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- good cooperation with the representatives of the employees. Trade Union organizations The Bank has two trade union organizations: - The National Trade Union of PKO BP SA Employees, with 2,842 members, including 2,805 employees, - “Solidarity” Independent Self-Governing Trade Union of PKO BP SA Employees, with 1,215 members, whereby only the former is a representative union. Approx. 16% of the total number of employees as at 31/12/2017, who were employees, were trade union members. Every person admitted to work at the Bank is informed of the existence of employee representation, including trade union organizations. All information related to it can be found in the Bank’s generally accessible intranet. The Employee Affairs Department is responsible for relations with the trade unions. Cooperation with the trade union organizations is good; there were no collective disputes either in 2017 or in previous years. The Bank’s Employee Council also operates at the Bank. Cooperation with these social partners takes place in accordance with the applicable regulations, including holding consultations in the case of planned organizational changes, resulting in significant changes in the organization of work, the level and basis of employment of employees. Meetings with trade unions and the Bank’s Employee Council are organized as necessary – at least several times a year. The Bank has internal regulations ensuring that employees can report complaints about a breach of employee rights. 47 complaints were filed with the Bank in 2017; all are encompassed by an investigation process. A trade union organization also exists at KREDOBANK SA, in which almost 16% of employees are members. Trade union organizations do not operate at other companies in the Group. The dialogue with the employees takes place in accordance with the applicable regulations. Its form is adapted to the size of the company and its specificity: the larger entities have Workers’ Councils, while the dialogue with employees at other companies is held, among others through selected employee representatives and forms of communication with employees, either direct or via e-mail and through the intranet, which are accepted at the given entity. No collective disputes were recorded at the Group entities. The employees have the opportunity to report complaints about a breach of employee rights and other irregularities. Support for employees The bank’s employees may obtain any information on employee matters from one place by calling or sending an e-mail to the internal HR Contact Centre. A team of consultants answers questions, among other things, on HR and payroll support, social issues, recruitment and training. The new solution accelerates and simplifies the communication process between employees and the HR services – the units responsible for personnel management. Employee satisfaction survey The Bank attaches a great deal of importance to the opinions of employees on matters related to their work, the opportunities for individual development, as well as the company’s organizational culture. A study of the organizational culture, employee satisfaction and commitment is held at the Bank every few years; the results of the last survey will be available in the spring of 2018. The results of the satisfaction surveys are presented to the employees as well as to the Bank’s governing bodies, for which they constitute an additional tool in analysing and shaping appropriate relations with the employees.	https://raportroczny2017.pkobp.pl/en/non-financial-information/stakeholders-employees/relations-employee-party.html
Many professionals who refer clientele to us or patients themselves want to know about IHC’s “approach” to therapy. What makes it integrative? First off, the thing that makes it integrative is that we don’t belong to any single “camp” in therapeutic approaches – we are “multi-discipline” in our approach. However, there are some philosophical “foundations” in therapy that underpin our counseling work. One is called “Solution-Focused Brief Therapy”, or SFB. The following is a brief overview of what it is about, with a link to a fuller description. SFBT has not only become one of the leading schools of brief therapy, it has become a major influence in such diverse fields as business, social policy, education, and criminal justice services, child welfare, domestic violence offenders treatment. Described as a practical, goal-driven model, a hallmark of SFBT is its emphasis on clear, concise, realistic goal negotiations. The SFBT approach assumes that all clients have some knowledge of what would make their life better, even though they may need some (at times, considerable) help describing the details of their better life and that everyone who seeks help already possesses at least the minimal skills necessary to create solutions. All therapy is a form of specialized conversations. With SFBT, the conversation is directed toward developing and achieving the client’s vision of solutions. The specific techniques and questions help clarify those solutions and the means of achieving them. One way of understanding the practice of SFBT is displayed through the acronym MECSTAT, which stands for Miracle questions, Exception questions, Coping questions, Scaling questions, Time-out, Accolades and Task. To read more, visit a Wikipedia Description of the therapeutic model.	https://www.ihcwestmichigan.com/2013/08/what-is-solution-focused-therapy/
The Saskatchewan Health Authority and 3sHealth recently became aware of a process issue that occurred in dictation and transcription, whereby a small number of referral and follow-up letters were delayed in their distribution. These letters include referrals and follow-up letters to specialists and the Saskatchewan Cancer Agency. The SHA and 3sHealth are working collaboratively to review the incident, and have taken immediate measures to correct this issue. All letters that had not been sent, were immediately sent upon discovery of the issue. An investigation was immediately launched in order to determine the scope. The investigation is ongoing; there are currently 250 patients throughout the province who may have been impacted, and the patients and their dictating physicians are being contacted directly for follow-up. 3sHealth is completing additional auditing to determine if there are any further cases. All physicians who may be impacted by the issue are working with the Saskatchewan Health Authority and 3sHealth to ensure proper investigation and assessment into any potential for harm to the patients affected by the delay in distribution for the follow-up and referral letters. Patients affected by this issue will receive direct contact from the Saskatchewan Health Authority, including direction on next steps and who they can contact if they have additional questions. The priority is on ensuring that immediate steps are taken to contact affected patients and their physicians to help rectify this issue. The Saskatchewan Health Authority and 3sHealth are currently working through process improvements to ensure that this issue does not occur in the future.	http://www.3shealth.ca/3shealth-news/news-release-transcription-issue-identified
After 3 major 4G LTE outages in the last month, Verizon has finally released a statement detailing the situation (and no, it wasn’t a half-baked Tweet) and what their plans are going forward. According to this release, each incident that occurred was different from a “technical standpoint” and has not re-occurred thanks to their engineering team. While Big Red is estimating that their LTE network has had approximately 99% up time for the year, they have admitted that as a “pioneer” in the LTE market, that there are growing pains and that they are doing everything in their power to rectify them. So what exactly happened though? We don’t know specifics, but we do now have somewhat of an idea as to how Verizon plans to move forward so that these massive nationwide outages do not happen again. The two biggest things are “geographic segmentation” which will allow them to isolate issues and correct them before they become widespread, and also fix backend software that will provide better performance and reliability. Update: GigaOM had a chance to speak with Mike Haberman, Verizon’s VP of network engineering, who was willing to provide some of the technical details. The first outage back in April was due to an IMS (IP Multimedia Subsystem) core software bug that “led to a complete failure.” The December 7 outage was due to a failure of a back-up communications database. The outages from the last two weeks were the result of IMS elements not communicating correctly. These bugs were not something that could have been predicted and simply decided to show themselves in the span of a few weeks here in December. I think the big key here, is to remember that this LTE network is still brand spankin’ new and will have issues. There may be more next week or we could get lucky and not see one for another year. Just know that Verizon will have an extra $2 per person starting January 15 to help pay for the corrections (Hah! Sorry, one last cheap shot before the end of the year just felt necessary). 🙂 The full statement from Verizon is after the break. Statement From Verizon Wireless on 4GLTE Network 12/29/2011 In light of recent events, Verizon Wireless shared the following statement about its 4GLTE Network: The Verizon Wireless 4GLTE Network is BY FAR the largest and the most advanced 4GLTE wireless network in the world. It is available in 190 US markets and covers more than 200 million people, providing the fastest 4G Network in the US. Being a pioneer comes with growing pains. The recent issues that affected our customers’ 4GLTE service were unforeseen despite careful, diligent planning, deployment and ongoing upgrade programs. Problems customers experienced affected connectivity to the 4GLTE Network and data service. Several times, we have proactively “moved” 4GLTE customers onto our 3G Network to ensure all would have a data connection. For brief periods, such as on Wednesday (12/28), 4GLTE customers could not connect to the 3G Network as quickly as we would have liked. Nonetheless, we estimate that 4GLTE connectivity has been available approximately 99 percent of the time this year. Why have these issues occurred with our 4GLTE Network? Each incident has been different from a technical standpoint. Our engineers have successfully diagnosed those past triggering events, and they have not re-occurred. We also work diligently to rectify technical problems in the Network before they affect any customers. Our 3G and 1X Networks continue to reliably process calls, texts and data for customers with 3G devices and, when necessary, 4GLTE devices. It continues to perform at the high level that established it as the nation’s largest and most reliable 3G Network. We are taking a number of steps, working closely with our network suppliers, to ensure the integrity of our 4GLTE Network. We continue to fortify and improve its performance, and our goal is that our 4GLTE Network meets the same high standards that our 3G Network has set for performance and reliability. Among the numerous measures we have taken or will take are: geographic segmentation, which enables us to isolate, contain and rectify network performance issues, and maintain service to the majority of customers when an issue does develop; and software fixes that we have developed, tested and applied regularly – and will continue to do so. Both will improve performance and reliability. And finally, we are learning from these issues and applying the same gold standard to our 4GLTE Network that make our 3G Network the nation’s largest and most reliable. Verizon Wireless is a leader and pioneer in this cutting edge technology that provides very fast wireless data speeds, enabling customers to enjoy the best experience in video and other wireless data usage. Clear unbuffered streaming video, super fast file downloads and wide availability are among the advantages we offer to customers. The capabilities of 4GLTE have exceeded many expectations. We will not rest until our 4GLTE network performs at the very highest levels that our customers have come to expect from us. Cheers Matt and Jigga_Z! ______________________ Some of our best videos.	https://www.droid-life.com/2011/12/30/verizon-issues-statement-on-their-4g-lte-outages-taking-number-of-steps-to-ensure-the-integrity-of-the-network-going-forward/
When a U.S. Navy ship needs repairs, they call us. Join our team as we keep the most powerful Navy the world has known afloat and ready to serve! This Marine Mechanic position will support contracted skilled trades work on our Elevator Support Unit (ESU). You will help us with installations and alterations to Weapon Elevators, Aircraft Elevators, and their associated systems on U.S. Navy ships. Travel within and outside of the continental United States may be required. What You Will Do - The selected candidate will support ESU by performing a variety of skilled trades, maintenance and technical tasks on aircraft carrier elevators, cargo handling systems and associated equipment, including aircraft elevators, weapons elevators and vertical stores conveyors. - Selected candidate will work closely with higher level employee in specialized assignments. - May train/assist other employees/navy personal on shipboard systems and day-to-day operation. - Work includes daily activities of physical labor in an industrial and shipboard environment. - Applies comprehensive understanding of production and processes toward completion of assignments. - Responsible for interfacing with customers, managing subcontractors and ability to provide work direction to others. - Develops and uses technical documents including controlled work packages, formal work processes and procedures, test documents, reports and task or trip reports. - Schedules, reports and briefs customers and senior management. - Performs duties outside of specialty in order to complete installation or work assignment. What You Must Have - Must have a High School Diploma or equivalent and 2 years of related experience. - Must have experience performing troubleshooting, preventative maintenance and testing of mechanical systems. - Must be able to read blueprints, technical manuals and/or related technical documents. - Must be capable and have knowledge of using various mechanical industrial tools such as precision measuring instruments, minor rigging equipment, portable power units and mechanical fastening devices or equivalent. - Must have experience conducting on-site installation of equipment while following established safety, qualify control & testing procedures. - Must be able to calibrate, and make minor repairs on tools/equipment. - Must be able to obtain/maintain base access credentials (DBIDS), a DoD Security Clearance, and must be a U.S. Citizen. - Must be able to provide own hand tools as designated per trades specialty. Bonus Points For... - 4-8 years of related experience preferred. - Experience in the operation, repair and maintenance of marine hydraulic systems highly desired - Prior Shipboard experience preferred, prior experience on elevators or similar equipment is highly desired. - Candidates who hold a current or active DoD confidential clearance or higher preferred. - Candidate with related technical training, degrees, and/or certifications preferred. Physical Requirements Must be able to lift, carry and transport heavy equipment and boxes. The exact weight requirements will be determined by the specific job, but no less than 30 lbs. Able to work on and climb ladders, work in extreme temperature environments, aboard ships, in shipyards, under industrial conditions and in confined spaces. Able to perform other duties as required which may involve high heat, humidity, noise and dirty conditions, working aloft or over the sides of vessels. May ride ships at sea for extended periods. May require wearing a respirator. Travel may be required within and outside of the continental United States. MV SG TL EP *TE HII’s Mission Technologies division develops integrated solutions that enable today’s connected, all-domain force. Capabilities include C5ISR systems and operations; the application of AI and machine learning to battlefield decisions; defensive and offensive cyberspace strategies and EW; unmanned, autonomous systems; LVC solutions; platform modernization; and critical nuclear operations. Together, HII's domain expertise and advanced technologies support mission partners anywhere around the globe. For more information, visit tsd.huntingtoningalls.com. HII is a global engineering and defense technologies provider. With a 135-year history of trusted partnerships in advancing U.S. national security, HII delivers critical capabilities ranging from the most powerful and survivable naval ships ever built, to unmanned systems, ISR and AI/ML analytics. HII leads the industry in mission-driven solutions that support and enable a networked, all-domain force. Headquartered in Virginia, HII’s skilled workforce is 44,000 strong. Huntington Ingalls Industries is an Equal Opportunity/Vets and Disabled Employer. U.S. Citizenship may be required for certain positions.	https://jobs.hii-tsd.com/job/Bremerton-Marine-Mechanic-ESU-4788-WA-98312/827218000/
Gauss's Electrical law defines the relation between charge ("Positive" & "Negative") and electric field. The law was initially formulated by Carl Friedrich... Maxwell's Equations are a set of fundamental relationships, which govern how electric and magnetic fields interact. The equations explain how these fields... Photovoltaic (PV) systems are typically more efficient when connected in parallel with a main power gird. During periods when the PV system generates energy... Insulation on a motor prevents interconnection of windings and the winding to earth. When looking at motors, it is important to understand how the insulation... One of the requirements to ensuring that everything works is to have equipment selected, manufactured and verified [tested] to IEC standards. Not all equipment... "I can live with doubt and uncertainty and not knowing. I think it is much more interesting to live not knowing than to have answers that might be wrong... Various arguments exist around SF6 Gas Insulated (GIS) and Air Insulated (AIS) medium voltage switchgear. Recently we had to change a GIS design to AI... This is the first of two posts on the resistance of conductors. In the next post I will look at the ac resistance, including skin effect and we deal with... It starts with me reading one of the Horrible History books with my son (Groovy Greeks). Arrows were mentioned which lead to the discussion of the bodkin... A UPS is an uninterruptible power supply. It is a device which maintains a continuous supply of electrical power, even in the event of failure of the...	https://myelectrical.com/questions/view/browse?tag=mccb%2Fmcb
Did we replace the conscience with consciousness? And if human consciousness is expanding, why do we seem to be regressing in our ability to heal? Darwin pitted religion against science with his theory of biological evolution. Modern chemists still have failed to explain the origin of the genetic code. Are humans actually millions of years old? Is the Earth not our only home in the universe? Is there a cyclical transfer of life process from planet to planet? David Icke introduces the concept of creation of matter from the void. What our five senses can perceive from the band of visible light frequency is tiny compared with what becomes possible when we connect to the greater self (consciousness). The facts are increasingly stacking up that civilization and our biosphere are in terminal decline; it’s just happening in slow motion, so that in these early stages, it’s possible to ignore for a while the magnitude of what’s taking place all around us. We need to get real. We need to open our eyes and embrace the truth. Because only the truth can set us truly free. What’s needed now is a wide scale Spiritual Realignment. That’s the message we captured in this video. We believe it’s of upmost importance and therefore thank you for sharing widely Karma occurs where the soul becomes identified and therefore attached to the physicality of life. In other words, where the soul identifies with the illusion. This might happen for example where one is in fear during death or a particularly traumatic experience such as an accident. When the soul attaches in this way, then it essentially experiences the sense of disconnection from the source, loses a ‘fragment’ of itself in an eddy current, identifies with the illusion, takes on distorted behaviors and therefore deposits karmic energy within the causal body.	https://consciouslifenews.com/category/realtys-edge/ascension-conscious-living/page/8/
Shopkick survey finds rising concerns about COVID are leading to empty store shelves as consumers revert to stocking up COVID cases are surging in record-breaking numbers across the country. As a result, consumers are again adjusting their shopping habits. Nearly half of Americans (48 percent) are more concerned about the pandemic now than just a month ago, leading shoppers to stockpile essentials at higher rates than at the start of the pandemic. Shopkick surveyed nearly 8,000 consumers across the country to gain insights into how the uptick in national COVID cases is impacting shopping habits. The findings help illuminate the current state of consumer behavior. Key Trends Include: - Steady In-Store Shopping: Increasing numbers of COVID cases and the return of state restrictions do not seem to be stopping consumers from heading in-store for essentials. According to 92 percent of Americans, someone in their household is still purchasing essential items from physical stores, including big box retailers (88 percent), grocery stores (80 percent), drug stores (61 percent), dollar stores (54 percent), club stores (43 percent), and convenience stores (30 percent). - Consumer Discomfort: Although most are still shopping in-store, 36 percent of consumers feel less comfortable doing so now than a month ago. In fact, almost half of Baby Boomers (47 percent) say they are taking fewer store trips per week than one month ago, compared to Gen X (43 percent), Millennials (38 percent), and Gen Z (38 percent). - Stockpile Spike: Sixty-one percent of consumers say they are stocking up on essentials like toilet paper (87 percent), food items and water (85 percent), cleaning supplies (67 percent), hand sanitizer (61 percent), medicine and medical items (48 percent), and pet supplies (37 percent). This is a noticeable jump from the first wave of COVID in March, when a Shopkick survey found that less than half of consumers (47 percent) were stocking their pantries. - T. P. Troubles: With more people stocking up, items like toilet paper have become a hot commodity, yet again. Seventy-six percent of consumers have noticed that essential items that were in-stock a month ago, like toilet paper and cleaning supplies, are now less available at their local store. - Keeping an Eye on Cases: Of the 39 percent of consumers who are not currently stockpiling the essentials, nearly half (47 percent) say they will if COVID cases continue to rise at the current rates. - More Millennials are Stocking Up: While similar across the board, Millennials are the segment stocking up the most (65 percent), followed by Gen X (62 percent), Gen Z (59 percent), and Baby Boomers (57 percent). “These findings should serve as a huge wake-up call for retailers and brands,” said Dave Fisch, general manager of Shopkick. “The same issues that severely impacted supply chains during the first wave of COVID have returned as consumers revert to stocking up and panic buying. Retailers and brands must act immediately to implement strategies that will help keep store shelves well-stocked in order to maintain sales and consumer loyalty during this time. This survey was conducted online between Nov. 23 and Nov. 25, 2020.	https://www.shopkick.com/partners/blog/surging-covid-cases-means-stocked-pantries-consumers-stockpiling-more-now-than-in-march
"Good evening...." An anthology series of (generally non-Lovecraftian) morbid suspense, crime, and thriller dramas, hosted by Alfred Hitchcock, who would introduce and close each grimly ironic episode with dark comedy sketches, while poking gentle (or not-so-gentle) fun at his sponsors. In 1962, the half-hour Alfred Hitchcock Presents changed format, lengthened into The Alfred Hitchcock Hour. In 1985, many episodes were re-made, spliced together with colourized versions of Hitchcock's introductions. Details - Release Date: 1955-1962 (Alfred Hitchcock Presents), 1962-1965 (Alfred Hitchcock Hour), 1985-1989 (Alfred Hitchcock Presents remakes) - Country/Language: US, English - Genres/Technical: Crime, Mystery, Suspense, Thriller, Drama, Comedy (black comedy), occasional Horror and Fantasy, Anthology, black-and-white - Runtime: (formatted for either a 30-minute (Alfred Hitchcock Presents) or 1-hour (Alfred Hitchcock Hour) commercial television slot) - Starring: (various), host Alfred Hitchcock - Director: (various) - Writer: (various) - Producer/Production Co: CBS, NBC, Revue Studios, Shamley Productions, Universal Television, - View Trailer: (link) Ratings MPAA Ratings - Rated: (not rated) (equivalent of a TV-PG for mild, off-screen, 1950s TV-friendly Violence and Adult Content) Tentacle Ratings A rough measure of how "Lovecraftian" the work is: - s____ (One Half Tentacle: Debateably Lovecraftian, at most) Most of the episodes of Alfred Hitchcock's shows were focused on crime and suspense, with a little comedy tossed in from time to time; very few episodes involved more fantastic elements, and even fewer could be considered even remotely "Lovecraftian". Still, after about ten years, a handful of episodes were produced that might be of some interest to "Lovecraftians", including stories by John Wyndham, Ray Bradbury, and Robert Bloch. Note: This rating is not intended as a measure of quality, merely of how closely related to Lovecraftian "Weird" fiction the work is. Reviews Review Links: - (review needed) Synopsis - "And So Died Riabouchinska" (Ep. 1x20) - A detective investigates a murder at a run-down vaudeville theater, and gets a hot lead from the ventriloguist's dummy.... By Ray Bradbury. - "The Gentleman from America" (Ep. 1x31) - A rich American visits London and bets 1000 pounds that he can spend the night in a room that is said to be haunted. - "The Glass Eye" (Ep. 3x01) - Captivated by the actor's physical beauty, an aging spinster pulls up stakes to follow a ventriloquist and his dummy from performance to performance; finally, the man consents to a much-wanted meeting. - "Human Interest Story" (Ep. 4x32) - A newspaperman is assigned to interview a man who claims to be a Martian possessing a human body.... (Remade for the colorized 1980s revival series.) - "Special Delivery" (Ep. 5x10) - Mental suggestions and odd behavior have some people believing a special delivery of quick-growing mushroom spores may be an invading life form. By Ray Bradbury. - "An Occurrence at Owl Creek Bridge" (Ep. 5x13) - In the Civil War, Union soldiers are about to hang a defiant Confederate planter from a bridge, for sabotage. The noose is placed around his neck, but the rope breaks and he plummets from the bridge into a river. Dazed, he swims the rapids downstream, while the soldiers fire at him. He clambers on a river bank, and excitedly starts his journey back to his family plantation. By Ambrose Bierce. - "Summer Shade" (Ep. 6x15) - After a family moves into their new home in rural Massachusetts, they become concerned for their 9-year-old daughter's only playmate turns out to be an "imaginary friend" who may be related to a witch who once lived in the house.... - "Annabel" (Ep. 8x07) - A disturbed man's pyschotic fantasy world ensnares others in a perilous web. By Robert Bloch, starring Dean Stockwell. - "A Home Away from Home" (Ep. 9x01) - A patient at a mental hospital kills the head doctor and takes over, replacing the staff with fellow patients. Things get complicated when the niece of the real doctor makes an unexpected visit. By Robert Bloch. - "The Magic Shop" (Ep. 9x13) - After a little boy vanishes in a magic shop, he comes back later with supernatural powers and evil intentions. - "The Jar" (Ep. 9x17) - A carnival barker sells a jar containing a mysterious, shapeless mass to a disrespected yokel, who uses it to command the awe of his neighbors.... (Remade for the colorized 1980s revival series.) - "The Sign of Satan" (Ep. 9x27) - A group of studio executives view a screening of a purported occult ritual involving a mysterious European actor, and fly him to Hollywood to lead their next picture, only to discover that the film was real, and the cult now seeks to kill the actor for betraying their secrecy.... - "Consider Her Ways" (Ep. 10x11) - A woman awakens from an experiment in astral projection to find herself in the body of a mother in a dystopic distant future. By John Wyndham. - "Where the Woodbine Twineth" (Ep. 10x13) - An orphaned girl's playmate turns out to be a menacing "imaginary" friend.... - "The Monkey's Paw--A Retelling" (Ep. 10x26) - A desperate businessman tests the power of a gypsy woman's monkey paw charm which is said to grant three wishes. His son suffers the consequences. By W.W. Jacobs. Notes Comments, Trivia, Dedication - An aggressive ratings war with Boris Karloff's Thriller (1960 series) resulted in such heavy losses for Karloff's show in terms of ratings, sponsors, and writing talent, that Thriller collapsed under the pressure and had to be canceled in 1962.	http://yog-sothoth.com/wiki/index.php?title=Alfred_Hitchcock_Presents_(1955_series)&oldid=23093
THROW ME DOWN: FROM HUMBLE BEGINNINGS The seed for Throw Me Down was planted in the final year of my bachelor’s degree in 2015, when I was studying Fashion Design at London College of Fashion. I’d decided to source only eco-friendly and sustainable fabrics for my final collection, through a desire to reduce the environmental impact of my decisions, and learn more about eco-friendly options. After graduating I was conflicted as to whether or not I wanted to work in the fashion industry. Some of the major issues for me were the harmful effects that many fabric production processes have on the environment, and often the exploitation of those who produce them. AAW, SHUCKS! Whilst taking time to figure out my own direction, I took on a part-time job in Borough Market, shucking oysters. It was here that the first building bricks for Throw Me Down began to slot into place. I had decided to make fairly basic aprons for the pop-up, just as a way to stand out and feel different, and also in order to have work wear that I actually felt good in. And then the unexpected happened: customers and others from the market started asking where my apron was from, and I even got a few orders. When the pop-up closed at the end of summer 2015, with only a few orders under my belt, I decided to take the plunge and see if I could make a business doing something I enjoyed, using high-quality, eco-friendly fabrics. I’m not going to lie, it was a slow starter, but I went from having no clue what I was doing, to having my own studio space, setting up a website, social media, and creating my Etsy page. SUSTAINABILITY: LOOKING TO THE FUTURE It hasn’t always been smooth sailing, but along the way I’ve learned an awful lot, and my enthusiasm for making sustainable choices has flourished. Every day I'm inspired by different ideas about sustainability, leading to improved products. Keep an eye out for new products in the future, as well as a blog on sustainability and different ways to reduce your environmental impact. Because sharing is caring!	https://www.throwmedown.co.uk/about
Parallel Extensions to the .NET Framework is a managed programming model for data parallelism, task parallelism, and coordination on parallel hardware unified by a common work scheduler. Parallel Extensions makes it easier for developers to write programs that scale to take advantage of parallel hardware by providing improved performance as the numbers of cores and processors increase without having to deal with many of the complexities of today’s concurrent programming models. Parallel Extensions provides library based support for introducing concurrency into applications written with any .NET language, including but not limited to C# and Visual Basic. ParallelFX runs on .NET FX 3.5, and relies on features available in C# 3.0 and VB 9.0 and includes: Imperative data and task parallelism APIs, including parallel for and foreach loops, to make the transition from sequential to parallel programs simpler. Declarative data parallelism in the form of a data parallel implementation of LINQ-to-Objects. This allows you to run LINQ queries on multiple processors. (PLINQ) First class tasks that can be used to schedule, wait on, and cancel parallel work. New concurrency runtime used across the library to enable lightweight tasks and effectively map and balance the concurrency expressed in code to available concurrent resources on the execution platform. Several great examples of how to use parallelism in real world problems to obtain impressive speedups, including a raytracer, Sudoku puzzle generator, and other simple puzzle solvers and smaller samples.
YOUR QUALITY OF LIFE PROGRAM A One-to-One Wellness Program Your Quality of Life program is designed to address the needs of individuals leaving physical therapy and or needing a closely supervised exercise/rehabilitative program. Individuals currently involved in cancer treatment, aging issues, or graduating from phase 3 cardiac rehab will benefit from this program. Our fitness center is equipped with state-of-the-art exercise equipment. This equipment is designed for a wide range of training needs. Results can be achieved safely and efficiently regardless of participant’s physical limitations. The primary goal of our fitness center and staff is to serve the needs of our members and community. We are committed to a high level of hands-on staff involvement in a non-medical, non-clinical setting. Our staff perform personal health and physical evaluations in order to design the appropriate program of rehabilitation exercise for each individual. Our non-clinical therapeutic programs support individuals on their journey to achieving a healthier and more productive life style.
