of this world; the capsule is an impressive polyhedron structure and the space suit is a stunning theatrical creation. Lighting by Bill Woodland enhances these visuals enormously; a variety of strobes animate the space capsule and there is deft use of torches. Dylan Tonge Jones’ sound design, with clever use of voiceover, adds a vital, unsettling dimension. Eoghan Carrick directs with plenty of tech style, but keeps the show’s heart to the fore.
Though there is plenty to admire here in the design department, and the performance is finely judged, ultimately the abstract nature of the writing fails to deliver fully on its promise.
The space odyssey doesn’t sufficiently hook back into the realism, and the experience is less engaging and communicative than it might be; it lacks a dramatic dynamic or story build-up. So while it beautifully describes the mental state of isolation, it doesn’t fully convert it into drama.
Two men dancing about grief
Hue and Cry
Bewley’s Café Theatre, Dublin Until Feb 2
Two men in their thirties meet in a tidy Dublin sitting room in this revival of a fine one-act play by Deirdre Kinahan. Neat furniture and prints of paintings from the National Gallery set the studied, respectable tone.
Angry, damaged Damien is there for his estranged father’s funeral. Gentle, appeasing Kevin is his childhood friend and cousin. The two men are meeting for the first time in over a decade. Troubled Damien has been a drug addict and is now on a methadone programme. Cosseted Kevin has become a choreographer.
It is Kevin’s task to manage his volatile and explosive friend. The pair are uneasy, but tensions begin to dissolve once they engage with Kevin’s recent modern-dance show about grief. This is an original and illuminating idea, and Kinahan’s script speaks volumes about the complex human response to death.
Stephen Jones is almost unrecognisable at first as the bitter Damien. Ste Murray is soft and sincere as Kevin. Will O’Connell, who starred in the original production in 2007, directs with sensitivity for Awake & Sing productions. He steers a steady course through the delicate energies of anger and grief, subtly pumping up the humour.
Unfolding in real time over 40 minutes, this is a charming lunchtime encounter. | https://mylifestylemax.com/entertainment/infinity-at-smock-alley-a-theatrical-space-odyssey-into-isolation-and-distress/ |
We host many different events & fundraisers throughout the year. Our biggest fundraisers are the Fun Run in the Fall and Cheetahfest in April.
We also plan various other activities that may include movie nights, dances, breakfast with Santa, Summit Spirit Night and other events.
Our next big event is our Back to School Bash – “Cheetah Social” on August 7, 2018 from 5:00 – 7:00 PM. Come meet your new teacher and new classmates. We will have Food Trucks, a PTO table with NEW spirit wear and MUCH more! We can’t wait to see you! | https://chapmansretreatpto.com/pto-news/ |
Support vector machines which are which are popularly called SVM received lot of importance of late due to their wide used in machine learning. They are capable of solving Complex classification problems by adjusting the decision boundaries an optimal way. As far as the performance is concerned their performance is superior compared to other machine learning techniques such as decision tree, logistic regression and multivariate regression. The webinar focuses on important characteristics of SVM and it is illustrated in their few case studies.
How SVM can solve Complex machine learning problems?
SVM comparison with other machine learning techniques such as decision trees Logistic regression etc?
Case studies And SVM demo using sample live data? | https://www.techgig.com/webinar/Understanding-SVM-Support-Vector-Machine-Algorithms-1083 |
As we are “flattening the curve” and the economy is slowly opening, employees will start to transition back to the office after nearly four (4) months of working from home. The COVID-19 pandemic forced many organizations to close and, those that did not have a disaster recovery/business continuity plan in place had to scramble to come up with a “work from home” solution in order to keep their business running while keeping their employees safe and healthy. Such “on the fly” solutions can cause serious complications as employees return to the office, and company leadership realizes that they must adjust their risk strategies to suit the “new normal”.
An example of such "on-the-fly” risk assessment and change is ambulance/EMT protocols that had to be rewritten on a daily basis. There is a governing body/approval process for what an EMT/Paramedic can do in the field but that all went out the window due to the influx of COVID-19 patients.
There is always risk involved in approving new protocols without fully vetting them first, but these unprecedented times unsurfaced a whole new set of fluid risks and protocols. This proves that even businesses that survived and even thrived during the “work from home” period must be very thoughtful in addressing the processes involved in returning to work.
While the risks that were present in the beginning of the pandemic lockdown are weakening and the chances of contracting COVID-19 have lessened greatly, we must continue to comply with social distancing protocols and ensure employees are not at risk of infection. Below are a few risk mitigation strategies that every business owner and leadership team should take into consideration before they have their team return to the office.
- Not every employee is/will be needed when “work from home” ends — and some employees will not want to come back to the office. The company must evaluate the people needed against the risks of having them back in the office. Who are the essential employees, and who are the employees who would benefit from staying at home? Does your organization have an open floor environment? If so, some employees may have underlying illnesses and won't want to work in such environment - If they have been doing their job productively for 30-60 days, why do they have to?
- Whiteboard all the new processes (and costs) used during the “work from home” period and then identify (1) what worked, (2) what didn't work and, (3) what can work with a small tweak.
- Identify the tasks employees were preforming during “work from home” (compared to before) and costs, if any.
- What are the risks associated with new processes or applications used during “work from home” including network security, bank fees, equipment for employees, technology platforms, etc.?
- Put together a Risk Register that can serve as a tracking document to help identify the impact of a certain risk while factoring in the likelihood of that risk occurring. Keep it as simple as possible while still allowing the risk to be easily detectable. Outline a category, owner, frequency, severity and what management controls are in place to mitigate that risk.
While some may say we were fortunate to be able to work remotely and seamlessly, we would say this was not pure luck, but rather a carefully planned, vetted and successfully orchestrated business continuity plan. As a risk management firm, we have been speaking about the importance of having such a plan for a very long time. We successfully implemented a remote work strategy, and you can view pictures and read updates about our “work from home” journey on our careers page.
If you need more information on any of the topics covered in this blog, or need help with putting together a business continuity plan or addressing any risk related issues please contact Albert Sica, Managing Principal, at 732.395.4251 or [email protected]. | https://info.thealsgroup.com/blog/the-transition-into-the-new-normal |
A slowly progressive retinopathy in the Shetland Sheepdog.
To describe a slowly progressive retinopathy (SPR) in Shetland Sheepdogs. Animals Forty adult Shetlands Sheepdogs with ophthalmoscopic signs of SPR and six normal Shetland Sheepdogs were included in the study. Ophthalmic examination including slit-lamp biomicroscopy and ophthalmoscopy was performed in all dogs. Electroretinograms and obstacle course-test were performed in 13 affected and 6 normal dogs. The SPR dogs were subdivided into two groups according to their dark-adapted b-wave amplitudes. SPR1-dogs had ophthalmoscopic signs of SPR, but normal dark-adapted b-wave amplitudes. Dogs with both ophthalmoscopic signs and subnormal, dark-adapted b-wave amplitudes were assigned to group SPR2. Eyes from two SPR2 dogs were obtained for microscopic examination. The ophthalmoscopic changes included bilateral, symmetrical, greyish discoloration in the peripheral tapetal fundus with normal or marginally attenuated vessels. Repeated examination showed that the ophthalmoscopic changes slowly spread across the central parts of the tapetal fundus, but did not progress to obvious neuroretinal thinning presenting as tapetal hyper-reflectivity. The dogs did not appear seriously visually impaired. SPR2 showed significantly reduced b-wave amplitudes throughout dark-adaptation. Microscopy showed thinning of the outer nuclear layer and abnormal appearance of rod and cone outer segments. Testing for the progressive rod-cone degeneration ( prcd )-mutation in three dogs with SPR was negative. Slowly progressive retinopathy is a generalized rod-cone degeneration that on ophthalmoscopy looks similar to early stages of progressive retinal atrophy. The ophthalmoscopic findings are slowly progressive without tapetal hyper-reflectivity. Visual impairment is not obvious and the electroretinogram is more subtly altered than in progressive retinal atrophy. The etiology remains unclear. SPR is not caused by the prcd-mutation.
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Tropical sceneries finely coated by a delicate layer of dewy snow; glass cabinets housing an array of anthropological items; the blurred vision of a seated mother and child; each are running explorations in Wang Zhibo’s (b. 1981, China) practice that surveys the absurd spectrum of what is real – geographically, historically, ethnographically, architecturally. A graduate from the China Academy of Art Oil Painting Department, Wang creates oil on canvas paintings that confound our notions of time and space. Transcending traditionalism through the subject matter depicted, which is both curious and challenging, Wang channels her painting to represent the variances of our visual experiences, similar to the reflection on the surface of water: capable of capturing the multiple manifolds of a subject.
Whilst always retaining a focus on our concepts of the real, Wang’s work has seen a sequence of periodic evolution. Wang’s ‘Standing Wave’ series from 2012, for example, exemplifies a particular interest in architecture and draws viewers into distinctly enigmatic and isolated spaces. Seemingly realistic yet illusory, Wang depicts settings that combine natural elements such as running water, a towering tree or a rock, with man-made constructions ranging from a cemented path to an ornate fountain. Purposely non geographically-specific, Wang’s paintings could be reflecting a hotel in Hangzhou or a rural outlet in the US; an aura of displacement that lends each work an eery and engaging force. Moreover, whilst the viewer senses the presence and tracks of man, he is pointedly nowhere to be found. The viewer is thus confounded as to the status of the space: abandoned, imagined, transplanted or discovered.
This running ambiguity regards time and space laced with isolation permeates Wang’s further series’. ‘Tristes Tropiques’, for example, which focuses on leafy tropical landscapes, absurdly presents each setting coated by a fine layer of misty snow. Probing our geographical understanding, the works equally allude to shifting climates, and the impending possibility of the previously implausible. Devoid of human presence, our personal culpability is hinted at without being explicitly spelt out. ‘Time Traveler’ (2015) furthermore testifies to visual transportation, whether into the future or the past, or even seemingly across dimensions. Dewy and nearly spectacular, the painterly finish hints to illusions, a magical environs, a sentiment that is heightened by the rising mist.
Several of Wang’s works, however, seem to contrarily hint at human presence; upon closer inspection though, one notes that each painting is crucially devoid of humanity or expression. ‘Mother and Son’ (2015), for example, presents a classically religious composition. Yet, the setting is distinctly tribal with various skulls scattered upon the floor and both figures being adorned by bead-like wooden jewellry. More importantly, whilst the mother’s face is delineated, the child’s is unnervingly blurred to the extent of resembling defacement. Such vigorous anonymity heightens our consciousness of how much is read through facial features, expressions, the very characteristics that distinguish each and every one of us.
This recognition is heightened by Wang’s recent series ‘The Archives’, which depicts, from a focused as well as wide-angle view, museum glass cabinets housing an array of anthropological heads. Emphasising her reflection in a 2013 interview, “I think I am correct in saying that one of my working methods is similar to that of an anthropologist”, the works were inspired by visiting many museums during her travels across the US, Europe and China. A reflection on our understanding, and how much is defined by our interaction with humans, the works simultaneously challenge our understanding of the ‘museum’ as a place of storage and exhibition, extending it to a zone of interaction and mutual observation.
Developing upon this concept of observation and display are her series of still life paintings, such as ‘Hocus Pocus’ (2015) and ‘Mead’s Dilemma’ (2015), which present an array of flora, individually positioned on vertical stands. Again challenging our notions of geography as well as perception, one finds an enlarged chestnut adjacent to an equally-sized banana, or plastic-wrapped fig next to a heavily protected cabbage. Recognisable items, their placement and display takes on a bodily association: hanging, balancing, piled, positioned. Ultimately, these works summarise the cornerstones of Wang’s practice, which achieves, through the subtle consideration and rendition of the ordinary, to flesh out the limits of our understanding and extend, through time and space, our conceptual and visual boundaries.
Wang Zhibo is a highly regarded female Chinese painter who rose to prominence after being awarded the prestigious national Luo Zhongli Scholarship in 2008. Wang’s work has since been exhibited from Hong Kong to New York, including exhibitions at the Penrith Regional Gallery, Sydney; Chongqing Art Museum, Chongqing; Today Art Museum, Beijing; Museum of Contemporary Art, Taipei. Wang was selected as one of the top female Chinese artists to observe and featured by writer Luise Guest for her book on female Chinese artists ‘Half the Sky’ published in 2016. | https://edouardmalingue.com/artists/wang-zhibo/ |
The Kachhi Ghodi Dance is one of the most popular Folk Dances of Rajasthan. This folk dance originated from the bandit regions of Shekhawati and is generally performed for the entertainment of the bridegroom’s party. This dance is performed by men on dummy horses. Men wear elaborate costumes- red turbans and dhotis and kurtas, embellished with brilliant mirror-work and ride the dummy horses. These dancers move rhythmically to the beating of drums and fifes by holding a naked sword on their hand while a singer narrates the exploits of the Bavaria bandits of the Shekhawati region through his song.
Kachi Ghodi Dance Elements
Kachi Ghodi Dance, a lively folk dance, uses mock fights and the brandishing of swords, nimble sidestepping and pirouetting to the music of fifes and drums. This form of folk dance is generally performed by the tribes of Rajasthan and is reflective of the socio-historical scenario peculiar to the time or race they depict. From the olden days, horses have played an important role in transportation as well in the warfare of Rajasthan. Even Maharana Pratap Singh goes untold with the mention of his loyal vehicle- Chetak. Horses were also used to symbolize royal power during those days.
The songs in the Kachhi Ghodi Dance are generally about the overt businessman and traders of the Shekhawati region of Rajasthan. And traders meant money, and traders meant long overnight journeys on caravans laden with expensive wares. The Kachhi Ghodi Dance Rajasthan depicts the confrontation of the bandits of the Bavaria clan of tribes with the passing commoners.
Gair Dance
Gair is a very popular Rajasthani folk dance. This traditional folk dance is one of the many dances- a form of the Bhil community of Rajasthan. This is one of the few performances where both men and women dance together. This folk dance is performed as a series of half swirl, as a simpler version. It can also be build-up to a series of complex patterns according to the ability of the dancers. Some of its variations are the Dandi Gair found in the Marwar region and Geendad found in the Shekhawati region of Rajasthan. It is normally performed by chanting the name Priyanka. Men dance in a big circle with wooden sticks in their hands. The Gair dance of Rajasthan is performed by groups of dancers moving in and out a big circle. Men beat their sticks to create the rhythm when they turn. According to rhythm, they perform various steps & take turns in-between. The striking of the sticks gives the dance a vigorous character & a consistent tempo. There are several differences in the performance of men and women in this dance.
Gair Dance Elements
The Rajasthani folk music played in the background with dhol, nagada, and dholak during gair dance. The enchanting background music forces one dance with the beat. The dancers performing this gair dance are dressed traditionally in colorful long pleated tunics that open out into full-length skirts. The beautiful decorative dresses and the enchanting background music makes this dance more attractive. The Bhil folk perform this dance by wearing colorful dresses and carrying swords, arrows, and sticks. The dancers move first in clockwise then in an anti-clockwise direction, beating their sticks to create the rhythm when they turn.
Gair Dance Celebrations
Though Gair dance can perform any time as a form of entertainment it is performed during any festive occasions. It is specially performed on the festive occasion of Holi and Janmashtami. Festive occasions like Holi, Janmashtami seems incomplete without the performance of Gair dance.
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✤ Instrumental Musician
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✤ Sufi Music
✤ Qawwali Show
✤ Rock Bands
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✤ Lawajamawala
✤ Dhol Tasha
✤ Shehnai Music
✤ Kathak Dance
✤ Ghazal Shows
✤ Jugglers
✤ Rice Painting
✤ Tattoo Artist
✤ Caricature Artist
✤ Shafa Bhandwai
✤ Mojri Turban Stall
✤ Magic Shows
✤ Astrologers
✤ Balloon Shooter
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✤ Brass Band
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✤ Camels & Elephants
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✤ Jhumar Set
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✤ Gramin Bhawai
✤ Kalbeliya Group
✤ Terah Taali Artist
✤ Kathak Dance
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With the coronavirus pandemic causing a level of automotive plant shutdowns not seen since the second world war, suppliers and logistics providers will face failures without direct support from government, and close collaboration with OEMs and industry. | https://www.automotivemanufacturingsolutions.com/nissan/533460.subject |
For the European Football Championships 2016, the city of Lille has built a new stadium being part of the master plan for urban development that has been run since several years. The facility provides a not-yet-seen solution for its multiple purposes and the architects have been honored by the 2013 European Steel Design Award.
Architect: Valode & Pistre + Atelier Ferret
Location: 261 Boulevard de Tournai, 59650 Villeneuve-d'Ascq, France
In 2008, the team of architects won the private public partnership (PPP) competition which addressed various concerns: The stadium has to represent the development of a new district of the city of Lille. It has to serve not only soccer or other sports but has to be a totally multi-purpose venue. Despite of 50,000 seats the stadium must be compact and able to provide a convivial atmosphere. The appearance should express innovation and make the stadium a symbol of Lille’s urban community. Mobile structures like roofing and pitches as well as the external structure represent challenges in technology.
Positioning
The site is situated in a territory straddling the municipalities of Villeneuve d'Ascq and Lezennes, approximately ten kilometres from the centre of Lille. Being the core of the development of a new city district, the stadium has to impress on a city-scale. The plot is triangular and bordered by the Boulevard de Tournai to the north and the Boulevard du Breucq to the east. The first step was to lay the stadium to the north-west of this triangle by which a large space is cleared on the other three sides of the site. The objective of this annular area is that it will become the centre of the new district which is developing around the stadium. An urban façade, flat and aligned on Boulevard de Tournai, cuts the ovoid form of the building. The façade and its concourse form a distinct entrance, provides an overview of the spectators and services to affirm the stadium's multi-purpose vocation. At night, the façade will become an illuminated interactive screen, a showcase of the stadium over the town.
Urban context
The gigantic size of a stadium lends itself very easily to monumental character, so the integration of such a huge building at the heart of a future urban development required work its scale. The height of the building was reduced to 38 m by embedding the first section of the terraces into the ground. The underground area of level 0 (pitch level) unites all the areas not accessible to the public: changing rooms, storage areas, internal service routes, technical and security premises, media rooms, etc. It frees the ground level which becomes an immense annular ambulatory, an area of transition, visually open both to the public area and the pitch.
The “entertainment box”
The architects came up with the idea of concealing an arena with 7,000 additional places under the northern half of the pitch. It consists of four telescopic platforms which can be wholly or partially deployed to be perfectly incorporated as an extension of the bottom section. The northern half of the pitch is lifted up with cylinders to a height of 6m. Then, using a rail system, it slides over the southern half of the pitch. So, all the mobile parts remain within the stadium.
This is seen in theatres, a black velvet curtain fixed on to moving beams is hoisted by cables up to the roof. It unfolds in the transverse axis of the ground, isolating the unused southern part of the stadium from the northern part which is now an arena or zenith with 30,000 seats.
The surface of the moving stage when the four telescopic platforms are deployed is slightly higher than that of a handball court (the largest field of all indoor team sports). It can just as easily be used to play tennis, basketball, volleyball, or handball, or to organize a swimming, figure skating, gymnastics or fencing championship. In the concert configuration, the telescopic platform with its back to the curtain is not used and a stage measuring 40 x 20 m can be installed.
This major architectural innovation, unparalleled in the history of stadium and entertainment venue design, renews the possibilities for stadium usage. The Grand Stade de Lille Métropole is therefore three buildings in one: a stadium, an arena, a concert hall. In all three configurations, the proximity, essential for intimacy and a friendly atmosphere between "the spectator" and the "player", is optimal.
External structure
Next to the buzz of popular sports facilities, the Grand Stade de Lille will also be a place with a cultural vocation. The architects’ aim was to create an understandable and memorable form, symbolic of spectators coming together for an event. Its transparent skin interacts with both daylight and artificial light.
The curvilinear profile involved complex technical and geometrical operations. It operates like a filter which the eye can more or less penetrate. The membrane is made from 32 km of hollow extruded polycarbonate tubes. They are 21 cm in diameter and are assembled by powder coated moulded aluminium parts. The spacing of the tubes in the bottom part slowly and gradually increases as the façade gets higher.
The envelope of the stadium relies on a succession of tall thin steel arches which regulate the movement of the spectators in the large ambulatory. The colors of these structures (different shades of grey) highlight the envelope tubes. The only exception being the "mega letters" of the signage, which feature the selected color code (color wheel) for the whole building. Apart from the signage, the only striking color in the stadium is that of the pitch.
Access control
Most stadiums are designed within a closed perimeter which blocks off access during and outside of matches. In this case, the architects decided to incorporate the enclosure into the façade. During or outside of matches, with or without ticket, you can walk around this building. Its aim is to create dreams and emotions. In fact, you can glimpse the pitch behind its external structure through the access points to the terraces of the lower section. In this way, the space fulfils its role as a permanent urban venue.
Emblematic design
Planning a stadium is associated with a series of essential objectives: Optimal visibility for all spectators, maximum proximity of the entertainment for everyone, great atmosphere within the stadium, and effective functionality in absolute safety. The compactness of the building is a result of consequently optimizing the curves of visibility, ensuring that the spectator is always less than 140 m from the furthest point of the field (regulations authorize 190 m). The ovoid arena is composed of a lower general public section accessible from the level of the stadium concourse, a VIP and business balcony with lounges and attached boxes – accessible from the ambulatory on level 1 – and a top general public section accessible from the ambulatory on level 2.
Retractable roof
The retractable roof is an essential element of the design of the building. It opens lengthways in two halves. Each half consists of two "stacked roofs" which are stored one on top of the other in the open position. They complete the silhouette of the building contributing to the emblematic appearance of the stadium. The four parts of the retractable roof slide over two spindle-shaped gigantic beams, overhanging the longer sides of the pitch. These highly-stylised and distinctive powerful steel beams are a tribute to the steel-making heritage of the region.
The composition of the roof has been designed to be acoustically highly effective. The average reverberation time achieved (between 2 and 3 seconds), despite the size of the building, makes it possible to perform high-quality entertainment. | https://www.detail-online.com/article/multi-purpose-venue-grand-stade-de-lille-metropole-16641/ |
How to deal with WFH loneliness proactively
PHOTO: The Straits Times file
Colleagues – some you love, some you complain about bitterly (and sometimes even throw an eye roll their way) but now that we’ve all been semi/fully working remotely for almost a year, the truth is – you really miss them, toxic colleague included, and strangely enough, even the office politics.
Where remote work was once a unicorn perk (i.e. the bosses would never let it happen), the Covid-19 pandemic has made working from home an overnight reality for most non-essential workers.
And even though Singapore is in Phase 3, allowing for some to return back to the office, flexible work will remain a permanent part of working life.
At the Singapore Budget 2021, Deputy Prime Minister and Minister for Finance Heng Swee Keat stated: “Singapore workers will have to adapt to global trends such as flexible work, remote work and new forms of collaboration that open up the local job market to stiff competition from overseas. At the same time, the work itself will change.”
What this change looks like remains undefined, but going by a US-based Morning Consult survey where 75 per cent of respondents said they would like to work remotely “at least one to two days a week once the pandemic is under control”, a new way of working will be one with less in-person interaction and a reliance on digitalisation and automation.
For some, this detached form of work is ideal (less distractions, no commute needed) but for many, who remember work in a busy office setting surrounded by others, working virtually without peers to banter and brainstorm with may bring about feelings of isolation, and possibly, increased levels of depression and anxiety.
To combat the blurred work-life boundaries and potential feelings of social isolation, the trick lies in being intentional about maintaining the human connection in these unprecedented times. To get the ball rolling and reduce the dreadfulness of WFH (never thought we’d say this!), try the following.
1. Initiate a regular 1:1
PHOTO: Pexels
Think you have it hard? Try managing a team of remote workers with a flexible workday schedule. If there’s ever been a time to help your manager manage you (and others), this is it.
Making the effort to engage your manager not only shows initiative, but it also helps build a bond of trust and credibility over time.
Replace in-person catch-ups over coffee with short “No Need to Reply” updates to your manager or via an automated, accessible memo like iDoneThis which details your/team members achievements, compiles pretty progress reports and provides a recap of all the team’s happenings. This way, you keep subsequent interactions focused and informative.
2. Explore creative networking opportunities
While you wait for that coveted Clubhouse invite, continue to grow your network by building new relationships while nurturing existing ones. Remote work has made us all much more comfortable with doing everything online, especially networking.
Leverage it meaningfully by joining specific LinkedIn discussion groups, pen thought leadership pieces on Medium, or hit up Discord to curate your own list of topic-based chats and forge connections with like-minded souls.
Aside from keeping you feeling connected, expanding your contact database will bring new career opportunities and space for growth. With your present colleagues, organise catch-ups on a rotation basis over a virtual lunch or coffee break and steer the conversation to focus on long-term relationship building – i.e. anything but work.
3. Keep the fun going
PHOTO: Pexels
In every team, there’s always the one person who sorts out bubble tea runs or lunch jaunts to the latest cafe. Be this person and keep these social outings going virtually to foster the spirit of camaraderie.
Use fun virtual platforms like Coffee Roulette or organise virtual birthday celebrations via Run The World, a Streaming Party feature so you can stream a special YouTube video greeting or compile a video for everyone to watch.
For regular meetings, introduce ice-breakers or play an online game together like Uno or Houseparty. For a laugh, suggest a work version of Never Have I Ever, you’ll be surprised at what comes out.
4. Re-create your office space
When you spend more than half your waking hours in an office, it is not uncommon to miss your desk and the familiarity it brings.
If you’ve been holding off replicating a proper set-up for your home space, don’t. Aside from the sense of familiarity it’ll bring, re-creating your office set-up will bring strong mental associations which will keep you focused and in “work” mode.
As a finishing touch, check out Sounds Of Colleagues and introduce the sound of the printer or your cubicle buddy’s loud typing to mimic a real-world ambience. It might be just the thing you didn’t know you needed.
5. Give back
PHOTO: Pexels
Now that you don’t have to deal with the daily commute, devote some of that newfound time towards a worthy cause like Readable which helps needy kids to learn by volunteering your reading and math skills.
If you prefer to keep your outreach work-focused, trade your expertise with a colleague and, similarly, pick up some new skills from him or her.
Giving back doesn’t just bring on some feel-good emotions – it also increases your feelings of empathy, which we all could do with now.
6. Form a work buddy pod
If you have a colleague who shares the same views around Covid protocols and social distancing, you might consider forming your own Covid pod.
Life, for the most part, may be back to normal but having someone you can work in person with, or swop days entertaining the kids after school will mitigate feelings of loneliness and buy you some uninterrupted time.
Doing this though, will take some upfront conversation about daily habits and honesty about any symptoms of illness or exposure, but with remote work being the future, this might be another way to avoid the WFH isolation.
7. Find a virtual co-work buddy
PHOTO: Pexels
If a Covid pod is not possible, you can still pair up with a colleague and co-work together once a week. Working in tandem albeit virtually on Skype or Zoom will keep you both accountable and focused on completing certain tasks.
If some guidance is needed, try the Pomodoro Technique so there are proper guidelines about when to work and when to zone out and watch some Netflix together.
8. Introduce activities, not just virtual meetings
Instead of keeping everyone a prisoner on Zoom, suggest a weekly or bi-weekly meeting to take place outdoors. Whether it is organised as a catch-up over coffee or a walking brainstorm around Marina Bay at sunset, it’ll inject variety to everyone’s workday, spark new creative ideas and help fight cabin fever.
9. Talk about it
PHOTO: Pexels
Feeling the WFH burnout is not something to be ashamed about. Whether you’re the most junior member of the team or the boss, this is an opportunity to display empathy and encourage others to share their vulnerabilities.
Often, we’ve been told to leave our personal matters at home, but now that the home and office are basically the same thing, it is okay to share the struggles you’re facing.
Work on communicating in a balanced, objective manner (no one enjoys an unhinged rant), ask your colleagues open-ended questions to get them to describe what and how they are feeling… you’ll be surprised at how a simple act of unloading will alleviate stress and forge a closer connection with the rest of your colleagues. | |
Recent research indicates that complex-valued neural networks whose parameters (weights and threshold values) are all complex numbers are in fact useful, containing characteristics bringing about many significant applications.
Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters covers the current state-of-the-art theories and applications of neural networks with high-dimensional parameters such as complex-valued neural networks, quantum neural networks, quaternary neural networks, and Clifford neural networks, which have been developing in recent years. Graduate students and researchers will easily acquire the fundamental knowledge needed to be at the forefront of research, while practitioners will readily absorb the materials required for the applications.
Up to the early 1980s, there were many studies on symbolic processing. I was also engaged in R&D of the Expert shell. Along with the development of Von Neumann-type computers, studies started on information processing different from symbolic processing but similar to that in the human brain. The neural network is one of such processes. Neural network is a network composed of artificial neurons and can be trained to find nonlinear relationships in data. Because there are many introductory references (for example, (Rojas, 1996)), only typical examples are outlined in this Preface. The first study on neural networks was reported by MacCulloch and Pitts in 1943. Stimulated by the results of anatomical and physiological studies, they proposed a network model consisting of a small number of very simple neurons and showed that the model could be used for logical calculations, etc. The original model of the present neural network was proposed by Rosenblatt in 1958 and was called Perceptron. In 1969, Minsky and Perpert showed mathematically that Perceptron cannot solve linearly non-separable problems (Minsky, & Papert, 1969), which requires identifying multi-dimensional data that are mutually interrelated. Perceptron was shown to be applicable only to simple problems. A feedforward neural network is a network in which signals are transmitted only in one direction. Rumelhart, Hinton, and Williams (1986) proposed a learning algorithm called back-propagatioN (BP), which was applicable to multilayer feedforward neural networks (Multilayer Perceptron). Multilayer feedforward neural networks with BP attracted attention as they could solve linearly non-separable problems, which could not be solved by Perceptron. By learning, the multilayer feedforward neural network acquires the ability to generalize. With this helpful ability, the network can output a sort of answer to unlearned patterns. This generalization ability is very useful when using the network in various fields. Hopfield proposed a kind of fully connected recurrent neural network (Hopfield, 1984; Hopfield & Tank, 1985). In fully connected recurrent neural networks, signals are transmitted not only in one direction but also in the opposite direction, and the signals can pass through the same neurons not only once but many times. The operation of the network is very simple. First, an arbitrary neuron is selected, and a simple computation is performed. Then the result of the computation is transmitted to all neurons in the network. Hopfield defined an index for showing the behavior of a fully connected recurrent neural network as a whole and called it energy function. He proved mathematically that the energy function decreases monotone with time and showed that combinational optimization problems could be quickly solved by approximation by using the monotone decreasing characteristic of the energy function. Kohonen (1995) showed that concept formation can be achieved using a neural network. Concept formation means automatic classification of a large amount of data. Two two-dimensional planes installed with two or more neurons are used. One plane is for receiving the input pattern (the input layer), and the other outputs the results (the output layer). The neurons on the input and output layers are weighted with weight parameters. The weight value is modified by Hebbian learning, which involves changing the value of the weight parameter according to the activity of the neuron, and a larger change is made at a higher activity.
The usual real-valued neural networks have been applied to various fields such as telecommunications, robotics, bioinformatics, image processing and speech recognition, in which complex numbers (2 dimensions) are often used with the Fourier transformation. This indicates that complex-valued neural networks whose parameters (weights and threshold values) are all complex numbers, are useful. In addition, in the human brain, an action potential may have different pulse patterns, and the distance between pulses may be different. This suggests that it is appropriate to introduce complex numbers representing phase and amplitude into neural networks. Furthermore, it is obvious that vectors with more than 2 dimensions are used in the real world to represent a cluster of something, for example, a 4-dimensional vector consisting of height, width, depth and time, and an N-dimensional vector consisting of N particles and so on. Thus, a model neuron that can deal with N signals as a cluster, is useful.
Aizenberg, Ivaskiv, Pospelov and Hudiakov (1971) (former Soviet Union) proposed a complex-valued neuron model for the first time, and although it was only available in the Russian literature at the time, their work can now be read in English (Aizenberg, Aizenberg & Vandewalle, 2000). Prior to that time, most researchers other than Russians had assumed that the first persons to propose a complex-valued neuron were Widrow, McCool and Ball (1975). Interest in the field of neural networks started to grow around 1990, and various types of complex-valued neural network models were subsequently proposed. Since then, their characteristics have been researched, making it possible to solve some problems which could not be solved with the real-valued neuron, and to solve many complicated problems more simply and efficiently. From 2001, several special sessions on complex-valued neural networks have been organized in several international conferences (KES, 2001, 2002, 2003; ICONIP, 2002, 2004; ICANN/ICONIP, 2003; IJCNN, 2006, 2008; ICANN, 2007).
There appear to be several approaches for extending the real-valued neural network to higher dimensions. One approach is to extend the number field, i.e. from real numbers x (1 dimension), to complex numbers z = x + iy (2 dimensions), to quaternions q = a + ib + jc + kd (4 dimensions; see chapter 16), to octonions (8 dimensions), to sedenions (16 dimensions), and so forth (Weyl, 1946; Nitta, 1995; Arena, Fortuna, Muscato, & Xibilia, 1998; Pearson, 2003; Nitta, 2005; Buchholz, & Sommer, 2008). In this approach, the dimension of the input signal fed into the neural network is restricted to the form of 2n, n = 1, 2, …, that is, 1, 2, 4, 8, 16, … Another approach is to extend the dimension of the threshold values and weights from 1 dimension to N dimensions using N-dimensional real-value vectors. In this approach, the dimension of the input signal fed into the neural network takes a natural number, that is, N = 1, 2, 3, 4, … Moreover, there are two types of the latter approach: (a) weights are N-dimensional matrices (Nitta, & Garis, 1992; Nitta, 2006), or (b) weights are N-dimensional vectors (Nitta, 1993, 2007; Kobayashi, 2004). Also, there is an approach using hyperbolic numbers (2 dimensions) (Buchholz, & Sommer, 2000; Nitta, & Buchholz, 2008). Hyperbolic numbers, which are closely related to the popular complex numbers, are numbers of the form z = x + uy where x, y are real numbers and u is called unipotent which has the algebraic property that u ? ± 1 but u2 = 1 (Sobczyk, 1995). Quantum neural networks can be viewed as one type of complex-valued neural network (see chapters 13-15).
This book describes the latest developments in the theories and applications of neural networks with high-dimensional parameters which have been progressing in recent years. Graduate students and researchers will easily acquire the fundamental knowledge needed to be at the forefront of research, while practitioners will readily absorb the information required for applications. This book also provides a snapshot of current research and thus serves as a workbench for further developments in neural networks with high-dimensional parameters.
The following four books related to neural networks with high-dimensional parameters have been published: (Arena et al., 1998; Aizenberg et al., 2000; Hirose, 2003; Hirose, 2006). (Arena et al., 1998) was the first monograph on neural networks with high-dimensional parameters, and described the results of research on complex-valued neural networks, vectorial neural networks, and quaternary neural networks. The results of research up to 1997 are well organized in the monograph. The detailed descriptions of the function approximation capabilities of complex-valued neural networks with an analytic activation function and networks with a non-analytic activation function, are excellent. (Aizenberg et al., 2000) is a comprehensive book on the complex-valued neuron models proposed by the authors, and is well organized from theories to applications. (Hirose, 2003) is an edited book which contains fourteen articles on complex-valued neural networks written by various authors. The article on the Clifford neural network written by Pearson is of interest to the complex-valued neural network community. (Hirose, 2006) is a translation of a book in Japanese (Hirose, 2005) that systematically describes complex-valued neural networks in the first half, and application examples obtained by the author’s laboratory in the second half.
It took a long time for mathematicians to accept complex numbers (Ebbinghaus, et al., 1988). During the Renaissance, when complex numbers were first discovered, they were called quantitates impossibiles. They were carefully calculated but were not recognized in mathematics. In the mid 19th century mathematicians finally recognized the real power of complex numbers. Today, physicists do not hesitate to speak of complex numbers as physical targets. Complex numbers appear in Schrödinger’s equation of quantum mechanics and are used in electrical engineering quite naturally. Complex numbers, which were once called quantitates impossibiles, are now firmly established in all fields of natural science and engineering, and scientists and engineers do not hesitate to use them in calculations. Unlike complex numbers, complex-valued neural networks were easily accepted in general. In my experience, I received only several negative comments in 1991 when I first proposed a complex-valued neural network. This quick recognition was likely because studies have focused on the engineering usefulness of complex-valued neural networks. Actually, most studies on complex-valued neural networks have been on engineering applications (usefulness) and were independent from those on the brain. It will be interesting to understand the actual relationships with the neural network of the brain. Neural networks are frequently grouped in soft computing together with evolutionary computation and fuzzy computation. Hybridizing neural networks with high-dimensional parameters with evolutionary computation or fuzzy computation looks promising (Chapter 15 describes an example) for extending the potential of neural networks with high-dimensional parameters. In practice, there are many more study results and fields of application than are described in this book. Initially, this book was to contain 26 chapters, but the number was reduced to 16 for various reasons. It is a pity that we could not include the study on chaos by Nemoto and Saito (2002) and the studies on fractals by Miura and Aiyoshi (2003). For the special issue on complex-valued neural networks of the International Journal of Neural Systems (Rao, Nitta, & Murthy, 2008), for which I served as guest editor, 24 papers were submitted. Special sessions on complex-valued neural networks are also held in many international conferences as described above. We hope that readers all over the world will find this book both useful and enjoyable.
ORGANIZATION OF THE BOOK
The book is divided into three main sections: Complex-Valued Neural Network Models and Their Analysis (chapters 1-6), Applications of Complex-Valued Neural Networks (chapters 7-12), and Models with High-Dimensional Parameters (chapters 13-16).
A brief description of each of the chapters follows.
Chapter 1 applies information geometry to complex-valued Boltzmann machines. The author of this chapter constructs the complex-valued Boltzmann machines, and investigates the structure of the complex-valued Boltzmann manifold. The author also derives an effective learning algorithm, called an em algorithm, for complex-valued Boltzmann machines with hidden neurons. Some important notions of information geometry, exponential families, mixture families, Kullback-Leibler divergence, connections, geodesics, Fisher metrics, potential functions and so on are explained for readers who are unfamiliar with information geometry.
Chapter 2 introduces the complex-valued network inversion method to solve inverse problems with complex numbers. The original network inversion is applied to usual multilayer neural networks with real-valued inputs and outputs, which solves inverse problems to estimate causes from results using a multilayer neural network. Regularization for the complex-valued network inversion is explained, which solves difficulties attributable to the ill-posedness of inverse problems.
Chapter 3 attempts to extend the Clustering Ensemble method and the Kolmogorov’s Spline Network to complex numbers, in the context of adaptive dynamic modeling of time-variant multidimensional data. The chapter is intended to provide an introduction to these subjects and to stimulate the participation of both young and experienced researchers in solving challenging and important problems in theory and practice related to this area.
Chapter 4 describes a complex-variable version of the Hopfield neural network (CHNN), which can exist in both fixed point and oscillatory modes. In the fixed-point mode, CHNN is similar to a continuous-time Hopfield network. In the oscillatory mode, when multiple patterns are stored, the network wanders chaotically among patterns. It is shown that adaptive connections can be used to control chaos and increase memory capacity. Electronic implementation of the network in oscillatory dynamics, with fixed and adaptive connections, shows an interesting tradeoff between energy expenditure and retrieval performance. Some interesting applications are presented.
Chapter 5 presents global stability conditions for discrete-time and continuous-time complex-valued recurrent neural networks, which are regarded as nonlinear dynamical systems. Global asymptotic stability conditions for these networks are derived by suitably choosing activation functions. According to these stability conditions, there are classes of discrete-time and continuous-time complex-valued recurrent neural networks whose equilibrium point is globally asymptotically stable.
Chapter 6 presents models of fully connected complex-valued neural networks which are complex-valued extensions of Hopfield-type neural networks and discusses methods of studying their dynamics. In particular, the author investigates existence conditions of energy functions for complex-valued Hopfield-type neural networks. As an application of the energy function, a qualitative analysis of the network by utilizing the energy function is shown and a synthesis method of complex-valued associative memories is discussed.
Chapter 7 addresses a grey-box approach to complex-valued RBF modeling and develops a complex-valued symmetric RBF (SRBF) network model. The application of this SRBF network is demonstrated using nonlinear beamforming assisted detection for multiple-antenna aided wireless systems that employ complex-valued modulation schemes. Two training algorithms for this complex-valued SRBF network are proposed. The effectiveness of the proposed complex-valued SRBF network and the efficiency of the two training algorithms in a nonlinear beamforming application are demonstrated.
Chapter 8 illustrates the application of various types of complex-valued neural networks such as radial basis function networks (RBFN), multilayer feedforward networks and recurrent neural networks for training sequence-based as well as blind equalization of communication channels. The structures and algorithms for these equalizers are presented and performances based on simulation studies are analyzed, highlighting their advantages and the important issues involved.
Chapter 9 presents the complex backpropagation (BP) algorithm for complex backpropagation neural networks (BPN) consisting of suitable node activation functions having multi-saturated output regions. The complex BPN is used as a nonlinear adaptive equalizer that can deal with both quadrature amplitude modulation (QAM) and phase shift key (PSK) signals of constellations of any size. In addition, four nonlinear blind equalization schemes using complex BPN for M-ary QAM signals are described and their learning algorithms are presented.
Chapter 10 presents new design methods for the complex-valued multistate Hopfield associative memories (CVHAMs). The stability of the presented CVHAM is analyzed by using the energy function approach which shows that in synchronous update mode a CVHAM is guaranteed to converge to a fixed point from any given initial state. Next, a generalized intraconnected bidirectional associative memory (GIBAM) is introduced, which is a complex generalization of the intraconnected BAM (IBAM).
Chapter 11 proposes a method for automatically estimating nuclear magnetic resonance (NMR) spectra of metabolites in the living body by magnetic resonance spectroscopy (MRS) without human intervention or complicated calculations. In the method, the problem of NMR spectrum estimation is transformed into the estimation of the parameters of a mathematical model of the NMR signal. To estimate these parameters, the author designed a complex-valued Hopfield neural network, noting that NMR signals are essentially complex-valued.
Chapter 12 introduces an Independent Component Analysis (ICA) approach to the separation of linear and nonlinear mixtures in the complex domain. Source separation is performed by an extension of the INFOMAX approach to the complex environment. The neural network approach is based on an adaptive activation function, whose shape is properly modified during learning. A simple adaptation algorithm is derived and several experimental results are shown to demonstrate the effectiveness of the proposed method.
Chapter 13 introduces the authors’ qubit neural network, which is a multilayered neural network composed of quantum bit neurons. In this description, it is indispensable to use the complex-valued representation, which is based on the concept of quantum bits (qubits). The authors clarify that this model outperforms the conventional neural networks via computer simulations such as a bench mark test.
Chapter 14 shows the effectiveness of incorporating quantum dynamics and then proposes a neuromorphic adiabatic quantum computation algorithm based on the adiabatic change of Hamiltonian. The proposed method can be viewed as a complex-valued neural network because a qubit operates like a neuron. Next, the performance of the proposed algorithm is studied by applying it to a combinatorial optimization problem. Finally, the authors discuss learning ability and hardware implementation.
Chapter 15 studies neural structures with weights that follow the model of the quantum harmonic oscillator. The proposed neural networks have stochastic weights which are calculated from the solution of Schrödinger's equation under the assumption of a parabolic (harmonic) potential. The learning of the stochastic weights is analyzed. In the case of associative memories the proposed neural model results in an exponential increase of pattern storage capacity (number of attractors).
Chapter 16 describes two types of quaternionic neural network model. One type is a multilayer perceptron based on 3D geometrical affine transformations by quaternions. The operations that can be performed in this network are translation, dilatation, and spatial rotation in three-dimensional space. The other type is a Hopfield-type recurrent network whose parameters are directly encoded into quaternions. The fundamental properties of these networks are presented.
This book provides a snapshot of current research and thus serves as a workbench for further developments in neural networks with high-dimensional parameters.
This collection of research articles on complex-valued neural networks with high-dimensional parameters concentrates on how this technology can find non-linear relationships in data through development processes based on anatomy and physiology. | https://irma-international.org/book/complex-valued-neural-networks/174/ |
Today it is universally known that the brain is the seat of human consciousness and the organ which controls the rest of our body. However, it took our ancestors a very long time to agree on this. Many ancient scholars downplayed the importance of the strange-looking organ within our skulls.
One example of this can be found in the culture of Ancient Egypt. Namely, the Egyptians were known for their pioneering embalming techniques, which placed great emphasis on preserving the heart – it was the only internal organ left inside the mummy. This was because they considered the heart to be the center of emotion and intelligence, while all other organs were considered less important and removed. Most were placed in special canoptic jars. The brain was believed to be among the lowliest of organs, and was discarded – in fact the Egyptians didn’t even have a proper word for it!
This belief was adopted by the famous Ancient Greek philosopher Aristotle, who also considered the heart to be the seat of consciousness, in contrast to his mentor Plato, who claimed it was the brain. Aristotle believed the brain only served as a sort of radiator whose function was to “cool the passions of the heart”. He explained the human brain’s large size to be the result of humans needing large brains to cool their warm hearts. Namely, he also believed that the more complex and rational creatures produced more heat than the simpler ones (e.g. insects were among the coldest, with vertebrates being warmer, and human beings the most complex and therefore the warmest of creatures).
Many other scholars of his time shared his belief, and it was only in the time of Galen (a famous Greek physician who lived in the time of the Roman Empire) that the “heart theory” was definitely relocated to the fringe of science, though many kept believing the center of human emotions was in the heart. Even today we still use expressions like “learn by heart”, “broken heart” etc. | https://history.info/did-you-know/aristotle-believed-human-brain-bodys-radiator/ |
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GIMPS
has discovered a new
largest known prime number
: 2
82589933
-1 (24,862,048 digits)
A titan, as defined by Samuel Yates, is anyone who has found
a titanic prime
. This page provides data on those that have found these primes. The data below only reflect on the primes currently on the list. (Many of the terms that are used here are explained on
another page
.)
Proof-code(s):
L4203
E-mail address:
b
o
i
nc
(at)
basicxp
(dot)
ru
Username:
Azarenko
(entry created on 10/30/2015)
Database id:
4465
(entry last modified on 09/28/2016)
Active primes:
on current list: 1 (unweighted total: 1),
rank by number
542
Total primes:
number ever on any list: 1 (unweighted total: 1)
Production score:
for current list 46 (normalized: 16),
rank by score
309
Largest prime:
191 · 2
3548117
+ 1
(1068092 digits) via code
L4203
on 10/30/2015
Most recent:
191 · 2
3548117
+ 1
(1068092 digits) via code
L4203
on 10/30/2015
Entrance Rank:
mean 105.00 (minimum 105, maximum 105)
Descriptive Data:
(
report abuse
)
Computer science student at Moscow Polytechnical University, Russian Federation.
I am Roman Azarenko and I would like to
Edit this page
Submit primes using the proof-code:
(a password will be required)
(Reuse an old code if your are using the same programs, projects... Only create a new code if you are doing something differently than in the past. Duplicate codes will be merged.)
Surname: Azarenko (used for alphabetizing and in codes)
Unverified primes are omitted from counts and lists until verification completed. | https://primes.utm.edu/bios/page.php?id=4465 |
Every early education program aims at helping students develop a strong reading culture. It is through reading that students learn about the world and expand their knowledge. Reading is also the key to writing and spelling. Unfortunately, not every learner enjoys reading; and it’s not an exception for adult students.
How reading works
Learners usually acquire reading skills at different rates. Reading begins when we master pre-literacy skills, such as enhancing phonemic awareness. During the early years of learning, children are taught how to map sounds to letters and to say the words. As they enter middle school, they are expected to achieve higher milestones of comprehension such as understanding intricate texts and processing a large volume of information within a short period. Being an efficient reader means that you will understand concepts faster than an inefficient reader. As an adult student, speed plays an important part in how well you perform at school.
Common reading difficulties
· Poor comprehension
While you are reading, you should be able to understand the narrative. You need to identify the gist, main message and specific details. If the student is unable to make inferences about what they are reading, chances are that they will not understand the text. As such, they need to go back to basic reading; where they start from letter and word recognition to comprehending the phrase.
· Issues with decoding
This problem is usually seen in young learners. Students who have this problem are unable to put sounds to letters. Although it’s common for one to struggle with new, complex terms, repetition lessens the issue. Children who continue to struggle should find help during their development years. It is the teacher’s responsibility to notice such a child and correct the issue early. If they fail to fix it, and the person grows up struggling with sounds, they might have a difficult time later. | http://educationpotent.com/common-reading-problems-experienced-by-adult-students/ |
Within the framework of trilateral cooperation His Excellency Hamid Karzai President of Islamic Republic of Afghanistan, His Excellency Mahmoud Ahmadinejad, President of the Islamic Republic of Iran and His Excellency Asif Ali Zardari, President of Islamic Republic of Pakistan held the Third Trilateral Summit in Islamabad on 17 February 2012.
The three Presidents pledged to enhance cooperation among the countries comprehensively for realizing the shared aspiration of their peoples for peace, security, stability and economic prosperity.
The three Presidents stressed the need for implementation of the earlier decisions taken at the Trilateral Summits held at Tehran in May 2009 and June 2011 respectively. While underscoring that the three countries were bound by ties of history, geography, culture and religion, the three sides agreed as follows:
i. To develop framework of comprehensive cooperation and to take pragmatic steps for realizing mutually beneficial cooperation to promote stability, peace and shared prosperity.
ii. Ensure respect for sovereignty, independence, unity and territorial integrity, as enshrined in the UN Charter.
iii. To proceed on the basis of mutual interest, mutual respect, non interference and non intervention in internal affairs.
iv. Not to allow any threat emanating from their respective territories against each other. All parties agreed to commence trilateral consultations on an agreement in this regard.
v. Contribute to the development and reconstruction in Afghanistan.
vi. Broaden cooperation in the political, security, economic, cultural, social and educational fields and enhance people to people contacts including exchange visits of parliamentarians, academicians and journalists.
vii. Strengthen cooperation for eradicating extremism, terrorism and militancy and to address the root causes of these menaces, condemning the killings of civilians as well as any kind of assassinations.
viii. Cooperate in combating the problems of narcotic drugs production and trafficking and in combating transnational organized crimes.
ix. Prioritize cooperation for socio-economic development.
x. Enhance three-way trade by facilitation measures, including preferential tariff and free trade arrangements as well as barter trade.
xi. Also expressed commitment to expand trade in transit and encourage the private sector to invest in the three countries.
xii. Enhance connectivity by promoting project cooperation in infrastructure, road and rail links, transport and communications.
xiii. Develop mutually beneficial cooperation in the energy, mining and minerals, agriculture and other sectors.
xiv. Cooperate for the safe, voluntary and early return of Afghan refugees to their homeland in honour and dignity.
xv. Emphasized the need for enhancing their cooperation at international level, especially within the United Nations system.
xvi. Mandated the Foreign Ministers to prepare and coordinate a Road Map for Trilateral Cooperation for submission to the next Summit.
xvii. Also mandated the Interior/Security Ministers to develop a framework of trilateral cooperation particularly in the areas of counter terrorism, counter-narcotics and border management within six months.
xviii. Further mandated the Commerce Ministers to outline steps for enhancing three-way economic cooperation.
xix. Mandated senior officials (Deputy Foreign Minister level) to meet regularly to monitor the implementation of the decisions taken by the Trilateral Summits.
xx. Decided that the Fourth Trilateral Summit shall be held in Kabul by the end of 2012. The exact dates will be communicated through diplomatic channels.
Presidents of the Islamic Republic of Iran and the Islamic Republic of Pakistan reiterated their full support for an Afghan-led and Afghan-owned inclusive process of peace and reconciliation. They assured the President of the Islamic Republic of Afghanistan that they would extend full cooperation and stressed that any initiative in this regard must have authentic Afghan ownership.
His Excellency Mahmood Ahmadinejad, President of the Islamic Republic of Iran and His Excellency Hamid Karzai, President of Islamic Republic of Afghanistan expressed profound gratitude to President Asif Ali Zardari and Prime Minister Yusuf Raza Gilani of the Islamic Republic of Pakistan for the warm hospitality extended to both delegations and for excellent arrangements made for the Third Trilateral Summit.
In witness whereof the Presidents of the three countries have signed this document.
Done in Islamabad on 17 February 2012 in three originals in English, Persian/Dari, all texts being equally authentic.
Hamid Karzai Mahmoud Ahmadinejad Asif Ali Zardari
President of I.R.of President of I.R.of President of I.R. of
Afghanistan Iran Pakistan
Islamabad
17 February 2012
Last modified: November 21, 2019
Our foreign policy is one of friendliness and goodwill towards all the nations of the world. | http://mofa.gov.pk/joint-statement-of-trilateral-summit-islamic-republic-of-afghanistan-islamic-republic-of-iran-and-islamic-republic-of-pakistan-on-a%C2%A2a%C2%ACaenhancing-trilateral-cooperationa/ |
By Philip C. Kendall
This e-book discusses the foundation of thoughts, predicting melancholy, and attributional bias in competitive childrens. The context goodness of healthy version of adjustment, position of cognition in behavioral medication, elaboration probability version of persuasion, and private constructs in medical perform also are deliberated during this textual content.
This e-book is efficacious to researchers and clinicians interested in cognition and behavior.
Read Online or Download Advances in Cognitive—Behavioral Research and Therapy: Volume 4 PDF
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FIELD OF THE INVENTION
BACKGROUND OF THE INVENTION
OBJECT OF THE INVENTION
DETAILED DESCRIPTION OF THE INVENTION
The present invention relates to the installation of seats in enclosed spaces, such as performance spaces, sports halls, etc., where the option is needed to be able to change the seating arrangements, such that the seats may be arranged, wholly or in part, in a position of use on the floor of the enclosed space or in a concealed position such that the surface of the floor is clear.
In enclosed spaces which include seating installations which it would be useful to be able to arrange in a position of use or to remove so that the enclosed space is partially or totally clear, solutions are already known in which the seats are stowed away under a raised access floor.
The existing solutions of this type are nonetheless of very complex configuration and require a cavity or pit of considerable height underneath the raised access floor, which makes it necessary to reduce the useful height of the enclosed space. In addition, to support the raised access floor structures are required which increase costs considerably.
The invention proposes an installation which enables the seats in an enclosed space to be cleared away in a position under the floor where they take up only a little height, so advantageously overcoming the disadvantages of the conventional installations used in this way.
With the installation according to the invention, low pillars are arranged over the base floor of the enclosed space in which it is to be used, there being fitted on said pillars swivellably mounted seat assemblies and, in turn, also swivellably mounted covering flaps, by means of which a raised access floor is formed, underneath which the seat assemblies may be concealed in a lowered position.
The seat assemblies are preferably arranged on a load-bearing structural beam, which is connected to a number of pillars of the installation by means of respective arms articulated thereto with the possibility of swivelling, with manual or motorised actuation, between a raised seat position and a lowered seat position, cylinders of gas being provided to assist in the swivelling movements and to prevent abrupt shocks.
Furthermore, each seat assembly has one or more locking devices, by means of which the seats are locked in the raised position, all the locking devices of each seat assembly being connected for simultaneous unlocking actuation thereof to lower the seats.
Articulation of the arms of the seat assembly support structure to the pillars of the installation is achieved with an arrangement which is displaced laterally with regard to the longitudinal axis of said arms, this resulting, upon lowering of the seat assemblies, in a position which allows the system to be compact with minimal space between the rows of seats as well as enabling the seat assemblies to be lowered into a position which allows the covering raised access floor to be at the lowest possible height.
The flaps which cover the seats when concealed in the lowered position are in turn articulated to the pillars of the installation, said flaps having a number of independent parts fixed to the mounting pillars, in association with which fixed parts said flaps form a number of recesses which enable swivelling between a raised position and a lowered position of the above-mentioned flaps, while the fixed parts in turn have a zone capable of swivelling, which zone allows passage of the arms providing swivelling mounting of the corresponding seat assembly for swivelling said assembly into the raised position.
In the lowered position the covering flaps together form a raised access floor, through which may extend the arms of the support structure for the seat assemblies in the raised position, said flaps forming a free, clear surface when the seat assemblies are lowered into the stowed position underneath, wherein the successive flaps may be continuously flush, if the installation is mounted on level floors, or indeed staggered to form a stepped surface, if the installation is mounted on inclined floors.
Furthermore, seat assemblies mounted swivellingly on the associated pillars, and the respective covering flaps, may be arranged in modular blocks capable of being mounted as a whole in the installations used, wherein said modular blocks may be incorporated into raised structures, so that the seats may be situated at selected heights for use, for example to form tiers of stepped seats.
In any case, swivelling of the seat assemblies and of the flaps that make up the raised access floor between their respective lowered and raised positions may be brought about by manual actuation, but automatic actuation may also be provided, by means of any system that allows said swivelling of the seat assemblies and of the flaps to be actuated in automated manner.
All in all, the installation of the invention gives rise to a number of features which are definitely advantageous, it being suitable and preferred for the application for which it is intended.
The invention provides a seating installation for enclosed spaces that require the possibility of arranging the seats in a position of use and of clearing them away such that the surface of the floor is clear, of the type that allows the seats to be concealed under a raised access floor.