One of the principle challenges for Mobile Apps development has been distribution of the application. Traditional computer applications have relied on clunky installers called wizards to sort out and set up the components of a program, but this paradigm does not work well across multiple mobile platforms. Now that we have learned the basics of Mobile App Testing, let’s see different file extensions across multiple mobile OS. An .ipa file is an iOS application archive file which stores an iOS app. Each .ipa file includes a binary for the ARM architecture and can only be installed on an iOS-device. Files with the .ipa extension can be uncompressed by changing the extension to .zip and unzipping. iTunes can be used to install their contents on a device, provided the included files are signed. Most .ipa files cannot be installed on the iPhone Simulator because they do not contain a binary for the x86 architecture. To run applications on the simulator, original project files which can be opened using the Xcode SDK are required. However, some .ipa files can be opened on the simulator by extracting and copying over the .app file found in the Payload folder. /iTunesMetadata.plist — contains various bits of information, ranging from the developer’s name and ID, the bundle identifier, copyright information, genre, the name of the app, release date, purchase date, etc. The extension has no official definition, but is commonly called “iPhone Application Archive” or “iOS App Store Package” by the iOS community. Android application package (APK) is the package file format used by the Google’s Android OS for distribution and installation of Mobile Apps and middleware. APK files are a type of archive file, specifically in zip format packages based on the JAR file format, with .apk as the filename extension. The MIME type associated with APK files is application/vnd.android.package-archive. Mobile Apps development – To make an APK file, a program for Android is first compiled, and then all of its parts are packaged into one file. An APK file contains all program code (such as .dex files), resources, assets, certificates, and manifest file. As is the case with many file formats, APK files can have any name needed, provided that the file name ends in “.apk”. APK files can be installed on Android powered devices just like installing software on PC. lib: the directory containing the compiled code that is specific to a software layer of a processor, the directory is split into more directories within it. xml: An additional Android manifest file, describing the name, version, access rights, referenced library files for the application. Mobile Apps development file format introduced in Microsoft Windows 8 and Windows Phone 8.1 operating systems. Files with an “APPX” extension are basically an application package ready for distribution and installation. The AppX approach is particularly effective for distributing applications suited for multiple devices, including PCs, tablets and smartphones. XAP is the file format used to distribute and install application software and middleware onto Microsoft’s Windows Phone 7/8/8.1/10 operating system, and is the file format for Silverlight applications. Beginning with Windows Phone 8.1, XAP was replaced by APPX as the file format used to install apps on the Windows Phone platform, a move which was done by Microsoft in order to unify the app development platforms for Windows Store apps and Windows Phone apps. The MIME type associated with XAP files is application/x-silverlight-app. An XAP file is a ZIP archive that usually contains the AppManifest.xaml & DLLs required files.	http://www.softwaretestingstudio.com/mobile-apps-development-file-extensions/
Kirstin Lamb Curatorial and The Yard, Williamsburg are pleased to present a new survey of Greg Hopkins’ recent paintings, looking closely at Greg’s work in multiples, mid-sized and smaller works. Greg Hopkins makes stunning abstract paintings. Something to note about Greg and his work is his tendency to make intricate and clean spaces of painting somehow warm and inviting. There is no cold geometry to one of his paintings, though the complexity of each painstakingly hand-drawn or hand-cut component initially suggests a cooler, less vibrant and less strange abstraction. Greg doesn’t use rulers. He carefully hand-cuts layers of masking tape for each artwork, creating such complex systems and blue tape tangles, that it is hard for a fellow painter to follow. Which line comes first? How is the chevron woven into the larger loom of the picture? Where does that neon color recur, but with an elegant veil of subtle glaze over top? The hand that makes these pictures prefers soft and imperfect lines with the finest of paint application. For his more gestural abstract marks, Greg draws and drips first with ink, to create an improvisational line, which is then laboriously hand-cut and masked. Greg is both carving into ornate and dandyish wallpaper and also laying something like a gestural applique on top of the weave. Greg’s work functions as a pattern excavation, laden with a sweet and sometimes sad personal intensity, Greg is peeling off layers of wallpaper, burrowing down into his glowing 8 bit maze, a warm and welcome counterpoint to hard-edged and sometimes dry geometric formalism.	http://www.nitsrik.com/greghopkinsshow/ten-ten-ten-2010-acrylic-on-canvas-24-x-24-in
In this assignment you will explore meanings and motivations attached to choosing to go to university. To do this you will interview one student at the University of Brighton (any course – as long as you record what it is) and carry out a short thematic analysis of the interview. Prior to the interview you need to make some preparations: 1. Devise a research question based on ‘Why do people choose to go to university?’ (You can use this wording if you like or come up with different wording based on your approach). Choose a theoretical framework that you think can help us to understand students’ choices. This could be an identity-based theory, a structural theory (e.g. class, gender, etc.) or a discourse-based model (e.g. governmentality). Construct a research question that will link the theory and the topic. 2. Reflecting on the research question you are considering think about what form the interview should take – structured, semi-structured, unstructured, narrative? You should evidence your choice of method with references. 3. Write the interview questions. 4. Identify your research participant and tell them what this exercise entails. Consider any ethical implications that may attend to the research process: is the participant vulnerable, likely to disclose criminal activity or potentially distressed by the topic and research question? Remember that you should maintain confidentiality and anonymity and therefore the participant should not be named in your report. 5. Carry out the interview. Make sure you have an appropriate recording device. Take notes as you listen to the responses; your thoughts about what is being said, how it is being said and what your role in the interview process is are important. 6. Transcribe the interview. You are not doing conversation analysis, so you only need to transcribe all of the words. 7. Carry out a thematic analysis of the interview. You will need to code the transcript, using either an inductive process where the codes emerge from the data, or a deductive process where you construct a coding framework using your theory. The next stage is to identify themes and then link them to the research question. Finally, show how you address the research question drawing from the thematic analysis. 8. Write your report. This should include: • Introduction – what this report is about. • Research question including the theory that informs it • Sampling – who did you get to participate and why • Methodology and method – what is your methodological approach and why did you choose the interview method that you did, and how does this relate back to theory. • Ethical considerations • Interview process – what happened? • Thematic analysis – what was the process of analysis that you carried out and what did you find? • Critical reflection – look back at the process and your role and provide a brief assessment of the process as a whole. • Summary and conclusion • Appendix: interview transcript. Read through your report to check spelling, grammar and style. Assessment criteria: 1 Demonstrate that you can design and carry out an interview 2 Identify an appropriate theoretical framework to inform and structure the interview 3 Demonstrate an ability to analyse interview data using thematic analysis 4 Present your research in an appropriate report format with introduction, methods and methodology, ethics, analysis, and a conclusion that summarises your argument. Information of the student getting interviewed: Name: Ahmed Fakhroo Nationality: Qatari Course: Politics and Social Policy Year in university: Second year CHECK THE ADDITIONAL FILES IT WILL SHOW YOU WHAT MUST BE IN THE REPORT 1500 words NOT MORE than that. Are you interested in this answer? Please click on the order button now to have your task completed by professional writers. Your submission will be unique and customized, so that it is totally plagiarism-free.	https://legitwriting.com/thematic-analysis/
Academic Profile: https://europe.naverlabs.com/p Reflections on trustworthy and ethical technology from a Human Computer Interaction perspective. Abstract The objective to help people flourish has been a part of the agenda of the Human Computer Interaction community since its early days. Current concerns around the impacts of technology and its ethics make these early endeavours even more relevant and prominent. The reasons are many and relate to issues of broad societal concern such as sustainability, work organisation and perpetration of social inequities. In this talk I will first discuss emerging attributes that help to assess a technology as trustworthy and ethical. I will then draw on some examples of projects we have carried out in our industrial lab to explain how we included a value orientation in our research and will propose some concrete methodologies we have found useful. Biography M. Antonietta Grasso is Principal Scientist at Naver Labs Europe in the AI for Robotics group. Prior to that she has been leading the Work Practice Technology team at the Xerox Research Centre Europe. She has been an early member of the Computer Supported Cooperative Work and Human Computer Interaction communities, studying a variety of collaborative settings, mainly in the work environment. Interested in novel interfaces, her concern has always been on how to design those to mediate and reconcile the various service stakeholder needs. She has authored more than 50 peer reviewed articles and patents, and serves on a variety of scientific committees in the field. Prof. Jiannong Cao Chair Professor of Distributed and Mobile Computing, Hong Kong Polytechnic University, Hong Kong Towards Distributed Intelligence in Future Edge Computing Abstract The emerging advanced IoT applications in connected healthcare, industrial internet, multi-robot systems, and other areas demand higher intelligence of the connected devices, larger scale of the systems, and better decision making leveraged by analyzing the data being continuously generated and the advancement of AI technologies. In this context, centralized cloud computing would face high data transmission cost, high response time, and data privacy issues. The edge cloud paradigm seeks to alleviate these inefficiencies by moving the computation and analytics tasks closer to the end devices. It facilitates the evolution of IoT from instrumentation and interconnection to distributed intelligence. This talk focuses on future collaborative edge computing where edge nodes share data and computation resources and perform tasks by leveraging distributed intelligence. It covers the major problems in distributed collaboration at the edge we are currently studying, namely collaborative task execution, distributed machine learning, and distributed autonomous cooperation. Solutions need to address the challenging issues such as distributed data sources, conflicting network flows, heterogeneous devices, consistency, and mutual influence during the training. Biography Dr. Cao is the Otto Poon Charitable Foundation Professor in Data Science and the Chair Professor of Distributed and Mobile Computing in the Department of Computing at The Hong Kong Polytechnic University. He is the Dean of Graduate School, director of Research Institute for AIoT, director of Internet and Mobile Computing Lab and the associate director of University’s Research Facility in Big Data Analytics. He served the department head from 2011 to 2017. Dr. Cao’s research interests include parallel and distributed computing, wireless networking and mobile computing, big data and machine learning, and cloud and edge computing. He published 5 co-authored and 9 co-edited books, and over 500 papers in major international journals and conference proceedings. He also obtained 13 patents. Dr. Cao received many awards for his outstanding research achievements. He is a member of Academia Europaea, a fellow of IEEE and a distinguished member of ACM. In 2017, he received the Overseas Outstanding Contribution Award from China Computer Federation. Prof. Christine Julien Annis & Jack Bowen Professor in Engineering, Electrical and Computer Engineering, The University of Texas at Austin, U.S.A Opportunistic Collaborative Learning in Pervasive Computing Applications Abstract Smartphones, wearable devices, and other computational units that are ubiquitous in our environments are imbued with increasingly more complex sensing, computational, and communication capabilities. These devices can generate (and distribute) vast quantities of data that can be used to build sophisticated machine learning models for a variety of applications, e.g., classification and recommendation. Opportunistic collaborative learning (OppCL) is a framework for individual devices in pervasive computing environments to train a deep learning model that caters to the device’s personalized needs. In OppCL, each device maintains a local, personalized model. When the device encounters another device via peer-to-peer communication, it shares its model parameters and asks the neighbor to train the model using the neighbor’s local data. This talk will present the motivation and use cases behind the creation of OppCL and a basic model for collaboratively training personalized models using opportunistically available neighboring devices (and their data!). The talk will discuss multiple schemes for incorporating encountered model updates as well as techniques for handling heterogeneity in the pervasive computing environment, including bandwidth and latency constrained communication links as well as computationally constrained neighboring devices. The talk will also include presentations of practical implementations for OppCL in both large scale simulation and in real world devices. The talk will close with a look forward into open challenges and opportunities in employing OppCL to diverse pervasive computing applications. Biography Dr. Christine Julien is a professor in the Department of Electrical and Computer Engineering at the University of Texas at Austin. She is also the Associate Dean for Diversity, Equity, and Inclusion in the Cockrell School of Engineering. She is the director of the Mobile and Pervasive Computing Group, where her research focuses on the intersection of software engineering and dynamic, unpredictable networked environments. Her specific focus is on the development of models, abstractions, tools, and middleware whose goals are to ease the software engineering burden associated with building applications for pervasive and mobile computing environments. Dr. Julien’s research has been supported by the National Science Foundation (NSF), the Air Force Office of Scientific Research (AFOSR), the Department of Defense, and Google.	https://ie2022.iutbayonne.univ-pau.fr/keynotes/
New Procedural Rules for Labour Disputes This Legal Alert aims at providing you with an outline on the new procedural rules for labor disputes. Please note that the Law on Labor Courts numbered 7036 dated October 12, 2017 (“LLC”) entered into force on October 25, 2017, the date of its publishing in the Official Gazette numbered 30221. The main objective of the LLC is to speed up the resolution of employee-employer disputes by introducing an alternative dispute resolution method (i.e. mandatory mediation) and by this means to lessen the workload of the labor courts. The provisions of the LLC pertaining to mandatory mediation procedures shall enter into force on January 1, 2018. Such provisions of the LLC concerning the mandatory mediation process will not apply to pending lawsuits. We kindly note that this Legal Alert does not cover the entire provisions of the LLC, but only those that we consider to be currently of importance. No statement herein contains any opinion or professional legal advice. I. MANDATORY MEDIATION AS A DISPUTE RESOLUTION METHOD The most important change introduced by the LLC that profoundly effects the judiciary structure of the labor disputes is changing the voluntarily nature of the mediation process into an obligatory system for both parties. Application to the mediation procedures is now a ‘prerequisite of lawsuits’. This means, if an employee or employer wishes to initiate a lawsuit based on claims of receivables and compensation associated with employment or in case an employee files a reemployment lawsuit, the relevant party must initiate mediation proceedings prior to filing of a lawsuit. Differently put, the court shall reject the lawsuit on procedural grounds without any additional proceedings, if it is clear that the lawsuit was initiated without applying to mediation first. Please note that applying to mediation is not mandatory for material or immaterial compensation lawsuits arising from occupational accidents, diseases and related recourse claims. Application for the mandatory mediation should be made to the mediation office established in the counterparty’s residential address or to the mediation office having jurisdiction on the region covering the workplace address. After receiving an application from the parties, the mediation office shall appoint a mediator from the list of mediators, who will run the mediation procedures. Of course, the parties may also mutually choose a mediator from the same list of mediators. In accordance with the LLC, parties may attend to the mediation meetings in person, or be represented through their representatives or lawyers. The mediator is required to finalize the mediation proceedings within 3 (three) weeks starting from his/her appointment date. Further, he/she can extend this period for 1 (one) more week if he/she deems necessary for the purposes of investigation. In general, the mediator will end the mediation process in cases where the parties: - reach an agreement to resolve their disputes; or - cannot come to an agreement. Moreover, the mediator may also end the process for various other reasons, such as not being able to contact the parties or not being able to hold a meeting as a result of parties’ non-attendance. At the end of the mediation process, the mediator writes down the details of the agreement or disagreement to the final mediation minutes. Where the final mediation agreement is issued and signed by the mediator and parties (or their representatives), such final agreement is deemed to have the force of a court verdict. In case of failing to reach an agreement through the mediation process, the party that intends to file a lawsuit is required to attach the original final mediation minutes or its certified copy (certification is made by the mediator) to the lawsuit petition. The deadline for initiating a lawsuit, for claims other than reemployment is 5 (five) years. The employee who requests to be reemployed must apply to a mediator within 1 (one) month as of the date of the termination notice served by the employer. In case the parties fail to reach an agreement through the mediation process, the employee must initiate a lawsuit before the court within 2 (two) weeks as of the date of issuance of the mediator’s final report on the disagreement of the parties. If, at the end of the mediation process, the parties agree on reemployment of the employee, then the starting date of the reemployment and the payment amount relating to the wages and other claims accrued for the time of the unemployment must be determined by the parties. In addition to that, amount of compensation must also be determined by the parties, in cases where the employer does not reinstate the employee. II. AMENDMENTS IN LIMITATION PERIODS According to the previous applicable legislation, the claims relating to the annual paid leave days, severance payments, notice payments and compensations arising from discrimination between employees were subject to statute of limitation of 10 (ten) years. The LLC amends and determines such limitation period as 5 (five) years.	http://dirilegal.com/2018/01/03/new-procedural-rules-for-labour-disputes/
Soursop is a fruit that is green with a prickly outer texture and a soft and creamy internal texture. The taste is commonly compared to a strawberry or pineapple. The fruit is mainly found in the rainforest of Southeast Asia, South America, and Africa. The scientific name is Annona muricata. Other names include custard apple, cherimoya, guanabana, and Brazilian pawpaw. In America, the fruit is most widely known as soursop. Soursop has many nutritional benefits, such as protein, fiber, potassium, vitamin C, iron, folate, riboflavin, niacin, high antioxidant properties, and more. Other soursop benefits are purported to be treating fevers, as well as managing diabetes, hypertension, insomnia, and inflammatory conditions. In the Caribbean, soursop is a popular herbal remedy used for patients who have prostate, colorectal, breast cancer and more.	https://ahprenaturals.com/blogs/wellness/what-is-soursop-guanabana
There are many conditions by which facial appearance of individuals get affected. Age spots appears with aging. line and wrinkles are consequences of skinaging and external factors like sun damage and smoking. anti-aging procedures reduce lines and wrinkles and other cosmetic condition while enhancing skin texture. - You can login using your social profile - - Problem with login?	https://cosmeticfacial.co.uk/page/1241
StatCard Sports is a new technology that could change the way athletes track their progress and performance in a big way. Using point totals, players can keep track of their performance in every game, practice, and workout and compare it to other athletes on the platform. Users can track their progress in various sports and see detailed information, such as how far they’ve gone, how long they’ve been moving, how fast they’re going, and where they are. Users can also join or make groups with people in similar jobs to talk about common interests and work on projects together. StatCard Sports has information, tools, and inspiration to help athletes reach their full potential.	https://www.justalternativeto.com/statcard-sports/
How to Become a Software Engineer Entering Software Engineering as Your First Career Go to a Software Engineer’s Career As technology develops and becomes a big part of everyday life, the need for technology professionals also increases. Software engineers develop and guide the programs that computers use to make our life a little easier. 1. Software Engineering as Your primary Career a. Gain a Degree in Computer Science or a Relative Field: Every software engineer positions require a Bachelor Degree. Majoring software in computer science will provide the most useful background for designing and improving. Many times, the interviewee will ask questions centered on data and algorithm, so conventional computer science degrees prepare you best for it. However, to learn how the theoretical concepts you have learned can be applied in the practice of writing actual software, you will need to spend a lot of time writing software in addition to the classrooms. It is also possible to get work based on the degree of an Associate or only on the basis of your learned experience. Moving on this path, you have a good collection of complete and functional projects that demonstrate your skills on websites like Github. If you do not have your own concept then you can also target open-source projects to contribute to certain and new features. Open source means that the code for a part of the software is open (open) for public viewing. Often, it allows anyone to give code for the project, the project maintenance managers have to take it afterward. Once you have established your skills, finding an open-source project in which the developer’s community welcomes you, can speed up your skill-development. Gain a Degree in Computer Science b. Start programming immediately: If you are still in school grade, you can still give a good edge by teaching yourself the programming. Software engineering is not focused solely on coding, but you will need to know at least a few languages, and also have a deep understanding of how they work. There is no unanimity about which languages are more useful, but these are all popular choices: Python Ruby Java script C # Java C ++ Keep in mind that some languages may be better for solving some problems than others. But no language is better than any other. No language is fairly easy, unlike any other. By keeping some of the problems in mind most of the problems in the brain, which are better in solving them, but weak to solve others decide your style by testing. First of all, concentrate on acquiring most basic programs in only one language. Once you are good with one, start trying with the other. There is no need to learn all the languages. Create a place for yourself and be amazing in that! For the youth, the Massachusetts Institute of Technology, MIT, created the website and programming tool Scratch. This tool teaches programming concepts using visual signals rather than intimidating text. It is also useful for adults who will feel more comfortable focusing on visual signals instead of abstract concepts and lessons. start to learn programming language immediately c. Note the data structure and algorithm: “Algorithm” generally means a formula or process to solve a problem. The common example is finding the path for the shortest distance between two points, searching for a specific object of data in a large set of data, and sorting to organize the data in a particular sequence. The “data structure” is a definite way of organizing data to make it easier to solve some problems. General examples are such formatted compositions that include the data items and the hash table Are those that store data by a “key” rather than a status in a list. After becoming a software engineer, concentrate on developing and maintaining your skills to do your best. Note the data structure and algorithm Study Mathematics (Optional): Mathematics will be part of any computer science major, and many algorithms and data structures are generated only from mathematics. Although not mandatory, having a strong background in math will give you more robust core skills to analyze and design new algorithms. If your goal is to have companies that make sophisticated research and development, mathematics will be necessary. If you want a comfortable corporate job, you can just leave the glance at high-level mathematics. Discrete mathematics is a special useful field of study, just as any math course involving software. Study Mathematics d. Include some extra in your study: The educational system is often outdated. The modification of textbooks is slow compared to software. The academic institutions, the theoretical concepts, and methods of thinking that can be important for your success, and therefore they should not be left. However, you will be paid for how much you will be able to apply the principle to real-world software. This is where your extra study comes. Look at Stack Overflow. There is a Q & A website for Stack overflow developers. You can search by tag to identify that technique, problem site or language, in which you want to improve. Seeing others’ answers will give you insight into how engineers solve problems. Bookmarking knowledgeable solutions will also help you to develop problem-solving ability toolkit. Always try to work on practice sites for better coding tips. Sites like Code Wars and Coding Game provide thousands of problems to test your skills. Find a genuine community for inspiration, to develop contact, and guide where to focus your education. Sites like Meet Up can be a great place to find software engineers and learn more about the business. If you are unable to find common engineering meetings, try focusing on specific languages or techniques. Also, see social media sites e. Create Software: The best way to improve your skills is to use them. Regardless of whether the projects are professional or personal, the design and coding of the software will teach you a lot. For many employers, achievements found are more meaningful than GPA or theoretical knowledge. Unless you plan to earn money from the software you have created, keep it online! By allowing potential employers to see their projects and give them the code, they get an opportunity to assess your skills. It is also a great way to get feedback to help improve your skills. Create Software on your own f. Try to get an internship: Many software engineers work as interns while studying their studies. This can be a great way to create practical training and network with potential employers. Find opportunities for an internship through job posting websites and networking. Try to get an internship g. Find job opportunities: Software engineering is a fast-growing area. There is a good opportunity for immediate employment, although you can start as a programmer and make your own way for software development. Start your search before your degree: Colleges often help in finding the work of their alumni. Speak to professors, department staff, and carrier services offices to find career opportunities. A big percentage of jobs opportunities available through third party or job providing consultancy network. Use your personal contacts, and meet people from that area through career meetups and conferences. Regularly check job search websites. Create profiles and post your resume on business sites and use them for networking as well as for job applications. Find job opportunities h. Consider your career goals: The software industry is constantly changing. Improve your knowledge and practical skills, and you will have many possibilities to shape your career direction. Here are some ways to improve your job prospects: Join a business organization for networking opportunities. If you intend to stay long in this field, then think of taking a masters degree. Although it is not required for most posts, Masters degree improves the possibilities of working in industry leadership, management status, or embedded software. Masters degree can also give you an increase in the initial salary of your career. Authentication can be useful in some sub-areas and areas but can reduce your desirability in others. Before enrolling in any of these programs, talk to other specialist engineers in your area. Often, certificates are required in traditional corporate environments, but start-up and highly progressive companies can understand them as a waste of time. However, there are always exceptions. Some country certificates also look differently, so try to connect with software engineers and understand how the industry operates in your area. Consider your career goals 2. Going to a Software Engineer’s Career Careers-as-a-Software-Engineer a. Know your job prospects: Prospects for progress in the software development sector are good. Software engineering is desirable to focus compared to basic programming. The average software developer income in the United States is approximately $ 80,000- $ 100,000 per year. b. Learn programming instantly: Practical software design and coding should be your first priority. There are several ways to earn this experience: Teach yourself with the help of programming, online tutorials or friends who are willing to teach you. Complete a large open online course (MOOC). If you already have some experience, then work together with other programmers on the blueprint. If you are interested in investing money and free time, then coding-Boot camp is one of the fastest learning methods. Just do a little research, because the reputation of some boot camps is not good in the industry and it can be a waste of money. Learning-Computer-Programming-instantly c. Take advantage of your experience: The software can be a special topic, but to support you, it is not mandatory to have a computer in the past career. Software engineering can be very dependent on analytical skills, troubleshooting, and teamwork. Apart from this, your knowledge of the industry can help you to prepare the software for that industry. Even hobbies and other hobbies can give you networking opportunities, or at least you can add passion to your work. Sports apps, digital music suits, or business software are all examples of this. If possible, automate the parts of your work. Build tools to speed up tasks and make things easier. Solving the problem is the core of software engineering. Writing software, a software engineer has chosen a way to solve problems. There are problems with you! There is no such reason that you cannot start right now. d. Enroll in a degree program (optional): It is possible to get a job in programming within a few months after receiving one or two years of experience, or with enough dedication, in a few months. If, with some coding skills, you already have a bachelor in any subject, then consider directly for a Master’s degree in software engineering. Keep in mind that this is an incredibly expensive option. However, if you are having difficulty getting motivated and joining a community or being a hobby, it can be the most effective option. e. Get a job with network support: Almost every industry requires software developers, so the network of the last career can be invaluable. Think also about joining a professional association, such as the IAEG Society of Software Engineering, IEEE Computer Society Technical Council on Software Engineering, or Association for Computing Machinery. Also see, in local Meetups or online communities. The software world can be astonishingly short, and finding the right contacts can give you tremendous opportunities. PAGES About Us Place for top articles from all over the world covering fashion, sports, celebrities, shopping, entertainment, politicians, current affairs and public interest. DISCLAIMER The information published on this site is just for reference & it is not the official source of respective content. We kindly request all our readers/visitors to visit the official website of their concerned department or authority for any issues/complaints regardingany schemes, departments etc published on this blog.
JACKSONVILLE, Fla — Regency Square Mall has been given a warning citation from the City of Jacksonville’s Municipal Code Compliance Division. The citation was given to the property owner last week, citing various commercial violations in the common areas, including a roof leak, interior ceiling damage, exposed wiring and flooring. >>> STREAM ACTION NEWS JAX LIVE <<< “It looks like it needs to be remodeled and stuff,” said Jacksonville resident Roderick Anderson. “It was real bad.” Since 1967, Regency Square Mall has welcomed customers through its doors, but many say that lately the conditions inside have not been welcoming at all. Many have shared that they’re concerned about their health and safety while inside the mall, describing holes in the ceiling and caution signs at nearly every turn. Read: ‘It’s very sad’: Neighbors concerned about Regency Square Mall, owners say repairs are on the way “I wouldn’t want to be in those conditions trying to shop,” Anderson said. On Tuesday, a spokesperson with the City of Jacksonville told Action News Jax that a supervisor with Jacksonville’s Municipal Code Compliance Division met with the mall’s general manager last week. According to the city: “The general manager stated that the roofing contractor was making roof repairs prior to TS Nicole. He is working on obtaining quotes to address the damaged ceilings and drywall to provide to the corporate office to approve the work. He will continue to work to cure the issues and will update our office on the repairs.” A warning citation was also issued to Rhythm Factory for operating without a COU (Certificate of Use). According to the city, they currently have an active permit and are trying to obtain a COU. [DOWNLOAD: Free Action News Jax app for alerts as news breaks] Read: Read: [SIGN UP: Action News Jax Daily Headlines Newsletter] Click here to download the free Action News Jax news and weather apps, click here to download the Action News Jax Now app for your smart TV and click here to stream Action News Jax live.	https://www.wokv.com/news/local/regency-square-mall-given-warning-citation-safety-health-hazards/F6TQ5WFMJJCCLFYHLVTRQX7EN4/
More than 3.6 million Australians over the age of 25 have high blood pressure or are on medication for the condition, but findings recently released by the Chiropractors’ association of Australia indicate there is a non-drug alternative that can lower abnormal blood pressure in healthy bodies by 7.8% – 13%. The latest findings published in the Journal of Manipulative and Physiological Therapeutics Vol, 24,No.2,by Dr Gary Knutson DC., show chiropractic adjustments to the upper neck can lower systolic blood pressure almost immediately. According to Dr Laurie Tassell, National Spokesperson for the Chiropractors’ Association of Australia, a chiropractic pilot study involving 80 people found there is a relationship between the upper neck vertebrae and the body’s natural blood pressure control reflexes.	https://www.revivefamilychiro.com/chiropracticslider/blood-pressure/
While we were within the Luxembourg Gardens in the 6th Arrondissement of Paris, we took these high definition photos showing Pot No 34 holding a Punica Granatum Flore Pleno shrub. Luxembourg photos - << Previous 111 112 113 114 115 116 117 118 119 120 Next >> This first HD photo shows the Punica Granatum Flore Pleno, which is the scientific name, or botanical name for the Flowering Pomegranate, which is an ornamental flowering shrub that can often be found in pots like you can see here and thrives in places that have full sun. This is a close up photograph showing the stem of the Pomegranate and its branches, yet if you look very carefully between the leaves you will see a few bits of red colour, and this is the start of the double red flowers that blossom on this shrub during the summer months. So here you can see the Punica Granatum Flore Pleno from behind, that has been positioned in the central formal garden area of the Jardin du Luxembourg next to the stairs leading up to the western terrace and opposite the Grand Basin, and this particular shrub is taken out of the Orangerie and placed within the gardens during the warmer months. However, this last image shows the tourist information plaque fixed to the oak panelled green crate, and as you can see from the details of Pot 34, the Punica Granatum Flore Pleno originally came from places such as South East Europe and Asia, and this is an ornamental Flowering Pomegranate that has double flowers in the family of punicaceae. Luxembourg photos - << Previous 111 112 113 114 115 116 117 118 119 120 Next >> If you would like to use any of these photos for non commercial use we only ask that you please do include recognition to ourselves "eutouring.com", but if you are not sure with regards to usage, please contact us.	https://www.eutouring.com/images_jardin_du_luxembourg_117.html
3-Day artists in residence workshop. The contemporary music ensemble Insomnio experimented with improvised music inspired by various spatial contexts. Colors, materials, architecture and acoustic qualities interacted with the mainly classical and contemporary music background of the musicians and composers. Insomnio explored their core values through confrontation with the experimental architecture of Parasites Paradis at Leidsche Rijn.	https://bureaubakker.com/portfolio/insomnioparasites/
- No updates yet. the project More than three years after the BP disaster, and a couple of years after the "clean up" has ended, the impacts of BP's oil on Louisiana marshes remain. Although the Coast Guard has stood down, there remains a need to monitor the sensitive salt marshes. This is left to the Louisiana communities most affected by the BP disaster. Public Lab, with Gulf Restoration Network, has received some funding to montior the heavily-oiled wetlands of Barataria Bay, but the full goal of empowering those most affected by BP's impact requires the next step. With your help, Public Lab and GRN staff will organize several outreach and training sessions, so that the people of Barataria Bay can learn low-cost aerial monitoring and annotate the resulting maps themselves. Because many on the Gulf Coast fall on one side of the community divide, printed maps are an essential part of outreach. The maps that Public Lab printed of oiled marshes in Barataria Bay in 2011 were very popular along the coast, and we seek to update people on the status of their wetlands the way that they engage information. Other funds will go to finalization of these community maps, so that people around the world will be able to view them via the Google Earth Platform. the steps Gulf Restoration Network and Public Lab will hold trainings and mapping sessions with Gulf leaders to learn low-cost mapping techniques, but also learn how the Barataria landscape has changed since 2011. why we're doing it The impacts of BP's oil on the Barataria ecosystem will unfold over decades. As Gulf communities struggle to adapt to an altered ecosystem, low-cost environmental monitoring techniques can provide a window into the world around us, as well as a compelling method of communicating our environmental challenges post-BP. In line with the Gulf Future goals, GRN and PublicLab can train Barataria residents with the ability to monitor their environment, to hold government and BP accountable for restoration of Barataria Bay marshes. In late Winter 2014, we will hold several training, mapping, and annotation sessions with local residents to complete a second round of high-quality maps based upon low-altitude aerial photography methods Public Lab pioneered in 2010. By spring, and the fourth anniversary of the disaster, we will be able to present, among ourselves and to the media and scientific conferences, some results of a community-led mapping of BP's impacts. budget Final production of maps ($1,000) Printing hardcopy booklets ($3,000) Engagement, outreach, community meetings ($2,000) \|SUBTOTAL =\|\|$6,000\| \|ioby Platform Fee\|\|$35\| \|ioby Fiscal Sponsorship Fee (5%)\|\|$300\| \|3rd Party Credit Card Processing Fee (3%)\|\|$180\| \|TOTAL TO RAISE =\|\|$6,515\| updates Sorry, but this project doesn't have any updates yet. photosThis is where photos will go once we build flickr integration donors - Scott E. - Shannon D. - Rebecka C.	https://ioby.org/project/put-people-picture-barataria-wetlands-co-monitoring
BACKGROUND OF THE INVENTION SUMMARY OF THE INVENTION DESCRIPTION OF THE PREFERRED EMBODIMENTS 1. Field of the Invention The present invention relates to a high-frequency coupler and a communication device that perform large-volume data transmission in proximity through a weak UWB (Ultra Wide Band) communication method using a high-frequency wide-band, and particularly to a high-frequency coupler and a communication device that secure a communication range in the transverse direction in weak UWB communication using electric field coupling. 2. Description of the Related Art Non-contact communication has been widely used as a medium for authentication information, electronic money, or other value information. In addition, in recent years, as additional applications of such a non-contact communication system, large-capacity data transmission such as downloading and streaming of moving images, music, or the like can be exemplified. Such large-volume data transmission can also be implemented by the operations of a single user, preferably completed within the same access time as used by the existing authentication or billing process, and therefore it is necessary to increase the communication rate. The general RFID standard uses the 13.56 MHz band, is for proximity type (0 to 10 cm or shorter: Proximity) non-contact bidirectional communication adopting the main principle of electromagnetic induction, and employs a communication rate of about 106 kbps to 424 kbps. On the other hand, TransferJet (for example, refer to Japanese Patent No. 4345849 and www.transferjet.org/en/index.html) that uses weak UWB signals can be exemplified as a proximity wireless transfer technology applicable to high-speed communication. The proximity wireless transfer technology (TransferJet) is basically a method for transmitting signals by using the action of electric field coupling, and a high-frequency coupler of such a communication device includes a communication circuit unit that processes high-frequency signals, a coupling electrode that is arranged in a certain height apart from the ground, and a resonating unit that supplies high-frequency signals to the coupling electrode efficiently. The proximity wireless transfer using the weak UWB has a communication distance of about 2 to 3 cm, only about as wide both in the longitudinal and transverse directions, is without polarized waves, and has a communication range in the shape of a substantially hemisphere dome. For that reason, it is necessary to activate electric field coupling effectively by facing the coupling electrodes appropriately to each other between communication devices for performing data transmission. If a functioning unit of proximity wireless transfer is manufactured in a small size, the function will be suitable for incorporation, and can be mounted in various kinds of information equipment, for example, personal computers, mobile phones, or the like. However, if the size of a coupling electrode in a high-frequency coupler is reduced, there is a problem that the communication range diminishes particularly in the transverse direction. For example, if a target point, which indicates a spot where a high-frequency coupler is embedded, is marked on the housing surface of information equipment, a user may conduct an alignment aimed toward the target point. However, if the communication range of the transverse direction is narrow, a target point may be obscured by the shadow of the other equipment when they are adjacent, resulting that the target point is aligned while shifted from the center thereof in the transverse direction. In order to improve usability in practical use of the proximity wireless transfer function, it is necessary to extend the communication range in the transverse direction. However, if the size of a coupling electrode in a high-frequency coupler is simply increased, a standing wave occurs on the surface of a coupling electrode. Then, since charges with different polarities are distributed and electric fields of both of the adjacent electric fields with the different polarities are cancelled at a portion where the amplitude of the standing wave travels in opposite directions, places having the electric field with high intensity and low intensity appear. The place having the electric field with low intensity becomes a dead-point (null point) in which fine effect of electric field coupling is not easily obtained, even when the coupling electrode of a communication partner is aligned. A high-frequency coupler basically radiates electric field signals only in the front direction and does not radiate signals in the side direction. For this reason, unless the front faces of communication devices incorporated with high-frequency couplers face each other, stable communication is not secured, and therefore, usability is unsatisfactory. It is desirable for the present invention to provide an excellent high-frequency coupler and a communication device that enable the large-volume data transmission in proximity in a weak UWV communication method using a high-frequency wide-band. It is further desirable for the invention to provide an excellent high-frequency coupler and a communication device that can secure a sufficient communication range in the transverse direction in proximity wireless transfer using the weak UWB without polarized waves. According to an embodiment of the present invention, there is provided a high-frequency coupler including a ground, a coupling electrode which faces the ground and is supported so as to be separated by a negligible height with respect to the wavelength of a high-frequency signal, a resonating unit for increasing a current flowing into the coupling electrode via a transmission path, a supporting unit which is connected to the resonating unit at about the center of the coupling electrode, and a short-circuiting unit which short-circuits the tip portions of the coupling electrode to the ground, in which an infinitesimal dipole constituted by a line connecting the center of the charges accumulated in the coupling electrode and the center of mirror-image charges accumulated in the ground is formed, and the high-frequency signal is transmitted toward a high-frequency coupler of a communication partner side arranged to face each other so that the angle θ formed in the direction of the infinitesimal dipole is substantially 0 degrees. According to the embodiment of the present invention, the coupling electrode in the high-frequency coupler has a size of ½ of the wavelength from the root of the supporting unit to the tip portions which are short-circuited to the ground via the short-circuiting unit. According to the embodiment of the present invention, the front direction of the coupling electrode is the radiation direction of electric field signals in which the face can serve as a first radiating face, and the side direction of the short-circuiting unit is a radiation direction of electric field signals in which the face can serve as a second radiating face. According to an embodiment of the present invention, there is provided a communication device including a communication circuit unit which performs a process of a high-frequency signal transmitting data, a transmission path of a high-frequency signal connected to the communication circuit unit, a coupling electrode which faces the ground and is supported so as to be separated by a negligible height with respect to the wavelength of the high-frequency signal, a resonating unit for increasing a current flowing into the coupling electrode via the transmission path, a supporting unit which is connected to the resonating unit at about the center of the coupling electrode, and a short-circuiting unit which short-circuits the tip portions of the coupling electrode to the ground, in which the coupling electrode has a size of ½ of the wavelength from the root of the supporting unit to the tip portions which are short-circuited to the ground via the short-circuiting unit, and an infinitesimal dipole constituted by a line connecting the center of the charges accumulated in the coupling electrode and the center of mirror-image charges accumulated in the ground is formed, and the high-frequency signal is transmitted toward a high-frequency coupler of a communication partner side arranged to face each other so that the angle θ formed in the direction of the infinitesimal dipole is substantially 0 degrees. According to an embodiment of the invention, there is provided an excellent high-frequency coupler and a communication device that enable large-volume data transmission in proximity by a weak UWB communication method using a high-frequency wide-band. According to an embodiment of the invention, there is provided an excellent high-frequency coupler and a communication device that can secure a sufficient communication range in the transverse direction in proximity wireless transfer using the weak UWB without polarized waves. According to an embodiment of the invention, there is provided an excellent high-frequency coupler and a communication device that can expand the communication range particularly in the transverse direction by increasing the size of a coupling electrode and radiating an electric field signal in a wide range. According to an embodiment of the invention, since the communication range can be expanded in the transverse direction mainly from the center of the coupling electrode, users can conduct stable communication even without having to bring the marks of the target points into close proximity for alignment when, for example, the information equipment incorporated with high-frequency couplers are made to face each other. Other goal, characteristics, advantages of the present invention will be clarified by detailed descriptions based on embodiments of the present invention to be described later and accompanying drawings. Hereinbelow, an embodiment of the present invention will be described in detail with reference to drawings. FIG. 1 14 24 10 20 11 14 24 21 20 is a diagram schematically illustrating the composition of a proximity wireless transfer system in the weak UWB communication method using the action of electric field coupling. In the same drawing, coupling electrodes and used in transmission and reception that belong to a transmitter and a receiver respectively are arranged apart, for example, by about 3 cm (or about ½ of the wavelength of the frequency band being used) from each other in an opposed manner so as to enable electric field coupling. The transmission circuit unit in the transmitter side generates high-frequency transmission signals such as UWB signals based on transmission data when a transmission request is made from an higher level application, and the signals penetrate from the transmitting electrode to the receiving electrode as electric field signals. In addition, the reception circuit unit in the receiver side performs the processes of demodulation and decoding for the received high-frequency electric field signals and passes the produced data to the higher level application. If the UWB is used in the proximity wireless transfer, ultra-high-speed data transfer of 100 Mbps can be realized. In addition, in the proximity wireless transfer, the coupling action of an electrostatic field or an induced electric field is used as described later, not a radiated electric field. Since the intensity of an electric field is in proportion to the cube or the square of a distance, a proximity wireless transfer system can be used as weak wireless unnecessary with license from a radio station by suppressing the intensity of the electric field to a certain level or lower within a distance of 3 meters from the wireless facility and formed at a low cost. In addition, since data communication is performed in the electric field coupling method in the proximity wireless transfer, it is advantageous in that interference influences only slightly as reflected waves from reflective objects in the peripheral environment are small, and that consideration of preventing hacking or securing confidentiality on the transmission path is not necessary. On the other hand, in wireless communication, the propagation loss gets greater according to the extent of the distance that the wavelength propagates. In the proximity wireless transfer that uses high-frequency wide-band signals as the UWB signals, the communication distance of about 3 cm is equivalent to ½ of the wavelength. In other words, the communication distance can be said to be proximal but is a length that is not negligible, and therefore, the propagation loss is necessary to be suppressed to a sufficiently low level. Above all, a high-frequency circuit has a more serious problem in characteristic impedance in comparison to a low-frequency circuit, and has significant influence caused by impedance mismatch in the coupling point between the electrodes of the transmitter and the receiver. FIG. 1 11 14 14 24 For example, in the proximity wireless transfer system shown in , even if the transmission path of high-frequency electric field signals connecting the transmission circuit unit and the transmitting electrode is on a coaxial line where 50Ω of impedance is matched, the electric field signals are reflected causing propagation losses when the impedance in the coupling portion between the transmitting electrode and the receiving electrode is mismatched, thereby lowering communication efficiency. FIG. 2 10 20 14 24 12 22 13 23 Accordingly, as shown in , the high-frequency coupler arranged in each of the transmitter and the receiver is configured such that plate-shaped electrodes and and a resonating unit that includes series inductors and and parallel inductors and are connected to a high-frequency signal transmission path. The high-frequency signal transmission path referred here can be constituted by a coaxial cable, a micro-strip line, a coplanar line or the like. If high-frequency couplers of such a kind are arranged to face each other, a coupling portion acts as a band-pass filter in extreme proximity where a quasi-electric field is dominant, thereby high-frequency signals can be transferred. In addition, even in a distance that is not negligible with respect to a wavelength and an induced electric field is dominant, the high-frequency signals can be transferred efficiently between two high-frequency couplers via an induced electric field generated from an infinitesimal dipole (described later) formed by charges and mirror-image charges respectively accumulated in the coupling electrode and the ground. 10 20 14 24 12 22 14 13 23 14 24 14 14 14 24 Hence, if it is aimed to simply match impedance and only suppress reflected waves between the electrodes of the transmitter and the receiver , that is, in the coupling portion, the impedance in the coupling portion can be designed to be continuous even when each coupler employs a simple configuration where the plate-shaped electrodes and and the series inductors and are in series connection on the high-frequency signal transmission path. However, since characteristic impedance in the front and rear parts of the coupling portion does not change, the current amplitude does not change. With respect to the point, bigger charges can be sent to the coupling electrode by providing the parallel inductors and , and strong electric field coupling action can occur between the coupling electrodes and . In addition, a large electric field is induced around the surface of the coupling electrode , and the generated electric field propagates from the surface of the coupling electrode to the front direction (the direction of the infinitesimal dipole to be described later) as an electric field signal of an oscillating longitudinal waves. The waves of the electric field enable the electric field signal to propagate even when the distance between the coupling electrodes and (phase height) is relatively long. To summarize, vital conditions of a high-frequency coupler in a proximity wireless transfer system by a weak UWB communication method are as follows. (1) To provide a coupling electrode facing the ground in order to perform coupling with an electric field at a location separated from the wavelength of a high-frequency signal by a negligible height (2) To provide a resonating unit in order to perform coupling with a stronger electric field (3) To set a constant of a capacitor by series/parallel inductors and a coupling electrode or the height of a stub so as to take impedance matching when coupling electrodes are placed to face each other in a frequency band used for communication. 14 24 10 20 FIG. 1 When the coupling electrodes and of the transmitter and the receiver are faced with an appropriate distance apart from each other in the proximity wireless transfer system shown in , two high-frequency couplers operate as a band-pass filter through which electric field signals pass in a predetermined high-frequency band, and a single high-frequency coupler acts as an impedance converting circuit that amplifies currents, thereby flowing currents with high amplitude in the coupling electrodes. On the other hand, when the high-frequency coupler is independently placed in a free space, the input impedance of the high-frequency coupler does not correspond to a characteristic impedance on the high-frequency signal transmission path, the signal that enters into the high-frequency signal transmission path is reflected in the high-frequency coupler, but not emitted to the outside, and therefore, the signal does not give influence on other neighboring communication systems. In other words, when there is no communication partner, the transmitter does not release radio waves as antennas of the past did, and high-frequency electric field signals are transferred by taking impedance matching only when the communication partner gets closer. FIG. 3 FIG. 2 10 20 14 15 17 16 15 15 14 shows an embodiment of the high-frequency coupler shown in . Both of the high-frequency couplers of the transmitter and the receiver can be configured in the same manner. In the drawing, the coupling electrode is provided on the top surface of a spacer made of a dielectric, and electrically connected to the high-frequency signal transmission path on the printed board via a through-hole penetrating the spacer . In the same drawing, the spacer has a substantially cylindrical shape, and the coupling electrode has a substantially circular shape, but neither of them is limited to a specific shape. 16 16 14 17 15 17 17 18 14 16 16 12 18 13 FIG. 2 For example, after a dielectric having a desired height is formed with the through-hole therein, the through-hole is filled with a conductor, and a conductor pattern to be the coupling electrode is deposited on the top surface of the dielectric using, for example, by a plating technique. In addition, a wiring pattern serving as the high-frequency signal transmission path is formed on the printed board . Then, the high-frequency coupler can be made by mounting the spacer on the printed board by conducting reflow soldering. The appropriate adjustment of the height from the circuit-mounted surface on the printed board (or the ground ) to the coupling electrode , that is, the length of the through-hole (phase height) in accordance with a wavelength to be used makes it possible for the through-hole to have inductance and to be substituted for the series inductor shown in . In addition, the high-frequency signal transmission path is connected to the ground via the chip-shaped parallel inductor . 14 10 Herein, the electromagnetic field generated in the coupling electrode in the side of the transmitter will be discussed. FIGS. 1 and 2 14 11 14 12 13 As shown in , the coupling electrode is connected to one end of the high-frequency signal transmission path, and accumulates charges with high-frequency signals that are output from the transmission circuit unit and flow therein. At this moment, the charges flowing into the coupling electrode via the transmission path are amplified by a resonating effect of the resonating unit formed of the series inductor and the parallel inductor , and larger charges are accumulated. 18 14 14 18 In addition, the ground is provided separated from the wavelength of the high-frequency signal by a negligible height (phase height) so as to face the coupling electrode . Then, if charges are accumulated in the coupling electrode as described above, mirror-image charges are accumulated in the ground . If point charges Q are placed outside the planar conductor, mirror-image charges −Q (which is virtual and replaces the surface charge distribution) are provided in the planar conductor, but this matter is the related art as described in, for example, “Electromagnetics” written by Tadashi Mizoguchi (pp. 54 to 57, Shokabo). 14 18 θ R φ As a result of the point charges Q and the mirror-image charges −Q being accumulated as described above, the infinitesimal dipole formed by a line connecting the center of the charges accumulated in the coupling electrode and the center of the mirror-image charges accumulated in the ground is formed. Strictly speaking, the charges Q and the mirror-image charges −Q have the volume, and the infinitesimal dipole is formed so that the center of the charges and the center of the mirror-image charges are connected to each other. The “infinitesimal dipole” mentioned here refers to “a dipole that has a very short distance between charges of an electric dipole”. For example, “Antennas and Propagation” written by Yasuto Mushiake (pp. 16 to 18, Corona) also describes the “infinitesimal dipole”. In addition, the infinitesimal dipole causes to generate a transverse wave component E of the electric field, a longitudinal wave component Eof the electric field, and a magnetic field H in the circumference of the infinitesimal dipole. FIG. 4 FIG. 5 θ R φ shows the electric field of the infinitesimal dipole. In addition, illustrates the state where the electric field is matched on the coupling electrode. As shown in the drawings, the transverse wave component E of the electric field oscillates in a direction perpendicular to the propagating direction, and the longitudinal wave component Eof the electric field oscillates in parallel with the propagating direction. In addition, the magnetic field H is generated in the circumference of the infinitesimal dipole. Formulas (1) to (3) below express the electromagnetic field generated by the infinitesimal dipole. In the formulas, the component in inverse proportion to the cube of the distance R is a static electromagnetic field, the component in inverse proportion to the square of the distance R is an induced electromagnetic field, and the component in inverse proportion to the distance R is a radiated electromagnetic field. <math overflow="scroll"><mtable><mtr><mtd><mrow><msub><mi>E</mi><mi>θ</mi></msub><mo>=</mo><mrow><mfrac><mrow><mi>p</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msup><mi>ⅇ</mi><mrow><mrow><mo>-</mo><mi>j</mi></mrow><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>k</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>R</mi></mrow></msup></mrow><mrow><mn>4</mn><mo>⁢</mo><mi>πɛ</mi></mrow></mfrac><mo>⁢</mo><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><msup><mi>R</mi><mn>3</mn></msup></mfrac><mo>+</mo><mfrac><mrow><mi>j</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>k</mi></mrow><msup><mi>R</mi><mn>2</mn></msup></mfrac><mo>-</mo><mfrac><msup><mi>k</mi><mn>2</mn></msup><mi>R</mi></mfrac></mrow><mo>)</mo></mrow><mo>⁢</mo><mi>sin</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>θ</mi></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>E</mi><mi>R</mi></msub><mo>=</mo><mrow><mfrac><mrow><mi>p</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msup><mi>ⅇ</mi><mrow><mrow><mo>-</mo><mi>j</mi></mrow><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>k</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>R</mi></mrow></msup></mrow><mrow><mn>2</mn><mo>⁢</mo><mi>πɛ</mi></mrow></mfrac><mo>⁢</mo><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><msup><mi>R</mi><mn>3</mn></msup></mfrac><mo>+</mo><mfrac><mrow><mi>j</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>k</mi></mrow><msup><mi>R</mi><mn>2</mn></msup></mfrac></mrow><mo>)</mo></mrow><mo>⁢</mo><mi>cos</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>θ</mi></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>H</mi><mi>ϕ</mi></msub><mo>=</mo><mrow><mfrac><mrow><mi>jω</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>p</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msup><mi>ⅇ</mi><mrow><mrow><mo>-</mo><mi>j</mi></mrow><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>k</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>R</mi></mrow></msup></mrow><mrow><mn>4</mn><mo>⁢</mo><mi>π</mi></mrow></mfrac><mo>⁢</mo><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><msup><mi>R</mi><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mrow><mi>j</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>k</mi></mrow><mi>R</mi></mfrac></mrow><mo>)</mo></mrow><mo>⁢</mo><mi>sin</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>θ</mi></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mtd></mtr></mtable></math> θ R θ R FIG. 1 In order to suppress interfering waves to peripheral systems, it is preferably considered that the transverse wave E that includes the component of the radiated electric field is suppressed and the longitudinal wave Ethat does not include the component of the radiated electric field is used in the proximity wireless transfer system shown in . The reason is because the transverse wave component E of the electric field includes the radiated electric field that is in inverse proportion to a distance (in other words, that shows slight reduction in a distance), but the longitudinal wave component Edoes not include the radiated electric field, as understood from the formulas (1) and (2) above. θ R θ 1 2 FIG. 2 FIG. 6 First of all, in order not to bring about the transverse wave E of the electric field, it is necessary for the high-frequency coupler not to operate as an antenna. The high-frequency coupler shown in has a similar structure to a “capacity-loaded type” antenna that has electrostatic capacity by attaching metal on the tip of an antenna element and of which the height is reduced. Therefore, it is necessary for the high-frequency coupler not to operate as a capacity-loaded type antenna. shows a composition example of the capacity-loaded type antenna, and the longitudinal wave component Eof the electric field is generated largely in the direction of Arrow A and the transverse wave E of the electric field is generated in the directions of Arrows Band B. FIG. 3 FIG. 6 15 16 14 18 12 18 14 12 17 14 15 17 14 15 12 14 18 12 θ 1 2 θ In the composition example of the coupling electrode shown in , the dielectric and the through-hole play both roles of avoiding the coupling of the coupling electrode and the ground and of forming the series inductor . The electric coupling of the ground and the electrode is avoided and the effect of the electric coupling with the high-frequency coupler of the receiver side is secured by configuring the series inductor with a sufficient height from the circuit mounting surface on the printed board to the electrode . However, if the height of the dielectric is high, in other words, if the distance from the circuit mounting surface on the printed board to the electrode has a length that is not able to be negligible for the used wavelength, the high-frequency coupler acts as a capacity-loaded type antenna, and thus the transverse wave E is generated as indicated by Arrows Band Bin . Therefore, there are conditions that the height of the dielectric is to be a sufficient length for forming the series inductor necessary for acquiring characteristics as a high-frequency coupler by avoiding coupling of the electrode and the ground and for acting as an impedance matching circuit, and is short to the extent that unnecessary electric waves E by the current flowing the series inductor are not radiated heavily. R R On the other hand, it is understood from the formula (2) that the longitudinal wave component Eis maximized when the component forms an angle θ=0 with the direction of the infinitesimal dipole. Therefore, in order to conduct non-contact communication by using the longitudinal wave component Eof the electric field, high-frequency electric field signals are preferably transmitted by placing the high-frequency coupler of the communication partner in an opposed manner so that the angle θ formed with the direction of the infinitesimal dipole is about 0 degrees. 14 12 13 14 R In addition, the current of the high-frequency signals flowing into the coupling electrode can be greater by the resonating unit formed of the series inductor and the parallel inductor . As a result, the moment of the infinitesimal dipole formed by the charges accumulated in the coupling electrode and the mirror-image charges in the ground side can be greater, and the high-frequency electric field signals formed of the longitudinal wave Ecan be efficiently radiated toward the propagating direction where the angle θ formed with the direction of the infinitesimal dipole is about 0 degrees. FIG. 2 0 1 2 In the high-frequency coupler shown in , the operating frequency fis decided in an impedance matching unit by constants Land Lof the parallel inductor and the series inductor. However, generally, since the band of a lumped constant circuit is narrower than that of a distributed constant circuit in a high-frequency circuit, and the constant of an inductor gets smaller as the frequency gets higher, it is problematic in that the resonating frequency is deviated by unevenness in the constants. With regard to this matter, it can be considered that a wider bandwidth is realized with a solution that the high-frequency coupler is constituted by replacing the lumped constant circuit with the distributed constant circuit in the impedance matching unit and the resonating unit. FIG. 7 72 71 73 75 74 73 72 76 71 73 78 77 shows a composition example of a high-frequency coupler in which a distributed constant circuit is used for the impedance matching unit and the resonating unit. In the example shown in the drawing, a high-frequency coupler is provided where a ground conductor is formed on the bottom surface, and a printed board formed with a printed pattern is arranged on the top surface. As the impedance matching unit and the resonating unit of the high-frequency coupler, a micro-strip line or a coplanar waveguide, that is, a stub is formed as a distributed constant circuit instead of a parallel inductor and a series inductor, and is connected to a transmission/reception circuit module via a signal line pattern . The stub is connected and short-circuited to the ground in the bottom surface via a through-hole penetrating the printed board at the tip of the stub. In addition, around the center of the stub , a coupling electrode is connected thereto via one terminal formed of a thin metal line. Furthermore, “stub” referred to in the technological field of electrical engineering is a collective term of electric wires of which one end is connected, and the other end is not connected or ground-connected, and provided in the middle of a circuit for the use of adjustment, measurement, impedance matching, filter, or the like. 73 73 73 74 73 71 73 73 73 73 73 78 77 73 FIG. 8 The signal input from the transmission/reception circuits via the signal line is reflected in the tip portion of the stub and a standing wave occurs in the stub . The phase height of the stub is about ½ of the wavelength of the high-frequency signal (180 degrees in terms of phase), the signal line and the stub are formed of the micro-strip line, coplanar line, and the like on the printed board . As shown in , when the tip is short-circuited with the phase height of the stub of ½ of the wavelength, the voltage magnitude of the standing wave occurring in the stub is 0 at the tip of the stub , and reaches the maximum at the center of the stub , that is, a point ¼ of the wavelength (90 degrees) from the tip of the stub . If a coupling electrode is connected to one terminal around the center of the stub where the voltage magnitude of the standing wave reaches the maximum, a high-frequency coupler having excellent propagating efficiency can be made. 73 71 73 FIG. 7 Since the stub shown in is the micro-strip line or the coplanar waveguide on the printed board , and the DC resistance is small, the high-frequency signal has little loss, and therefore, propagation loss between the high-frequency couplers can be reduced. In addition, since the size of the stub constituting the distributed constant circuit is as large as ½ of the wavelength of the high-frequency signal, errors in the dimension due to tolerance during the production are very slight relative to the entire phase height, and unevenness in characteristics does not easily occur. Subsequently, a method of expanding the communication range will be considered in the proximity wireless transfer using the weak UWB. When the proximity wireless transferring function is applied to be incorporated into information equipment, a user is not able to see the mark of the target point attached on the housing of the equipment for the purpose of aligning, and the equipment contact deviates in the transverse direction from the center. For this reason, in order to improve the advantage of the proximity wireless transferring function in practical use, it is necessary to expand the communication range in the transverse direction. FIG. 9 90 92 91 92 92 92 shows the state of a high-frequency coupler formed by mounting a coupling electrode on a ground board , in which charges are accumulated in the coupling electrode when a high-frequency signal is input into the coupling electrode. As shown by the drawing, the amount of the charges accumulated in the coupling electrode changes in the form of a sine wave. In the high-frequency band of a GHz class of which the wavelength is as short as the UWB, the size of a coupling electrode becomes non-negligibly high relative to the wavelength. For this reason, distribution of charges such as a standing wave occurs on the coupling electrode . In addition, in the same drawing, the electric field occurring from the coupling electrode is indicated by dotted lines. FIG. 9 92 93 91 92 92 92 91 In the example of , in terms of the size of the coupling electrode , the height from the root of a supporting unit connected to the ground board (resonating unit) to the tip is designed to be ¼ of the wavelength. In addition, the tip of the coupling electrode is in an open-ended state. The open state corresponds to the fixed end of the standing wave of the current, and to an anti-node where the amplitude of the charges accumulated in the tip portion becomes the maximum. If high-frequency signals are input to the coupling electrode , the standing wave of the current occurs. In that case, the charges accumulated in each portion on the coupling electrode have the same polarities at all times. In addition, the ground board accumulates mirror-image charges with reverse polarity according to the charges accumulated in each portion. FIG. 6 FIG. 10A FIG. 10A Herein, ¼ of the wavelength as the size of the coupling electrode will be described. As described before with reference to , the structure in which the coupling electrode is supported on the ground board in the high-frequency coupler is similar to that of a “capacity-loaded type” antenna which enables reduction in the height thereof. An antenna in which a metal line having the length of ¼ wavelength is erected perpendicular to the ground as shown in is called a ¼ of the wavelength type monopole antenna. When a high-frequency signal is input to the metal line, the standing wave of the current occurs, the tip of the metal line serves as a fixed end of the standing wave of the current, and the current amplitude is 0. On the other hand, a power feeding point of the root of the metal line has the maximum current amplitude. Therefore, the current distribution as shown in appears. FIG. 10B Incidentally, as in the related art, if the length of the metal line is shortened and the tip thereof is fixed to a metal plate, the height of the antenna can be lowered while maintaining the resonating state of ¼ of the wavelength. This is because the metal plate can accumulate charges as an electrode of one capacitor does. shows the structure of a capacity-loaded type antenna of which the height is lowered. The drawing also shows the current distribution occurring in the antenna, but the current amplitude in the metal plate corresponding to the location of the tip of the shortened metal plate does not become 0, and the current distribution appears as if the metal line is lengthened to the end. θ θ R FIG. 10C The capacity-loaded type antenna can be obtained by reducing the height of a monopole antenna, but what effectively operates absolutely as the radiating element of an antenna, in other words, what generates the transverse wave components E of an electric field is the metal line portion. Generally, if the height of the antenna is reduced, in other words, the length of the metal line is shortened, radiation efficiency of the antenna decreases. On the other hand, in the case of a high-frequency coupler, it is desirable that the transverse wave components E of an electric field, that is, the radiation of an electric wave, is small. Hence, as shown in , the length of the metal line is designed to be very short relative to the wavelength, but a high-frequency coupler that radiates stronger electric field signals of the longitudinal wave component Eby setting the size of the metal plate at the tip of the metal line to the resonating state of ¼ of the wavelength together with the metal line. Anyway, if the tip of the coupling electrode is in an open state, it is certain that the length from the root connected to the resonating unit to the tip is ¼ of the wavelength. This indicates that the communication range of the high-frequency coupler expands only up to about ¼ of the wavelength in the transverse direction. With regard to this matter, the present inventor suggests a structure of a high-frequency coupler in which the tip portion of a coupling electrode is short-circuited to the ground. FIG. 11 110 115 116 118 112 113 112 113 115 114 112 schematically shows the composition of a high-frequency coupler . In the example shown in the drawing, a resonating unit is a stub with its length of ½ of the wavelength, and the tip portion thereof is short-circuited to the ground via a trough-hole . In addition, a coupling electrode is supported by a supporting unit at the center of the stub. The coupling electrode is supported by the supporting unit about at the center on the resonating unit , and is in the grounded state in the short-circuiting unit at the tip portions of the coupling electrode . 114 113 115 114 116 117 112 Herein, the grounded state in the short-circuiting unit corresponds to a free end of the standing wave of a current, and the amplitude of charges becomes zero. In this case, the size from the root of the supporting unit connected to the resonating unit to the tip portion of the short-circuiting unit short-circuited to the ground is ½ of the wavelength, which enables to obtain the resonating state. If a high-frequency signal is input via a signal line formed of a micro-strip line, the standing wave of a current occurs in the coupling electrode . FIG. 12 FIG. 11 FIG. 9 110 112 113 114 112 90 112 112 110 shows a cross-sectional view of the high-frequency coupler shown in by the line XII-XII, and the distribution of accumulated charges. In addition, in the drawing, the electric field occurring from the coupling electrode is shown by dotted lines. If a high-frequency signal is input via a signal line formed of a micro-strip line, the standing wave of the current occurs. Since the amplitude of the charges becomes zero at the anti-node where the current amplitude becomes the maximum, the amplitude of the charges becomes zero at the root of the supporting unit and the short-circuiting unit of the tip portions of the coupling electrode , and a resonating state of ½ of the wavelength can be obtained as shown in the drawing. In comparison to the high-frequency coupler shown in , the size of the coupling electrode is doubled, and the distribution of the charges expands in the transverse direction. This indicates that the communication range of the coupling electrode in the high-frequency coupler is widened to be double in the transverse direction. FIG. 11 FIG. 17 112 114 112 112 114 112 114 112 112 In the composition example shown in , both ends of the metal plate that forms the coupling electrode are subject to a bending process to form the short-circuiting unit . If the resonating state of ½ of the wavelength is obtained in the coupling electrode , only charges with the same polarity are distributed not only to the front of the coupling electrode but also to the short-circuiting unit to the side. In such a case, the front direction of the coupling electrode is a radiation direction of electric field signals in which the face can serve as a first radiating face, and on the other hand, the side direction of the short-circuiting unit is a radiation direction of electric field signals in which the face can serve as a second radiating face. With the increased size of the coupling electrode and the action of the second radiating face, the communication range of the coupling electrode can be expected to expand further in the transverse direction. shows the state where electric fields are radiated each from the first radiating face and the second radiating face of the coupling electrode . 110 112 112 In the case where the high-frequency coupler is installed in a wireless communication terminal, if the first radiating face of the coupling electrode is arranged inside the front of the housing of the terminal, and the second radiating face of the coupling electrode is in the side of the housing, electric field signals can be radiated from a plurality of directions of the front and the side direction of the wireless communication terminal. FIG. 18 FIG. 19 In such a case, communication is possible not only when the target point is contacted to the front direction of the wireless communication terminal as shown in but also when the target point is contacted to the side direction thereof as shown in . Thus, the degree of freedom in designing the housing of the wireless communication terminal can be increased, and convenience for users in using a proximity wireless transfer system can be improved. 110 A wireless communication terminal that enables communication in two directions of the front and the side can be realized by one high-frequency coupler . For example, when communication is to be performed between high-frequency couplers, which are used for producing small-sized wireless communication terminals built in notebooks, communication is possible such that the wireless communication terminals are put over target points arranged on the palm rests of notebooks or the like. In addition, if the wireless communication terminal is so big that it is not able to be put over the target point, communication can be performed by placing the terminal transversely. 112 114 132 134 FIG. 11 FIG. 13 Furthermore, the gist of the present invention is not limited to the configuration where the coupling electrode and the short-circuiting unit are formed by subjecting the metal plate to the bending process, as shown in . For example, as shown in , the tip portions of the coupling electrode may be short-circuited by the short-circuiting unit made of a wire. FIG. 14 FIG. 11 FIG. 11 112 shows the results obtained by measuring coupling intensities when the high-frequency couplers shown in face in the front direction. However, the coupling intensities were measured while both of the coupling electrodes are moved in the transverse direction in the face perpendicular to the first radiating face that includes the line XII-XII in . FIG. 14 FIG. 11 FIG. 15 FIG. 11 FIG. 16 150 152 155 110 160 162 165 110 In addition, as a comparison, the results are shown in which are obtained by measuring the coupling intensities in the same manner for a high-frequency coupler provided with a coupling electrode having the size of ¼ of the wavelength on a resonating unit formed of the same stub as that of the high-frequency coupler shown in (refer to ), and a high-frequency coupler provided with a coupling electrode , which has the size of about ½ of the wavelength but is not short-circuited by a short-circuiting unit, on a resonating unit formed of the same stub as that of the high-frequency coupler shown in (refer to ). 110 150 112 110 FIG. 11 FIG. 15 FIG. 15 When the measurement results of the high-frequency coupler shown in and the high-frequency coupler shown in are compared to each other, since the charges in the coupling electrode that have twice the size of the counterpart in are dispersed in the high-frequency coupler , the coupling intensity in the right front face (distance in the transverse direction=0 mm), that is, in the peak location is weak, but reduction of the coupling intensity when the distance of the transverse direction is increased is lessened. Therefore, it can be understood that the communication distance is widened according to the deviation in the transverse direction. 110 160 162 162 FIG. 11 FIG. 16 In addition, when the measurement results of the high-frequency coupler shown in and the high-frequency coupler shown in are compared to each other, the coupling electrode of the latter is remarkably low. This is because a resonating state of ½ of the wavelength is not able to be obtained as the tip portions of the coupling electrode are not short-circuited to the ground, and charges with different polarities are distributed inside the surface of the coupling electrode , thereby cancelling the electric fields of the charges with both polarities. 110 160 110 112 FIG. 11 FIG. 16 When it comes to comparing the measurement results of the high-frequency coupler shown in and the high-frequency coupler shown in , the reason that the communication range of the high-frequency coupler is expanded in the transverse direction is understood not because the size of the coupling electrode is doubled simply, but because the tip portions are short-circuited to the ground to obtain the resonating state of ½ of the wavelength and then only the charges with the same polarities are distributed in the radiating direction of the electric field signal. The present application contains subject matter related to that disclosed in Japanese Priority Patent Application JP 2010-056561 filed in the Japan Patent Office on Mar. 12, 2010, the entire contents of which are hereby incorporated by reference. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and alterations may occur depending on design requirements and other factors insofar as they are within the scope of the appended claims or the equivalents thereof. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagram schematically illustrating the configuration of a proximity wireless transfer system by a weak UWB communication method; FIG. 2 is a diagram illustrating the basic composition of a high-frequency coupler where a transmitter and a receiver are arranged; FIG. 3 FIG. 2 is a diagram illustrating an embodiment of the high-frequency coupler shown in ; FIG. 4 is a diagram showing an electric field by an infinitesimal dipole; FIG. 5 FIG. 4 is a diagram in which the electric field shown in is matched on a coupling electrode; FIG. 6 is a diagram illustrating the composition example of a capacity-loaded type antenna; FIG. 7 is a diagram illustrating the composition example of the high-frequency coupler using a distributed constant circuit in a resonating unit; FIG. 8 FIG. 7 is a diagram showing the state where a standing wave occurs on a stub in the high-frequency coupler shown in ; FIG. 9 is a diagram showing the state where charges are accumulated in a coupling electrode in a high-frequency coupler where the coupling electrode is mounted on a ground circuit when the coupling electrode is input with high-frequency signals; FIG. 10A is a diagram for describing ¼ of the wavelength as the size of a coupling electrode; FIG. 10B is a diagram for describing ¼ of the wavelength as the size of a coupling electrode; FIG. 10C is a diagram for describing ¼ of the wavelength as the size of a coupling electrode; FIG. 11 is a diagram showing a composition example of a high-frequency coupler of which the tip portions of a coupling electrode are short-circuited to the ground; FIG. 12 FIG. 11 is a cross-sectional view of the high-frequency coupler shown in ; FIG. 13 is a diagram showing a modified example of a high-frequency coupler; FIG. 14 FIG. 11 is a diagram showing a result obtained by measuring coupling intensities when the high-frequency couplers shown in face each other in the front direction; FIG. 15 FIG. 11 is a diagram showing a high-frequency coupler provided with a coupling electrode having the size of ¼ of the wavelength on a resonating unit formed of the same stub as the high-frequency coupler shown in ; FIG. 16 FIG. 11 is a diagram showing a high-frequency coupler provided with a coupling electrode that has the size of about ½ of the wavelength but of which a tip portion is not short-circuited on a resonating unit formed of the same stub as the high-frequency coupler shown in ; FIG. 17 FIG. 11 is a diagram showing the state where electric fields are radiated each from a first radiating face and a second radiating face of the coupling electrode of the high-frequency coupler shown in ; FIG. 18 FIG. 11 is a diagram showing the state where a wireless communication terminal mounted with the high-frequency coupler shown in approaches a target point in the front direction; and FIG. 19 FIG. 11 is a diagram showing the state where a wireless communication terminal mounted with the high-frequency coupler shown in approaches a target point in the side direction.