1
1
2
3
4
In the case of the recommended installation, the seats () belonging thereto are arranged in assemblies of several seats () fitted on a structural supporting beam (), said assemblies being mounted in articulated manner on an arrangement of low pillars () fixed to the base floor () of the relevant enclosed space.
1
3
5
2
5
3
6
The seat assemblies () are mounted on the pillars () by means of a number of arms () which are firmly connected to the structural beam (), said arms () being connected to the corresponding mounting pillars () by means of an articulation ().
1
6
5
3
7
In this arrangement, each seat assembly () may swivel between a lowered position and a raised position, pivoting on the articulations () of the arms () relative to the pillars (), a number of gas cylinders () being provided to assist with the raising and lowering movements, these additionally cushioning the final strokes of said movements so as to prevent abrupt shocks.
1
8
9
10
1
11
12
11
1
1
12
11
8
FIGS. 9 and 10
In conjunction with this swivelling mounting of the seat assemblies (), there are provided () a number of devices taking the form of a catch () which is urged to move forwards by a spring () via a lever (), while, associated with the load-bearing structure of the seat assembly (), there is provided a link () provided with an orifice () at one end, said link () moving together with the seat assembly () during the swivelling movement, such that, in the raised position of the seat assembly (), the orifice () in the link () faces the catch ().
1
8
12
11
1
1
In this way, when the seat assembly () is situated in the raised position, the catch () enters the orifice () in the link (), so bringing about locking, which ensures that the seat assembly () is held in said raised position, which is the position of use, preventing said assembly from being able to swivel accidentally downwards as a result of the forces exerted on the seats () by users.
10
8
11
1
Through action on the lever (), the catch () may move backwards, releasing the lock relative to the link (), the result being that the corresponding seat assembly () becomes free and is thus able to be swivelled into the lowered position.
1
3
1
10
13
10
1
Each seat assembly () may have one or more locking devices, one locking device preferably being provided on each mounting pillar () so as reliably to ensure that the seat assembly is held in the raised use position. All the locking devices of each seat assembly () are arranged, in such a case, with their levers () connected by means of a bar (), such that acting on the lever () of any one of the locking devices brings about actuation of all of them so as to release the seat assembly () in order to be able to swivel it downwards.
3
1
14
15
On the actual pillars () for mounting the seat assemblies () there are in turn mounted by means of corresponding articulations () a number of flaps (), which can likewise swivel between a lowered position and a raised position.
15
3
1
In the lowered position, said flaps () form a raised access floor on the pillars () of the installation, underneath which are stowed the seat assemblies () when said assemblies are in the lowered position, such that in this position the surface of the floor of the enclosed space is totally clear.
FIGS. 2 to 5
15
1
1
1
15
1
As shown in the series of , raising the flaps () opens up the space for stowing the corresponding seat assemblies (), it then being possible to swivel said assemblies into the raised position for use of the seats (), such that, when the seat assemblies () are in said raised position, the flaps () may swivel back into the lowered position, in which the floor is closed, the supports for the seat assemblies () projecting therethrough, said seat assemblies thus being in the position of use above the closed floor.
FIGS. 2 to 5
6
5
3
5
1
5
6
1
1
15
4
As is shown in the same , the point of articulation () of the arms () on the pillars () of the installation is displaced laterally relative to the longitudinal axis of said arms (), such that, when the seat assemblies () are in the lowered position, the end of the arms () is positioned below the respective articulation point (), so resulting in an arrangement which allows the system to be compact, with minimal space separating the rows of seats () of the installation, and the seat assemblies () to be so situated in the lowered position that the covering raised access floor made up of the flaps () is positioned at a minimal height relative to the base floor ().
3
15
16
3
15
17
15
3
FIGS. 6 to 8
In the associated areas of the pillars (), the flaps () have independent parts () which are fastened fixedly to the above-mentioned pillars (), in such a way that in said areas the flaps () define a number of recesses (), thanks to which the flaps () may swivel on the pillars () without obstacles arising thereon which would impede said swivelling, as may be seen from the series of .
16
15
18
5
1
1
5
18
5
1
18
FIGS. 11 to 13
FIGS. 6 and 11
The above-mentioned fixed parts () of the flaps () nevertheless have a number of zones () which are capable of swivelling, in association with the position of the arms () of the support structure of the seat assemblies (), such that, when said seat assemblies () are swivelled into the raised position, the arms () force the above-mentioned zones () to swivel, said arms () thus being able to move out into the raised position as shown in the series of , whereas, when the seat assemblies () are in the concealed position beneath the raised access floor, said zones () remain lowered, forming a totally closed surface of the raised access floor, as shown in .
4
15
1
4
15
FIG. 14
FIG. 15
The installation formed in this way may be arranged on a horizontal base floor (), in which case the flaps () that form the raised access floor for stowing away the seat assemblies () therebelow form a continuous flush surface, as shown in ; however, it is also possible, without modifying essential features, for the installation to be arranged on an inclined base floor (), in which case the flaps () that form the raised access floor may define a stepped surface of horizontal sections, as shown in .
1
3
15
An embodiment is also provided in which the seat assemblies (), together with the associated mounting pillars () and the respective flaps (), take the form of modular assemblies in the manner of structural units, which facilitate mounting of the installation, since it is merely necessary to position said modular assemblies at the sites at which the installation is to be located, it being possible to incorporate the modular assemblies into raised structures so as to adapt the height of the installation as convenient, for example to form stepped tiers of seats capable of being arranged in the position of use or of being cleared away in a concealed arrangement.
1
15
1
15
In any case, the swivelling arrangement of the seat assemblies (), as well as of the flaps (), for movement between the respective lowered and raised positions, may be achieved by mounting with manual actuation, but an arrangement with automatic actuation may also be provided, using any motorised, pneumatic or hydraulic system, or any other currently existing system, which permits automation of said swivelling movements of the seat assemblies () and of the flaps ().
DESCRIPTION OF THE FIGURES
FIG. 1
is a side view of the arrangement of a group of seats in the lowered position, according to the invention.
FIG. 2
is a sectional view on a smaller scale of the arrangement of the previous Figure.
FIG. 3
is a sectional view of the same arrangement, with the covering flap partially raised.
FIG. 4
is a view of the same arrangement, with the flap and the seat assembly in the raised position.
FIG. 5
is a view of the same arrangement, with the seat assembly raised and the flap lowered.
FIG. 6
is a perspective view of the assembly of the previous arrangement, with the flap raised and the seats lowered.
FIG. 7
is a perspective view of the previous assembly with the seats partially raised.
FIG. 8
is a perspective view of the same previous assembly with the flap and the seats in the raised position.
FIG. 9
FIG. 7
shows an enlarged detail of the zone IX indicated in .
FIG. 10
FIG. 8
shows an enlarged detail of the zone X indicated in .
FIG. 11
is a perspective view of the articulated structure supporting seats on a pillar of the installation, with the seat support in the lowered position.
FIG. 12
is a perspective view of an assembly like the previous one, with the seat support partially raised.
FIG. 13
is a perspective view of the same previous assembly with the seat support in the raised position.
FIG. 14
is a partial view of a series of seat assemblies in an installation situated on a horizontal floor.
FIG. 15
is a partial view of a series of seat assemblies in an installation situated on an inclined floor. | |
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Report The Forrester Banking Wave™: Indian Mobile Apps, Q2 2019
While Evolving New Functionality, Focus On Usability TooMay 30, 2019 | Arnav Gupta, Amit Bhatia
Mobile apps have become the touchpoint of choice for millions of Indians to manage their finances. Digital banking teams need to build mobile banking experiences around customer needs, empowering... | https://www.forrester.com/search?searchOption=10001&N=10001+25015+20490+35017+200509&tmtxt= |
Itinerary | Arrival information | Things to do | Diving & Snorkeling in Sipadan | My first dive | Departure to Tawau
All the while, I don’t dare to dive into deep water, I am worry that I am not able to breathe normally underwater. Since I experienced snorkeling in Sipadan, I decided to give scuba diving a try. Hence, I joined the Discovery Scuba Dive in Mataking Dive Centre.
Since there are only 2 days left on the island, so I am only able to join Discovery Scuba Dive. My dive instructor, Dan, prepared all the necessary diving equipment and explained the basic information of diving to me. After passed a simple test, he brought me to a shallow area to learn 3 diving skills, “clear air in regulator”, “find regulator” and “clear mask underwater”. Dan is a very patient instructor, he demonstrates again and again just to show me and explain to me the proper way of diving. After several attempts, I passed the technical test and able to follow a rope to dive deep into the water. I dived into the deep water at 10m, the feeling of diving and snorkeling is completely different. I managed to see a lot of fish species and such experience is so fantastic until I forget how nervous I am in the beginning.
This Discovery Scuba Diving experience is absolutely great, I am not that nervous while in underwater now and also convinced myself to get an open water diver course. Any recommended diver course in Singapore or Malaysia? | https://www.holidaygogogo.com/luxury-retreat-in-mataking-reef-resort-my-first-discovery-dive/ |
As the 250th anniversary of the birth of Ludwig van Beethoven (1770-1827) approaches, it is a good time to get in the celebratory spirit by answering some FAQs. A warning, though: behind every seemingly straightforward answer, there are always more questions! 1. What editions should I use? Simple answer: There are excellent Urtext editions av...
A Place in the Sun: Recent Editions of Beethoven's Piano Sonatas
Tags:
There have been numerous collected editions of Chopin's music since his death, and few of them agree on anything. Why is this? The answer lies principally in the complexity of the source tradition, and I include under that heading both manuscript and early printed sources. It may be helpful to attempt a rough classification of these sources. Sketch... | https://www.claviercompanion.com/article-details/tags/editions |
Check Eligibility Criteria For JEE Advanced
The second phase of IIT JEE is the JEE Advanced exam. The top 2,50,000 JEE Main candidates will be shortlisted by the exam conducting authority to appear for the JEE Advanced. Candidates are recommended to check the detailed information on the eligibility criteria published by the exam conducting authority. This helps them to get a clear understanding of important details such as age limit, number of attempts, nationality, marks percentage, etc.
In 2021, the JEE Advanced is expected to be conducted on 3, October. Before filling the application form, students are advised to understand the JEE Advanced eligibility criteria. This will help students to check whether they are eligible for the exam or not. The application of those candidates who do not meet the eligibility criteria will be rejected. Since JEE Advanced is considered a difficult exam, proper preparation and hard work are required to score a high rank in this exam.
IIT JEE Advanced 2021 Eligibility Criteria
The JEE Advanced eligibility criteria, released by the IIT Kharagpur is available on the official website. Following are some of the eligibility criteria.
- Age limit
- Nationality
- Marks percentage
- Number of attempts
Students who are born on or after the 1st of October 1996 are eligible. Age relaxation of 5 years is provided for those belonging to the reserved category. Students who are Person of Indian origin (PIO), the citizen of India, Foreign nationals and OCIs (Overseas Citizen of India) are eligible to appear for the JEE Advanced exam. The number of attempts is two. Percentage-wise reservations are there for different categories. For the Open category, the percentage is 46.5.
The eligibility criteria on the basis of 12th-grade exams are as follows.
- Students appearing for the 2021 board exams are eligible for the JEE Advanced.
- Candidates who have cleared class 12th board exams or any other equivalent exam in 2020 are eligible for the JEE Advanced.
- A minimum of 75% of marks (12th board exam) is mandatory for the students belonging to the general category.
- A minimum of 65% of marks (12th board exam) is mandatory for the candidates belonging to SC, ST, and PWD categories.
- There is no reservation of seats for foreign nationals under any categories as directed by the Govt. of India.
JEE Advanced Exam Pattern
Before preparing for the JEE Advanced exam, students should be familiar with the JEE Advanced exam pattern. The exam conducting body publishes the exam pattern. Usually, the JEE Advanced question paper is quite tough and tricky. The exam is designed to judge not only the theoretical knowledge but also the comprehension skills, reasoning ability, and analytical power of the candidates. Hence, it is important to have a clear understanding of the exam pattern.
The question paper contains MCQs with one or more correct answers, numerical value answer type questions, and paragraph-based questions. There are 2 papers (paper 1 and paper 2) for the JEE Advanced exam. Students have to appear for both papers. Students will get questions from Physics, Chemistry, and Mathematics. Students are advised to go through the previous year’s question papers so that they can get more information about the exam pattern. | https://digitalmedianew.com/check-eligibility-criteria-for-jee-advanced/ |
What is cost-effectiveness analysis?
This type of study measures whether adopting the new diagnostic provides value for money. The analysis measures the cost of adopting the new diagnostic relative to the potential benefits to the patient and the healthcare system.
When should cost-effectiveness analysis be done?
For this type of analysis we require the developers to have a CE marked product and data to demonstrate the diagnostic accuracy of the test.
What we do
We perform cost-effectiveness analysis of the developer’s diagnostic and compare this to current practice. This work requires knowledge of the care pathways and a systematic literature review to collect the values for the analysis. We will also perform sensitivity analysis to characterise decision uncertainty.
We will:
- Develop the decision problem and health economics analysis plan
- Collect values to use in the analyses
- Analyse and communicate the results
Look at the impact posts below for examples of our cost-effectiveness analysis work. | https://newcastle.mic.nihr.ac.uk/expertise/evaluation-themes/health-economics-evidence-development/cost-effectiveness-analysis/ |
Each of the layers’ wooden puzzle focuses on a different system that exists within the human body (skeletal, respiratory, digestive, muscular, and integumentary/skin). This will improve kids’ imagination ability, practical ability, and cognitive ability.
This promotes hand-eye coordination and fine motor skills as your toddler will concentrate to place the pieces in all its proper places. The Puzzles are made of Non-toxic finishes and child safe materials. | http://www.momandmilly.com/product/body-structure-puzzle/ |
Published by George Slater, London, UK. No date but 1850. First edition in English. Original red cloth gilt. Size: 10.4cm x 13.8cm. pp. 201 + 2 pp ads. A novel. One of ‘Slater’s Universal Series’. Sand is recognised as being one of the most notable writers of the European Romantic era but also gained notoriety for wearing men’s attire in public and smoking, neither of which had been sanctioned in France at the time. Victor Hugo would observe: “George Sand cannot determine whether she is male or female. I entertain a high regard for all my colleagues, but it is not my place to decide whether she is my sister or my brother.” (Source: Wikipedia) Cloth very slightly dulled and rubbed to the spine. A near fine, bright, clean copy. Very scarce. | https://hornseys.com/product/the-uscoque-a-venetian-story/ |
These four honey face mask recipes use different additional ingredients, based on your skin type. They are all made with food-based ingredients that are probably in your kitchen right now. I love skincare you can eat! And the raw honey face mask is one of my favorite homemade recipes. Raw honey was prized for its healing properties in ancient civilizations.
Add 1 teaspoon honey and 1 teaspoon coconut oil and mix thoroughly. Using clean fingers, apply a thick coat of this mixture onto your face. Sit for fifteen minutes while you let the mask do its work. You can use this time to soak in a bath or get lunch ready. When the time is up, gently scrub off the mask using warm water. Pat dry with a towel. Enjoy the silky new feel and look of your moisturized skin!
I noticed once at a club last year. She barely missed being bounced off the floor only because it was in another country. Idgaf if they look, but at some point it was blatantly disrespectful to me. He saw her but doesn't care. However, she saw we were together and continued to keep trying to get his attention. She was about to get mine. | https://yngvethoresen.com/public-masturbation/3937.php |
White Witch Cauldron Mug
This brilliant white mug is designed to look like a cauldron and features the words 'White Witch'.
White magic has traditionally referred to the use of supernatural powers or magic for selfless purposes.White magic was practiced through healing, blessing, charms, incantations, prayers, and songs.
Suitable for microwave or dishwasher use. | https://folio-gothichippy.com/white-witch-cauldron-mug-17954-p.asp |
3DPersonnel’s client, a Consulting Engineering company are seeking to employ a BIM / CAD Technician for our South County Dublin office.
Qualifications:
Recognised formal training courses in AutoCAD and Revit supported by an Appropriate Certificate and or Diploma.
Requirements:
The candidate should possess excellent communication skills and have at least 2 years’ experience acting in the roles of BIM/AutoCAD Technician within a team of technicians and engineers and hold a recognised qualification in BIM.
Responsibilities:
Follow BIM / CAD content standards and development procedures, BIM MEP Modelling. Adhere to BIM Execution Plan and BIM project workflow criteria, AutoCAD MEP, drawing production, clash detection and resolution.
Preference:
Preference will be given to candidates fulfilling the above requirements and who can demonstrate a working experience of Revit and AutoCAD software within the MEP field.
Roles and responsibilities:
- Develop, implement and maintain the BIM Protocol and BEP
- Ensure all stakeholders are in alignment with the BIM Protocol and BEP.
- Create and maintain a BIM Coordination Programme that is aligned with the Project Programme.
- Identify any impact on the BIM Coordination Programme arising from errors in the transmission and use of information during the BIM process.
- Establish BIM Coordination workshops and report progress at the Project Design Team meetings.
- Keep a record of BIM models and their status. | https://www.3dpersonnel.com/job/bim-slash-cad-technician/ |
The concept Slavery in literature represents the subject, aboutness, idea or notion of resources found in Bowdoin College Library.
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Slavery in literature
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The concept Slavery in literature represents the subject, aboutness, idea or notion of resources found in Bowdoin College Library.
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- Slavery in literature
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- American slaves in Victorian England : abolitionist politics in popular literature and culture
- Apocalyptic sentimentalism : love and fear in U.S. antebellum literature
- Bernard Shaw : Slaves of Duty and Tricks of the Governing Class
- Between the lines : literary transnationalism and African American poetics
- Black imagination and the Middle Passage
- Bound to respect : Antebellum narratives of black imprisonment, servitude, and bondage, 1816-1861
- Caryl Phillips, David Dabydeen and Fred D'Aguiar : representations of slavery
- Characters of blood : black heroism in the transatlantic imagination
- Charles Johnson's novels : writing the American palimpsest
- Counterlife : slavery after resistance and social death
- Debating the slave trade : rhetoric of British national identity, 1759-1815
- Democratic discourses : the radical abolition movement and antebellum American literature
- Domestic abolitionism and juvenile literature, 1830-1865
- Dreams for dead bodies : blackness, labor, and the corpus of American detective fiction
- El intersticio de la colonia : ruputura y mediación en la narrativa antiesclavista cubana
- Empire and slavery in American literature, 1820-1865
- Empire of ruin : black classicism and American imperial culture
- Exhibiting slavery : the Caribbean postmodern novel as museum
- Fathering the nation : American genealogies of slavery and freedom
- Fictions of the Black Atlantic in American foundational literature
- Figures in black : words, signs, and the "racial" self
- Freedom in a slave society : stories from the antebellum South
- Gender and race in antebellum popular culture
- Gender issues in African literature
- Gendered resistance : women, slavery, and the legacy of Margaret Garner
- Ghosts of slavery : a literary archaeology of Black women's lives
- Hard facts : setting and form in the American novel
- Haunted property : slavery and the gothic
- Hell hath no fury : gender, disability, and the invention of damned bodies in early Christian literature
- Her voice will be on the side of right : gender and power in women's antebellum antislavery fiction
- History, abolition, and the ever-present now in antebellum American writing
- Laughing fit to kill : black humor in the fictions of slavery
- Mark Twain's Pudd'nhead Wilson : race, conflict, and culture
- Martin Delany, Frederick Douglass, and the politics of representative identity
- Modernity disavowed : Haiti and the cultures of slavery in the age of revolution
- Mothering across cultures : postcolonial representations
- Narrating the slave trade, theorizing community
- Nat Turner : a troublesome property
- Nat Turner before the bar of judgment : fictional treatments of the Southampton slave insurrection
- Neo-slave narratives : studies in the social logic of a literary form
- Novel bondage : slavery, marriage, and freedom in nineteenth-century America
- Postcolonial narrative and the work of mourning : J.M. Coetzee, Wilson Harris, and Toni Morrison
- Race and time : American women's poetics from antislavery to racial modernity
- Race mixture in nineteenth-century U.S. and Spanish American fictions : gender, culture, and nation building
- Race, citizenship, and law in American literature
- Race, slavery, and liberalism in nineteenth-century American literature
- Reading Toni Morrison's 'Beloved' : a literature insight
- Reaping something new : African American transformations of Victorian literature
- Representing the body of the slave
- Rethinking Uncle Tom : the political philosophy of Harriet Beecher Stowe
- Romantic ecologies and colonial cultures in the British Atlantic world, 1770-1850
- Romantic reformers and the antislavery struggle in the Civil War Era
- Romanticism and slave narratives : transatlantic testimonies
- Sacraments of memory : Catholicism and slavery in contemporary African American literature
- Satire or evasion? : Black perspectives on Huckleberry Finn
- Searching for Jim : slavery in Sam Clemens's world
- Slavery and the Roman literary imagination
- Slavery and the Roman literary imagination
- Slavery and the politics of place : representing the colonial Caribbean, 1770-1833
- Slavery in American children's literature, 1790-2010
- Slavery on trial : law, abolitionism, and print culture
- Slavery, philosophy, and American literature, 1830-1860
- Slaves and slavery in ancient Greek comic drama
- Slaves to Rome : paradigms of empire in Roman culture
- Slaves, masters, and the art of authority in Plautine comedy
- Something akin to freedom : the choice of bondage in narratives by African American women
- Spectacular Suffering : Witnessing Slavery in the Eighteenth-Century British Atlantic
- Spectres from the past : slavery and the politics of history in West African and African-American literature
- The "tragic mulatta" revisited : race and nationalism in nineteenth-century antislavery fiction
- The Algerine captive; or, The life and adventures of Doctor Updike Underhill: six years a prisoner among the Algerines. : [Three lines from Shakespeare] : Vol. I[-II]. : Published according to act of Congress
- The Cambridge companion to slavery in American literature
- The Edge of Modernism : American Poetry and the Traumatic Past
- The French Atlantic triangle : literature and culture of the slave trade
- The archive of fear : white crisis and black freedom in Douglass, Stowe, and Du Bois
- The captive woman's lament in Greek tragedy
- The collected writings of Edward Rushton (1756-1814)
- The death-bound-subject : Richard Wright's archaeology of death
- The fugitive's properties : law and the poetics of possession
- The logic of slavery : debt, technology, and pain in American literature
- The making of racial sentiment : slavery and the birth of the frontier romance
- The origins of African American literature, 1680-1865
- The poetics and politics of the American Gothic : gender and slavery in nineteenth-century American literature
- The slave in the swamp : disrupting the plantation narrative
- The slave's rebellion : literature, history, orature
- The trickster comes west : Pan-African influence in early Black diasporan narratives
- The war on words : slavery, race, and free speech in American literature
- Toni Morrison's Beloved and the apotropaic imagination
- Transatlantic Stowe : Harriet Beecher Stowe and European culture
- Transnational black dialogues : re-imagining slavery in the tTwenty-first century
- Uncle Tom's cabin : evil, affliction, and redemptive love
- Uncle Tom's cabins : the transnational history of America's most mutable book
- Untimely democracy : the politics of progress after slavery
- What is African American literature?
- Whose Antigone? : the tragic marginalization of slavery
- William Blake and the impossible history of the 1790s
- Women in chains : the legacy of slavery in Black women's fiction
- Women in chains : the legacy of slavery in Black women's fiction
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Magnetic resonance imaging uses magnetic fields and radio waves to form images of the body. These images can be used to diagnose a wide variety of health conditions, making reading these images a critical part of a radiologist’s training. Sometimes, structures appear in the MRI imaging that is not anatomically present. These artifacts can mimic pathologies, leading to improper diagnoses. Learning to recognized common artifacts and how to avoid them improves the diagnostic properties of MRI.
Artifacts can be categorized into three main types. Physiologic artifacts are caused by patient movement, including breathing, heartbeat, and blood flow. Artifacts can arise from the inherent physics of the MRI, such as the presence of metal or chemical shift. Finally, the hardware and software involved in constructing MRI images can cause artifacts.
Physiologic artifacts
Patient motion – intentional or not – cause artifacts on the MRI image. Motion artifacts typically show up as blurring or ghosting, especially in the phase-encoding direction. Recognizing that these ghost images are due to motion can help radiologists diagnose patients more accurately.
Because motion can make the images harder to read, patients should be advised to hold still during the exam. Make sure the patient is comfortable prior to beginning the sequence, and advise them when it is especially important remain still. You may need antispasmodic medications for some patients.
All patients will continue to breathe, have heartbeats, and blood flow during the exam. This periodic motion cannot be avoided, and can cause artifacts. Using faster sequences and respiratory-ordered phase encoding can help eliminate artifacts, as can navigator echo gating to track the motion of the diaphragm to time image acquisition.
Flow artifacts are also common, especially in gradient echo (GRE) sequences. Due to the nature of GRE sequences, blood flow will produce a bright signal. Using saturation bands can minimize this artifact, saturating the slice upstream so the blood will not produce a signal. Gradient moment nulling can also be applied to try to correct flow artifacts.
Inherent physical artifacts
Chemical-shift artifacts occur during the frequency encoding of the MRI process. Fat and water molecules oscillate differently within the magnetic field, causing them to show up differently during the encoding. This causes a black or bright band at the edge of the anatomy, and can sometimes be misinterpreted as pathology. Increasing the bandwidth, reducing the matrix size, or suppressing the fat-frequency signal can all minimize this artifact.
Magnetic susceptibility artifacts can occur when a patient has an implant or medical device in the MR room that responds to the magnetic field. These materials cause the image to have bright areas and dark areas near the magnetic object that are not anatomically correct. While this effect can be reduced by avoiding gradient echo sequences, occasionally this type of artifact can be useful in diagnosing patients, such as in the detection of hematomas. When used in certain circumstances these artifacts can enhance the image quality.
Hardware and software artifacts
Zipper artifacts can cause noise on the image, making it difficult to read. These occur when something in the environment interferes with the MRI unit, such as devices in the MR room, blinking light bulbs, the door not being securely shut, or nearby construction. Removing the source of interference should eliminate the artifact. MR rooms are typically isolated and strictly controlled to minimize the chance of interference.
While there are many types and causes of artifacts, being able to identify them and minimize their effects helps radiologists make proper diagnoses. Patient movement, the inherent aspects of MR imaging, and contamination are the most common sources of artifacts in MRI images.
Have MRI questions? Please contact Aston Diaz at 212-366-9100 x110 or [email protected]
Some blogs you may have missed:
- Your MRI and Cryogen Venting
- 8 Channel MRI vs. 4 Channel MRI—What is the Difference?
- The Growing Need for MRI in Veterinary Medicine
- Before You Order That MRI: A Checklist
- Used CT & MRI Trade-ins: Get a Bang for Your Buck! | https://info.atlantisworldwide.com/blog/artifacts-in-mri |
Before Auckland-born Vicki Jeffels, otherwise known as VegemiteVix, was named as one of the UK's top 25 expat mum bloggers, she was to be wooed by her British husband in the so-called romantic Lake District.
7:30 The Sampler
A weekly review and analysis of new CD releases.
8:15 Windows on the World
International public radio documentaries - visit the Windows on the World web page to find links to these documentaries.
8:40 The World At Night: Russia
Managing director of the Trans-Siberian Experience, Neil McGowan is our British-born Moscow-based expert on Russia and classical music... everyday Russians are still protesting for government reform, and a falling satellite is a setback to the Russian space programme.
9:00 News and Weather
9:06 The Tuesday Feature: Smart Talk - Water Crisis
This final edition of Smart Talk from the Auckland Museum focusses on the issue of water sustainability and how we use our country's waterways.
10:00 News and Weather
10:17 Late Edition
A review of the leading news from Morning Report, Nine to Noon, Afternoons and Checkpoint. Also hear the latest news from around the Pacific on Radio New Zealand International's Dateline Pacific.
11:06 Best of WOMAD Taranaki 2011: All-Stars Gala
The gala is a tradition of the Womad festival that brings together many of the artists and their diverse musical styles on the final night.
The resulting fusion of sounds and rhythms is unique to every festival and every performance. UK artist and producer Nitin Sawhney was this year’s music director and creative juggler, bringing together performers from 17 Hippies, Faiz Ali Faiz, Horace Andy and New Zealand’s own Sola Rosa. | https://www.rnz.co.nz/national/programmes/nights/20120124 |
"The House That Haunted Batman!": Batman checks up on Rupert Thorne, who now occupies a padded cell at Arkham Asylum. Batman is concerned as to why Thorne gave away all his plans and revealed his information, clearing Batman's name in
Appearing in "The House That Haunted Batman!"
Featured Characters:
- Batman (Flashback and main story)
Supporting Characters:
- Commissioner Gordon (Flashback and main story)
Villains:
- Clayface III (First appearance)
- Doctor Tzin-Tzin (Flashback only)
- Tzin-Tzin's Deadly Dozen (Flashback only)
- Fong Wu (Flashback only)
Other Characters:
- Rupert Thorne
- Alfred Pennyworth (Flashback only)(as an illusion only)
- Superman (Flashback only)(as an illusion only)
- Robin (Flashback only)
- Flash (Flashback only)(as an illusion only)
- Green Arrow (Flashback only)(as an illusion only)
- Martian Manhunter (Flashback only)(as an illusion only)
- Hawkman (Flashback only)(as an illusion only)
Locations:
Items:
Vehicles:
Synopsis for "The House That Haunted Batman!"
Batman checks up on Rupert Thorne, who now occupies a padded cell at Arkham Asylum. Batman is concerned as to why Thorne gave away all his plans and revealed his information, clearing Batman's name in the process and a clearly deranged Thorne explains that he was forced by the ghost of Hugo Strange, a man he killed on his quest to learn Batman's secret identity.
Commissioner Gordon and Batman leave the madman to himself and they reflect upon the current situation. While Gordon pities the once notorious gangster, Batman feels sympathy, as he was once tricked by another formidable enemy, making him believe that he had lost his mind.
This story is reprinted from Detective Comics #408.
Robin has gone missing and Batman sets out to find him in a decrepit old house; a place which appeared on the outskirts of Gotham City as sudden as Robin's disappearance.
As Batman enters deeper into the place, he shouts Robin's name, hoping that his young sidekick would answer his call. A few moments later, Batman is startled by the standing figure of Robin at the end of a long hallway. Batman runs to his young partner and once he is within reach, Robin collapses, forcing Batman to stop his fall with his arms. Batman takes a closer look at his partner and he is extremely shocked to see Robin aging at an inhuman speed until he becomes ashes in Batman's hands.
Suddenly, a raging scream breaks the silence of the abandoned house and Batman follows the source of the appalling sound, spawned from the darkest confines of the mansion. Opening a door in the upper floor, Batman is swarmed by a cloud of bats, but he contines his search despite the harrowing scenario until he finds the room form which the shriekings are coming. Once inside, Batman finds that it is all coming from a gramophone and just as he stop the record, he is attacked by an unknown assailant, who instantly runs away. Batman gives chase to the attacker, who is armed with a gun and is shooting backwards as he escapes, aiming at Batman. Dodging the bullets, Batman finally manages to corner the attacker in one of the mansion's hallways, but he is paralyzed when he realizes that the attacker is none other than Robin.
As Batman is being attacked by his parter, he is forced to step back until he falls in a dark room and a door is closed in front of him. Surrounded by absolute darkness, Batman lights a match and is able to see members of the Justice League and Batman's personal friends, gathered together around a macabre open coffin. When Batman gets closer, he realizes that the body inside the casket is his own. Soon, the members attending Batman's funeral start giving their own eulogies about the Dark Knight. Unfortunately, they all speak dreadful thins, as Commissioner Gordon calls him a hypocrite and Superman resents him for stealing the glory on their past missions together. Finally, Batman realizes that everything is just a strange illusion, almost at the same time as Robin steps up and expressses his contempt for his late mentor and plans to reveal his secret identity to the world. At that moment, the light from the match fades out and the darkness returns. Lighting a second match, Batman realizes that everyone is gone and that it was in fact, all part of an illusion. However, he soon notices that the dark walls start closing in until they leave a very narrow space for Batman to move.
It is then that Batman's mind returns to reality and he realizes that he is locked in a special tube that makes him bounce up and down, with a monitor counting the number of times Batman has repeated the cycle. Besides Batman is an unconscious Robin, who is also locked in a similar tube, with the counter higher that Batman's. Finally, the mastermind behind it all reveals himself to the hero and Batman is shocked to see Dr. Tzin-Tzin on a large monitor, controlling evey movement. Wanting to know how Tzin managed to escape prison, Tzin explains that it was easy for him to breach out and after he escaped, he tried to rejoin his old gang, but they scorned him after his defeat at the hands of Batman. Wanting revenge against the Dark Knight, Tzin was promptly contacted by the League of Assassins, whose plans had been thwarted twice by Batman and they provided the money and equipment to create this elaborate death trap. Tzin then proceeds to explain that the monitor counting Batman and Robin's movements on the tubes are actually triggers that would set explosions once the number reaches 100. Knowing that Robin's counter is far ahead than his own, Batman starts moving inside the tube in order to accelerate the counter so his tube would explode first. Tzin tries to get Batman to plead for Robin's life, but Batman manages to get the counter to 100 before Robin is killed.
Tzin believes that he has succeeded, but Batman appears again and breaks Robin out of the deadly tube. Batman explains that he used his Utility Belt to trigger the bomb and avoided being hurt by the explosion. Frustrated, but prepared for such eventuality, Tzin releases a dozen of highly trained killers to attack Batman. The Dark Knight uses his honed fighting skills to take down ten of his attackers, but the last couple of them manage to hold him, long enough for Tzin to reach him and end his vendetta. Batman is unable to break free and his hour of doom seems to finally have arrived, when Robin appears out of nowhere and tackles Tzin-Tzin, giving Batman the chance to defeat the last two killers.
Finally, Batman and Robin take Tzin-Tzin out of the abandoned mansion and they take him towards the Batmobile waiting outside. However, as they reach their vehicle, the duo hear laughter coming from the house and when they turn around, they see Tzin-Tzin mocking them from one of the upper windows. Turning their attention back to the car, they realize that Tzin is not their prisoner any longer and seconds after this realization, the abandoned house explodes and the whole place comes crumbling down in ashes and fire.
As dawn breaks, the Batmobile silently retires from the ghastly scenario and disappears in the first mists of dawn that cover Gotham City.
As Batman's memories fade away, his attention is drawn back to Arkham, where Gordon has been talking to him, but Batman had not listened, busy with his own memories.
At that moment in the Bowery of Gotham, a mysterious cloaked figure regretfully attacks a homeless man, leaving no trace of him after the attack.
Notes
- Editor Julius Schwartz explains in the letter column of this issue the reason why they published a reprint instead of a new story. Writer Len Wein was then finishing business with Marvel Comics and this caused him to get behind schedule and he couldn't meet the deadline. On the other hand, previous inker Terry Austin withdrew at last moment from his inking assignments in Detective Comics, which had to be filled by Dick Giordano. Unfortunately, due to Giordano's previous commitment to the Superman vs. Muhammad Ali special issue, he was unable to finish the inks for this issue's story. For this reason, Schwartz decided to reprint one of the most demanded stories from the past, which was first published in Detective Comics #408.
- There is however new story and art, developed as a framing sequence for accompanying the reprint. This consists on 2 pages in the beginning and one page at the end, which are part of the current storyline developed in the title.
Trivia
- No trivia.
See Also
- Write your own review of this comic! | http://dc.wikia.com/wiki/Detective_Comics_Vol_1_477 |
Writing can be of many types - academic, journalistic, letter writing, essay writing, creative and fiction. The third section should have comprehensive details about Topic B.
Even though crunch is often a verb, it can also be a noun. We can crunch numbers for a math class. Many words in English have more than one function. Verbs have two important functions: The book would be perfect for an introduction to the concept of comparing and contrasting using similarities and differences.
You may write an informative essay on an author or a literary work, and an interpretive essay on certain science issue as well. Other than the Novel and Short Story General Questions on Literature Each heading contains two questions, with the exception of the General Questions section which has four.
The aroma of the grilled octopus smells appetizing. All aspects of this topic that will be used later for Compare and contrast essay on two characters should be discussed in this section in great detail. Stock learned off answers are not being rewarded — and rightfully so!
Move or delete text if you have to: I promise you they are extremely easy to use! Why are you comparing these two specific characters? During bad storms, trailer parks are often magnets for tornadoes. Finally, differentiated task cards are a perfect way to transition into comparing and contrasting from longer reading passages.
Realize that a verb can have more than one part.
Next, Topic A is introduced in great detail. You want to examine the two characters and the work they come from until you can complete the following statements: For example, a problem solution essay form is used when discussing a social issue, while a narrative essay studies an anecdotal or personal experience as a reference.
The more important these are, the more important—and interesting—the comparison. Otherwise, you will have written a fragmenta major writing error. For instance, if writing about Mahatma Gandhi, one will need to decide whether his life from the day he was born to the moment he breathed his last should be covered or just one facet, such as his relation with his wife, has to be concentrated upon.
Thus, you need to have a research field areatools that you will use for researching, research methods, and of course, you have to come to certain results.
Using the Part 3 works the candidates have studied throughout the year, the candidates are required to write an essay based on a selection of prompts.
The exhaustive description can continue for quite a few paragraphs. While you are not required to do so, it will show your dedication and complete understanding of the text, especially if the quotes are used as pillars for your arguments.
On the other hand, if you compare Ophelia and Hamlet, as two adults following their respective fathers' advice to their deaths, you've demonstrated superior comprehension. Even though it only asks for how the two items are alike, you can challenge students to think of differences too before you turn the page and get to the funny similarity.
You may also choose the wrong angle to look at the chosen historical event. You may feel that everyone else has already said everything there is to say about your subject.
Consider word function when you are looking for a verb. Be sure to properly cite each quote or paraphrase in whatever format your instructor requests e. Obviously, purpose 2 and purpose 3 are closely linked. So, you have to devote some time to choosing an essay topic, as it usually happens that students who have chosen an essay topic in haste, later regret it.
We can crunch popcorn during a movie. Are you examining how the characters speak for themselves—or how other characters respond to them?ESSAY QUESTIONS ON HAMLET Note: Some of the questions are examination-type questions; others are questions for learners to answer as a means to understanding the play.
Hamlet: Essay Topics 1) Conflict is essential to drama. Show that Hamlet. presents both an outward and inward conflict. 2) How do Hamlet's seven soliloquies reveal his character? 3) Is Hamlet primarily a tragedy of revenge? 4) Discuss Hamlet's relationship with Gertrude.
5) How important is the general setting of Denmark to the overall play. 6) Of what significance is Ophelia to Hamlet? What is a compare-contrast essay?
Have you encountered an essay prompt that directs you to compare or contrast two elements (e.g., two characters in a story, two different political theories, two different religious doctrines or scientific explanations, two different historical events, and so forth)? Compare and Contrast Characters in Beowulf and The Niebelungenlied - The hero of Beowulf, one of the oldest written Germanic epics, is a leader of the Geats and a hero unlike all others before him.
A compare-and-contrast essay might seem like the easiest type of paper to write: just find things that are alike and then find things that are different. For this lesson, I will be sharing how we used the book to compare and contrast two or more characters in a story, drawing on specific details from the text. | https://fajoped.cheri197.com/compare-and-contrast-essay-on-two-characters-15522db.html |
The Centre for Social Justice (CSJ) at Institute of Law, Nirma University hereby invites articles/research papers, case studies, and book reviews on the theme ‘Social Justice in Contemporary India: Issues and Challenegs_ for publication in the Journal of Centre for Social Justice (JCSJ _ March 2017 Issue) bearing ISSN Number 2348-599X. The entries sent can be an inter-disciplinary study reflecting socio-economic and political ideas or contemporary issues. The journal is a peer-reviewed ISSN serial publication from Institute of Law, Nirma University, Ahmedabad, Gujarat. It showcases contemporary issues and challenges specific to social justice with an inter-disciplinary approach towards assimilating knowledge. It is an endeavour of the Institute to become the beacon of legal education by encouraging synthesis of knowledge and best practices cutting across the academia and research fraternity.
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1. Word Limit: Submissions are invited of research paper (5,000-6,000 words), policy brief / critique (up to 3,000 words), innovative initiative or practice (up to 3,000 words), case studies (up to 3,000 words), and book reviews (up to 1,000 words) excluding the footnotes. However, looking at the quality and depth of research, relaxation may be given and word limit may vary.
2. Background of writers: We are a peer reviewed Journal. Hence entries from students pursuing Bachelors or Masters Course in law and any other allied discipline of Social Science would be accepted.
3. Authorship: Entries can be co-authored. However, a maximum of two authors per entry is allowed.
4. Citation Style: The American Psychological Association (APA) Style of Citation (6th edition).
5. Format of Main Text & the Footnotes: The Times New Roman font, in font size 12 is prescribed for all entries. Further, the footnotes shall be in font size 10 and line spacing of 1.5 and 1.0 shall be followed respectively.
6. Mode of Submission: Entries are to be sent at [email protected] latest by February 01st, 2017 (11:59 pm). No hard copy of the same is required.
TIMELINE FOR SUBMISSIONS
Date and Time Details
01st February 2017 (11:59 pm) Submission of full paper
02nd to 19th February 2017 Peer Review
20th to 25th February 2017 Communication regarding the acceptance to the authors
Last week of March 2017 Release of the Journal
The submissions are to be mailed to [email protected]. The deadline for submissions is February 01st, 2017.
For any further queries, kindly contact us on: Phone: 079-30642803/824; email: [email protected].
For further details, click here. | https://www.scconline.com/blog/post/2016/12/30/journal-of-centre-for-social-justice-institute-of-law-nirma-university-call-for-papers/ |
The present invention relates generally to telephone communications, and specifically to automated interactive telephone systems.
Interactive telephone systems, generally known as Interactive Voice Response (IVR) systems, have achieved very broad use in businesses and particularly in telephone-based services. A user phoning into such a system receives a computer-generated voice prompt and responds by pressing an appropriate key or keys of the telephone. Pressing the telephone keys generates standard DTMF (Dual-Tone Multi-Frequency) signals, which are received by the IVR. There are sixteen different DTMF signals defined by the International Telecommunications Union (ITU), twelve of which (corresponding to digits 0 through 9, * and #) are used with standard telephone keypads. The user input can lead to additional voice prompts and responses, continuing until the IVR has received all of the information it is programmed to solicit. The IVR may also receive and record voice inputs from the user.
Anyone who has interacted with IVRs of this sort is aware of their shortcomings and the frustrations that they cause. Generally, at each stage of the interaction, the user must listen to an entire menu of choices. The process is time-consuming and requires that the user remember which key will invoke the desired choice. Because of the limitations of this interaction model, the user must navigate linearly from one stage to the next in a rigid, pre-programmed branching structure. There is generally no choice but to return to the beginning if it turns out that the user has chosen the wrong branch at some stage. Verification of the user's input is provided by time-consuming voice playback. The user can generally correct errors, when they occur, only by repeating the entire erroneous entry.
Telephones with graphic user interfaces are known in the art. For example, U.S. Patent 5,838,775 describes a telephone with a touch screen (a "screen telephone"), having selectable graphical objects displayed on the screen to correspond to the push buttons of traditional telephones. The screen can also be used to display enhanced telephone service features, such as caller identification and automatic redial. A user of the screen telephone is able to download over the telephone network different multimedia interactive interfaces to run on the screen, including textual, graphic, animation, audio and video media.
The present invention seeks to provide improved systems and methods for automated interactive telephone applications
Some aspects of the present invention additionally seek to provide interactive telephone systems and devices offering enhanced flexibility, speed and ease of use.
Further some aspects of the present invention seek to provide interactive telephone systems and devices that are accessible to the hearing-impaired.
In preferred embodiments of the present invention, an interactive telephone subscriber unit comprises a display on which a flexible graphic user interface is shown. The interface is configured and varied in real time responsive to DTMF signals conveyed over a telephone line from an interactive telephone system, or IVR, in accordance with a predetermined communication protocol. The protocol enables an operator of the IVR to generate screens on the user device that include both text and graphical elements, and which prompt the user to make selections and input data in response. Optionally, the IVR is programmed to generate voice prompts, as well, in conjunction with the screens that are displayed. Preferably, the display comprises a touch screen, by means of which the user enters selections and alphanumeric responses. Alternatively or additionally, user responses may be entered using a standard telephone keypad. In either case, the user inputs are coded and returned to the IVR as DTMF signals.
In some preferred embodiments of the present invention, the subscriber unit comprises a full-function telephone, with an appropriate display. The telephone includes a microprocessor programmed to generate the graphic user interface based on the DTMF communication protocol. In other preferred embodiments, the subscriber device comprises a stand-alone box with a suitable processor and display, which is connected to the telephone line together with a conventional voice telephone.
The present invention thus enables businesses and other service providers to construct combined visual and audio applications for automated transaction processing and information retrieval over the telephone. Depending on how the present invention is implemented, little or no modification is generally required to the service provider's existing telephony infrastructure or to IVRs known in the art (although it is necessary that the subscriber have an appropriate subscriber unit). Rather, a suitable authoring tool is used to design the screens and then to generate the DTMF codes corresponding to the screens, in accordance with the protocol. These DTMF codes are then recorded for playback by the IVR instead of or in addition to the recorded voice prompts that are currently the sole means available for user interaction. For users who are equipped with suitable subscriber units, interaction with IVRs that are programmed in this manner is substantially faster and more efficient than with IVRs known in the art, and enables service providers to provide greatly enhanced functionality. Such subscriber units and IVRs can also be used by the hearing-impaired.
According to a first aspect of the present invention, there is provided an interactive telephone system, which stores an encoded representation of a screen to be displayed by a telephone subscriber unit for the purposes of interaction between the subscriber and the system, the screen comprising one or more graphic elements selected from among a predetermined set of graphic element, and the representation comprising coded signals that encode the elements in accordance with a protocol that defines a relation between the graphic elements in the set and respective coded signals, and which transmits the encoded representation over a telephone line to a telephone subscriber unit, whereby the one or more graphic elements are displayed by the subscriber unit responsive to the encoded representation of the screen to indicate possible responses for or information required from the subscriber for interaction with the system.
providing a protocol that defines a relation between predetermined graphic elements and respective sequences of dual-tone multi-frequency (DTMF) signals;
designing a screen to be displayed including one or more of the graphic elements;
generating an encoded representation of the screen using DTMF signals in accordance with the protocol; and
transmitting the encoded representation over a telephone line to a telephone subscriber unit, whereby the one or more graphic elements are displayed by the subscriber unit responsive to the encoded representation of the screen.
There is therefore provided, in accordance with a preferred embodiment. According to a second aspect of the present invention, a method for telephone communications, including:
Preferably, providing the protocol includes providing an ordering mechanism, which enables different arrangements of the graphic elements to be defined on the screen, wherein designing the screen includes defining an order of the graphic elements using the ordering mechanism, and wherein the telephone subscriber unit renders the graphic elements to a display associated with the unit responsive to the defined order and in an arrangement dependent upon a characteristic of the display.
Preferably, the predetermined graphic elements include one or more on-screen push-buttons. Additionally or alternatively, the predetermined graphic elements include one or more alphanumeric elements, wherein designing the screen includes determining a font in which one of the one or more alphanumeric elements is to be displayed and generating an indication of the font in accordance with the protocol. Further additionally or alternatively, providing the protocol includes providing a mechanism for playing a voice output at the subscriber unit in conjunction with displaying the one or more graphic elements. Moreover, additionally or alternatively, providing the protocol includes providing a mechanism for generating a representation of a non-predetermined graphic element, and wherein designing the screen includes inputting a bitmap in accordance with the mechanism.
Preferably, transmitting the encoded representation includes loading the encoded representation into a interactive voice response system (IVR) and programming the IVR to transmit the representation in response to a call from the subscriber unit.
Preferably, designing the screen includes designing an interactive screen so as to generate a prompt for a reply at the subscriber unit, and the method includes receiving a user input at the subscriber device responsive to the prompt. Most preferably, receiving the user input includes receiving an encoded representation of the user input using DTMF signals in accordance with the protocol. Additionally or alternatively, receiving the user input includes receiving a voice input. Further preferably, the method includes transmitting an encoded representation of a further display screen responsive to the user input.
receiving dual-tone multi-frequency (DTMF) signals corresponding to an encoded representation of a screen to be displayed including one or more graphic elements; and
rendering the one or more graphic elements to a display responsive to the received DTMF signals.
There is also provided, in accordance with a preferred embodiment. According to a third aspect of the present invention, a method for telephone communications, including:
Preferably, receiving the DTMF signals includes receiving signals that define an order of the graphic elements in accordance with a predetermined ordering mechanism, which enables different arrangements of the graphic elements to be defined on the display screen, and rendering the one or more graphic elements includes rendering the elements responsive to the defined order and in an arrangement dependent upon a characteristic of the display. Most preferably, rendering the elements in the arrangement dependent upon the characteristic of the display includes arranging the elements in a manner consonant with a resolution of the display. In a preferred embodiment, arranging the elements includes adding a scroll bar when a resolution needed to view all of the one or more graphic elements exceeds the resolution of the display.
a display;
a telephone line interface, adapted to receive dual-tone multi-frequency (DTMF) signals over a telephone line; and
a processor, which is coupled to receive from the telephone line interface a sequence of the DTMF signals representing a screen to be displayed including one or more graphic elements, which are encoded using the DTMF signals, and to decode the DTMF signals and, responsive thereto, to render to the display the one or more graphic elements.
There is additionally provided, in accordance with a preferred embodiment. According to a fourth aspect of the present invention, a telephone subscriber unit, including:
Preferably, the subscriber unit includes a memory, which stores data associated with a predefined protocol for use by the processor in decoding the DTMF signals and rendering the one or more graphic elements. Further preferably, the one or more graphic elements include alphanumeric characters, and the memory stores a plurality of fonts, which are recalled by the processor so as to render the characters as specified by the protocol. Alternatively or additionally, the one or more graphic elements include graphic icons, which are recalled by the processor for display as specified by the protocol.
Preferably, the processor renders the graphic elements responsive to the order and in an arrangement dependent upon a characteristic of the display. Preferably also, the characteristic of the display responsive to which the processor arranges the graphic elements comprises a resolution of the display.
Preferably, the screen rendered by the processor includes an interactive screen that includes a prompt for a reply by a user of the device, and the unit includes a user input device, which is operated by the user to provide an input responsive to the prompt. Further preferably, the processor generates an encoded representation of the user input using DTMF signals and transmits the DTMF signals through the telephone line interface. Preferably, the user input device includes a touch-sensitive screen. Alternatively or additionally, the user input device includes a keypad. Further alternatively or additionally the user input device includes a microphone, through which the user inputs a voice response.
There is further provided, in accordance with a preferred embodiment According to a fifth aspect of the present invention there is provided, a computer software product, including a computer-readable medium in which program instructions are stored, which instructions, when read by a computer, cause the computer to display a screen including one or more graphic elements selected by a user from among a predetermined set of graphic elements, and to generate an encoded representation of the screen using dual-tone multi-frequency (DTMF) signals, to be transmitted over a telephone line to a telephone subscriber unit, in accordance with a protocol that defines a relation between the graphic elements in the set and respective sequences of DTMF signals, whereby the one or more graphic elements are displayed by the subscriber unit responsive to the encoded representation of the screen.
There is moreover provided, in accordance with a sixth aspect preferred embodiment of the present invention, an interactive telephone system, which stores an encoded representation of a screen to be displayed by a telephone subscriber unit, the screen including one or more graphic elements selected from among a predetermined set of graphic element, and the representation including DTMF signals that encode the elements in accordance with a protocol that defines a relation between the graphic elements in the set and respective sequences of dual-tone multi-frequency (DTMF) signals, and which transmits the encoded representation over a telephone line to a telephone subscriber unit, whereby the one or more graphic elements are displayed by the subscriber unit responsive to the encoded representation of the screen.
Fig. 1 is a schematic illustration of a system for interactive telephone applications, in accordance with a preferred embodiment of the present invention;
Fig. 2 is a schematic block diagram of an interactive telephone subscriber device, in accordance with a preferred embodiment of the present invention; and
Fig. 3 is a flow chart that schematically illustrates a method for user interaction with an interactive telephone system, in accordance with a preferred embodiment of the present invention.
The present invention will be more fully understood from the following detailed description, by way of example, of the preferred embodiments thereof, taken together with the drawings, in which:
Fig. 1 is a schematic illustration of a system 20 for interactive telephone applications, in accordance with a preferred embodiment of the present invention. A telephone service provider facility 22 comprises an IVR 28, which is typically coupled by a switchboard, such as a PBX 24, to a telephone network, generally a public switched telephone network (PSTN) 26. For example, a suitable IVR for this purpose is the IBM Corepoint Voice Response system, which is described at http://www.corepoint.com. When a user dials in to the service provider through the telephone network, the call is connected by the PBX to the IVR for response. In response to the call, the IVR is programmed to generate sequences of DTMF signals in accordance with a standard IVR protocol. A suitable protocol of this type is described in detail hereinbelow. These DTMF signals are received by the user's subscriber unit, such as a telephone, and cause the unit to generate interactive, graphic user interface screens, as described in detail hereinbelow.
The response of IVR 28 to the user call depends on the type of subscriber device from which the user is calling, which is identified by the IVR in an initial handshaking procedure. One such subscriber device is a "smart" telephone 30 with a display 32, typically a LCD, and a microprocessor which is programmed to respond to the IVR protocol. Preferably, display 32 comprises a touch screen, as is known in the art. Alternatively, the user may interact with and make selections from the display using suitable push-buttons provided on telephone 30 for this purpose. Although smart telephones having such user interaction capabilities are known in the art, telephone 30 is modified relative to such telephones, typically by addition of suitable software to an embedded microprocessor in the telephone. This software enables the microprocessor to decode DTMF signals and generate graphic screens on display 32 in accordance with the standard protocol.
The subscriber may also use a decoding box 36, with a graphic display 38, in conjunction with an ordinary "dumb" telephone 34. In this case, box 36 intercepts DTMF signals sent by IVR 28 and generates the appropriate graphic screens on display 38 in response to the signals. Ordinary audio signals and DTMF signals that do not accord with the protocol are simply passed on to telephone 34. The function of decoding box 36 may also be carried out by a personal computer (not shown in the figure) that has a suitable telephone connection or audio peripherals and has software for placing outgoing telephone calls for the user, as is known in the art. In this case, a suitable software module for DTMF decoding is simply added to the telephony software running on the computer. The software module may be downloaded to the personal computer over a network, or else it may be supplied on tangible media, such as CD-ROM.
On the other hand, if the user is calling from an ordinary, audio-only telephone, or if there is some failure in protocol handshaking, then IVR 28 responds to the user with a sequence of voice prompts, as is known in the art.
As illustrated on display 38, the screens generated by DTMF signals from IVR 28 may include a variety of textual elements 33 and graphic elements 39, as well as other media. These screens are preferably generated using a suitable authoring tool, which typically runs on a standard computer workstation 29, such as a personal computer. The authoring tool enables an operator of facility 22 to lay out the desired elements on the screen, and then automatically encodes each screen as a corresponding sequence of DTMF signals, in accordance with the IVR protocol. These sequences are recorded in a memory of IVR 28 for playback in response to user calls. Authoring software for laying out the screens and encoding them as DTMF signals may be downloaded to workstation 29 over a network, or alternatively, it may be supplied on tangible media, such as CD-ROM, for installation on the workstation.
Push buttons, such as a "send now" button 39 shown on the display. Preferably, the protocol defines a variety of standard button shapes, such as square, circle, oblong, etc., that may be invoked for this purpose. Most preferably, display 38 comprises a touch screen, by means of which the user selects these push buttons and interacts with other graphic elements on the display. Alternatively, off-screen buttons may be provided for this purpose, as noted above with reference to telephone 30.
Fixed text fields, used, for example, to generate textual elements 33, which prompt the user to input appropriate data, or to convey information to the user.
Numeric input fields, represented by a line 35 on display 38. Preferably, the user inputs data to these fields using a numerical keypad 27 on the telephone or, alternatively, using selectable number keys on a touch screen or a keypad or keyboard (not shown) associated with box 36.
Alphanumeric input fields, represented by a line 37 on display 38. The user can input data for these fields using the telephone keypad, as well. Typically, multiple keystrokes are used to generate the different letters represented by each of the telephone keys. Alternatively, an alphanumeric keyboard 31, already provided with some "smart" telephones, may be used for this purpose. Further alternatively or additionally, display 38 may include a pressure-sensitive region on which the user writes characters with a suitable stylus. The strokes of the stylus are recognized and identified as letters or numbers. This feature is used in personal digital assistants known in the art, such as "Palm" devices produced by 3Com, and could be implemented in box 36 in a straightforward manner. Still further alternatively, a touch- sensitive keyboard or keypad may be presented on display 38.
Custom graphic icons, typically 8x8 or 12x12 pixels in size. These icons may be predefined and stored in a memory of box 36 or telephone 30, as described hereinbelow. Alternatively or additionally, the protocol enables workstation 29 to define, and IVR 28 to transmit, bitmap fields of one or more different sizes, so that non-predefined icons can be displayed.