“Take what you need, leave what you can.” That is Destiny Potter’s motto for “Van Buren’s Little Free Pantry,” which she established in her own front yard earlier this year. The simple wooden cabinet contains only two shelves and a glass door, mounted on a post. Destiny stocks it each morning, afternoon and evening with nonperishable food and some basic hygiene items and leaves it open 24/7 to benefit anyone who is hungry. Destiny’s motivation for starting the project stems from her own experiences as a child. Growing up, her family relied heavily on local food banks and churches for meals. “It was a good day when we got to go the church pantry,” recalled Destiny. As an adult, she was inspired by a similar pantry in Northwest Arkansas and decided to establish one to benefit children in her own neighborhood. Word of Van Buren’s Little Free Pantry has spread quickly. As more people have begun to utilize it, there has also been a swell of community support. Destiny has encountered a few skeptics who suggest some will take advantage of the pantry. She insists that the project, which operates entirely on the honor system, is meeting an important need and being used as it is intended. When giving to a tiny pantry such as hers, Destiny suggests items such as canned tuna or chicken, soup and canned pastas. Barbie’s project has been aided by dedicated volunteers Jayme and Valan Collins who, through the power of social media, have helped raise awareness about the pantries. “It takes more than one person, it takes the community,” Barbie noted. She recognizes that many have been blessed by the project, including those who help keep it stocked. Donors include moms bringing children over after swim practice to deliver items and cancer patients who say that the highlight of their day is giving to the pantry. “There is so much joy in giving,” noted Barbie. Destiny is proud of how her project’s influence has spread, but she isn’t stopping there. For Thanksgiving, she has invited pantry partakers to join her family for a traditional holiday feast. A sign-up sheet in the pantry encourages visitors to dine at her house on Thanksgiving Day. No name is required, just an expected total attending so Destiny can make sure she has enough supplies on hand. This story appears in the November 2016 issue of Entertainment Fort Smith Magazine.	http://www.efortsmith.com/features/index.cfm/aid/285/print
first commercial-scale project, in Wales. The funds will be used to build a power plant off the port city of Holyhead, in the Irish Sea, and to establish Minesto’s U.K. headquarters in the North Wales region, the Gothenburg, Sweden-based company said in a statement Wednesday. Minesto’s Deep Green systems are shaped like underwater kites that generate electricity from low-velocity tidal and ocean currents. Minesto will install the plant’s first 500-kilowatt system as part of an array that will grow to 10 megawatts of capacity by 2019, according to the statement. The full development will generate enough power for about 8,000 homes. Wales has about 1,200 kilometers (746 miles) of coastline with low-velocity tidal currents, enough to supply as much as 5 percent of the U.K.’s total electricity demand. “We have extensive raw wave and tidal energy resources along our shorelines, and this is an excellent example of commercial solutions being developed in Wales to help drive our potential to be a world-leader in the marine-energy market,” First Minister Carwyn Jones said in the statement. To contact the reporter on this story: Justin Doom in New York at [email protected] To contact the editors responsible for this story:	https://about.newenergyfinance.com/blog/minesto-receiving-13-million-euros-for-welsh-marine-power-plant/
Harbor porpoises in the North Pacific are found in coastal waters from southern California to Japan, but population structure is poorly known outside of a few local areas. We used multiplexed amplicon sequencing of 292 loci and genotyped clusters of SNPs as microhaplotypes (N=271 samples) in addition to mtDNA sequence data (N=413 samples), to examine the genetic structure from samples collected along the Pacific coast and inland waterways from California to southern British Columbia. We confirmed an overall pattern of strong isolation-by-distance, suggesting that individual dispersal is restricted. We also found evidence of regions where genetic differences are larger than expected based on geographic distance alone, implying current or historical barriers to gene flow. In particular, the southernmost population in California is genetically distinct (FST = 0.02 (microhaplotypes); 0.31 (mtDNA)), with both reduced genetic variability and high frequency of an otherwise rare mtDNA haplotype. At the northern end of our study range, we found significant genetic differentiation of samples from the Strait of Georgia, previously identified as a potential biogeographic boundary or secondary contact zone between harbor porpoise populations. Association of microhaplotypes with remotely-sensed environmental variables indicated potential local adaptation, especially at the southern end of the species’ range. These results inform conservation and management for this nearshore species, illustrate the value of genomic methods for detecting patterns of genetic structure within a continuously distributed marine species, and highlight the power of microhaplotype genotyping for detecting genetic structure in harbor porpoises despite reliance on poor-quality samples. Methods Amplicon libraries were prepared following the GT-seq protocol, including the optional Exo-SAP pre-treatment of the samples (Campbell et al., 2015), and pooled libraries were sequenced on an Illumina NextSeq500 sequencer, 1x150 bp reads. Custom scripts for processing GT-seq data (Campbell et al., 2015) were used to demultiplex the sample files and conduct preliminary genotyping. Genotypes were quality checked for duplicate samples, percent missing genotypes per locus and sample, and percent homozygosity using the strataG package in R. Microhaplotypes were generated for all loci using the R package MicrohaPlot (Baetscher et al., 2017). The MicrohaPlot algorithm inserts N’s for missing sequence data at SNPs within haplotypes, so we used a custom R-scripts (supplemental materials) to identify SNPs with >10% N’s. The identified SNPs were removed from the original vcf file using vcfTools, and MicrohaPlot was used to generate new microhaplotypes with the remaining variable SNP positions. The unfiltered haplotypes were exported for subsequent filtering with custom scripts to view and call genotypes. Mitochondiral DNA control region haplotype sequences were generated using Sanger dideoxy sequencing of PCR products, sequenced in both directions. Usage Notes Sample ID's, collection location (Latitude, Longitude) and a priori geographic stratification are provided in Table S1 of the supplemental materials.	https://datadryad.org:443/stash/dataset/doi:10.5061/dryad.4tmpg4f6v
Weather extremes predicted with climate change, in the form of global warming and dry seasons, put the country’s key water sources at risk. That Linggiu reservoir in Johor, which provides Singapore with a sizable 250 million gallons of its water supply, was at significant risk of running dry in 2017 shocked many. Why does Singapore have a water supply issue? Singapore is considered to be one of the most water-stressed countries in the world. It is heavily dependent on rainfall due to the lack of natural water resources, and limited land is available for water storage facilities. Prolonged dry spells cause or threaten to cause water shortages, the most recent being in 1990. Is Singapore facing water shortage? Singapore uses about 430 million gallons of water per day, and this could double by 2060 – that’s 782 Olympic-sized swimming pools! Water is a precious and scarce resource for Singapore, and our water supply remains vulnerable to factors such as climate change. Why is our water supply being threatened? Water pollution is a serious threat to the world’s water. Microbes, salts, and pollution from agriculture and industry all contribute to the problem. Global warming will likely have major impacts on the world’s freshwater resources. Why was Singapore successful in preventing water shortage? With the Public Utilities Board (PUB) pumping more water into reservoirs in response to the lack of rain, Singapore is in no danger of water shortage in the near future. … Combined, Singapore’s two desalination plants produce 100 million gallons per day (mgd) of water, which meets 25 per cent of the country’s needs. Is Singapore self sufficient in water? Singapore currently uses about 1.95 billion litres per day – enough to fill 782 Olympic-sized swimming pools, according to national water agency PUB. How much water should you drink a day in Singapore? The Health Promotion Board recommends drinking eight cups of water a day. Do you drink enough amid your busy schedule? Dive in to find out how staying hydrated can enhance your productivity at work. In 2019, Singapore was ranked the second most overworked country among 40 countries. What threats are there to Earth’s water supply? These threats include pollution, the impacts of climate change, a resurgence of water-related diseases, and the destruction of freshwater ecosystems. What are the major threats for the lacking of water supply? Climate change, such as altered weather-patterns (including droughts or floods), deforestation, increased pollution, green house gases, and wasteful use of water can cause insufficient supply. What is the problem of water supply? Growing populations, expanding agriculture, industrialization and high living standards have all boosted demand for water while drought, overuse and pollution have all decreased supplies. To make up for the shortfall water is often taken from lakes, rivers and wetlands, causing serious environmental damage.	https://bonkairesort.com/sightseeing/why-does-singapore-have-threats-to-its-water-supply.html
The new-generation recycling robot Daisy of Apple works in a workshop in Austin, Texas, the United States, April 15, 2019. (Photo: Xinhua) Washington's threat of additional tariffs on consumer electronics products from China will only make its importers and consumers suffer from higher costs, and it will not be easy for the sector's supply chain to shift from China, analysts and entrepreneurs told the Global Times on Thursday. American consumers would pay over $8.1 billion more for cellphones and over $8.2 billion for laptops and tablets, which will be a substantial negative impact on American consumers, if the US government imposes tariffs of up to 25 percent on imports of approximately $300 billion in goods from China, said a report released on Monday by the US-based company Trade Partnership Worldwide. The report was prepared for the US Consumer Technology Association. A net $4.5 billion loss for the US economy in the cellphone sector would occur, while the number is $3.6 billion in terms of laptops and tablets, it noted. China accounts for about three quarters of total imports of cellphones, and over 90 percent of total imports of laptops and tablets for the US, according to the report. "In the short term, US consumers have no choice but to suffer higher prices if they want to buy those electronic goods," said David Huang, marketing manager at JXV Micromotor Co, a camera supplier based in Baotou, North China's Inner Mongolia Autonomous Region. "Major cellphone brands like Apple and Samsung in the US market are mainly reliant on original design or equipment manufacturing in China thanks to the country's cumulative supply-chain advantages," Huang told the Global Times on Thursday. It will be difficult and time-consuming if a large volume of supply is shifted to other countries, the report said. Although international smartphone brands have been expanding their manufacturing facilities in India and some Southeast Asian countries in recent years, they cannot compete with China's supply chain in terms of comprehensiveness and labor quality, said Huang. Samsung built a new mobile phone manufacturing plant on the outskirts of New Delhi, India last year, its biggest mobile phone plant in the world, media reports said. According to Huang, China's supply-chain advantage in electronic goods is still unshakable in the world, giving the country's companies the upper hand when bargaining with US clients. "On that side, the US importers have no other choices but to digest higher costs and then transfer those to their consumers," he noted. According to a Bloomberg report on Thursday, US electric goods makers Dell Technologies Inc, HP Inc, Intel Corp and Microsoft Corp have submitted joint comments opposing the tariff escalation, saying it would hurt consumer products and the industry. The companies said they spent a collective $35 billion on research and development in 2018, and tariff costs would divert resources from innovation while providing "a windfall" to manufacturers based outside the US that are less dependent on American sales, the Bloomberg report noted. James Yan, Beijing-based research director at Counterpoint, told the Global Times on Thursday that compared with the shoe and garment industries that have largely transferred from China to other countries, consumer electric goods have higher requirements in terms of raw materials, design and labor quality, meaning a complex and complete supply chain is needed. "Also, Southeast Asian countries tend to have weak delivery capability," Yan added. Wu, a production line manager at an electronic devices company based in Dongguan, a manufacturing hub in South China's Guangdong Province, told the Global Times that he moved two production lines back to Dongguan just two years after entering in Cambodia in 2016. "The country's undeveloped port infrastructure, transport and logistics and most importantly, cultural differences matter. People there are not as industrious as Chinese workers," Wu said. "Besides, the supply chain in Cambodia, generally in all the Southeast Asian countries, is not complete. Sometimes you have to import parts from Dongguan and that further increases transportation costs," he added.	https://peoplesdaily.pdnews.cn/business/tariffs-to-hit-us-importers-consumers-24256.html
Alex Ross’s New Yorker pieces on music are always worth reading, and I particularly enjoyed his latest, on Josquin Desprez — I remember enjoying Josquin’s music in my college music-history class and have heard it with pleasure on the radio over the years, but I never really knew how to listen to it. Renaissance music is very different from classical and later, so it takes significant immersion in it to figure out what’s going on, and I never got that immersion. (Of course, in this age of YouTube it’s easy to get whatever you want; here’s a nice clip of Josquin’s “Ave Maria,” one of the pieces Ross discusses, with an animated graphical score that lets you follow the music easily.) What brings it to LH are the opening and a passage near the end. Here’s the first paragraph: The singer and composer Josquin Desprez traversed his time like a diffident ghost, glimpsed here and there amid the splendor of the Renaissance. He is thought to have been born around 1450 in what is now western Belgium, the son of a policeman who was once jailed for using excessive force. In 1466, a boy named Gossequin completed a stint as a choirboy in the city of Cambrai. A decade later, the singer Jusquinus de Pratis turned up at the court of René of Anjou, in Aix. In the fourteen-eighties, in Milan, Judocus Despres was in the service of the House of Sforza, which also employed Leonardo da Vinci. At the end of the decade, Judo. de Prez joined the musical staff at the Vatican, remaining there into the reign of Alexander VI, of the House of Borgia. The name Josquin can be seen carved on a wall of the Sistine Chapel. In 1503, the maestro Juschino took a post in Ferrara, singing in the presence of Lucrezia Borgia. Not long afterward, Josse des Prez retired to Condé-sur-l’Escaut, near his presumed birthplace, serving as the provost of the local church. There he died, on August 27, 1521. His tomb was destroyed during the French Revolution. Gossequin, Jusquinus, Judocus, Judo., Josquin, Juschino, and Josse — that’s what I call variety! And here’s a thought-provoking passage on the perils of not leaving a name behind; it comes after an account of how an analysis suggests that the motet “O virgo virginum” is not actually by Josquin: What happens to “O virgo virginum” if it is no longer stamped with the Josquin brand? Barring some new revelation, its composer is now a Renaissance ghost: Composer X. The business of music doesn’t know what to do with anonymity. The “Missa Caput,” for example, was once attributed to Dufay, and for that reason it used to receive more performances than it does now, even though it is still the same paradigm-altering piece. Too often, we simplify the history of the arts by reducing it to a parade of strong personalities. When that logic is applied to music before 1600, it consigns to oblivion vast numbers of works that cannot be linked to one exceptional individual. Consider an anonymous publication from 1543 titled “Musica quinque vocum motteta materna lingua vocata” (“Music in five voices, called motets in the mother tongue”). The musicologist and conductor Laurie Stras, who has recorded this repertory with the British ensemble Musica Secreta, has floated the possibility that the motets were written for singers at the convent of Corpus Domini, in Ferrara, where Leonora d’Este, Lucrezia Borgia’s daughter, served as the abbess. Leonora was a noted musical intellectual, almost certainly a composer. Some or all of these works could be hers. Nobles typically maintained anonymity in their artistic endeavors; a noblewoman turned nun would have had special incentive to keep her identity hidden. Why do we focus so much on creators’ names? Would we value the Iliad and Odyssey less if we didn’t have the label “Homer” to paste on them, however questionable that label is? Probably. We are a foolish species.	https://languagehat.com/many-names-and-none/
Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1515/IJDHD.2011.052 Abstract/Summary Older people increasingly want to remain living independently in their own homes. The aim of the ENABLE project is to develop a wearable device that can be used to support older people in their daily lives and which can monitor their health status, detect potential problems, provide activity reminders and offer communication and alarm services. In order to determine the specifications and functionality required for the development of the device, user surveys and focus groups were undertaken, use case analysis and scenario modeling carried out. The project has resulted in the development of a wrist-worn device and mobile phone combination that can support and assist older and vulnerable wearers with a range of activities and services both inside their home and as they move around their local environment. The device is currently undergoing pilot trials in five European countries. The aim of this paper is to describe the ENABLE device, its features and services, and the infrastructure within which it operates.	http://centaur.reading.ac.uk/33384/
compensation: $200K — $250K * industry: specialty: experience: The Director of Enterprise Applications is responsible for the design, implementation, delivery and maintenance of Banking Technology platforms. The position will oversee the long-term strategic planning of MVB Operations Technology, including the functionality, scalability, and interoperability of hardware, software, and middleware platforms. The Director manages and supports business plans, defines the strategic long-term roadmap, facilitates the planning of contingencies, establishes metrics, and ensures that the delivery of all products & services to support ongoing operations across the MVB companies. Duties and responsibilities include: Education and work experience includes:	https://www.theladders.com/job/director-enterprise-applications-mvbfinancialcorp-morgantown-wv_43135798
This invention relates to thrust vectoring of aircraft gas turbine engines and, more particularly, to thrust vectoring of FLADE engines. High performance variable cycle gas turbine engines are being designed because of their unique ability to operate efficiently at various thrust settings and flight speeds both subsonic and supersonic. An important feature of the variable cycle gas turbine engine which contributes to its high performance is its capability of maintaining a substantially constant inlet airflow as its thrust is varied. This feature leads to important performance advantages under less than full power engine settings or maximum thrust conditions, such as during subsonic cruise. One particular type of variable cycle engine called a FLADE engine (FLADE being an acronym for "fan on blade") is characterized by an outer fan driven by a radially inner fan and discharging its FLADE air into an outer fan duct which is generally co-annular with and circumscribes an inner fan duct circumscribing the inner fan. One such engine, disclosed in U.S. Patent No. 4,043,121, entitled "Two Spool Variable Cycle Engine", by Thomas et al., provides a FLADE fan and outer fan duct within which variable guide vanes control the cycle variability by controlling the amount of air passing through the FLADE outer fan duct. Other high performance aircraft variable cycle gas turbine FLADE engines capable of maintaining an essentially constant inlet airflow over a relatively wide range of thrust at a given set of subsonic flight ambient conditions such as altitude and flight Mach No. in order to avoid spillage drag and to do so over a range of flight conditions have been studied. This capability is particularly needed for subsonic part power engine operating conditions. Examples of these are disclosed in U.S. Patent No. 5,404,713, entitled "Spillage Drag and Infrared Reducing Flade Engine", U.S. Patent No. 5,402,963, entitled "Acoustically Shielded Exhaust System for High Thrust Jet Engines", U.S. Patent No. 5,261,227, entitled "Variable Specific Thrust Turbofan Engine", and European Patent No. EP0,567,277, entitled "Bypass Injector Valve For Variable Cycle Aircraft Engines". A FLADE aircraft gas turbine engine with counter-rotatable fans is disclosed in U.S. Patent Application No. (133746), entitled "FLADE GAS TURBINE ENGINE WITH COUNTER-ROTATABLE FANS". FLADE engines have the fan blade attached to one of the front fans. This can lead to low pressure spool designs that are compromised because of the limitations in rotor speeds and increased stresses caused by the FLADE blade attachment and location. The front fan mounted FLADE fan blades also are difficult to adapt to present engines or engine designs. It would be very expensive to adapt an existing engine to test a front fan mounted FLADE fan. It would be difficult to demonstrate some of the system benefits offered by a FLADE engine concept at a reasonable cost relative to that of a new low pressure system or defined around an existing core engine. It is highly desirable to have a FLADE engine that allows a low pressure spool design that is uncompromised because of limitations in rotor speeds and increased stresses caused by the FLADE blade attachment and location. It is highly desirable to have an engine in which FLADE fan blades are not difficult to adapt to present engines or engine designs and that would not be very expensive to adapt to an existing engine to test as compared to a front fan mounted FLADE fan. It is also desirable to be able to demonstrate some of the system benefits offered by a FLADE engine concept without a great deal of difficulty and at a reasonable cost relative to that of a new low pressure system or defined around an existing core engine. Another concern of aircraft and aircraft engine designers and particularly those designing high speed highly maneuverable military aircraft are constantly seeking better ways for controlling the aircraft and increasing its maneuverability in flight. These are needed for anti-aircraft missile avoidance and other combat maneuvers. Additionally, aircraft designers are trying to improve short take off and landing capabilities of aircraft. Exhaust systems, particularly for modern, high speed, military aircraft, have been adapted to provide a high degree of maneuverability over a wide variety of flight conditions including altitude, speed and Mach number while maintaining cruise efficiency. Aircraft maneuverability may be provided by aircraft control surfaces such as wing flaps or ailerons or vertical fins or rudders. Aircraft control surfaces, however, are somewhat limited in their effectiveness because of large differences in operational flight conditions such as air speed. Aircraft control surfaces also increase an aircraft's radar signature making it more vulnerable to anti-aircraft fire and missile. Thrust vectoring nozzles, are more effective because they allow large thrust loads to be quickly applied in the yaw and pitch directions of the aircraft, thereby, providing the aircraft with enhanced maneuverability which is relatively independent of air speed. Thrust vectoring nozzles are complicated, bulky, heavy, and expensive. Other thrust vectoring methods include use of nozzle internal fluidic injection and/or mechanical flow diversion devices to skew the thrust. The thrust vectoring aft FLADE aircraft gas turbine engine powered aircraft is highly maneuverable. The thrust vectoring aft FLADE aircraft gas turbine engine is not complex, heavy, bulky, or expensive, and yet, is very effective for thrust vectoring. According to the present invention, an aft FLADE gas turbine engine includes a fan section drivenly connected to a low pressure turbine section, a core engine located between the fan section and the low pressure turbine section, a fan bypass duct circumscribing the core engine and in fluid communication with the fan section, a mixer downstream of the low pressure turbine section and in fluid communication with the fan bypass duct, and an aft FLADE turbine downstream of the mixer. At least one row of aft FLADE fan blades is disposed radially outwardly of and drivenly connected to the aft FLADE turbine. The row of aft FLADE fan blades radially extend across a FLADE duct circumscribing the aft FLADE turbine. At least one thrust vectoring nozzle is in pressurized fluid flow receiving communication with the FLADE duct. One embodiment of the engine includes spaced apart right and left hand FLADE exhaust nozzles in pressurized fluid flow receiving communication with the FLADE duct and offset from a main engine exhaust nozzle located downstream of the aft FLADE turbine. Right and left hand valves may be disposed in right and left hand ducts extending between a FLADE airflow manifold in pressurized fluid flow receiving communication with the FLADE duct. The right and left hand valves being operable to control amounts of FLADE exhaust airflow flowed from the FLADE duct to each of the right and left hand FLADE exhaust nozzles respectively to vector thrust. The right and left hand FLADE exhaust nozzle may be fixed or thrust vectoring nozzles. An aircraft may be constructed with the aft FLADE gas turbine engine within a fuselage of the aircraft. The aircraft may include FLADE air intakes and an engine air intake mounted flush with respect to the fuselage. The FLADE air intakes are axially offset from the engine air intake which is connected to and in fluid communication with a fan inlet to the fan section by an engine fixed inlet duct. The FLADE air intakes are connected to and in fluid communication with FLADE inlets to the FLADE duct by FLADE fixed inlet ducts. More particular embodiments of the engine include a row of variable first FLADE vanes radially extending across the FLADE duct axially forwardly of the row of aft FLADE fan blades. One embodiment of the engine further includes a fan inlet to the fan section and an annular FLADE inlet to the FLADE duct arranged so that the FLADE inlet is axially located substantially aftwardly of the fan section and, in a more particular embodiment, the FLADE inlet is axially located aftwardly of the core engine. The aft FLADE turbine may be connected to and rotatable with a low pressure turbine of the low pressure turbine section or may be a free turbine. The engine may incorporate a variable area turbine nozzle with variable turbine nozzle vanes located aft and downstream of the mixer and the low pressure turbine. A power extraction apparatus may be placed within the engine and drivenly connected to the aft FLADE turbine. In one embodiment, the power extraction apparatus may be located in a hollow engine nozzle centerbody of the engine located aft and downstream of the aft FLADE turbine. One embodiment of the power extraction apparatus is an electrical generator drivenly connected through a speed increasing gearbox to the aft FLADE turbine. Another embodiment of the power extraction apparatus is a power takeoff assembly including a housing disposed within the engine such as in the hollow engine nozzle centerbody and having a power takeoff shaft drivenly connected to the aft FLADE turbine through a right angle gearbox. A variable or fixed throat area engine nozzle may be incorporated downstream and axially aft of the mixer and the fan bypass duct. Another more particular embodiment of the engine includes a plurality of circumferentially disposed hollow struts in fluid flow communication with the FLADE duct and a substantially hollow centerbody supported by and in fluid flow communication with the hollow struts. Cooling apertures in the centerbody and in a wall of the engine nozzle downstream of the variable throat area are in fluid communication with the FLADE duct. A variable area FLADE air nozzle including an axially translatable plug within the hollow centerbody and a radially outwardly positioned fixed nozzle cowling of the centerbody may also be used in the engine. Aft thrust augmenting afterburners may be incorporated aft and downstream of the aft FLADE turbine. A forward afterburner may be axially disposed between the mixer and the aft FLADE turbine to provide additional energy upon demand to the aft FLADE turbine and additional power to the row of aft FLADE fan blades and the power extraction apparatus such as the electrical generator or the power takeoff assembly. It is, thus, highly desirable to provide an FLADE aircraft gas turbine engine powered aircraft with a thrust vectoring nozzle that is not complex, heavy, bulky, nor expensive, and yet, very effective for thrust vectoring.The aft FLADE gas turbine engine may be used within a fuselage of the aircraft. FLADE air intakes and an engine air intake may be mounted flush with respect to the fuselage. The FLADE air intakes are axially offset from the engine air intake. The engine air intake may be connected to and in fluid communication with the fan inlet by an engine fixed inlet duct. The FLADE air intakes may be connected to and in fluid communication with the FLADE inlets by FLADE fixed inlet ducts. Inlet duct passages of the engine and the FLADE fixed inlet ducts respectively may be two-dimensional and terminating in transition sections between the inlet duct passages and the fan and FLADE inlets respectively. The aft FLADE turbine allows a FLADE engine to have a low pressure spool design that is uncompromised because of limitations in rotor speeds and increased stresses caused by the FLADE blade attachment and location. Aft FLADE fan blades mounted on the aft FLADE turbine are not difficult to adapt to present engines or engine designs. The aft FLADE turbine is not very expensive to adapt to an existing engine to test as compared to a front fan mounted FLADE fan. FIG. 1 is a schematical cross-sectional view illustration of an aircraft thrust