Display 38 shows a number of the different types of elements that may be included in screens generated by workstation 29 and transmitted to the user in DTMF-coded form by IVR 28. Such elements are displayed in like fashion by display 32 on telephone 30. These elements include:
Preferably, at least some of the screens defined by workstation 29 also include voice output and voice input fields. Thus, audible instructions to the user of telephone 30 or 34 may be played over the telephone in conjunction with the screens, and the user may be prompted to provide voice responses instead of or in addition to numeric and/or alphanumeric inputs.
The elements described above are listed by way of example, rather than limitation. Other media, such as animations, may also be incorporated in the protocol to be played on display 32 or 38. Furthermore, additional elements and even program modules may be downloaded to telephone 30 or box 36 in the form of DTMF codes, in a manner analogous to downloading of applets and software plug-ins over the Internet.
Fig. 2 is a block diagram that schematically illustrates functional elements of box 36, in accordance with a preferred embodiment of the present invention. Similar elements are implemented in telephone 30. A telephone interface 40 receives signals conveyed over PSTN 26, including the DTMF codes generated by IVR 28. After a connection has been made between telephone 34 and service facility 22 (typically, although not necessarily, after the telephone user has dialed in to the facility), interface 40 listens to the signals received from the IVR and diverts any DTMF signals to a coding and decoding block 42. This block converts the DTMF signals into a sequence of the corresponding 4-bit digital values and passes these values to a central processing unit (CPU) 44. Although block 42 and CPU 44 are shown in Fig. 2 as separate units, these elements, as well as a memory 46 associated with the CPU, are preferably implemented in a single integrated circuit that includes a microprocessor, memory and suitable interfaces.
CPU 44 interprets the digital values in accordance with the IVR protocol, based on instructions and data stored in memory 46. Preferably, the stored data include standard fonts, buttons, fields, icons and data vocabulary defined by the protocol and factory-programmed in memory 46. The data vocabulary includes frequently-used words and expressions, which are pre-stored in the memory in the form of short sequences of 4-bit values, to reduce the time needed to download a screen. Preferably, the protocol also provides message formats for conveying additional elements, such as fonts, graphics, data vocabulary and program modules to box 36, over PSTN 26. CPU 44 stores these elements in memory 46 for use in generating screens on display 38. The memory may also be programmed with user data, such as the name, address, credit card number and other identifying details of a subscriber, using box 36. The subscriber can then select these data in response to appropriate prompts from IVR 28, without having to input all of the information from scratch each time he or she communicates with such an IVR.
Fig. 3 is a flow chart that schematically illustrates a method for communication between service facility 22 and a user of box 36, in accordance with a preferred embodiment of the present invention. Although this preferred embodiment is described with reference to box 36, it may likewise be implemented using telephone 30 or any other suitably-configured subscriber unit.
TABLE I
<b>Field</b>
<b>Length (bits)</b>
<b>Contents</b>
NS/US
4 or 8
NS (new screen) is sent at the beginning of a transmission to clear the screen. US (update screen) is sent to update the current screen.
NE
8
Number of elements in the screen.
NC
4 or 8
Signals beginning of a new column on screen.
H
16+
Identifies entity type and payload length for each element on the screen. Typical entity types and the corresponding headers are listed below in Table II.
Payload
Defined by header
Generally text, but may also comprise a bitmap, a voice output (to be generated at an appropriate time by IVR 28) or a voice input (which the user is prompted to provide through telephone 34).
ECC
8 or 16
An error-correcting code, as is known in the art, such as a CRC.
EOB
4 or 8
End of buffer.
At an interface screen creation step 50, workstation 29 is used to generate a family of screens to be shown on display 38. These screens may include data entry screens, as shown in Fig. 1, or user information and selection screens, such as a listing of services available and/or telephone extensions at facility 22, or substantially any other type of screen that is supported by the protocol. Branching from one screen to the next within the family, based on user responses, is preferably also specified at this stage. At an output coding step 52, the workstation generates an encoded representation of each screen according to the protocol, comprising sequences of DTMF signals representing the elements on the screen in their proper order. The contents of a communication buffer are defined in accordance with the protocol with respect to each screen that is to be transmitted. Table I below shows the elements that are typically included in such a buffer, in accordance with a preferred embodiment of the present invention:
The protocol elements listed above are given here by way of example. Those skilled in the art will appreciate that the field definitions may be refined, altered and expanded to meet the functional needs of different applications.
TABLE II
<b>Type</b>
<b>Header</b>
<b>Payload</b>
Button (B)
[ID], Type (text/graphic), TextLength
Text
Fixed text (FT)
[ID], Font, Size, TextLength
Text
Alphanumeric input (AI)
[ID], Type (numeric/ alphanumeric), TextLength
Text (to be input by user)
Voice output (VO)
[ID], Type, Length
Audio
Voice input (VI)
[ID], Type, Length
Audio (to be input by user)
Icon (I)
[ID], Type (8x8, 12x12 or other predefined size)
Bitmap or reference to stored picture
Table II lists the data to be included in the buffer for different types of elements that may be included in screens to be transmitted by IVR 28, in accordance with a preferred embodiment of the present invention:
Alternatively, if the subscriber unit, such as box 36 or telephone 30, has appropriate speech synthesis and speech recognition capabilities, the voice output and input fields may have text payloads, which are respectively converted to or from audio signals by the subscriber unit.
As shown in the table above, each of the headers includes an optional identifier (ID) field, indicating the order in which the corresponding elements are to appear on the screen. Alternatively, if the ID field is not used, the elements are simply enumerated in sequence.
Returning now to Fig. 3, at step 52, the DTMF code sequences corresponding to each of the relevant screens are downloaded from workstation 29 to IVR 28, as mentioned hereinabove. The IVR is programmed to play the DTMF sequences, along with any required voice output fields, in the appropriate order. At a DTMF send step 54, a user dials in to facility 22, using telephone 34, for example, and the call is routed to the IVR. Preferably, at this stage, the IVR initiates a handshaking routine in order to determine whether the user's subscriber equipment is configured to receive and display data screens in accordance with the protocol. The handshake may be in the form of a voice query, such as "If your telephone is equipped to display IVR data, press '5'." Alternatively, the handshake may take place automatically between IVR 28 and CPU 44 at the user end. It is also noted that although this preferred embodiment is described with reference to a user dialling in to facility 22, a similar routine may be used on outgoing calls placed automatically by the IVR. Once the IVR has verified that the user is equipped to display the data screens, the first screen is downloaded to box 36 over PSTN 26. Otherwise, the IVR reverts to a voice-only interaction mode.
At a decoding step 56, decoding block 42 of box 36 decodes the DTMF signals received from interface 40 and passes them to CPU 44. Preferably, when an incoming DTMF code sequence is detected by box 36, the output from interface 40 to telephone 34 is blocked, so that the user does not hear the DTMF tones. The CPU refers to memory 46 in order to determine which elements are to be displayed on screen and to render the elements in accordance with the protocol. To the extent that any of the data conveyed by the DTMF code sequence appears to be erroneous, either because of an incorrect ECC computation or an unrecognized header, for example, CPU 44 preferably sends a resend request back to IVR 28.
At a formatting step 58, the CPU arranges the elements and displays them on display 38. Preferably, the arrangement of the elements on display 38 is not fixed in advance by the protocol, since different subscriber units may have displays of differing sizes and resolution. CPU 44 is programmed to arrange the elements on display 38 in a manner appropriate to the characteristics of the display, albeit in an order that corresponds to the IDs given in the header fields or sequential ordering of the elements, as described hereinabove. Preferably, if the pixel area of the visual data in a given screen exceeds the available area on display 38, the CPU automatically adds vertical and/or horizontal scroll bars to the screen.
At a user input step 60, the user of box 36 inputs data in response to the prompts appearing on the screen. To input the data, the user selects each of the input fields in turn, preferably using the touch screen of display 38. The user then inputs the data using either the touch screen or other controls on box 36 or telephone 34, as described hereinabove. The user makes voice inputs simply by speaking into telephone 34. The selections and alphanumeric data input by the user are coded as DTMF signals by CPU 44 and DTMF block 42 at an input coding step 62. The coded data are organized for uploading to IVR 28 in a buffer format similar to that used for the screens downloaded to box 36. In the case of uploaded data, however, it is sufficient that each field have an identifier, corresponding to the ID number of the element on the screen, followed by the appropriate user input data.
At a send data step 64, the user input data are returned via PSTN 26 to IVR 28. The IVR is programmed to respond to the data by calling up the next appropriate data screen, at a next screen step 66, and transmitting the screen to be shown on display 38. Alternatively, as appropriate, the IVR routes the call to a human agent at facility 22 or terminates the call.
Although preferred embodiments are described hereinabove with reference to DTMF codes, it will be appreciated that the principles of the present invention may similarly be applied using other methods for coding data in the form of audio signals. DTMF coding has the advantage that it is supported by existing IVRs and other common telephone devices, so that the present invention may be implemented without substantial investments in new infrastructure and equipment and without the addition of costly modem circuitry at either the service facility or the subscriber end.
It will be appreciated that the preferred embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art. | |
They are responsible for working to improve systems and devices that contribute to environmental health.
What Does an Environmental Health and Safety Technician Do?
The environmental health & safety technician is on the front line of implementing policy and equipment that contribute towards general environmental quality. While not responsible for deciding on organizational policy, they will act under the instructions of those who do make decisions such as environmental health & safety managers. Together, they will report back to line managers on such issues as compliance, devices to install, methods and implementation. They may act as a go-between for front-line employees and the decision makers in an advisory capacity or consulting.
They will need to understand and keep up with modern developments in environmental health & safety engineering. Although they do not design the technology, one of their roles may be to implement, install, repair and replace technology - being qualified and experienced enough to do so. They will be licensed where necessary to implement such changes and repairs. With environmental health & safety training being so important today in all organizations in all sectors, they may either double up as or work alongside trainers to ensure that employees understand their obligations.
They will have extensive knowledge of health & safety policy and law as it pertains to the environment in which they work and will develop procedures for the implementation.
Where Does an Environmental Health and Safety Technician Work?
Environmental health & safety is required in all sectors and in all businesses. Protection of the environment, the ecology and individual animal and plant species is just as important as human health.
According to 2015 BLS data, the employer of the largest number of this type of employee is government with 18% of the workforce. This includes Federal, state and local. These employees will work at government businesses ensuring compliance or may work as government consultants for organizations to ensure compliance.
16% work in manufacturing. EPA and other government regulations now ensure strict compliance with regard to practice within manufacturing - the proper use and disposal of industrial chemicals and substances, and mitigation of accidents. They will work for the organizing companies, mostly on site.
10% work in management, scientific and technical consulting. They will work with government, businesses of all sizes and third sector and hired on a contractual basis to analyze business practice, usually producing a report for decision makers within that organization.
7% work in hospitals. Medical facilities use implements and substances potentially toxic to the environment or if handled by the wrong people. There are regulations and law on disposal; technicians ensure compliance.
6% worked in mining. Industrial chemicals and waste materials need proper handling, storage and disposal for environmental protection and human health.<!- mfunc search_btn -> <!- /mfunc search_btn ->
What Is the Average Environmental Health and Safety Technician Salary?
Environmental health and safety technicians earn a median salary of $46,850, according to the BLS. With experience, the highest 10% of earners most in demand can earn in excess of $80,530. The lowest 10% earn about $29,280.*
Environmental Healthy and Safety Technician Jobs & Job Description
Recent Environmental Health and Safety Tech Job Listings
Use the search box below to find all the environmental health and safety technician job listings in our job board.
An environmental health and safety technician is responsible for a variety of tasks that improve and protect environmental health. While the day-to-day tasks may vary based on employer and location, this position generally requires a technician to:
- Perform laboratory and field tests to monitor the environment and investigate sources of pollution, generally under the direction of an environmental health & safety manager
- Collect samples of gases, soil, water and other materials for scientific testing
- Record test data and prepare reports, summaries or charts that interpret the results
- Implement programs for monitoring of environmental pollution or radiation
- Calibrate microscopes or test instruments
- Examine and analyze material for presence and concentration level of contaminants
- Monitor emission control devices to ensure they are working properly and comply with state and federal regulation
- Install and repair environmental health and safety technology and systems as needed
- Develop extensive knowledge of health and safety policy and laws
A more senior environmental health and safety technician would likely take on more consulting duties and advise internal and external audiences. Their job description would include the above, as well as:
- Provide technical or program assistance to government representatives, employers or the general public on issues of environmental protection
- Present test results or summary reports to internal and external audiences
- Develop and provide advisory services for programs that monitor and treat environmental health
- Act as liaison between front-line employees and management on issues of compliance, devices to install, methods and implementation
What Is the Job Demand for Environmental Health and Safety Technicians?
Demand for this role is expected to grow some 11% between 2020 and 2030 - that's faster than the average of all occupations during this time.* As Federal and international compliance on health and environmental protection pushes forward, more people will be required to fill these roles. Part of the “green economy”, the sector overall has seen an improvement in the last few years.
What Are the Education Requirements to Become an Environmental Health and Safety Technician?
High school students will require good grades in scientific subjects such as math, geography, chemistry and biology. Students should also ensure they have good communication skills as the role does require liaising with multiple stakeholders - employees down the chain of command and decision makers and management above. Written, oral and electronic communication skills are essential. Equally important is interpersonal communication and a professional presentation to the right people.
Although most occupations health & safety roles do not require degree education, environmental health & safety is a specialist area that will require an associate degree at the very minimum. Although the role is practical rather than academic, this is especially so for environmental professionals. You will need to understand the balance between practical solutions to pollution and health, and understand ecology. Useful degrees include environmental health, ecology, environmental law or policy, or environmental studies.
Postgraduate degrees such as masters and doctorates will not be required unless the student intends to enter into a teaching or research career. The practical nature means the student may need to keep up with developments in technology and latest research but not from an academic point of view.
Environmental Health and Safety Technician - Related Degrees<!- mfunc search_box_body ->
What Kind Of Societies and Professional Organizations Do Environmental Health and Safety Technicians Have?
Environmental health & safety is an enormous area with the following professional organizations and groups. | https://www.environmentalscience.org/career/environmental-health-safety-technician |
A detailed and comprehensive pensions report, which looks at the three main pension areas – private sector, state and public sector pensions – was published recently by the OECD at the request of the Minister for Social Protection Joan Burton TD.
A number of recommendations, which could affect everyone, were made, including the prospect of compulsory pension saving requirements being introduced as a way to increase levels of coverage. There are also recommendations for a radical reform of the state pension system and a much more aggressive introduction of changes to public sector pensions.
From the perspective of the private sector, the report looks at the future of private sector defined benefit (DB) pension arrangements. It is particularly critical of the adequacy of existing member protection requirements and concludes that “at any rate, the future for traditional DB plans in Ireland is rather bleak given the current funding situation, longevity risk and investment challenges”.
Any mandatory pension saving structure introduced in future years will almost certainly be on a defined contribution (DC) basis. In the meantime, it is clear, at least for those in the private sector, that much greater individual reliance on individual savings (along with employer support where available) through DC pension arrangements will be the new norm.
The proposals in relation to the state pension include moving to a fully means tested benefit in place of the (near) universal benefit that is currently available. This would result in a reduction or complete stoppage of the state pension benefit for many current retirees. The proposals put forward also include eliminating the household benefit package and free travel allowance by incorporating them as a monetary amount into a means tested core benefit.
In relation to public sector pensions, the report identifies that more could be done to reduce government liabilities for public servants, and to ensure more equity between public and private sector workers. The report specifically recommends acceleration of the planned changes to pensions for public servants, to impact existing staff and not just new recruits, and also says that any pension scheme for the private sector should also cover public servants.
So, in conclusion, there is no doubt that Ireland’s current pension policy will dramatically change in the coming years. From the Government’s perspective, it has to take the necessary actions to avoid the system hitting the various icebergs that the OECD and others have clearly outlined in this report. For individuals with DC pensions, they need to look out for themselves and pay particular attention to governance, contribution levels, investment choices and costs. | http://www.galwayindependent.com/20130612/business/pensions-icebergs-ahead-S19446.html |
Domestic violence commonly refers to violent or abusive behavior committed against intimate partners or family members in domestic settings. The Texas Family Code refers to these types of crimes as dating violence or family violence, and convictions can carry steep consequences for alleged offenders.
When police officers respond to possible domestic violence calls, they often arrest alleged offenders simply out of caution to avoid alleged victims suffering any additional harm. Unfortunately, some people can be arrested for alleged family violence or dating violence offenses that are based on exaggerated or flat-out false allegations.
If you were recently arrested for any kind of alleged domestic violence offense in Denton County, it is in your best interest to exercise your right to remain silent until you have legal counsel. Law Offices of Richard C. McConathy aggressively defends clients in Lewisville, Little Elm, The Colony, Argyle, Flower Mound, Highland Village, and many surrounding areas of Denton County.
Denton criminal defense lawyers Richard McConathy and Brian Bolton will fight to help you achieve the most favorable outcome to your case, including possibly having criminal charges reduced or dismissed. Call 940-222-8004 today to have our attorneys provide a complete evaluation of your case during a free, confidential consultation.
Overview of Domestic Violence Crimes in Denton County
Several key definitions of terms relating to domestic violence offenses are established under Chapter 71 of the Texas Family Code. Some of the common terms relating to these crimes and their respective definitions include:
Many different criminal offenses may be considered crimes related to domestic violence. The severity of the criminal charges in these cases often depends on several factors, including the alleged offender’s prior criminal record and whether the alleged offense resulted in any injuries.
Some of most common domestic violence offenses include, but are not limited to:
Victims Assistance Division | Denton County, Texas — The Victim Assistance Division of the Denton County Criminal District Attorney's Office helps the victims many different crimes, including family violence. On this website, you can learn more about Texas VINE (Victim Information and Notification Everyday), the free, anonymous, computer-based telephone service that provides crime victims with information and notification concerning the custody and court status of offenders. You can also find information about the rights of crime victims and other useful resources.
Denton County Criminal District Attorney
1450 E. McKinney St.
Denton, TX 76209
(940) 349-2600
Denton County Friends of the Family — Denton County Friends of the Family identifies its mission “is dedicated to providing compassionate, comprehensive services to those impacted by rape, sexual abuse, and domestic violence, while partnering with our community to promote safety, healing, and prevention.” Learn more about the organization’s history and guiding philosophies. You can also find information to get help, including emergency shelter, advocacy, and counseling services.
Denton Outreach Office
4845 S. Interstate 35 E, Suite 200
Corinth, TX 76210
(940) 387-5131
Were you arrested in Denton County for any kind of alleged domestic violence crime? Do not say anything to authorities without legal representation. Contact Law Offices of Richard C. McConathy as soon as possible.
Richard McConathy and Brian Bolton are experienced criminal defense attorneys in Denton who represent individuals all over Denton County, including Highland Village, Flower Mound, Argyle, The Colony, Little Elm, Lewisville, and several other nearby communities. You can have our lawyers review your case and help you understand all of your legal options when you call 940-222-8004 or fill out an online contact form to schedule a free initial consultation. | https://www.dwilawyersdenton.com/criminal-defense/domestic-violence |
Phylogenetics and dating
However, it is quite feasible to determine the sequence of a defined area of a particular chromosome.Typical molecular systematic analyses require the sequencing of around 1000 base pairs.The base sequences for the haplotypes are then compared.In the simplest case, the difference between two haplotypes is assessed by counting the number of locations where they have different bases: this is referred to as the number of substitutions (other kinds of differences between haplotypes can also occur, for example, the insertion of a section of nucleic acid in one haplotype that is not present in another).Molecular phylogenetics and molecular evolution correlate. Molecular evolution is the process of selective changes (mutations) at a molecular level (genes, proteins, etc.) throughout various branches in the tree of life (evolution).Molecular phylogenetics makes inferences of the evolutionary relationships that arise due to molecular evolution and results in the construction of a phylogenetic tree. Work with protein electrophoresis began around 1956.
BEAST uses MCMC to average over tree space, so that each tree is weighted proportional to its posterior probability. BEAST is built on a large body of prior work and appropriate citations for individual modules, models and components will be listed when BEAST is run.
The result of a molecular phylogenetic analysis is expressed in a phylogenetic tree.
Molecular phylogenetics is one aspect of molecular systematics, a broader term that also includes the use of molecular data in taxonomy and biogeography.
In principle, since there are four base types, with 1000 base pairs, we could have 4 distinct haplotypes.
However, for organisms within a particular species or in a group of related species, it has been found empirically that only a minority of sites show any variation at all, and most of the variations that are found are correlated, so that the number of distinct haplotypes that are found is relatively small.
Search for phylogenetics and dating:
We include a simple to use user-interface program for setting up standard analyses and a suit of programs for analysing the results. Users are strongly advised to join the BEAST mailing-list. | https://elt-edel.ru/phylogenetics-and-dating-626.html |
What started as a simple gender equality survey has grown into a programme of staff development and diversity initiatives designed to explore and celebrate intersectionality in our workplace.
The PlayFair Steps Initiative at the University of Edinburgh is focused on a large group of staff who work within the University’s central Information Technology (IT) and Library departments, collectively known as the Information Services Group (ISG), to recognise that people’s identities and social positions at work – particularly in the technology industry – are shaped by multiple and interconnected factors. We have developed a range of activities exploring how a person’s age, disability status, race and ethnicity, gender, gender identity, religion or belief, sexual orientation, socioeconomic background, and parent status contribute towards their specific experiences in and perspectives of our workplace. Using the local expertise of our academic colleagues and students, we seek to move beyond anecdote and create a more inclusive workplace with support from senior management for both top-down and bottom-up change.
ISG is the largest support group at the University with over 600 employees. Within the context of the University’s commitment to Athena Swan, and in line with a broader approach to change management in ISG, we have taken an opportunity to make some innovative moves to address equality and diversity issues for our staff in an industry that is heavily male dominated.
The organisational studies literature has long included intersectionality in its discussions of diversity and academic leadership development. Less is understood, however, in practice for support teams in the University setting. Through this initiative we explore how gender connects to various other experiences and characteristics to exacerbate ‘imposter syndrome’ and stifle feelings of inclusiveness in our workplace and create barriers to leadership.
We have developed a programme called The PlayFair Steps. The name was deliberately chosen to draw upon an understanding of ‘fair play’ at work, which involves everyone, and to sound familiar. The Playfair family are historically connected to the University and the name is well known in the city. The University is home to the Playfair Library, and the Playfair Steps take one quickly from the ‘old town’ to the ‘new town’ alongside the national galleries. Willian Henry Playfair was an architect and his nephew (also) William was an early pioneer of infographics and the inventor of both the line and bar chart. Given that our initiative started after the preparation and reporting of data from a gender equality survey, the name seems fitting.
PlayFair Steps in ISG has manifested in two ways: via a Lecture Series and an Equality Working Group. Through these manifestations, the initiative has four distinct themes, each of which are discussed within this case study:
- Myth-busting
- Staff Engagement
- Visibility and accountability
- Data driven decision making and reporting
Myth-busting
The aim of the PlayFair Steps Lecture Series is to take advantage of our situation as part of a large research institution. Across the campus, we have world-class researchers with up-to-date expertise on the equality and diversity issues that impact our workplace. In an effort to move past anecdote and hackneyed stereotypes, we have invited academic colleagues from gender studies, business and management, social policy, and education to present to groups of ISG staff on their specific areas of research.
Topics covered have included ageism, an aging workforce, race relations in Scotland, managerial perspectives for understanding gender, disability and class intersectionality, and policy development for family and for parental leave. For each of these discussions, we have been afforded an exceptional opportunity to learn from current data, understand areas of contention and subjectivity and hear how gender and other characteristics intersect while also learning of established solutions toward inclusivity. At the end of each lecture we ask colleagues to consider how this knowledge can be applied within ISG. These recommendations are then promoted within our organisation.
While it may be unusual to invite our academic colleagues to speak within the university to a non-academic audience, we have found the experience to be particularly insightful. As a result, for the coming year, we have planned to include more topics which are intersectional across gender, age and family structures such as parenting, menopause and ‘Millennials’ in the workplace.
Staff Engagement
In addition to the PlayFair Steps Lecture Series, we also host a PlayFair Steps Equality Working Group. This distinct manifestation of PlayFair Steps give staff the opportunity to voice issues of note to them that the Equality and Diversity team within ISG can address. The group works very well alongside the lecture series and allows us to gather ideas about new takes on equality and diversity and present them to our staff in a unique and easily accessible way while also providing recommendations to senior managers.
These meetings have expanded from informal sessions to hosting external organisations to offer trainings/workshops on aspects of diversity that can lead to practical changes at work. For instance, we have hosted an Equality Working Group session with an outside organisation, Equate Scotland, to show staff the importance of language in our recruitment materials. Being aware of this can help ISG create the most diverse workforce possible. This workshop led to significant changes in our job applications, which are now written to show that ISG is inclusive for everyone and so that individuals no matter their characteristic or combination of characteristics will feel welcomed in applying for open positions with ISG. In addition, we have transformed our profile as an employer/recruiter on LinkedIn to project positive, inclusive messages and show the rich range of people and projects which characterise our University.
This is a particularly important and relevant change for ISG. In the city of Edinburgh, the University is one of the largest employers in the region, but we compete for staff against the many banks, technology start-ups and internationally famous computer games houses located nearby. The perceptions of our staff and potential recruits with regard to ISG being an attractive workplace may be key to ensuring that we can recruit and retain talent to support the university in its business of teaching, learning and research.
Visibility and accountability
The aim of the work undertaken in ISG is to establish a visible and accountable set of equality and diversity actions tailored specifically to our workplace context but situated within a larger university, city, and technology sector. With senior management support for change and bottom up staff initiatives, we aim to ensure that it is clear to all that we are working to ensure that all members of staff, no matter the gender, race, or other identity, have a fair and inclusive workplace.
One of the ways in which we use Playfair Steps to increase visibility is to target areas of technology in which there was underrepresentation from women. Discussions about gender representations, role models and women’s participation in developing technology have begun to cross into a wide set of our activities. At University of Edinburgh we have established a high profile partnership with Wikimedia UK. This partnership is designed to increase participation by women editors in contributing to Wikipedia. Currently less than 15% of people regularly editing Wikipedia are women and topic coverage is skewed as a result. We have also hosted speakers from the technology sector specifically on topics around ‘coding for diversity’ and ‘asking about gender’ to improve the user experience of the systems we build for the university. We have also taken the opportunity to name high profile systems after women, including our media asset management platform and cloud computing service. We took the opportunity afforded by a move to a new open plan office to ensure that there were no ‘single sex silos’ , and proactively commissioned art by women for our new glass walls.
Data driven decision making and reporting
The PlayFair Steps initiative began in 2015 following an initial data gathering task. In early 2015, more than half of the 600 staff replied to a gender equality survey. The results of the survey provided the ISG senior management team with a starting place to promote equality and diversity in the workplace. In late 2015, we hired a PhD intern from within the university to interrogate the data from the gender equality plan, set SMART targets, manage our communication strategies, gather data on progress, and challenge the senior management team with new ideas.
Our Equality and Diversity Intern ( Dominique) drafted a gender equality plan mapped against ISG strategic goals and objectives for the next 5 years, which included the implementation of PlayFair Steps. The ISG Directors and other key staff were consulted and provided feedback and recommendations to gender equality plan. The latest version of that plan incorporates feedback from nearly 20 staff members. The plan was presented to and accepted by ISG senior management team and each group division regularly reports progress in specific areas against 1-5 year targets.
Our focus on driven decision making has led to important policy changes being implemented within our organisation. For instance, after a presentation to the senior management team in ISG on the analysis of the gender equality survey related to policy and human resource management, ISG’s senior management team immediately implemented a policy requiring all staff involved in recruitment to participate in unconscious bias training and an online diversity in the workplace course. In addition, we have set a short-term goal that 25% of all staff in ISG to participate in Equality and Diversity trainings. ISG’s HR staff monitor the trainings that have been undertaken by staff. We pleased to say that between October 2016 and February 2017, we surpassed our short-term goal and that 44.5% of staff within ISG have participated in some form of equality and diversity training.
The work we do with The PlayFair Steps show that its success depends on the involvement of everyone. Based on decisions that generated by data, our senior managers take a unique opportunity to implement policies that will support and benefit all staff. This, in turn, allows us to have the most inclusive workplace we possibly can.
Existing resources?
The University of Edinburgh is committed gaining Athena Swan certification. As a support department, we have fashioned our efforts in line with it. In the development of our own gender equality plan, we have found plans developed by the academic departments for Athena Swan particularly helpful. We used the plan developed from the University’s Chemistry Department (Athena Swan Gold award holders) as a guide for our own plan. The Chemistry department are also our partners in celebrating Ada Lovelace Day.
We have also used materials and guidance from Equate Scotland and from LinkedIn to improve our company profile online.
In addition, we find working with community organisations particularly helpful. For instance, after an engaging presentation at our PlayFair Steps Equality Working Group meeting on International Women’s Day, ISG became a partner with Girl Geek Scotland. The Girl Geek Scotland network and community is for people working and studying in the technology, computing, IT, digital, creative, media, business, enterprise and related sectors in Scotland who are able connect and support each other. This partnership means that all ISG staff, regardless of gender, can now be involved and participate in networking or learning-based events and access a mentoring programme. Resources such as these provide great support to the Equality and Diversity team but to all of our staff. We have provided them opportunities to expand their own networks outwith of the University.
Successes?
As an initiative, PlayFair Steps has been successful by allowing ISG staff to look at diversity and equality from various lenses and offering suggestions to change culture and attitudes to improve the workplace for all ISG staff, now and in the future.
Via the PlayFair Steps Initiative, we have shown staff and senior managers that there is a need to support women of various characteristics. After an initial focus on grade, promotions, pay and unconscious bias, we have moved forward into finding visible role models and case studies. By bringing academic expertise into the mix we have reminded colleagues that many areas of equality and diversity practice are contested, evolving and context situated. It is important for us as University staff members who support a diverse mix of students to recognise that people can face a mix of stereotypes that prohibit the inclusivity for which we are striving. We are consistently seeking solutions for this challenge.
impact ?
PlayFair Steps has been successful in that it allows staff to look at diversity and equality in various ways and from various points of view, all of which contributes to improving ISG. Since our work started promoting equality and diversity and the implementation of PlayFair Steps, we do believe our efforts have had some impact. The largest impact may be one of perception. ISG colleagues are well aware that there is a programme of equality activities. They recognise that there are talks and seminars underway, that our human resources efforts are much more focused on equality and diversity, and that the monitoring of training is in place. During the last two years, there has been a renewed focus on recruitment and selection, with proactive effort made to widen (and gain data insights into) the field of applicants and interviewees for our vacant posts. As a result, the number of women at Director level has increased three-fold and our vacancies are advertised in a more diverse range of places.
reflections to share with other institutions
The PlayFair Steps is an initiative which would be generalizable and applicable to many university central IT departments. The delivery of the programme is sponsored by senior managers and engaged staff across a range of grades including several student interns who bring fresh perspectives and up to date expertise from their own studies in gender equality, diversity and intersectionality.
One of the key messages arising from our staff survey and working group meetings was that ‘equality involves everyone’. This indicates that the success of any equality and diversity effort depends on ensuring that our plans target all groups and include a range of positive actions, in addition to those specifically designed for women. | https://thinking.is.ed.ac.uk/melissa/playfair-steps/ |
The United Nations Educational, Scientific and Cultural Organization (UNESCO) has designated 129 World Heritage Sites in Africa, but these 36 are listed as Outstanding Universal Value for natural heritage. As you might expect, there is a wide diversity of flora and fauna in each. Sadly, some of these have also been placed on UNESCO’s List of World Heritage Sites in Danger, most often due to poaching of endangered wildlife. The UNESCO committee may inscribe new sites on the list, or it may delist sites if the area no longer meets the criteria, but this is UNESCO’s current list for Africa in 2013 as of the time of publishing. | http://www.lovethesepics.com/2013/08/ |
Want to prevent injuries while playing netball?
Follow our tips this week to reduce the risk, enhance performance and prolong game time.
1. Ensure you complete an adequate warm up. This has been shown to decrease injuries in netball.
2. Book in with us for an assessment for individualised advice and exercises to enhance your performance and decrease injury risk.
3. Follow the KNEE program developed by Netball Australia to practice and perfect techniques involving landing, take off, deceleration and change of direction
4. Improve strength and power in the lower limb muscles.
5. Practice landing! Reducing injuries is not only about having a powerful jump, but having good technique on landing.
6. Ensure you wear the correct shoes. Netball shoes are designed for the surface and movements.
Leave a Reply. | http://www.beachlifephysio.com/blog/6-tips-to-prevent-netball-injuries |
Highlights from the ballot …
Given all the changes you’ll find below, this seems like an appropriate time to remind readers of two voting guidelines the Associated Press provides the 63 participants in its weekly poll.
The first guideline mentioned each year is, “Base your vote on performance, not reputation.”
This seems self-explanatory but is difficult to apply across the board early in the season. Many teams have yet to face high-level opponents, creating an uneven distribution of quality results.
Some teams on my ballot have a quality win; some have a quality loss; others have zippo and are ranked based on an admitted subjective assessment.
The second guideline is often overlooked by fans (and sometimes by voters):
“Don’t hesitate to make significant changes in your ballot from week to week. There’s no rule against jumping a 16th-ranked team over the eighth-ranked team if No. 16 is coming off a big victory and No. 8 survived an unranked team.”
We made several “significant” changes this week, based on the results:
— Notre Dame and Texas A&M aren’t on the ballot following their upset losses, for example.
— BYU cracked the top-10 after beating Baylor.
— Washington State made an appearance after winning at Wisconsin.
And there are other examples.
The new names and placements could be temporary — or they could last the season. We have no idea and will adjust weekly as the results dictate.
To the ballot …
1. Georgia
2. Alabama
3. Ohio State
4. Michigan
5. Oklahoma
6. Clemson
7. Arkansas
8. Brigham Young
9. Baylor
10. USC
11. Oklahoma State
12. Cincinnati
13. Kentucky
14. Mississippi
15. Florida
16. Utah
17. Florida State
18. Washington State
19. Wake Forest
20. Tennessee
21. Michigan State
22. Texas
23. Oregon State
24. Marshall
25. Penn State
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Rimon Bouchiba November 20, 2020 Math Worksheets
Good questions are particularly suitable for this because they have the potential to make children more aware of what they do know and what they do not know. That is, students can become aware of where their understanding is incomplete. The earlier question about area and perimeter showed that by thinking about area and perimeter together the student is made aware of the fact that the area can change even though the perimeter is fixed. The very act of trying to complete the question can help children gain a better understanding of the concepts involved. The manner in which some children went about answering the following question illustrates this point.
James and Linda measured the length of the basketball court. James said that it was 25 yardsticks long, and Linda said that it was 24 ½ yardsticks long. How could this happen?
Some fifth and sixth grade students were asked to discuss this question in groups. They suggested a variety of plausible explanations and were then asked to suggest what they need to think about when measuring length. Their list need to agree on levels of accuracy, agree on where to start and finish, and the importance of starting at the zero on the yardstick, avoid overlap at the ends of the yardsticks, avoid spaces between the yardsticks, measure the shortest distance in a straight line.
By answering the question the students established for themselves these essential aspects of measurement, and thus learned by doing the task.
As we have discussed, the way students respond to good questions can also show the teacher if they understand the concept and can give a clear indication of where further work is needed. If Linda's teacher had not presented her with the good question she would have thought Linda totally understood the concepts of area and perimeter. In the above example, the teacher could see that the children did understand how to use an instrument to measure accurately. Thus we can see that good questions are useful as assessment tools, too.
Several Acceptable Answers
Many of the questions teachers ask, especially during mathematics lessons, have only one correct answer. Such questions are perfectly acceptable, but there are many other questions that have more than one possible answer and teachers should make a point of asking these, too. Each of the good questions that we have already looked at has several possible answers. Because of this, these questions foster higher level thinking because they encourage students to develop their problem-solving expertise at the same time as they are acquiring mathematical skills.
There are different levels of sophistication at which individual students might respond. It is characteristic of such good questions that each student can make a valid response that reflects the extent of their understanding. Since correct answers can be given at a number of levels, such tasks are particularly appropriate for mixed ability classes. Students who respond quickly at a superficial level can be asked to look for alternative or more general solutions. Other students will recognize these alternatives and search for a general solution.
In this article, we have looked more closely at the three features that categorize good questions. We have seen that the quality of learning is related both to the tasks given to students and to the quality of questions the teacher asks. Students can learn mathematics better if they work on questions or tasks that require more than recall of information, and from which they can learn by the act of answering the question, and that allow for a range of possible answers.
Good questions possess these features and therefore should be regarded as an important teaching tool for teachers to develop.
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The first rule of foraging is never mention the spot where you went foraging.
OK. Maybe its not quite that dramatic. But keeping the location secret was the only condition chef Nick Strawhecker, who owns and cooks at Dante Ristorante, made me agree to before inviting me into the wilderness, along with his sous chef, Dave Smyrk, and chef de cuisine, Jake Newton.
We spent the better part of four hours – precious daytime prep and kitchen time for most chefs — tromping through wooded areas and swampy meadows looking for coveted, truly local ingredients.
“When I worked in Oregon and Washington state, we paid $25 a pound for morels in the spring,” Strawhecker said. “I never knew until I moved back here that I could go out into the woods and pick them myself. Foraging season is one of the most exciting times of the year.”
Strawhecker and his crew are among many Omaha chefs who have turned to the wild for indigenous ingredients. Diners may have eaten hand-foraged morel mushrooms with their pizzas at Dante. They might have seen menus list stinging nettle, a plant that turns from violent to gentle once cooked. And as the summer rolls on, chefs will be spending time in fields hunting for ingredients such as wild mustard greens, horseradish, garlic shoots, asparagus, berries and other native edibles.
One of the biggest reasons chefs are turning to wild food is flavor. “We have hit this place as foodies where we have tried so many things, but they are all kind of the same thing,” said Adam Hintz, who is an edible forager, owner of Lincoln’s Meadowlark Coffee and the president of Lincoln’s Friends of Wilderness Park. “Those dishes are mixed with the same ingredients.
With wild edibles, you add to that palate of flavor. You are expanding it.” Tama Matsuoka Wong, a professional forager who gathers ingredients for Daniel Boulud’s New York City restaurant Daniel, agreed. “Foraged food has a deeper taste,” she said. “When you start to think about what you buy in the grocery store, it all tastes kind of the same — bland and watery.”
As we tromped through the damp woods, Strawhecker, Smyrk and Newton started tossing recipe ideas back and forth. Pheasant with greens. Beef with morels and butter. Pasta with arugula and wild nettles. Many came to fruition later that day.
A classic margherita pizza topped with tender, meaty morels. A simple, fresh dish of seasonal asparagus, an Italian cured meat, a soft-poached egg, morel mushrooms and house-made croutons meant to be eaten in place of a classic green salad. Handmade ravioli filled with house-made ricotta and cooked wild nettles, which taste almost like a more randy version of spinach. And the creme de la creme, a medium-rare, tender rib-eye topped with nettle butter, fennel pollen, frisee and morels — a decadent dish embracing the season’s wild side.
Wong, who wrote a book in 2012 called “Foraged Flavor,” said when she first began collecting wild edibles, she didn’t know what to do with the ingredients beyond tossing them in salads or steeping them into tea. She found the lack of recipes frustrating. She was dining at Daniel in New York City with friends who encouraged her to drop off some of her foraged, wild ingredients for the chef to consider using in their meal. The chef used her plants, and after dinner, the restaurant’s chef de cuisine, Eddy LeRoux, asked her for more. She began bringing him ingredients foraged from the meadow near her home, hauling huge trash bags full of weeds into the city on the subway. Eventually the two co-wrote their guide book to foraging with lots of recipes for full dishes.
Wong encourages first-time foragers not to get overwhelmed. “I started with knowing what was around me, and then knowing whether it was edible or not came next,” she said. “The worst is to overdo it and have a list of hundreds of plants. Just start with one thing.” Wong has a sustainability code for each plant listed in her book. Plants marked green grow in abundance and should be harvested. Those marked yellow are endangered, and the ones marked with red shouldn’t be harvested in bulk.
“Foraging really isn’t free,” she said. “Someone is managing the landscape. You want to make sure you are a part of that and not taking it away and not giving back.” Hintz recommended two books for beginning foragers: a Peterson Field Guide for edible plants, which comes in many regional varieties, and “Wild Seasons: Gathering and Cooking Wild Plants of the Great Plains” by Kay Young. | https://www.danteomaha.com/owh-dante-foraged-flavor/ |
In particular, Long Binh Border Gate Station presented 400 gifts, including a ton of vegetables and fruits, 500 kilograms of fish, 100 kilograms of pork in total, to households in the locked-down areas of Tan Thanh and Tan Khanh hamlets in Long Binh townlet, An Phu district.
The station divided its troops into different teams. These teams delivered food to residents by various transport means, including trucks, tricycles, motorbikes, handcarts.
As known, over the past time, the officers and soldiers of Long Binh Border Gate Station have promoted production to help pandemic-hit people while calling on other benefactors in the locality to donate for needy people.
Amid the complicated developments of the COVID-19 pandemic, the border troops have conducted meaningful activities, such as offering rice, necessities and face masks, opening “Zero-VND stall” programs, and others.
This practical support of the troops has contributed to helping locals overcome their difficulties and feel more secure during the pandemic. | https://en.qdnd.vn/military/public-relations/border-guards-support-local-people-in-locked-down-area-533049 |
Manufacturing has changed a lot due to the COVID-19 pandemic as technologies thought to be happening down the road are happening now. Five key drivers are highlighted.
The COVID-19 pandemic and government-mandated shutdowns had a significant impact on our lives. Supply chain disruptions became part of regular news debates and discussions. Manufacturers had to pivot their operations according to the new reality. The change in industry leaders expected to happen by 2025 are happening now. Industry 4.0 is now closer than ever with widespread adoption by industry leaders across the world.
Let us take a look at how manufacturing is changing for good in the post-pandemic world.
Future of manufacturing
Multifaceted changes are happening in the manufacturing industry. They address the various inefficiencies in manufacturing facilities. The focus is on process improvements for the current industry landscape. There are five key drivers in the change:
Automation and robotics
IoT and artificial intelligence
Upskilled workforce
Localized supply chain
Digital supply chain.
1. Automation and robotics
Automation was the hallmark of Industry 3.0. The introduction of programmable logic controllers (PLCs) and supervisory control and data acquisition (SCADA) systems in manufacturing facilitated this. The rise of microprocessors and associated software has increased access to automation. It also made it easier to implement automated manufacturing facilities. It led to the rise of versatile robots, like six-axis robots. The cost of implementation is also dropping every year.
The lockdowns due to the pandemic gave an edge to manufacturers with automated facilities. They ensured a socially distanced work environment and worked with a smaller workforce. Manufacturing facilities will move to an automated production line. It will use programmable robots and control systems. Turnkey assembly line solutions help manufacturers to install automated production lines.
2. Upskilled labor force
The workforce of the future needs a completely different skillset from that of today. Today forklift operators are prevalent in almost all manufacturing facilities. Forklift drivers will become redundant with automated guided vehicles (AGVs) and other automated moving technologies.
However, it necessitates the need for labor force with other specialized skill sets. Automated factories will need maintenance technicians more than operators. Production loss is costly in an automated manufacturing facility. Maintenance technicians are the ones who have to ensure the machines run according to the specifications. They will also need to conduct predictive maintenance.
There will be an increase in demand for other technical services. These include troubleshooting, equipment assembly, researchers, engineers, and operations executives. There will also be a shift in industries that demand more labor. The pandemic increased the reliance on e-commerce for everyday shopping. This led to a higher requirement for labor in warehouses and distribution centers. The workforce has to adapt to the changes by investing in improving their knowledge and skills.
Courtesy: RedViking
3. IIoT and the data economy
The Industrial Internet of Things (IIoT) will be widespread in manufacturing facilities of the future. The basic tenet of IIoT is that every device in a manufacturing facility will have sensors that collect data round the clock. The data thus collected is relayed through a low-latency, fast network for automation control and analysis. Automation control systems will work faster with 5G and Wi-Fi 6E coming up soon.
The vast amount of data collected can be analyzed using artificial intelligence. Machine learning algorithms can draw insights from data. Traditional analytics would not be able to handle the large volume of complex data. Cloud computing enables big data analysis using artificial intelligence. Edge computing helps to analyze data faster on devices within the premises of the factory.
The vast amount of data collected is useful for predictive maintenance. Machine learning algorithms analyze various streams of data to predict machine failure. IIoT data is also useful in implementing digital twins. Digital twins help OEMs monitor all their assets while in operation. Data from assets in one part of the world can be used to improve assets in another facility. They also can be used for predictive maintenance.
4. Localized manufacturing capability
COVID-19 exposed the vulnerabilities in the global supply chain. This was aggravated by the blockage of the Suez Canal. Manufacturers are now aware of the danger of concentrating their production capabilities in one part of the world. They are setting up localized supply chains for a robust logistics infrastructure.
U.S manufacturers will move more manufacturing facilities to the United States. This will reduce the dependency on production facilities in Asian countries. Strong political and social pressures are also factors in the change. Consumers also view goods produced in China negatively. Various states in the United States are giving businesses incentives for setting up manufacturing facilities in the U.S.
Manufacturers shifting production facilities to the U.S will have to balance the need for a strong supply chain and cost concerns. Automation with the use of specialized robots is the way forward for them. This will be complemented by recruiting skilled labor from within the country. This helps the businesses to have a reliable and robust supply chain. Also, provides an economic boost to local communities.
5. Digital supply chain
The supply chain is the complete infrastructure from sourcing raw materials to delivering products to the end consumer. Supply chain shocks experience due to coronavirus disruptions made companies rethink the entire supply chain function. Supply chain visibility became important in managing it.
Supply chain visibility is the capability to track movement in the entire supply chain from one location. This includes monitoring a lot of moving parts. These include,
Suppliers
Vendors
Warehouses
Distribution centers
Point of sale data
Manufacturing data
Live transport data
Employee information
Macroeconomic data
Geopolitical news.
The variables are limitless as every stakeholder has to be monitored. Supply chain visibility is enabled by software integrations with all the stakeholders. Another aspect is the trust between various parties that leads to open and transparent communication.
The future of manufacturing awaits
The changing trade landscape necessitates a change in the approach to manufacturing in the future. Automation, skilled labor, local US manufacturing facilities, and a robust supply chain will form the bedrock for the future of manufacturing in the post-pandemic world. RedViking is a pioneer in bringing solutions to challenging manufacturing problems. RedViking has turnkey solutions for assembly lines, robotic applications, and other challenging engineering problems.
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Introduction
============
Hypertension is an important risk factor for the development of stroke, coronary heart disease, and congestive heart failure ([@b29-vhrm-4-0963]; [@b47-vhrm-4-0963]). The estimated total number of adults with hypertension in 2000 was 972 million, and this may increase by about 60% to a total of 1.56 billion in 2025 ([@b18-vhrm-4-0963]). A prolonged reduction of diastolic blood pressure (BP) of only 5 mmHg in the general population may reduce the number of strokes by 34% and the number of myocardial infarctions by 21% ([@b29-vhrm-4-0963]; [@b47-vhrm-4-0963]). Many dietary and lifestyle factors have been implicated in the etiology of hypertension ([@b3-vhrm-4-0963]), of which overweight, physical inactivity, excessive salt consumption, and low potassium intake are the most important contributors in Western societies ([@b9-vhrm-4-0963]). The epidemiological evidence for an effect of coffee on BP is summarized in this review, with a focus on habitual ('chronic') intake because of its relevance to public health. Short-term, acute effects of coffee intake or caffeine administration on BP have been addressed by others ([@b35-vhrm-4-0963]), and are beyond the scope of this review. Before discussing scientific evidence on the relation between coffee and BP, the state of the art on coffee intake in relation to cardiovascular disease is briefly discussed, and an overview of different epidemiological study designs is given with their strengths and limitations. Subsequently, cross-sectional and prospective cohort data on coffee and BP are summarized, followed by a discussion of experimental evidence from randomized controlled trials (RCTs). Finally, potential biological pathways for an effect of coffee on BP are briefly described, which is followed by an overall discussion of the total available evidence. Coffee in this review is considered to be filtered caffeinated coffee, except when stated otherwise.
Coffee and cardiovascular disease
=================================
Several large cohort studies reported no association between habitual coffee intake and risk of CVD ([@b11-vhrm-4-0963]; [@b57-vhrm-4-0963]; [@b60-vhrm-4-0963]; [@b2-vhrm-4-0963]; [@b27-vhrm-4-0963]). Coffee neither influenced prognosis after myocardial infarction ([@b31-vhrm-4-0963]). [@b46-vhrm-4-0963] performed a meta-analysis of 23 epidemiological studies on coffee, that included in total 403,631 participants. Despite a significant association between high daily coffee intake and coronary heart disease in case-control studies, no significant relation emerged from long-term follow-up prospective cohort studies ([@b46-vhrm-4-0963]). Among the studies that suggested an inverse relation of coffee with CVD are the Iowa Women's Health Study in over 41,000 women aged 55--69 ([@b2-vhrm-4-0963]), and the Scottish Heart Health Study in over 11,000 men and women aged 40--59 ([@b60-vhrm-4-0963]). Coffee may also protect against diabetes mellitus type 2. In a Dutch epidemiological study among over 17,000 men and women, subjects who drank 7 or more cups of coffee per day had only half the risk of developing diabetes compared to subjects who drank 2 cups or less ([@b52-vhrm-4-0963]). [@b53-vhrm-4-0963] conducted a meta-analysis of 15 epidemiological studies in which they showed that the risk of type 2 diabetes was 35% lower in subjects who drank over 6 or 7 cups of coffee per day, and 28% lower in subjects who drank 4--6 cups per day, compared to subjects with zero or low intake (∼2 cups per day). The underlying mechanisms for a potentially protective effect of coffee on CVD and diabetes, including the possible role of BP, remain to be elucidated.
Methodological aspects of epidemiological studies
=================================================
Observational (cohort) studies, mainly cross-sectional studies, have the major advantage that they can provide insight into the long-term effects of coffee on BP. Furthermore, the large sample size allows examination of different doses of coffee and possible effect modification by gender, age, race, cardiovascular risk profile, and other characteristics. It should be noted, however, that observational evidence can never be used to demonstrate causality. Coffee drinking is part of an individual's lifestyle ([@b44-vhrm-4-0963]) and is related to many other factors, such as alcohol intake, mental stress, and dietary habits, which may also influence BP. Therefore, when interpreting observational data, one should make certain that potential confounders have been adequately adjusted for. Residual confounding in the data, eg, by lack of adjustment for physical activity, may distort the relation between coffee consumption and BP. Cohort studies often include many subjects. However, a large sample size is by no means a guarantee for the internal validity of a study and may even hamper the accurate measurement of dietary and lifestyle factors (leading to residual confounding). Inaccurate measurement of coffee intake further leads to misclassification of subjects, which could yield a diluted (attenuated) estimate for the coffee-BP association. Cross-sectional studies or surveys, in which coffee intake and BP are measured at the same point in time, have the additional problem of 'reverse causation'. Since there is no time span between the assessment of coffee intake and BP measurement, it is possible that people who are aware of having high BP have already adapted their level of coffee consumption. As a result, a biased relation may be found between low (in fact: lowered) coffee intake and high BP levels.
A main feature of experimental studies, or RCTs, is that both the intervention (eg, use of coffee or caffeine tablets) and control treatment (eg, decaffeinated coffee or placebo) are randomly assigned to participating subjects. By this means, any confounders that could distort the relation between coffee and BP are equally distributed over both groups, and a valid estimate of the effect of coffee on BP can be obtained. RCTs are therefore considered the 'gold standard' in epidemiological research, and may even provide insight into causal effects when conducted in a double-blind manner. However, compared to observational epidemiological studies, they have the disadvantage that only fixed doses of coffee or caffeine can be studied during a relatively short period of time. Furthermore, trials may suffer from poor adherence to the assigned treatments, unsuccessful randomization (in small trials), or lack of blinding of the participant and/or investigator, which could introduce bias. Also, the number of subjects that can participate in a RCT is limited.
Coffee and BP: evidence from observational studies
==================================================
Cross-sectional studies
-----------------------
Cross-sectional studies of coffee intake and BP date from the early 1980s. [@b24-vhrm-4-0963] performed a cross-sectional analysis of coffee and BP in 6,321 adults from Paris. After controlling for age, sex, BMI, alcohol consumption, smoking and socioeconomic status, systolic BP appeared to be higher in coffee drinkers ([@b24-vhrm-4-0963]). In a similar analysis by this group among 1,491 subjects from Algiers, diastolic BP was elevated in coffee drinkers after adjustment for sex, age, BMI, physical activity, rural versus urban residency, smoking, and tea consumption ([@b25-vhrm-4-0963]). BP differences in both studies were modest (2--3 mmHg). A small study in 255 Dutch elderly showed a positive relation of coffee use with BP, but only in women ([@b28-vhrm-4-0963]). [@b5-vhrm-4-0963] also showed a positive relation in 843 Australian men and women aged 60--87, but only in coffee drinkers who used antihypertensive drugs. [@b33-vhrm-4-0963] found higher systolic BP in Italian men who took 4 or more cups of coffee per day compared to nondrinkers, but only for daytime ambulatory BP and not for office BP.
In 5,147 Australian adults, caffeine consumption (mainly through coffee) within the last 3 hours was associated with higher BP in both sexes after controlling for age, adiposity, family history of hypertension, serum cholesterol, alcohol use, and smoking ([@b45-vhrm-4-0963]). Average daily caffeine intake, on the other hand, was not associated with BP in this survey. Similarly, in a Swiss study in 338 young women, coffee consumption on the testing day was related to elevated BP whereas no association was found with habitual coffee intake ([@b14-vhrm-4-0963]). In the CARDIA study of 5,115 black and white young adults ([@b26-vhrm-4-0963]), caffeine intake (up to 800 mg/d) through foods and beverages was not consistently related to BP when controlling for age, sex, race, physical activity, BMI, oral contraceptive use, alcohol use, smoking, and other potential confounders. An analysis of Framingham data that comprised over 6,000 middle-aged men and women neither showed a significant relation of coffee intake with BP ([@b58-vhrm-4-0963]).
Two large US cross-sectional studies showed a negative (inverse) correlation of coffee with BP ([@b39-vhrm-4-0963]; [@b21-vhrm-4-0963]). This was confirmed in a survey of 500 Italian health care workers ([@b38-vhrm-4-0963]), where BP declined by 0.8/0.5 mmHg per cup. Another Italian study by [@b42-vhrm-4-0963] among 9,601 adults showed 2--3 mmHg lower systolic BP in subjects who drank 4--5 cups of coffee per day compared to abstainers. Similarly, in 336 male self-defense officials in Japan, daily coffee drinking was associated with lower BP (around 0.5 mmHg/cup), after adjustment for green tea intake, alcohol use, smoking, body mass index (BMI), and diabetes ([@b55-vhrm-4-0963]). In another Japanese study of 1,902 men and women aged 40+ from Tanushimaru, one of the cohorts of the Seven Countries Study, coffee consumption was inversely related to BP whereas intake of green tea was not ([@b13-vhrm-4-0963]). Coffee was also weakly inversely correlated with systolic and diastolic BP in the Danish MONICA cohort after multivariable adjustment ([@b19-vhrm-4-0963]). In the Copenhagen Male Study of 2,975 older men, BP levels and prevalence of hypertension declined across coffee categories after multivariable adjustment, ie, 123/74 mmHg (14% hypertensive) for 1--4 cups, 121/72 mmHg (11%) for 5--8 cups, and 117/70 mmHg (7%) for 9+ cups per day ([@b12-vhrm-4-0963]). BP data in abstainers were not presented in this study. A UK health check in 1989--1993 showed that habitual coffee intake (mainly instant) was inversely related to systolic BP in 478 men, with levels gradually declining from 134 mmHg in abstainers to 126 mmHg in subjects drinking more than 6 cups per day ([@b23-vhrm-4-0963]). In 586 UK women an inverse U-shaped relation was seen, with highest systolic BP levels for 1--2 cups per day (128 mmHg) and lowest levels for \>6 cups per day (117 mmHg). Data were adjusted for age, BMI, smoking, alcohol use, and physical activity ([@b23-vhrm-4-0963]). A Norwegian study of almost 30,000 middle-aged men and women also showed an inverse U-shaped relation, with lowest BP values both in abstainers and in coffee drinkers who took 9 or more cups per day ([@b48-vhrm-4-0963]). [@b27-vhrm-4-0963] in a cross-sectional analysis of 730 healthy and 663 diabetic women from the Nurses' Health Study I cohort, studied caffeinated and decaffeinated coffee in relation to endothelial function and found no association. In these data, an inverse U-shaped relation between coffee intake and presence of hypertension was seen in healthy women, with a larger proportion of hypertensives for intakes around 1 cup per day (25%) compared to \<1 cup per month (8%) and 2+ cups per day (17%). However, these data were not adjusted for confounders although mean age was similar across coffee categories ([@b27-vhrm-4-0963]).
Summarizing, data from cross-sectional studies provide little support for a BP-raising effect of coffee, with the possible exception for BP measured shortly after coffee intake. Rather, the data suggest an inverse linear or U-shaped relation of habitual coffee intake with BP in populations from Europe, Asia and USA ([@b39-vhrm-4-0963]; [@b21-vhrm-4-0963]; [@b38-vhrm-4-0963]; [@b48-vhrm-4-0963]; [@b42-vhrm-4-0963]; [@b19-vhrm-4-0963]; [@b23-vhrm-4-0963]; [@b12-vhrm-4-0963]; [@b55-vhrm-4-0963]; [@b27-vhrm-4-0963]; [@b13-vhrm-4-0963]), although this inverse relation may be absent at young age as shown in the CARDIA study ([@b26-vhrm-4-0963]). Gender does not seem to influence the relation of coffee with BP on basis of cross-sectional evidence.
Prospective studies
===================
Only few prospective (ie, longitudinal or follow-up) studies of coffee and (change in) BP or incidence of hypertension have been performed. In an Australian cohort of working men, coffee consumption was associated with elevated BP during 6 years of follow-up ([@b17-vhrm-4-0963]). In a prospective study in 1,017 male medical alumni with 33 years of follow-up, coffee intake was positively associated with self-reported systolic BP (0.19 mmHg) and diastolic BP (0.27 mmHg) per cup per day, after adjustment for parental hypertension, BMI, smoking, alcohol use, and physical activity ([@b20-vhrm-4-0963]). Compared with abstainers, coffee drinkers were at higher risk of developing hypertension, with the risk maximally increased by 49% for baseline intakes of 3--4 cups/day, but findings were no longer statistically significant after multivariable adjustment ([@b20-vhrm-4-0963]).
In a large study of habitual caffeine intake and risk of hypertension, [@b59-vhrm-4-0963] analyzed data from a large prospective cohort study in 155,594 US nurses. Intake of caffeinated coffee was weakly inversely related to incident hypertension, with around 10% reduction in risk in women who drank 4 or more cups compared to women drinking 3 or less cups per day. Data were adjusted for age, BMI, family history of hypertension, physical activity, smoking, oral contraceptive use (in female subjects), and intake of alcohol, tea, and cola. Interestingly, contrary to coffee, an high intake of cola significantly increased the risk of hypertension in these women ([@b59-vhrm-4-0963]).
Recently, a prospective analysis of coffee intake and incident hypertension has been performed in 2,985 men and 3,383 women in The Netherlands with over 10 years of follow-up ([@b50-vhrm-4-0963]). This study showed an inverse U-shaped relation in women, with abstainers having a 49% reduced risk and women who drank more than 6 cups per day having a 33% reduced risk of hypertension compared to light coffee drinkers (\>0--3 cups per day). Data were adjusted for age, height and weight, smoking, socioeconomic status, and intake of tea, alcohol, and total energy. In men, the risk of hypertension also tended to be reduced in abstainers but data were not statistically significant ([@b50-vhrm-4-0963]). Overall, the inverse association between coffee and hypertension was mainly present in older subjects (\>39 years). On the other hand, an Italian study in 800 men and 307 women with elevated BP (mean age: 33 years) showed that coffee drinkers developed sustained hypertension more frequently than abstainers (53% vs 44%) during more than 6 years of follow-up ([@b15-vhrm-4-0963]). The Italian 'espresso' coffee was the predominant type of coffee in this study, which is prepared without a paper filter. In 2,505 Finnish subjects aged 25--64 with 13 years of follow-up, the risk of initiating antihypertensive treatment was increased by 20%--30% in subjects who drank 2--7 cups daily, compared to those who drank 0--1 cups ([@b37-vhrm-4-0963]). Around 12% of this Finnish cohort drank unfiltered pot-boiled coffee. Interestingly in this study, the risk in subjects who drank 8 or more cups per day was only increased by 14%, and adjustment for baseline BP attenuated the associations ([@b37-vhrm-4-0963]).
In conclusion, prospective epidemiological studies do not provide a clear picture on the role of coffee intake in the development of hypertension. Risks may be lower both in abstainers and in subjects with a relatively high intake, although this was not found in all studies. Especially in female coffee drinkers, the risk of hypertension may be reduced at higher intakes (\>4--6 cups/day). The number of studies, however, is small, which hampers the drawing of conclusions.
Coffee and BP: evidence from RCTs
=================================
A large number of RCT of either coffee or caffeine intake on BP have been performed, which have been systematically reviewed by different research groups ([@b32-vhrm-4-0963]; [@b16-vhrm-4-0963]; [@b35-vhrm-4-0963]; [@b34-vhrm-4-0963]). [@b32-vhrm-4-0963] provided an overview of BP trials with daily caffeine doses around 100--500 mg that were published between 1978--1987 and found that caffeine did not cause any persistent increase in BP. Furthermore, he concluded that individuals who do not regularly ingest caffeine may experience an increase in BP when drinking coffee, but that tolerance develops in 2--3 days with BP returning to initial levels ([@b32-vhrm-4-0963]). [@b16-vhrm-4-0963] performed a meta-analysis of 11 RCT with a median duration of 56 days. After pooling of trials, they found a significant increase in BP of 2.4 mmHg systolic and 1.2 mmHg diastolic for a median coffee intake of 5 cups per day ([@b16-vhrm-4-0963]). Also, they reported a dose-response relation between number of cups consumed and change in BP, and larger effects in younger subjects ([@b16-vhrm-4-0963]).
[@b35-vhrm-4-0963] performed an extensive descriptive review of both epidemiological and experimental studies, from which they concluded that regular coffee consumption may be harmful to hypertension-prone subjects. In their paper, the authors separated studies with continuous ambulatory BP monitoring from studies with BP measurements at the research center. The 10 studies that used ambulatory BP were of shorter duration, and half of these lasted less than 1 week. Caffeinated coffee (3+ cups per day) increased ambulatory BP by around 3--6 mmHg in 7 studies, whereas BP was not affected in the remaining 3 studies ([@b35-vhrm-4-0963]). In controlled trials that used office BP, caffeinated coffee caused BP elevation in one-third of the studies ([@b35-vhrm-4-0963]).
[@b34-vhrm-4-0963] performed a meta-analysis of caffeine and coffee trials with a median duration of 42 days, excluding studies that lasted \<7 days. When caffeine trials (n = 7) and coffee trials (n = 18) were analyzed separately, BP elevations appeared to be 4 times greater for caffeine given as tablets (4.2 mm Hg systolic and 2.4 mm Hg diastolic) than for caffeinated coffee (1.2 and 0.5 mm Hg, respectively). These differences could not be explained by caffeine dose, since the median daily caffeine dose in caffeine trials was 400 mg per day (range, 295--750 mg) and in coffee trials was 455 mg per day (range, 225--798 mg) ([@b10-vhrm-4-0963]). Overall, this study showed a somewhat larger systolic BP response to coffee or caffeine in younger populations (mean age \<40 years), as was also the case in the meta-analysis by [@b16-vhrm-4-0963]. It should be noted that the trials that formed the basis of the abovementioned meta-analyses were mostly conducted in normotensive Caucasian populations that were relatively young ([@b16-vhrm-4-0963]; [@b34-vhrm-4-0963]). Therefore, the BP estimates from these meta-analyses cannot be generalized to other type of populations, eg, hypertensives, elderly or Asian subjects, or to the population at large.
Recently, a number of new trials related to coffee and BP have been published. A Japanese research group repeatedly demonstrated a beneficial effect of chlorogenic acid from green bean coffee extract on vasoreactivity and BP in mild hypertensives, with reductions around 3--4 mmHg ([@b36-vhrm-4-0963]; [@b22-vhrm-4-0963]; [@b56-vhrm-4-0963]). Another Japanese trial showed that coffee (3+ cups per day) reduced BP by 7--10 mmHg systolic and 3--7 mmHg diastolic in (pre)hypertensive men who consumed 60 ml of alcohol per day ([@b8-vhrm-4-0963]). [@b49-vhrm-4-0963] showed that caffeinated coffee blunted the BP response to mental stress in habitual, but not in nonhabitual coffee drinkers, despite preserved muscle sympathetic nervous activation. Their findings led to the conclusion that ingredients other than caffeine could be responsible for the stimulating effect of coffee on the cardiovascular system ([@b49-vhrm-4-0963]).
When combining evidence from RCT of coffee and BP, it can be concluded that short-term (\<12 weeks) intake of caffeinated coffee, both filtered and instant, causes BP elevations around 2/1 mmHg when compared to abstinence or use of decaffeinated coffee. BP elevations were more apparent when ambulatory BP monitoring was applied ([@b35-vhrm-4-0963]). Stratified meta-analyses suggest larger BP elevations in the case of prolonged coffee use (\>6 weeks), a short run-in period (\<1 week), younger age (\<40 years) and high levels of coffee intake (\>5 cups/d) ([@b16-vhrm-4-0963]; [@b34-vhrm-4-0963]). However, it should be emphasized that there is a lack of trials of coffee and BP in elderly, hypertensives and non-Caucasians and no conclusions with regard to these subgroups can be drawn. In addition, long-term trials of coffee and BP are warranted. As a suggestion, habitual noncoffee drinkers may be randomized to daily use of pills or capsules that contain filtered coffee extract or placebo for a period of \>1 year. Preferably, a 2 × 2 factorial design should be used so that the effect of caffeine can be studied separately from other substances in coffee.
Coffee and BP: biological pathways
==================================
Most available evidence points toward caffeine as the BP-raising agent in coffee. Caffeinated and decaffeinated coffee were compared in a randomized double-blind, crossover trial in 45 habitual coffee drinkers ([@b54-vhrm-4-0963]). Daily intake of 5 cups of decaffeinated coffee for a period of 6 weeks significantly reduced ambulant BP by 1.5 mmHg systolic and 1.0 mmHg diastolic, compared to a similar amount of regular coffee ([@b54-vhrm-4-0963]). A number of mechanisms have been proposed by which caffeine could raise BP, including sympathetic overactivation, antagonism of adenosine receptors, increased norepinephrine release via direct effects on the adrenal medulla, renal effects, and activation of the renin--angiotensin system. These mechanisms have been discussed in detail by others ([@b40-vhrm-4-0963]; [@b32-vhrm-4-0963]; [@b35-vhrm-4-0963]). More recently, a Japanese group showed enhanced endothelium-dependent vasodilatation after acute caffeine administration in young healthy men ([@b51-vhrm-4-0963]), a mechanism by which caffeine could lower BP. From experimental research it has become clear the caffeine administration acutely raises BP, but tolerance to this effect develops rapidly and heavy coffee drinkers are less likely to show a BP response after caffeine intake ([@b41-vhrm-4-0963]; [@b1-vhrm-4-0963]; [@b32-vhrm-4-0963]).
As shown in the meta-analysis by [@b34-vhrm-4-0963] the BP-raising effect of caffeine when ingested through coffee is probably less compared to caffeine tablets. One possible explanation could be a difference in bioavailability of caffeine from coffee and tablets. Also, coffee is a rich source of bioactive compounds that may lower BP ([@b6-vhrm-4-0963]; [@b43-vhrm-4-0963]; [@b30-vhrm-4-0963]; [@b4-vhrm-4-0963]; [@b7-vhrm-4-0963]). The amount of caffeine and other components in coffee made in a household coffee-maker with a paper filter was quantified in the Netherlands ([@b43-vhrm-4-0963]). It was estimated that 5 cups of coffee per day contribute to approximately 26% of the daily intake of potassium, 12% of the daily intake of magnesium, 10% of the daily intake of manganese, and 15% of the daily intake of niacin ([@b43-vhrm-4-0963]). Apart from minerals and trace elements, coffee is a rich source of polyphenols, including chlorogenic acid and the lignan secoisolariciresinol ([@b30-vhrm-4-0963]; [@b4-vhrm-4-0963]). Recently, it was shown that brewed coffee (espresso, filter, instant) contains high amounts of soluble fibre and associated antioxidant polyphenols ([@b7-vhrm-4-0963]). It is possible that BP-lowering minerals and polyphenols in coffee outweigh potential adverse effects of caffeine. This hypothesis was confirmed by the prospective study in US Nurses ([@b59-vhrm-4-0963]), in which caffeinated cola that is poor in polyphenols increased the risk of hypertension whereas coffee did not. Also, the meta-analysis by [@b34-vhrm-4-0963] showed that caffeine intake through tablets could be more detrimental to BP than caffeine intake through coffee.
In the present review, psychosocial factors related to the habit of coffee drinking are not addressed, but it is conceivable that such factors may contribute to either beneficial or adverse effects on BP. Furthermore, interaction of coffee with smoking, alcohol consumption and mental stress may affect BP ([@b32-vhrm-4-0963]), but a discussion of mechanisms that could underlie such effects is beyond the scope of this review.
In summary, there are many possible biological pathways through which a variety of bioactive substances in coffee may influence BP, either resulting in an overall BP-lowering or a BP-raising effect of coffee. Effects of coffee on BP, if any, probably result from activation or inhibition of different pathways, and not from caffeine-related pathways only.
Discussion
==========
Epidemiological studies of long-term consumption of filtered coffee do not support the hypothesis that filtered caffeinated coffee is detrimental to BP. On the contrary, there is observational evidence that high intake (\>4 cups per day) may even reduce the risk of hypertension, especially in women. The nature of the relationship between coffee and BP is not yet clear, and further investigation is needed to find out whether abstainers are at a lower or higher risk of hypertension than occasional coffee drinkers (1--2 cups per day). Findings from experimental studies suggest a BP-raising effect of coffee of a few mmHg in the short-term (\<3 months), but apparently this effect does not translate into an increased risk of hypertension in the long-term. Both observational and experimental data suggest larger BP elevations during coffee intake at younger compared to older age (ie, \>40 years). However, it should be noted that studies on coffee and BP in the elderly are sparse, as are studies in several other population subgroups, and long-term intervention studies.
A number of methodological issues need further consideration. Firstly, it has been well established that caffeinated coffee causes an acute rise in BP shortly after exposure ([@b35-vhrm-4-0963]), as is the case for other lifestyle factors such as smoking, alcohol intake, physical activity, and even talking. Such acute physiological responses are mostly transient, with BP returning to initial levels within hours. It is not yet clear whether repeated BP elevations during the day could eventually lead to persistent hypertension. For coffee, on basis of available evidence from prospective studies, this does not seem to be the case. In this respect, it should be noted that office BP measurements both in epidemiological and experimental studies are not always performed in fasting conditions. From available data, it is hard to judge to what extent coffee intake prior to BP assessment (ie, acute BP effects) influenced the outcomes of the studies. To illustrate, in a trial in young Swiss women, coffee consumption on the testing day was associated with elevated BP whereas no association was found with habitual intake ([@b14-vhrm-4-0963]). Also, ambulatory BP monitoring that captures repeated acute BP elevations during coffee intake throughout the day may point towards a BP raising effect of coffee, while such BP elevations are probably transient. It is recommended that in future studies a sufficient time period is incorporated between the last cup of coffee and BP assessment, to avoid measurement of acute effects. Also, investigators should clearly state in their papers the time when the last cup of coffee was consumed.
Secondly, it is unclear whether occasional coffee drinkers are at higher risk of hypertension than heavy coffee drinkers. Also here, acute BP effects may blur the view on the role of coffee in the development of hypertension. There is ample evidence that habitual coffee users develop tolerance to caffeine and show no elevation in BP shortly after intake. BP responses will probably not occur in people who take many cups of coffee throughout the day ('continuous infusion' with caffeine). In studies that have no proper time period between BP readings and the last intake of coffee or other caffeinated beverages (eg, cup of coffee or tea offered at the research center), BP may be temporarily increased in occasional, but not in heavy coffee drinkers.
Thirdly, observational epidemiological studies suggest that there may be a U-shaped relation between habitual coffee intake and BP. Such relation is less clear from RCTs, in which effects of coffee on BP are mostly in the positive direction or absent. This discrepancy may be related to the duration of trials compared to cohort studies, and it is possible that short-term BP effects are not persistent in time. However, other (methodological) aspects may also contribute to the discrepancy. Trials generally focus on one or two specific doses of coffee, mostly in the high range (around 5 cups per day), and there is a lack of experimental data on the effect of low intakes on BP. Furthermore, in many trials the control treatment comprises cessation of coffee use, which from a physiological point of view is truly different from non-use in observational studies. 'Habitual abstainers' do not drink coffee because of disliking, health problems (eg, stomach complaints), financial aspects, or other reasons. In addition, observational studies are often population-based, whereas trials are conducted in selected groups subjects. Finally, coffee consumption in trials is carefully monitored whereas observational studies make use of self-reported data. The latter could lead to misclassification of subjects. To illustrate, subjects who are aware of having high BP may find it socially desirable to report occasional use of coffee rather than higher levels of intake because of a general belief that coffee could be harmful to health. Random misclassification of coffee intake, as discussed previously, can lead to weakened associations between coffee and BP levels or hypertension.
In conclusion, it is at present unclear whether habitual coffee drinking is related to risk of hypertension, although most evidence suggest that this is not the case. At this moment, there is no reason to refrain from coffee for the prevention of hypertension. The precise nature of the relation between coffee and BP is not yet clear. More prospective studies of coffee intake and incident hypertension are needed, as are long-term randomized placebo-controlled trials. Future studies may focus on different doses of coffee, and on specific population subgroups such as the elderly, hypertensives, and non-Caucasians. With regard to underlying biological mechanisms, research should not only focus on the BP-raising properties of caffeine but also on the potentially beneficial effect of other substances in coffee, such as polyphenols, soluble fibre, and potassium.
**Disclosure**
The author reports no conflicts of interest in this work.
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The reliability and validity of a group-administered version of the body image assessment.
The Body Image Assessment (BIA) is a simple measure of body image disturbance. However, it has currently only been used with an individual administration format and only to assess ratings of current body size, ideal body size, and body dissatisfaction. It has also only been validated for use with women. In the current two studies, the reliability and validity of a group-administered version of the BIA procedure for both men and women that also assessed ratings of the ideal opposite sex and predictions about what the opposite sex would prefer as most attractive was examined. In the first study, results indicated good test-retest reliability for the group version for current and ideal body size and good concurrent validity with the individual administration format of the BIA. The results of the second study supported the construct and predictive validity of the group administered BIA, suggesting that it is a time-efficient alternative to the original, individually administered assessment.
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There are currently 2 SciDAC institutes with 24 participating institutions and a total annual funding of $12 million. The mission of the SciDAC-4 institutes is to provide intellectual resources in applied mathematics and computer science, expertise in algorithms and methods, and scientific software tools to advance scientific discovery through modeling and simulation in areas of strategic importance to the US Department of Energy (DOE) and the DOE Office of Science (SC).
Tools and resources for lowering the barriers to effectively use state-of-the-art computational systems.
Mechanisms for taking on computational grand challenges across different science application areas.
Mechanisms for incorporating and demonstrating the value of basic research results from applied mathematics and computer science.
Plans for building up and engaging our nation's computational science research communities.
The FASTMath Institute develops and deploys scalable mathematical algorithms and software tools for reliable simulation of complex physical phenomena and collaborates with domain scientists to ensure the usefulness and applicability of FASTMath technologies.
The RAPIDS Institute solves computer science and data technical challenges for SciDAC and SC science teams, works directly with SC scientists and DOE facilities to adopt and support RAPIDS technologies, and coordinates with other DOE computer science and applied mathematics activities to maximize impact on SC science. | https://www.scidac.org/institutes.html |
The UN released the 2022 HNO and an updated multi-year HRP for Haiti on March 11 and April 14, respectively, requesting nearly $372.6 million to reach 2.5 million people with humanitarian assistance during the year.
Up to 2.5 million people in Haiti will likely experience Crisis—IPC 3—levels of acute food insecurity through October 2022 and require emergency food assistance, FEWS NET reports.
With USAID support, WFP reaches 45,000 individuals in Haiti with life-saving food assistance during April.
Background
Haiti’s endemic poverty and civil unrest—combined with recurring shocks from natural disasters, including droughts, earthquakes, floods, and hurricanes—have resulted in food insecurity and other humanitarian needs throughout the country. Since the January 2010 earthquake and October 2010 cholera outbreak, USAID has focused both on providing immediate response to affected populations and on supporting disaster risk reduction (DRR) programs that promote local and national self-sufficiency in disaster preparedness, response, and management. Since 2010, USAID has provided approximately $186 million to support stand-alone DRR programs throughout Latin America and the Caribbean, including nearly $32.2 million in funding to support DRR efforts in Haiti. In addition to stand-alone DRR programs, USAID contributed nearly $133 million to support programs integrating preparedness and mitigation activities into early recovery and transition programs in response to the January 2010 earthquake and subsequent cholera outbreak in Haiti.
Since 2011, USAID has supported the International Organization for Migration to pre-position emergency relief supplies in the event of disasters, as well as to develop Government of Haiti personnel capacity to manage facilities and deploy supplies when necessary. Pre-positioning relief commodities—including plastic sheeting, hygiene kits, and water containers—ensured that relief supplies were available for distribution to affected populations immediately following Hurricane Matthew in October 2016, and Hurricane Irma in September 2017.
In recent years, USAID has deployed Disaster Assistance Response Teams to Haiti following Hurricane Matthew and Hurricane Irma to conduct disaster assessments and coordinate response activities with the Government of Haiti and humanitarian organizations. | https://www.usaid.gov/humanitarian-assistance/haiti |
Information gathering can be from a variety of sources. Importantly to say, there are no best method of data collection. In principle, how data are being collected depends on the researcher?s nature of research or the phenomena being studied.
Data collection is a crucial aspect in any level of research work. If data are inaccurately collected, it will surely impact the findings of the study, thereby leading to false or invaluable outcome.
What is data collection?
Data collection is a systematic method of collecting and measuring data gathered from different sources of information in order to provide answers to relevant questions. An accurate evaluation of collected data can help researchers predict future phenomenon and trends.
Data collection can be classified into two, namely: primary and secondary data. Primary data are raw data i.e. fresh and are collected for the first time. Secondary data, on the other hand, are data that were previously collected and tested.
Methods of data collection
The system of data collection is based on the type of study being conducted. Depending on the researcher?s research plan and design, there are several ways data can be collected.
The most commonly used methods are: published literature sources, surveys (email and mail), interviews (telephone, face-to-face or focus group), observations, documents and records, and experiments.
1. Literature sources
This involves the collection of data from already published text available in the public domain. Literature sources can include: textbooks, government or private companies? reports, newspapers, magazines, online published papers and articles.
This method of data collection is referred to as secondary data collection. In comparison to primary data collection, tt is inexpensive and not time consuming.
2. Surveys
Survey is another method of gathering information for research purposes. Information are gathered through questionnaire, mostly based on individual or group experiences regarding a particular phenomenon.
There are several ways by which this information can be collected. Most notable ways are: web-based questionnaire and paper-based questionnaire (printed form). The results of this method of data collection are generally easy to analyse.
3. Interviews
Interview is a qualitative method of data collection whose results are based on intensive engagement with respondents about a particular study. Usually, interviews are used in order to collect in-depth responses from the professionals being interviewed.
Interview can be structured (formal), semi-structured or unstructured (informal). In essence, an interview method of data collection can be conducted through face-to-face meeting with the interviewee(s) or through telephone.
4. Observations
Observation method of information gathering is used by monitoring participants in a specific situation or environment at a given time and day. Basically, researchers observe the behaviour of the surrounding environments or people that are being studied. This type of study can be contriolled, natural or participant.
Controlled observation is when the researcher uses a standardised precedure of observing participants or the environment. Natural observation is when participants are being observed in their natural conditions. Participant observation is where the researcher becomes part of the group being studied.
5. Documents and records
This is the process of examining existing documents and records of an organisation for tracking changes over a period of time. Records can be tracked by examining call logs, email logs, databases, minutes of meetings, staff reports, information logs, etc.
For instance, an organisation may want to understand why there are lots of negative reviews and complains from customer about its products or services. In this case, the organisation will look into records of their products or services and recorded interaction of employees with customers.
6. Experiments
Experiemental research is a research method where the causal relationship between two variables are being examined. One of the variables can be manipulated, and the other is measured. These two variables are classified as dependent and independent variables.
In experimental research, data are mostly collected based on the cause and effect of the two variables being studied. This type of research are common among medical researchers, and it uses quantitative research approach.
If you are interested in my services, drop me a message or what you need. I will get back to you as soon as possible. | https://911weknow.com/6-methods-to-collect-data-for-your-market-research |
On March 8, 2022, just five months after the creation of the Department of Justice’s (“DOJ”) new Civil Cyber-Fraud Initiative (previously discussed here), the DOJ announced its first settlement of a cyber-related fraud case. Under the settlement agreement, Comprehensive Health Services LLC (“CHS”) will pay $930,000 to resolve whistleblower allegations that it violated the False Claims Act by (among other things) failing to properly store and handle confidential information. This likely is just the start for increased cyber-related enforcement actions.
CHS had contracts to provide medical support services at government facilities in Iraq and Afghanistan. As described in the settlement agreement, CHS failed to properly store patient medical records on a secure electronic medical record (“EMR”) system as required by its contract, while at the same time submitting claims for payment to the government for the cost of a secure EMR system. In particular, CHS staff allegedly saved and left copies of some medical records on an internal network drive that was accessible to non-clinical staff. Additionally, as set forth in the settlement agreement, after concerns were raised internally CHS failed to take adequate steps to properly and securely store the information on the EMR system and failed to disclose to the Government that it had not securely stored such records. The settlement also describes allegations that CHS provided patients with controlled substances that were unapproved by the U.S. Food and Drug Administration (“FDA”) or European Medicines Agency (“EMA”), and falsely represented such substances were approved.
Although this particular case involves medical records, it is not likely to be long before we see enforcement actions against federal contractors that handle or store other types of confidential or sensitive government information on their systems. Federal contractors have cybersecurity obligations under existing regulations to protect federal contract information and controlled unclassified information (“CUI”), and many Department of Defense contractors have additional obligations to protect and perform cybersecurity assessments relating to covered defense information (a type of CUI). It is not hard to imagine the potential for a significant False Claims Act case against a defense contractor that performs a subpar assessment and/or misreports the results of an assessment, particularly where submission of every invoice to the government may constitute an implied certification that the company is compliant with all contractual cybersecurity obligations.
In its press release, the DOJ highlighted this settlement as a demonstration of “the department’s commitment to use its civil enforcement tools to pursue government contractors that fail to follow required cybersecurity standards,” and noted that it “will continue to ensure that those who do business with the government comply with their contractual obligations, including those requiring the protection of sensitive government information.” Contractors should take immediate note and ensure any representations made regarding the security of information systems housing sensitive government information are current and accurate. | https://www.governmentcontractslawblog.com/2022/03/articles/cybersecurity/well-that-didnt-take-long-doj-announces-its-first-settlement-of-a-civil-cyber-fraud-case/ |
NASA selects concept technologies for phase 2 NIAC fundingView gallery - 5 images
NASA has chosen five studies to advance to phase 2 of its Innovative Advanced Concepts (NIAC) Program. The successful projects were chosen via a system of peer review, and represent the most promising technological concepts with the greatest potential to revolutionize the agency's approach to the building and operating of aerospace systems.
Each of the selected studies had previously been granted phase 1 NIAC funding of up to US$100,000, allowing teams to prove the feasibility of their initial concepts. The studies advancing to Phase 2 will receive an additional funding grant of up to $500,000 over the course of a two-year period, with an emphasis on developing and refining the concepts, whilst at the same time considering real world application with regard to future NASA missions.
"Technology drives our futures in exploration, science and commercial space; and investments in these advanced concepts must be made to ensure we will have the spectrum of capabilities for the near term and well into the 21st century," states Michael Gazarik, associate administrator for Space Technology. "NASA's Space Technology Mission Directorate is creating the technologies needed for today, while also investing in the concepts that will become technological realities of tomorrow.”
The five technology concepts selected to advance to phase 2 of the NIAC program are as follows:
Spacecraft-rover hybridThis Stanford University-designed concept is designed to explore small celestial bodies such as comets or moons, deploying from a parent spaceship in much the same way that the Rosetta comet chaser will deploy the
"Rover" puts you in mind of NASA's Curiosity or Opportunity programs, which incorporate wheeled laboratories that trundle across the surface of Mars like a snail traversing a particularly large pebble. Pavone's hybrid is designed to take a more daredevil approach, tumbling and hopping to the next site of scientific curiosity under the power of a series of three spinning flywheels. The lower the gravity of the celestial body, the further the rover will be able to hop.
Aesthetically, the rover/spacecraft hybrid takes the form of a cube, with short struts protruding from each corner. The simple design of this little explorer allows for scientific equipment to be stored safely inside a single sealed enclosure. It is hoped that this design will be able to explore a much greater distance than conventional rovers. The hybrid will cover the longer distances with the altitude-controlled hops, whilst moving in a more precise manner via a slower tumbling process, with mission commands, navigation, and communication being relayed by the parent spacecraft from orbit.
Low-Mass Planar Photonic Imaging Sensor (AKA SPIDER)This University of California, Davis proposal would seek to provide a smaller, lighter, and ultimately cheaper alternative to large-aperture space telescopes such as the Hubble observatory. The aim of the project is to create a wide-field electro-optical imaging sensor, via the use of millions of white-light interferometers mounted onto
By doing away with the bulky platform set-up required for conventional large-aperture telescopes, it is hoped that this technology will be compact and light enough to be put to use in some of the agency's planned next generation missions, including a planned Europa, Mars Reconnaissance orbiter.
10 meter Sub-Orbital Large Balloon Reflector (LBR)The LBR concept aims to deploy a vast balloon, housing a 10-meter spherical reflector telescope, which will float up to the edge of Earth's atmosphere, operating from radio to THz frequencies. The LBR, designed under Christopher Walker of the University of Arizona, will fulfill a multifunctional role. Primarily the balloon will act as a 10-meter inflatable spherical reflector, however it will also be able to study the Earth's atmosphere, taking readings on greenhouse gasses whilst providing a focal point for selected telecommunications and surveillance operations.
By positioning the LBR high in Earth's stratosphere, the balloon-borne telescope could operate free from 99 percent of the distorting effects created by our planet's atmosphere, allowing it to obtain much clearer observations of distant celestial objects than any comparative ground-based telescope. The LBR will also achieve this without going through the costly requirement of mounting the equipment in a modified Boeing 747, as is the case with the SOFIA observatory. This is because the housing for the large 10-meter telescope acts as its own launch vehicle, making the project a very appealing prospect from a fiscal perspective.
Orbiting RainbowsThis ambitious project, led by Marco Quadrelli of NASA's JPL, was inspired by the light scattering and focusing effects observed in nature. Quadrelli's ultimate aim is to place a cloud-like formation of tiny spacecraft in orbit that could be manipulated to create any size of aperture in-situ, with each constituent element of the swarm moving into position under its own power (albeit with guidance from an external source).
It is hoped that this "smart dust" concept could eventually be used to carry out advanced imaging tasks, such as searching for exoplanets, and even undertaking high-resolution observation of other planets in order to discern specific features, for example continents.
Deep mapping of small solar system bodies with galactic cosmic ray secondary particle showersThe concept put forward by Thomas Prettyman of the Planetary Science Institute, Tucson, Arizona, investigates the use of muon particles, the charged component of galactic cosmic rays, to image both the interior and the exterior of small solar system bodies (SSBs) such as comets and asteroids.
Data collected from such a technique could be used to determine not only an object's surface features that could aid in the mapping and navigating of an SSB for either robotic or human explorers, but also to determine the composition of the inside of an SSB, identifying potential resource-rich areas that could be exploited by future mining missions.
Source: NASA
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Winner of French Scrabble Title Does Not Speak French (2015) - hirundo
https://www.npr.org/sections/thetwo-way/2015/07/21/424980378/winner-of-french-scrabble-title-does-not-speak-french
======
nippoo
I was at the World Scrabble Championships in Prague a few years ago (with
Nigel Richards). The amazing thing was how many of the highest-level Scrabble
players were Thai and spoke barely any English. There are about 200,000 words
in the Scrabble dictionary and and an average English speaker only knows
40,000. So knowing the language doesn't give a huge advantage, and all
competitors end up spending years memorising word lists with no definitions -
at a high level it's basically just a combinatorics game. The majority of the
English-speaking competitors were mathematicians / scientists, rather than
linguists for similar reasons.
This sometimes has amusing repercussions - the world no 2 at the time, who was
Thai, played the word "hetairas" and then challenged the word "twigs"...
~~~
Benjammer
At the highest levels, Scrabble is not a word game at all. It's a territory
control game with 200,000 different valid ways to play resources.
~~~
mkl
Territory control? Either player can build off any word, so I don't think you
can control any territory. You capture valuable squares before your opponent
can when you have the opportunity, because unused squares are no man's land,
and up for grabs.
~~~
TheNorthman
Because Scrabble is turn based, any opportunities you create for yourself, you
create for your opponent first. Making sure you don't make `valuable squares'
available to your opponent is, arguably, more essential to winning than
claiming them for yourself.
~~~
Someone
‘scorched earth’, wasting a valuable square on a low-scoring move, say (as an
extreme example) by playing a blank tile on a triple-character square, just to
deny the next player from using it, can also be a valuable tactic at times.
Many people don’t realize that, in competitive games, the goal isn’t to make a
high score, it is to make a score that’s higher than that of your opponents.
Another game where many players dont realize that is Twister
([https://en.wikipedia.org/wiki/Twister_(game)](https://en.wikipedia.org/wiki/Twister_\(game\))
). You shouldn’t play to make it easy for yourself to stay in play, you should
play to make it easier for you than for your opponents to stay in play. In
general, that means occupying circles close to your opponent, rather than
those easily reachable by you. You should try to ‘lock’ your opponents in a
corner of the playing area.
------
walrus01
Memorizing an entire dictionary is kind of like the cases I've read about with
persons whose native language isn't arabic, but have successfully memorized
and can recite verbally the entire Quran.
~~~
zakki
In Indonesia it is more on learning on recognizing Arabic letters, write it
and spell it. For Quran also learning the tajwid (تجويد). I want to say that
it is not memorizing the entire dictionary. Off course it raises new problem,
they can recite Quran but not understanding much the meaning unless they read
the translation.
~~~
vxNsr
This true for many Jewish kids as well. We can read, and write in Hebrew but
have no idea what it means without a translation.
~~~
samatman
True, but less so.
I've learned a couple alphabets, Hebrew among them, just for fun. I'm pretty
confident I could learn to _recite_ the Quran with a month of steady practice.
But memorize the whole thing? Like, name a sura, and I'm off to the races?
That's very impressive.
And without any understanding of the underlying words! That's even more
impressive, but my heart sinks a little at the waste of human potential which
it represents.
Perhaps they're right, and they earn a lifetime in Paradise for their trouble.
I can't help but thinking there are better ways to spend ones youth.
~~~
danielheath
I mean, if they’re right it seems like a pretty good trade.
~~~
smabie
Just do it when you're old. More efficient that way.
------
kebman
Back when I worked in sales, there was a guy on my sales team that would have
the entire Norwegian Top 40 billboard memorized since its inception in the
50's, complete with producers and writers of lyrics. While a bit socially
awkward, he still did alright at sales by following the script. So by that
token he was regarded by my collegues as a bit of a savant.
"Lest you suspect," also makes for quite unusual language in the article, btw.
Haven't seen that in many modern news articles, at least. But strangely this
rather archaic phrase seems to be more common in modern American litterature
than in British literature. Together with the verbal addition of "I would
think" at the end of that quote in the start, the article takes on a rather
rustic feel.
~~~
asveikau
> But strangely this rather archaic phrase seems to be more common in modern
> American litterature than in British literature.
There is an interesting phenomenon I've read about where distant colonies,
kept isolated from where their language originated, end up sounding _more
archaic_ than their home territory. The act of crossing an ocean can serve as
a linguistic time capsule and changes made in the homeland don't always
propagate.
I've heard this claimed about a few languages:
* Quebec French vs. France. (true to the form of TFA I do not speak French, so I cannot assess this claim.)
* Judaeo-Spanish spoken by expelled Jewish communities vs. Spain. (from what I recall of recordings of the former it did seem like it lacks some phonetic changes that Spain had around the 15th-16th centuries, like [ʒ] and [ʃ] moving to [x], loss of initial /f/ in words like _hijo_ , _hablar_ ... and consequently generally has this almost Portuguese-sounding feel to it. Interestingly these same phonetic changes made it across to Latin American colonies but not to expelled Spanish Jews in Europe)
* American English vs. England. (I've heard this claimed variously, as if to say that Shakespeare spoke with one of today's American accents, and frankly that sounds kind of dubious. But there may be bits and pieces of American English that sound old fashioned across the pond.)
~~~
kibwen
_> as if to say that Shakespeare spoke with one of today's American accents,
and frankly that sounds kind of dubious_
To suggest that Shakespeare spoke with an American accent would be silly, but
it is true that the non-rhotic "r" didn't become widespread until after
Shakespeare's time, starting as a marker of prestige among the British upper
classes in the mid-1700s (and spreading to the wannabe-aristocracy in the
colonies, hence the stereotypical accent of the American Southern plantation
owner). If the pronunciation of words like "car" is how one distinguishes
British from American, then I suppose yes, Shakespeare would sound a bit less
British than you might expect.
[https://en.m.wikipedia.org/wiki/Rhoticity_in_English](https://en.m.wikipedia.org/wiki/Rhoticity_in_English)
~~~
DFHippie
To complicate things a little, the non-rhotic accents of the eastern seaboard
of North America aren't generally considered posh: Southie, Mainer, Brooklyn.
Newfoundland is the region of North American longest settled by English
speakers, I believe. Google "Newfie accent" to hear true Shakespearean
English.
~~~
stan_rogers
Newfanese is pretty much crystallized Hiberno-English, at least if we're
talking the language of the bay wops rather than townies. It has a surprising
amount of commonality with African-American vernacular, likely due to
transportation and indenture (which is why AAVE, while distinct, barely edges
into typical creole patterns).
The English of Shakespeare's time, or at least of his plays, has been largely
reconstructed by linguist David Crystal, whose son, the actor and director Ben
Crystal, is probably the best-known practitioner. There are a number of videos
on YouTube of Ben doing Shakespeare in OP. A good starting point is
[https://www.youtube.com/watch?v=gPlpphT7n9s](https://www.youtube.com/watch?v=gPlpphT7n9s)
\- and if one had to tie it closely to a modern regional variant, it would be
West Country. But that would just be something it would remind you of rather
than a template.
~~~
DFHippie
It was a joke.
------
hartator
I wonder if that give him any advantage learning actual French or if this so
different area of the brain that actually doesn’t matter.
~~~
claudeganon
He memorized the French scrabble dictionary, so I doubt it’s in any way
useful. He doesn’t know the meaning of any of the terms.
~~~
echelon
His brain is now wired with the space of possible spellings and phonemes. That
can't have a nonzero impact on learning. He might have a jump on pattern
recognition for conjugation, for instance.
~~~
LudwigNagasena
I don’t think it’s allowed to conjugate verbs in Scrabble.
~~~
minitoar
You can definitely use conjugated verbs: "All words labeled as a part of
speech (including those listed of foreign origin, and as archaic, obsolete,
colloquial, slang, etc.) are permitted with the exception of the following:
words always capitalized, abbreviations, prefixes and suffixes standing alone,
words requiring a hyphen or an apostrophe" [https://scrabble.hasbro.com/en-
us/rules](https://scrabble.hasbro.com/en-us/rules)
~~~
LudwigNagasena
Ah, ok, in Russia in scrabble-like games (Scrabble itself is not very popular)
subjugation and declension usually aren’t allowed.
~~~
317070
Same in Dutch, I assume because of the possibility of just adding an "e" or a
"t" to most words to score its points again.
~~~
minitoar
Nice I love these sort of language differences. In English of course you can
add an "s" to many words to make them plural, and that is permitted in
Scrabble.
------
11001001011010
Indeed memory, the point where computers totally outsmart us all. That's why
traditional school where you get to the next grade by showing off your memory
is totally deprecated.
It might be me, but these kind of contests and our excitement about it only
shows our stupidity even more. Our specialty is very fortunately not memory,
it should never be. We are incredibly special creatures with much more
interesting capabilities.
~~~
nickelpro
Machines can also throw javelins and shots farther than any human can ever
hope to. Hydraulics can trivially lift more than any strong man. A large
enough spring can outperform any long jumper. More directly relatable, chess
engines have been outperforming the grand masters for a decade now.
That a machine can outperform a human doesn't make a human doing it
unimpressive. The excitement and fun of the competition remains.
~~~
wozniacki
But games like Scrabble seem even more pointless than the Spelling bee which
is in itself pointless ( making a competition out of memorizing or
constructing from memory similar rooted words that one would barely use in any
but the most scholarly of arcane academia or in the practice of law, is
anything but useful or worthy of one's time ).
A more worthwhile competition would test the participants on their reasoning /
logic and turn it into an engaging game. Even gamifying brevity of language is
a worthwhile pursuit since so many of todays youth speak so poorly or struggle
expressing their thoughts in a coherent and curt manner.
Scrabble and Spelling Bee encourage rote learning and little beyond that. A
terrible waste of potential like OP alluded to. Memorizing and parroting,
needless to say, is just not a very good use of the human intellect. Its
really bad form and speak to the vanity and vainness of the organizers and
contestants to have these silly competitions in this day and age.
~~~
DFHippie
I've always been embarrassed that spelling bees are a thing in English. It's
interesting that you can see the etymology of a word in its spelling, but
horrific spelling sure is a barrier to literacy. How do you pronounce "lough"?
How about "rough" or "dough"? And "plough"? Now try "hiccough".
I envy Finnish kids. They've already mastered the grammar and are well on
their way with the vocabulary. Spelling is barely a speed bump. English
speakers have national competitions to demonstrate that they've mastered
spelling.
------
kregasaurusrex
Scrabble is largely a game of area-based combinatorics, which rewards finding
sequences of letters that happen to be words and fit into the board's
multiplier spaces. Memorizing the two-letter word list is extraordinarily
helpful when playing competitively because it allows for playing a tighter
game that doesn't resemble words commonly used in English.
~~~
TwoBit
Makes me wonder if he could have won while knowing only a fraction of the
French dictionary.
------
zacwest
If you're interested in watching competitive Scrabble, the NASPA YouTube
channel recently did a virtual Tournament of Champions:
[https://www.youtube.com/playlist?list=PLhvDB0pE-3ptFJBqemMOh...](https://www.youtube.com/playlist?list=PLhvDB0pE-3ptFJBqemMOhxe3Z625OUbDY)
------
cm2012
I would find a scrabble tournament a lot more interesting if it limited it to
the top 10k most common english words.
------
United857
Similarly, a lot of Chinese students do surprisingly well in the verbal
section of US admissions exams like the SAT and GRE, despite being non-native
speakers. They just memorize long lists of obscure English words that would
rarely ever be used in practice.
~~~
jgr0
Not sure if this is a good comparison. For SAT, GRE you need to know a word
innately, be able to use it in a proper context, understand homonyms,
distinguish between similar words and know which one to use in the given
prompt etc.
Yes, this does involve remembering long lists of words, but there is a lot of
context and I would consider this proper language learning. It is vastly
different from the memorization referred to in the article.
~~~
loxs
From my experience as an English language student (non-native), I disagree to
some extent. Taking (and learning) the SAT is quite a different experience
than learning the language. It seems that people who are good at "taking
tests" excel at it and this does not correlate completely with their ability
to use the language. Of course often they ALSO learn the language (by other
means), but I know people who successfully took the SAT in order to
participate in student exchange programs and when they go to the USA they
realize that they are quite poor at English and tend to stick to ethnic
communities, because they are not comfortable to use the language at a higher
level.
On the other hand, if you study for the SAT when you already know the
language, it seems to indeed improve your English a lot.
~~~
DFHippie
I think being good at test taking correlates with perfectionism. The ones who
test well but then stick to speakers of their native language may simply be
perfectionists who are horrified at being seen as stupid when their English
isn't perfect.
~~~
loxs
As far as I can attest (I studied together with them), this is not the case :)
------
mongol
The Wikipedia page of this fellow:
[https://en.wikipedia.org/wiki/Nigel_Richards_(Scrabble_playe...](https://en.wikipedia.org/wiki/Nigel_Richards_\(Scrabble_player\))
------
cainxinth
Two documentaries about word games came out at similar times. “Word Wars”
(2004) was about Scrabble and “Wordplay” (2006) was about crosswords. Both are
excellent films about high-level play in these games.
After watching them, what struck me was that the best Scrabble players were
all, shall I say, a bit weirder than the best crossword players.
Crossword requires a large general fund of knowledge. Scrabble only requires
rote memorization. Crossword attracted well-rounded people. Top Scrabblers
were monomaniacs.
------
pinewurst
(2015)
~~~
alex_young
Thank you. I was just telling my friend about this and she insisted this
happens every few years. That didn’t seem likely, and your comment helped us
figure out that we’d actually talked about this years ago :)
~~~
disown
It's likely you guys talked about it twice.
"He competed in the French Championship and won his second Classique
Championship" (2018)
[https://en.wikipedia.org/wiki/Nigel_Richards_(Scrabble_playe...](https://en.wikipedia.org/wiki/Nigel_Richards_\(Scrabble_player\))
There was even a brief HN comment thread about it 2 years ago.
"Fun fact: the current top player of French scrabble is from New Zealand and
doesn’t speak a word of French. He just memorized all ~200k valid words in the
OSD."
[https://news.ycombinator.com/item?id=18689565](https://news.ycombinator.com/item?id=18689565)
------
zzo38computer
You can play Scrabble without knowing how to speak the language, or what the
grammar is, or what any of the words mean; you only need to know how to spell
the words of that language (or least the ones which are permitted in
Scrabble).
------
komali2
IIRC this person was interviewed for "Ultra learning," which reminds me I need
to read that book still.
~~~
slyall
Ultralearning: Master Hard Skills, Outsmart the Competition, and Accelerate
Your Career by Scott Young
[https://www.amazon.com/Ultralearning-Master-Outsmart-
Competi...](https://www.amazon.com/Ultralearning-Master-Outsmart-Competition-
Accelerate/dp/006285268X)
------
apricot
Is this Duplicate Scrabble (all contestants playing the same letters)? If so,
I imagine computers reached perfect play long ago, as it seems to involve
nothing beyond memorizing huge lists of numbers and searching the board for
the best place to put them.
But what about regular Scrabble? Sometimes, the best play is not the word
that's worth the most points, because it might give your opponent a chance to
make a big play (the simplest example is refraining to play a high-value word
that opens a triple score square for your opponent). The best play depends on
the probabilities of your opponent holding, now or in the future, certain
letters, and you can make a probabilistic model of that based on the letters
that are in play at any moment. Perfect play seems to involve a lot of
computation. What's the state of the art on this?
------
aj7
What Scrabble degenerates into.
~~~
justwalt
Many enjoyable games become quite a bit different when they’re played at a
high level. Whether or not the game is still enjoyable at that point is not
always easy to say. I definitely would not enjoy memorizing lists of words in
order to be more competitive.
------
abnry
This makes sense when you realize Scrabble isn't a word game, it is a board
control game.
------
maest
Analogous to this:
GPT-3 doesn't speak English.
------
Khelavaster
From 2015..
------
Khelavaster
In 2015..
------
feralimal
Imagine memorising the best part of 200,000 words in a foreign language in
order to win a game of scrabble! And not being able to string a sentence
together in that language!
Some people have waaaaayyyy too much time on their hands!
~~~
jobigoud
Many sports & activities feel like this at high level. An athlete will train
everyday and build muscle memory in order to jump over a bar placed as high as
possible. A chess player, a football player, etc. Highly specialized skills
that are of no use in day to day life. The collateral benefits like fitness or
entertainment value can also be found here.
~~~
feralimal
I can understand the value of sports, and of doing anything at a high level.
Mastery of anything is its own reward. I get that. But what these Thai champs
are doing seems crazy.
Imagine, as an English speaker, waking up wanting to win the Hungarian
scrabble tournament. No, you don't want to know how to speak Hungarian. You
only want to win the Hungarian scrabble tournaments. And you're prepared to
invest months of your life memorising sequences of letters to do it!
Its insane.
~~~
jobigoud
When you do something competitively it decouples the activity from the
original use. Just like a Pole vault champion is not really interested in
being able to reach the second floor with a stick.
In this sense the fact that the words have to match the Hungarian dictionary
feels arbitrary. But it's a bit like the rules for triple jump where you have
to land the first jump on the same foot, or the rules of high jump that
prevent you from taking off with two feet at the same time, these rules feel
arbitrary in the context of the original utility of the skill.
~~~
feralimal
You like to argue huh? :)
Triple jump is valuable in itself - you train your body, and that has
consequent benefits. Learning strings of consecutive characters characters
perhaps has a memory benefit. But then, why not train your memory to get that
benefit AND get a consequent benefit at the same time. Eg card counting to
make money at casinos? Or actually learn English, so this becomes a vocab
extension exercise? But all that effort to win....? At scrabble?!? The mind
boggles.
And anyway, if you were that good, no-one would want to play scrabble with you
at Christmas...
| |
Always wanted to do this and I finally found the chairs! This is a great way to upcycle, especially if the chairs aren't in perfect condition. In this case one of the chairs had a spindle broken on the seat.
Enjoyed the project?
Want more details about this and other DIY projects? Check out my blog post!
Published December 3rd, 2013 4:43 PM
Frequently asked questions
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2 questions
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Diana on Jan 25, 2017Love the idea, but a bit confused...If only the back of the middle chair is used, did you install the rods across the "bottom front" of the (once existing) middle chair since the legs of both the right and left chairs provide support for the whole unit?
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John Biermacher on Jan 31, 2018From one Michigander to another- REALLY NICE job. I have done a similar bench, but I like the idea of only using parts of the middle chair. Still have three more chairs so will eventually give it a try. Like many of your other projects. | https://www.hometalk.com/diy/build/furniture/make-a-bench-out-of-3-chairs-2639443 |
Theory:
1. A fielder in the cricket ground pulls his hands backwards with the fast-moving cricket ball during the action of catching. By this action, the fielder prolongs the time to decrease the velocity of the fast-moving ball to zero. Hence, the impact of catching the fast-moving ball is reduced by decreasing the acceleration of the ball.
If the fielder suddenly stops the ball, its high velocity drastically decreases to zero in a very short period.
As a result, the rate of change of momentum will be large, and thus, a large force should be exerted for taking the catch that may hurt the fielder's palm.
2. Athletes in high jump sporting events are forced to land on a cushioned or a sand bed. This is done to prolong the time it takes for the athlete's fall to come to a halt after completing the jump. An increase in the time of fall reduces the force by lowering the rate of change of momentum.
3. With the same technique, a karate player breaks an ice slab with a powerful single blow.
From the second law's mathematical expression, the first law of motion can be easily stated.
When the force \(F\) is zero, the final velocity is equal to the initial velocity (\(v =u\)), whatever the time \(t\) may be.
Hence, it implies that the object will continue its motion with uniform velocity, \(u\) throughout the time, \(t\). If \(u\) is zero, then \(v\) will also be zero, keeping the object at rest.
Reference: | https://www.yaclass.in/p/science-cbse/class-9/force-and-laws-of-motion-6590/re-59b6d574-aba4-4a55-bb71-0e68979a50b0 |
---
abstract: 'The paper is aimed at analysing a singular perturbation of the Navier-Stokes equations on a compact closed manifold. The case of compact smooth manifolds with boundary under the Dirichlet conditions is also included. Global existence and uniqueness is established for the weak solutions of the Cauchy problem. The solution of the regularised system is shown to converge to the solution of the conventional Navier-Stokes equations provided it is uniformly bounded in parameter.'
address:
- 'Siberian Federal University, Institute of Mathematics and Computer Science, pr. Svobodnyi 79, 660041 Krasnoyarsk, Russia'
- 'Institute of Mathematics, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam OT Golm, Germany'
author:
- Alexander Shlapunov
- Nikolai Tarkhanov
date: 'February 23, 2018'
title: |
On a Singular Perturbation\
of the Navier-Stokes Equations
---
Introduction {#s.Introdu .unnumbered}
============
The classical Navier-Stokes equations for the incompressible viscous fluid in a domain ${\mathcal{X}}$ of ${\mathbb{R}}^n$ have the form $$\label{eq.cNSefivf}
\begin{array}{rcl}
\partial_t v - \nu {\mathit{\varDelta}}v + N (v) + \mathrm{grad}\, p
& =
& f,
\\
\mathrm{div}\, v
& =
& 0
\end{array}$$ for $(x,t) \in {\mathcal{X}}\times I$, where $I = (0,T)$ is finite or infinite time interval. Here, $v$ stands for the velocity vector of the flow, $p$ for the pressure and $f$ for the outer force field, all of them being functions of $(x,t)$. The quantity $\nu$ is the so-called kinematic viscosity of the fluid and $\nu$ is assumed to be a positive constant. The resistance of system (\[eq.cNSefivf\]) to mathematical study is caused by the nonlinear term $N (v) = v'_x v$, where $v'_x$ is the Jacobi matrix of the mapping ${\mathcal{X}}\to {\mathbb{R}}^n$ given by $x \mapsto v (x,t)$ at any instant $t \in I$. Being a bidifferential operator, $N$ fails to be Lipschitz continuous on unbounded subsets of fit function spaces. There is a huge literature devoted to the Navier-Stokes equations, for which we refer the reader to [@Tema79], [@Lady03] and [@Tao16].
As the Navier-Stokes equations are nonlinear, one needs a specific trick to introduce the concept of a weak solution for them. To wit, a locally square integrable vector $v$ on ${\mathcal{X}}\times I$ is called a weak solution of (\[eq.cNSefivf\]) if it is weakly divergence-free and if $$\label{eq.weaksol}
\int \!\!\!\! \int_{{\mathcal{X}}\times I}
\left( - (v, \partial_t w)_{x,t} - \nu\, (v, {\mathit{\varDelta}}w)_{x,t} - (v, w'_x v)_{x,t}
\right)
dx dt
= \int \!\!\!\! \int_{{\mathcal{X}}\times I}
(f,w)_{x,t}
dx dt$$ for all smooth vector fields $w$ with compact support in ${\mathcal{X}}\times I$ satisfying $\mathrm{div}\, w = 0$. This definition is due to [@Hopf51] who specified it for solutions of the first mixed problem for the Navier-Stokes system in the cylinder ${\mathcal{X}}\times I$ with initial data at $t = 0$ and zero Dirichlet data on the lateral surface $\partial {\mathcal{X}}\times I$ and established the existence of a weak solution to the first mixed problem with finite energy norm. In [@Lady70], [@Lion69] and [@Tema79] one uses a slightly different concept of a weak solution which refines that of [@Hopf51] in the case where the weak solution belongs to $H^1 (I, L^2 ({\mathcal{X}},{\mathbb{R}}^n)) \cap L^2 (I, H^1_0 ({\mathcal{X}},{\mathbb{R}}^n))$. It does not apply to define weak solutions in $L^2_{\mathrm{loc}} ({\mathcal{X}}\times I,{\mathbb{R}}^n)$. Note that, under finite energy norm, the uniqueness property for the classical Navier-Stokes equations takes place first in $L^r (I, L^q ({\mathcal{X}},{\mathbb{R}}^n))$ with $q > n$ and $2/r + n/q \leq 1$, see *ibid*.
Suppose $f = 0$. Then a direct calculation shows that $v = c (t) \mathrm{grad}\, h (x)$ is a solution of (\[eq.weaksol\]), provided only that $c$ is a square integrable function and $h$ is harmonic. The vector field $v$ is infinitely differentiable so far as the space variables are concerned but need not possess any time derivatives whatever. The conclusion which we draw from this example is that the order of time differentiability of a weak solution is intimately tied to the amount of time regularity which is originally assumed. On the other hand, quite modest assumptions concerning the spatial regularity of a weak solution are enough to guarantee $C^\infty$ with respect to the space variables, see [@Serr62].
As usual the velosity $v$ is subject to an initial condition $v = v_0$ on the lower base of ${\mathcal{X}}\times I$ and a Dirichlet condition $v = v_l$ on the lateral boundary of the cylinder. If one wants to work in a framework where the boundary conditions are understood in the sense of traces, and not just weakly, then one can choose an $L^q$ setting and require that the solution $v$ belongs to the space $W^{1,q} (I, L^q ({\mathcal{X}},{\mathbb{R}}^n)) \cap L^q (I, W^{2,q} ({\mathcal{X}},{\mathbb{R}}^n))$ for some $q \in (1,\infty)$. In order to obtain the optimal spaces for the data, one needs sharp trace results for the space. It is known that the trace $v_0$ of $v$ at $t = 0$ belongs to $W^{2 - 2/q,q} ({\mathcal{X}},{\mathbb{R}}^n)$ and the restriction $v_l$ of $v$ to the lateral boundary belongs to the anisotropic space $W^{1-1/2q,q} (I, L^q (\partial {\mathcal{X}},{\mathbb{R}}^n)) \cap L^q (I, W^{2-1/q,q} (\partial {\mathcal{X}},{\mathbb{R}}^n))$, cf. [@Slob58]. Observe that the restriction to the lateral boundary still retains some time regularity. Moreover, one has $f \in L^q (I, L^q ({\mathcal{X}},{\mathbb{R}}^n))$, the latter space being $L^q ({\mathcal{X}}\times I,{\mathbb{R}}^n)$, and the compatibility condition $v_0 = v_l$ should hold at $t = 0$, if $v_l$ has a trace at $t = 0$, which happens for $q > 3$. One often takes a large $q$ to simplify the treatment of the nonlinearity. Thus, the norm of $W^{2 - 2/q} ({\mathcal{X}},{\mathbb{R}}^n)$ is far away from the norms one can control by the usual a priori estimates, such as the norms of $H^1$ or $L^\infty$.