vectoring aft FLADE gas turbine engine with a short FLADE duct and dual thrust vectoring nozzles installed in an aircraft. FIG. 2 is a schematical cross-sectional view illustration of a thrust vectoring aft FLADE gas turbine engine with a long duct FLADE duct and dual thrust vectoring nozzles installed in an aircraft. FIG. 3 is a schematical cross-sectional view illustration of the aft FLADE gas turbine engine with a single direction of rotation fan section and an aft FLADE blade and turbine illustrated in FIGS. 1 and 2. FIG. 4 is a schematical cross-sectional view illustration of an alternative aft FLADE gas turbine engine with two fan sections and two bypass inlets. FIG. 5 is an alternative schematical cross-sectional view illustration of the engine in FIG. 3 with exhaust nozzle cooling. FIG. 6 is a schematical cross-sectional view illustration of another exemplary embodiment of an aircraft thrust vectoring aft FLADE gas turbine engine with an aft FLADE blade and turbine and a short FLADE duct. FIG. 7 is a schematical cross-sectional view illustration of the aircraft thrust vectoring aft FLADE aircraft gas turbine engine illustrated in FIG. 3 with a first afterburner upstream of a free aft FLADE turbine. FIG. 8 is a schematical cross-sectional view illustration of the aft FLADE gas turbine engine illustrated in FIG. 3 with a variable area turbine nozzle and a thrust augmenting afterburner downstream of an aft FLADE turbine. FIG. 9 is a schematical cross-sectional view illustration of yet another embodiment of an aircraft thrust vectoring aft FLADE aircraft gas turbine engine with counter-rotatable fans and an aft FLADE blade and turbine. FIG. 10 is a schematical cross-sectional view illustration of the aft FLADE gas turbine engine illustrated in FIG. 3 with an aft FLADE blade and turbine driving connected to a power takeoff shaft. FIG. 11 is a schematical cross-sectional view illustration of the aft FLADE gas turbine engine illustrated in FIG. 3 with an aft FLADE blade and turbine driving connected to an electrical generator located within the engine. FIG. 12 is a schematical cross-sectional view illustration of the aft FLADE gas turbine engine illustrated in FIG. 3 with an aft FLADE blade and turbine driving connected to two electrical generators located within the engine. Schematically illustrated in cross-section in FIG. 1 is an exemplary embodiment of an aircraft 124 having a single offset flush mounted engine air intake 127 connected to and in fluid communication with an aircraft thrust vectoring aft FLADE aircraft gas turbine engine 1. An annular fan inlet 11 of the aircraft aft FLADE engine 1 is connected to the air intake 127 by an engine fixed inlet duct 126. The fan inlet 11 is axially offset from an annular FLADE inlet 8 to a FLADE duct 3. Flush mounted dual FLADE air intakes 129 are connected to and in fluid communication with the annular FLADE inlets 8 by FLADE fixed inlet ducts 128. The FLADE air intakes 129 are axially offset from the engine air intake 127. This provides great flexibility in designing and constructing efficient engines, aircraft, and aircraft with engines completely mounted within the aircraft's fuselage 113 or body and the FLADE air intakes 129 and the engine air intake 127 are mounted flush with respect to the fuselage 113. Inlet duct passages 111 of the engine fixed inlet duct 126 and the FLADE fixed inlet ducts 128 may be two-dimensional terminating in transition sections 119 between the inlet duct passages 111 and the axisymmetric annular fan and FLADE inlets 11 and 8. The foregoing aspects and other features of the invention are explained in the following description, taken in connection with the accompanying drawings where: The FLADE duct 3 leads to at least one thrust vectoring nozzle 123 for maneuvering the aircraft. Right and left hand FLADE exhaust nozzles 125 and 135, respectively, illustrated in FIG. 1 serve as thrust vectoring nozzles 123. The right and left hand FLADE exhaust nozzles 125 and 135 are fixed nozzles and are offset from a main engine exhaust nozzle 218 which may be a variable or fixed throat area engine nozzle. A FLADE airflow manifold 231 collects FLADE exhaust airflow 154 from the FLADE duct 3 and directs it through FLADE air exhaust right and left hand ducts 155 and 156 to the right and left hand FLADE exhaust nozzles 125 and 135, respectively. More than one pair of FLADE exhaust nozzles may be used. Right and left hand valves 162 and 164, respectively, disposed in the right and left hand ducts 155 and 156 control the amount of the FLADE exhaust airflow 154 that goes to each of the right and left hand FLADE exhaust nozzles 125 and 135, respectively. Thrust vectoring and yaw of the aircraft is accomplished by flowing unequal amounts of the FLADE exhaust airflow 154 to the right and left hand FLADE exhaust nozzles 125 and 135. The unequal amounts of the FLADE exhaust airflow 154 to the right and left hand FLADE exhaust nozzles 125 and 135 produces a turning moment about a center of gravity CG of the aircraft. Equal amounts of the FLADE exhaust airflow 154 flowed through the right and left hand valves 162 and 164 in the right and left hand ducts 155 and 156 provides unvectored flight of the aircraft. Pitch may be accomplished by having vectoring versions of the right and left hand FLADE exhaust nozzles 125 and 135. Thrust vectoring versions of the right and left hand FLADE exhaust nozzles 125 and 135 may be gimballing nozzles, two-dimensional pitch inducing nozzles, fluidic nozzles, and other types of thrust vectoring nozzles which individually vector the exhaust flow coming out of the right and left hand FLADE exhaust nozzles 125 and 135. The engine 1 illustrated in FIGS. 1-3, 7, 8, 10, and 11 are of the single bypass type having but a single bypass inlet 272 as compared to the engine 1 illustrated in FIGS. 4-6 and 9 having both the first and second bypass inlets 42 and 46 to the fan bypass duct 40 and have counter-rotating first and core fans. Schematically illustrated in cross-section in FIG. 2 is an alternative exemplary embodiment of the aircraft 124 in which the FLADE duct 3 is a long duct extending to the annular fan inlet 11 of the aircraft aft FLADE engine 1. The FLADE duct 3 is also connected to the air intake 127 by the engine fixed inlet duct 126. Schematically illustrated in cross-section in FIG. 3 is an exemplary aircraft aft FLADE engine 1. The engine 1 illustrated in FIG. 3 includes a fan section 115 with a single direction of rotation fan 330 with three fan stages 332 downstream of a fan inlet 11. Downstream and axially aft of the fan section 115 is a core engine 18 having an annular core engine inlet 17 and a generally axially extending axis or centerline 12 generally extending forward 14 and aft 16. A single fan bypass duct 40 located downstream and axially aft of the fan section 115 circumscribes the core engine 18. The single bypass inlet 272 includes an annular splitter 293 to split fan airflow 50 into bypass airflow 258 and core airflow 256. The core engine 18 includes, in downstream serial axial flow relationship, a high pressure compressor 20, a combustor 22, and a high pressure turbine 23 having a row of high pressure turbine blades 24. A high pressure shaft 26, disposed coaxially about the centerline 12 of the engine 1, fixedly interconnects the high pressure compressor 20 and the high pressure turbine blades 24. The combination or assembly of the high pressure compressor 20 drivenly connected to the high pressure turbine 23 by the high pressure shaft 26 is designated a high pressure spool 47. The core engine 18 is effective for generating combustion gases. Pressurized air from the high pressure compressor 20 is mixed with fuel in the combustor 22 and ignited, thereby, generating combustion gases. Some work is extracted from these gases by the high pressure turbine blades 24 which drives the high pressure compressor 20. The combustion gases are discharged from the core engine 18 into single direction of rotation low pressure turbine 319. The low pressure turbine 319 is drivingly connected to the single direction of rotation fan 330 by a low pressure shaft 321, the combination or assembly being designated a low pressure spool 290. A mixer 49, illustrated as a lobed or chute mixer, is disposed downstream of and at an aft end of the fan bypass duct 40 and downstream of and aft of low pressure turbine blades 328 of the low pressure turbine 319. The mixer 49 is used to mix bypass air 78 with core discharge air 70 exiting the low pressure turbine 319 to form a mixed flow 188. One alternative version of the mixer 49 is an aft variable area bypass injector (VABI) door disposed at an aft end of the fan bypass duct 40 to mix bypass air 78 with core discharge air 70. Exhaust gases from the mixer 49 are directed through an aft FLADE turbine 160 having a plurality of aft FLADE turbine blades 254 and located downstream and aft of the mixer 49. The FLADE duct 3 circumscribes an aft FLADE turbine 160. An aft FLADE fan 2 includes at least one row of aft FLADE fan blades 5 which extend radially outwardly from and are drivenly connected to the aft FLADE turbine 160 across the FLADE duct 3 circumscribing the aft FLADE turbine 160. A FLADE airflow 80 is powered by the aft FLADE fan blades 5 and put to use downstream of the aft FLADE fan blades 5. The aft FLADE fan blades 5 extend radially outwardly from an annular rotatable FLADE turbine shroud 250 attached to and circumscribing the aft FLADE turbine blades 254 of the aft FLADE turbine 160. The FLADE turbine shroud 250 separates the aft FLADE fan blades 5 from the aft FLADE turbine blades 254. Schematically illustrated, in cross-section in FIG. 4, is an alternative exemplary aircraft aft FLADE engine 1. The engine 1 in FIG. 4 includes a fan section 115 with a fan 330 downstream of variable inlet guide vanes 4 at an inlet 11 and a long duct FLADE duct 3. Fairings 190 disposed across the FLADE duct 3 surround variable vane shafts 194 passing through the FLADE duct 3 that are used to vary and control the pitch of the variable inlet guide vanes 4. Downstream of the fan section 115 is a core engine 18 including, in downstream serial axial flow relationship, a core driven fan 37 having a row of core driven fan blades 36, a high pressure compressor 20, a combustor 22, and a high pressure turbine 23 having a row of high pressure turbine blades 24. A high pressure shaft 26, disposed coaxially about the centerline 12 of the engine 1, fixedly interconnects the high pressure compressor 20 and the high pressure turbine blades 24. The combination or assembly of the core driven fan 37 and the high pressure compressor 20 drivenly connected to the high pressure turbine 23 by the high pressure shaft 26 is designated a high pressure spool 47. A first bypass inlet 42 to the fan bypass duct 40 is disposed axially between the fan section 115 and the core driven fan 37. The fan blades 333 of the fan 330 radially extend across a first fan duct 138. A row of circumferentially spaced-apart fan stator vanes 35 radially extend across the first fan duct 138, downstream of the fan blades 333, and axially between the fan blades 333 and the first bypass inlet 42 to the fan bypass duct 40. The row of the core driven fan blades 36 of the core driven fan 37 radially extend across an annular second fan duct 142. The second fan duct 142 begins axially aft of the first bypass inlet 42 and is disposed radially inwardly of the fan bypass duct 40. An annular first flow splitter 45 is radially disposed between the first bypass inlet 42 and the second fan duct 142. The full engine airflow 15 is split between the FLADE inlet 8 and the fan inlet 11. A fan airflow 50 passes through the fan inlet 11 and then the fan section 115. A first bypass air portion 52 of the fan airflow 50 passes through the first bypass inlet 42 of the fan bypass duct 40 when a front variable area bypass injector (VABI) door 44 in the first bypass inlet 42 is open and with the remaining air portion 54 passing through the core driven fan 37 and its row of core driven fan blades 36. A row of circumferentially spaced-apart core driven fan stator vanes 34 within the second fan duct 142 are disposed axially between the row of second fan blades 32 and the core driven fan blades 36 of the core driven fan 37. The row of the core driven fan stator vanes 34 and the core driven fan blades 36 of the core driven fan 37 are radially disposed across the second fan duct 142. A vane shroud 106 divides the core driven fan stator vanes 34 into radially inner and outer vane hub and tip sections 85 and 84, respectively. The fan shroud 108 divides the core driven fan blades 36 into the radially inner and outer blade hub and tip sections 39 and 38, respectively. A second bypass airflow portion 56 is directed through a fan tip duct 146 across the vane tip sections 84 of the core driven fan stator vanes 34 and across the blade tip sections 38 of the core driven fan blades 36 into a second bypass inlet 46 of a second bypass duct 58 to the fan bypass duct 40. An optional middle variable area bypass injector (VABI) door 83 may be disposed at an aft end of the second bypass duct 58 for modulating flow through the second bypass inlet 46 to the fan bypass duct 40. The fan tip duct 146 includes the vane and fan shrouds 106 and 108 and a second flow splitter 55 at a forward end of the vane shroud 106. First and second varying means 91 and 92 are provided for independently varying flow areas of the vane hub and tip sections 85 and 84, respectively. Exemplary first and second varying means 91 and 92 include independently variable vane hub and tip sections 85 and 84, respectively (see U.S. Patent No. 5,806,303). The independently variable vane hub and tip sections 85 and 84 designs may include having the entire vane hub and tip sections 85 and 84 be independently pivotable. Other possible designs are disclosed in U.S. Patent Nos. 5,809,772 and 5,988,890. Another embodiment of the independently variable vane hub and tip sections 85 and 84 includes pivotable trailing-edge hub and tip flaps 86 and 88 of the independently variable vane hub and tip sections 85 and 84. The first and second varying means 91 and 92 can include independently pivoting flaps. Alternative varying means for non-pivotable, fan stator vane designs include axially moving unison rings and those means known for mechanical clearance control in jet engines (i.e., mechanically moving circumferentially surrounding shroud segments radially towards and away from a row of rotor blade tips to maintain a constant clearance despite different rates of thermal expansion and contraction). Additional such varying means for non-pivotable, fan stator vane designs include those known for extending and retracting wing flaps on airplanes and the like. Exemplary first and second varying means 91 and 92, illustrated in FIG. 4, include an inner shaft 94 coaxially disposed within an outer shaft 96. The inner shaft 94 is rotated by a first lever arm 98 actuated by a first unison ring 100. The outer shaft 96 is rotated by a second lever arm 102 actuated by a second unison ring 104. The inner shaft 94 is attached to the pivotable trailing edge hub flap 86 of the vane hub section 85 of the fan stator vane 34. The outer shaft 96 is attached to the pivotable trailing edge tip flap 88 of the vane tip section 84 of the fan stator vane 34. It is noted that the lever arms 98 and 102 and the unison rings 100 and 104 are all disposed radially outward of the fan stator vanes 34. Other such pivoting means include those known for pivoting variable stator vanes of high pressure compressors in jet engines and the like. Referring to FIG. 4 by way of example, a variable throat area main engine exhaust nozzle 218, having a variable throat area A8, is downstream and axially aft of the aft FLADE turbine 160 and the fan bypass duct 40. The main engine exhaust nozzle 218 includes an axially translatable radially outer annular convergent and divergent wall 220 spaced radially outwardly apart from a radially fixed and axially translatable annular inner wall 222 on the centerbody 72. The translatable radially outer annular convergent and divergent wall 220 controls a throat area A8 between the outer annular convergent and divergent wall 220 and the radially fixed and axially translatable annular inner wall 222. The translatable radially outer annular convergent and divergent wall 220 also controls a nozzle exit area A9 of the main engine exhaust nozzle 218. Alternatively, a variable throat area convergent/divergent nozzle with flaps may be used as disclosed in U.S. Patent No. 5,404,713. Illustrated in FIGS. 3, 10, and 11 is a fixed throat area engine nozzle 216 axially aft of the mixer 49 and the fan bypass duct 40. The plurality of circumferentially disposed hollow struts 208 are in fluid communication with and operable to receive air from the FLADE duct 3. The hollow struts 208 structurally support and flow air to the centerbody 72 which is substantially hollow. A variable area FLADE air nozzle 213 includes an axially translatable plug 172 which cooperates with a radially outwardly positioned fixed nozzle cowling 174 of the centerbody 72 to exhaust FLADE airflow 80 received from the hollow struts 208 and return work to the engine in the form of thrust. An optional variable area turbine nozzle 180 with variable turbine nozzle vanes 182 is illustrated in FIG. 4 located between the mixer 49 and the aft FLADE turbine 160. Variable area nozzle vane shafts 192, that are used to vary and control the pitch of the variable turbine nozzle vanes 182, pass through the variable vane shafts 194 that are used to vary and control the pitch of the variable first FLADE vanes 6. A row of second FLADE vanes 7 is illustrated in FIG. 1 as being fixed but may be variable. The row of second FLADE vanes 7 is also located within the FLADE duct 3 but axially aftwardly and downstream of the row of FLADE fan blades 5. The second FLADE vanes 7 are used to deswirl the FLADE airflow 80. FIGS. 5-8 illustrate a nozzle cooling arrangement in which at least some of the FLADE airflow 80 is used as cooling air 251 which flowed through the hollow struts 208 into the substantially hollow centerbody 72. The cooling air 251 is then flowed through cooling apertures 249 in the centerbody 72 downstream of the variable throat area A8 to cool an outer surface of the centerbody. Some of the FLADE airflow 80 may also be used as cooling air 251 for cooling the radially annular outer wall 220 of the main engine exhaust nozzle 218 downstream of the variable throat area A8 in the same manner. Cooling of the annular outer wall 220 and the hollow centerbody 72 is helpful when thrust augmenting forward and aft afterburners 226 and 224, illustrated in FIGS. 7 and 8 respectively, are ignited. The thrust augmenting forward afterburner 226 is forward and upstream of the aft FLADE turbine 160 and the aft afterburner 224 is aft and downstream of the aft FLADE turbine 160. The apertures may be angled to provide film cooling along the centerbody 72 and/or the hollow struts 208. Holes, shaped and angled holes, and slots and angled slots are among the types of cooling apertures 249 that may be used. Referring to FIG. 8, the augmenter includes an exhaust casing 233 and liner 234 within which is defined a combustion zone 236. The thrust augmenting afterburner 224 is mounted between the turbines and the exhaust nozzle for injecting additional fuel when desired during reheat operation for burning in the augmenter for producing additional thrust. In a bypass turbofan engine, an annular bypass duct extends from the fan to the augmenter for bypassing a portion of the fan air around the core engine to the augmenter. The bypass air is used in part for cooling the exhaust liner and also is mixed with the core gases prior to discharge through the exhaust nozzle. Various types of flameholders are known and typically include radial and circumferential V-shaped gutters which provide local low velocity recirculation and stagnation regions therebehind, in otherwise high velocity core gas flow, for sustaining combustion during reheat operation. Since the core gases are the product of combustion in the core engine, they are initially hot when they leave the turbine, and are further heated when burned with the bypass air and additional fuel during reheat operation. The embodiments of the engine 1 illustrated in FIGS. 3 and 6 have the fan inlet 11 to the fan section 115 axially offset from the annular FLADE inlet 8 to the FLADE duct 3. The exemplary axially offset FLADE inlet 8 is illustrated as being axially located substantially aftwardly of the fan section 115 and, more particularly, it is axially located aftwardly of the core engine 18. Further illustrated in FIG. 3 is a variation of the embodiment of the aft FLADE engine 1 incorporating a "bolt on" aft FLADE module 260 which incorporates a free aft FLADE turbine 160 and can be added to an existing engine 262 for various purposes including, but not limited to, testing and design verification. Another feature illustrated in FIG. 3 is a FLADE power extraction apparatus 264, illustrated as an electrical generator 266 disposed within the engine 1 and drivenly connected through a speed increasing gearbox 268 to the aft FLADE turbine 160. The electrical generator 266 is illustrated as being located within the hollow engine nozzle centerbody 72 but may be placed elsewhere in the engine 1 as illustrated in FIG. 12. Another embodiment of the power extraction apparatus 264 is a power takeoff assembly 270, as illustrated in FIG. 10, including a housing 274 disposed within the hollow engine nozzle centerbody 72. A power takeoff shaft 276 is drivenly connected to the aft FLADE turbine 160 through a right angle gearbox 278 within the housing 274. A power takeoff shaft is typically used to drive accessory machinery mounted external to the engine such as gearboxes, generators, oil and fuel pumps. The FLADE power extraction apparatus 264 allows more flexibility in the design of the engine 1 so that the power used by the aft FLADE fan blades 5 is a small percentage of the power extracted by the aft FLADE turbine 160 from the mixed flow 188 and, therefore, varying and controlling the amount of the FLADE airflow 80 will have a small effect on the efficiency of the aft FLADE turbine 160. Illustrated in FIG. 11 is an engine 1 with the FLADE inlet 8 and the fan inlet 11 axially located together and not axially offset from each other as the embodiments illustrated in FIGS. 3 and 6. The engine 1 includes a long duct FLADE duct 3. The electrical generator 266 is disposed within the hollow engine nozzle centerbody 72 and drivingly connected through the speed increasing gearbox 268 to the aft FLADE turbine 160. The fan 330 is downstream of variable inlet guide vanes 4 at the inlet 11. Fairings 190 disposed across the FLADE duct 3 surround variable vane shafts 194 passing through the FLADE duct 3 that are used to vary and control the pitch of the variable inlet guide vanes 4. Illustrated in FIG. 12 is a portion of an engine 1 with more than one FLADE power extraction apparatus 264 disposed within the engine 1. Forward and aft electrical generators 366 and 367 are disposed within the engine 1 forward and aft or downstream and upstream of the aft FLADE turbine 160. The forward and aft electrical generators 366 and 367 are drivenly connected through forward and aft speed increasing gearboxes 368 and 369 to the aft FLADE turbine 160. Also illustrated in FIGS. 10-12 is a fixed throat area main engine exhaust nozzle 216 having a fixed throat area A8 downstream and axially aft of the aft FLADE turbine 160. Power extraction may be accomplished in such a fixed throat area engine with the variable first FLADE vanes 6 scheduled closed. Illustrated in FIG. 7 is an engine 1 with a forward afterburner 226 axially disposed in the mixed flow 188 between the mixer 49 and the aft FLADE turbine 160. The forward afterburner 226 includes forward fuel spraybars 230 and forward flameholders 232. The forward afterburner 226 may be used to add additional energy to the mixed flow 188 upstream of the aft FLADE turbine 160 if more power is required for the aft FLADE turbine 160 to provide additional energy upon demand to the aft FLADE turbine 160 for the aft FLADE fan blades 5 and/or the power extraction apparatus 264 such as the electrical generator 266 or the power takeoff assembly 270. Schematically illustrated in cross-section in FIG. 9 is an aircraft aft FLADE engine 1 having a fan section 115 with first and second counter-rotatable fans 130 and 132. The variable first FLADE vanes 6 are used to control the amount of a FLADE airflow 80 allowed into the FLADE inlet 8 and the FLADE duct 3. Opening of the FLADE duct 3 by opening the first FLADE vanes 6 at part power thrust setting of the FLADE engine 1 allows the engine to maintain an essentially constant inlet airflow over a relatively wide range of thrust at a given set of subsonic flight ambient conditions such as altitude and flight Mach No. and also avoid spillage drag and to do so over a range of flight conditions. This capability is particularly needed for subsonic part power engine operating conditions. The FLADE inlet 8 and the fan inlet 11 in combination generally form the engine inlet 13. Downstream and axially aft of the first and second counter-rotatable fans 130 and 132 is the core engine 18 having an annular core engine inlet 17 and a generally axially extending axis or centerline 12 generally extending forward 14 and aft 16. A fan bypass duct 40 located downstream and axially aft of the first and second counter-rotatable fans 130 and 132 circumscribes the core engine 18. The FLADE duct 3 circumscribes the first and second counter-rotatable fans 130 and 132 and the fan bypass duct 40. One important criterion of inlet performance is the ram recovery factor. A good inlet must have air-handling characteristics which are matched with the engine, as well as low drag and good flow stability. For a given set of operating flight conditions, the airflow requirements are fixed by the pumping characteristics of the FLADE engine 1. During supersonic operation of the engine, if the area of the engine inlet 13 is too small to handle, the inlet airflow the inlet shock moves downstream of an inlet throat, particularly, if it is a fixed inlet and pressure recovery across the shock worsens and the exit corrected flow from the inlet increases to satisfy the engine demand. If the FLADE engine inlet area is too large, the engine inlet 13 will supply more air than the engine can use resulting in excess drag (spillage drag), because we must either by-pass the excess air around the engine or "spill" it back out of the inlet. Too much air or too little air is detrimental to aircraft system performance. The FLADE fan 2 and the FLADE duct 3 are designed and operated to help manage the inlet airflow delivered by the inlet to the fans. The core engine 18 includes, in downstream serial axial flow relationship, a core driven fan 37 having a row of core driven fan blades 36, a high pressure compressor 20, a combustor 22, and a high pressure turbine 23 having a row of high pressure turbine blades 24. A high pressure shaft 26, disposed coaxially about the centerline 12 of the engine 1, connects the high pressure compressor 20 and core driven fan 37 to the high pressure turbine 23 with the high pressure turbine blades 24. The core engine 18 is effective for generating combustion gases. Pressurized air from the high pressure compressor 20 is mixed with fuel in the combustor 22 and ignited, thereby, generating combustion gases. Some work is extracted from these gases by the high pressure turbine blades 24 which drives the core driven fan 37 and the high pressure compressor 20. The high pressure shaft 26 rotates the core driven fan 37 having a single row of circumferentially spaced apart core driven fan blades 36 having generally radially outwardly located blade tip sections 38 separated from generally radially inwardly located blade hub sections 39 by an annular fan shroud 108. The combustion gases are discharged from the core engine 18 into a low pressure turbine section 150 having counter-rotatable first and second low pressure turbines 19 and 21 with first and second rows of low pressure turbine blades 28 and 29, respectively. The second low pressure turbine 21 is drivingly connected to the first counter-rotatable fan 130 by a first low pressure shaft 31, the combination or assembly being designated a first low pressure spool 242. The first low pressure turbine 19 is drivingly connected to the second counter-rotatable fan 132 by a second low pressure shaft 30, the combination or assembly being designated a second low pressure spool 240. The second counter-rotatable fan 132 has a single row of generally radially outwardly extending and circumferentially spaced-apart second fan blades 32. The first counter-rotatable fan 130 has a single row of generally radially outwardly extending and circumferentially spaced-apart first fan blades 33. The aft FLADE fan blades 5 are primarily used to flexibly match inlet airflow requirements. The high pressure turbine 23 includes a row of high pressure turbine (HPT) nozzle stator vanes 110 which directs flow from the combustor 22 to the row of high pressure turbine blades 24. Flow from the row of high pressure turbine blades 24 is then directed into counter-rotatable second and first low pressure turbines 21 and 19 and second and first rows of low pressure turbine blades 29 and 28, respectively. A row of fixed low pressure stator vanes 66 is disposed between the second and first rows of low pressure turbine blades 29 and 28. Alternatively, a row of variable low pressure stator vanes may be incorporated between the second and first rows of low pressure turbine blades 29 and 28. The first low pressure turbine 19 and its first row of low pressure turbine blades 28 are counter-rotatable with respect to the row of high pressure turbine blades 24. The first low pressure turbine 19 and its first row of low pressure turbine blades 28 are counter-rotatable with respect to the second low pressure turbine 21 and its second row of low pressure turbine blades 29. The aft FLADE turbine 160 is illustrated, in FIG. 9 as a free turbine not connected to a spool or fan in the fan section 115. Alternatively, the aft FLADE turbine 160 may be drivingly connected to the first low pressure shaft 31 of the second low pressure spool 242. The total flow available for vectoring is set by the rotational speed of the aft FLADE fan and the setting of the variable first FLADE vanes 6. The right and left hand valves 162 and 164 control flow to the right and left hand FLADE exhaust nozzles 125 and 135 and control the total pressure ratio at which the aft FLADE turbine 160 and aft FLADE fan 2 operate. The turbofan engine operating conditions may be modulated as necessary to provide the desired combination of overall propulsion system thrust and vectoring forces. Turbofan engine controls would be modified or configured to react to the demands of the thrust vectoring system. This may be achieved by biasing existing control schedules based on the variable first FLADE vane 6 and the right and left hand valves 162 and 164 settings. Alternatively, the primary control mode for the turbofan may be modified such as replacing the typical fan speed control with a system that controls the pressure ratio between an exit of the aft FLADE turbine 160 and the fan inlet 11 of the aircraft aft FLADE engine 1. The engines illustrated herein are single and double bypass types and it is thought that a turbojet type may be used in which there is no bypass duct or bypass flow and the aft FLADE turbine would be placed downstream of any turbine section used to drive the fan and/or compressor. Turbojet type engines may also use augmenters and variable area two-dimensional nozzles.