Since [@Hopf51] much efforts were made to prove the uniqueness and regularity of the weak solution to the first mixed problem for the Navier-Stokes equations. However, there has been no breakthrough unless $n = 2$, in which case the results are due to [@Lera34a; @Lera34b] and independently [@Lady70]. In [@Lady03] one finds certain indirect evidence to the fact that the weak solution of [@Hopf51] might be not unique, and so fail to be regular. The paper [@Tao16] establishes a finite time blowup for an averaged three-dimensional Navier-Stokes equation. Our starting point in [@ShlaTark16] is to give the Navier-Stokes equations a regular domain to have got the uniqueness from the very beginning. We proved in [@ShlaTark16] that the Cauchy problem for (\[eq.cNSefivf\]) in all of ${\mathbb{R}}^n$ is stable in weighted Hölder spaces, i.e., the corresponding mapping is open. On the other hand, the proof of the range closedness requires hard a priori estimates which we have not been able to prove. They seem to be closely tied to the very specific form of the nonlinear term $v'_x v$ in (\[eq.cNSefivf\]). As mentioned, on replacing $v'_x v$ away from a ball of any radius by a mapping which is Lipschitz continuous we immediately get existence. To understand to what extent it is physically meaningful to perturb the nonlinear term we introduced in [@MeraShlaTark15] generalised Navier-Stokes equations related to elliptic complexes.
The first paper to consider the Navier-Stokes equations on Riemannian manifolds is the classical paper [@EbinMars70]. There, the authors employ the Hodge Laplacian but add a note in the proof emphasizing that the “correct” Laplacian for Navier-Stokes should be constructed from the Bochner Laplacian, referring to [@Serr59]. This point is reiterated by [@Tayl10] and taken up again in [@ChanCzub13] and [@Lich16], the last papers dealing precisely with the issue of non-uniqueness for the Navier-Stokes equations on manifolds.
In this paper we analyse a regularised form of the conventional Navier-Stokes equations. More precisely, we consider the first mixed problem for solutions of the system $$\label{eq.gNSefivf}
\begin{array}{rcl}
\partial_t v + \varepsilon (- {\mathit{\varDelta}})^m v - \nu {\mathit{\varDelta}}v + N (v) + \mathrm{grad}\, p
& =
& f,
\\
\mathrm{div}\, v
& =
& 0
\end{array}$$ in the cylinder ${\mathcal{X}}\times I$, where $m$ is a natural number satisfying $2 m - 1 \geq n/2$ and $\varepsilon$ a small positive parameter. Given any data $f \in L^2 ({\mathcal{X}}\times I,{\mathbb{R}}^n)$ and $v_0 \in H^m_0 ({\mathcal{X}},{\mathbb{R}}^n)$, we show the existence of a weak solution $v \in L^\infty (I, L^2 ({\mathcal{X}},{\mathbb{R}}^n)) \cap L^2 (I, H^m_0 ({\mathcal{X}},{\mathbb{R}}^n))$ to the problem with zero data on the lateral surface of the cylinder. Moreover, the solution fulfills an energy estimate, it is unique and inherits the regularity from $f$ and $u_0$.
If the solution $u$ is bounded in $L^2 (I, H^m_0 ({\mathcal{X}},{\mathbb{R}}^n))$ uniformly in $\varepsilon$, then it approaches the unique weak solution to the conventional problem in the norm of $L^\infty (I,L^2 ({\mathcal{X}},{\mathbb{R}}^n)) \cap L^2 (I,H^1_0 ({\mathcal{X}},{\mathbb{R}}^n))$. The conclusion which we might draw from these results is that system (\[eq.gNSefivf\]) with $m \geq (n+2)/4$ is an adequate regularisation of the equations of dynamics of incompressible viscous fluid in an $n\,$-dimensional space. We focus on the case where ${\mathcal{X}}$ is a compact $C^\infty$ manifold without boundary. The case of compact smooth manifolds with boundary under the zero Dirichlet conditions is also included.
\[p.tgNSequ\]
The Navier-Stokes equations for elliptic complexes {#s.tNSefec}
==================================================
Let ${\mathcal{X}}$ be a compact closed Riemannian manifold of dimension $n$. Consider an elliptic complex $$\label{eq.ellcomp}
0
\longrightarrow
C^\infty ({\mathcal{X}},F^0)
\stackrel{A^0}{\longrightarrow}
C^\infty ({\mathcal{X}},F^1)
\stackrel{A^1}{\longrightarrow}
\ldots
\stackrel{A^{N-1}}{\longrightarrow}
C^\infty ({\mathcal{X}},F^N)
\longrightarrow
0$$ of first order differential operators $A^i$ on ${\mathcal{X}}$ acting between sections of smooth vector bundles $F^i$ over ${\mathcal{X}}$. As usual, we write $A$ for the graded operator associated with sequence (\[eq.ellcomp\]), which is defined by $Au = A^i u$ for sections $u$ of $F^i$. The operator $A$ is called the differential of complex (\[eq.ellcomp\]) and its square $A^2$ vanishes, for the composition of any two neighbouring operators in (\[eq.ellcomp\]) is zero by the definition of a complex.
\[r.copsdo\] Slight changes in the proofs actually show that the theory still applies to complexes of pseudodifferential operators. But it is not our purpose to develop this point here.
Choosing a volume form $dx$ on ${\mathcal{X}}$ and a Riemannian metric $(\cdot,\cdot)_x$ in the fibres of $F^i$, we equip each bundle $F^i$ with a smooth bundle homomorphism $\ast : F^i \to F^i{}^\ast$ defined by $\langle \ast u, v \rangle = (v,u)_x$ for $u, v \in F^i_x$, and the space $C^\infty ({\mathcal{X}},F^i)$ with the unitary structure $$(u,v) = \int_{{\mathcal{X}}} (u,v)_x dx$$ giving rise to the Hilbert space $L^2 ({\mathcal{X}},F^i)$. Write $A^i{}^\ast$ for the formal adjoint of $A^i$ and $A^\ast$ for the corresponding graded operator given by $A^\ast u = A^{i-1}{}^\ast u$ for sections $u$ of $F^i$. By analogy with the terminology used in hydrodynamics, we call divergence-free those sections $u$ of $F^i$ which satisfy $A^\ast u = 0$, by the vorticity of $u$ is meant the section $Au$, and any section $\pi$ of $F^{i-1}$ satisfying $A \pi = u$ is said to be a potential of $u$.
The ellipticity of complex (\[eq.ellcomp\]) proves to be equivalent to saying that the Laplacian ${\mathit{\varDelta}}= A^\ast A + A A^\ast$ is an elliptic pseudodifferential operator of order two on sections of $F^i$, for every $i = 0, 1, \ldots, N$, see [@Tark95]. The Laplacian ${\mathit{\varDelta}}$ is nonnegative on $C^\infty ({\mathcal{X}},F^i)$, for $({\mathit{\varDelta}}u, u) = \| Au \|^2 + \| A^\ast u \|^2$ for all sections $u \in C^\infty ({\mathcal{X}},F^i)$. In the sequel we tacitly assume that $i$ is fixed, thus restricting our attention to complex (\[eq.ellcomp\]) at step $i$.
Let $m$ be a nonnegative integer. Our standing assumption on $m$ will be that $m \geq (n+2)/4$. The system $$\label{eq.mhdefivf}
\begin{array}{rcl}
\partial_t v + \varepsilon {\mathit{\varDelta}}^m v + \nu {\mathit{\varDelta}}v + N (v) + Ap
& =
& f,
\\
A^\ast v
& =
& 0
\end{array}$$ in the cylinder ${\mathcal{C}}= {\mathcal{X}}\times I$ for the unknown sections $v$ and $p$ of $F^i$ and $F^{i-1}$, respectively, is an obvious reformulation of (\[eq.gNSefivf\]) within the framework of elliptic complexes. If (\[eq.ellcomp\]) is the de Rham complex on ${\mathcal{X}}$ and $i = 1$, then (\[eq.mhdefivf\]) just amounts to (\[eq.gNSefivf\]) up to the duality between one-forms and vector fields on ${\mathcal{X}}$. In the general case, by $N$ is meant any nonlinear cochain mapping of complex (\[eq.ellcomp\]) given by a sequence of first order bidifferential operators $N^i (u,v)$ on ${\mathcal{X}}$, and $N^i (u)$ stands for $N^i (u,u)$.
\[eq.mietn/2\] One can take specifically $m = (n+2)/4$ but we did not so to avoid considering the fractional powers of pseudodifferential operators, see [@Shub87] and elsewhere.
Note that system (\[eq.mhdefivf\]) is equivalent to the generalised Navier-Stokes equations in the sense of [@MeraShlaTark15] corresponding to the elliptic complex of (\[eq.ellcomp\]) whose differential is changed to $\sqrt{{I}+ (\varepsilon/\nu) {\mathit{\varDelta}}^{m-1}} A$.
If $s \in {\mathbb{Z}}_{\geq 0}$, we use the designation ${\mathbf{s}}(s)$ for the pair $(2ms,s)$. Let $H^{{\mathbf{s}}(s)} ({\mathcal{C}},F^i)$ stand for the Hilbert space of all sections of the bundle $F^i$ over ${\mathcal{C}}$ of Slobodetskij class $H^{{\mathbf{s}}(s)}$, see [@Slob58]. A section $u$ is said to belong to $H^{{\mathbf{s}}(s)} ({\mathcal{C}},F^i)$ if, for any coordinate patch $U$ in ${\mathcal{X}}$ over which the bundle $F^i$ is trivial, the derivatives $\partial_x^\alpha \partial_t^j u$ are locally square integrable in $U \times \overline{I}$ whenever $|\alpha| + 2mj \leq 2ms$. On choosing a finite covering of ${\mathcal{X}}$ by such patches and a $C^\infty$ partition of unity on ${\mathcal{X}}$ subordinate to the covering we introduce a scalar product in $H^{{\mathbf{s}}(s)} ({\mathcal{C}},F^i)$. The corresponding norm is independent on the choice of coordinates and local trivialisations up to the norm equivalence. It is well known that each section of $H^{{\mathbf{s}}(s)} ({\mathcal{C}},F^i)$ possesses a trace on the base of the cylinder which belongs to $H^{2m (s-1/2)} ({\mathcal{X}},F^i)$, the result being due to [@Slob58].
To specify a solution $v$ to system (\[eq.mhdefivf\]) we prescribe initial values at $t = 0$ to $v$. To wit, $$\label{eq.initval}
v (\cdot,0) = v_0$$ on ${\mathcal{X}}$, where $v_0$ is a given section of $F^i$. We will look for a velocity in $H^{{\mathbf{s}}(1)} ({\mathcal{C}},F^i)$, hence $v_0$ is assumed to be in $H^{m} ({\mathcal{X}},F^i)$ unless otherwise stated. One imposes no initial condition on the pressure, for (\[eq.mhdefivf\]) does not contain any time derivative of $p$. Equations (\[eq.mhdefivf\]) supplemented with initial condition (\[eq.initval\]) constitute the Cauchy problem for the generalised Navier-Stokes equations. For the existence of a solution to the Cauchy problem it is necessary that $A^\ast v_0 = 0$ on ${\mathcal{X}}$, which we will always assume. While the velocity $v$ seems to be uniquely determined by the data $f$ and $v_0$, the pressure $p$ is determined only up to solutions of the homogeneous equation $Ap = 0$ on ${\mathcal{X}}$. The non-uniqueness of $p$ is evaluated by the dimension of the cohomology of complex (\[eq.ellcomp\]) at step $i-1$. Since the complex is elliptic, the cohomology is finite dimensional, see [@Tark95]. We make use of this fact in the next section.
Elimination of the pressure {#s.eliotpr}
===========================
The approach of [@ShlaTark16] which consists in applying the differential $A$ to the both sides of (\[eq.mhdefivf\]) and passing to the equation for the vorticity of $v$ requires the cohomology of (\[eq.ellcomp\]) to be zero at step $i$. If this is the case, then the Hodge decomposition theorem for elliptic complexes on compact closed manifolds implies readily $
v = A^\ast G (Av)
$ for all divergence-free sections $v$ of $F^i$, where $G$ is the so-called Green operator related to the Laplacian ${\mathit{\varDelta}}$, see [@Tark95]. Hence it follows that $
A N (v) = A N A^\ast G (Av),
$ and so we can choose $N^{i+1} = A N^{i} A^\ast G$ as the $(N\!+\!1)\,$-th component of a new cochain mapping of complex (\[eq.ellcomp\]). This mapping satisfies the commutativity relation $A N (v) = N (Av)$ for all divergence-free sections $v$ of $F^i$ and bears moreover the property that $(N (w),z) = 0$ for all divergence-free sections $z$ of $F^{i+1}$. Since pseudodifferential operators are involved in the very formulation of (\[eq.mhdefivf\]), we focus on the classical approach which expoits the Helmholtz projection, cf. [@MeraShlaTark15].
The idea is to project the first equation of (\[eq.mhdefivf\]) onto the space of divergence-free sections of $F^i$. Denote by $H$ the orthogonal projection onto the null-space of ${\mathit{\varDelta}}$ in $L^2 ({\mathcal{X}},F^i)$.
\[l.Helmholtz1\] For $H$ and $G$ defined above, the operator $
Pv := Hv + A^\ast A\, Gv
$ is an orthogonal projection in $L^2 ({\mathcal{X}},F^i)$.
Since the Laplacian is elliptic, the space of all $h \in L^2 ({\mathcal{X}},F^i)$ satisfying ${\mathit{\varDelta}}h = 0$ in ${\mathcal{X}}$ is finite dimensional. The elements of this space are called harmonic sections and they actually satisfy both $Ah = 0$ and $A^\ast h = 0$ in ${\mathcal{X}}$. The harmonic sections are $C^\infty$ sections of $F^i$, and so the orthogonal projection $H$ onto the space is a smoothing operator. Moreover, the Green operator is a formally selfadjoint pseudodifferential operator of order $-2$ on sections of $F^i$, such that $H G = 0$ and $A G = G A$, and the identity operator on sections of $F^i$ splits into $H + A^\ast A G + A A^\ast G$. The decomposition $v = Hv + A^\ast A Gv + A A^\ast Gv$ valid for all $v \in L^2 ({\mathcal{X}},F^i)$ is usually referred to as the generalised Hodge decomposition. Since $A^2 = 0$, the summands are pairwise orthogonal, and so both $A^\ast A G$ and $A A^\ast G$ are orthogonal projections, too. For a thorough discussion of Hodge theory we refer the reader to [@Tark95 Ch. 4].
The projector $P$ is an analogue of the Helmholtz projector onto vector fields which are divergence-free. A slightly different approach to this decomposition is presented in [@Lady70].
\[l.Helmholtz2\] In order that $Pv = v$ be valid it is necessary and sufficient that $A^\ast v = 0$ in ${\mathcal{X}}$.
Suppose that $Pv = v$. Then $A^\ast v = A^\ast (Hv + A^\ast A\, Gv)$ vanishes in ${\mathcal{X}}$. On the other hand, if $A^\ast v = 0$ in ${\mathcal{X}}$, then $A^\ast (Gv) = 0$ whence $Pv = v$, as desired.
From Lemma \[l.Helmholtz2\] it follows that $P$ vanishes on sections of the form $Ap$ with $p \in L^2 ({\mathcal{X}},F^{i-1})$ and $Ap \in L^2 ({\mathcal{X}},F^i)$. Indeed, to prove this it suffices to show that $Ap$ is orthogonal to all sections $v$ satisfying $A^\ast v = 0$ in ${\mathcal{X}}$. For such a section $v$ we get $$\begin{aligned}
(Ap, v)_{L^2 ({\mathcal{X}},F^i)}
& = &
(p, A^\ast v)_{L^2 ({\mathcal{X}},F^{i-1})}
\\
& = &
0,\end{aligned}$$ as desired.
On applying the Helmholtz projector to the first equation of system (\[eq.mhdefivf\]) one obtains $$(Pv)'_t + \varepsilon\, P ({\mathit{\varDelta}}^m v) + \nu\, P ({\mathit{\varDelta}}v) + P (Ap) + P N (v) = Pf$$ while the second equation of (\[eq.mhdefivf\]) means that $Pv = v$ in ${\mathcal{C}}$. Since $P (Ap) = 0$, this allows one to eliminate the pressure from the first equation, thus obtaining an equivalent form $$\begin{array}{rcl}
(Pv)'_t + \varepsilon\, P {\mathit{\varDelta}}^m (Pv) + \nu\, P ({\mathit{\varDelta}}v) + P N (Pv)
& = &
Pf,
\\
({I}\!-\!P) Ap + ({I}\!-\!P) N (Pv)
& = &
({I}-P) f
\end{array}$$ of equations (\[eq.mhdefivf\]), for $({I}\!-\!P) P = 0$ and $$\begin{aligned}
({I}- P) {\mathit{\varDelta}}^m P
& = &
({I}- H - A^\ast A G)\, {\mathit{\varDelta}}^m\, (H + A^\ast A G)
\\
& = &
A A^\ast G \left( A^\ast A \right)^{m+1} G
\\
& = &
0,\end{aligned}$$ the last equality being due to the fact that $A^\ast G = G A^\ast$.
In other words, we separate the Cauchy problem (\[eq.mhdefivf\]), (\[eq.initval\]) into two single problems $$(Pv)'_t + \varepsilon\, P {\mathit{\varDelta}}^m (Pv) + \nu\, P ({\mathit{\varDelta}}v) + P N (Pv)
= Pf$$ in ${\mathcal{C}}$ under the initial condition $$Pv\, (\cdot,0) = v_0$$ on ${\mathcal{X}}$ and $$\label{eq.sefp}
\begin{array}{rclcl}
Ap
& =
& ({I}- P)\, (f - N (Pv))
& \mbox{in}
& {\mathcal{C}},
\\
(p,u)_{L^2 ({\mathcal{X}},F^{i-1})}
& =
& 0
& \mbox{for}
& u \in \ker A.
\end{array}$$
The operator $P {\mathit{\varDelta}}^m$ is sometimes called the Stokes operator. It is a pseudodifferential operator of order $2m$ on sections of $F^i$. The only solution of problem (\[eq.sefp\]) is given by $$p = A^\ast G ({I}- P)\, (f - N (Pv)).$$
\[l.Stokes\] Suppose that $u \in H^{{\mathbf{s}}(1)} ({\mathcal{C}},F^i)$ is a solution of the Cauchy problem $$\label{eq.Stokes}
\begin{array}{rclll}
u'_t + \varepsilon\, P {\mathit{\varDelta}}^m u + \nu\, P ({\mathit{\varDelta}}u) + P N (u)
& =
& Pf
& \mbox{in}
& {\mathcal{C}},
\\
u (\cdot,0)
& =
& v_0
& \mbox{on}
& {\mathcal{X}}\end{array}$$ in the cylinder. Then $A^\ast u = 0$ in ${\mathcal{C}}$.
Indeed, from the differential equation of (\[eq.Stokes\]) it follows that $$\frac{\partial}{\partial t}\, A^{\ast} u = 0$$ in ${\mathcal{C}}$. Since $A^\ast u = A^\ast v_0 = 0$ for $t = 0$, we deduce readily that $A^\ast u = 0$ for all $t \in I$, as desired.
On summarising what has been said we choose the following way of solving equations (\[eq.mhdefivf\]). We first construct a solution $u$ of Cauchy problem (\[eq.Stokes\]). According to Lemma \[l.Stokes\], $u$ satisfies $A^\ast u = 0$ in ${\mathcal{C}}$, and so $Pu = u$. Substitute the section $v := u$ into equation (\[eq.sefp\]) for $p$. From this equation the pressure $p$ is determined uniquely and bears the appropriate regularity of the canonical solution of the inhomogeneous equation related to complex (\[eq.ellcomp\]) at step $i$. Finally, on combining equations (\[eq.Stokes\]) and (\[eq.sefp\]) we conclude that the pair $(v,p)$ is a solution of (\[eq.mhdefivf\]) under condition (\[eq.initval\]).
In the sequel we focus on the study of operator equation (\[eq.Stokes\]) by Hilbert space methods.
Fundamental solution to the heat equation {#s.fsttheq}
=========================================
For sections of $F^i$, consider the equation of evolution $$\label{eq.heatequ}
\frac{\partial u}{\partial t}
= - \varepsilon {\mathit{\varDelta}}^m u - \nu {\mathit{\varDelta}}u$$ on the semiaxis $t > 0$. It is easily seen that the endomorphism of $F^i_x$ given by the principal symbol $- \varepsilon \left( \sigma^2 ({\mathit{\varDelta}}) (x,\xi) \right)^m$ of the operator on the right-hand side of (\[eq.heatequ\]) at any nonzero vector $\xi \in T^\ast_x {\mathcal{X}}$ has only real eigenvalues strictly less than zero. Therefore, the equation (\[eq.heatequ\]) is actually one of the well-known type of partial differential equations, called parabolic, which enjoy a behaviour essentially like that of the classical equation of the heat conduction. For instance, one has as a smoothing operator the fundamental solution $
t \mapsto \psi^i (x,y,t) \in C^{\infty} ({\mathcal{X}}\times {\mathcal{X}}, F^i \otimes F^i{}^\ast)
$ which generates the solution of the Cauchy problem for (\[eq.heatequ\]) in the sence that, for any $u_0 \in C^{\infty} ({\mathcal{X}},F^i)$, $$(\varPsi^i u_0) (x,t)
= \int_{{\mathcal{X}}} (u_0, \ast^{-1} \psi^i (x,\cdot,t))_{y} dy$$ is regular for $t > 0$, satisfies (\[eq.heatequ\]) and has initial value $u_0$. The fundamental solution $\varPsi^i$ is here unique by virtue of the compactness of ${\mathcal{X}}$. We write $\varPsi$ for the corresponding graded operator.
We recall briefly the Hilbert-Levi procedure for constructing the fundamental solutions for parabolic operators, and state certain basic estimate for them, only to the extent which we shall need later. For the details we refer the reader to [@Eide56] and elsewhere.
Denote by $
L = \partial_t + \varepsilon {\mathit{\varDelta}}^m + \nu {\mathit{\varDelta}}$ the parabolic operator of (\[eq.heatequ\]) on sections of the induced bundle $F^i$ over ${\mathcal{X}}\times {\mathbb{R}}_{> 0}$. We can cover ${\mathcal{X}}$ by a finite number of coordinate patches $U$ such that over each $U$ the bundle $F^i$ is trivial, i.e., the restriction $F^i \restriction_U$ is isomorphic to the trivial bundle $U \times \mathbb{C}^{k_i}$, where $k_i$ is the fibre dimension of $F^i$. Let $x = (x^1, \ldots, x^n)$ be local coordinates in $U$. Then any section of $F^i$ over $U$ can be regarded as a $k_i\,$-column of complex-valued functions of coordinates $x$. Under this identification, for any $u \in C^\infty (U,F^i)$, the $k_i\,$-column ${\mathit{\varDelta}}^m u$ of functions in $U$ is represented by $${\mathit{\varDelta}}^m u
= \Big( \sum_{|\alpha| \leq 2} {\mathit{\varDelta}}_{\alpha} (x)\, \partial^{\alpha} \Big)^m u,$$ where ${\mathit{\varDelta}}_{\alpha} (x)$ are $(k_i \times k_i)\,$-matrices of $C^\infty$ functions of $x$, by $\partial^{\alpha}$ is meant the derivative $(\partial/\partial x^1)^{\alpha_1} \ldots (\partial/\partial x^n)^{\alpha_n}$, and the upper index $m$ refers to the power with respect to the composition of operators. So, the principal symbol of ${\mathit{\varDelta}}^m$ is given by $$\sigma^{2m} ({\mathit{\varDelta}}^m) (x,\xi)
= \Big( - \sum_{|\alpha| = 2} {\mathit{\varDelta}}_{\alpha} (x)\, \xi^{\alpha} \Big)^m$$ for $(x,\xi) \in U \times {\mathbb{R}}^n$, where $\xi^{\alpha} = \xi_1^{\alpha_1} \ldots \xi_n^{\alpha_n}$. As already mentioned, $\sigma^{2m} ({\mathit{\varDelta}}^m) (x,\xi)$ has only strictly negative eigenvalues for each nonzero vector $\xi$, and hence the matrix $$\label{eq.paramet}
p_U (x,y,t)
= \frac{1}{(2 \pi)^n}
\int
\exp \left( t\, \varepsilon \sigma^{2m} ({\mathit{\varDelta}}^m) (x,\xi) + \sqrt{-1}\, \langle x-y, \xi \rangle\, {I}\right)
d \xi$$ is well defined for all $x, y \in U$ and $t > 0$, where ${I}$ stands for the unity matrix of type $k_i \times k_i$.
It will be seen below that $p_U$ describes the principal part of singularity for the fundamental solution of the parabolic operator $L$ in $U$. For that reason $p_U$ is said to be a local parametrix for this operator. Letting now $$\sum \varphi_U^2 \equiv 1$$ be a quadratic partition of unity on ${\mathcal{X}}$ subordinate to a covering $\{\, U\, \}$, and considering the expression $
\varphi_U (x) p_U (x,y,t) \varphi_U (y)
$ as a section of $F^i \otimes (F^i)^\ast$ with support in $U \times U$, we define a global parametrix for (\[eq.heatequ\]) by $$p (x,y,t)
= \sum_U \varphi_U (x) p_U (x,y,t) \varphi_U (y).$$ The fundamental solution $\psi (x,y,t)$ of $L$ will then be given as the unique solution of the integral equation of Volterra type $$\psi (x,y,t)
= p (x,y,t)
- \int_0^t dt' \int_{{\mathcal{X}}} (L p (\cdot,y,t'), \ast^{-1} \psi (x,\cdot,t-t'))_{z} dz,$$ the operator $L$ acting in $z$. Since the singularities of $p$ and $Lp$ are relatively weak, we can solve the integral equation by the standard method of successive approximation. The kernel $\psi (x,y,t)$ obtained in this way is easily verified to be of class $C^\infty$, when $t > 0$, and, $$u (x,t)
= \int_{{\mathcal{X}}} (u_0, \ast^{-1} \psi (x,\cdot,t))_{y} dy$$ satisfies $Lu = 0$ for $t > 0$ and $u (x,0) = u_0 (x)$ for all $x \in {\mathcal{X}}$.
As for the estimates, note that if we define, relative to a Riemannian metric $ds$ on ${\mathcal{X}}$, a distance function to be $$d (x,y) = \inf \int_{\widehat{xy}} ds$$ for $x, y \in {\mathcal{X}}$, where $\widehat{xy}$ is a path from $x$ to $y$, then $$\label{eq.eotfsps}
|\partial_x^{\alpha} \partial_y^{\beta} \psi (x,y,t)|
\leq
c\,
\frac{1}{t^{\frac{\scriptstyle{n + |\alpha| + |\beta|}}{\scriptstyle{2m}}}}\,
\exp \Big( - c' \frac{(d (x,y))^{(2m)'}}{t^{(2m)' - 1}}\Big)$$ locally on ${\mathcal{X}}'$ and for each entry of the matrix, where $(2m)'$ is the conjugate number for $2m$ given by $1/(2m) + 1/(2m)' = 1$. Also, as can be inferred and in fact easily proved from (\[eq.paramet\]) and (\[eq.eotfsps\]), we get $$|\psi (x,y,t) - p_U (x,y,t)|
\leq
c\,
\frac{1}{t^{\frac{\scriptstyle{n-1}}{\scriptstyle{2m}}}}\,
\exp \Big( - c' \frac{(d (x,y))^{(2m)'}}{t^{(2m)' - 1}}\Big)$$ uniformly on each compact subset of $U \times U$, showing that locally $p_U$ yields a first approximation to the fundamental solution $\psi (x,y,t)$.
\[l.Greenhe\] Suppose that $u$ is a section of $F^i$ over ${\mathcal{C}}$ of Slobodetskij class $H^{{\mathbf{s}}(1)} ({\mathcal{C}})$. Then $$\label{eq.Greenhe}
u (x,t)
= (\varPsi u (\cdot,0)) (x,t)
+ \int_0^t dt' \int_{{\mathcal{X}}} (Lu (\cdot,t'), \ast^{-1} \psi (x,\cdot,t-t'))_{y} dy$$ for all $(x,t) \in {\mathcal{C}}$.
Since $C^\infty (\overline{{\mathcal{C}}}, F^i)$ is dense in $H^{{\mathbf{s}}(1)} ({\mathcal{C}}, F^i)$, it suffices to establish the formula for those sections $u$ which are $C^\infty$ in the closure of ${\mathcal{C}}$. As is well known, the Cauchy problem $$\label{eq.Cpftheq}
\Big\{
\begin{array}{rclcl}
Lu
& =
& f
& \mbox{in}
& {\mathcal{C}},
\\
u (\cdot,0)
& =
& u_0
& \mbox{on}
& {\mathcal{X}}\end{array}$$ has a unique solution in $C^\infty (\overline{{\mathcal{C}}}, F^i)$ for all smooth data $f$ in $\overline{{\mathcal{C}}}$ and $u_0$ on ${\mathcal{X}}$. By the above, the first term on the right-hand side of (\[eq.Greenhe\]) is a solution of the Cauchy problem with $f = 0$ and $u_0 = u (\cdot,0)$. Hence, we shall have established the lemma if we prove that the second term is a solution of the Cauchy problem with $f = Lu$ and $u_0 = 0$. To this end, we rewrite the second summand on the right-hand side of (\[eq.Greenhe\]) in the form $$\int_0^t \varPsi \left( Lu (\cdot,t') \right) (x,t-t')\, dt'$$ for $(x,t) \in {\mathcal{C}}$. Obviously, the initial value at $t = 0$ of this integral vanishes, and so it remains to calculate its image by $L$. We get $$\begin{aligned}
\lefteqn{
L \int_0^t \varPsi \left( Lu (\cdot,t') \right) (x,t-t')\, dt'
}
\\
& = &
\varPsi \left( Lu (\cdot,t) \right) (x,0)
+ \int_0^t L\, \varPsi \left( Lu (\cdot,t') \right) (x,t-t')\, dt'
\\
& = &
Lu (x,t),\end{aligned}$$ as desired.
Reduction to an integral equation {#s.rtaiequ}
=================================
Given integrable sections $f$ and $u_0$ of $F^i$ over ${\mathcal{C}}$ and ${\mathcal{X}}$, respectively, we introduce two potentials $$\begin{array}{rcl}
\mathcal{P}_v (f)\, (x,t)
& =
& \displaystyle
\int_0^t \varPsi \left( f (\cdot,t') \right) (x,t-t')\, dt',
\\
\mathcal{P}_i (u_0)\, (x,t)
& =
& (\varPsi u_0)\, (x,t)
\end{array}$$ for $(x,t) \in {\mathcal{C}}$. They are said to be parabolic volume and initial value potentials, respectively.
\[l.bounopp\] As defined above, the parabolic potentials induce continuous linear mappings $$\begin{array}{rrcl}
\mathcal{P}_v\, :
& L^2 ({\mathcal{C}}, F^i)
& \to
& H^{{\mathbf{s}}(1)} ({\mathcal{C}}, F^i),
\\
\mathcal{P}_i\, :
& H^m ({\mathcal{X}}, F^i)
& \to
& H^{{\mathbf{s}}(1)} ({\mathcal{C}}, F^i).
\end{array}$$
Let $f \in L^2 ({\mathcal{C}},F^i)$. Define $u = \mathcal{P}_v (f)$. The proof of Lemma \[l.Greenhe\] shows that $u$ is a solution of problem (\[eq.Cpftheq\]) with $u_0 = 0$. By the maximal regularity theorem of [@Slob58], we get $u \in H^{{\mathbf{s}}(1)} ({\mathcal{C}}, F^i)$. Moreover, $u$ depends continuously of $f$, which proves the continuity of $\mathcal{P}_v$. Analogously one establishes the continuity of the initial value potential.
In terms of potentials formula (\[eq.Greenhe\]) looks like $
u = \mathcal{P}_i (u (\cdot,0)) + \mathcal{P}_v (Lu)
$ in the cylinder ${\mathcal{C}}$. This leads immediately to a reformulation of the Cauchy problem of Lemma \[l.Stokes\].
\[t.reducti\] A section $u \in H^{{\mathbf{s}}(1)} ({\mathcal{C}},F^i)$ is a solution of Cauchy problem (\[eq.Stokes\]) if and only if it satisfies $$\label{eq.reducti}
u + \mathcal{P}_v (P N (u)) = \mathcal{P}_i (v_0) + \mathcal{P}_v (Pf)$$ in ${\mathcal{C}}$.
[*Necessity*]{} Suppose that $u \in H^{{\mathbf{s}}(1)} ({\mathcal{C}},F^i)$ is a solution of the Cauchy problem $$\begin{array}{rclll}
& =
\\
& =
& {\mathcal{X}}\end{array}$$ in the cylinder. Then $A^\ast u = 0$, which is due to Lemma \[l.Stokes\], and so on applying Lemma \[l.Helmholtz2\] we see that $Pu = u$. Since the operators ${\mathit{\varDelta}}$ and $P$ commute, it follows that $Lu = Pf - P N (u)$ in ${\mathcal{C}}$. By (\[eq.Greenhe\]), $
u = \mathcal{P}_i (v_0) + \mathcal{P}_v (Pf - P N (u))
$ in ${\mathcal{C}}$, showing (\[eq.reducti\]).
[*Sufficiency*]{} Let $u \in H^{{\mathbf{s}}(1)} ({\mathcal{C}},F^i)$ satisfy equation (\[eq.reducti\]). By the very definition of parabolic potentials, we get $$\begin{array}{rclll}
Lu
& =
& Pf - P N (u)
\\
& =
& {\mathcal{X}}.
\end{array}$$ Since $v_0$ satisfies $A^\ast v_0 = 0$ on ${\mathcal{X}}$, we conclude that $P v_0 = v_0$. Therefore, applying the projection $P$ to both sides of the above equalities yields $L (u - Pu) = 0$ in ${\mathcal{C}}$ and $(u - Pu) (\cdot,0) = 0$ on ${\mathcal{X}}$. By uniqueness, $Pu = u$ in the cylinder, and so $u$ is a solution of Cauchy problem (\[eq.Stokes\]).
Note that (\[eq.reducti\]) is a nonlinear integral equation of Volterra type for the unknown section $u$ in $H^{{\mathbf{s}}(1)} ({\mathcal{C}}, F^i)$. The nonlinear operator $N$ maps $H^{{\mathbf{s}}(1)} ({\mathcal{C}},F^i)$ continuously and compactly into $L^2 ({\mathcal{C}},F^i)$ while $P$ is a continuous mapping of $L^2 ({\mathcal{C}},F^i)$ into itself and $\mathcal{P}_v$ maps $L^2 ({\mathcal{C}},F^i)$ continuously into $H^{{\mathbf{s}}(1)} ({\mathcal{X}},F^i)$, the latter being due to Lemma \[l.bounopp\]. Hence it follows that the composition $K = \mathcal{P}_v \circ P \circ N$ is a compact continuous operator in $H^{{\mathbf{s}}(1)} ({\mathcal{C}},F^i)$. Thus, equation (\[eq.reducti\]) is of the Leray-Schauder type $({I}+ K) u = f$, where moreover $K$ is differentiable. Our next concern will be to show that the mapping ${I}+ K$ is actually a diffeomorphism of $H^{{\mathbf{s}}(1)} ({\mathcal{C}},F^i)$ for each $\varepsilon > 0$.
Comments on the Navier-Stokes equations for quasicomplexes {#eq.coNSefq}
==========================================================
For any complex (\[eq.ellcomp\]), the composition $A^{i} A^{i-1}$ of any two neighbouring operators vanishes. Using the language of differential geometry one can think of the composition $A \circ A$ as the curvature of (\[eq.ellcomp\]). In this way the complexes are flat sequences of topological vector spaces and their continuous mappings. Differential geometry gives a convincing motivation to those sequences which fail to be flat but whose curvature is small in some sense. Let alone the extended sequence of connections associated to any smooth vector bundle, whose curvature proves to be a bundle morphism. More generally, we call (\[eq.ellcomp\]) a quasicomplex if each composition $A^{i} A^{i-1}$ is actually a pseudodifferential operator of order one. Given any quasicomplex, the sequence of principal symbols still constitutes a complex, and so the ellipticity survives under “small” perturbations of complexes. The Laplacians $
{\mathit{\varDelta}}^i = A^i{}^\ast A^i + A^{i-1} A^{i-1}{}^\ast
$ of an elliptic quasicomplex are nonnegative symmetric second order elliptic operators between sections of vector bundles $F^i$, for $i = 0, 1, \ldots, N$. Therefore, we are in a position to introduce the generalised Navier-Stokes equations also for elliptic quasicomplexes in much the same way as in (\[eq.mhdefivf\]). Note, however, that neither $A$ nor $A^\ast$ commute with ${\mathit{\varDelta}}$, and so the elimination of the pressure is no longer possible using the Neumann problem after Spencer, as it is done in Section \[s.eliotpr\].
\[p.sorNSeq\]
We now return to problem (\[eq.gNSefivf\]). For this problem it is possible to prove global existence and uniqueness of the weak as well as strong solutions. The characterisation of weak solutions is analogous to that of [@Hopf51]. The description of strong solutions is similar to that of [@KiseLady57]. The characterisation of strong solutions to the conventional system in [@KiseLady57] can be improved using the eigenfunctions of the Stokes operator $$\Big( \begin{array}{cc}
\nu {\mathit{\varDelta}}& A
\\
A^\ast
& 0
\end{array}
\Big)$$ and taking the estimates of [@Prod62] but we will not develop this point here. A regularisation similar to (\[eq.gNSefivf\]) was first studied by Ladyzhenskaya in [@Lady62]. She established a convergence theorem for the strong solutions of this system to those of the Navier-Stokes equation as the regularisation parameter tends to zero. Lions proposed a regularisation of the Navier-Stokes equations by adding a higher order viscosity term $\varepsilon (- {\mathit{\varDelta}})^m u$ and requiring the solution to vanish up to order $m$ on the lateral boundary of the cylinder, see Remark 6.11 in [@Lion69]. For this problem he proved the global existence of unique weak solutions. The paper [@Veig85a] concerns regularisations of this type in the whole space ${\mathbb{R}}^n$ and establishes convergence theorems as the regularisation parameter approaches zero, see also [@Veig85b].
Governing equations and functional framework {#s.geaffra}
============================================
To proceed we first make more precise our assumptions on the structure of nonlinearity in problem (\[eq.gNSefivf\]). Namely, we consider $N (u,v) := T (v) u$ for differentiable sections $u$ und $v$ of $F^i$, where $T$ is a first order differential operator on ${\mathcal{X}}$ mapping sections of $F^i$ into sections of the bundle $\mathrm{Hom}\, F^i$ of homomorphisms of $F^i$. Our standing assumption on the differential operators $T$ under study is that there is a sesquilinear mapping $Q (v,w)$ of $C^\infty ({\mathcal{X}}, F^i) \times C^\infty ({\mathcal{X}}, F^i)$ into $C^\infty ({\mathcal{X}},F^{i-1})$, such that $(T (v))^\ast v = A Q (v,v)$ for all smooth sections $v$ of $F^i$. For the conventional nonlinearity, we get $T (v) = v'_x$ and $$Q (v,w) = \frac{1}{2}\, (v,w)_x,$$ as is easy to check. As usual, we abbreviate $N (u,u)$ to $N (u)$, and similarly for $Q (v,v)$.
\[l.algestr\] As defined above, the differential operator $T$ satisfies the anticommutativity relation $$\label{eq.algestr}
(T (v))^\ast w + (T (w))^\ast v
= A \left( Q (v) - Q (v-w) + Q (w) \right)$$ for all $v, w \in C^\infty ({\mathcal{X}},F^i)$.
Since $T$ is linear, it follows that $$\begin{aligned}
(T (v))^\ast w + (T (w))^\ast v
& = &
(T (v))^\ast v - (T (v-w))^\ast (v-w) + (T (w))^\ast w
\\
& = &
A \left( Q (v) - Q (v-w) + Q (w) \right),\end{aligned}$$ as desired.
The following lemma clarifies why (\[eq.algestr\]) is referred to as an anticommutativity relation.
\[c.algestr\] Assume that $u \in C^\infty ({\mathcal{X}}, F^i)$ satisfies $A^\ast u = 0$ and has zero Cauchy data on the boundary of ${\mathcal{X}}$ with respect to the differential operator $A^\ast$. Then, one has $$(N (u,v), w) = - (N (u,w), v)$$ for all $v, w \in C^\infty ({\mathcal{X}},F^i)$.
Indeed, we get $$\begin{aligned}
(N (u,v), w) + (N (u,w), v)
& = &
(T (v)\, u, w) + (T (w)\, u, v)
\\
& = &
(u, (T (v))^\ast w) + (u, (T (w))^\ast v)
\\
& = &
(u, A \left( Q (v) - Q (v-w) + Q (w) \right))
\\
& = &
0,\end{aligned}$$ as desired.
The equality $(N (u,v), w) = - (N (u,w), v)$ is actually a crucial property characterising those nonlinear terms $N (u,v)$ which are permitted in this work. In particular, we see that $(N (u), u) = 0$ holds for any smooth solenoidal section $u$ of the bundle $F^i$.
\[e.algestr\] For the conventional Navier-Stokes equations on a compact Riemannian manifold with boundary ${\mathcal{X}}$ one chooses $N (u,v) = \partial_u v$, see [@EbinMars70]. Here, we interpret $u$ and $v$ as one-forms on ${\mathcal{X}}$ and $\partial$ stands for a connection on (the tangent bundle of) the manifold, so that $\partial_u v$ is the derivative of $v$ in the direction $u$. By definition we get $\partial_u v = \iota (u) \partial v$, where by $\iota (u)$ is meant the interior multiplication by $u$. Show that if $\partial$ is compatible with the Riemannian metric of ${\mathcal{X}}$, then the equality $(N (u,v), w) = - (N (u,w), v)$ is fulfilled. Indeed, let $u$ be a differentiable one-form on ${\mathcal{X}}$ satisfying $d^\ast u = 0$ in ${\mathcal{X}}$ and whose normal part on the boundary vanishes. Then $$\begin{aligned}
(N (u,v), w)
& = &
\int_{{\mathcal{X}}} (N (u,v),w)_x dx
\\
& = &
\int_{{\mathcal{X}}} (\iota (u) \partial v, w)_x dx
\\
& = &
\int_{{\mathcal{X}}} \iota (u)\, (\partial v, w)_x dx
\\
& = &
\int_{{\mathcal{X}}} \iota (u) \big( (\partial v, w)_x + (v, \partial w)_x \big) dx
- \int_{{\mathcal{X}}} \iota (u)\, (v, \partial w)_x dx
\\
& = &
\int_{{\mathcal{X}}} \iota (u)\, d (v, w)_x dx
- \int_{{\mathcal{X}}} \iota (u)\, (\partial w, v)_x dx
\\
& = &
\int_{{\mathcal{X}}} d^\ast u\, (v, w)_x dx
- (N (u,w),v)
\\
& = &
-\, (N (u,w), v)\end{aligned}$$ for all $v, w \in \varOmega^1 ({\mathcal{X}})$, as desired. In particular, this is the case for the Levi-Civita connection on ${\mathcal{X}}$.
Denote by $\mathcal{S}$ the space of all sections $u \in C^\infty ({\mathcal{X}},F^i)$ which vanish up to the infinite order on the boundary of ${\mathcal{X}}$ and satisfy $A^{\ast} u = 0$ in ${\mathcal{X}}$. Note that while studying the problem for compact closed manifolds we present the framework to suit to compact manifolds with boundary as well. Let $H$ stand for the closure of $\mathcal{S}$ in $L^2 ({\mathcal{X}}, F^i)$. When equipped with the induced unitary structure, $H$ is a Hilbert space. The elements of $H$ are still solenoidal and inherit the property $n (u) = 0$ on the boundary of ${\mathcal{X}}$ in a weak sense, $n (u)$ being the Cauchy data of $u$ with respect to $A^\ast$. Furthermore, we write $S = S^m$ for the closure of $\mathcal{S}$ in $H^{m} ({\mathcal{X}},F^i)$. Using spectral synthesis in Sobolev spaces one sees that $S$ coincides with the subspace of $H^{m} ({\mathcal{X}},F^i)$ consisting of those solenoidal sections $u$ which vanish up to order $m$ on the boundary of ${\mathcal{X}}$.
\[l.Dirichl\] The norm in $S$ inherited from $H^m ({\mathcal{X}},F^i)$ is equivalent to that determined by the energy (or Dirichlet) inner product $$\label{eq.Dirichl}
D (u,v)
= \varepsilon\, ({\mathit{\varDelta}}^{m/2} u, {\mathit{\varDelta}}^{m/2} v)
+ \nu \left( (Au, Av) + (A^\ast u, A^\ast v) \right)
+ (u,v)$$ for $u, v \in S$.
This follows immediately from the fact that the Dirichlet problem for the differential operator $V = \varepsilon {\mathit{\varDelta}}^m + \nu {\mathit{\varDelta}}$ is elliptic in the classical setting of Sobolev spaces.
The space $S$ is contained in $H$, it is dense in $H$, and the embedding is continuous. Let $H'$ and $S'$ denote the dual spaces of $H$ and $S$, respectively, and let $\iota$ denote the embedding of $S$ into $H$. The transposed operator $\iota'$ maps $H'$ continuously into $S'$, and it is one-to-one since $\iota (S) = S$ is dense in $H$, and $\iota' (H')$ is dense in $S'$ since $\iota$ is one-to-one. Moreover, by the Riesz representation theorem, we can identify $H$ and $H'$, and so we arrive at the continuous inclusions $
S \hookrightarrow H \cong H' \hookrightarrow S',
$ each space being dense in the subsequent one. As a consequence of these identifications, the inner product in $H$ can be specified within the pairing of $S'$ and $S$. More precisely, there is a sesquilinear pairing $S' \times S \to \mathbb{C}$ (for which we continue to write $(f,v)$), such that $$(f, \iota (v)) = \overline{\langle \iota' \ast_H f, v \rangle}$$ for all $f \in H$ and $v \in S$, where $\ast_H : H \to H'$ is the conjugate linear isomorphism given by the Riesz theorem.
For each $u \in S$, the form $v \to D (u,v)$ is conjugate linear and continuous on $S$. Therefore, there is an element of $S'$ (which we denote by $(V + {I}) u$) with the property that $$\label{eq.Frieext}
((V + {I}) u,v) = D (u,v)$$ for all $v \in S$. In this way we get what is known as the Friedrichs extension of the differential operator $\varepsilon {\mathit{\varDelta}}^m + \nu {\mathit{\varDelta}}$, cf. [@AlfoSimo80]. The mapping $u \mapsto (V + {I}) u$ is linear and continuous and so is $u \mapsto Vu$. Moreover, $V + {I}$ is an isomorphism from $S$ onto $S'$.
Let $\mathcal{B}$ be any Banach space. For a finite real number $p \geq 1$, we denote by $L^{p} (I,\mathcal{B})$ the space of all measurable functions $u$ on the interval $I$ with values in $\mathcal{B}$, such that $$\label{eq.Bochner}
\Big( \int_I \| u (t) \|_{\mathcal{B}}^p\, dt \Big)^{1/p} < \infty.$$ This space is Banach under the norm (\[eq.Bochner\]). The space $L^\infty (I,\mathcal{B})$ is defined to consist of all essentially bounded functions $u$ of $t \in I$ with values in $\mathcal{B}$. As usual, this space is given the norm obtained from (\[eq.Bochner\]) by passing to the limit as $p \to \infty$. It is a Banach space.
By $C (\overline{I},\mathcal{B})$ is meant the space of all continuous functions on $I$ with values in $\mathcal{B}$. If $I$ is bounded, the space is topologised under norm induced by the embedding into $L^\infty (I,\mathcal{B})$, i.e., $$\| u \|_{C (\overline{I},\mathcal{B})}
= \sup_{t \in I} \| u (t) \|_{\mathcal{B}}.$$
The following technical lemma concerns the derivatives of functions with values in Banach spaces.
\[l.primiti\] Assume $U$ and $u$ are two functions of $L^1 (I,\mathcal{B})$. Then, the following are equivalent:
1\) $U$ is a.e. equal to a primitive function of $u$, i.e., $
\displaystyle
U (t) = U_0 + \int_0^t u (t') dt'
$ for a.a. $t \in I$.
2\) $U' = u$ weakly in $I$, i.e., $
\displaystyle
\int_I U (t) \phi' (t) dt = - \int_I u (t) \phi (t) dt
$ is valid for each $\phi \in C^\infty_{\mathrm{comp}} (0,T)$.
3\) For each $f \in \mathcal{B}'$, the equality $
\displaystyle
\frac{d}{dt} \langle f, U \rangle = \langle f, u \rangle
$ holds weakly in $I$.
If one of the conditions 1)-3) is satisfied, then $u$ is, in particular, a.e. equal to a continuous function on $I$ with values in $\mathcal{B}$.
See for instance [@Tema79 p. 169].
The basic linear problem {#s.basiclp}
========================
The basic linear problem relating to the generalised Navier-Stokes equations of (\[eq.mhdefivf\]) consists in finding sections $u$ and $p$ of $F^i$ and $F^{i-1}$ over ${\mathcal{C}}$, respectively, such that $$\label{eq.basiclp}
\begin{array}{rcl}
\partial_t u + (\varepsilon {\mathit{\varDelta}}^m + \nu {\mathit{\varDelta}}) u + Ap
& =
& f,
\\
A^\ast u
& =
& 0
\end{array}$$ in the cylinder ${\mathcal{C}}$ and $$\label{eq.mixedbc}
\begin{array}{rclcl}
u (\cdot,0)
& =
& u_0
& \mbox{on}
& {\mathcal{X}},
\\
u
& =
& 0
& \mbox{up to order $m$ on}
& \partial {\mathcal{X}}\times I,
\end{array}$$ where $f$ is a section of $F^i$ over the cylinder and $u_0$ a section of $F^i$ over its bottom ${\mathcal{X}}$. Conditions (\[eq.mixedbc\]) specify the first mixed problem for evolution equations (\[eq.basiclp\]). In the case of conventional Navier-Stokes equations this problem is referred to as the Stokes problem.
Let $(u,p)$ be a classical solution of problem (\[eq.basiclp\]), (\[eq.mixedbc\]), say $u \in C^{2m} (\overline{{\mathcal{C}}},F^i)$ and $p \in C^1 (\overline{{\mathcal{C}}},F^{i-1})$. Then $$(u'_t, v) + (Vu, v) = (f, v)$$ for each element $v$ of $\mathcal{S}$, as is easy to see. By continuity, this equation holds also for each $v \in S$. Since $(u'_t, v) = \partial_t\, (u,v)$, we are led to the following weak formulation of problem (\[eq.basiclp\]), (\[eq.mixedbc\]). Given sections $f \in L^2 (I,S')$ and $u_0 \in H$, find $u \in L^2 (I,S)$ satisfying $$\label{eq.Stokesw}
\begin{array}{rclcl}
\partial_t\, (u,v) + (Vu,v)
& =
& (f,v)
& \mbox{for all}
& v \in S,
\\
u (0)
& =
& u_0.
&
&
\end{array}$$ (By (\[eq.Stokes\]), any solution to this problem leads to a solution in some weak sense of problem (\[eq.basiclp\]), (\[eq.mixedbc\]).)
For $u$ belonging to $L^2 (I,S)$, the condition $u (0) = u_0$ need not make any sense in general. However, if $u \in L^2 (I,S)$ satisfies the first equation of (\[eq.Stokesw\]), then the value $u (0)$ is well defined. Indeed, we can write the first equality of (\[eq.Stokesw\]) as $
\partial_t\, (u,v) = (f - Vu,v)
$ for all $v \in S$. Since $V$ is linear and continuous from $S$ into $S'$ and $u \in L^2 (I,S)$, the function $Vu$ belongs to $L^2 (I,S')$. Hence it follows that $f - Vu \in L^2 (I,S')$, and Lemma \[l.primiti\] shows that $u' \in L^2 (I,V')$ and that $u$ is a.e. equal to an (absolutely) continuous function on $I$ with values in $S'$. Thus, any function of $L^2 (I,S)$ satisfying the first equation of (\[eq.Stokesw\]) is, after modification on a set of measure zero, a continuous mapping of $I$ into $S'$, and so the condition $u (0) = u_0$ makes sense.
If $f \in L^2 (I,S')$ and $u \in L^2 (I,S)$ satisfies the first equation of (\[eq.Stokesw\]) then, as observed, $u' \in L^2 (I,S')$ and $
\partial_t\, (u,v) = (f - Vu,v)
$ for all $v \in S$. According to Lemma \[l.primiti\] this equality is equivalent to $
u' + Vu = f
$ a.e. on $I$. Conversely, if $u$ satisfies the latter equation, then $u$ obviously satisfies the first equation of (\[eq.Stokesw\]). In this way we arrive at an alternative formulation of weak problem (\[eq.Stokesw\]). Namely, given sections $f \in L^2 (I,S')$ and $u_0 \in H$, find $u \in L^2 (I,S)$, such that $u' \in L^2 (I,S')$ and $$\label{eq.Stokesp}
\begin{array}{rclcl}
u' + Vu
& =
& f
& \mbox{a.e. on}
& I,
\\
u (0)
& =
& u_0.
&
&
\end{array}$$
\[t.exiuniS\] For any data $f \in L^2 (I,S')$ and $u_0 \in H$, there exists a unique function $u \in L^2 (I,S)$ which satisfies $u' \in L^2 (I,S')$ and (\[eq.Stokesp\]). Moreover, we get $u \in C (\overline{I},H)$.
We use the Faedo-Galerkin method. Since $S$ is separable, there is a sequence of linearly independent elements $( e_i )_{i = 1, 2, \ldots}$ which is complete in $S$. For every $k = 1, 2, \ldots$ we define an approximate solution of problem (\[eq.Stokesw\]) or (\[eq.Stokesp\]) by $$\label{eq.appsolS}
u_k = \sum_{i=1}^k c_{k,i} (t) e_i$$ and $$\label{eq.appsolc}
\begin{array}{rclcl}
(u_k',e_j) + (V u_k,e_j)
& =
& (f,e_j)
& \mbox{for all}
& j = 1, \ldots, k,
\\
u_k (0)
& =
& u_{0,k},
&
&
\end{array}$$ where $u_{0,k}$ is, for example, the orthogonal projection in $H$ of $u_0$ on the space spanned by the elements $e_1, \ldots, e_k$. (Note that $u_{0,k}$ can be any element of the space spanned by $e_1, \ldots, e_k$, such that $u_{0,k} \to u_0$ in the norm of $H$, as $k \to \infty$.)
The coefficients $c_{k,i}$, $1 \leq i \leq k$, are scalar-valued functions on the interval $I$, and (\[eq.appsolc\]) is a system of linear ordinary differential equations for these functions. Indeed, we obtain $$\sum_{i=1}^k (e_i,e_j)\, c_{k,i}' (t)
+ \sum_{i=1}^k (V e_i,e_j)\, c_{k,i} (t)
= (f,e_j)$$ for all $j = 1, \ldots, k$. Since the elements $e_1, \ldots, e_k$ are linearly independent, the matrix with entries $(e_i,e_j)$, where $1 \leq i, j \leq k$, is regular. Hence, on inverting this matrix we reduce the above system to a system of linear ordinary equations with constant coefficients $$\label{eq.resoode}
c_{k,i}' (t)
+ \sum_{j=1}^k a_{i,j}\, c_{k,j} (t)
= \sum_{j=1}^k b_{i,j}\, (f,e_j)$$ for $i = 1, \ldots, k$, where $a_{i,j}$ and $b_{i,j}$ are complex numbers. Furthermore, the condition $u_k (0) = u_{0,k}$ is equivalent to $k$ equations $c_{k,i} (0) = \pi_i (u_{0,k})$, where $\pi_i$ is the projection of $u_{0,k}$ on the one-dimensional space spanned by $e_i$. System (\[eq.resoode\]) together with the initial conditions determines uniquely the coefficients $c_{k,i}$ on the whole interval $I$.
Since the scalar functions $t \mapsto (f (t),e_j)$ are square integrable, so are the functions $c_{k,i}$. Hence it follows that $u_k \in L^2 (I,S)$ and $u_k' \in L^2 (I,S)$ for each $k$. We will obtain a priori estimates independent of $k$ for the functions $u_k$ and then pass to the limit.
*A priori estimates*. To this end, we multiply the first equation of (\[eq.appsolc\]) by $c_{k,j} (t)$ and sum up these equations for $j = 1, \ldots, k$. We get $$(u_k' (t),u_k (t)) + (V u_k (t),u_k (t))
= (f (t),u_k (t)).$$ Since $
\partial_t (u_k (t),u_k (t)) = 2\, \Re\, (u_k' (t),u_k (t)),
$ it follows that $$\partial_t\, \| u_k (t) \|_H^2 + 2 \left( D (u_k (t)) - \| u_k (t) \|_H^2 \right)
= 2\, \Re\, (f (t),u_k (t)),$$ where $D (u) := D (u,u)$ and $\sqrt{D (u)}$ is the equivalent norm in $S$. The right-hand side of this equality is majorised by $$2\, \| f (t) \|_{S'} \| u_k (t) \|_S
\leq
c\, \| f (t) \|_{S'}^2 + \frac{1}{c}\, D (u_k (t))$$ with arbitrary constant $c > 0$. We choose $c$ in such a way that $2 - 1/c > 0$. On the other hand, $$\partial_t\, \| u_k (t) \|_H^2 - 2 \| u_k (t) \|_H^2
= e^{2t}\, \partial_t \left( e^{- 2t} \| u_k (t) \|_H^2 \right),$$ as is easy to check. Therefore, $$\label{eq.tlhsoti}
\partial_t \left( e^{- 2t} \| u_k (t) \|_H^2 \right)
+ \Big( 2 - \frac{1}{c} \Big) e^{- 2t}\, D (u_k (t))
\leq
c\, e^{- 2t}\, \| f (t) \|_{S'}^2.$$ Integrating the inequality from $0$ to $t$, where $t$ is a fixed point of $I$, we readily deduce that $$\begin{aligned}
\| u_k (t) \|_H^2
& \leq &
e^{2t}\, \| u_{0,k} \|_H^2
+ c \int_0^t e^{2 (t-t')} \| f (t') \|_{S'}^2 dt'
\\
& \leq &
e^{2t}\, \| u_0 \|_H^2
+ c \int_0^t e^{2 (t-t')} \| f (t') \|_{S'}^2 dt'\end{aligned}$$ for almost all $t \in I$. Therefore, $$\sup_{t \in I} \| u_k (t) \|_H^2
\leq
e^{2T}
\Big( \| u_0 \|_H^2 + c \int_0^T \| f (t) \|_{S'}^2 dt \Big).$$ the right-hand side being finite and independent of $k$. We have thus proved that the sequence $u_k$ remains in a bounded subset of $L^\infty (I,H)$, i.e., there is a constant $C$ such that $$\label{eq.boinLiH}
\| u_k \|_{L^\infty (I,H)} \leq C$$ for all $k$.
Furthermore, on integrating inequality (\[eq.tlhsoti\]) in $t$ over all of $I$ we arrive at the estimates $$\begin{aligned}
\| u_k (T) \|_H^2
+ \Big( 2 - \frac{1}{c} \Big)
\int_0^T \!\!\! e^{2 (T-t)} D (u_k (t)) dt
\!\! & \!\! \leq \!\! & \!\!
e^{2T} \| u_{0,k} \|_H^2
+ c \int_0^T \!\!\! e^{2 (T-t)} \| f (t) \|_{S'}^2 dt
\\
\!\! & \!\! \leq \!\! & \!\!
e^{2T}\, \| u_0 \|_H^2
+ c \int_0^T \!\!\! e^{2 (T-t)} \| f (t) \|_{S'}^2 dt\end{aligned}$$ for each $k = 1, 2, \ldots$. This shows that the sequence $u_k$ remains in a bounded subset of $L^2 (I,S)$, i.e., $$\label{eq.boinLiS}
\| u_k \|_{L^2 (I,S)} \leq C$$ for all $k$, with $C$ a constant independent of $k$.
*Passage to the limit*. The a priori estimate of (\[eq.boinLiH\]) implies that there is a subsequence of $u_k$ which converges in the weak$^\ast$ topology of $L^\infty (I,H)$. By abuse of notation, we continue to write $u_k$ for this subsequence. Thus, there is an element $u \in L^\infty (I,H)$ such that $$\int_I (u_k (t) - u (t), v (t))\, dt \to 0$$ for all $v \in L^1 (I,H)$. By (\[eq.boinLiH\]), the subsequence $u_k$ belongs to a bounded set in $L^2 (I,S)$. Therefore, another passage to a subsequence shows the existence of some $\tilde{u}$ in $L^2 (I,S)$ and a subsequence (still denoted by $u_k$) which converges to $\tilde{u}$ in the weak$^\ast$ topology of $L^2 (I,S)$. (Note that the weak$^\ast$ and weak topologies of $L^2 (I,S)$ coincide.) This means $$\int_I (u_k (t) - \tilde{u} (t), v (t))\, dt \to 0$$ for all $v \in L^2 (I,S')$. This latter relation is fulfilled, in particular, if $v \in L^2 (I,H)$. Since $L^2 (I,H) \hookrightarrow L^1 (I,H)$, it follows that $$\int_I (u (t) - \tilde{u} (t), v (t))\, dt = 0$$ whenever $v \in L^2 (I,H)$. Hence, $u = \tilde{u}$ belongs to $L^\infty (I,H) \cap L^2 (I,S)$.
In order to pass to the limit in equations (\[eq.appsolc\]), we will consider scalar functions $\phi$ of $t \in I$, which are continuously differentiable and satisfy $\phi (T) = 0$. Given such a function $\phi$, we multiply the first equality of (\[eq.appsolc\]) by $\phi (t)$, integrate in $t \in I$ and use the formula $$\int_0^T (u_k' (t), e_j)\, \phi (t) dt
= - \int_0^T (u_k (t), e_j)\, \phi' (t) dt - (u_k (0), e_j)\, \phi (0).$$ In this way we find $$- \int_0^T \!\! (u_k (t), e_j) \phi' (t) dt
+ \int_0^T \!\! (V u_k (t), e_j) \phi (t) dt
= (u_{0,k}, e_j)\, \phi (0)
+ \int_0^T \!\! (f (t), e_j) \phi (t) dt$$ for all $j = 1, \ldots, k$.
The passage to the limit for $k \to \infty$ in the integrals on the left-hand side is easy, for the sequence $u_k$ converges to $u$ in the weak${}^\ast$ topology of both $L^\infty (I,H)$ and $L^2 (I,S)$. We recall that $u_{0,k}$ converges to $u_0$ strongly in $H$. Therefore, we find in the limit $$- \int_0^T \!\! (u (t), e_j) \phi' (t) dt
+ \int_0^T \!\! (V u (t), e_j) \phi (t) dt
= (u_0, e_j)\, \phi (0)
+ \int_0^T \!\! (f (t), e_j) \phi (t) dt.$$ This equality, which holds for each $j$, allows one to write by a linearity argument $$\label{eq.tewhfej}
- \int_0^T \!\! (u (t), v)\, \phi' (t) dt
+ \int_0^T \!\! (V u (t), v)\, \phi (t) dt
= (u_0, v)\, \phi (0)
+ \int_0^T \!\! (f (t), v)\, \phi (t) dt$$ for all $v$ which are finite linear combinations of functions $e_j$. Since every term of (\[eq.tewhfej\]) depends linearly and continuously in the norm of $V$ on $v$, the equality (\[eq.tewhfej\]) is still valid, by continuity, for all $v$ in $V$.
On writing (\[eq.tewhfej\]), in particular, with any $\phi \in C^\infty_{\mathrm{comp}} (0,T)$, we arrive at the equality $$\partial_t (u,v) + (Vu,v) = (f,v)$$ for all $v \in V$. This is precisely (\[eq.Stokesw\]) which is valid in the sense of distributions on $(0,T)$. As is shown immediately after (\[eq.Stokesw\]), this equality together with $u \in L^2 (I,S)$ implies that $u'$ belongs to $L^2 (I,S')$ and $u' + Vu = f$ a.e. on $I$.
Finally, it remains to check that $u (0) = u_0$. (The continuity of $u$ will be proved after the proof of existence.) For this purpose we multiply the first equation of (\[eq.Stokesw\]) by $\phi (t)$ with the same $\phi (t)$ as before, integrate in $t \in I$ and use the integration by parts formula $$\int_0^T \partial_t\, (u (t), v)\, \phi (t) dt
= - \int_0^T (u (t), v)\, \phi' (t) dt - (u (0), v)\, \phi (0).$$ We get $$- \int_0^T \!\! (u (t), v)\, \phi' (t) dt
+ \int_0^T \!\! (V u (t), v) \phi (t) dt
= (u (0), v)\, \phi (0)
+ \int_0^T \!\! (f (t), v)\, \phi (t) dt,$$ and so comparing this with (\[eq.tewhfej\]) yields $
(u (0) - u_0, v)\, \phi (0) = 0
$ for all $v \in S$ and for each function $\phi$ of the type considered. Choose $\phi$ such that $\phi (0) \neq 0$, then $
(u (0) - u_0, v) = 0
$ for all $v \in S$. This equality implies $u (0) = u_0$ and completes the proof of the existence.
The proof is based on a lemma which is a particular case of a general interpolation theorem of [@LionMage72].
\[l.interLM\] Let $S$, $H$ and $S'$ be three Hilbert spaces, each space being densely included into the subsequent one, and $S'$ being the dual of $S$. If $u$ is a function in $L^2 (I,S)$ and its derivative $u'$ belongs to $L^2 (I,S')$, then $u$ is equal a.e. to a continuous function on $I$ with values in $H$. Moreover, $\partial (u,u)_H = 2 \Re\, (u',u)_H$ holds in the sense of distributions on $(0,T)$.
Note that the equality $\partial (u,u)_H = 2 \Re\, (u',u)_H$ is meaningful since the functions $t \mapsto \| u (t) \|_H^2$ and $t \mapsto (u' (t),u (t))_H$ are both integrable on $I$.
For a more elementary proof than that of [@LionMage72] we refer the reader to [@Tema79 p. 177].
By Lemma \[l.interLM\], the continuity of the mapping $u : I \to H$ in Theorem \[t.exiuniS\] becomes obvious. It only remains to check the uniqueness. Suppose $u_1$ and $u_2$ are two solutions of problem (\[eq.Stokesp\]) which bear the desired properties. Set $u = u_1 - u_2$, then $$\begin{array}{rcl}
u & \in & L^2 (I,S),
\\
u' & \in & L^2 (I,S')
\end{array}$$ and $$\begin{array}{rclcl}
u' + Vu
& =
& 0
& \mbox{a.e. on}
& I,
\\
u (0)
& =
& 0.
&
&
\end{array}$$ Taking the scalar product of the first equality with $u (t)$ yields $$(u' (t), u (t)) + (Vu (t),u(t)) = 0$$ a.e. on $I$. Using Lemma \[l.interLM\] we get $$\begin{aligned}
\frac{1}{2}\, \partial_t (u (t),u (t))
& =
& -\, (Vu (t),u (t))
\\
& \leq
& 0\end{aligned}$$ whence $
\| u (t) \|_H^2 \leq \| u (0) \|_H^2 = 0
$ for all $t \in I$. Hence, $u_1 (t) = u_2 (t)$ for each $t \in I$, as desired.
On using the solution $u$ of problem (\[eq.Stokesp\]) given by Theorem \[t.exiuniS\] we determine the pressure $p$ from (\[eq.sefp\]). This leads to a solution $(u,p)$ of linearised problem (\[eq.basiclp\]). Assuming that both $f$ and $u_0$ are sufficiently smooth, we can actually obtain as much regularity as desired for $u$ and $p$. We establish only a simple result of this type.
\[t.regtflNS\] Suppose $f \in L^2 (I,H)$ and $u_0 \in S$. Then $u \in L^2 (I,H^{2m} ({\mathcal{X}},F^i))$ and $u' \in L^2 (I,H)$, i.e., $$\label{eq.domStoc}
\begin{array}{rcl}
u & \in & H^{{\mathbf{s}}(1)} ({\mathcal{C}},F^{i}),
\\
p & \in & L^2 (I,H^1 ({\mathcal{X}},F^{i-1})).
\end{array}$$
Here, we tacitly assume that the Neumann problem after Spencer for complex (\[eq.ellcomp\]) at step $i$ satisfies the Shapiro-Lopatinskij condition on the boundary of ${\mathcal{X}}$, if there is any.
The first point is to establish that $u' \in L^2 (I,H)$, i.e., $u' \in L^2 ({\mathcal{C}},F^i)$. This is proved by deriving another a priori estimate for the approximate solution $u_k$ constructed by the Galerkin method.
Using the notation of the proof of Theorem \[t.exiuniS\], we multiply the first equality of (\[eq.appsolc\]) by the derivative $c_{k,j}' (t)$ and sum up these equalities for $j = 1, \ldots, k$. This gives $$(u_k' (t),u_k' (t)) + (V u_k (t),u_k' (t))
= (f (t),u_k' (t)).$$ Since $
\partial_t (V u_k (t),u_k (t)) = 2\, \Re\, (V u_k (t),u_k' (t)),
$ we get $$2\, \| u_k' (t) \|_H^2 + \partial_t \left( D (u_k (t)) - \| u_k (t) \|_H^2 \right)
= 2\, \Re\, (f (t),u_k' (t))$$ for almost all $t \in I$.
We then integrate the latter equality in $t \in I$ and use the Schwarz inequality, obtaining $$\begin{aligned}
\lefteqn{
2 \int_0^T \| u_k' (t) \|_H^2 dt + D (u_k (T)) + \| u_k (0) \|_H^2
}
\\
& = &
D (u_k (0)) + \| u_k (T) \|_H^2
+ 2\, \Re \int_0^T (f (t),u_k' (t))\, dt
\\
& \leq &
D (u_{0,k}) + \| u_k (T) \|_H^2
+ \int_0^T \left( \| f (t) \|_H^2 + \| u_k' (t) \|_H^2 \right) dt\end{aligned}$$ whence $$\label{eq.bodiL2H}
\int_0^T \| u_k' (t) \|_H^2 dt
\leq
C
+ D (u_{0,k})
+ \int_0^T \| f (t) \|_H^2\, dt,$$ which is due to (\[eq.boinLiH\]).
The basis $e_j$ used in the Galerkin method may be chosen so that $e_j \in S$ for all $j$ and we can take $u_{0,k}$ to be the projection in $S$ of $u_0$ on the space spanned by $e_1, \ldots, e_k$. Hence it follows that $u_{0,k}$ converges to $u_0$ strongly in $S$, as $k \to \infty$, and $D (u_{0,k}) \leq D (u_0)$. With these choices of the basis $e_j$ and initial data $u_{0,k}$ estimate (\[eq.bodiL2H\]) shows that the sequence $u_k'$ belongs to a bounded set in $L^2 (I,H)$, and so $u' \in L^2 (I,H)$, as desired.
Having disposed of this preliminary step, we come back to equalities (\[eq.basiclp\]), (\[eq.mixedbc\]) and apply the regularity theorem in the stationary case. More precisely, we get $$\begin{array}{rcl}
(\varepsilon {\mathit{\varDelta}}^m + \nu {\mathit{\varDelta}}) u + Ap
& =
& f - u',
\\
A^\ast u
& =
& 0
\end{array}$$ in ${\mathcal{X}}$ and $u = 0$ up to order $m$ on the boundary of ${\mathcal{X}}$ (if there is any) for almost all $t \in I$. Since $f - u' \in L^2 (I,H)$, we deduce that $u (t)$ belongs to $H^{2m} ({\mathcal{X}},F^i)$ and $p (t)$ belongs to $H^1 ({\mathcal{X}},F^{i-1})$. Moreover, since $f (t) - u' (t) \mapsto (u (t),p (t))$ is a continuous linear mapping from $H$ into $H^{2m} ({\mathcal{X}},F^i) \times H^1 ({\mathcal{X}},F^{i-1})$, it is clear that (\[eq.domStoc\]) is satisfied.
Compactness theorems {#s.compact}
====================
The compactness theorems of this section go back at least as far as [@Lion69]. They are included for the sake of selfcontained presentation. The proofs are based on the following well-known lemma.
\[l.basicle\] Suppose that $\mathcal{B}_0$, $\mathcal{B}$ and $\mathcal{B}_1$ are three Banach spaces with the property that $\mathcal{B}_0 \hookrightarrow \mathcal{B} \hookrightarrow \mathcal{B}_1$, the embedding of $\mathcal{B}$ into $\mathcal{B}_1$ being continuous and the embedding of $\mathcal{B}_0$ into $\mathcal{B}$ being compact. Then for each $\epsilon > 0$ there is a constant $c (\epsilon)$ depending on $\epsilon$, such that $$\| v \|_{\mathcal{B}}
\leq
\epsilon\, \| v \|_{\mathcal{B}_0} + c (\epsilon)\, \| v \|_{\mathcal{B}_1}$$ for all $v \in \mathcal{B}_0$.
The proof is by contradiction. Saying that the lemma is not true amounts to saying that there exists some $\epsilon > 0$ with the property that for each $c \in {\mathbb{R}}$ one has $$\| v \|_{\mathcal{B}}
\geq
\epsilon\, \| v \|_{\mathcal{B}_0} + c\, \| v \|_{\mathcal{B}_1}$$ for at least one $v \in \mathcal{B}_0$. Taking $c = k$ we obtain a sequence of elements $v_k$ in $\mathcal{B}_0$ which satisfies $$\| v_k \|_{\mathcal{B}}
\geq
\epsilon\, \| v_k \|_{\mathcal{B}_0} + k\, \| v_k \|_{\mathcal{B}_1}$$ for all $k = 1, 2, \ldots$. We consider then the normalised sequence $
\displaystyle
w_k = \frac{v_k}{\| v_k \|_{\mathcal{B}_0}}
$ satisfying $$\label{eq.wcttnsw}
\| w_k \|_{\mathcal{B}}
\geq
\epsilon + k\, \| w_k \|_{\mathcal{B}_1}$$ for all $k$. Since $\| w_k \|_{\mathcal{B}_0} = 1$, the sequence $w_k$ is bounded in $\mathcal{B}$, and so (\[eq.wcttnsw\]) shows that $
\| w_k \|_{\mathcal{B}_1} \to 0,
$ as $k \to \infty$. Furthermore, since the embedding of $\mathcal{B}_0$ into $\mathcal{B}$ is compact, the sequence $w_k$ is relatively compact in $\mathcal{B}$. Hence, we can extract from $w_k$ a subsequence $w_{k_j}$ strongly convergent in $\mathcal{B}$. By the above, the limit of $w_{k_j}$ must be zero, however, this contradicts estimate (\[eq.wcttnsw\]) because $\| w_k \|_{\mathcal{B}} \geq \epsilon > 0$ for all $k$.
Let $\mathcal{B}_0$, $\mathcal{B}$ and $\mathcal{B}_1$ be three Banach spaces such that $\mathcal{B}_0 \hookrightarrow \mathcal{B} \hookrightarrow \mathcal{B}_1$, the embeddings being continuous. We moreover assume that $\mathcal{B}_0$ and $\mathcal{B}_1$ are reflexive and the embedding of $\mathcal{B}_0$ into $\mathcal{B}$ is compact. Given any real numbers $p_0$ and $p_1$ both greater than $1$, we consider the space $\mathcal{F}$ which consists of all functions $v \in L^{p_0} (I,\mathcal{B}_0)$ whose weak derivative $v' = \partial_t v$ belongs to $L^{p_1} (I,\mathcal{B}_1)$. The space $\mathcal{F}$ is provided with the norm $$\| v \|_{\mathcal{F}}
= \| v \|_{L^{p_0} (I,\mathcal{B}_0)} + \| v' \|_{L^{p_1} (I,\mathcal{B}_1)},$$ which makes it a Banach space. It is obvious that $\mathcal{F} \subset L^{p_0} (I,\mathcal{B})$, the embedding being continuous. We are actually going to prove that this embedding is compact.
\[t.tptteic\] Under the above assumptions, the embedding of $\mathcal{F}$ into $L^{p_0} (I,\mathcal{B})$ is compact.
Let $u_k$ be a bounded sequence in $\mathcal{F}$. We have to show that this sequence contains a subsequence which converges strongly in $L^{p_0} (I,\mathcal{B})$.
Since the spaces $\mathcal{B}_0$ and $\mathcal{B}_1$ are reflexive and both $p_0$ and $p_1$ are not extreme, the spaces $L^{p_0} (I,\mathcal{B}_0)$ and $L^{p_1} (I,\mathcal{B}_1)$ are likewise reflexive, and hence $\mathcal{F}$ is reflexive. Therefore, there exists a subsequence of $u_k$ (for which we continue to write $u_k$ by abuse of notation) such that $u_k$ converges to $u \in \mathcal{F}$ weakly in $\mathcal{F}$, as $k \to \infty$, which means that $u_k$ converges to $u$ weakly in $L^{p_0} (I,\mathcal{B}_0)$ and $u_k'$ converges to $u'$ weakly in $L^{p_1} (I,\mathcal{B}_1)$. It suffices to prove that $v_k = u_k - u$ converges to zero strongly in $L^{p_0} (I,\mathcal{B})$.
We shall have established the theorem if we prove that $v_k$ converges to zero strongly in $L^{p_0} (I,\mathcal{B}_1)$. In fact, due to Lemma \[l.basicle\], we get $$\| v_k \|_{L^{p_0} (I,\mathcal{B})}
\leq
\epsilon\, \| v_k \|_{L^{p_0} (I,\mathcal{B}_0)}
+ c (\epsilon)\, \| v_k \|_{L^{p_0} (I,\mathcal{B}_1)}$$ for all $k$. Since the sequence $v_k$ is bounded in $\mathcal{F}$, it follows that $$\| v_k \|_{L^{p_0} (I,\mathcal{B})}
\leq
\epsilon\, C
+ c (\epsilon)\, \| v_k \|_{L^{p_0} (I,\mathcal{B}_1)},$$ with $C$ a constant independent of $k$. On passing to the limit in this inequality we get $$\limsup_{k \to \infty} \| v_k \|_{L^{p_0} (I,\mathcal{B})} \leq \epsilon\, C,$$ for $v_k \to 0$ strongly in $L^{p_0} (I,\mathcal{B}_1)$. Since $\epsilon > 0$ is arbitrary small in Lemma \[l.basicle\], the upper limit is equal to zero, as desired.
To prove that $v_k$ converges to zero strongly in $L^{p_0} (I,\mathcal{B}_1)$, we observe that $\mathcal{F}$ is embedded continuously into $C (\overline{I},\mathcal{B}_1)$. This follows from Lemma \[l.primiti\], the continuity of the embedding is easy to check. We infer from this embedding that there is a constant $C > 0$ with the property that $$\| v_k (t) \|_{\mathcal{B}_1} \leq c$$ for all $t \in I$ and all $k$. By the Lebesgue theorem, the strong convergence of $v_k$ to zero in $L^{p_0} (I,\mathcal{B}_1)$ is now proved if we show that $v_k (t) \to 0$ in the norm of $\mathcal{B}_1$ for almost all $t \in I$.
Pick $t_0 \in I$. Write $$v_k (t_0) = v_k (t') - \int_{t_0}^{t'} v_k' (s) ds$$ and by integration $$v_k (t_0)
= \frac{1}{t-t_0}
\Big( \int_{t_0}^t v_k (t') dt' - \int_{t_0}^{t} dt' \int_{t_0}^{t'} v_k' (s) ds \Big)$$ for all $t \in I$. Hence it follows that $v_k (t_0) = I_k' + I_k''$, where $$\begin{array}{rcl}
I_k'
& =
& \displaystyle
\frac{1}{t-t_0}
\int_{t_0}^t v_k (t') dt',
\\
I_k''
& =
& \displaystyle
\frac{-1}{t-t_0}
\int_{t_0}^{t} (t-s) v_k' (s) ds.
\end{array}$$ For a given $\epsilon > 0$, we choose $t$ in such a way that $$\| I_k'' \|_{\mathcal{B}_1}
\leq
\int_{t_0}^{t} \| v_k' (s) \|_{\mathcal{B}_1} ds
\leq
\frac{\epsilon}{2}.$$ Then, for this fixed $t$, we observe that $I_k' \to 0$ weakly in $\mathcal{B}_0$, and so strongly in $\mathcal{B}_1$, as $k \to \infty$. For sufficiently large $k$, we thus obtain $
\| I_k' \|_{\mathcal{B}_1} \leq \epsilon/2
$ whence $\| v_k (t_0) \|_{\mathcal{B}_1} \leq \epsilon$, as desired.
As usual, the most efficient compactness theorem can be formulated within the framework of Hilbert spaces and it is based on the notion of fractional derivatives of a function. Assume that $\mathcal{B}_0$, $\mathcal{B}$ and $\mathcal{B}_1$ are Hilbert spaces with continuous embeddings $\mathcal{B}_0 \hookrightarrow \mathcal{B} \hookrightarrow \mathcal{B}_1$, where moreover the embedding of $\mathcal{B}_0$ into $\mathcal{B}$ is compact. If $v$ is a function of $t \in {\mathbb{R}}$ with values in $\mathcal{B}_1$, we denote by $\hat{v}$ its Fourier transform, i.e., $$\hat{v} (\tau)
= \int_{-\infty}^{+\infty} e^{- \imath \tau t} v (t) dt$$ for $\tau \in {\mathbb{R}}$. Given any $\lambda$ with $0 < \lambda \leq 1$, by the derivative of $v$ of order $\lambda$ in $t$ is meant the inverse Fourier transform of $(\imath \tau)^{\lambda} \hat{v}$, or $$\widehat{\partial_t^{\lambda} v} (\tau)
= (\imath \tau)^{\lambda} \hat{v} (\tau).$$ Following [@Tema79 p. 185] we define the space $\mathcal{H}^\lambda$ (depending on $\mathcal{B}_0$, $\mathcal{B}_1$ and $\lambda$) to consist of all functions $v \in L^2 ({\mathbb{R}},\mathcal{B}_0)$ such that $\partial_t^{\lambda} v \in L^2 ({\mathbb{R}},\mathcal{B}_1)$. This is a Hilbert space under the norm $$\| v \|_{\mathcal{H}^\lambda}
= \Big( \| v \|_{L^2 ({\mathbb{R}},\mathcal{B}_0)}^2
+ \| |\tau|^{\lambda} \hat{v} \|_{L^2 ({\mathbb{R}},\mathcal{B}_1)}^2
\Big)^{1/2}.$$ For a closed set $K \subset {\mathbb{R}}$, we denote by $\mathcal{H}^\lambda_K$ the (closed) subspace of $\mathcal{H}^\lambda$ consisting of all functions with support in $K$. The following theorem is contained in [@Tema79 p. 186].
\[t.Temam79\] Under the above hypotheses, if moreover $K$ is a compact subset of ${\mathbb{R}}$ and $\lambda > 0$, the embedding of $\mathcal{H}^{\lambda}_K$ into $L^2 ({\mathbb{R}},\mathcal{B})$ is compact.
Let $u_k$ be a bounded sequence in $\mathcal{H}^{\lambda}_K$. We must show that $u_k$ contains a subsequence strongly convergent in $L^2 ({\mathbb{R}},\mathcal{B})$.
Since $\mathcal{H}^{\lambda}$ is a Hilbert space, the sequence $u_k$ contains a subsequence which converges weakly in this space. To shorten notation, we continue to write $u_k$ for this subsequence. It is clear that the limit function $u$ also belongs to $\mathcal{H}^{\lambda}$. Therefore, on setting $v_k = u_k - u$ we see that $v_k$ is a bounded sequence in $\mathcal{H}^{\lambda}$, which converges to zero weakly in $\mathcal{H}^{\lambda}$. This means that $v_k$ converges to zero weakly in $L^2 ({\mathbb{R}},\mathcal{B}_0)$, and $|\tau|^\lambda \hat{v}_k$ converges to zero weakly in $L^2 ({\mathbb{R}},\mathcal{B}_1)$. The theorem is proved if we show that $u_k$ converges to $u$ strongly in $L^2 ({\mathbb{R}},\mathcal{B})$, which is the same as $v_k \to 0$ strongly in $L^2 ({\mathbb{R}},\mathcal{B})$.
Our next goal is to show that if $v_k$ converges to zero strongly in $L^2 ({\mathbb{R}},\mathcal{B}_1)$ then the same is true in the norm of $L^2 ({\mathbb{R}},\mathcal{B})$. Due to Lemma \[l.basicle\], for each $\epsilon > 0$ there is a constant $c (\epsilon)$ such that $$\| v_k \|_{L^2 ({\mathbb{R}},\mathcal{B})}
\leq
\epsilon\, \| v_k \|_{L^2 ({\mathbb{R}},\mathcal{B}_0)}
+ c (\epsilon)\, \| v_k \|_{L^2 ({\mathbb{R}},\mathcal{B}_1)}$$ for all $k$. Since the sequence $v_k$ is bounded in $L^2 ({\mathbb{R}},\mathcal{B}_0$, it follows that $$\| v_k \|_{L^2 ({\mathbb{R}},\mathcal{B})}
\leq
\epsilon\, C
+ c (\epsilon)\, \| v_k \|_{L^2 ({\mathbb{R}},\mathcal{B}_1)},$$ with $C$ a constant independent of $k$. On passing to the limit in this inequality we obtain $$\limsup_{k \to \infty} \| v_k \|_{L^2 ({\mathbb{R}},\mathcal{B})} \leq \epsilon\, C.$$ Since $\epsilon > 0$ is arbitrary small in Lemma \[l.basicle\], the upper limit must be equal to zero, as desired.
It remains to establish that $v_k$ converges to zero strongly in $L^2 ({\mathbb{R}},\mathcal{B}_1)$. To this end, write $$I_k
= \int_{- \infty}^{+ \infty} \| v_k (t) \|_{\mathcal{B}_1}^2 dt
= \frac{1}{2 \pi} \int_{- \infty}^{+ \infty} \| \hat{v}_k (\tau) \|_{\mathcal{B}_1}^2 d \tau,$$ which is due to the Plancherel theorem. We have to show that $I_k$ tends to zero, as $k \to \infty$. We get $$\begin{aligned}
I_k
& = &
\frac{1}{2 \pi}
\int_{|\tau| \leq R}
\| \hat{v}_k (\tau) \|_{\mathcal{B}_1}^2
d \tau
+ \frac{1}{2 \pi}
\int_{|\tau| > R}
\frac{\langle \tau \rangle^{2 \lambda}}{\langle \tau \rangle^{2 \lambda}}\,
\| \hat{v}_k (\tau) \|_{\mathcal{B}_1}^2
d \tau
\\
& \leq &
+ \frac{C}{\langle R \rangle^{2 \lambda}},\end{aligned}$$ for $v_k$ is bounded in $\mathcal{H}^{\lambda}$. Here, $\langle \tau \rangle := (1 + |\tau|^2)^{1/2}$. Given any $\epsilon > 0$, we choose $R$ sufficiently large, so that $$\frac{C}{\langle R \rangle^{2 \lambda}}
\leq
\frac{\epsilon}{2}.$$ Then $$I_k
\leq
\frac{1}{2 \pi} \int_{|\tau| \leq R} \| \hat{v}_k (\tau) \|_{\mathcal{B}_1}^2 d \tau
+ \frac{\epsilon}{2},$$ and the proof is completed by showing that, for this fixed $R$, $$\label{eq.atpicbs}
\int_{|\tau| \leq R} \| \hat{v}_k (\tau) \|_{\mathcal{B}_1}^2 d \tau
\to
0,$$ as $k \to \infty$. This is proved by the Lebesgue theorem. If $\chi$ denotes the characteristic function of $K$, then $v_k = \chi v_k$ and $$\hat{v}_k (\tau)
= \int_{-\infty}^{+\infty} e^{- \imath \tau t} \chi (t) v_k (t) dt.$$ Thus, $$\| \hat{v}_k (\tau) \|_{\mathcal{B}_1}
\leq
\| e^{- \imath \tau t} \chi \|_{L^2 ({\mathbb{R}})}
\| v_k \|_{L^2 ({\mathbb{R}},\mathcal{B}_1)}$$ which is dominated by a constant independent of both $\tau$ and $k$. On the other hand, if $\tau$ is fixed and $w$ an arbitrary element of $\mathcal{B}_0$, then $$(\hat{v}_k (\tau), w)_{\mathcal{B}_0}
= \int_{-\infty}^{+\infty} (v_k (t), e^{- \imath \tau t} \chi (t) w)_{\mathcal{B}_0} dt,$$ which tends to zero, as $k \to \infty$, for $v_k \to 0$ weakly in $L^2 ({\mathbb{R}},\mathcal{B}_0)$. It follows that the sequence $\hat{v}_k (\tau)$ converges to zero weakly in $\mathcal{B}_0$, and so strongly in $\mathcal{B}$ and $\mathcal{B}_1$. With this latter remark, the Lebesgue theorem on dominated convergence implies (\[eq.atpicbs\]), as desired.
Using the methods of the last theorem, we are in a position to prove another compactness theorem similar to Theorem \[t.tptteic\]. Nevertheless, this theorem is not contained in nor itself contains Theorem \[t.Temam79\].
\[t.tptteil\] Assume that $\mathcal{B}_0$, $\mathcal{B}$ and $\mathcal{B}_1$ are Hilbert spaces with continuous embeddings $\mathcal{B}_0 \hookrightarrow \mathcal{B} \hookrightarrow \mathcal{B}_1$, the embedding of $\mathcal{B}_0$ into $\mathcal{B}$ being compact, and $I = (0,T)$ a finite interval. Then the embedding of $\mathcal{F}$ with $p_0 = 2$ and $p_1 = 1$ into $L^2 (I,\mathcal{B})$ is compact.
Let $u_k$ be a bounded sequence in the space $\mathcal{F}$. Denote by $v_k$ the function defined on all of ${\mathbb{R}}$, which is equal to $u_k$ on $[0,T]$ and to zero outside this interval. By Theorem \[t.Temam79\], we shall have established the theorem if we show that the sequence $v_k$ remains bounded in the space $\mathcal{H}^\lambda$ with some $\lambda > 0$.
By Lemma \[l.primiti\], each function $u_k$ is, after possible modification on a set of measure zero, continuous on $[0,T]$ with values in $\mathcal{B}_1$. More precisely, the embedding of $\mathcal{F}$ into $C (\overline{I},\mathcal{B}_1)$ is continuous. Since $v_k$ has two discontinuities at $0$ and $T$, the distribution derivative of $v_k$ is given by $$v_k' = w_k + u_k (0) \delta_0 - u_k (T) \delta_T,$$ where $\delta_0$ and $\delta_T$ are the Dirac distributions at $0$ and $T$, and $w_k$ the derivative of $u_k$ on $[0,T]$ extended by zero to the complement of $[0,T]$. After a Fourier transformation we get $$\label{eq.aaFtwge}
(\imath \tau)\, \hat{v}_k (\tau)
= \hat{w}_k (\tau) + u_k (0) - u_k (T)\, \exp (- \imath T \tau)$$ for all $\tau \in {\mathbb{R}}$.
Since the functions $u_k'$ remain bounded in $L^1 (I,\mathcal{B}_1)$, the functions $w_k$ are bounded in $L^1 ({\mathbb{R}},\mathcal{B}_1)$ and the functions $\hat{w}_k$ are bounded in the space $L^{\infty} ({\mathbb{R}},\mathcal{B}_1)$, i.e., $$\| \hat{w}_k (\tau) \|_{\mathcal{B}_1} \leq C$$ for all $\tau \in {\mathbb{R}}$ and all $k$. As mentioned, the embedding of $\mathcal{F}$ into $C (\overline{I},\mathcal{B}_1)$ is continuous whence $$\begin{array}{rcl}
\| u_k (0) \|_{\mathcal{B}_1}
& \leq
& c,
\\
\| u_k (T) \|_{\mathcal{B}_1}
& \leq
& c
\end{array}$$ and (\[eq.aaFtwge\]) implies that $$|\tau|^2\, \| \hat{v}_k (\tau) \|_{\mathcal{B}_1}^2
\leq
(C + 2 c)^2$$ for all $\tau \in {\mathbb{R}}$ and all $k$.
Fix any positive $\lambda$ satisfying $\displaystyle \lambda < \frac{1}{2}$. From the inequality $$|\tau|^{2 \lambda}
\leq
c (\lambda)\, \frac{1 + |\tau|^2}{1 + |\tau|^{2 (1-\lambda)}}$$ for all $\tau \in {\mathbb{R}}$, the constant $c (\lambda)$ depending on $\lambda$, it follows that $$\begin{aligned}
\int_{-\infty}^{+\infty}
|\tau|^{2 \lambda}\, \| \hat{v}_k (\tau) \|_{\mathcal{B}_1}^2
d \tau
& \leq &
c (\lambda)
\int_{-\infty}^{+\infty}
\frac{1 + |\tau|^2}{1 + |\tau|^{2 (1-\lambda)}}\,
\| \hat{v}_k (\tau) \|_{\mathcal{B}_1}^2
d \tau
\\
& \leq &
c (\lambda)
\Big(
\int_{-\infty}^{+\infty}
\| \hat{v}_k (\tau) \|_{\mathcal{B}_1}^2
d \tau
+ \int_{-\infty}^{+\infty}
\frac{(C + 2 c)^2}{1 + |\tau|^{2 (1-\lambda)}}\,
d \tau
\Big).\end{aligned}$$ By the Plancherel theorem, we see that $$\int_{-\infty}^{+\infty}
\| \hat{v}_k (\tau) \|_{\mathcal{B}_1}^2
d \tau
= \int_0^T
\| v_k (t) \|_{\mathcal{B}_1}^2
dt$$ and these integrals are bounded uniformly in $k$. On the other hand, since $\displaystyle \lambda < \frac{1}{2}$, the integral $$\int_{-\infty}^{+\infty}
\frac{1}{1 + |\tau|^{2 (1-\lambda)}}\,
d \tau$$ is convergent. Summarising we conclude that $$\int_{-\infty}^{+\infty}
|\tau|^2\, \| \hat{v}_k (\tau) \|_{\mathcal{B}_1}^2
d \tau
\leq
C,$$ where $C$ depends on $\lambda$. It is now clear that the sequence $v_k$ is bounded in $\mathcal{H}^\lambda$ and each $v_k$ has support in $[0,T]$.
Assuming only that $\mathcal{B}_0$ and $\mathcal{B}$ are Banach spaces and $\mathcal{B}_1$ a Hilbert space, it can be proved in a similar way that the embedding of $\mathcal{F}$ with $1 < p_0 < \infty$ and $p_1 = 1$ into $L^{p_0} (I,\mathcal{B})$ is compact.
Existence of a weak solution {#s.exiweak}
============================
This section is concerned with existence theorem for a weak solution of the regularised Navier-Stokes equations. We start with a weak formulation of these equations, following [@Lera34a], and state an existence theorem for such solution. The proof of this theorem is due to [@Lion69], see also [@Lady70]. It is based on the construction of an approximate solution by the Galerkin method, followed by a passage to the limit using, in particular, an a priori estimate for a fractional derivative in time of the approximate solution and a compactness theorem contained in Section \[s.compact\]. Then we develop the uniqueness theorem for weak solutions provided that $\varepsilon > 0$. If $\varepsilon = 0$, the arguments still go in the case $n \leq 2$. In the case of $n > 2$ there is a gap between the class of functions where existence is known, and the smaller classes where uniqueness is proved. For $\varepsilon > 0$, we show the existence of more regular solutions, assuming more regularity on the data. A similar result holds in the conventional case $\varepsilon = 0$ for local solutions, i.e., those defined on a “small” time interval.
Recall that we define on $H^m_0 ({\mathcal{X}},F^i)$, and in particular on $S$, a trilinear form by setting $$(N (u,v),w) = \int_{{\mathcal{X}}} (T (v) u, w)_x dx.$$
\[l.(N(uv)w)\] The form $(N (u,v),w)$ is defined and trilinear continuous on the Cartesian product $H^m_0 ({\mathcal{X}},F^i) \times H^m_0 ({\mathcal{X}},F^i) \times H^m_0 ({\mathcal{X}},F^i)$, if $m \geq (n+2)/4$, $n$ being the dimension of ${\mathcal{X}}$.
We use here a well-known result on pointwise multiplication of functions in Sobolev spaces. Namely, let $s$ and $s_1$, $s_2$ be real numbers satisfying $s_1 + s_2 \geq 0$. $s_1, s_2 \geq s$ and $s_1 + s_2 - s > n/2$, where the strictness of the last two inequalities can be interchanged if $s = 0, 1, \ldots$. Then the pairwise multiplication of functions extends to a continuous bilinear mapping $H^{s_1} \times H^{s_2} \to H^s$. We apply this result with $s = 0$ and $s_1 = s_2 = m$. The condition $s_1 + s_2 - s \geq n/2$ is obviously fulfilled, for $m \geq (n+2)/4$. In coordinate patches on ${\mathcal{X}}$, over which the bundle $F^i$ is trivial, we get $$(T (v) u, w)_x
= \sum_{j = 1, \ldots, k_i \atop
k = 1, \ldots, k_i}
T_{j k} (v) u_k \overline{w}_j,$$ where $k_i$ is the rank of $F^i$, $u_k$ and $v_j$ are coordinates of $u$ and $v$ relative to a local frame of $F^i$, respectively, and $T_{j k}$ are first order scalar differential operators in local coordinates. Hence, $$\begin{aligned}
| (N (u,v), w) |
& \leq &
c\,
\| Tv \|_{L^2 ({\mathcal{X}},\mathrm{Hom}\, F^i)} \| u \|_{H^m ({\mathcal{X}},F^i)} \| w \|_{H^m ({\mathcal{X}},F^i)}
\\
& \leq &
c\, \sqrt{D (u)} \sqrt{D (v)} \sqrt{D (w)}\end{aligned}$$ for all $u, v, w \in H^m_0 ({\mathcal{X}},F^i)$, where $c$ is a constant independent of $u$, $v$ and $w$ and not necessarily the same in diverse applications. This estimate ensures the continuity of the trilinear form.
In particular, the form $(N (u,v),w)$ is well defined and trilinear continuous on $S \times S \times S$, if $m \geq (n+2)/4$.
If $A^\ast u = 0$ in ${\mathcal{X}}$ and $n (u) = 0$ on the boundary of ${\mathcal{X}}$, then $(N (u,v),v) = 0$ for all $v \in H^m_0 ({\mathcal{X}},F^i)$, which is due to Corollary \[c.algestr\]. For $u, v \in S$, the section $N (u,v)$ can be thought of as a continuous linear functional on $S$. Set $N (u) = N (u,u) \in S'$ for $u \in S$.
In the classical formulation the first mixed problem for the generalised Navier-Stokes equations consists in finding sections $u$ and $p$ of $F^i$ and $F^{i-1}$ over ${\mathcal{C}}$, respectively, such that $$\label{eq.classNS}
\begin{array}{rcl}
\partial_t u + (\varepsilon {\mathit{\varDelta}}^m + \nu {\mathit{\varDelta}}) u + N (u) + Ap
& =
& f,
\\
A^\ast u
& =
& 0
\end{array}$$ in the cylinder ${\mathcal{C}}$ and $$\label{eq.classmc}
& =
\\
& =
\end{array}$$ where $f$ and $u_0$ are given sections of $F^i$ over the cylinder and its bottom ${\mathcal{X}}$ respectvely. Conditions (\[eq.classmc\]) specify the first mixed problem for evolution equations (\[eq.classNS\]).
Let $(u,p)$ be a classical solution of problem (\[eq.classNS\]), (\[eq.classmc\]), say $u \in C^{2m} (\overline{{\mathcal{C}}},F^i)$ and $p \in C^1 (\overline{{\mathcal{C}}},F^{i-1})$. Then one can check easily that $$(u'_t, v) + (Vu, v) + (N (u), v) = (f, v)$$ for each element $v$ of $\mathcal{S}$. By continuity, this equation holds also for each $v \in S$. Since $(u'_t, v) = \partial_t\, (u,v)$, this suggests the following weak formulation of problem (\[eq.classNS\]), (\[eq.classmc\]), cf. [@Lera33; @Lera34a; @Lera34b]. Given sections $f \in L^2 (I,S')$ and $u_0 \in H$, find $u \in L^2 (I,S)$ such that $$\label{eq.NSweakf}
\begin{array}{rclcl}
\partial_t\, (u,v) + (Vu,v) + (N (u),v)
& =
\\
& =
&
&
\end{array}$$ (By (\[eq.Stokes\]), any solution to this problem leads to a solution in some weak sense of problem (\[eq.classNS\]), (\[eq.classmc\]).)
If a section $u$ merely belongs to $L^2 (I,S)$, the condition $u (0) = u_0$ need not make sense. But if $u$ belongs to $L^2 (I,S)$ and satisfies the variational equation of (\[eq.NSweakf\]) then we can argue as in the linear case (using Lemma \[l.primiti\]) to see that $u$ is equal a.e. to some continuous function, so that $u (0) = u_0$ is meaningful. Before showing this, we prove a lemma.
\[l.lapwtsB\] Suppose that $u \in L^2 (I,S)$. Then the function $N (u)$ defined by $(N (u) (t),v) = (N (u (t),u (t)),v)$, for almost all $t \in I$ and all $v \in S$, belongs to $L^1 (I,S')$.
For almost all $t \in I$, the value $N (u) (t)$ is an element of $S'$, and the measurability of the function $N (u)$ of $t \in I$ with values in $S'$ is easily verified. Moreover, since $(N (u,v),w)$ is a continuous trilinear form on the space $S$, we conclude immediately that $$\| N (v) \|_{S'} \leq c\, D (v)$$ for all $v \in S$. Therefore, $$\int_0^T \| N (u) (t) \|_{S'} dt
\leq
c\, \int_0^T D (u) (t)\, dt
< \infty,$$ and the lemma is proved.
Now, if $u \in L^2 (I,S)$ satisfies (\[eq.NSweakf\]), then, according to the above lemma, one can write (\[eq.NSweakf\]) as $$\partial_t\, (u,v)
= (f - Vu - N (u),v)$$ for all $v \in S$. Since $Vu$ belongs to $L^2 (I,S')$, as in the linear case, the function $f - Vu - N (u)$ belongs to $L^1 (I,S')$. Lemma \[l.primiti\] implies that $u' \in L^1 (I,S')$ and $u' = f - Vu - N (u)$, and that $u$ is equal a.e. to a continuous function of $t \in \overline{I}$ with values in $S'$. This remark makes the initial condition $u (0) = u_0$ meaningful, as desired.
An alternative formulation of problem (\[eq.NSweakf\]) reads as follows. Let $f \in L^2 (I,S')$ and $u_0 \in H$ be given sections. Find a section $u \in L^2 (I,S)$ such that $u' \in L^1 (I,S')$ and $$\label{eq.NSpowif}
\begin{array}{rclcl}
u' + Vu + N (u)
& =
\\
& =
&
&
\end{array}$$ We have shown that any solution of problem (\[eq.NSweakf\]) is a solution of problem (\[eq.NSpowif\]). The converse is very easily checked and these problems are thus equivalent. The existence of solutions of these problems is ensured by our next theorem, cf. Theorem 3.1 of [@Tema79 p. 191].
\[t.exnonNS\] Assume that $f \in L^2 (I,S')$ and $u_0 \in H$ are arbitrary data. Then there exists at least one function $u \in L^2 (I,S)$ satisfying $u' \in L^1 (I,S')$ and (\[eq.NSpowif\]). Moreover, $u \in L^\infty (I,H)$ and $u$ is a weakly continuous function of $t \in \overline{I}$ with values in $H$.
Note that by the weak continuity of $u$ is meant that, for each $v \in H$, the function $t \mapsto (u (t),v)$ is continuous on $I$. The weak continuity result is a direct consequence of $u \in L^\infty (I,H)$, the continuity of $u$ in $t \in \overline{I}$ with values in $S'$, and of Lemma 1.4 of [@Tema79 p. 178].
*Approximate solution*. We apply the Galerkin procedure as in the linear case. Since $S$ is separable and $\mathcal{S}$ is dense in $S$, there is a sequence of linearly independent elements $( e_i )_{i = 1, 2, \ldots}$ of $\mathcal{S}$, which is complete in $S$. (It should be noted that the $e_i$ are chosen in $\mathcal{S}$ for simplicity. With some technical modifications we could take these elements in $S$.) For every $k = 1, 2, \ldots$ we define an approximate solution of problem (\[eq.NSweakf\]) by $$u_k = \sum_{i=1}^k c_{k,i} (t) e_i$$ and $$\label{eq.appsNSc}
\begin{array}{rclcl}
(u_k',e_j) + (V u_k,e_j) + (N (u_k),e_j)
& =
\\
& =
&
&
\end{array}$$ where $u_{0,k}$ is the orthogonal projection in $H$ of $u_0$ onto the space spanned by the elements $e_1, \ldots, e_k$. (We could take for $u_{0,k}$ any element of the space spanned by $e_1, \ldots, e_k$, such that $u_{0,k} \to u_0$ in the norm of $H$, as $k \to \infty$.)
Equations (\[eq.appsNSc\]) form a system of nonlinear ordinary differenial equations for the unknown scalar-valued functions $c_{k,i}$ on the interval $I$, where $1 \leq i \leq k$. Indeed, we get $$\sum_{i=1}^k (e_i,e_j)\, c_{k,i}' (t)
+ \sum_{i=1}^k (V e_i,e_j)\, c_{k,i} (t)
+ \sum_{l = 1, \ldots, k \atop
m = 1, \ldots, k} (N (e_l,e_m),e_j)\, c_{k,l} (t) c_{k,m} (t)
= (f,e_j)$$ for all $j = 1, \ldots, k$. On inverting the regular matrix with entries $(e_i,e_j)$, where $1 \leq i, j \leq k$, we rewrite the differential equations in the usual form $$\label{eq.nfoeftc}
c_{k,i}' (t)
+ \sum_{j=1}^k a_{i,j}\, c_{k,j} (t)
+ \sum_{l = 1, \ldots, k \atop
m = 1, \ldots, k} a_{i,l,m}\, c_{k,l} (t) c_{k,m} (t)
= \sum_{j=1}^k b_{i,j}\, (f,e_j)$$ for $i = 1, \ldots, k$, where $a_{i,j}$, $a_{i,l,m}$ and $b_{i,j}$ are constant complex numbers. Furthermore, the condition $u_k (0) = u_{0,k}$ is equivalent to $k$ equations $c_{k,i} (0) = \pi_i (u_{0,k})$, where $\pi_i$ is the projection of $u_{0,k}$ on the one-dimensional space spanned by the element $e_i$.
The system of nonlinear equations (\[eq.nfoeftc\]) with initial conditions $c_{k,i} (0) = \pi_i (u_{0,k})$ has a maximal solution defined on some interval $[0,T (k)]$. If $T (k) < T$, then $\|u_k (t) \|_{H}$ must tend to $+ \infty$ as $t \to T (k)$. However, the a priori estimates we go to prove show that this does not happen, and so $T (k) = T$, showing that the coefficients $c_{k,i} (t)$ are defined on all of $[0,T]$.
*A priori estimates*. The first a priori estimates are established as in the linear case. We multiply the first equation of (\[eq.appsNSc\]) by $c_{k,j} (t)$ and sum up these equations for $j = 1, \ldots, k$. From the properties of the nonlinear term we deduce that $(N (u_k),u_k) = 0$ whence $$(u_k' (t),u_k (t)) + (V u_k (t),u_k (t))
= (f (t),u_k (t)).$$ Since $
\partial_t (u_k (t),u_k (t)) = 2\, \Re\, (u_k' (t),u_k (t)),
$ we write $$\begin{aligned}
\partial_t\, \| u_k (t) \|_H^2 + 2 \left( D (u_k (t)) - \| u_k (t) \|_H^2 \right)
& = &
2\, \Re\, (f (t),u_k (t))
\\
& \leq &
2\, \| f (t) \|_{S'} \| u_k (t) \|_S
\\
& \leq &
c\, \| f (t) \|_{S'}^2 + \frac{1}{c}\, D (u_k (t))\end{aligned}$$ with arbitrary constant $c > 0$. We choose $c$ in such a way that $2 - 1/c > 0$. On the other hand, $$\partial_t\, \| u_k (t) \|_H^2 - 2 \| u_k (t) \|_H^2
= e^{2t}\, \partial_t \left( e^{- 2t} \| u_k (t) \|_H^2 \right),$$ as is easy to check. Therefore, $$\label{eq.tlhsooa}
\partial_t \left( e^{- 2t} \| u_k (t) \|_H^2 \right)
+ \Big( 2 - \frac{1}{c} \Big) e^{- 2t}\, D (u_k (t))
\leq
c\, e^{- 2t}\, \| f (t) \|_{S'}^2.$$ Integrating the inequality from $0$ to $t$, where $t$ is a fixed point of $I$, we obtain, in particular, $$\begin{aligned}
\\
\Big( \| u_0 \|_H^2 + c \int_0^T \| f (t) \|_{S'}^2 dt \Big).$$ the right-hand side being finite and independent of $k$. We have thus proved that the sequence $u_k$ remains in a bounded subset of $L^\infty (I,H)$, i.e., there is a constant $C$ such that $$\label{eq.uboasiH}
\| u_k \|_{L^\infty (I,H)} \leq C$$ for all $k$.
Furthermore, on integrating inequality (\[eq.tlhsooa\]) in $t$ over all of $I$ we arrive at the estimates $$\begin{aligned}
\\
+ c \int_0^T \!\!\! e^{2 (T-t)} \| f (t) \|_{S'}^2 dt\end{aligned}$$ for each $k = 1, 2, \ldots$. This shows that the sequence $u_k$ remains in a bounded subset of $L^2 (I,S)$, i.e., $$\label{eq.uboasiS}
\| u_k \|_{L^2 (I,S)} \leq C$$ for all $k$, with $C$ a constant independent of $k$.
*Estimates for fractional derivative*. Let $v_k$ denote the function of $t \in {\mathbb{R}}$ with values in $S$, which is equal to $u_k$ on $[0,T]$ and to zero in the complement of this interval. The Fourier transform of $v_k$ is denoted by $\hat{v}_k$. In addition to the previous inequalities, which are similar to the estimates in the linear case, we want to show that $$\label{eq.eofdovk}
\int_{-\infty}^{+\infty} |\tau|^{2 \lambda} \| \hat{v}_k (\tau) \|_{H}^2 d \tau \leq C$$ for some $\lambda > 0$, both constants $\lambda$ and $C$ being independent of $k$. Along with (\[eq.uboasiS\]) this will imply that $v_k$ belongs to a bounded set of $\mathcal{H}^\lambda$ corresponding to $\mathcal{B}_0 = S$ and $\mathcal{B}_1 = H$, and this will enable us to apply the compactness result of Theorem \[t.Temam79\].
In order to prove (\[eq.eofdovk\]) we observe that equations (\[eq.appsNSc\]) can be written in the form $$\partial_t\, (v_k, e_j)
= (w_k, e_j) + (u_{0,k}, e_j)\, \delta_0 - (u_k (T), e_j)\, \delta_T$$ for all $j = 1, \ldots, k$, where $w_k$ is equal to $f - V u_k - N (u_k)$ on $[0,T]$ and zero outside this interval. (Compare this with the proof of Theorem \[t.tptteil\].) On applying the Fourier transform we get $$\label{eq.oatFtwg}
(\imath \tau)\, (\hat{v}_k (\tau), e_j)
= (\hat{w}_k (\tau), e_j) + (u_{0,k}, e_j) - (u_k (T), e_j)\, \exp (- \imath T \tau)$$ for all $\tau \in {\mathbb{R}}$.
We multiply (\[eq.oatFtwg\]) by (the complex conjugate of) the Fourier transform of the function equal to $c_{k,j} (t)$ for $t \in [0,T]$ and zero for $t \in {\mathbb{R}}\setminus [0,T]$, and sum up the resulting equalities for $j = 1, \ldots, k$. This yields $$\label{eq.eftFtovk}
(\imath \tau)\, \| \hat{v}_k (\tau) \|_H^2
= (\hat{w}_k (\tau), \hat{v}_k (\tau))
+ (u_{0,k}, \hat{v}_k (\tau))
- (u_k (T), \hat{v}_k (\tau))\, \exp (- \imath T \tau).$$ By inequality $\| N (v) \|_{S'} \leq c\, D (v)$ for all $v \in S$ (see the proof of Lemma \[l.lapwtsB\]), we obtain $$\int_0^T \| w_k (t) \|_{S'} dt
\leq
\int_0^T \left( \| f (t) \|_{S'} + \sqrt{D (u_k (t))} + c D (u_k (t)) \right) dt,$$ and the right-hand side remains bounded uniformly in $k$ according to (\[eq.uboasiS\]). It follows that $$\sup_{\tau \in {\mathbb{R}}} \| \hat{w}_k (\tau) \|_{S'}
\leq C$$ for all $k$, the constant $C$ being different in diverse applications.
By (\[eq.uboasiH\]) $$\begin{array}{rcl}
\| u_k (0) \|_H & \leq & c,
\\
\| u_k (T) \|_H & \leq & c,
\end{array}$$ and so we deduce from (\[eq.eftFtovk\]) that $$|\tau|\, \| \hat{v}_k (\tau) \|_H^2
\leq
C \sqrt{D (\hat{v}_k (\tau))} + 2c\, \| \hat{v}_k (\tau) \|_H$$ or $$|\tau|\, \| \hat{v}_k (\tau) \|_H^2
\leq
(C + 2 c)\, \sqrt{D (\hat{v}_k (\tau))}$$ for all $\tau \in {\mathbb{R}}$.