The history of mass spectrometry (MS) dates back to 1918, with the discovery by J.J. Thompson for identification of new isotopes of common elements like chlorine. The potential of mass spectrometry was immediately realized by the Governments and used in war efforts for the development of early nuclear weapons. Slowly, mass spectrometers transitioned to Chemical, Petroleum industries and Biotech companies. The revolutionary use of MS began by the introduction of microelectronics and advances in material science, where the instrument became user-friendly and easy to use. Finally, the stand-alone MS instruments for analyte identification and confirmation, transformed to computer interfaced modern mass spectrometers coupled to an analytical front end. These new forms are complete analytical systems to solve complex scientific problems. Mass spectrometry works by ionization and determination of the masses of charged analyte molecules. The introduction of tandem mass spectrometry has led to rapid expansion into new fields of science. This article highlights some of the wide range of applications which can be achieved using mass spectrometry. 1. Metabolomic snapshots Metabolomics is the analysis of all the small molecule metabolites in a biological system. This can be very challenging to analyze, given the complexity of the system and internal and external interferences. But, MS coupled to liquid chromatography (LC-MS) based metabolomics applications remarkably changed its use in drug discovery and development. An example worth mentioning here, is using high content LC-MS/MS assays to study the peptidoglycan pathway response in bacteria and for understanding antibiotic resistance [1,2]. By these studies, new drug targets can be identified with the chance of least possible resistance. Further, metabolomics studies can provide individualized patient care to treat the bacterial infections without the risk of developing antibiotic resistance. 2. Biomarker discovery Pushing the limits of detection and quantification in LC-MS specialized its use to biomarker research. Comparative analysis between a healthy person and patient biological specimens using MS can easily identify the significant differences between the two samples in terms of metabolites or proteins or lipids. Sometimes, quantification of biomarkers in ng- fmol range can be achieved by mass spectrometry, not possible with the conventional methods. A good example here will be profiling analysis in cancer patients. Many papers have been published using this technique for discovering unique identifiers of the disease [3,4]. A recent study showed quantification of circulating tumor DNA as a diagnostic marker using mass spectrometry for 1) identification and differentiation of liver diseases 2) determination of treatment response. 3. Biologics front-screening A transition from conventional ligand based assays to mass spectrometry based assays has added practical value in biotech industries. The number of protein drugs and monoclonal antibodies has increased over the past few years, but, there are no rapid quantification methods which can differentiate the isoforms of proteins or to determine if the protein is active or folded, etc. The power of mass spectrometry to overcome these disadvantages of ligand based assays has taken center stage and is currently being explored for biologics quantification. Given the specificity of MS/MS assays, this approach is currently being used complimentary to the conventional methods. Currently, MS methods are being used to study different post translational modifications on proteins in different diseases. This helps with patient stratification and cost-effective rapid clinical sample analysis. 4. Genomics and epigenetic applications Cancer is a well- known disease characterized by mutations in the functional genes. Recent studies have shown the importance of epigenetics in causing cancer and other related diseases . These epigenetic changes can be easily quantified using mass spectrometry. Chromatographic separations were a challenge before and now, with recent advances in HPLC and mass spec techniques, this approach has been made possible. For example, in acute myeloid leukemia, genetic mutations and epigenetic TET effects play an important role in controlling the disease condition . In this study, LC-MS technique can be used to explore the underlying biology, study the treatment response and identify the new drug targets. 5. Forensic lab Did you know that the detector sensors we find at the airports are nothing but compact mass spectrometry instruments? They are used as homeland security checks for identification of illegal drugs, explosive compounds, exotics or to confirm substance drug abuse. Steroid overuse especially by athletes and celebrities can be easily measured using MS. In Forensic studies, MS really comes in handy to identify the barely detectable traces left by the suspect. In toxicology studies, MS is used to detect potential toxins by analyzing the blood samples. This will help determine the poison dose in the blood of victims and identify the time and death of the person . A more recent scientific progress is analyzing the nicotine levels (smoking) or chemical pollutants in human lungs just by a simple inhaler MS system. 6. Newborn screening With advances in science over the past 25 years, we are able to screen newborns for the risk of diseases like cardiovascular disease or diabetes etc. by using MS/MS . This approach gives less false positives compared to the conventional newborn screening methods and includes testing of different biological specimens. For example, lysosomal storage disorders are asymptomatic during childhood, but progress with symptoms to advanced stages. MS has the capacity to identify these types of risks during childbirth using biomarkers or metabolomics based studies. 7. Geology and Space science Another exciting application of mass spectrometry is Astronomy and Environmental Sciences. MS can determine the elements and isotopes in solar wind, record climate changes or geographically locate oil deposits by analyzing the petroleum precursors in rock. Therefore, MS instruments are widely used by NASA to explore the universe. E.g. Saturn’s atmosphere is analyzed for its air composition and quality to estimate the percentage of chemicals and toxins on that planet. 8. The taste of food MS is being used in the food industry for pesticide testing, allergens, etc. and to check the quality of food before being released into the market. This application dominates the use of MS in supply chains and product safety departments. For example, honey, a daily ingredient is constantly adulterated with sulfonilamides which can lead to antibiotic resistance in the consumer with time. By using MS, quick and rapid assays to determine the content of sulfanilamides in honey can be tested. The famous chipotle scandal and horse meat scandal are a few examples where MS testing was done to detect the microbes and specific protein biomarkers to check the quality of meat used in their food products. Imagination and creativity are the limit There are many misconceptions about mass spectrometry and its usage – Often, it is imagined as a huge instrument and sample analysis using this technique is very complex and challenging. In reality, MS instruments are very compact, accurate, easy-to-use, flexible and rapid. The data analysis is performed by user-friendly automated software and can be used even for discoveries. The use of mass spectrometry as forensic detectors, newborn screening tools, breath analyzers, and an antibiotic resistance profiling technique, are a few applications, and there are many more with the recent new advances in technology. We may not be always be aware of this, but, mass spectrometry is used in our daily life on a regular basis. Biography Harika Vemula, PhD in Analytical Chemistry with strong background in analytical method development, chromatographic separations, MS/MS, metabolomics and antibodies. She is currently working as a Senior Scientist for Merck MSD, Missouri, USA in Analytical R&D. She is a member of American Association of Pharmaceutical Scientists, American Society of Mass Spectrometry (ASMS), Sigma Xi Research Society – Kansas City Chapter and member of Mid-west Mass spectrometry group References 1. Vemula H, Ayon NJ, Gutheil WG (2016) Cytoplasmic peptidoglycan intermediate levels in Staphylococcus aureus. Biochimie 121: 72-78. 2. Vemula H, Bobba S, Putty S, Barbara JE, Gutheil WG (2014) Ion-pairing liquid chromatography-tandem mass spectrometry-based quantification of uridine diphosphate-linked intermediates in the Staphylococcus aureus cell wall biosynthesis pathway. Anal Biochem 465: 12-19. 3. Yuan J (2016) Circulating protein and antibody biomarker for personalized cancer immunotherapy. J Immunother Cancer 4: 46. 4. Huang W, Qi CB, Lv SW, Xie M, Feng YQ, et al. (2016) Determination of DNA and RNA Methylation in Circulating Tumor Cells by Mass Spectrometry. Anal Chem 88: 1378-1384. 5. Lin CL, Kao JH (2016) New perspectives of biomarkers for the management of chronic hepatitis B. Clin Mol Hepatol 22: 423-431. 6. Hamidi T, Singh AK, Chen T (2015) Genetic alterations of DNA methylation machinery in human diseases. Epigenomics 7: 247-265. 7. Jaiswal M, Bhar S, Vemula H, Prakash S, Ponnaluri VK, et al. (2017) Convenient expression, purification and quantitative liquid chromatography-tandem mass spectrometry-based analysis of TET2 5-methylcytosine demethylase. Protein Expr Purif 132: 143-151. 8. Ojanpera I, Kolmonen M, Pelander A (2012) Current use of high-resolution mass spectrometry in drug screening relevant to clinical and forensic toxicology and doping control. Anal Bioanal Chem 403: 1203-1220. 9. Ombrone D, Giocaliere E, Forni G, Malvagia S, la Marca G (2016) Expanded newborn screening by mass spectrometry: New tests, future perspectives. Mass Spectrom Rev 35: 71-84.	https://www.technologynetworks.com/analysis/lists/eight-emerging-applications-of-mass-spectrometry-288234
Mice can wreak havoc on your RV and nobody likes to have little pests living in their walls or cabinets. They can also chew through your electrical wiring and leave droppings all over the vehicle. Imagine relaxing in your RV for a good night’s rest after a long day of outdoor adventures and hearing a bump somewhere in the RV, a scratching against a wall, or a tiny squeak. You don’t know where it came from or what it is, so you check it out. You get out of bed, turn on your flashlight and you see it: a pair of beady, little rodent eyes reflecting back at you. You scream, and it scurries away. There are other ways to tell if mice are in your RV and some ways are more obvious than others. However, as we all know, mice are elusive and very shy rodents. Many of them manage to go unseen and so we are often left to depend on other ways to detect their presence. The best way to detect them without physically seeing them is to look for proof of mouse activity and there are several ways to do that. Mouse droppings go wherever mice go. So, if you have mice in your RV, you will also have mouse droppings. While mice do a pretty good job of hiding themselves from us, they aren’t as careful with their poop. Their droppings are typically about a quarter-inch in length. You can tell if they are fresh by the color: newer droppings are darker and shinier while older droppings look dusty and dry. Mice also tend to leave their droppings in larger concentrations in areas closer to their nest. Related: Tips for Cleaning and Disinfecting Your RV If you have mice, you probably have a mouse nest, too. Mice build their nests with whatever small, lightweight materials that they can get their little hands on. They typically shred and gnaw on paper, fabrics, insulation, electric wires, small plastics, other household materials, and really just about anything that a mouse can use to make their nest. Look around the inside of your RV for evidence of shredded or gnawed on materials. Also, be sure to check your pantry, cabinets, closets, and drawers for any proof. In case you’re wondering, mice like to multiply once they find a nice place to stay and they do it pretty fast. One day, you’ll have just one mouse, and the next week, you’ll have a dozen. Don’t let this be your reality. Here is some important information to know about keeping the mice out of your adventures. Mice can be kept out of an RV by using preventative measures such as sealing any holes under your RV, in your door/window frame, and keeping a clean space. Other methods help with mice removals, such as spring-trap mousetraps, mouse bait block, box traps, mint essential oil, and glue traps. What attracts mice to your RV Most often, mice are drawn to warm places because the outdoors is cold and damp. That warm air drifting out of the RV is a big invitation to the mice to come and join the party. That is the last thing that I want! These mice are not the cute, friendly ones you see in the cartoons; they will invade, multiply, and destroy your space. Mice also are attracted by food whether that means crumbs, leftover scents, or even things that smell like food but are inedible. Think of the mouse in 2007 computer-animated comedy film, Ratatouille; he lifted his nose up into the air to sniff out the scent, smelled some food that was a block away, and then chased it down. They might not have the same culinary skills as the mouse in the movie, but mice do have the same senses. They will smell that food you left out the night before, the crumbs left on the table, or the food that hasn’t been stored away properly. And they will come for it if they’re desperate enough and chances are they are always desperate enough. Any small hole in an RV can be a possible entrance for mice. Common entry point areas are the underbelly, the shore power cord compartment, sewer hose, and openings above the wheels. Keep in mind that mice don’t require much room to wiggle through. A quarter-inch diameter hole is large enough for them to squeeze through. Related: Raise Your RV IQ with These Tips Once the mice have snuck their way through an opening to the inside of your RV or a heated basement storage area, the one thing that offers them a nice stay is any form of loose materials laying around. As soon as they have their nest and have found good sources of food and warmth in your RV, they’re all set and ready to stay. Inspect your RV for any entryways for mice One of the greatest skills of an average mouse is being able to fit through tight spaces. They might not be able to fit through every tiny crack you might have in your RV but they will chew through most anything they can’t fit their bodies into. The reason why this is so important to know is that those holes and cracks in your RV let out streams of warmth or scents of food. This is all a mouse needs to be interested enough in the space to check it out. Don’t think you have any cracks or holes in your RV? Have you checked underneath your RV? The easiest ways for mice to get into your RV are typically through any sort of gaps around the sewage, electrical, and water lines at the entry points of your RV. Take a very close look at the underside of the RV, and make sure you don’t have any of these gaps. If you do have a few gaps, have no fear, spray foam is here! You can use the foam that will harden itself to fill the gaps and keep the pesky mice out. You can also use steel wool to stuff inside other holes because it tends to be too difficult for the mice to chew through. Now that you have inspected the RV from the outside for any cracks and holes that could be serving as secret entryways for mice, you need to inspect the inside as well. Inspect the RV interior for signs of mice or possible attractions Are there crumbs lying around on the counter or floor? Is there food sitting out that should have been put away? Are there loose papers randomly scattered throughout? Is there a bunch of dirty socks or dirty laundry lying on the floor instead of being stored somewhere? Don’t be embarrassed if this is what the inside of your RV looks like. This isn’t a clean-check or cleanliness contest. I’m just asking because these are all things that could be attracting the mice or serve as great nesting materials for the mice. Believe it or not, a clean RV is boring and unattractive to mice and they’re more likely to leave it alone because there’s nothing left for them to snack on or nest in. Sounds like something a mom would tell a messy little kid to convince them to clean up their room, right? Except, in this case, it’s true! Preventative measures If you have any open food on counters or tables you should place the food in storage containers to keep the scents out of your RV and away from those little mousy noses. You can also ensure that mice won’t be making a nest out of your favorite shirts and socks by using scented detergent and freshening spray. Mice can’t handle strong perfume scents and tend to stay away from them. This also comes in handy because you can use the scented dryer sheets to put into some of the questionable holes inside your RV. Related: How to Reduce Moisture and Condensation in Your RV I’m also not a big fan of using mouse poison or any of those other chemicals. Like I already said, mice aren’t big fans of fresh scents. Mice have good senses of smell and there are some scents that they tend to avoid. You can try spraying or placing these scents around your RV (especially around entrances). Some deterrents to try include: - Mint - Cayenne pepper - Mothballs - Peppermint - Cinnamon - Vinegar - Dryer sheets - Tea bags (peppermint is best) Soak cotton balls with peppermint oil and leave them in the mice-infested area. Be sure to refresh often. And you could try using a mint-scented cleaner for your RV or just drop a bit of mint essential oil into your cleaner and not only will it keep your RV smelling fresh, but it will help to keep the mice away. These may have varying degrees of success, especially if they sit for a long time and begin to lose potency. And then, of course, there are cats, but I don’t think we need to get into that at this time. Any of these natural solutions may work as mouse repellent and should help to keep the mice away or scare them away if they are already inside your RV. So you read through my list of natural solutions for evicting or repelling mice, and you’re not a firm believer in the all-natural? It’s okay. I’m not offended. I understand, and I’ll even give you some other ways how to kill off those pesky mice. There are a wide variety of natural scents and products that are at the very least rumored to get rid of mice (see above). However, once you have a bona fide mouse problem underway, these might not be strong enough to deal with the problem quickly and effectively. That said, it’s never a bad idea to add some peppermint oil or mothballs to your cabinet to help prevent future visits from more mousey friends. But in the meantime, you may need to amp up your game and turn to actual mousetraps to get the job done. There are a variety of different types of mousetraps available on the market. Box traps work by luring the mouse in with bait and then trapping the mouse inside the box with no way to exit. Once the mouse goes into the box, it closes and traps the mouse inside. This is probably one of the easier ways to kill off your mice because you don’t have to go searching for them once they die because they cannot escape. In theory, you could collect box traps with still-living mice inside them and release them outdoors (but, why would you?) though most people usually simply dispose of the boxes once they’re full. Related: Top 10 RV Travel Tips of All Time Glue traps are simple but effective: you place these sticky sheets in areas where mice are likely to travel and when the mouse steps on the trap, its feet get stuck and it can’t move. Glue traps are affordable, easy to use, and small enough to fit in areas that may not be usable with larger traps, such as below your windows along the kitchen counter. Old-fashioned spring traps are the type you remember from Saturday morning cartoons and they work just as advertised. These are probably self-explanatory but basically, you put some sort of bait like cheese or peanut butter on the tip, the mouse creeps up, and…SNAP! Pretty basic, and you need to watch your fingers when setting it, but they get the job done. They can be a really effective way to kill off the mice you have which, combined with targeted cleaning efforts, can lead to a pest-free area. Finally, you can try using an ultrasonic sound device as part of your efforts into how to mouse-proof an RV. These are small electronic devices that emit an ultrasonic pitch that humans can’t hear. Mice have sensitive ears and will want to avoid anything that is loud or distressing. The downside of this tactic is that dogs and other pets may be affected by it as well and may become distressed and irritated by the noise. If you don’t have pets though, this can be a good method to try. So far this winter I’ve bagged three mice with glue traps. Worth Pondering… I have a very bad relationship with mice.	https://rvingwithrex.com/2022/01/25/the-ultimate-guide-to-keeping-mice-out-of-an-rv/
Organisations in the process of assessing their cyber security defences have been given a new tool that claims to calculate the risk of sustaining an email-based attack. The Insider Breach Calculator, launched today by Egress, calculates how many potential breaches a business may expect to sustain by feeding factors such as employee email habits and mood into an algorithm. These factors include the number of employee inboxes and the industry they work, as well as the perceived stress level and fatigue level of workers between zero and ten. When the figures are plugged in, the results are tallied and presented as the estimated number of emails sent per week and per year, and how many potential breaches an organisation may sustain during those periods. This fictional local government agency with 500 mailboxes could face over 10,000 incidents per year These results can then be broken down by the proportion of accidental versus malicious incidents, as well as the leading potential causes for each category. The explanations provided span employees clicking on a malicious phishing link to employees sharing data to personal systems. "Every organisation knows that it is leaking data in one way or another, yet we find there is a bit of a 'head-in-the-sand' mentality where the insider breach is concerned," said Egress CTO Neil Larkins. "With an average of 60 emails sent every day by one individual within an organisation, the chances of employees accidentally leaking data, continues to grow exponentially. This is before we even consider intentional and malicious leaks, as well as 'forced errors' caused by sophisticated phishing attacks. Based on calculations, a small business in the telecoms sector with 100 employees that are moderately fatigued and stressed (five out of ten) could suffer as many as 5,288 potential breaches in 12 months. When broken down further, the most likely cause of an accidental breach is employees unaware of information that shouldn't be shared, while the most likely cause of a malicious breach would be employees leaking data to a competitor. A large telecoms business of 2,000 employees under the same pressures, by contrast, would suffer more than 35,000 potential breaches within 12 months. Meanwhile, a hypothetical NHS organisation with 6,000 employees under maximum stress and fatigue will likely suffer 131,914 potential breaches in just one year, equivalent to 361 breaches per day. The weight placed on employee welfare is significant, with the same workplace sustaining only 94,224 potential breaches when its hypothetical staff are under no stress or fatigue. Research has shown that one of the biggest factors in cyber risk are employee-based intrusions, with 89% of risks now internal. Moreover, 48% of businesses will experience at least one security incident each year as a result of unintentional employee action.	https://www.itpro.com/security/34577/this-tool-can-work-out-how-often-your-company-will-be-hit-by-insider-attacks
Part 2: Total package oxygen (TPO) and the importance of headspace oxygen. • www.BruniErben.co.uk • [email protected] • 07805 081677 There are Implications of TPO for wine post-bottling development. It appears clear that, from a quantitative point of view, TPO is a major component of the pool. The question arises therefore as to whether above average TPO levels can significantly affect wine shelf-life. The influence of HSO management was investigated in a series of studies carried out by the Geisenheim Research Institute in partnership with Nomacorc. The experimental design adopted is shown in Figure 3. Wines were bottled with different HSO values by different degree of CO2 flushing of the headspace. The Headspace volume of 6mL represents typical industry settings for cylindrical closures. However, as 375 mL bottles were used in this study, the levels of oxygen contained in these headspaces (expressed in mg/L wine) would be 50% lower if 750 mL bottles were used. When HSO values are calculated for 750mL bottles, final values of 0.2, 1.45, and 2.9 mg/L wine are obtained for the three inerting levels. It can be concluded that the range of HS oxygen concentrations in this study is similar to that found in other studies. Therefore, although obtained in an experimental setup, the observations of this study provide meaningful indications regarding bottling management in large-scale winemaking. Free SO2 evolution was followed over time during bottle aging (375 mL bottles were used for this study). Results for the three HSO levels studied are shown in Figure 1. Initial HSO (and therefore TPO) had a great influence on the decline of SO2 in the first fpur months. HSO values of 5.7 mg/L resulted in a loss of free SO2 of 32 mg/L (> 50% of the initial value) in this timeframe, while in the case 0.4 mg/L HSO only 15 mg/L were lost. Interestingly, free SO2 loss between four and fourteen months of bottle storage was comprised between 6 mg/L and 8 mg/L, corresponding to about ¼ of the free SO2 lost in the first four months under conditions of high HSO at bottling. This indicates that TPO at bottling plays a primary role in the evolution of free SO2 in the first months after bottling, highlighting the importance of TPO components, such as HSO in this case, in wines for rapid consumption. The direct connection between initial HSO and loss of SO2 suggest that TPO management could be of primary importance to increase the shelf-life of low-SO2 wines which are highly sought by today’s consumers, including organic and biodynamic wines. Long term variations However, the importance of TPO is not restricted to short term scenarios, as variations in TPO can result in changes in wine aroma profiles that will manifest after longer bottling periods. Sensory analysis carried out on the wines after 24 months of bottle storage at 14°C is shown in Figure 2. Wines with the lowest and highest HSO levels were found to be different in the intensity of the ‘developed’ character, with wines bottled with lower HSO having lower developed notes and higher overall impression. Differences in the ‘reduction’ attribute were negligible Conclusion When it comes to wine post-bottling development, closure oxygen permeability (OTR) is not the only factor affecting the evolution of wine in the bottle. TPO (total package oxygen), namely the sum of dissolved (DO) and headspace (HSO) oxygen present at bottling can play a major role. Too high TPO, often resulting from excessive oxygen pickup during bottling operations, is associated with premature loss of SO2, and uncontrolled TPO variations can determine significant bottle to bottle variation. Monitoring of TPO is crucial to reduce unpredictable variations during bottle storage, and could provide a powerful means to reduce SO2 doses at bottling.	https://www.vineyardmagazine.co.uk/wine-making/optimise-wine-post-bottling-development-2/
The courtroom is rarely a place that most people want to visit when dealing with their matrimonial issues. More often than not, a day in court is a stressful experience, particularly when it comes to dealing with things like divorce, child custody, and visitation rights. It’s no wonder that many individuals prefer to negotiate their divorce outside of court if possible. While there are ways for people to avoid the courts, such as using divorce mediation, not all spouses know for definite whether their spouse will agree to an alternative dispute resolution process like divorce mediation or collaborative law. In these circumstances, it’s important to keep your options open. When a spouse contacts my office to arrange their initial consultation (free for up to 30 minutes with the potential to move to paid consultations after), we try to screen them first to see if they are looking to utilize me as their neutral divorce mediator. It’s important for us to find out whether they want a one-on-one consultation with me as an attorney, or whether they are looking for a divorce mediator. Meeting with someone one-on-one when they’re considering mediation could compromise my position as a neutral party in the eyes of their partner. If the individual tells me that they want to have a one-on-one consultation with me, I may not be able to be their mediator, but we can keep their options open. Setting Up Negotiations with Spouses One option I can offer my clients is for my office to write a letter to their spouse indicating that my office currently represents their other half in connection with various “marital difficulties”. This phrase is commonly used during the introductory correspondence letters. In this letter, we can outline that you desire to resolve the situation as amicably, whether in divorce mediation, traditional negotiations, or otherwise. We can ask the other party, or a lawyer of their selection, to contact the office so that they can discuss options on how to proceed. We do make it clear that the other side is recommended to utilize an attorney, but, of course, they can choose to represent themselves. Within the letter, I often note that although an amicable resolution is desired, it’s still important for the other party to respond to the letter as quickly as possible. The process that occurs as a result could be the correspondence between lawyers, or if one side decides that they want to represent themselves, a negotiation with one spouse and their lawyer. Settlement agreements in the form of separation documents can be drafted in this case and followed up by an application for uncontested divorce. On the other hand, the divorce may be filed and settled with a stipulation of settlement. The couple can also choose whether they would like to remain legally separated for a while, or whether they would prefer to file for a divorce immediately once their agreement has been signed. From there, any lawyers involved can negotiate and draft the language of the agreement and submit an uncontested divorce package once the agreement is signed. Setting Up Divorce Mediations In the letter sent to the other party in a marriage, I could also mention that the client I represent is open to the idea of divorce mediation for the case. The letter may mention that while I am a lawyer for the other spouse, I can also take a step back and the couple will be able to choose a different divorce mediator of their choosing. In this instance, I would act as the review attorney for the client that originally approached me. This means that I could work behind the scenes to help my client prepare for their mediation sessions and debrief after those sessions. I could also help my client to prepare for upcoming sessions and review or draft the settlement agreement too. The other lawyer or I, or the mediator involved with the case (assuming they are a lawyer as some divorce mediators are not) could then submit a package for uncontested divorce to the court. The possibility of collaborative law is available here too. In the letter to the other spouse, I could outline that the spouse is open to the idea of collaborative law, if that is the situation. Here, I would explain what collaborative law means, and even offer some information that the other spouse can use to determine whether the process suits them. I will also be able to point out that I am a collaborative trained lawyer. If my client is intent on a specific process, then we could attempt to steer the process in that direction in correspondence with the other side. Filing and Serving In some cases, my client may want the impact of filing for divorce with a lawyer such as myself and serving the other party with papers. In this case, we could then move back to one of the aforementioned processes to settle the case. However, sometimes our client will need help with bills or will not be able to wait for a negotiation. We might then consider things like Pendente Lite motions for maintenance, child support, requests for a preliminary conference, requests for judicial intervention, financial discovery, a trial to be scheduled and requests for orders about payment when a divorce is pending. To learn more about keeping your options open with a divorce lawyer and family law attorney such as myself, contact our office to schedule your free initial consultation. You can reach out at (516) 333-6555.	https://www.longislandfamilylawandmediation.com/different-divorce-process-options/