Choose any positive $\lambda$ satisfying $\displaystyle \lambda < \frac{1}{4}$. From the inequality $$|\tau|^{2 \lambda}
\leq
c (\lambda)\, \frac{1 + |\tau|}{1 + |\tau|^{1 - 2 \lambda}}$$ for all $\tau \in {\mathbb{R}}$, the constant $c (\lambda)$ depending on $\lambda$, it follows that $$\begin{aligned}
\lefteqn{
\int_{-\infty}^{+\infty}
|\tau|^{2 \lambda}\, \| \hat{v}_k (\tau) \|_{H}^2
}
\\
\frac{1 + |\tau|}{1 + |\tau|^{1-2 \lambda}}\,
\| \hat{v}_k (\tau) \|_{H}^2
\\
\| \hat{v}_k (\tau) \|_{H}^2
d \tau
+ (C + 2 c)
\int_{-\infty}^{+\infty}
\frac{\sqrt{D (\hat{v}_k (\tau))}}{1 + |\tau|^{1-2 \lambda}}\,
d \tau
\Big).\end{aligned}$$ By the Plancherel theorem, we see that $$\int_{-\infty}^{+\infty}
\| \hat{v}_k (\tau) \|_{H}^2
d \tau
= \int_0^T
\| v_k (t) \|_{H}^2
dt$$ and these integrals are bounded uniformly in $k$. Hence, we shall have established (\[eq.eofdovk\]) if we show that the integral $$\int_{-\infty}^{+\infty}
\frac{\sqrt{D (\hat{v}_k (\tau))}}{1 + |\tau|^{1-2 \lambda}}\,
d \tau$$ is bounded uniformly in $k$. By the Schwarz inequality and the Plancherel theorem we can bound these integrals by $$\Big( \int_{-\infty}^{+\infty} \frac{d \tau}{(1 + |\tau|^{1-2 \lambda})^2}\, \Big)^{1/2}
\Big( \int_{-\infty}^{+\infty} D (v_k (t))\, dt \Big)^{1/2},$$ the first factor being finite, for $\lambda < 1/4$, and the second factor is bounded uniformly in $k$ by (\[eq.uboasiS\]). The proof of (\[eq.eofdovk\]) is complete.
*Passage to the limit*. Estimates (\[eq.uboasiH\]) and (\[eq.uboasiS\]) enable us to assert that there is a subsequence of $u_k$ which converges to an element $u \in L^\infty (I,H) \cap L^2 (I,S)$ both in the weak$^\ast$ topology of $L^\infty (I,H)$ and in the weak topology of $L^2 (I,S)$. It will cause no confusion if we continue to write $u_k$ for this subsequence. By (\[eq.eofdovk\]) and the compactness result of Theorem \[t.Temam79\] there is no loss of generality in assuming that $u_k$ converges to $u$ strongly in $L^2 (I,H)$. The former of the convergence results allows us to pass to the limit. We argue essentially in the same way as in the linear case.
Let $\phi$ be a continuously differentiable scalar-valued function of $t \in [0,T]$ satisfying $\phi (T) = 0$. We multiply (\[eq.appsNSc\]) by $\phi (t)$ and then integrate by parts. This leads to the equations $$\begin{aligned}
\lefteqn{
- \int_0^T \!\! (u_k (t), e_j) \phi' (t) dt
+ \int_0^T \!\! (V u_k (t), e_j) \phi (t) dt
+ \int_0^T \!\! (N (u_k (t)), e_j) \phi (t) dt
}
\\
& = &
(u_{0,k}, e_j)\, \phi (0)
+ \int_0^T \!\! (f (t), e_j) \phi (t) dt
\hspace{4cm}\end{aligned}$$ for $j = 1, \ldots, k$. Passing to the limit with the subsequence of $u_k$ is easy for the linear terms. For the nonlinear term we apply Lemma \[l.ptlfnlt\] to be proved below. In the limit we find that the equality $$\begin{aligned}
\label{eq.ptlfthe}
\lefteqn{
- \int_0^T \!\! (u (t), v) \phi' (t) dt
+ \int_0^T \!\! (V u (t), v) \phi (t) dt
+ \int_0^T \!\! (N (u (t)), v) \phi (t) dt
}
\nonumber
\\
& = &
(u_{0}, v)\, \phi (0)
+ \int_0^T \!\! (f (t), v) \phi (t) dt
\hspace{4cm}
\nonumber
\\\end{aligned}$$ holds for $v = e_1, e_2, \ldots$. Hence it follow that the equality is valid for any element $v \in S$ which is a finite linear combination of the $e_k$. And by the continuity argument (\[eq.ptlfthe\]) is still true for any $v \in S$. In particular, on writing (\[eq.ptlfthe\]) with arbitrary functions $\phi \in C^\infty_{\mathrm{comp}} (I)$ we conclude readily that $u$ satisfies (\[eq.NSweakf\]) in the sense of distributions.
Finally, it remains to prove that $u$ satisfies $u (0) = u_0$. For this purpose we multiply (\[eq.NSweakf\]) by $\phi$ and integrate in $t \in I$. After integrating the first term by parts we get $$\begin{aligned}
}
\\
& = &
(u_{0}, v)\, \phi (0)
+ \int_0^T \!\! (f (t),v)\, \phi (t) dt
\hspace{4cm}\end{aligned}$$ for all $v \in S$. On comparing this with (\[eq.ptlfthe\]) we see that $
(u (0) - u_0, v)\, \phi (0) = 0
$ for all $v \in S$ and for each function $\phi$ of the type considered. We can choose $\phi$ with $\phi (0) = 1$. Thus, $
(u (0) - u_0, v) = 0
$ for all $v \in S$. This equality implies $u (0) = u_0$, as desired.
The proof of Theorem \[t.exnonNS\] will be complete once we show the lemma mentioned above.
\[l.ptlfnlt\] Assume that $u_k$ converges to $u$ weakly in $L^2 (I,S)$ and strongly in $L^2 (I,H)$. Then $$\int_0^T (N (u_k (t)), w (t))\, dt
\to
\int_0^T (N (u (t)), w (t))\, dt$$ for any section $w \in C^1 (\overline{{\mathcal{C}}},F^i)$.
We write $$\begin{aligned}
\int_0^T (N (u_k (t)), w (t))\, dt
& = &
- \int_0^T (N (u_k (t), w (t)), u_k (t))\, dt
\\
& = &
- \int_0^T (T (w (t)) u_k (t), u_k (t))\, dt,\end{aligned}$$ which is due to Corollary \[c.algestr\]. The right-hand side converges to $$\begin{aligned}
- \int_0^T (T (w (t)) u (t), u (t))\, dt
& = &
- \int_0^T (N (u (t), w (t)), u (t))\, dt
\\
& = &
\int_0^T (N (u (t)), w (t))\, dt,\end{aligned}$$ and the lemma is proved.
The solution $u$ given by Theorem \[t.exnonNS\] satisfies an energy estimate. In order to show it we integrate the equality $$\partial_t\, \| u_k (t) \|_H^2
+ 2 \left( D (u_k (t)) \! - \! \| u_k (t) \|_H^2 \right)
= 2\, \Re\, (f (t),u_k (t))$$ to conclude that $$\| u_k (t) \|_H^2 + 2 \int_0^t \! \left( D (u_k (t')) \! - \! \| u_k (t') \|_H^2 \right) dt'
= \| u_{0,k} \|_H^2 + 2\, \Re \int_0^t \! (f (t'),u_k (t')) dt'$$ for all $t \in [0,T]$. Multiplying this equality by a nonnegative function $\phi \in C^\infty_{\mathrm{comp}} (I)$ and integrating in $t \in I$ yields $$\begin{aligned}
\lefteqn{
\int_0^T
\Big(
\| u_k (t) \|_H^2 + 2 \int_0^t \! \left( D (u_k (t')) \! - \! \| u_k (t') \|_H^2 \right) dt'
\Big)
\phi (t)
dt
}
\\
& = &
\int_0^T
\Big( \| u_{0,k} \|_H^2 + 2\, \Re \int_0^t \! (f (t'),u_k (t')) dt' \Big)
\phi (t)
dt.\end{aligned}$$ Since $u_k$ converges to $u \in L^\infty (I,H) \cap L^2 (I,S)$ in the weak$^\ast$ topology of $L^\infty (I,H)$, weakly in $L^2 (I,S)$ and strongly in $L^2 (I,H)$, we can pass to the lower limit in this relation and obtain $$\begin{aligned}
\lefteqn{
\int_0^T
\Big(
\| u (t) \|_H^2 + 2 \int_0^t \! \left( D (u (t')) \! - \! \| u (t') \|_H^2 \right) dt'
\Big)
\phi (t)
dt
}
\\
& \leq &
\int_0^T
\Big( \| u_0 \|_H^2 + 2\, \Re \int_0^t \! (f (t'),u (t')) dt' \Big)
\phi (t)
dt\end{aligned}$$ for all $\phi \in C^\infty_{\mathrm{comp}} (I)$ satisfying $\phi \geq 0$. (We have used the fact that if $v_k \to v$ weakly in a normed space $V$ then $\| v \|_V \leq \liminf \| v_k \|_V$.) The last inequality amounts to saying that $$\label{eq.enerest}
\| u (t) \|_H^2 + 2 \int_0^t \! \left( V u (t'), u (t') \right) dt'
\leq
\| u_0 \|_H^2 + 2\, \Re \int_0^t \! (f (t'),u (t')) dt'$$ for almost all $t \in I$.
Regularity and uniqueness {#s.reguniq}
=========================
As but one generalisation of Lemma \[l.(N(uv)w)\] we note that on applying the Hölder inequality and the Sobolev embedding theorem one establishes immediately that the form $(N (u,v),w)$ is actually trilinear continuous on the Cartesian product $H^{s_1} ({\mathcal{X}},F^i) \times H^{s_2+1} ({\mathcal{X}},F^i) \times H^{s_3} ({\mathcal{X}},F^i)$, where $s_1 + s_2 + s_3 \geq n/2$, if each of $s_1$, $s_2$ and $s_3$ is different from $n/2$, and $s_1 + s_2 + s_3 > n/2$, if some of the $s_1$, $s_2$ and $s_3$ just amounts to $n/2$. That is, there is a constant $c$ depending on $s_1$, $s_2$ and $s_3$, such that $$\label{eq.tricont}
|(N (u,v),w)|
\leq
c\, \| u \|_{H^{s_1} ({\mathcal{X}},F^i)} \| v \|_{H^{s_2+1} ({\mathcal{X}},F^i)} \| w \|_{H^{s_3} ({\mathcal{X}},F^i)}$$ provided $s_1, s_2, s_3 \geq 0$.
Moreover, if ${\mathcal{X}}$ is compact, which is the case indeed, then the interpolation inequality $$\label{eq.interpo}
\| u \|_{H^{(1-\vartheta) s_1 + \vartheta s_2} ({\mathcal{X}},F^i)}
\leq
c\, \| u \|_{H^{s_1} ({\mathcal{X}},F^i)}^{1-\vartheta} \| u \|_{H^{s_2} ({\mathcal{X}},F^i)}^{\vartheta}$$ holds for all $u \in H^{s_2} ({\mathcal{X}},F^i)$, where $s_1 \leq s_2$, $\vartheta \in [0,1]$, and $c$ is a constant independent of $u$, see [@LionMage72 Ch. 1].
Clearly, various estimates for the trilinear form $(N (u,v),w)$ can be obtained by using (\[eq.tricont\]) and (\[eq.interpo\]). We mention one of these.
\[l.totnwst\] Assume that $m \geq (n+2)/4$. Then there is a constant $c$ with the property that $$|(N (u,v),w)|
\leq
c\, \| u \|_H^{1/2} D (u)^{1/4} \| v \|_H^{1/2} D (v)^{1/4} D (w)^{1/2}$$ for all $u, v, w \in H^m_0 ({\mathcal{X}},F^i)$.
Choose $$\begin{array}{rcl}
s_1 & = & \displaystyle \frac{1}{2} 0 + \frac{1}{2} m,
\\
s_2 + 1 & = & \displaystyle \frac{1}{2} 0 + \frac{1}{2} m,
\\
s_3 & = & m
\end{array}$$ and apply both (\[eq.tricont\]) and (\[eq.interpo\]) with $\displaystyle \vartheta = \frac{1}{2}$.
In particular, $$|(N (u),w)|
\leq
c\, \| u \|_H D (u)^{1/2} D (w)^{1/2}$$ for all $u, w \in S$, and hence $
\| N (u) \|_{S'}
\leq
c\, \| u \|_H D (u)^{1/2}
$ for all $u \in S$. If now $u \in L^\infty (I,H) \cap L^2 (I,S)$, then $N (u (t))$ belongs to $S'$ for almost all $t \in I$ and the estimate $$\| N (u (t)) \|_{S'}
\leq
c\, \| u (t) \|_H D (u (t))^{1/2}$$ shows that $N (u)$ belongs to $L^2 (I,S')$ and implies $$\label{eq.efN(u)iS}
\| N (u) \|_{L^2 (I,S')}
\leq
c\, \| u \|_{L^\infty (I,H)} \| u \|_{L^2 (I,S)}$$ with $c$ a constant independent of $u$.
We are now in a position to prove the main result of this section, cf. Theorem 3.2 of [@Tema79 p. 198].
\[t.uniqrNS\] Assume that $m \geq (n+2)/4$. Then the solution $u$ of problem (\[eq.NSweakf\]) (or (\[eq.NSpowif\])) given by Theorem \[t.exnonNS\] is unique. Moreover, $u$ is equal almost everywhere to a function continuous of $t \in [0,T]$ with values in $H$, and $u (t) \to u_0$ in $H$, as $t \to 0$.
*Regularity*. We first prove the result of regularity. According to the first equality of (\[eq.NSpowif\]) we get $$u' = f - Vu - N (u)$$ almost everywhere on $I$. By (\[eq.efN(u)iS\]), each term on the right-hand side of this equality belongs to $L^2 (I,S')$. This remark improves the condition $u' \in L^1 (I,S')$, showing that $u' \in L^2 (I,S')$. This improvement enables us to apply Lemma \[l.interLM\], which states exactly that $u$ is almost everywhere equal to a continuous function of $t \in [0,T]$ with values in $H$. Thus, $u \in C (\overline{I},H)$, and the last part of Theorem \[t.uniqrNS\] follows immediately.
We also recall that Lemma \[l.interLM\] asserts that for any function $u$ in $L^2 (I,S)$, such that $u' \in L^2 (I,S')$, the equality $$\label{eq.dotntp2}
\partial_t \| u \|_H^2 = 2 \Re\, (u',u)_H$$ holds in the sense of distributions on $I$. This result will next be used in the proof of uniqueness which we now start.
*Uniqueness*. Suppose $u_1$ and $u_2$ are two solutions of (\[eq.NSpowif\]). Consider the difference $u = u_1 - u_2$. By the above, both $u_1'$ and $u_2'$, and thus $u'$, belong to $L^2 (I,S')$. The difference satisfies $$\label{eq.fdu1-u2}
\begin{array}{rclcl}
u' + Vu
& =
& N (u_2) - N (u_1)
\\
& =
&
&
\end{array}$$ For almost all $t \in I$ we take the scalar product of the first equality in (\[eq.fdu1-u2\]) with $u (t)$ in the duality between $S$ and $S'$. Using (\[eq.dotntp2\]) yields $$\label{eq.rospwut}
\partial_t \| u (t) \|_H^2 + 2 \left( D (u (t)) - \| u (t) \|_H^2 \right)
= 2 \Re \left( (N (u_2 (t)), u (t)) - (N (u_1 (t)), u (t)) \right).$$ From Corollary \[c.algestr\] it follows that the right-hand side of this equality just amounts to $$- 2 \Re\, (N (u (t),u_2 (t)), u (t))
= 2 \Re\, (N (u (t)), u_2 (t)).$$ On applying Lemma \[l.totnwst\] we can majorise this expression by $$2 c\, \| u (t) \|_H D (u (t))^{1/2} D (u_2 (t))^{1/2}
\leq
\epsilon c^2\, \| u (t) \|_H^2 D (u_2 (t)) + \frac{1}{\epsilon}\, D (u (t)),$$ where $\epsilon > 0$ is an arbitrary constant. We choose $\epsilon$ in such a way that $2 - 1/\varepsilon \geq 0$. Substituting this into (\[eq.rospwut\]) we conclude that $$\partial_t \| u (t) \|_H^2
\leq
\left( 2 + \epsilon c^2\, D (u_2 (t)) \right) \| u (t) \|_H^2$$ for almost all $t \in I$. Since the function $t \mapsto D (u_2 (t))$ is integrable, this shows readily that $$\partial_t
\Big( \exp \Big( - \int_0^t \left( 2 + \epsilon c^2\, D (u_2 (t')) \right) dt' \Big)
\| u (t) \|_H^2
\Big)
\leq
0.$$ On integrating and applying the equality $u (0) = 0$ we find $\| u (t) \|_H^2 \leq 0$ for all $t \in [0,T]$. Hence, $u_1 = u_2$, and the solution is unique, as desired.
Note that if $n = 2$ then $m = 1$ satisfies the condition $m \geq (n+2)/4$. Hence, we recover the classical result on the existence and uniqueness of a weak solution to the Navier-Stokes equations in dimension $2$, see for instance Theorem 3.2 of [@Tema79 p. 198].
It is also worth pointing out that $$L^\infty (I,H) \cap L^2 (I,S)
\hookrightarrow
L^{\frac{\scriptstyle 2}{\scriptstyle 1 - \vartheta}} (I, H^{(1-\vartheta) m} ({\mathcal{X}},F^i))$$ for all $\vartheta \in [0,1]$, see [@LionMage72] for an interpolation argument. The reader may also consult [@BatzBere67].
\[s.lttNSeq\]
More regular solutions {#s.moresol}
======================
Our purpose in this section is to prove that on assuming more regularity of the data $f$ and $u_0$ we can obtain more regular solutions to the regularised Navier-Stokes equations, cf. Theorem 3.5 of [@Tema79 p. 202].
The domain ${\mathcal{D}}_V$ of the closed unbounded operator $V$ in $H$ is well known to consist of all sections $u \in H^{2m} ({\mathcal{X}};F^i)$ which satisfy $A^\ast u = 0$ in ${\mathcal{X}}$ and vanish up to order $m$ on the boundary of ${\mathcal{X}}$.
\[l.regtfNS\] Suppose $m \geq (n+2)/4$. If $u \in {\mathcal{D}}_V$ then $N (u) \in H$ and $$\| N (u) \|_H \leq c\, \| u \|_H^{1/2} D (u)^{1/2}\, \| (V + {I}) u \|_H^{1/2}$$ with $c$ a constant independent of $u$.
We exploit the estimate of (\[eq.tricont\]) with $\displaystyle s_1 = \frac{1}{2} m$, $\displaystyle s_2 + 1 = \frac{1}{2} m + \frac{1}{2} 2m$ and $s_3 = 0$, obtaining $$|(N (u,v),w)|
\leq
c\, \| u \|_{H^{s_1} ({\mathcal{X}},F^i)} \| v \|_{H^{s_2+1} ({\mathcal{X}},F^i)} \| w \|_{H^{s_3} ({\mathcal{X}},F^i)}$$ for all $u \in H^{s_1} ({\mathcal{X}},F^i)$, $v \in H^{s_2+1} ({\mathcal{X}},F^i)$ and $w \in H^{s_3} ({\mathcal{X}},F^i)$, where $c$ is a constant independent of $u$, $v$ and $w$. By the interpolation inequality of (\[eq.interpo\]), the norm of $u$ in $H^{s_1} ({\mathcal{X}},F^i)$ is dominated by $\| u \|_H^{1/2} D (u)^{1/4}$. If moreover $v$ belongs to $H^{2m} ({\mathcal{X}},F^i)$, then on applying inequality (\[eq.interpo\]) with $s_1 = m$, $s_2 = 2m$ and $\vartheta = 1/2$, we deduce that the norm of $v$ in $H^{s_2+1} ({\mathcal{X}},F^i)$ is majorised by $D (v)^{1/4} \| v \|_{H^{2m} ({\mathcal{X}},F^i)}^{1/2}$. Since the Dirichlet problem for the operator $V + {I}$ in ${\mathcal{X}}$ is elliptic and has unique solution, the norm $\| v \|_{H^{2m} ({\mathcal{X}},F^i)}$ is in turn majorised by $\| (V+{I}) v \|_H$, provided that $v \in {\mathcal{D}}_V$. On summarising we see immediately that there is a constant $c$ with the property that $$\label{eq.peoNuvw}
|(N (u,v),w)|
\leq
c\, \| u \|_H^{1/2} D (u)^{1/4} D (v)^{1/4} \| (V+{I}) v \|_H^{1/2} \| w \|_H$$ for all $u \in S$, $v \in {\mathcal{D}}_V$ and $w \in H$. By the Riesz representation theorem it follows readily that $\| N (u,u) \|_H \leq c\, \| u \|_H^{1/2} D (u)^{1/2} \| (V+{I}) u \|_H^{1/2}$ for all sections $u \in {\mathcal{D}}_V$, as desired.
The following lemma is usually referred to as Gronwall’s inequality, see [@Gron19]. It is an important tool to obtain various estimates in the theory of ordinary differential equations. In particular, it provides a comparison theorem that can be used to prove the uniqueness of a solution to the initial value problem. There are two forms of the lemma, a differential form and an integral form. We adduce here the integral form.
\[l.Gronwall\] Let $a$, $b$ and $y$ be real-valued functions on an interval $I = (0,T)$. Assume that $a$ and $y$ are continuous on the closed interval $\overline{I}$ and the negative part of $b$ is locally integrable in $I$. If $a$ is nonnegative and if $y$ satisfies the integral inequality $$y (t) \leq b (t) + \int_0^t a (t') y (t') dt'$$ for all $t \in I$, then $$y (t) \leq b (t) + \int_0^t b (s) a (s) \exp \Big( \int_s^t a (t') dt' \Big) ds$$ for all $t \in I$.
If, in addition, the function $b$ is nondecreasing, then $$\label{eq.Gronwall}
y (t) \leq b (t)\, \exp \Big( \int_0^t a (t') dt' \Big)$$ for all $t \in I$.
See [@Bell43].
It is worth pointing out that there are no assumptions on the signs of the functions $b$ and $y$. Compared to the differential form, the differentiability of $y$ is not needed for the integral form. There are also versions of Gronwall’s inequality which need not any continuity of $a$ and $y$.
The lemma is very useful when establishing a uniform estimate in a priori esimates.
\[t.regtfNS\] Suppose $m \geq (n+2)/4$. Let $f \in L^2 (I,H)$ and $u_0 \in S$. Then there is a unique solution $u$ of problem (\[eq.NSweakf\]) (or (\[eq.NSpowif\])) which satisfies $u \in L^2 (I,{\mathcal{D}}_V)$ and $u' \in L^2 (I,H)$, i.e., $$\label{eq.domrNSe}
\\
Moreover, the proof shows that the solution $u$ given by this theorem belongs to $C (\overline{I},S)$.
Proof of Theorem \[t.regtfNS\] {#s.proofTh}
==============================
Consider the Galerkin approximation used in the proof of weak solutions in Theorem \[t.exnonNS\]. In order to obtain further regularity properties of solutions, we choose the basis functions $e_i$ as the eigenfunctions of the operator $V+{I}$ in (\[eq.NSpowif\]). We get $e_i \in {\mathcal{D}}_V$ and $(V+{I}) e_i = \lambda_i e_i$ for all $i = 1, 2, \ldots$, where $\lambda_i \geq 1$, for $V$ is nonnegative. Write $u_{0,k}$ for the orthogonal projection in $S$ of $u_0$ onto the space spanned by the elements $e_1, \ldots, e_k$. Hence it follows that $u_{0,k}$ converges to $u_0$ strongly in $S$ as $k \to \infty$.
The first equations of (\[eq.appsNSc\]) read $$(u_k',e_j) + (V u_k,e_j) + (N (u_k),e_j) = (f,e_j)$$ for all $j = 1, \ldots, k$. On multiplying both sides of these equalities by $\lambda_j$ we obtain immediately $$(u_k',(V+{I}) e_j) + (V u_k,(V+{I}) e_j) + (N (u_k),(V+{I}) e_j) = (f,(V+{I}) e_j),$$ and so multiplying the latter equalities by $c_{k,j} (t)$ and summing up over $j = 1, \ldots, k$ yields $$\label{eq.uoj1lky}
(u_k',(V+{I}) u_k) + (V u_k,(V+{I}) u_k) + (N (u_k),(V+{I}) u_k) = (f,(V+{I}) u_k)$$ a.e. on $I$. Since $$\Re\, (u_k',(V+{I}) u_k) = \frac{1}{2}\, \partial_t D (u_k)$$ and $$\begin{aligned}
|(N (u_k),(V+{I}) u_k)|
& \leq &
\| N (u_k) \|_H \| (V+{I}) u_k \|_H
\\
& \leq &
c\,
\| u_k \|_H^{1/2}
D (u_k)^{1/2}\,
\| (V + {I}) u_k \|_H^{3/2}\end{aligned}$$ which is due to Lemma \[l.regtfNS\], Therefore, from (\[eq.uoj1lky\]) we conclude by the Schwarz inequality that $$\begin{aligned}
\lefteqn{
\frac{1}{2}\, \partial_t D (u_k) + \| (V+{I}) u_k \|_H^2
}
\\
& \leq &
\big( \| f \|_H + \| u_k \|_H \big) \| (V+{I}) u_k \|_H
+ c\, \| u_k \|_H^{1/2} D (u_k)^{1/2}\, \| (V + {I}) u_k \|_H^{3/2}\end{aligned}$$ a.e. on $I$.
By Young’s inequality, $$\begin{aligned}
\lefteqn{
2 \big( \| f \|_H + \| u_k \|_H \big) \| (V+{I}) u_k \|_H
+ 2c\, \| u_k \|_H^{1/2} D (u_k)^{1/2}\, \| (V + {I}) u_k \|_H^{3/2}
}
\\
& \leq &
a_k (t) D (u_k) + b_k (t) + \| (V+{I}) u_k \|_H^2,
\hspace{4cm}\end{aligned}$$ where $$\begin{array}{rcl}
a_k (t)
& = &
\displaystyle \frac{27}{2} c^4 \| u_k \|_H^2 D (u_k),
\\
b_k (t)
& = &
2 \big( \| f \|_H + \| u_k \|_H \big)^2.
\end{array}$$ We thus arrive at the differential inequality $$\label{eq.difineq}
\partial_t D (u_k) + \| (V+{I}) u_k \|_H^2 \leq a_k (t) D (u_k) + b_k (t)$$ for almost all $t \in I$. Since $u_k$ are bounded uniformly in $k$ both in $L^\infty (I,H)$ and $L^2 (I,S)$, it follows that $$\int_t^{t+r} a_k (t') dt'
\leq
\frac{27}{2} c^4\,
\sup_{t' \in I} \| u_k (t') \|_H^2
\int_{t}^{t+r} D (u_k (t')) dt'
\leq
A$$ for all $t \in I$ satisfying $t+r \leq T$, the constant $A$ being independent of $k$. Similarly we obtain $$\int_t^{t+r} b_k (t') dt'
\leq
4 \int_t^{t+r} \big( \| f (t') \|_H^2 + \| u_k (t') \|_H^2 \big) dt'
\leq
B$$ for all $k$, with $B$ a constant independent of $k$. We now drop the term $\| (V+{I}) u_k \|_H^2$ in (\[eq.difineq\]) and apply the uniform Gronwall inequality of Lemma \[l.Gronwall\] to the resulting inequality to get $$\label{eq.uniesiS}
\sup_{t \in [0,T]} D (u_k (t)) \leq C$$ uniformly in $k$. This just amounts to saying that the sequence $\{ u_k \}$ belongs to a bounded set in $L^\infty (I,S)$.
Now go back to inequality (\[eq.difineq\]) and integrate it in $t$ over the interval $I$. This gives $$D (u_k (T)) + \int_0^T \| (V+{I}) u_k (t) \|_H^2 dt
\leq
D (u_0) + \int_0^T a_k (t) D (u_k (t)) dt + \int_0^T b_k (t) dt$$ for all $k = 1, 2, \ldots$. Hence, $$\label{eq.uniesiD}
\int_0^T \| (V+{I}) u_k (t) \|_H^2 dt
\leq
D (u_0) + A\, C + B$$ holds uniformly in $k$, where $C$ is a constant from (\[eq.uniesiS\]). We have thus proved that $\{ u_k \}$ belongs to a bounded set in $L^2 (I,{\mathcal{D}}_V)$.
The passage to the limit and the uniqueness is established as above. We can conclude that some subsequence of $\{ u_k \}$ converges to the solution $u$ which belongs to $L^\infty (I,S) \cap L^2 (I,{\mathcal{D}}_V)$.
Our next goal is to show that $u' \in L^2 (I,H)$. For this purpose we use Lemma \[l.regtfNS\] to estimate $$\begin{aligned}
\int_0^T \| N (u) \|_H^4 dt
& \leq &
c \int_0^T \| u \|_H^2 D (u)^2\, \| (V + {I}) u \|_H^2 dt
\\
& \leq &
c\, \| u \|_{L^\infty (I,H)}^2 \| u \|_{L^\infty (I,S)}^4 \| u \|_{L^2 (I,{\mathcal{D}}_V)}^2,\end{aligned}$$ where $c$ is a constant independent of $u$. This implies $N (u) \in L^4 (I,H)$. On the other hand, since $V + {I}$ is an isomorphism of ${\mathcal{D}}_V$ onto $H$, it follows easily that $Vu \in L^2 (I,H)$. Therefore, the derivative $u' = f - Vu - N (u)$ belongs to $L^2 (I,H)$, as desired.
Now $u \in L^\infty (I,S) \cap L^2 (I,{\mathcal{D}}_V)$ and $u' \in L^2 (I,H)$ imply $u \in C (\overline{I},S)$ due to the lemma below. This establishes the strong convergence $u (t) \to u (0)$ in $S$, as $t \to 0$.
\[l.tetscut\] Suppose that $u \in L^\infty (I,S) \cap L^2 (I,{\mathcal{D}}_V)$ and $u' \in L^2 (I,H)$. Then $u \in C (\overline{I},S)$.
Fix an arbitrary point $t_0 \in [0,T]$. We have to show that $D (u (t) - u (t_0)) \to 0$, as $t \to t_0$. That is, $$\lim_{t \to t_0}
\big( D (u (t)) - 2 \Re\, D (u (t),u (t_0)) + D (u (t_0)) \Big)
= 0.$$
A direct calculation shows that $D (u (t),u (t_0))$ reduces to $$\varepsilon\, ({\mathit{\varDelta}}^{m/2} u (t),{\mathit{\varDelta}}^{m/2} u (t_0))
+ \nu \big( (A u (t),A u (t_0)) + (A^\ast u (t),A^\ast u (t_0)) + (u (t),u (t_0)) \big).$$ By Lemma \[l.interLM\], the function $u$ is equal a.e. to a continuous function on $I$ with values in $H$, for $u \in L^2 (I,S)$ and $u' \in L^2 (I,S')$. Since moreover $u \in L^\infty (I,S)$ and the embedding $S \hookrightarrow H$ is continuous and has dense range, it follows that $u$ is weakly continuous from $[0,T]$ into $S$, i.e., the function $t \mapsto D (u (t),v)$ is continuous for all $v \in S$, see Lemma 1.4 in [@Tema79 p. 178]. In particular, $D (u (t),u (t_0)) \to D (u (t_0))$, as $t \to t_0$.
We will now show that $D (u (t)) \to D (u (t_0))$, as $t \to t_0$. To this end, we first establish that $$\partial_t\, D (u (t)) = 2 \Re\, (u', (V + {I}) u)$$ holds in the sense of distributions on $(0,T)$. Note that both $t \mapsto D (u (t))$ and $t \mapsto (u' (t),(V + {I}) u (t))$ are integrable functions on the interval $I$, for $u \in L^2 (I,{\mathcal{D}}_V)$ and $u' \in L^2 (I,H)$.
Choose any sequence of smooth functions $u_\iota \in C^\infty ({\mathbb{R}},{\mathcal{D}}_V)$ which is obtained by mollifying the function which is equal to $u$ on the interval $[0,T]$ and to zero outside this interval. (Mollifiers are also known as approximations to the identity.) Since $u \in L^2 (I,{\mathcal{D}}_V)$, the sequence $\{ u_\iota \}$ converges to $u$ in the norm of this space. Similarly, as $u' \in L^2 (I,H)$, the sequence of derivatives $\{ u_\iota' \}$ converges to $u'$ in the $L^2 (I,H)\,$-norm. This implies that $$\begin{array}{rcl}
D (u_\iota (t))
& \to
& D (u (t)),
\\
(u_\iota' (t), (V + {I}) u_\iota (t))
& \to
& (u' (t), (V + {I}) u (t))
\end{array}$$ in $L^1 (I)$, as $\iota \to \infty$. To clarify the second limit passage, we argue in the following way. We get $$\begin{aligned}
\lefteqn{
\int_0^T |(u', (V + {I}) u) - (u_\iota', (V + {I}) u_\iota)|\, dt
}
\\
& \! \leq \! &
\int_0^T
\big( \| u' - u_\iota' \|_H \| (V + {I}) u \|_H
+ \| u_\iota' \|_H \| (V + {I}) u - (V + {I}) u_\iota \|_H
\big)
dt
\\
& \! \leq \! &
\| u'\!-\!u_\iota' \|_{L^2 (I,H)} \| (V\!+\!{I}) u \|_{L^2 (I,H)}
+ \| u_\iota' \|_{L^2 (I,H)} \| (V\!+\!{I}) u - (V\!+\!{I}) u_\iota \|_{L^2 (I,H)}\end{aligned}$$ for all $\iota$. Since $u \in L^2 (I,{\mathcal{D}}_V)$, the norms $\| u_\iota' \|_{L^2 (I,H)}$ are bounded uniformly in $\iota$ and $(V + {I}) u_\iota$ converges to $(V + {I}) u$ in the $L^2 (I,H)\,$-norm, we see immediately that $(u_\iota', (V + {I}) u_\iota) \to (u', (V + {I}) u)$ in $L^1 (I)$ and, in particular, in the sense of distributions on $I$, as $\iota \to \infty$.
Note that from $D (u_\iota (t)) \to D (u(t))$ in the sense of distributions on $I$ it follows that $$\partial_t D (u_\iota (t)) \to \partial_t D (u (t))$$ in the same sense on $I$. Thus, $
\partial_t\, D (u (t)) = 2 \Re\, (u' (t), (V + {I}) u (t))
$ is valid in the sense of distributions on $(0,T)$. Since $
(u' (t), (V + {I}) u (t))
$ is integrable on $I$, we write $$D (u (t)) - D (u (t_0)) = 2 \Re \int_{t_0}^t (u' (t'), (V + {I}) u (t')) dt'$$ and conclude that $D (u (t)) \to D (u (t_0))$, as $t \to t_0$, showing the lemma.
Estimates for the solution uniform in parameter {#s.eftsuip}
===============================================
When comparing to the conventional Navier-Stokes equations, the regularised equations of (\[eq.NSpowif\]) contain a higher order viscosity term ${\mathit{\varDelta}}^m u$ multiplied by a small parameter $\varepsilon > 0$. Theorem \[t.exnonNS\] asserts that, given any data $f \in L^2 (I,S')$ and $u_0 \in H$, problem (\[eq.NSpowif\]) possesses at least one solution $u \in L^2 (I,S) \cap L^\infty (I,H)$ satisfying $u' \in L^1 (I,S')$. Moreover, if $m$ is large enough, to wit $m \geq (n+2)/4$, then this solution is unique. From now on we write $u_{\varepsilon}$ for this solution to point out its dependence upon $\varepsilon$. Our next concern will be the behaviour of $u_{\varepsilon}$ when $\varepsilon \to 0$. One might expect naively that the family $u_{\varepsilon}$ converges to a weak solution of the conventional equations. However, the problem under study is specified within the framework of singularly perturbed boundary value problems, let alone nonlinear, see [@GlebKiseTark18]. If $\varepsilon = 0$, then the order of the regularised Navier-Stokes equations in $x$ reduces to $2$. This corresponds to $m = 1$, in which case the condition $m \geq (n+2)/4$ is fulfilled only for small dimensions $n = 1$ and $n = 2$. While the existence of a weak solution $u \in L^2 ({\mathcal{C}},F^i)$ is still known for all $n > 2$, see [@Hopf51], there have been indirect plausible arguments showing that the solution fails to be unique. Hence, there seems to be no natural weak solution of the conventional Navier-Stokes equations to which the family $u_{\varepsilon}$ might converge. Perhaps the family has a number of accumulation points, each of them being a weak solution to the classical Navier-Stokes equations in certain sense. Whatever the case one needs a priori estimates for the solution $u_{\varepsilon}$ uniform in $\varepsilon$ to establish the existence of accumulation points in a weak topology.
\[l.aeuniie\] Let $m \geq (n+2)/4$. If $f \in L^2 (I,H)$, then the weak solution of Theorem \[t.exnonNS\] satisfies $$\begin{aligned}
\lefteqn{
\| u_{\varepsilon} (t) \|_H^2
+ 2 \nu
\int_0^t
e^{(1/c) (t-t')}
\big( \| A u_{\varepsilon} (t') \|_H^2 + \| A^\ast u_{\varepsilon} (t') \|_H^2 \big)
dt'
}
\\
& \leq &
e^{(1/c) t}\, \| u_0 \|_H^2
+ c
\int_0^t
e^{(1/c) (t-t')}\, \| f (t') \|_H^2 dt'
\hspace{1cm}\end{aligned}$$ for almost all $t \in I$, where $c$ is an arbitrary positive constant independent of $t$ and $\varepsilon$.
Since $u_{\varepsilon} \in L^2 (I,S)$, we can multiply both sides of (\[eq.NSpowif\]) by this section, obtaining $$(u_\varepsilon' (t),u_\varepsilon (t))
+ (V u_\varepsilon (t),u_\varepsilon (t))
+ (N (u_\varepsilon (t)),u_\varepsilon (t))
= (f (t),u_\varepsilon (t))$$ for almost all $t \in I$. Using the equality $
\partial_t \| u_\varepsilon (t) \|_H^2 = 2 \Re\, (u_\varepsilon' (t),u_\varepsilon (t)),
$ which is due to (\[eq.efN(u)iS\]), and $
(N (u_\varepsilon (t)),u_\varepsilon (t)) = 0
$ we get $$\begin{aligned}
\partial_t \| u_\varepsilon (t) \|_H^2
+ 2\, (V u_\varepsilon (t),u_\varepsilon (t))
& = &
2 \Re\, (f (t),u_\varepsilon (t))
\\
& \leq &
2\, \| f (t) \|_H \| u_\varepsilon (t) \|_H
\\
& \leq &
c\, \| f (t) \|_H^2 + \frac{1}{c}\, \| u_\varepsilon (t) \|_H^2\end{aligned}$$ a.e. on $I$, where $c$ is an arbitrary positive constant. On the other hand, one easily checks that $$\partial_t \| u_\varepsilon (t) \|_H^2 - \frac{1}{c}\, \| u_\varepsilon (t) \|_H^2
= e^{(1/c) t} \partial_t \big( e^{- (1/c) t} \| u_\varepsilon (t) \|_H^2 \big)$$ whence $$\partial_t \big( e^{- (1/c) t} \| u_\varepsilon (t) \|_H^2 \big)
+ 2 e^{- (1/c) t}\, (V u_\varepsilon (t),u_\varepsilon (t))
\leq
c e^{- (1/c) t}\, \| f (t) \|_H^2$$ a.e. on the interval $I$. Integrating this inequality from $0$ to $t$, where $t$ is a fixed point of $I$, we obtain $$\begin{aligned}
\lefteqn{
\| u_\varepsilon (t) \|_H^2
+ 2 \int_0^t e^{(1/c) (t-t')}\, (V u_\varepsilon (t'),u_\varepsilon (t')) dt'
}
\\
& \leq &
e^{(1/c) t}\, \| u_0 \|_H^2
+ c\, \int_0^t e^{(1/c) (t-t')}\, \| f (t') \|_H^2 dt'.
\hspace{1cm}\end{aligned}$$ As $$\begin{array}{rcl}
(V u_\varepsilon (t'),u_\varepsilon (t'))
& \geq &
(\nu\, {\mathit{\varDelta}}u_\varepsilon (t'),u_\varepsilon (t'))
\\
& \geq &
\nu \big( \| A u_{\varepsilon} (t') \|_H^2 + \| A^\ast u_{\varepsilon} (t') \|_H^2 \big),
\end{array}$$ the lemma follows.
Perhaps the choice $c = 1$ is optimal.
A uniqueness theorem for the conventional equations {#s.uniqthe}
===================================================
We now consider the unperturbed equations corresponding to $\varepsilon = 0$, which are the classical Navier-Stokes equations. Recall that $S^1$ stands for the closure of $\mathcal{S}$ in $H^1 ({\mathcal{X}},F^i)$. Given $f \in L^2 (I, S^1{}')$ and $u_0 \in H$, we look for $u \in L^\infty (I,H) \cap L^2 (I,S^1)$ satisfying $$\label{eq.conveNS}
\begin{array}{rclcl}
(u',v) + \nu ({\mathit{\varDelta}}u,v) + (N (u),v)
& =
& (f,v)
& \mbox{for all}
& v \in S^1 \cap L^n ({\mathcal{X}},F^i),
\\
u (0)
& =
& u_0
& \mbox{on}
& {\mathcal{X}}.
\end{array}$$
Note that the condition $u (0) = u_0$ is interpreted in the same way as in problem (\[eq.NSweakf\]). The additional condition $v \in S^1 \cap L^n ({\mathcal{X}},F^i)$ is used to make the trilinear form $(N (u,v),w)$ continuous on $S^1 \times S^1 \times (S^1 \cap L^n ({\mathcal{X}},F^i))$, cf. Lemma 6.1 of [@Lion69 p. 79].
By the above, there is at least one solution $u \in L^\infty (I,H) \cap L^2 (I,S^1)$ to problem (\[eq.conveNS\]). The question if this solution is unique remains still open. One may ask what additional conditions on $u$ guarantee its uniqueness. The following theorem is due to [@Lady70].
\[t.uniqcla\] The solution of (\[eq.conveNS\]) in $L^r (I,L^q ({\mathcal{X}},F^i))$, if exists, is unique, provided that $q > n$ and $$\frac{2}{r} + \frac{n}{q} \leq 1.$$
We consider the most interesting case where $2/r + n/q = 1$. Using the Hölder inequality, we get $$\label{eq.utHiqwg}
| (N (u,v),w) |
\leq
c\, \| u \|_{L^q ({\mathcal{X}},F^i)} \| v \|_{H^1 ({\mathcal{X}},F^i)} \| w \|_{L^s ({\mathcal{X}},F^i)}$$ where $1/q + 1/s = 1/2$. On the other hand, if $\phi$ is a function with scalar values, then $$\| \phi \|_{L^s ({\mathcal{X}})}
\leq
\| \phi \|_{L^2 ({\mathcal{X}})}^{2/r} \| \phi \|_{L^{2n/(n-2)} ({\mathcal{X}})}^{n/q},$$ for $$\frac{1}{s} = \frac{2/r}{2} + \frac{n/q}{2n/(n-2)}.$$ We have used here the inequality $
\| \phi \|_{L^s ({\mathcal{X}})}
\leq
\| \phi \|_{L^{s_1 p} ({\mathcal{X}})}^{s_1/s} \| \phi \|_{L^{s_2 p'} ({\mathcal{X}})}^{s_2/s},
$ where $p'$ is the dual exponent for $p$ and $s_1 + s_2 = s$. Since $H^1_0 ({\mathcal{X}},F^i) \hookrightarrow L^{2n/(n-1)} ({\mathcal{X}},F^i)$, it follows that $$\| w \|_{L^s ({\mathcal{X}},F^i)}
\leq
c\, \| w \|_{L^2 ({\mathcal{X}},F^i)}^{2/r} \| w \|_{H^1 ({\mathcal{X}},F^i)}^{n/q}$$ with $c$ a constant independent of $w$ and different in diverse applications. Hence, (\[eq.utHiqwg\]) implies that $$\label{eq.utHiwgc}
| (N (u,v),w) |
\leq
c\,
\| u \|_{L^q ({\mathcal{X}},F^i)}
\| v \|_{H^1 ({\mathcal{X}},F^i)}
\| w \|_{H}^{2/r}
\| w \|_{H^1 ({\mathcal{X}},F^i)}^{n/q}.$$
Our next objective is to show that if $u$ is a solution of problem (\[eq.NSweakf\]), satisfying $u \in L^r (I,L^q ({\mathcal{X}},F^i))$ with $q > n$ and $2/r + n/q \leq 1$, then $u' \in L^2 (I,S^1{}')$. Indeed, from (\[eq.utHiwgc\]) it follows that $$\begin{aligned}
| (N (u),v) |
& = &
| - (N (u,v),u) |
\\
\| u \|_{H}^{2/r}
\| u \|_{H^1 ({\mathcal{X}},F^i)}^{n/q}
\\
\| u \|_{H^1 ({\mathcal{X}},F^i)}^{n/q},\end{aligned}$$ for the norm $\| u \|_H$ is bounded uniformly in $u$. Since the function $t \mapsto \| u (t) \|_{L^q ({\mathcal{X}},F^i)}$ belongs to $L^r (I)$ and the function $t \mapsto \| u (t) \|_{H^1 ({\mathcal{X}},F^i)}^{n/q}$ belongs to $L^{2q/n} (I)$, we see that their product $$t \mapsto \| u (t) \|_{L^q ({\mathcal{X}},F^i)} \| u (t) \|_{H^1 ({\mathcal{X}},F^i)}^{n/q}$$ belongs to $L^2 (I)$. By the Riesz representation theorem, the section $t \in N (u (t))$ is of class $L^2 (I,S^1{}')$. Hence it follows that $u' = f - \nu {\mathit{\varDelta}}u - N (u)$ belongs to $L^2 (I,S^1{}')$, as desired.
In particular, on applying Lemma \[l.interLM\] we conclude that the mapping $u : I \to H$ is continuous.
Having disposed of this preliminary step, we can now establish the uniqueness of the solution $u$. Suppose that $u_1$ and $u_2$ be two solutions of problem (\[eq.NSweakf\]) of class $L^r (I,L^q ({\mathcal{X}},F^i))$, where $q > n$ and $2/r + n/q \leq 1$. Write $u = u_1 - u_2$. Then we obtain $$(u',v) + \nu\, ({\mathit{\varDelta}}u,v) + (N (u,u_1),v) + (N (u_1,u),v) - (N (u),v) = 0$$ for all $v \in S^1 \cap L^n ({\mathcal{X}},F^i)$. On substituting $u$ for the test section $v$ (which is allowed, for $u' \in L^2 (I,S^1{}')$) we get $$\begin{aligned}
\frac{1}{2} \partial_t \| u (t) \|_H^2 + \nu\, ({\mathit{\varDelta}}u (t),u (t))
& = &
-\, \Re\, (N (u (t),u_1 (t)),u (t))
\\
& = &
\Re\, (N (u (t)),u_1 (t))\end{aligned}$$ for almost all $t \in I$.
Using a version of inequality (\[eq.utHiwgc\]) yields $$| (N (u (t)),u_1 (t)) |
\leq
c\,
\| u_1 (t) \|_{L^q ({\mathcal{X}},F^i)}
\| u (t) \|_{H}^{2/r}
\| u (t) \|_{H^1 ({\mathcal{X}},F^i)}^{n/q + 1}$$ where $c$ is a constant independent of both $u_1$, $u_2$ and $t$. Set $$a (t) = \| u_1 (t) \|_{L^q ({\mathcal{X}},F^i)}^r,$$ then $a \in L^1 (I)$ and $$\begin{aligned}
| (N (u (t)),u_1 (t)) |
& \leq &
c\,
(a (t))^{1/r}
\| u (t) \|_{H}^{2/r}
\| u (t) \|_{H^1 ({\mathcal{X}},F^i)}^{n/q + 1}
\\
& \leq &
\Big( c C (a (t))^{1/r} \| u (t) \|_{H}^{2/r} \Big)
\Big( \frac{1}{C}\, \| u (t) \|_{H^1 ({\mathcal{X}},F^i)}^{n/q + 1} \Big),\end{aligned}$$ where $C$ is an arbitrary positive constant to be determined. By Young’s inequality for the product we obtain $$| (N (u (t)),u_1 (t)) |
\leq
\frac{(c C)^r}{r}\, a (t) \| u (t) \|_{H}^2
+ \frac{1}{r' C^{r'}}\, \| u (t) \|_{H^1 ({\mathcal{X}},F^i)}^2$$ where $r' = r/(r-1)$ is the dual exponent for $r$. We have used here the inequality $2/r + n/q \leq 1$.
On summarising we deduce that $$\begin{aligned}
\lefteqn{
\frac{1}{2} \partial_t \| u (t) \|_H^2
+ \nu\, (({\mathit{\varDelta}}+ {I}) u (t),u (t))
- \frac{1}{r' C^{r'}}\, \| u (t) \|_{H^1 ({\mathcal{X}},F^i)}^2
}
\\
& \leq &
\Big( \frac{(c C)^r}{r}\, a (t) + \nu \Big) \| u (t) \|_H^2
\hspace{3cm}\end{aligned}$$ for almost all $t \in I$. Since the Dirichlet problem for the differential operator ${\mathit{\varDelta}}+ {I}$ is elliptic, there is a sufficiently large constant $C > 0$ independent of $u$ and $t \in I$, such that $$\nu\, (({\mathit{\varDelta}}+ {I}) u (t),u (t))
\geq
\frac{1}{r' C^{r'}}\, \| u (t) \|_{H^1 ({\mathcal{X}},F^i)}^2.$$ It follows that $$\frac{1}{2} \partial_t \| u (t) \|_H^2
\leq
\Big( \frac{(c C)^r}{r}\, a (t) + \nu \Big) \| u (t) \|_H^2$$ for alsmost all $t \in I$. Since $u (0) = 0$, on arguing as in the proof of Theorem \[t.uniqrNS\] we see that $u \equiv 0$, as desired.
Limit to the conventional Navier-Stokes equations {#s.lttcNSe}
=================================================
In this section we establish that the weak solution $u_\varepsilon \in C (\overline{I},H) \cap L^2 (I,S)$ to the regularised Navier-Stokes equations has a strong limit to a weak solution to the Navier-Stokes equations. We will consider a limit passage for the weak solution of problem (\[eq.NSweakf\]) whose existence and uniqueness have been proved in Theorems \[t.exnonNS\] and \[t.uniqrNS\].
By Theorem \[t.regtfNS\], if $f \in L^2 (I,H)$ and $u_0 \in S$, then the unique solution $u_\varepsilon$ of problem (\[eq.NSweakf\]) belongs to the space $u_\varepsilon \in L^2 (I,{\mathcal{D}}_V)$. Since $m \geq (n+2)/4$ is greater than $n/4$, we conclude by the Sobolev embedding theorem that ${\mathcal{D}}_V \hookrightarrow C ({\mathcal{X}},F^i)$. Therefore, Theorem \[t.uniqcla\] implies that the family $u_\varepsilon$ belongs to a uniqueness class for problem (\[eq.conveNS\]). However, the family need not be bounded in this class uniformly in $\varepsilon$.
On the other hand, Lemma \[l.aeuniie\] shows that the family $u_\varepsilon$ is bounded uniformly in $\varepsilon$ both in $L^\infty (I,L^2 ({\mathcal{X}},F^i))$ and $L^2 (I,H^1 ({\mathcal{X}},F^i))$. By Theorem \[t.uniqcla\], the former space is a uniqueness class for the conventional problem, if $n \leq 2$, while the second one is such merely for $n < 2$. More generally, on combining Theorem \[t.uniqcla\] with the Sobolev embedding theorem we see that $L^2 (I,H^m ({\mathcal{X}},F^i))$ is a uniqueness class for problem (\[eq.conveNS\]), provided that $m > n/2$. Although the latter condition is stronger than $m \geq (n+2)/4$, the authors find the boundedness of the family $u_\varepsilon$ in $L^2 (I,H^m ({\mathcal{X}},F^i))$ an optimal condition for the singular perturbation under consideration.
\[t.lttcNSe\] Suppose $m > n/2$. Let $u_\varepsilon$ be the weak solution of problem (\[eq.NSweakf\]) given by Theorem \[t.regtfNS\] with $f \in L^2 (I,H)$ and $u_0 \in S$. If the family $u_\varepsilon$ is bounded uniformly in $\varepsilon$ in $L^2 (I,H^m ({\mathcal{X}},F^i))$, then it approaches the unique weak solution $u$ to the conventional problem of (\[eq.conveNS\]) in the norm of $L^\infty (I,H) \cap L^2 (I,S^1)$ and weakly in $L^2 (I, S)$.
We first estimate the difference $u_\varepsilon - u_\delta$ for any positive $\delta$ and $\varepsilon$. To be specific, consider $0 < \delta < \varepsilon$.
By Theorem \[t.regtfNS\], the difference $u_\varepsilon - u_\delta$ belongs to $C (\overline{I},H) \cap L^2 (I,{\mathcal{D}}_V)$ and vanishes at $t = 0$. Moreover, on subtracting equality (\[eq.NSpowif\]) for $u_\delta$ from that for $u_\varepsilon$ we obtain $$(u_\varepsilon - u_\delta)'
+ \left( \varepsilon {\mathit{\varDelta}}^m u_{\varepsilon} - \delta {\mathit{\varDelta}}^m u_{\delta} \right)
+ \nu {\mathit{\varDelta}}(u_\varepsilon - u_\delta)
+ \left( N (u_{\varepsilon}) - N (u_{\delta}) \right)
=
0$$ a.e. on $I$.
In order to find appropriate estimates for the difference $u_\varepsilon - u_\delta$ we take the duality pairing of the latter equality with the special test section $v (t) = u_\varepsilon (t) - u_\delta (t)$, and integrate it from $0$ to $t$ for arbitrary fixed $t \in I$. A trivial verification leads to the equality $$\begin{aligned}
\lefteqn{
\int_0^t ((u_\varepsilon - u_\delta)', v) dt'
+ \varepsilon \int_0^t ({\mathit{\varDelta}}^m (u_\varepsilon - u_\delta), v) dt'
+ \nu \int_0^t ({\mathit{\varDelta}}(u_\varepsilon - u_\delta), v) dt'
}
\\
& = &
-\,
(\varepsilon - \delta) \int_0^t ({\mathit{\varDelta}}^m u_\delta, v) dt'
- \int_0^t (N (u_\varepsilon) - N (u_\delta), v) dt'
\hspace{2cm}\end{aligned}$$ which is valid for all $t \in I$. Since $$\begin{aligned}
\Re\, ((u_\varepsilon - u_\delta)', u_\varepsilon - u_\delta)
& = &
\frac{1}{2} \frac{\partial}{\partial t'}\, \| u_\varepsilon - u_\delta \|_H^2,
\\
({\mathit{\varDelta}}^m (u_\varepsilon - u_\delta), u_\varepsilon - u_\delta)
& = &
\| {\mathit{\varDelta}}^{m/2} (u_\varepsilon - u_\delta) \|_H^2,
\\
({\mathit{\varDelta}}^m u_\delta, u_\varepsilon - u_\delta)
& = &
({\mathit{\varDelta}}^{m/2} u_\delta, {\mathit{\varDelta}}^{m/2} (u_\varepsilon - u_\delta))\end{aligned}$$ and $$\begin{aligned}
\lefteqn{
\left( N (u_{\varepsilon}) - N (u_{\delta}), u_{\varepsilon} - u_{\delta} \right)
}
\\
& = &
\left( N (u_{\varepsilon} - u_{\delta}, u_{\varepsilon})
+ N (u_{\delta}, u_{\varepsilon})
- N (u_{\delta}, u_{\delta} - u_{\varepsilon})
- N (u_{\delta}, u_{\varepsilon}),
u_{\varepsilon} - u_{\delta}
\right)
\\
& = &
\left( N (u_{\varepsilon} - u_{\delta}, u_{\varepsilon})
+ N (u_{\delta}, u_{\varepsilon} - u_{\delta}), u_{\varepsilon} - u_{\delta}
\right)
\\
& = &
-\,
\left( N (u_{\varepsilon} - u_{\delta}), u_{\varepsilon} \right)\end{aligned}$$ a.e. on $I$, the last equality being a consequence of Corollary \[c.algestr\], we arrive at the equality $$\begin{aligned}
\label{eq.coteieq}
\lefteqn{
\frac{1}{2}\, \| u_\varepsilon (t) - u_\delta (t) \|_H^2
+ \varepsilon \int_0^t \| {\mathit{\varDelta}}^{m/2} (u_\varepsilon - u_\delta) \|_H^2 dt'
+ \nu \int_0^t \| {\mathit{\varDelta}}^{1/2} (u_\varepsilon - u_\delta) \|_H^2 dt'
}
\nonumber
\\
\!\! & \!\! = \!\! & \!\!