--- abstract: 'The effect of Prandtl number on the linear stability of a plane thermal plume is analyzed under quasi-parallel approximation. At large Prandtl numbers ($Pr>100$), we found that there is an additional unstable loop whose size increases with increasing $Pr$. The origin of this new instability mode is shown to be tied to the coupling of the momentum and thermal perturbation equations. Analyses of the perturbation kinetic energy and thermal energy suggest that the buoyancy force is the main source of perturbation energy at high Prandtl numbers that drives this instability.' date: 1 July 2007 and in revised form 10 September 2007 title: Effects of Prandtl number and a new instability mode in a plane thermal plume --- Introduction ============ The classic problem of natural-convection flow above a horizontal line heat source has received considerable attention during the last few decades (Batchelor 1954; Fujii 1963; Gebhart 1988). The temperature of the heat source is larger than that of the ambient fluid, and the resulting density difference creates a plume that rises up against the gravity. For steady laminar plumes, the similarity solutions of the pertinent boundary layer equations have been published by many researchers (Fujii 1963; Gebhart, Pera & Schorr 1970; Riley 1974); experimental studies on laminar plane plumes are in good agreement with similarity solutions (Riley 1974). Experiments (Pera & Gebhart 1971) have confirmed that the laminar plumes are unstable, and they sway in a plane perpendicular to the axis of the source. Pera & Gebhart (1971) have shown that the initial instability of plane plumes to two-dimensional disturbances can be analyzed by the linear stability theory and developed the coupled Orr-Sommerfeld type equations using a quasi-parallel flow approximation. Since Squire’s theorem holds for natural convection flows (Gebhart 1988), it is sufficient to consider two-dimensional disturbances for the stability analysis of a thermal plume. Strictly speaking, the thermal plume is a non-parallel flow field, and the streamwise variations of both the laminar and disturbed flows should be incorporated in the stability analysis (Hieber & Nash 1975; Wakitani 1985). From a weakly non-parallel spatial stability analysis (Wakitani 1985), it has been shown that the critical Grashof number of a plane thermal plume is slightly larger than that predicted from the quasi-parallel theory, even though its precise value depends on the flow quantity (fluctuating kinetic energy or thermal energy, etc.) that is being monitored to calculate non-parallel corrections. It was shown that a lower branch of the neutral stability curve in the (frequency, Grashof number)-plane exists when the non-parallel corrections are taken into account. The upper branch of the neutral curve at moderate-to-large values of Grashof number remains relatively unaffected, however, with non-parallel corrections. Two non-dimensional numbers involved in natural convection phenomena are the Grashof number ($Gr$), the ratio of the buoyancy force and the viscous force, and the Prandtl number ($Pr$), the ratio of the kinematic viscosity and the thermal diffusivity. In terms of $Pr$, there are two limiting cases: zero Prandtl number limit (e.g. molten metals $Pr\sim 10^{-2}$) and infinite Prandtl number limit (e.g. $Pr\sim 10^{3}$ for magmas, and $Pr\sim 10^{21}$ for Earth’s mantle plume). Geological flows involve fluids with large Prandtl numbers (Worster 1986; Lister 1987; Grossman & Lohse 2000; Kaminski & Jaupert 2003; Majumder, Yuen & Vincent 2004) and are studied in the limit of infinite Prandtl number (Wang 2004) for which the inertial terms in the momentum equations are neglected. The goal of the present work is to understand the stability characteristics of high Prandtl number plane thermal plumes. To the best of our knowledge, all stability analyses of plane thermal plumes (Pera & Gebhart 1971; Hieber & Nash 1975; Wakitani 1985) are confined to that of air ($Pr=0.7$) and water ($Pr=6.7$). We use the quasi-parallel approximation to analyse the linear stability of a thermal plume which is found to be unstable for very small Grashof numbers at any Prandtl number. At high Prandtl numbers, we find a new instability loop which is shown to be tied to the coupling of the hydrodynamic and thermal perturbation equations. An analysis of the perturbation energy unveils the driving mechanism of this instability. Governing equations and base flow ================================= We consider the convective flow generated above a line heat source in an otherwise stagnant fluid which is maintained at a constant temperature $T_{\infty}$. Let the Cartesian coordinate system is ($x, y$), with $x$ being directed along the flow direction (i.e. against gravity) and $y$ is the transverse direction, and $u$ and $v$ are the corresponding velocity components along $x$ and $y$ directions, respectively, and $t$ is the time. With Boussinesq approximation, the governing equations for the velocity and the temperature fields are given by $$\begin{aligned} {{\partial}u\over{\partial}{t}} + u{{\partial}u\over{\partial}x} + v{{\partial}u\over{\partial}y} &=& {\nu}{\nabla^2 u} - {1\over\rho}{{\partial}p\over{\partial}x} + g{\beta}{(T -T_{\infty})} \label{eqn:de2} \\ {{\partial}v\over{\partial}{t}} + u{{\partial}v\over{\partial}x} + v{{\partial}v\over{\partial}y} &=& \nu \nabla^2 v - {1\over\rho}{{\partial}p\over{\partial}y} \label{eqn:de3}\\ {{\partial}T\over{\partial}{t}} + u{{\partial}T\over{\partial}x} + v{{\partial}T\over{\partial}y} &=& {\kappa \nabla^2 T}, \quad\quad {{\partial}u\over{\partial}x} + {{\partial}v\over{\partial}y} \; =\; 0 \label{eqn:de4}\end{aligned}$$ Here $\rho$ is the mean density of the fluid, $p$ is the pressure, $g$ is the acceleration due to gravity; the thermo-physical properties of the fluid are the thermal expansion coefficient $\beta$, the kinematic viscosity $\nu$, the thermal conductivity $k$, the specific heat at constant pressure $c_p$ and the thermal diffusivity $\kappa = k/\rho c_p$. The boundary conditions on velocity and temperature are: $u = v = 0,{\;}T = {T_s}{\;} {\;}\mbox{at}{\;} x = y = 0{\;}{\;}$ and $u = v = T = 0$ at $x^{2} + y^{2} \rightarrow \infty$. Base flow: similarity solution ------------------------------ The steady laminar base flow is given by the leading-order boundary-layer equations (Fujii 1963; Gebhart 1970; Pera & Gebhart 1971; Riley 1974) that can be expressed in terms of a stream function: $u = {{\partial}\psi}/{{\partial}y}$, $v = - {{\partial}\psi}/{{\partial}x}$. The resulting partial differential equations (not shown) can be transformed into a set of ODEs in terms of a similarity variable $\eta = {y}/{\delta}$, with $\delta = {4x}/{G}$, where $$Gr= \frac{g\beta(T_0(x) - T_\infty)x^3}{\nu^2} \quad\mbox{and} \quad G=4\left(\frac{Gr}{4}\right)^{1/4} \quad \label{eqn:Grashoff1}$$ are the local Grashof number and the ‘modified’ Grashof number, respectively, and $T_0(x)\equiv T(x,y=0)$ is the local centerline temperature. The non-dimensional stream-function and temperature are defined via $$f(\eta) = \frac{\psi}{U_c\delta}, \quad h(\eta) = \frac{T-T_\infty}{T_0(x) - T_\infty} = \frac{T-T_\infty}{(\nu U_c/g\beta\delta^2)} , \label{eqn:nondim1}$$ where $U_c=\nu G^2/4x$ is the local convective velocity and $T_c=(T_0(x) - T_\infty)=\nu U_c/g\beta\delta^2$ is the local excess temperature at the centerline of the plume. With the assumption of power-law variation of $T_c$ ($\sim x^{-3/5}$), the similarity equations can be obtained as $$f^{'''} + {12\over 5}ff^{''} - {4\over 5}{f^{'}}^2 + h = 0, \quad h^{''} + {12\over 5}Pr\left(fh\right)^{'} = 0, \label{eqn:Base}$$ where the prime denotes differentiation with respect to $\eta$, and the related boundary conditions are (Gebhart 1970): $f(0) = f^{''}(0) = h^{'}(0) = 0$, $h(0) = 1$, $f^{'}(\infty) \rightarrow 0$, $h(\infty) \rightarrow 0$. These equations have been solved by using the fourth-order Runge-Kutta method with Newton-Raphson correction. The far-field boundary condition was implemented at $\eta=12$, and the results were checked by using different values of $\eta=8, 16, 20, 50$. Figure 1 shows the velocity and the temperature profiles for a range of Prandtl numbers. With increasing $Pr$, the velocity profile flattens across the plume width, and the temperature boundary layer becomes narrower. ![ Variations of the base-state ($a$) velocity ($f'$) and ($b$) temperature ($h$) with Prandtl number. []{data-label="fig:Fig1"}](Figure1a.eps "fig:"){width="5.50cm"} ![ Variations of the base-state ($a$) velocity ($f'$) and ($b$) temperature ($h$) with Prandtl number. []{data-label="fig:Fig1"}](Figure1b.eps "fig:"){width="5.50cm"} Linear stability analysis: quasi-parallel approximation ======================================================= To analyse the stability of a thermal plume, we decompose each dynamical variable into a mean part (base flow) and a small-amplitude perturbation: $$\begin{aligned} u(x,y,t) &=& u(x,y) + {\tilde u}(x,y,t), \quad v(x,y,t) \;=\; v(x,y) + {\tilde v}(x,y,t) \\ T(x,y,t) &=& T(x,y) + {\tilde T}(x,y,t), \quad {p}(x,y,t) \;=\; p(x,y) + {\tilde p}(x,y,t) \end{aligned}$$ with the base flow being taken as that given by the similarity solution (\[eqn:Base\]) over which the perturbation equations are linearized. The base flow quantities $v$ and the $x$-derivatives of $u$ and $T$ are taken as zero in the linearized perturbation equations– this is called the [quasi-parallel]{} approximation. The perturbations are assumed to be of the form such that their amplitudes depend on the similarity variable $\eta$, as does the base flow. As in the case of the base flow, it is straightforward to show that the perturbation equations can be expressed in terms of a stream function: $\tilde{u} = {{\partial}\tilde\psi}/{{\partial}y}$, $\tilde{v} = -{{\partial}\tilde\psi}/{{\partial}x}$. The resulting perturbation equations (not shown) are amenable to normal-mode analysis: $$(\tilde{\psi}, \tilde{T})(x,\eta,t) = (\tilde{\phi},\tilde{s})(\eta) {{\rm e}^{{\rm i}({\alpha}{x}-{\omega}{t})}}, \label{eqn:normalmode}$$ where $\alpha$ and $\omega$ are the non-dimensional wavenumber and frequency, respectively, with $\delta$ and $\tau=\delta/U_c$ being the reference length and time scales. The amplitudes for the perturbation stream function and temperature are made dimensionless via $\phi={{\tilde\phi}/{{U_{c}}\delta}}$ and $s = {\tilde{s}}/{T_c}$. Substituting the normal-mode decomposition (\[eqn:normalmode\]) into the linearized perturbation equations, the coupled Orr-Sommerfeld stability equations are obtained: $$\begin{aligned} \left({\phi^{''''}} - 2{\alpha^2}{\phi^{''}} + {\alpha^{4}}{\phi} + {s^{'}}\right) &=& {\rm i}{\alpha}G\left[ \left({f^{'}}-{\omega\over\alpha}\right)({\phi^{''}} -{\alpha^2}{\phi}) - {f^{'''}}{\phi} \right] \label{eqn_OS1}\\ {{s^{''}}-{\alpha^2}s} &=& {\rm i}{\alpha}Pr G \left[\left({f^{'}} - {\omega\over\alpha}\right)s - {h^{'}}{\phi}\right] \label{eqn_OS2}\end{aligned}$$ The boundary conditions on $\phi(\eta)$ and $s(\eta)$ are: $$\phi(\pm\infty) = \phi^{'}(\pm\infty) = s(\pm\infty) = 0 . \label{eqn_BC}$$ Varicose and sinuous modes -------------------------- For [varicose]{} modes, both the velocity and temperatures are [symmetric]{} about the mid-plane ($\eta=0$) which can be translated into following conditions on $\phi$ and $s$: $$\phi(0)=\phi^{''}(0)=s^{'}=0, \label{eqn_BCS}$$ whereas for [sinuous]{} modes both the velocity and temperatures are [asymmetric]{} about the mid-plane ($\eta=0$) for which the conditions on $\phi$ and $s$ are: $${\phi^{'}}(0)={\phi^{'''}}(0)=s(0)=0. \label{eqn_BCA}$$ It is known that the thermal plumes are more unstable to sinuous modes (Pera & Gebhart 1971) which has been confirmed in our study too. Hence, all results are presented only for sinuous perturbations (\[eqn\_BCA\]). Generalized eigenvalue problem and numerical method --------------------------------------------------- The linear stability equations (\[eqn\_OS1\]-\[eqn\_OS2\]), along with boundary conditions (\[eqn\_BC\], \[eqn\_BCA\]), constitute a generalized eigenvalue problem: $$\begin{aligned} {\bf A\Phi} &=& \lambda{\bf B\Phi}. \label{eqn:evalue1}\end{aligned}$$ For the [temporal]{} stability analysis, $\lambda=\omega$ is the eigenvalue, ${\Phi}=(\phi, s)^T$ is the eigenfunction and ${\bf A}$ and ${\bf B}$ are $2\times 2$ matrix differential operators whose elements can be easily obtained from (\[eqn\_OS1\]-\[eqn\_OS2\]). For the [spatial]{} stability analysis, the spatial eigenvalue $\lambda=\alpha$ appears nonlinearly in (\[eqn\_OS1\]-\[eqn\_OS2\]) which are subsequently transformed into a linear problem in wavenumber ($\alpha$) by using the ‘companion-matrix’ method (Bridges & Morris 1984). For this case, ${\Phi}=(\alpha^3\phi, \alpha^2\phi, \alpha\phi, \phi, \alpha s, s)^T$ is the eigenfunction and ${\bf A}$ and ${\bf B}$ are $6\times 6$ matrix differential operators; the non-zero elements of ${\bf A}$ are (with $D={\rm d}/{\rm d}\eta$): $A_{11}=-{\rm i}Gf'$, $A_{12}= {\rm i}\omega G + 2D^2$, $A_{13}={\rm i}Gf'D^2-{\rm i}Gf^{'''}$, $A_{14}= -D^4 - {\rm i}\omega G D^2$, $A_{16}=-D$, $A_{53}={\rm i} Pr G h^{'} $, $A_{55}=-{\rm i} Pr G f^{'}$, $A_{56}= D^2 + {\rm i}\omega Pr G$, $A_{21}=1=A_{32}=A_{43}=A_{65}$, and ${\bf B}$ is an unit diagonal operator. For the temporal stability, the wavenumber, $\alpha$, is real and the frequency, $\omega=\omega_r+{\rm i}\omega_i$, is complex, with $\omega_i$ being the ‘temporal’ growth/decay rate of the perturbation. For the [spatial]{} stability, the frequency, $\omega$, is real and the wavenumber, $\alpha=\alpha_r+{\rm i}\alpha_i$, is complex, with $\alpha_i$ being the ‘spatial’ growth/decay rate. In either case, the flow is said to be stable/unstable if $\omega_i$ or $-\alpha_i >,<0$, respectively, and neutrally stable if $\omega_i$ or $\alpha_i=0$. For both temporal and spatial analyses, the differential eigenvalue problem (\[eqn:evalue1\]) is transformed into an matrix eigenvalue problem by discretizating the related differential operators along the non-periodic $\eta$-direction. We have used two numerical methods for discretization (Malik 1990): (1) the finite difference method with second-order accuracy; (2) the Chebyshev spectral collocation method. The resulting matrix-eigenvalue problem has been solved by the QZ-algorithm of Matlab. The growth-rate and the phase speed of the least-stable mode, obtained from finite difference and spectral methods, were compared for a few test cases with different number of grid/collocation points ($N=101$ and $151$). We found that both the growth rate and the phase speed agreed upto the third decimal place for two methods. Moreover, from a comparison with published literature, we found that our neutral stability curve for air ($Pr=0.7$) agrees well with that of Pera & Gebhart (1971). Results and discussion ====================== We have carried out both temporal and spatial stability analyses of a thermal plume, and most of the results are presented for the temporal case (except in figure \[fig:Fig3\]). ![ For the [temporal]{} analysis, the stability diagrams in the (${\alpha},G$)-plane at $Pr = 200$; panel $b$ is the zoomed part of low-G region. []{data-label="fig:Fig2"}](Figure2a.eps "fig:"){width="6.00cm"} ![ For the [temporal]{} analysis, the stability diagrams in the (${\alpha},G$)-plane at $Pr = 200$; panel $b$ is the zoomed part of low-G region. []{data-label="fig:Fig2"}](Figure2b.eps "fig:"){width="6.00cm"} ![ For the [spatial]{} analysis, ($a$) the stability diagram in the (${\omega},G$)-plane at $Pr = 200$; ($b$) the variation of spatial growth-rate ($-\alpha_i$) with $G$ for $\omega=0$. []{data-label="fig:Fig3"}](Figure3a.eps "fig:"){width="6.00cm"} ![ For the [spatial]{} analysis, ($a$) the stability diagram in the (${\omega},G$)-plane at $Pr = 200$; ($b$) the variation of spatial growth-rate ($-\alpha_i$) with $G$ for $\omega=0$. []{data-label="fig:Fig3"}](Figure3b.eps "fig:"){width="6.40cm"} Results for various Prandtl numbers ----------------------------------- Figure \[fig:Fig2\]($a$) displays a typical stability diagram in the (${\alpha},G$)-plane at high Prandtl numbers ($Pr = 200$) for the [temporal]{} stability analysis; figure \[fig:Fig2\]($b$) is the zoomed part of the low-G region of figure \[fig:Fig2\]($a$). In each panel, the neutral contour ($\omega_i=0$) is marked by ‘0’, and the flow is unstable inside it (see the positive growth rate contours) and stable outside. There are two distinct unstable zones: (a) one at low wavenumbers ($\alpha$) that spans the whole range of Grashof number ($G>G_{cr}$), and (b) the other at relatively higher wavenumbers that spans a limited range of $G$. Figure \[fig:Fig2\]($b$) suggests that there is a minimum value of $G$ below which the plume is stable. The thick line in figure \[fig:Fig2\]($a$-$b$) demarcates the regions of [downstream-propagating]{} (phase speed, $c_r=\omega_r/\alpha>0$) and [upstream-propagating]{} ($c_r<0$) modes in the ($\alpha, G$)-plane. The origin of such upstream-propagating modes (at low $\alpha$) remains unclear to us at present. We have checked that the locus of $c_r=0$ line in the ($\alpha, G$)-plane does not change by increasing the size of the computational domain from $\eta=12$ to $\eta=100$ or by increasing the number of collocation points. We should point out that the possibility of having upstream-propagating modes in a plane thermal plume (which exist for any $Pr$ at very small values of $\alpha$) has not been mentioned in previous works (Pera & Gebhart 1971; Hieber & Nash 1975; Wakitani 1985). Such modes might be analogous to certain backward-propagating modes in Ekman boundary layer (Lilly 1966) – this issue is relegated to a future study. Figure \[fig:Fig3\]($a$) displays the analogue of figure \[fig:Fig2\]($a$) in (${\omega},G$)-plane for the [spatial]{} stability analysis. As expected, the stability diagram in the (${\omega}, G$)-plane also contains two unstable loops which are analogues of the two-loops of the temporal case, figure \[fig:Fig2\]($a$). Focussing on the zero-frequency modes ($\omega=0$) in figure \[fig:Fig3\]($a$), we plot the variation of the spatial growth rate of the least-stable mode ($-\alpha_i$) with $G$ in figure \[fig:Fig3\]($b$). It is seen that the flow is unstable to $\omega=0$ modes beyond a minimum Grashof number, $G\sim 0.185$, for $Pr=200$, and the corresponding real wavenumber is $\alpha_r\sim 0.47$. This critical point $(G, \alpha_r)=(0.185, 0.47)$ from the spatial analysis exactly matches with the intersection point between the neutral curve and the locus of $c_r=0$ modes in figure \[fig:Fig2\]($b$) for the temporal analysis. This result establishes that the upstream propagating modes ($c_r<0$) for the temporal case are not an artifact of the numerical method. ![ Variations of the ‘temporal’ growth rate ($\omega_i$) and the phase speed ($c_r=\omega_r/\alpha$) of the least stable mode with wavenumber $\alpha$ for ($a$) $G=50$ and ($b$) $G=100$, with $Pr=200$. []{data-label="fig:Fig4"}](Figure4a.eps "fig:"){width="6.00cm"} ![ Variations of the ‘temporal’ growth rate ($\omega_i$) and the phase speed ($c_r=\omega_r/\alpha$) of the least stable mode with wavenumber $\alpha$ for ($a$) $G=50$ and ($b$) $G=100$, with $Pr=200$. []{data-label="fig:Fig4"}](Figure4b.eps "fig:"){width="6.00cm"} Here onwards, we present results only for temporal stability. Focussing on figure \[fig:Fig2\]($a$), we show the variations of the growth-rate and phase speed of the least-stable mode with wavenumber in figures \[fig:Fig4\]($a$) and \[fig:Fig4\]($b$) for $G=50$ and $G=100$, respectively. Two humps in each growth-rate curve correspond to two unstable loops in figure \[fig:Fig2\]($a$), and the second hump is referred to as [new mode]{} since it does not have an analogue in low-$Pr$ fluids. The discontinuities in each phase-speed curve correspond to crossing of different modes. For a range of Prandtl numbers ($Pr = 0.7$, $100$, $200$ and $500$), the stability diagrams, containing the neutral contour ($\omega_i=0$) along with a few positive growth-rate contours ($\omega_i>0$), are compared in the ($G,\alpha$)-plane in figure \[fig:Fig5\]($a$-$d$). For $Pr=0.7$ (air), the stability diagram has one loop, and the upper branch of the neutral curve is well defined and has an inviscid asymptotic limit: $\alpha=1.3847$ (Pera & Gebhart 1971). In the limit $G\rightarrow \infty$, there exists a range of wave-numbers over which the flow is unstable. At high Prandtl numbers ($Pr > 100$), as in figure \[fig:Fig5\]($c$), the neutral curve contains a kink, and there is an additional unstable loop at large $\alpha$ and low $G$. The size of this new unstable loop increases with increasing Prandtl number, see figure \[fig:Fig5\]($d$). As mentioned before, this new unstable loop is referred to as a new mode since it does not appear in low-$Pr$ fluids. Comparing the growth rate contours for different $Pr$ in figure \[fig:Fig5\], we find that the growth rate of the least-stable mode decreases with increasing Prandtl number, even though the size of the unstable zone in the $(\alpha, G)$-plane increases in the same limit. The thick solid contour in each panel of figure \[fig:Fig5\] is explained in the next section. ![Stability diagrams at various Prandtl numbers: (a) $Pr=0.7$; (b) $Pr = 100$; (c) $Pr =200$; (d) $Pr=500$. Thick line in each panel corresponds to the neutral contour for ‘uncoupled’ stability equations (see §4.2 for related explanation). []{data-label="fig:Fig5"}](Figure5a.eps "fig:"){width="6.00cm"} ![Stability diagrams at various Prandtl numbers: (a) $Pr=0.7$; (b) $Pr = 100$; (c) $Pr =200$; (d) $Pr=500$. Thick line in each panel corresponds to the neutral contour for ‘uncoupled’ stability equations (see §4.2 for related explanation). []{data-label="fig:Fig5"}](Figure5b.eps "fig:"){width="6.00cm"} ![Stability diagrams at various Prandtl numbers: (a) $Pr=0.7$; (b) $Pr = 100$; (c) $Pr =200$; (d) $Pr=500$. Thick line in each panel corresponds to the neutral contour for ‘uncoupled’ stability equations (see §4.2 for related explanation). []{data-label="fig:Fig5"}](Figure5c.eps "fig:"){width="6.00cm"} ![Stability diagrams at various Prandtl numbers: (a) $Pr=0.7$; (b) $Pr = 100$; (c) $Pr =200$; (d) $Pr=500$. Thick line in each panel corresponds to the neutral contour for ‘uncoupled’ stability equations (see §4.2 for related explanation). []{data-label="fig:Fig5"}](Figure5d.eps "fig:"){width="5.60cm"} Now we suggest one possible experiment to realize this new instability mode. Suppose a laminar plume is disturbed by a small-amplitude sinusoidal excitation of the source with a specified frequency, $f=\omega/2\pi$ (the temperature at the source is constant such that $G=100$, say, in figure 3$a$). For small enough $f$ the plume will show a wavy instability according to the lower instability loop in figure 3($a$), however, for relatively larger $f$ the plume is unstable to our new instability loop and there is a window of frequencies between two instability modes over which the plume remains stable. It would be interesting to verify this transition scenario at a given Grashof number, ‘unstable$\to$stable$\to$unstable’ with increasing frequency, in experiments of high $Pr$-fluids. Origin of new instability loop: coupling of hydrodynamic and thermal fluctuations --------------------------------------------------------------------------------- To shed light on the origin of the new instability loop at high $Pr$, here we assume that the velocity and the temperature perturbations are decoupled from each other. The full set of stability equations, (\[eqn\_OS1\]-\[eqn\_OS2\]), can be made independent from each other by dropping $s^{'}$ and ${h^{'}}{\phi}$ from equations (\[eqn\_OS1\]) and (\[eqn\_OS2\]), respectively. These two sets of equations can now be solved separately to determine the least stable eigen-value – we have verified that the least stable mode belongs to the Orr-Sommerfeld equation (i.e. a purely hydrodynamic mode, eqn. \[eqn\_OS1\]), and the energy equation (\[eqn\_OS2\]) always yields a stable mode. For the uncoupled perturbations, the neutral stability curve for each $Pr$ is superimposed as a thick solid contour in figure \[fig:Fig5\]. (The flow is unstable inside the thick contour and stable outside.) A comparison of the thick line in each panel with the corresponding neutral contour of [coupled]{} stability equations (denoted by the thin curve $0$) clearly reveals that the coupling between the hydrodynamic and the thermal disturbance equations is responsible for the origin of our new instability mode at high $Pr$. It is observed that the lower parts of the instability loops in figures \[fig:Fig5\]($c$-$d$) closely follow the instability loop of the ‘uncoupled’ Orr-Sommerfeld equation, and are, therefore, purely hydrodynamic in origin. It is clear that the coupling terms in the stability equations (\[eqn\_OS1\]-\[eqn\_OS2\]) are responsible for appearance of the additional instability loop at high Prandtl numbers, and solving the uncoupled perturbation equations would lead to incorrect results. The importance of this coupling between hydrodynamic and thermal perturbations at high $Pr$ can be understood from the fact that the gradient of the base-flow temperature, ${h^{'}}$, (which appears in the energy perturbation equation) increases with Prandtl number: $h'(\eta) \sim Pr f(\eta)h(\eta) \sim Pr^\epsilon$, with $0 < \epsilon < 1$, and hence cannot be neglected at large $Pr$. (From an order-of-magnitude analysis of the pertinent boundary-layer equations, we find $\epsilon=1/2$.) Analysis of perturbation energy: instability mechanism ------------------------------------------------------ Lastly, to understand the underlying instability mechanism, we analyse different components of perturbation energy. The time-evolution equations of perturbation kinetic energy and thermal energy are obtained from (\[eqn\_OS1\]-\[eqn\_OS2\]) by multiplying them with the corresponding complex conjugate quantity $\phi^{\dagger}$ and $s^{\dagger}$, respectively, and integrating them from $\eta=0$ to $\eta=\infty$. Considering the real parts, the resulting evolution equations boil down to (Nachtsheim 1963; Gill & Davey 1969) $$\begin{aligned} \frac{{\rm d}{\mathcal E}_K}{{\rm d}t} &\equiv& \omega_i\int_0^\infty e_K {\rm d}\eta \;=\; \int_0^\infty e_{trK} {\rm d}\eta + \int_0^\infty e_{VD} {\rm d}\eta + \int_0^\infty e_B {\rm d}\eta, \label{eqn:E_K}\\ \frac{{\rm d}{\mathcal E}_T}{{\rm d}t} &\equiv& \omega_i\int_0^\infty e_T {\rm d}\eta \;=\; \int_0^\infty e_{trT} {\rm d}\eta + \int_0^\infty e_{TD} {\rm d}\eta , \label{eqn:E_T}\end{aligned}$$ where $$\begin{aligned} e_K &=& \left({\mid{\phi}\mid^2}+{\alpha^2}{\mid\phi\mid^2}\right), \quad e_{trK} = {\alpha}{f^{''}}\left(\phi_r \phi_i^{'}-\phi_r^{'}\phi_i\right), \quad e_{VD} = G^{-1}{\mid{{\phi^{''}}-{\alpha^2}\phi}\mid^2}, \label{eq:de37}\\ e_B &=& G^{-1}\left(s_r\phi_r^{'}+s_i\phi_i^{'}\right), \label{eq:de39}\\ e_T &=& {\mid{s}\mid^2}, \quad e_{trT} \;=\; {\alpha}{h^{'}}\left(\phi_r s_i-\phi_i s_r\right), \quad e_{TD} \;=\; - Pr^{-1} G^{-1}\left({\mid{s^{'}}\mid^2} +{\alpha^2}{\mid{s}\mid^2}\right), \label{eq:de41}\end{aligned}$$ and the suffixes $r$ and $i$ denote the real and imaginary parts, respectively. For hydrodynamic fluctuations, ${\rm d}{\mathcal E}_K/{\rm d}t$ represents the rate of change of perturbation kinetic energy, $E_{trK}=\int e_{trK}$ the rate of transfer of kinetic energy from the mean flow to perturbations via the Reynolds stress, $E_{VD}$ the rate of viscous dissipation, and $E_B$ the rate of gain of kinetic energy through the [buoyancy]{} force. For thermal fluctuations, ${\rm d}{\mathcal E}_T/{\rm d}t$ is the rate of change of perturbation thermal energy, $E_{trT}$ is the rate of gain of thermal energy from the mean temperature field and $E_{TD}$ is the rate of dissipation of thermal energy. ![Distributions of ($a$) kinetic and ($b$) thermal energies across the plume width for $Pr=0.7$ (air), $G=100$, $\alpha=1.2923$. Vertical line indicates the location of the critical layer.[]{data-label="fig:Fig6"}](Figure6a.eps "fig:"){width="5.6cm"} ![Distributions of ($a$) kinetic and ($b$) thermal energies across the plume width for $Pr=0.7$ (air), $G=100$, $\alpha=1.2923$. Vertical line indicates the location of the critical layer.[]{data-label="fig:Fig6"}](Figure6b.eps "fig:"){width="6.0cm"} ![ Same as figure 6, but for $Pr=200$, $G=100$, $\alpha=2.74645$. []{data-label="fig:Fig7"}](Figure7a.eps "fig:"){width="5.6cm"} ![ Same as figure 6, but for $Pr=200$, $G=100$, $\alpha=2.74645$. []{data-label="fig:Fig7"}](Figure7b.eps "fig:"){width="6.0cm"} The variations of different kinetic and thermal energy components across the plume width $\eta$ are displayed in figures \[fig:Fig6\] and \[fig:Fig7\] for $Pr=0.7$ ($\alpha=1.2923$) and $200$ ($\alpha=2.74645$), respectively, at $G=100$. (These two cases correspond to the neutral modes on the upper branch of the neutral contour in figures \[fig:Fig5\]$a$ and \[fig:Fig5\]$c$.) In each figure, the location of the corresponding critical layer is indicated by the vertical line. Since the instability mode is neutral ($\omega_i=0$), the net rate of gain of kinetic/thermal energy is $E_K=\omega_i\int e_K {\rm d}\eta = 0 =E_T$, denoted by the dotted zero-line in each panel. For $Pr=0.7$, the kinetic energy gained by the perturbation mainly comes from the Reynold’s stress term ($E_{trK}$) and a small amount is contributed from the perturbation buoyancy force ($E_B$); the maximum amount of energy is dissipated at the center line ($\eta=0$) by viscous forces ($E_{VD}$). With increasing $Pr$, the rate of gain of kinetic energy by Reynolds stress becomes progressively smaller, and the [buoyancy]{} force ($E_B$) takes over as the main source of perturbation kinetic energy (see figure 7$a$ at $Pr=200$) which balances the energy lost due to viscous dissipation. We conclude that at high $Pr$ the contribution from the Reynold’s stress term is negligible compared to the gain in kinetic energy by buoyancy force which drives instability. Conclusions =========== Based on a quasi-parallel stability analysis of a plane thermal plume, we have uncovered a new instability loop at high Prandtl numbers. The origin of this new mode is shown to be tied to the coupling between the hydrodynamic and thermal fluctuations. The importance of this coupling is tied to the increasing magnitude of the base-state temperature gradient with increasing Prandtl number. It is shown that the perturbation kinetic energy gained from the [buoyancy]{} force drives this instability at high $Pr$. The underlying instability mechanism differs from the well-known hydrodynamic instability mechanism for which the perturbation energy is gained from the mean flow via the Reynolds stress. In future, it would be interesting to analyse the effects of non-parallel corrections as well as the temperature-dependent transport coefficients on our new instability loop. We acknowledge financial support from two grants (DRDO/RN/4124 and PC/EMU/MA/35). M.A. acknowledges Prof. Vijay Arakeri for motivating this research. [REFERENCES]{} - [Batchelor, G. K.]{} (1954) [Heat convection and buoyancy effects in fluids.]{} Q. J. R. Met. Soc. 80, p. 339-359. - [Bridges, T. J. & Morris, P. J.]{} (1984) [Differential eigenvalue problems in which the parameter appears nonlinearly.]{} [J. Comp. Phys.]{} [55]{}, p. 437-460. - [Fujii, T.]{} (1963) [Theory of the steady laminar natural convection above a horizontal line heat source and a point heat source.]{} [Int. J. Heat Mass Transfer]{} [6]{}, p. 597-606. - [Gebhart, B., Pera, L. & Schorr, A.]{} (1970) [Steady laminar natural convection plumes above a horizontal line heat source.]{} [Int. J. Heat Mass Transfer]{} [13]{}, p. 161-171. - [Gebhart, B., Jaluria, J., Mahajan, R. L. & Sammakia, B.]{} (1988) [Buoyancy Induced Flows and Transport.]{} Hemisphere Publishing, Washington. - [Gill, A. E. & Davey, A.]{} (1969) [Instabilities of a buoyancy-driven system.]{} [J. Fluid Mech.]{} [35]{}, p. 775-798. - [Grossmann, S. & Lohse, D.]{} (2000) [Scaling in thermal convection: a unifying theory.]{} [J. Fluid Mech.]{} [407]{}, p. 27-56. - [Hieber, C. A. & Nash, E. J.]{} (1975) [Natural convection above a line heat source: Higher order effects and stability.]{} [Int. J. Heat Mass Transfer]{} [18]{}, p. 1473-1479. - [Kaminski, E. & Jaupart, C.]{} (2003) [Laminar starting plumes in high Prandtl number fluids.]{} [J. Fluid Mech.]{} [478]{}, p. 287-298. - [Lilly, K. L.]{} (1966), [On the instability of Ekman boundary flow.]{} [J. Atmos. Sci.]{} [21]{}, p. 481-494. - [Lister, J. R.]{} (1987), [Long-wavelingth instability of a line plume.]{} [J. Fluid Mech.]{} [175]{}, p. 571-591. - [Majumder, C. A. H., Yuen, D. A. & Vincent, A. P.]{} (2004) [Four dynamical regimes for a starting plume model.]{} [Phys. Fluids]{} [16]{}, p. 1516-1531. - [Malik, M. R.]{} (1990) [Numerical methods for boundary layer stability.]{} [J. Comp. Phys.]{} [86]{}, p. 376-413. - [Nachtsheim, P. R.]{} (1963) [Stability of free convection boundary layers.]{} NASA Tech. Note, TN D-2089. - [Pera, L. & Gebhart, B.]{} (1971) [On the stability of laminar plumes: Some numerical solutions and experiments.]{} [Int. J. Heat Mass Transfer]{}, [14]{}, p. 975-984. - [Riley, N.]{} (1974) [Free convection from a horizontal line source of heat.]{} [ZAMP]{} [25]{}, p. 817-828. - [Wakitani, S.]{} (1985) [Non-parallel flow instability of a two dimensional buoyant plume.]{} [J. Fluid Mech.]{} [159]{}, p. 241-258. - [Wang, X.]{} (2004) Infinite Prandtl number limit of Rayleigh-Benard convection. [Comm. Pure Appl. Math.]{} [57]{}, p. 1265-1282. - [Worster, M. G.]{} (1986) [The axisymmetric laminar plume: Asymptotic solution for large Prandtl number.]{} [Stud. Appl. Math.]{} [75]{}, p. 139-152.