-\,
(\varepsilon - \delta)\, \Re \int_0^t ({\mathit{\varDelta}}^{m/2} u_\delta, {\mathit{\varDelta}}^{m/2} (u_\varepsilon - u_\delta)) dt'
+ \Re \int_0^t \left( N (u_{\varepsilon} - u_{\delta}), u_{\varepsilon} \right) dt'
\nonumber
\\\end{aligned}$$ for almost all $t \in I$. Here, we write $
\| {\mathit{\varDelta}}^{1/2} v \|_H^2
= \| Av \|_H^2 + \| A^\ast v \|_H^2
$ to shorten notation.
Using the inequality $
\displaystyle
a b \leq \frac{c}{2} a^2 + \frac{1}{2c} b^2
$ with $
\displaystyle
c = \frac{1}{2}
$ we estimate the first term on the right-hand side of (\[eq.coteieq\]) by $$\begin{aligned}
\lefteqn{
\Big|
-\,
(\varepsilon - \delta)\, \Re \int_0^t ({\mathit{\varDelta}}^{m/2} u_\delta, {\mathit{\varDelta}}^{m/2} (u_\varepsilon - u_\delta)) dt'
\Big|
}
\\
& \leq &
\frac{\varepsilon-\delta}{4}
\int_0^t \| {\mathit{\varDelta}}^{m/2} u_\delta \|_H^2 dt'
+ (\varepsilon-\delta)
\int_0^t \| {\mathit{\varDelta}}^{m/2} (u_\varepsilon - u_\delta) \|_H^2 dt'\end{aligned}$$ for all $t \in I$.
In order to estimate the second term on the right-hand side of (\[eq.coteieq\]), we apply inequality (\[eq.utHiqwg\]) with $q = 2$ and $s = \infty$. Namely, there is a constant $c$ independent of $\delta$ and $\varepsilon$, such that $$| (N (u_{\varepsilon} - u_{\delta}), u_{\varepsilon}) |
\leq
c\,
\| u_{\varepsilon} - u_{\delta} \|_{L^2 ({\mathcal{X}},F^i)}
\| u_{\varepsilon} - u_{\delta} \|_{H^1 ({\mathcal{X}},F^i)}
\| u_{\varepsilon} \|_{L^\infty ({\mathcal{X}},F^i)}$$ a.e. on $I$ for all $\delta$ and $\varepsilon$. As the Dirichlet prolem for the Laplacian ${\mathit{\varDelta}}$ is elliptic, it follows that $$\| u_{\varepsilon} - u_{\delta} \|_{H^1 ({\mathcal{X}},F^i)}^2
\leq
C\,
\Big( \| {\mathit{\varDelta}}^{1/2} (u_{\varepsilon} - u_{\delta}) \|_{L^2 ({\mathcal{X}},F^i)}^2
+ \| u_{\varepsilon} - u_{\delta} \|_{L^2 ({\mathcal{X}},F^i)}^2 \Big)$$ with $C$ a constant independent of $\delta$, $\varepsilon$ and $t \in I$. Hence, on arguing as above we obtain $$\begin{aligned}
\lefteqn{
\Big| \Re \int_0^t \left( N (u_{\varepsilon} - u_{\delta}), u_{\varepsilon} \right) dt'
\Big|
}
\\
& \leq &
\frac{c}{2}
\int_0^t
\Big( \Big( \frac{1}{C'} \| u_\varepsilon - u_\delta \|_{H^1 ({\mathcal{X}},F^i)}^2 \Big)^2
+ \Big( C' \| u_\varepsilon \|_{L^\infty ({\mathcal{X}},F^i)} \| u_\varepsilon - u_\delta \|_H \Big)^2
\Big)
dt'
\\
& \leq &
\frac{\nu}{2}
\int_0^t \| {\mathit{\varDelta}}^{1/2} (u_\varepsilon - u_\delta) \|_H^2 dt'
+ \int_0^t
\Big( \frac{\nu}{2} + \frac{c}{2} \frac{C c}{\nu} \| u_\varepsilon \|_{L^\infty ({\mathcal{X}},F^i)}^2 \Big)
\| u_\varepsilon - u_\delta \|_H^2
dt',\end{aligned}$$ where $
\displaystyle
(C')^2 = \frac{C c}{\nu}.
$
Substituting these estimates into (\[eq.coteieq\]) yields $$\begin{aligned}
\lefteqn{
\| u_\varepsilon (t) - u_\delta (t) \|_H^2
+ 2 \delta \int_0^t \| {\mathit{\varDelta}}^{m/2} (u_\varepsilon - u_\delta) \|_H^2 dt'
+ \nu \int_0^t \| {\mathit{\varDelta}}^{1/2} (u_\varepsilon - u_\delta) \|_H^2 dt'
}
\nonumber
\\
& \leq &
\frac{\varepsilon - \delta}{2}
\int_0^t \| {\mathit{\varDelta}}^{m/2} u_\delta \|_H^2 dt'
+ \int_0^t
\Big( \nu + c \frac{C c}{\nu} \| u_\varepsilon \|_{L^\infty ({\mathcal{X}},F^i)}^2 \Big)
\| u_\varepsilon - u_\delta \|_H^2
dt'\end{aligned}$$ for all $t \in I$. We now apply the Gronwall inequality for continuous functions (\[eq.Gronwall\]) to obtain $$\| u_\varepsilon (t) - u_\delta (t) \|_H^2
\leq
\frac{\varepsilon - \delta}{2}
\int_0^t \| {\mathit{\varDelta}}^{m/2} u_\delta \|_H^2 dt'\,
\exp
\int_0^t \Big( \nu + c \frac{C c}{\nu} \| u_\varepsilon \|_{L^\infty ({\mathcal{X}},F^i)}^2 \Big)
dt'$$ for all $t \in I$. By assumption, the family $u_\varepsilon$ is bounded in $L^2 (I,H^m ({\mathcal{X}},F^i))$ uniformly in the parameter $\varepsilon$. Therefore, there is a constant $B$ with the property that $$\begin{aligned}
\int_0^t \| {\mathit{\varDelta}}^{m/2} u_\delta (t') \|_H^2 dt'
& \leq &
c' \int_0^T \| u_\delta (t') \|_{H^m ({\mathcal{X}},F^i)}^2 dt'
\\
& \leq &
B\end{aligned}$$ for all $t \in I$ and $\delta > 0$. Furthermore, since $m > n/2$, we deduce from the Sobolev embedding theorem that $$\begin{aligned}
\int_0^t \Big( \nu + c \frac{C c}{\nu} \| u_\varepsilon (t') \|_{L^\infty ({\mathcal{X}},F^i)}^2 \Big) dt'
& \leq &
\nu T + c' c \frac{C c}{\nu} \int_0^T \| u_\varepsilon (t') \|_{H^m ({\mathcal{X}},F^i)}^2 dt'
\\
& \leq &
A\end{aligned}$$ for all $t \in I$ and $\varepsilon > 0$, where $A$ is a constant independent of $t$ and $\varepsilon$. It follows that $$\begin{aligned}
\label{eq.coteieqe}
\sup_{t \in I} \| u_\varepsilon (t) - u_\delta (t) \|_H^2
+ \nu \int_0^T \| {\mathit{\varDelta}}^{1/2} (u_\varepsilon - u_\delta) \|_H^2 dt'
& \leq &
\frac{B}{2}\, \Big( 1 + A \exp A \Big)\,
|\varepsilon - \delta|
\nonumber
\\\end{aligned}$$ whenever $\delta, \varepsilon > 0$.
Estimate (\[eq.coteieqe\]) shows that $u_{\varepsilon}$ is a uniformly continuous function of parameter $\varepsilon > 0$ with values in both $L^\infty (I, L^2 ({\mathcal{X}},F^i))$ and $L^2 (I, H^1 ({\mathcal{X}},F^i))$. Since these are Banach spaces, $u_\varepsilon$ converges in both the spaces to a section $u$ which lies in $L^\infty (I, L^2 ({\mathcal{X}},F^i))$ and $L^2 (I, H^1 ({\mathcal{X}},F^i))$, as $\varepsilon \to 0$. Moreover, the limit $u$ belongs to $L^2 (I,H^m ({\mathcal{X}},F^i))$, for the family $u_\varepsilon$ is bounded in $L^2 (I,H^m ({\mathcal{X}},F^i))$ uniformly in $\varepsilon$ and so it contains a subsequence $u_{\varepsilon_k}$ which converges in the weak topology of this space to $u$.
It remains to show that $u$ is a solution of the conventional Navier-Stokes equations with initial data $u_0$ and zero Dirichlet data on the lateral boundary of ${\mathcal{C}}$. Since $\mathcal{S}$ lies dense in $S^1 \cap L^n ({\mathcal{X}},F^i)$, it suffices to prove the first equality of (\[eq.conveNS\]) for all $v \in \mathcal{S}$.
Let $v \in \mathcal{S}$. Since $u_\varepsilon$ is a solution of the regularised Navier-Stokes equations, we get $$\begin{aligned}
\lefteqn{
\Big( (u_\varepsilon (t), v) - (u_0, v) \Big)
+ \nu \int_0^t ({\mathit{\varDelta}}^{1/2} u_\varepsilon (t'), {\mathit{\varDelta}}^{1/2} v) dt'
}
\\
& = &
\int_0^t (f (t'), v) dt'
- \varepsilon \int_0^t ({\mathit{\varDelta}}^{m/2} u_\varepsilon (t'), {\mathit{\varDelta}}^{m/2} v) dt'
- \int_0^t (N (u_\varepsilon (t')), v) dt'\end{aligned}$$ for all $t \in I$. The second summand on the right-hand side converges to zero, for the family $u_\varepsilon$ in bounded uniformly in $\varepsilon$ in the space $L^2 (I,H^m ({\mathcal{X}},F^i))$. On the other hand, $$\int_0^t (N (u_\varepsilon (t')), v) dt' \to \int_0^t (N (u (t')), v) dt'$$ as $\varepsilon \to 0$, which is due to Lemma \[l.ptlfnlt\]. Hence, letting $\varepsilon \to 0$ in the above equality yields $$\label{eq.yeati0t}
\Big( \! (u (t), v) - (u_0, v) \! \Big)
+ \nu \! \int_0^t \! ({\mathit{\varDelta}}^{1/2} u (t'), {\mathit{\varDelta}}^{1/2} v) dt'
+ \! \int_0^t \! (N (u (t')), v) dt'
= \! \int_0^t \! (f (t'), v) dt'$$ for almost all $t \in I$. Since the integrands in (\[eq.yeati0t\]) are integrable functions of $t' \in I$, we may differentiate this equality in $t$, thus achieving $$(u' (t), v))
+ \nu\, ({\mathit{\varDelta}}^{1/2} u (t), {\mathit{\varDelta}}^{1/2} v)
+ (N (u (t)), v)
= (f (t), v)$$ for almost all $t \in I$ and all $v \in S^1$. As $u \in L^\infty (I,H) \cap L^2 (I,S^1)$, we establish as in Section \[s.exiweak\] that $u$ coincides with a continuous function of $t \in [0,T]$ with values in $H$. Hence, yet another consequence of (\[eq.yeati0t\]) is that $u (0) = u_0$, and so $u$ is a solution of (\[eq.conveNS\]), as desired.
As mentioned, problem (\[eq.NSweakf\]) is a singular perturbation of the conventional Navier-Stokes equations. Hence, its solution need not converge to a solution of the conventional problem in any strong topology even if this latter is unique. For instance, the family $
u_\varepsilon (t) = (u_0 - 1) \exp (-t/\varepsilon) + 1
$ of solutions to the singularly perturbed initial problem $$\begin{array}{rclcl}
\varepsilon u' + u
& =
& 1
& \mbox{for $t \in I$},
\\
u (0)
& =
& u_0
&
\end{array}$$ converges to the solution of the unperturbed equation $u = 1$ uniformly on $\overline{I}$ if and only if $u_0 = 1$.
*Acknowledgments* The authors are greatly indebted to Prof. A. Feldmeier for helpful comments concerning the von Neumann-Richtmyer artificial viscosity in numerical simulations with second order partial differential equations. The first author gratefully acknowledges the financial support of the Russian Federation Government for scientific research under the supervision of leading scientist at the Siberian Federal University, contract N 14.Y26.31.0006, and the Alexander von Humboldt Foundation.
Appendix {#l.appendix .unnumbered}
========
The following lemma is needed to obtain the weak form of the singularly perturbed Navier-Stokes equations satisfied by the weak solution. This lemma is also used to describe the behaviour of the solution of the regularised equations as $\varepsilon \to 0+$.
**Lemma** *Suppose $m \geq (n+2)/4$. Let $\{ u_k \}$ be a sequence of sections of $F^i$ over ${\mathcal{C}}$ which converges in the weak\* topology of $L^\infty (I,H)$, weakly in $L^2 (I,S)$ and strongly in $L^2 (I,H)$. Then $$\begin{aligned}
\lim_{k \to \infty} \int_0^T (u_k (t), v' (t))\, dt
& = &
\int_0^T (u (t), v' (t))\, dt,
\\
\lim_{k \to \infty} \int_0^T ({\mathit{\varDelta}}^{m/2} u_k (t), {\mathit{\varDelta}}^{m/2} v (t))\, dt
& = &
\int_0^T ({\mathit{\varDelta}}^{m/2} u (t), {\mathit{\varDelta}}^{m/2} v (t))\, dt,
\\
\lim_{k \to \infty} \int_0^T (N (u_k (t)), v (t))\, dt
& = &
\int_0^T (N (u (t)), v (t))\, dt\end{aligned}$$ for all sections $v \in C (\overline{I},S)$ satisfying $v' \in L^2 (I,H)$.*
The first equality follows from the facts that $u_k \to u$ strongly in $L^2 (I,H)$ and $v' \in L^2 (I,H)$.
To prove the second equality we use the fact that $u_k \to u$ in the weak topology of $L^2 (I,S)$. That is, $$\lim_{k \to \infty} \int_0^T (u_k - u, w) dt = 0$$ for all $w \in L^2 (I,S')$. On the other hand, the operator ${\mathit{\varDelta}}^m$ maps $S$ continuously into $S'$. Hence it follows that $$\begin{aligned}
\int_0^T ({\mathit{\varDelta}}^{m/2} u_k (t), {\mathit{\varDelta}}^{m/2} v (t))
& = &
\int_0^T (u_k (t), {\mathit{\varDelta}}^m v (t)) dt
\\
& \to &
\int_0^T (u (t), {\mathit{\varDelta}}^{m} v (t)) dt
\\
& = &
\int_0^T ({\mathit{\varDelta}}^{m/2} u (t), {\mathit{\varDelta}}^{m/2} v (t)) dt,\end{aligned}$$ as desired.
Finally, in order to show the last equality of the lemma we observe that the difference $$\int_0^T (N (u_k (t)), v (t))\, dt - \int_0^T (N (u (t)), v (t))\, dt$$ just amounts to $$\int_0^T (N (u_k (t) - u (t), u_k (t)), v (t))\, dt
+ \int_0^T (N (u (t), u_k (t) - u (t)), v (t))\, dt.$$ Consider the first integral and recall the estimate of the trilinear form given by Lemma \[l.totnwst\]. Since $v \in C (\overline{I},S)$, we get $$\begin{aligned}
\lefteqn{
\big| \int_0^T (N (u_k - u, u_k), v)\, dt \big|
}
\\
& \leq &
c
\int_0^T
\| u_k - u \|_H^{1/2} D (u_k - u)^{1/4} \| u_k \|_H^{1/2} D (u_k)^{1/4} D (v)^{1/2}
dt
\\
& \leq &
c
\Big( \int_0^T \| u_k - u \|_H D (u_k - u)^{1/2} dt \Big)^{1/2}
\Big( \int_0^T \| u_k \|_H D (u_k)^{1/2} dt \Big)^{1/2}
\\
& \leq &
c
\Big( \| u_k - u \|_{L^2 (I,H)} \| u_k - u \|_{L^2 (I,S)} \Big)^{1/2}
\Big( \| u_k \|_{L^2 (I,H)} \| u_k \|_{L^2 (I,S)} \Big)^{1/2},\end{aligned}$$ where $c$ stands for a constant independent of $k$ and different in diverse applications. Since $u_k \in L^2 (I,S)$ and $u_k \to u$ in the norm of $L^2 (I,H)$, the right-hand side converges to zero, as $k \to \infty$. Convergence arguments for the second integral are similar.
[XXXXXX]{}
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When you are in the process of selecting an architect, it is important to know what to look for in order to make sure that the architectural professional you hire has experience and skills that can meet the needs of your particular project. As you are doing your research to choose an architect, there are a few things that you will need to keep in mind when looking for the right professional. This article will discuss some of the things that you should be looking for when choosing an architect.
Credentials Of The Architectural Specialist
source: archiadvisor.com
The first thing that you will need to do is research the credentials of the architectural specialist that you are considering hiring. In order to do this, you should contact the offices of several architecture firms that you are interested in working with. When you contact the offices of the architects, ask them about the experience and skill level that each of their clients have.
Experiences And Skill Level
In addition to looking at the experiences and skill level that each of the architectural specialists has, you will also want to do some research on the architectural firm in general. You will want to contact several offices in order to find the best one that meets your specific needs. One way that you will know whether a certain firm is worth working with is by contacting them and asking for information about how they handle projects. If you feel that they are not being responsive to any questions or concerns that you may have, then you will want to consider another firm.
Go Online And Search For Review Of Specific Firm
source: ucl.ac.uk
You should go online and search for reviews of specific firms. There are several different websites that offer reviews on architectural firms. You should be able to locate these sites fairly easily through your search engine.
Choose The One You Feel Comfortable With
Once you have researched a number of firms and have selected the one that you feel most comfortable with, you will want to talk with the architectural consultant that you are considering to learn more about his or her work. Make sure that you talk with each of the representatives that you meet so that you can get a good idea of what types of projects he or she has done.
Look At Firms Portfolio
source: propertyupdate.com.au
In addition to looking at the firm’s portfolio, you should also ask the consultant questions about his or her career history. If you know enough about an architectural professional to ask any questions that you are not sure of, this can help you get a good feeling of their knowledge and experience.
Check If He/She Is Licensed And Bonded
Another thing that you will want to keep in mind when choosing an architectural expert is to check to make sure that he or she is licensed and bonded. in your state. Many people that own architectural firms will not be licensed to practice in your area. You should make sure that the person you hire has this kind of license so that he or she can legally carry out all of the duties that are necessary to finish your project on time and within any guidelines that are set forth by your city or state.
Look Into The Reputation Of The Architectural Expert And Request Referral From Current Client
source: architectureforlondon.com
Finally, you will want to look into the reputation of the architectural expert when you are looking for someone to hire. Before you choose an architectural expert, you will want to make sure that you are choosing someone that has a good reputation. You can research this reputation by checking online as well as in print for reviews that are made by past clients of the firm. You can also request referrals from current clients as well.
Conclusion
When you are looking for an architect to design your project, you will want to be aware of the following things: the credentials that the firm that you hire has, the experience that the firm has, the reputation that the firm has, and the reputation that the firm has. You should be looking at all of these things before you finalize your decision so that you can be confident that you are making the best possible choice when it comes to hiring an architect. | https://thearchitecturedesigns.com/what-to-look-for-when-choosing-an-architectural-specialist/ |
It appears there are a number of cities and towns in the US with holiday type names, so how about a little trivia where the name is the same when it comes to holidays?
Probably the most recognized Christmas related town name is Bethlehem, and in the US there are (reportedly) eight to 12. I’ve discovered 9 of them: Bethlehem, CT; Bethlehem, GA; Bethlehem, IN; Bethlehem, KY, Bethlehem, MD; Bethlehem, MS; Bethlehem, NH; Bethlehem, PA; Bethlehem, WV, with Bethlehem, PA being the most prominently known.
It was on Christmas eve in 1741, when a group of Moravians founded the mission community of Bethlehem, which proved to be a town for the future when in 1762 it built the “first-water works in America to pump water for public use.”
After the Civil War Bethlehem became a city, and a center for heavy industry and trade during the industrial revolution, thus Bethlehem Steel Corporation was founded, becoming the 2nd largest steel producer in the US, and was also one of the largest shipbuilding companies in the world. Unfortunately they ceased their operations in 1995, after about 140 years of being in business.
Could it be the result of a grand ceremony on December 7, 1937, during the Great Depression, when the wife of Bethlehem Steel Corporation President, Charles F. Brown, flipped on the switch to turn on the new Christmas street lights and a large wooden star [that the city of Bethlehem still beckons visitors]? It was also at this time the Chamber of Commerce adopted the nickname ‘Christmas City, USA’. Today, that wooden star when lit up can be seen as far as Wind Gap, 20 miles away.
Bethlehem is also home to three large universities, including Lehigh University, and Money Magazine listed it at number 88 out of 100 ‘best cities to live’ . . . | https://www.bookroomsnow.com/get-packin/2013/12/ |
Railways around Peterborough and The National Rail Network and Heritage railways in the UK.
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UK National railway
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ukrailways1970tilltoday.me.uk
Wagons At The Nene valley Railway
Mainline ZBA DB972206
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The Nene Valley Railway
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Heritage Railways
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12T Mainline ZBA DB972206 at the Nene Valley Peterborough station.
This wagon was in the bay platform at the Nene Valley Railways Peterborough station that day. This wagon was one of two mainline ZBA wagons ZBA DB97584 being the other wagon.
Below are a links to lists of some of the wagons also saved at
Updated 27/11/2014
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This website is Ukrailways1970tilltoday.me.uk it is a webe site on railways, but it is not just on trains, but all things railways, with photos, which I have taken from the 1970s till now. I take photos of all things railways, steam diesel and electric trains, wagons like this page, any thing that is on the National Rail network, which was BR when I started taken photos.
Today EWS, East Coast, Central trains and EWS are just some of the names on the trains. The name on the train does not mean, thats whos train it is these days. These names keep changing, but that means I have to keep taking photos. I also take photos of preserved railways with steam diesel and electric trains.There is lots more to add and I keep taking More! | http://ukrailways1970tilltoday.me.uk/wagons_Mainline_ZBA_DB972206.html |
Metaglossary.com - Definitions for "market index"
A statistical composite of representative stocks. The Dow Jones Industrial Average, the Standard & Poor's 500, and the Nasdaq Composite are the three most widely quoted.
Measures the current price behavior of a sample of stocks in relation to a base period established for a previous time. (See Index).
Market measure that consists of weighted values of the components that make up certain list of companies. A stock market tracks the performance of certain stocks by weighting them according to their prices and the number of outstanding shares by a particular formula.
A market index measures changes in the value of a specific group of stocks, bonds, or other investments that it tracks from a specific starting point, which may be as recent as the previous day or some date in the past. An index may be broad, encompassing a large number of stocks or bonds, or quite narrow, including only a limited number.
A composite of stocks reflecting the market such as Toronto Stock Exchange 300 Composite Index (TSE 300) or the Dow Jones.
An index such as the FTSE-All Share has a base of 100, or more usually 1000, at a fixed moment in time. For the FTSE, this is January 3rd, 1984. Firms are sometimes given weightings in the index according to their market capitalisation. The index gives the percentage rise or fall in value of the market over the relevant timescale.
a measurement of the performance of a specific "basket" of stocks considered to represent a particular market or sector of the U.S. stock market or the economy. For example, the Dow Jones Industrial Average (DJIA) is an index of 30 "blue chip" U.S. stocks of industrial companies (excluding transportation and utility companies).
the current price behavior of a group of stocks that are representative of part of all the stock market in relation to a previous time period known as the base period. Index numbers are relative numbers rather than averages. Standard & Poor's 500 is one example of a market index.
A vehicle used to denote trends in securities markets. The most popular in Canada is the Toronto Stock Exchange 300 Composite Index (TSE 300). | http://metaglossary.com/define/market+index |
The following text is not about terminology of patterns, positions and other stuff around Kinbaku. It is a first try for a dictionary of tying itself.
Quite recently I wrote an article about a possible view on a grammar of tying. My claim was that there is no discontinuation of the conscious communication, called negotiation, between pre-scene, scene and post scene. There can only be a more or less smooth variation of vocabulary. The following lines are now dealing with this vocabulary. But instead of discussing the pre- and post-scene vocabulary, i.e. the spoken words, I want to focus entirely on the vocabulary used during a Kinbaku scene.
First let’s recall for a moment the interview metaphor used by me for describing a Kinbaku scene at all. It is said that in order to combine the two main discourses of tying, that are communication and power relationship, one can use the picture of an interview. The tying person becomes an interviewer and the tied person an interviewee. In an interview it can be regarded as a good interview, when the necessary and interesting information comes directly from the interviewee whereas the direction or path of the interview is chosen by the interviewer. This picture gained a wide acceptance in the rope community since I brought it up a couple months ago. But of course, it doesn’t tell anything about how to implement it to one’s own and personal tying process. It is more like telling somebody how beautiful and exact the German language can be. It doesn’t enable that person to speak German. For this purpose, one has to learn a certain vocabulary and some rules.
The vocabulary of any language is a set of symbols which are used to express some sort of information within a certain context. Although I would need to, I don’t want to go too much into what the terms symbol and information mean. In the following, I want to define a symbol as a minimal representation of an information within its context. Thinking of words, a syllable is not necessarily a symbol but a word can be. A sentence can be a symbol as well as an answer. The symbols are exchanged in various ways such as gestures, mimics, words or positions. Except the words, all of them can be expressed and/or caused through and by playing with ropes. (Of course, some people talk with each other while tying, but that’s another story.) In addition there is also something like tension and pattern that can be added as subsets of symbols and hence those enlarge the vocabulary. The symbols used besides the spoken language have some kind of an underestimated existence. Although everybody would admit that the roughly called body language is existent and even important, almost none of us learns its grammar and vocabulary as a subject on its own at school or so. It is something that grows somehow anyways depending on the cultural environment.
Doing ropes is a chance to get aware of this language and furthermore to use it consciously and explicitly. It’s a chance and a problem at the same time. Why is it a problem? I would claim, the fact that there is only a rough idea of the interpretation of the symbols in use can lead to a huge variety of misunderstandings. This is the reason why I want to come up with my little, far from complete dictionary of tying.
As I said before, I see a bondage scene as an interview. Hence I need basically two kinds of symbols to describe the content of such an interview – that is a set of questions and a set of answers. But I don’t want any troubles of too complicated answers, because I couldn’t be sure to understand them properly and so, I just reduce my set of questions to polar questions.
A yes and two different no’s are the answers I am asking for when I tie. A yes, i.e. something like a support from the tied person contradicts the power relationship. I give an example. When I softly push against the knee from the inside, i.e. asking if it’s ok to spread the legs and the answer is immediately spreading the legs on her/his own, it would lead to something like topping from the bottom.
A sharp and definite no must be interpreted as a no from outside the play and therefore must be respected. Such a no can be expressed by a sharp breath, a verbal and very explicit no, a search for eye contact and a sudden body tension but also by many other reactions and combinations of reactions depending on the context.
The last remaining answer is actually the only one that is interesting for me. It’s the kind of no that I would like to call a staged no. It is the kind of no within the play, that must have been negotiated before and that respects the power relationship.
We have the answers – what are the questions? Polar questions which lead to the above answers can be announcements like “I’m going to spread your legs” or “I will show your face, which you hide now”. They can also be grammatical questions like “Do you like it when everybody sees your breasts in a second?” There is basically no difference between the statements and the grammatical questions, although the way of asking them can differ. The above mentioned questions are those which deal with some sort of shame play. But there are of course much more directions.
The more tricky ones are about positions. In Osada Ryu, there is in principle no action that forces someone into a direction with pure power but it’s often just a hint at going into a certain position. Breaking the Seiza is a perfect example. Instead of pushing the partner into the broken Seiza, one just needs to touch intentionally the hips such that the partner feels this intention. It is then a question or not, whether the tied person is already in a right state of mind.
Another kind of question asks about the dynamics of the play. Those questions basically ask for some sort of resistance against actions. In the beginning of a scene, long before there is the first rope applied, I try to pull the person towards me. If the person falls into me, it might not be the best situation for going ahead in Ranboo-style. If she/he resists and fights against my subtle and very soft pull, why not getting stormy and overwhelming? Don’t get me wrong here! I don’t mean rope pulling like in Highland games…
A last remaining kind of question, I would say, asks about the pattern, that should be tied. But as the only two functions of a pattern are framing the beauty of the tied person and secures the person within a certain position, this kind of question can be reduced to asking for a position. “Where should be the hands, can there be something around the neck, shall one emphasises a certain part of the body, etc.?” All of those questions are basically questions for a certain position, the rest is creativity.
The above sets of questions are my personal questions and they should just give a hint of what is possible and how my view on the metaphor works in detail.
When we talk about communication and power, this could be a way to understand what can be meant with those terms. Because talking about communication and connection is easy, but the next step, namly talking about how to connect and communicate isn’t that easy. The above dictionary is a suggestion and my personal experience. Now find your dialect and create symbols consciously. | http://www.barkaskinbaku.com/a-vocabulary-of-tying/ |
Verizon unlikely to go ahead with partnership with Huawei
Huawei has been in the headlines for a while now. Towards the end of 2017, the company heavily touted its entry into the US. A deal with AT&T that would see the carrier sell the company's smartphones in the US was expected but that deal broke down, leading to the famous speech by Huawei's CEO, Richard Yu, at CES. Apparently, the company shifted its focus to working towards a deal with Verizon but even that may just be a pipe dream now, as the telecommunications giant is also said to be set pull out of the deal.
According to the report, much like the case with AT&T, Verizon's refusal to close the deal is due to pressure by the US government. The government is said to be leery of Huawei's ties with the Chinese upper echelon and believes introducing Huawei smartphones into the US could lead to a potential privacy breach.
What this means is that Huawei smartphones will likely not be sold under any carriers in the US for a while. The company already sells its smartphones, unlocked, through multiple retail outlets, and it's likely to stay that way. | https://www.notebookcheck.net/Verizon-unlikely-to-go-ahead-with-partnership-with-Huawei.280484.0.html |
Leaf cutter ants form one of the most complex societies in the animal kingdom! They live in massive colonies underground where the ants perform different job roles called ‘castes’. The leader of the colony is the queen ant, she is the only female ant that breeds and can create a colony of up to 8 million ants! The largest ants are called ‘soldiers’ and they defend the nest and territory. Smaller ants are workers and they help to collect food and rear the ant larvae.
Leaf- cutter ants are famous for chopping up bits of leaf and carrying them off back to the nest. Interestingly, they are not eating the cut-up leaves. They take the leaves in to their nest where they use it to feed a fungus. They then use the fungus to feed the new ant larvae. They are essentially the world’s smallest farmers! | https://www.blairdrummond.com/animals/leaf-cutter-ants |
MILA* Blueberry Muffins (Our guests and friends LOVE these! So light and fluffy
and delish with the warm blueberries – and so good for you – Enjoy!
Prep.Time: 10 mins Total Time: 30 mins Yield: 12 muffins Oven Temp: 400 degree F
Ingredients:
1.5 cups spelt flour (you may use all-purpose flour), ½ cup oatbran, ¼ cup MILA*, 2 tsps baking powder, ½
tsp baking soda, ¼ tsp salt, 1 egg – beaten, 3/4cup almond milk (or normal milk), ½ cup stevia or sugar, ¼
cooking oil(or coconut oil), ½ tsp pure vanilla extract, ¾ BC blueberries.
Directions:
1. Grease 12 medium muffin cups or 36 small muffin cups or line with organic bake cups, set aside.
2. Stir together flour, oat bran, MILA, baking powder, baking soda and salt in a bowl. Make a well in the
center of the mixture.
3. Combine egg, almond milk, sugar, oil and vanilla in another bowl. Add egg mixture all at once to the flour
mixture. Stir until moist, (batter should be a little lumpy). Fold blueberries into the batter. Spoon batter
(using an ice-cream ladle) in prepared muffin cups – fill to three-quarters full.
4. Bake in 400 degree F oven for 18 minutes for medium muffins or 10-12 minutes for small muffins, or until
done (test with wire skewer or toothpick – should be dry when pulled out.) Cool in muffin cups on a wire
rack for 5 minutes. Makes 12 regular muffins, or 36 small muffins.
For info on MILA (specialized Chia seed), contact Jennie Small at 604.902.2180 or jennie(at)findyourseat.ca
Peace. Tranquility. Serenity. | http://www.whistleralpinechalet.ca/mila-blueberry-muffins |
- Scott, Norman B. "Nipper"
Physical description area
Physical description
12 cm of mutiple media
Publisher's series area
Title proper of publisher's series
Parallel titles of publisher's series
Other title information of publisher's series
Statement of responsibility relating to publisher's series
Numbering within publisher's series
Note on publisher's series
Archival description area
Name of creator
Biographical history
Norman Bruce "Nipper" Scott was the son of Thomas Hunter Scott, the owner of the Scott Studio in St. Thomas, He was born in St. Thomas on December 28, 1898 and died in 1982.
On leaving high school, he joined the Imperial Bank of Canada in St, Thomas as junior clerk. He worked for a year at the bank before he decided to travel to Toronto in 1917 to make application to join the Royal Flying Corps. He was accepted, and spent two years with the Royal Flying Corps, Royal Air Force, spending eight months of that time in a front line squadron in France. He returned home in 1919 with the rank of Flight Commander.
Custodial history
Scope and content
Fonds consists of various materials relating to Captain Norman B. "Nipper" Scott's service with the Royal Flying Corps/ Royal Air Force, Squadron 11 in England and France during the First World War. Includes:
53-page typescript entitled "Diary of a War Bird"
Pilot's log book, August 14, 1917 to November 25, 1918, including miscellaneous correspondence and certificates
Diary, January 1, 1918 to December 31, 1918
Diary, January 1, 1919 to May 18, 1919
3 black and white photographs, circa late 1917 to early 1918
12 p. typescript entitled "A History of the Scott Family" | https://www.archeion.ca/norman-b-nipper-scott-fonds;rad?sf_culture=en |
Q:
Equilateral triangle in Semicircular
I have a geometry question. In this question, We have a Equilateral triangle ($ \triangle BDC$) that we draw it with one point on the circle and 2 point on the diameter. We want to prove if we draw this triangle then $OC = OD$.
Image1
I try to prove it But I can't find any good way to prove that. It must solve with central and inscribed angles. Is it possible to help me to solve it?
I'm sorry for bad English.
Thanks.
A:
As you can see from the picture, your claim is not true. You need some other hypotheses.
| |
A pair of rare tracks we recorded from a young Fraser Fifield twenty years ago. Fraser has recently been appointed Traditional Artist in Residence at the University of Edinburgh.
Uncategorized
Tommy Peoples, Edinburgh 2005
Three tracks from the master Irish fiddler at the Scots Fiddle Festival, Edinburgh, November 2005.
Aberdeen Strathspey and Reel Society
Start the new year with some historic tracks from the archives of this long-standing Scottish fiddle orchestra.
rareTunes 2022 statistics
2022 saw rareTunes draw 17,500 views and 8,000 visitors to the rareTunes site. These figures are slightly lower than in 2021 but satisfactory given that the site received little attention from the curator over the period due to illness.
The most popular pages by number of visitor are listed below:
Sarah Hoy and Fin Moore 292
Tony Cuffe 279
Alf Edwards 259
The Whistlebinkies 237
James Scott Skinner 230
Jean Redpath 206
Simon Bradley Trio 205
Newhaven Fisher Lasses 205
Jock Tamson’s Bairns 185
Molendinar 167
Davy Hutchison 165
Paul Robeson 159
Gizzenbriggs 156
Yehudi Menuhin 146
Jessie Niven MacLachlan 145
Roddy MacMillan 145
Dena Graham 139
The Easy Club 134
Many thanks..
..to Eileen Goodall for correcting the birth year we have given for the great William Mackenzie Murdoch. Eileen has recently transcribed the violin nist’s gravestone at Sighthill Cemetery, Glasgow.Continue reading
Folk on the Forth : Newhaven Fisher Women’s Choir
Will Ye No Come Back Again – Recorded at the 1954 Edinburgh International Festival.
Alec Sim
Listen here to four fine tracks from yet another obscure Scottish fiddler.
David McCallum, Scottish Fiddler
Early recordings by a great Scottish violinist – and the father of another famous David McCallum.
James Scott Skinner : The Strathspey King
Some great new tracks, images and information now online here.
Willie Kemp : McGinty’s Meal and Ale
Willie Kemp sings the classic cornkister in this recording from 1929.
KIndly donated by the Colin Bathe Collection. | https://raretunes.org/category/uncategorized/ |
R. Ishmael’s Rule No. 1, concerning a-fortiori argument, can be represented by a triangular star, at the center of which is the middle item (R) through which the three other items, P, Q, and S are related to each other.
Diagram 1a
The a-fortiori argument may also be represented, with reference to the comparative propositions that underlie it, as ordering items P, Q, and S, according to their position in a common continuum R:
Diagram 1b
This diagram is based on the following syllogisms:
Figure 1
Figure 2
Figure 3
Figure 4
Rp > Rq
Rp > Rq
Rp > Rq
Rp > Rq
Rq > Rs
Rp < Rs
Rs > Rp
Rs < Rq
So, Rp > Rs
So, Rq < Rs
So, Rs > Rq
So, Rs < Rp
Note that the four figures of a-fortiori should not be confused with the four of syllogism they imply, which are, in the order shown: the fourth, third, first and second figures. | http://thelogician.net/JUDAIC-LOGIC/A-Fortiori-Argument-Diagram1.htm |
The utility model discloses an imitation radio mould combined type stationery. The utility model is characterized in that the stationery comprises a main body, a pair of scissors, a pencil sharpener, a pen inserting hole, a clip box, an eraser box, a scribing block and a stapler, wherein the stapler is positioned at one side of the radio mould main body, the pen inserting hole is positioned at rear upper part of the radio mould main body, the scissors is positioned at the rear part of the radio mould main body, the clip box, the pencil sharpener and the eraser box are positioned at the front upper part of the radio mould main body, and the scribing block is positioned at the front lower part of the radio mould main body. The utility model has the advantages of multifunction and good decorative effect. | |
A fractal is a non-regular geometric shape that has the same degree of non-regularity on all scales. Fractals can be thought of as never-ending patterns.
Just as a stone at the base of a foothill can resemble in miniature the mountain from which it originally tumbled down, so are fractals self-similar whether you view them from close up or very far away. The term "fractal" was coined by Benoit Mandelbrot in 1975. It comes from the Latin fractus, meaning an irregular surface like that of a broken stone.
Fractals are the kind of shapes we see in nature. We can describe a right triangle by the Pythagorean theorem, but finding a right triangle in nature is a different matter altogether. We find trees, mountains, rocks and cloud formations in nature, but what is the geometrical formula for a cloud? How can we determine the shape of a dollop of cream in a cup of coffee? Fractal geometry, chaos theory and complex mathematics attempt to answer questions like these. Science continues to discover an amazingly consistent order behind the universe's most seemingly chaotic phenomena.
Mathematicians have attempted to describe fractal shapes for over one hundred years, but with the processing power and imaging abilities of modern computers, fractals have enjoyed a new popularity because they can be digitally rendered and explored in all of their fascinating beauty. Fractals are being used in schools as a visual aid to teaching math, and also in our popular culture as computer-generated surfaces for landscapes and planetary surfaces in the movie industry. The use of algorithms to generate fractals can produce complex visual patterns for computer generated imagery (CGI) applications.
See some fractal image examples.
See an introductory tutorial on fractals: | https://whatis.techtarget.com/definition/fractal |
This week was my first week as an unemployed, full-time real estate investor! It has been exciting and liberating to step into this next chapter of my life. On today’s show, I’m sharing the four major lessons I have learned this past week.
I’ll talk about what my first weekend was like without waking up to go in for the morning show, and why I don’t feel retired. I’ll also talk about the power of passive income, letting go of old ideals, and much more! Don’t miss episode 207 of Investing in Real Estate.
More About This Show
1) It’s liberating. The first thing I realized about quitting my job is that I feel free. I was able to sleep in this past weekend, and spend time with my family without having to worry about work. It was a strange feeling, but overall very empowering to have control over my time.
2) You can’t blame anyone else for your unhappiness. I’ve been thinking a lot about how important it is to take ownership over your own happiness. Many people blame their unhappiness on their boss or coworkers, but when you’re suddenly unemployed there’s no one else to blame. It’s important to realize that no matter the circumstance, we can choose to be happy.
3) Passive income works. Now that I’m without a regular paycheck, I’m able to truly see that passive income is the best way to build wealth. I even spoke to my accounting team this week, and they were incredibly encouraging about my decision.
4) You guys are amazing. So many of you have reached out to me via email, Facebook, Twitter, etc! I can’t say thank you enough for all of your incredible words of encouragement and love. Thank you for following along on my journey, and for allowing me to be a part of yours.
If you’re ready to begin building a passive income through rental real estate, book a FREE call with our team today. We’re ready to talk about your goals and want to help you learn more about earning legacy wealth for you and your family.
On this episode you’ll learn:
- At what age did I plan to retire?
- How does retirement feel?
- How did I overcome the paycheck mentality?
- Why is adversity essential to growth?
- And much more!
Episode Resources
Provision Wealth Strategists
Clayton Morris Says Goodbye to Fox & Friends
Subscribe to Investing in Real Estate on iTunes
Find Your Financial Freedom Number
Subscribe to the Morris Invest YouTube channel
Like Morris Invest on Facebook
Ready To Build Passive Income Through Rental Real Estate?
Ready to talk about your goals? We're here to show you the tools and teach you the process to begin earning legacy wealth for you and your family. | https://morrisinvest.com/podcast/2017/9/10/ep207-4-takeaways-from-my-first-week-being-unemployed/ |
Olympic Weightlifting Weight Classes
We'll discuss the olympic weightlifting classes for men, women, and young lifters in Olympic weightlifting in this article. We'll also cover how to select the weight class that's appropriate for you and how to accomplish that class comfortably.
Athletes in Olympic weightlifting compete in weightlifting divisions based on their body mass. In 2018 the International Weightlifting Federation approved the current weight classes - 10 for men and women, respectively. Only 5 of the total ten categories would be featured during the Paris Summer Olympics in 2024.
Olympic Weightlifting Weight Classes
Since 1920, every Olympics has included weightlifting competitions, which made their debut in 1896. The Sydney Olympic Games in 2000 saw the debut of the women's competition. Different Olympic weightlifting weight classes are created for the athletes based on their weight. For both the Men's and Women's competitions, there are 10 weight categories at the World, Continental and National Championships. Recently the International Weightlifting Federation and International Olympic Committee changed weight classes rules for Olympic Games participants, so at the Paris Olympics 2023, there will be five distinct Olympic weightlifting categories.
Men
During the World, Continental and National Championships Junior (under 20 years old) and Senior men compete in 10 weight classes:
55 kg, 61 kg, 67 kg, 73 kg, 81 kg, 89 kg, 96 kg, 102 kg, 109 kg, 109 kg +
For the 2024 Summer Olympics in Paris, there are five different Olympic weightlifting classes for men. There are two less weight divisions here than were in Tokyo in 2020. Only the 61 kg and 73 kg categories from the previous list have been kept. The weight categories range from 61 kg to 102 kg +. These are the five weight categories:
61 kg, 73 kg, 89 kg, 102 kg, 102 kg +
Women
Same as men, Junior (under 20 years old) and Senior women compete in 10 women's weightlifting weight classes at the World, Continental and National Championships.
Here is all of them:
45 kg, 49 kg, 55 kg, 59 kg, 64 kg, 71 kg, 76 kg, 81 kg, 87 kg, 87 + kg
Five weightlifting divisions will make up the women's weight divisions In Paris 2024, which is two fewer than in Olympics 2020. From the previous Games, only the 49 kg and 59 kg categories are still active. 49 kg is the lightest weight category, and +81 kg is the heaviest. The five various weight categories are as follows:
49 kg, 59 kg, 71 kg, 81 kg, 81 kg +
Youth
The International Weightlifting Federation recognizes YOUTH age groups as 13 - 17 years of age. For Youth men and women, there are 10 bodyweight categories, respectively. The following IWF weight classes and order must be followed for all IWF tournaments, with the exception of the Youth Olympic Games, which have unique requirements.
Also, National Weightlifting Federations can include a custom list of weight classes for younger lifters and use it on local and National competitions. Here is such example from USA Weightlifting Federation (USAW) Rules:
Youth 14-15 years old USAW weight classes:
Youth 13U (under 13 years old) Bodyweight Categories:
An athlete may only participate in one bodyweight category during a single competition, with the exception of situations where Youth events are mixed with Junior and/or Senior competitions. The competition schedule must be taken into account by event organizers for events that mix youth, junior, and senior divisions so that competitors can participate just once.
How To Decide Which Class Suits You Best
When choosing your weight category for Olympic weightlifting, you should take into account the following four factors:
- Height
- Body Weight
- Percentage of body fat
- Age
Height
Since height will be indicated when an athlete steps on the scale, it assists in determining weight class. If an athlete is at the top of his weight category due to height, but instead of muscle mass, he will be at a huge disadvantage to shorter and much more muscular weightlifters. Because of physical disadvantages, he would not only need to expend more effort to lift the same amount of load as a weightlifter who is shorter, but he would also have fewer force-generating capacity and less muscle mass.
Natural Weight
The weight that the body can naturally stabilize at is referred to as "set point." This is the body weight that weightlifters should compete at when they first start competing. When he knows his weight, he may check which bodyweight category he falls under for weightlifting and sign up to participate in that division. Athletes should choose a weight class that is close to where they naturally fall. It is feasible to go down or up one category, but moving up or down many weight classes requires time in order to maintain or acquire as much lean mass and prevent gaining fat mass.
Body Fat Percentage
Percentage of body fat may influence weight class selection since it will indicate if it is viable to move down a weight class while maintaining strength or whether it is preferable to move up a class and gain muscle mass. The average person's body fat may be reduced to between 10% and 15% for males and between 17 and 20% for women before performance starts to suffer. If you are in this position right now, you shouldn't drop a weight category. And eventually, when you put on more lean mass, you'll probably have to gain weight. You may afford to shed some fat mass by reducing a weight class if your body fat percentage is currently more than 30% for women or 25% for male athletes. This will boost your relative strength.
Age
Lifters in their early stages shouldn't drop out of a weight category while they are progressing. According to research, by doing this, they endanger the growth of their strength and power and may even prevent them from eventually realizing their full potential. Young weightlifters should compete in their native weight class and concentrate on optimizing muscle growth. Let's start by defining what a novice is. Anyone who has been training for less than one year or has only twice competed is considered a beginner. A novice shouldn't attempt to fit into a specific weight class. Athletes should instead compete in the division they belong in. The rationale for this is because a complete beginner should concentrate throughout the competition on enhancing performance and understanding the competition's flow.
Picking Weight Category as An Advanced Weightlifter
Lifters who have learned the fundamentals and are aiming for higher placings at regional, national, or international competitions are considered advanced. As experienced lifters, it should be objective to participate in the weight division in which athletes have the highest chance of succeeding. Lifter will be the most competitive in the weight category where he will have the greatest lean muscle mass, the least amount of body fat, and the ability to sustain strength and performance.
FAQ
What is the difference between group A and group B in weightlifting?
Athletes are divided into groups of 10 competitors at major and international championships. Lifters in group B are considered to be "worse" lifters since they submitted lower entries than weightlifters in group A. This is to prevent groups of more than 10 lifters from participating in a competition because of extended rest periods and TV timings. A competition with 10 lifters lasts roughly 90 minutes, but every additional lifter adds at least 5+ minutes to the session. This does not exclude a weightlifter from B group from winning a medal.
What is the most weight ever lifted in an Olympic lift?
Super heavyweight Georgian Lasha Talakhdze published a video showing himself clean-and-jerking 270 kilos on April 29, 2021. Since the lift was performed during training, it is not a world record. Talakhdze now holds the clean and jerk record with a weight of 267 kg.
Conclusion
In the early stages of Olympic weightlifting, selecting a weight class to participate in will come relatively easily. Changing categories might help to become more competitive as we get more experience. But keep in mind, that if you do poorly in the meet, the weight category you competed in won't matter. So, do you think I left anything out? Let's discuss it in the comments!
1 comment
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Abhijit Biswas
What are the best Exercises anyone can do to protect their elbows ?
Many arms have been broken during lifting…
Kindly tell…
Why some lifters broke their elbows? Wrong positioning? | https://torokhtiy.com/blogs/warm-body-cold-mind/olympic-weightlifting-weight-classes |
We saw the introduction of another Clever spy, Nightfall, in the last episode. She also works in the hospital alongside Loid as Fiona Frost and is known for being icy and harsh. If you’re a fan of the Spy x Family series and are looking forward to episode 22, we’ve got you covered with all the details from the upcoming episode.
Release Date of Spy X Family Season 2 Episode 22
Spy X Family Season 2 Episode 22 Underground Tennis Tournament: The Campbellton will premiere on Saturday, December 3, 2022, at 11 p.m. JST. As a result, the episode’s release date and timing will differ across different time zones.
In the United States, the episode will be accessible only on Crunchyroll. And meanwhile, Asian fans may watch the episode on the Muse Asia YouTube channel.
What to expect from Spy X Family season 2 episode 22
Spy X Family episode 22 will follow the Campbellton Tennis Arc, with Twilight and Nightfall working together.
They’ve been assigned a task together, and Nightfall will try to use this opportunity to get some brownie points with Twilight to win him over.
Twilight and Nightfall appear to be disguised as a couple as they prepare to play tennis against what appears to be a gang of goons. Since playing tennis is something other than what the WISE agents do regularly, this might be a complex problem.
Elsewhere, Yor will question her place in the Forger family since she suspects Loid has a lover in the hospital, most likely Fiona Frost.
Where can I watch Spy X Family season 2, episode 22, online?
Spy X Family episode 22 will air on TV Tokyo, TV Shizouka, and other Japanese television networks. In addition, the episode is available to international viewers through Crunchyroll, while South and South-East Asia viewers may watch it on the Muse Asia YouTube channel.
Netflix, Amazon Prime Video, Hulu, Bili Bili, and iQIYI are among the other streaming providers for the anime series.
Spy X Family season 2 episode 21 recap
Nightfall attempted to remove Yor from the Forger family in Spy X Family episode 21, titled Nightfall/First Fit of Jealousy since she intended to replace her. She had long been in love with Twilight and imagined herself as his ideal partner.
However, after reading Nighfall’s mind, Anya devised the ideal countermeasures to guarantee her mother’s status in the family.
Bond pulls apart Anya’s penguin plush toy in the second half of the episode, showing his jealousy. This produced friction between Anya and Bond, which was only eased after Twilight repaired the toy, and Bond apologized to Anya by providing peanuts. | https://dailyresearchplot.com/2022/12/02/spy-x-family-season-2-episode-22-release-date-time-and-every-detail-you-need-to-know/ |
Dr Muhamad Akmal Mohammad, a medical officer with the emergency department at Hospital Sultanah Bahiyah in Alor Setar, Kedah, is one of the many frontliners dealing with the Covid-19 outbreak.
Life, he says, has been more hectic than ever before for him and his colleagues who have their hands full dealing with the Covid-19 cases while also attending to other emergency cases that come to the hospital.
In the midst of this, the 34-year-old doctor says that he has a way of managing his stress levels and keeping himself sane: writing.
The self-confessed fountain pen enthusiast says that he whips out his fountain pen whenever he has a spare moment or two and he writes, scribbles or doodles.
"Writing gives me an avenue to vent and unwind. It also helps me organise my thoughts. I do it every chance I have... in between shifts, in between patients. Most of the time it is random scribbles and sometimes, it is work-related. But I find it therapeutic.
"The pandemic is a test for all of us, even more so as a frontliner. I work in shifts and when I am not on shift, I am on standby at the emergency department. We have to be prepared for the worst, both physically and mentally and so the little time we have in between our shifts is really more precious than ever. I use this time to write," says the doctor.
Dr Akmal's interest in pens started when he started working seven years ago. However, his “acquisition overdrive” started three years ago. He now has more than three dozen fountain pens and more than 50 bottles of ink in his collection.
"I also have about a dozen mechanical pencils!' he adds. "My grail pen at the moment is the Graf von Faber-Castell Intuition Gerenadilla Wood but my favorite pen is my bronze pen from Fine Writing International (Bronze Age, a limited edition pen).
"Handwriting, for me, not just conveys messages but emotions. It is therapeutic and it calms me. Also since getting into this hobby, I have made many friends who share this passion... people from all walks of life. Our passion for pens and handwriting unites us," says Dr Akmal.
Dr Akmal isn't the only one turning to their pens to get through the crisis. Others who are abiding by the directive to "just stay home" during the movement control order period are also turning to their pens to keep them occupied.
Fellow fountain pen enthusiast Ozilinah Othman says that the MCO has allowed her the time to spend on her pens and her writing.
"It's a chance for me to go through my array of inks and do a proper inventory of what I have. This way, when the MCO is lifted, I will know exactly what I can add (to my collection) and what I should stay away from," says Ozzie, as she is known..
Regarded as the "Lamy queen" in the fountain pen fraternity for her collection of the German-made pens (Ozzie has 160 Lamy pens, of which 120 are fountain pens), Ozzie says that she's taking full advantage of the time she has at home to practice her writing.
"I am currently learning Mandarin. One of my Chinese friends has told me that there isn't any quick and easy way to remember the characters other than writing. Hence, it's practice, practice and practice without interruption.
Using all the different nibs, pens and inks that I have has made studying and memorising the characters so simple. It has taken away the tedium of learning and has made me look at each character properly," she says, adding that she plans to learn Arabic next.
Owner of Pen Gallery, a shop in Petaling Jaya that also serves as a meeting place for fountain pen fans and collectors, Lai Kim Hoong says that although the community cannot meet physically in these times, they are active on social media and WhatsApp.
"My clients are my friends. They hang around the shop to chat or to write and try pens and I have been getting message from them saying how much they miss the sessions. We have quite a strong fountain pen community in Malaysia and we started a Facebook group, Fountain Pens Malaysia, that is growing daily with more than 800 people who regularly chat and share their passion, ” says Lai who has about 1,100 pens and 650 unique inks in his shop in Petaling Jaya.
On the Fountain Pens Malaysia Facebook page, enthusiasts are sharing what they are doing with their pens and inks while at home. They are posting photos of their scripts and doodles and also sharing links about... you guessed it, pens and inks.
"Writing is as old as mankind and despite the digital age, fountain pens are making a comeback. Let's not lose the art of handwriting because, after all, the pen is mightier than the sword, ” says Lai.
Did you find this article insightful? | https://www.thestar.com.my/lifestyle/people/2020/03/24/mystayhome-malaysian-fountain-pen-enthusiasts-find-solace-in-their-hobby |
Q:
Confusion about the output of this program
I am new to C programming and I am currently learning Data types revised chapter. In the below
program, my o/p is 36 but compiler is showing the o/p 35.
main( )
{
char ch = 291 ;
printf ( "\n%d %c", ch, ch ) ;
}
Can anyone explain me why the o/p is coming 35? I am currently using GCC 32-bit compiler.
A:
Your system apparently has an 8-bit char type. That means 291 is too big to fit - the compiler reduces it modulo 256 (28) and you end up with 35.
In this case, Clang provides a great warning:
example.c:3:11: warning: implicit conversion from 'int' to 'char' changes value
from 291 to 35 [-Wconstant-conversion]
char ch = 291 ;
~~ ^~~
You should probably avoid relying on this behaviour, since it may vary from implementation to implementation. The C99 and C11 specs (Section 6.3.1.3) say about signed integer conversions:
Otherwise, the new type is signed and the value cannot be represented in it; either the result is implementation-defined or an implementation-defined signal is raised.
Since you're using GCC, you might be interested to read this excerpt from the documentation:
The result of, or the signal raised by, converting an integer to a signed integer type when the value cannot be represented in an object of that type (C90 6.2.1.2, C99 6.3.1.3).
For conversion to a type of width N, the value is reduced modulo 2N to be within range of the type; no signal is raised.
And there you have your full explanation of the reduction modulo 256.
A:
Because a char can only contain 8 bits of information, and 291 require more than that to be stored. It will then discard the higher bits and keep only what fitted in the variable.
You can simulate that by both bitwise and module operation:
291 % 256 = 35
291 & 0xFF = 35
A 8-bit char can contain values of -128 to 127 or 0 to 255, depending if its signed or unsigned.
A:
You're actually making an overflow. A signed character can only go from values -128 to 127 (256 values = 28) in 8-bit character systems (which are pretty much everywhere).
So we go with an actual character which value equals 291 % 256 = 35.
Don't forget that the first character is 0, not 1.
Here is actually how a char is represented with the 2's complement system:
unsigned
0 ------- 127 128 ------- 255
signed
0 ------- 127 -128 ------- -1
So actually a signed char c1 = -128 equals an unsigned char c2 = 128
But here this problem is just irrelevant. We're talking about modulo because only the last eight bits are taken into account (where would the other be stored when there are only eight bits available for it in the memory ?).
291 = % 1 0010 0011
(% means binary representation)
It keeps only the % 0010 0011 which equals 35 and which will be considered exactly the same either you take it signed or not.
|
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