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A woman from the Thames Valley is preparing to swim the English Channel to raise money for her friend's son. Lisa Auchinvole from Oxfordshire, is hoping to raise £10,000 for her friend's 7 year old son, who suffers from Muscular Dystrophy. "Adam is the son of a close school friend," explains Lisa. "The swim is a personal challenge, but also aims at raising money for Action Duchenne which is the charity specifically working towards finding a cure for Duchenne Muscular Dystrophy. The research and imminent trials could make an enormous difference to Adam's life and that of his parents." 40 year old Lisa has been training hard and completed a six hour swim of Lake Windermere in the Lake District back in June, in preparation for the Channel swim in September. She has already had lots of support, with the current donation total currently standing at over £6,000. And she has received words of encouragement from the highest places. "This sort of challenge takes a huge amount of mental and physical strength - and Lisa has both," said Olympic medallist Sharon Davies. You can find out more about Lisa's challenge and make a donation here.	https://www.heart.co.uk/thamesvalley/news/local/thames-valley-woman-takes-channel-swim-challenge/
The Wonder of Words: Successful Vocabulary Strategies for English Learners Why is vocabulary development so critical to language development and literacy achievement for English learners? Vocabulary refers to the words we must know to communicate effectively. One of the most persistent findings in reading research is that the extent of students’ vocabulary knowledge relates directly to their ability to comprehend, and to their overall reading success (Bauman, Kame’enui & Ash, 2003). Furthermore, vocabulary knowledge is one of the best predictors of verbal ability. Researchers refer to four types of vocabulary which represent four tickets to successful second language acquisition. These four distinct and overlapping vocabularies are: (listening and reading = receptive, and speaking and writing = expressive). Young children have much larger listening and speaking vocabularies than reading and writing. That becomes our challenge in teaching English learners. When I started teaching and focusing on the needs of English learners, few materials were available for English as an Additional Language or Dialect (EAL/D) learner programs. So I adapted textbooks and workbooks from the general education curriculum to meet the linguistic needs of students who received EAL/D instruction in a pull-out service delivery model. But similar to the students that I served with special education needs, they spent most of their time in the general education classroom. It became evident to me that classroom teachers needed to learn to adapt their teaching methods and materials to meet the needs of EAL/D learners in their classes. I began to examine ways that I could help them do this. I focused on vocabulary development and modifying learning area teaching methods and materials. In this article, I will discuss methods and strategies for teaching vocabulary to EAL/D learners that can be used by EAL/D and learning area teachers alike. These techniques are hands-on, practical and effective – well suited to busy classroom literacy programs! Involve your students in the wonderful world of words. As students increase their vocabularies, they boost their reading comprehension and strengthen their ability to tackle informational text. In developing and enhancing your program for word learning, keep in mind the following features: it should be personal, active, flexible and strategic. Where do you start? Some questions to ask yourself as you wonder about words: - What do I believe about the importance of word learning? - Do I have a narrow- or broad-based view of integrating vocabulary instruction throughout the curriculum? - When I introduce new words, do I always follow the same procedure? - In my classroom, who does the most talking about new words? - How do I create the “wonder of words”? Do I make it personal, active, multi-sensory, flexible, strategic? (Perez, 2016). Use direct instruction in an explicit, systematic way Students acquiring English need particular attention to explicit vocabulary instruction because vocabulary difficulty strongly influences the readability of texts (Klare, 1984). They need much more and frequent exposure to new vocabulary than their native English-speaking classmates (August & Shanahan, 2006). EAL/D learners need to learn cognates, prefixes, suffixes and root words to enhance their ability to comprehend text. Teachers should focus on student understanding of context clues, pictures and charts as well as the words. Carefully choose the vocabulary that your EAL/D students must need to know in order to support their reading development. New vocabulary needs to be explicitly taught, and each new word should be directly linked to an appropriate strategy. Plan for repeated exposures using different modalities to ensure mastery. EAL/D learners should actively engage in activities to practise new vocabulary because learning words out of context is difficult for these students. Be sure to provide student-friendly definitions for words that are important to their understanding of the content. Simply memorising words on a list and their meaning will not equal transfer of learning unless they see the connection to their lives. It is important to focus on word meaning Ask yourself: when does a student truly know a word? The dilemma for teachers is the quandary of vocabulary vs. spelling. For struggling students and/or EAL/D learners, spelling has another set of challenges. Knowing a word by sight and sound, and being able to recite the dictionary definition, are not the same as being able to make meaning of the word, using it in various contexts and understanding it when it is heard or seen beyond the text (Miller & Gildea, 1987). When deciding on which words to teach, make vocabulary choices by asking: - Is the word critical to making meaning of the text or story? - Is the word useful to the student beyond the text in their lives? If yes – teach it! Students who are acquiring English need particular attention paid to explicit vocabulary instruction, because vocabulary difficulty strongly influences the readability of texts (Klare, 1984). Similarly, Beck and McKeown (1983) concur that teaching the vocabulary of a selection can improve students’ comprehension of that selection. Decades of research have consistently confirmed the relationship between vocabulary knowledge, reading comprehension and academic success (Baumann & Kame’enui, 2002). Understanding academic language is the key to school success Many students struggle with the academic language they encounter in school and in textbooks because their exposure to language outside of school does not include these advanced words and phrases. Therefore, a challenge facing EAL/D learners is that they not only have to develop the everyday language that is familiar to their monolingual peers, but they must also learn academic language skills to understand the informational texts found in the learning areas. This dilemma poses a double demand of language proficiency for EAL/D learners (O’Brien & Leighton, 2015). Introduce the most essential vocabulary before beginning a new chapter or unit Don’t overwhelm students with too many words or concepts. Pick what is absolutely essential in each chapter. Pronounce each word for students, and have them repeat after you. Organise vocabulary around a common theme of a content area you are studying, and choose reading materials that reinforce that vocabulary in context. Provide experiences that help demonstrate the meaning of the vocabulary words. Teach your students to be word detectives and help them discover a sense of wonder in gathering new words for their word bank. Make word learning visible, listing core vocabulary on the walls – there is no escape from learning! In fact, make a game out of it! Each time you use one of the key vocabulary words, have the students tally it and celebrate their word discoveries. Involve the students in selecting key words of the week. These words should be new, interesting and/or challenging. See if they can use the words in new and different ways, and have them earn points for their unique contributions. Students should keep a vocabulary log of these new and exciting words and use them in their writing as well as in their speaking. Make these words multi-dimensional – create word mobiles that hang in the classroom. Another way to help with retention and comprehension for visual learners is to sketch the meaning of a word and make a set of flashcards with the graphic symbols for new words. For the bodily–kinesthetic learner, let them act out the meanings of the new words by using time for “Word Theatre”. Have students use the words in meaningful sentences that are grounded in their own world, not just copied from the textbook. Give them “great, big, fancy” words to enrich their vocabulary! In order to foster this word-awareness, providing your students with a rich array of varied text types at different levels is essential for self-selection. When they come to a word that they do not know, explain word meanings in a conversational way. Don’t “sound like a dictionary”. Here are some other strategies to easily integrate into your curriculum: - Word chips – place keywords on a sheet of paper and have the students tear them apart into separate word chips. Work with a learning partner and have them use the word in a sentence that has a personal connection: “This reminds me of_____________.” - Let me count the ways – have students select a word chip and see if they can use it in five different ways. This helps them make connections. - Two for you – Have students work with a learning partner, each selecting two word chips to make a sample sentence that makes sense. For example, if the child chooses “sink” and “sand”, ask them to make a statement that uses both of the words in a meaningful way: “If I drop sand in the water, I know it will ” You might then ask them to do a visual to support their language. - Three for me – after they have mastered two word chips, have them try it with three word chips. The words are “water”, “sand” and “grains”. The student uses these three words to make a statement: “When water flows over sand, it tends to push the grains” Make sure that the words are appropriate to their age and developmental level. - Go for it! – Increase the complexity and level of difficulty after the student has successfully been able to make statements with two and three words, then have them make a sentence that uses all the word chips. Ask them to share their sentences with the group. - Explore homographs – Use games to teach multiple meaning of words – words that are spelled the same but have different meanings and origins. For instance: - Spell (to say letters) - Spell (words with magical power) - Spell (a duration of time) These activities provide more language links and more personal connections, so that when students read the text they will be more prepared to read the passage independently and look for specific words to pull out or highlight. This provides students with another context for the keywords that you just taught them and that they made meaning of. Build background knowledge It is important to provide explicit links to previously taught text to activate prior knowledge for English learners. Review relevant vocabulary that was already introduced, and highlight familiar words that have a new meaning. Access the knowledge that students bring from their native cultures. Use visuals when introducing new words and concepts Think of ways to scaffold vocabulary instruction for your English learners through visual or kinesthetic techniques. When a teacher simply lectures, EAL/D learners have very little understanding of the concepts being taught. It is therefore helpful to use realia, pictures, photographs, graphic organisers, maps and graphs. Write keywords on the board, and add gestures to help students interpret meaning. Have students create their own visuals to aid their learning. For example, assign each student a few content-specific vocabulary words. Have them write simple definitions in their own words and draw pictures to show what the words meant. - Group related words – Rather than teaching isolated words to memorise, teach words in related clusters that will enhance their meaning-making process. For instance, have students group words together about emotions or feelings. Then have them discuss what it means to be “frightened” or “delighted” or “terrified” vs. “ecstatic”. An extension activity would be to make posters that represent these groupings. Provide rich, language experiences that are multi-sensory Encourage deep processing of word knowledge through engaging, multimodal approaches and a variety of exposures. A hands-on approach to vocabulary development is far more meaningful to the students than the passive act of “look it up in the dictionary”. In fact, dictionary use needs to be strategic and purposeful. In this way, they are getting more learning done in less time and they are working smarter, not harder, by developing their psychomotor memory (Jensen, 2005). Be sure to keep an ongoing list of key vocabulary prominently displayed. This can take the form of a word wall that is constantly evolving as your students’ word knowledge grows and develops. If the words are visible and accessible to the students, they are more likely to see them, think about them and use them. Exposure to a wide variety of words can be further enhanced when the students are exposed to a variety of different kinds of texts on different topics and at different levels. Although wide reading builds word knowledge, direct instruction in vocabulary influences achievement and comprehension more than any other factor (Baumann & Kameenui, 2002; Blachowicz & Fisher, 2014). Vocabulary development is sustained over time through multiple exposures to words in different contexts. In addition, environmental words should surround them in the classroom. Label everything to give words more meaning in the real-world context around them. - Engaging teacher read-aloud – Choose books with vibrant vocabulary and powerful language. Share your own love of words with your students and ignite and excite students to share theirs. Print the key vocabulary words on index cards and deal them out to the students. If you have more students than word cards, have them work in partners. As you deal out the cards, pronounce each word to the student so that they recognise the sound of the word. As you read the story aloud, invite the students to hold up the word when they hear their word read. After the children are familiar with the story, during a repeated reading, you may want to pause before the target word and have the students guess which word would make sense in the sentence. This is a great way to use context clues for word meaning. Increase teacher read-aloud to at least three times a day. Use read-aloud for narrative as well as informational text. While reading, demonstrate curiosity about words and pause to wonder aloud and unpack fascinating words for the children. - Word Wall Whackers! Bring your traditional word wall to life by using a fly swatter that you have prepared by cutting out the plastic webbing so that it forms a frame. Have several fly swatters so that several students can participate in this lively game of “smack-down”. Some questions to use to bring the word wall to life include: - What word is the opposite of_________________? - Whack at least three nouns. - Which word rhymes with ___________________? - Whack at least three verbs. - Whack a word that has more than three syllables. - Which part of speech is_____________? - Whack at least three adjectives. - Whack the word that means ________________. - Whack a word that has a prefix. What does it mean? - Whack three words that were used in our story. - Whack a word that starts like your name. - Whack a word that means the same as______________. - What category does this word fit into? - What are some main characteristics? - What are some examples of it? You can change the questions to meet the needs of the lesson. This increases their speaking and listening skills, and provides a much-needed kinesthetic break in the instruction. - Group related words – Rather than teaching isolated words to memorise, teach words in related clusters that will enhance the meaning-making process. For instance, have students group words together about emotions or feelings, then have them discuss what it means to be “frightened”, “delighted” or “terrified” vs. “ecstatic”. An extension activity would be to make posters that represent these groupings. - “Real-world words” – Have students become “word detectives” in their neighbourhood. Provide bonus points for students who hear or see key vocabulary words outside of school. The student needs to write down the word, or take a picture of it, write down what it means and where they heard it or saw it. - Examples and non-examples – Using words that the students are familiar with, they provide examples and non-examples. This can be done with visual or kinesthetic demonstrations as well as verbal descriptions. They can work with partners and explain why something is a good example of a word or not. They are learning the important skill of comparing and contrasting and defending their ideas in writing. - Fill in the blanks – Try using sentences with the key word missing before the students are expected to construct sentences on their own. Be sure to point out how to use context clues to help them. Share with them a word bank of the target words to choose from to help them succeed. Another variation is to create sentence frames with blanks to generate new words. (Example: “Have a ________________ day.” to generate multiple synonyms for the word “nice”.) Provide a variety of activities to practise new vocabulary Research has shown that learning is more effective when students give input into the vocabulary they need to learn (Echevarria, Vogt & Short, 2000). To give students plenty of practice with words, I recommend providing two word walls. On one wall, I write everyday words that students need to learn and practise. These words are removed when students no longer need them. On the second wall, I write content-specific vocabulary. This wall is changed to make room for new units of study. I then ask students to post unfamiliar words from the text. I also have students make a personal word bank using an “alphabox” template which they keep in their binders so that they have their vocabulary handy when they do homework. New vocabulary should be reviewed every day. Students can work together to write a simple sentence for each word or complete a cloze activity. They can also draw pictures to illustrate vocabulary, make flashcards or compile their own dictionaries in a notebook. Some examples include: - “Quick Draw” – See how quickly the students can sketch out a symbolic image of the word on the board for the rest to guess. This can also be done with learning partners. Promote oral language development through flexible learning groups EAL/D learners need ample opportunities to interact and collaborate with their peers to speak English, and be provided with authentic reasons to use academic language. Working in small, flexible groups is especially beneficial because EAL/D learners expand the meanings of vocabulary words with their classmates and their applications. Some examples of these collaborative activities include: - Vo-back-ulary – Tape word cards onto the backs of your students, then have them mix and mingle to music, asking questions about their words to the other students until they guess the word. In turn, the other students provide clues to help the student guess the word on their back. This is an active way to review and reinforce word meanings (Bromley, 2002). - Word Headbands – Similar to Vo-back-ulary, but this time you place a headband made out of stapled sentence strips onto the student. They then mix and mingle, asking pertinent questions that will assist them in guessing what their “secret word” is. Conclusion English as an Additional Language or Dialect learners need robust vocabulary instruction integrated throughout their instructional day. It should not be an “add-on” lesson. By explicitly teaching multiple meaning words and content-related words utilising hands-on, minds-on techniques, your EAL/D learners will reap the rewards by developing greater comprehension and collaborative conversation skills. These techniques can be adapted in any text or learning area. The more words they know, the more they can understand and speak. The more they understand and speak, the more they will comprehend what they read and be able to write about what they have learned. There’s nothing to it, but to do it! If you are interested to learn more from Kathy Perez, her books The New Inclusion: Differentiated Strategies to Engage ALL Students, The Co-Teaching Book of Lists and 200+ Proven Strategies for Teaching Reading are all available from Hawker Brownlow Education right now. Kathy will also be presenting at the 2019 Hawker Brownlow Education Thinking & Learning Conference, so secure your spot today! References August, D. & Shanahan, T. (Eds.). (2006). Executive summary. In Developing literacy in second-language learners: Report of the National Literacy Panel on Language-Minority Children and Youth. Mahwah, NJ: Lawrence Erlbaum. Baumann, J. F., Kame’enui, E. J. & Ash, G. E. (2002). Research on vocabulary instruction: Voltaire redux. In J. Flood, D. Lapp, J. Squire, & J. Jensen, (Eds.), Handbook of research on teaching the English language arts (2nd ed.). Hillsdale, NJ: Erlbaum Beck, I. L., Kucan, L. & McKeown, M. G. (2002). Robust vocabulary instruction: Bringing words to life. New York, NY: Guilford Press. Blachowicz, C., & Fisher, P. J. (2014). Teaching vocabulary in all classrooms. Pearson Higher Ed. Bromley, K. (2002). Stretching students’ vocabulary. New York, NY: Scholastic, Inc. Echevarria, J., Vogt, M. & Short, D. (2000). Making content comprehensible for English language learners: The SIOP Model. Boston: Allyn & Bacon. Jensen, E. (2005)Teaching with the brain in mind, 2nd edition. Alexandria, VA: ASCD, Association of Supervision and Curriculum Development. Klare, G. R. (1984). Readability. In P. D. Pearson (Ed.), Handbook of reading research (681-744). New York, NY: Longman. Miller, G. A. & Gildea, P. M. (1987). Sf How Children Learn Words. Scientific American. O’Brien, L. M. & Leighton, C. M. (2015). Use of increasingly complex text to advance EL’s knowledge and academic language. Literacy Research: Theory, Method and Practice, 64, 169-192. Perez, K. (2017) 200+ Proven Strategies for Teaching Reading. Melbourne, Victoria: Hawker Brownlow Education.	http://blog.hbe.com.au/2018/09/27/the-wonder-of-words-successful-vocabulary-strategies-for-english-learners/
The library has many reference books like encyclopedias, dictionaries and atlases that are useful for US Immigration research. You can search for reference books by keyword or subject in the [http://apps.appl.cuny.edu:83/F?func=find-b-0&local_base=nycity library catalog]. + + Print reference books are located on the shelves behind the Reference Desk on the 4th floor of the library. Print reference books can only be used in the library. + + Many of our reference books are available electronically (ebooks) -- read them by clicking through the links in the library catalog. For off-campus access to ebooks, login with library number on the front of your ID. For more information or to report a problem, see [http://library.citytech.cuny.edu/instruction/how/offCampus.php Off-campus Access] on the Library website. + + Here are a few popular reference books for US Immigration: + + * ''American immigrant cultures: builders of a nation''. + CALL NUMBER: Reference - E 184 .A1 A63448 1997 + + * ''The Asian American encyclopedia''. + CALL NUMBER: Reference - E184.O6 A827 1995 + + * ''Encyclopedia Latina: history, culture, and society in the United States''. + CALL NUMBER: Reference - E184 .S75 E587 2005 + + * ''Encyclopedia of African-American culture and history: the Black experience in the Americas''. + CALL NUMBER: Reference - E185 .E54 2006 + + * ''Encyclopedia of African American history, 1619-1895: from the colonial period to the age of Frederick Douglass''. + CALL NUMBER: Reference - E185 .E545 20 + + * ''Encyclopedia of American cultural & intellectual history''. + CALL NUMBER: Reference - E 169.1 .E624 2001 + + * ''Encyclopedia of American immigration''. + CALL NUMBER: Reference - JV 6465 .E53 2000 + + * ''Encyclopedia of American social history''. + CALL NUMBER: Reference - HN57 .E58 1993 + + * ''Encyclopedia of American urban history''. + CALL NUMBER: Reference - HT123 .E49 2007 + + * ''Encyclopedia of the United States in the twentieth century''. + CALL NUMBER: Reference - E740.7 .E53 1996 + + * ''Encyclopedia of women in American history''. + CALL NUMBER: Reference - HQ1410 .E53 2002 + + * ''Gale encyclopedia of multicultural America. Primary documents''. + CALL NUMBER: Reference - E 184 .A1 G15 1999 + + * ''Immigration in America today: an encyclopedia''. + CALL NUMBER: Reference - JV6465 .I4754 2006 + + * ''The Italian American experience: an encyclopedia''. + CALL NUMBER: Reference - E184.I8 I673 2000 + + * ''The Oxford encyclopedia of Latinos and Latinas in the United States''. * To find books at other CUNY libraries, select All CUNY Libraries. To request a book from another CUNY library, click Request a Copy. + + '''Searching with Subject Headings''' + + Using subject headings to search the library catalog can help you quickly find useful books and multimedia. Once you have found a book on your research topic, click on the Subjects links to find more books on that topic. + + You can also search by subject from the Find Books tab on the [http://library.citytech.cuny.edu/ Library website]. Here's a sample of relevant subject headings for US Immigration research: + + * EXAMPLE + + + Here is a list of some resources at the library: + + '''Histories''' + + * ''A community of many worlds: Arab Americans in New York City''. + CALL NUMBER: Stacks - F 128.9.A65 C66 2002 + + * ''Double passage: the lives of Caribbean migrants abroad and back home''. + CALL NUMBER: Stacks - JV7331 D67 1992 + + * ''Immigrant women in the land of dollars: life and culture on the Lower East Side, 1890-1925''. + CALL NUMBER: Stacks - F128.9.I8 E83 1985 + + * ''The Italians of New York''. + CALL NUMBER: Stacks - F128.9.I8 F4 1969 + + * ''In a new land: a comparative view of immigration''. + CALL NUMBER: Stacks - JV6465 .F66 2005 + + * ''Jamaican migrants: a comparative analysis of the New York and London experience''. + CALL NUMBER: Stacks - F1401 .N4 no.36 + + * ''Memories of Migration: Gender, Ethnicity, and Work in the Lives of Jewish and Italian Women in New York, 1870-1924''. + CUNY Libraries (CLICS) + + * ''The uprooted''. + CALL NUMBER: Stacks - E 184 .A1 H27 2001 + + * ''The health and well-being of Caribbean immigrants in the United States''. Reference Resources The library has many reference books like encyclopedias, dictionaries and atlases that are useful for US Immigration research. You can search for reference books by keyword or subject in the library catalog. Print reference books are located on the shelves behind the Reference Desk on the 4th floor of the library. Print reference books can only be used in the library. Many of our reference books are available electronically (ebooks) -- read them by clicking through the links in the library catalog. For off-campus access to ebooks, login with library number on the front of your ID. For more information or to report a problem, see Off-campus Access on the Library website. Finding Books and More in the Library To find books at other CUNY libraries, select All CUNY Libraries. To request a book from another CUNY library, click Request a Copy. Searching with Subject Headings Using subject headings to search the library catalog can help you quickly find useful books and multimedia. Once you have found a book on your research topic, click on the Subjects links to find more books on that topic. You can also search by subject from the Find Books tab on the Library website. Here's a sample of relevant subject headings for US Immigration research: CALL NUMBER: Stacks - E184 .C27 H43 2004 In praise of new travelers: reading Caribbean migrant women writers. CALL NUMBER: Stacks - PR9205.4 .H68 2001 Asian and Hispanic immigrant women in the work force: implications of the United States Immigration policies since 1965. CALL NUMBER: Stacks - HD 6095 .H75 1997 The immigrant experience in New York City: a resource guide. CALL NUMBER: Stacks - F128.9 .A1 I43 2007 The golden door: Italian and Jewish immigrant mobility in New York City, 1880-1915. CALL NUMBER: Stacks F128.9.I8 K47 Suburban Sahibs: three immigrant families and their passage from India to America. CALL NUMBER: Stacks - F142 .M6 K35 2003 (East Indian Americans) The Arab Americans. CALL NUMBER: Stacks - E184 .A65 K39 2006 Becoming American, being Indian: an immigrant community in New York City.
Let's see the mechanism behind TRPO. If you feel that this part is hard to understand, you can skip it and go directly to how to run TRPO to solve MuJoCo control tasks. Consider an infinite-horizon discounted Markov decision process denoted by , where is a finite set of states, is a finite set of actions, is the transition probability ... Theory behind TRPO Get Python Reinforcement Learning Projects now with O’Reilly online learning. O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.	https://www.oreilly.com/library/view/python-reinforcement-learning/9781788991612/54c503aa-bc4d-4a45-96e1-5c2b25e4f2e8.xhtml
I love the sandbox style of SimCity game play so much. I think it stems from the same reason the developers implemented the tilt shift effect. They said they wanted to make it as if you were controlling your own little model city. When I was a kid, I had a model train set, and literally had my own little model city (er, town). I had my own little houses, trees, and grass you would sprinkle on the mountainside. (Did you know they even sell tiny plastic beads you melt down and pour on your town to create streams, lakes, and rivers? It is amazing how realistic it can look. ) That one thing drew me into the SimCity franchise. I was a little over 10 when SimCity 4 came out. It felt like I was creating the ultimate simulated train set. Yet it seems so odd to me that terraforming, and the ability to create your own region (a big part of that create your own town process) has been remove out of the game. I really thought that aspect of the simulation would be included upon, with seasons, different climates, streams, etc. Furthermore, regarding the management of resources from one city to the other, being able to experiment within a region considering where one would place mass transit seemed like something you would not want to have predetermined. It takes the freedom and creativity out of the sandbox aspect of the game. I do not just want to create a city; I want to create the backdrop from where it rests. I want to mold the mountainside, and carve the coastline, leaving my own original fingerprint on the model world I create. Finally, concerning city size: I understand cities are a little over 1×1 mile in size because of computing power, but if my computer can handle a larger area of computation, may I have the option to choose a larger city size? Beyond that, many small towns are larger than 4 square kilometers, yet have less than 10,000 inhabitants, and would be easy to simulate. Take Vashon Island for example. I used to live there, and it rests in the Puget Sound just across the bay from Seattle, WA. It’s the size of long island, yet houses only a few thousand inhabitants. I feel like having long winding roads in a small country town would be impossible with the current size requirements, and really, hope the team will reconsider giving us more options concerning terraforming (in SimCity 2013), as well as city size.	http://worldsims.org/dear-maxis-i-miss-simcity-terraforming-by-whyhellothere427/2869/
Objections raised to pro-life tent on Cass courthouse lawn WALKER - Mary Ackerman and Betty Hackett objected Tuesday to Cass County commissioners giving permission for the 40 Days Pro-Life Campaign to have a tent for 40 days on the courthouse lawn. WALKER - Mary Ackerman and Betty Hackett objected Tuesday to Cass County commissioners giving permission for the 40 Days Pro-Life Campaign to have a tent for 40 days on the courthouse lawn. The 40 Days Pro-Life Campaign area supporters have pitched a small tent in a corner of the courthouse lawn for 40 days each fall since the board approved their use of the lawn in 2008. The pro-life group is subject to restrictions county staff set, include restricting their presence to the tent and not interfering with any person's ability to come and go from the courthouse without harassment. There are no signs on or around the tent. Participants generally stay inside the tent. They indicated when they first asked board permission that they would be conducting a prayer vigil inside the tent. Ackerman, of Hackensack, asked first in a letter to the board to re-open the board's policy of ongoing permission. She objected to the 40-day length of the vigil. ADVERTISEMENT She indicated she sees this conflicting with separation of church and state. Because there have not been any groups expressing an opposing view on the courthouse lawn, Ackerman indicated she sees this as a case of commissioners promoting one viewpoint. She also wrote in her letter she does not believe the commissioners want a counter demonstration. She asked that the board inform the 40 Days Pro-Life group that this would be the last year they could use the courthouse lawn. Ackerman said at Tuesday's meeting she thinks prayer is counter to government functions. "Not everyone prays," She said. She called the precedent of allowing the tent "a slippery slope." Hackett said the board should get out of reviewing requests to use the lawn on a case by case basis. She also said the board should set time limits for people who want to voice their views, calling 40 days "an encampment" rather than a demonstration. Hackett said she thinks the fact that the tent has no sign to indicate its purpose as "insidious." "You should not have approved it," she concluded. Ackerman and Hackett described themselves as supporters of free speech and the First Amendment. ADVERTISEMENT Commissioner Neal Gaalswyk said the board does not want to get into limiting free speech. He said the board needs to either not allow any use of the courthouse lawn or approve all viewpoints, which he said, was the board's original intent when it first permitted the tent. He said Minnesota Supreme Court has restricted governments from preventing the exercise of religion even more than the federal courts. Gaalswyk said he realizes the tent does not reflect the views of everyone in the county. The only other recent use the county has been requested to permit on the lawn that was cited Tuesday is vendor booths during the city of Walker's Ethnic Fest celebration each year. Commissioner Bob Kangas said the county has had no complaints about the 40 Days Pro-Life Campaign harassing anyone or causing problems. In response to Ackerman's and Hackett's presentations, Gaalswyk said, while you state you support free speech, the content of your talk was more on how we can restrict other people's views. "I would be concerned about the chilling effect restrictions of time, content and viewpoints would have on free speech," Gaalswyk said. "Until there is an unlawful disruption, we should allow free speech," he added. County Attorney Christopher Strandlie noted demonstrations cannot block government activities and that the board cannot prevent people who peacefully assemble. He noted, however, there could be challenges on whether letting people use the lawn is content neutral or is in government interest. ADVERTISEMENT The board declined to change any policy Tuesday from that of allowing anyone to express their views on the courthouse lawn as long as they do not cause a disturbance or interfere with people coming and going from the building to do regular government business.	https://www.brainerddispatch.com/news/objections-raised-to-pro-life-tent-on-cass-courthouse-lawn
Puns & Anagrams #2 - PUZ \| PDF \| PDF (Grayscale) \| Solution It's been a while since I've posted a Puns & Anagrams puzzle, so happy to return to this format for the December puzzle. As I've written before, P&As are a variety format derived from cryptics, but they stand apart from cryptics in several key ways. To recap the major differences: 1) Fully interlocking grid. Unlike standard block cryptics, where roughly 50% of the squares are checked by crossing entries, P&A grids qualify as standard themeless crossword grids, with a max of 72 entries in the grid. Every square is a part of an across and down entry. This affords solvers many more opportunities to solve an entry than a cryptic does, which helps explain some of the looseness of P&A clues. 2) Anagram clues (which comprise about half of the clues in a P&A) do not include anagram indicators, which are required for cryptics. In addition, homophones of letters (or groups of letters) included in the anagram are fair game. So, the word "sea" could signal a C to be included in the anagram; the word "seize" could signal multiple Cs to be included in the anagram; and "seedy" could signal the letters CD to be included in the anagram. 3) While anagram clues will include a straight-forward hint to the entry, non-anagram clues do not require a straight-forward hint. Non-anagram clues will include cryptic tropes such as hidden words, containers, and homophones, as well as more P&A-typical conventions as visual rebuses, puns, and fill-in-the-blanks. For this P&A, I made sure that none of the clues would work as a cryptic clue. As such this might play a little harder than a New York Times P&A, and it might be a little less wacky than a Times P&A can tend to be. I hope solvers enjoy! I realize that P&As are somewhat of a divisive format, but I find them to be a fun challenge to write and I want them to stand apart from cryptics. As always, any and all feedback is welcomed. Happy holidays! I'm certainly ready to turn the page on 2020. I hope the puzzles were a welcome respite from this most challenging year. A reminder that you can always purchase monthly or yearly bundles of past subscription puzzles, and Rows Garden and Freestyle subscriptions are always open. Here's hoping for a better year in 2021!	https://www.ariespuzzles.com/2020/12/puns-anagrams-2.html
ore 11:53 PM? 1:19 PM What is 690 minutes before 2:17 AM? 2:47 PM How many minutes are there between 4:09 PM and 12:59 AM? 530 What is 582 minutes before 3:30 AM? 5:48 PM How many minutes are there between 5:34 PM and 4:20 AM? 646 How many minutes are there between 4:38 PM and 5:49 PM? 71 What is 439 minutes before 9:43 PM? 2:24 PM How many minutes are there between 12:17 AM and 9:05 AM? 528 How many minutes are there between 1:41 AM and 6:54 AM? 313 How many minutes are there between 12:36 PM and 7:20 PM? 404 What is 341 minutes after 5:45 PM? 11:26 PM What is 88 minutes before 9:09 AM? 7:41 AM What is 367 minutes before 10:47 AM? 4:40 AM How many minutes are there between 8:05 PM and 9:33 PM? 88 How many minutes are there between 8:48 PM and 11:43 PM? 175 How many minutes are there between 6:53 AM and 11:07 AM? 254 What is 678 minutes before 12:44 PM? 1:26 AM What is 702 minutes before 3:25 PM? 3:43 AM What is 639 minutes after 7:02 AM? 5:41 PM What is 303 minutes after 12:10 PM? 5:13 PM How many minutes are there between 2:38 AM and 5:53 AM? 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682 What is 303 minutes after 12:58 AM? 6:01 AM What is 643 minutes after 4:20 AM? 3:03 PM What is 320 minutes after 5:14 PM? 10:34 PM What is 97 minutes before 7:58 AM? 6:21 AM What is 127 minutes before 4:20 PM? 2:13 PM What is 634 minutes before 11:20 PM? 12:46 PM What is 573 minutes after 1:03 PM? 10:36 PM What is 647 minutes after 4:29 PM? 3:16 AM What is 546 minutes after 9:05 AM? 6:11 PM What is 310 minutes before 2:08 AM? 8:58 PM How many minutes are there between 6:24 AM and 11:47 AM? 323 What is 454 minutes after 1:47 PM? 9:21 PM What is 592 minutes before 1:17 AM? 3:25 PM How many minutes are there between 6:44 AM and 6:01 PM? 677 How many minutes are there between 7:30 AM and 8:59 AM? 89 How many minutes are there between 11:01 AM and 7:53 PM? 532 What is 195 minutes after 9:12 PM? 12:27 AM What is 576 minutes after 1:05 PM? 10:41 PM How many minutes are there between 5:16 AM and 9:16 AM? 240 How many minutes are there between 11:11 PM and 10:28 AM? 677 What is 69 minutes before 6:30 PM? 5:21 PM What is 418 minutes before 5:04 AM? 10:06 PM What is 50 minutes before 7:06 AM? 6:16 AM What is 204 minutes before 3:04 PM? 11:40 AM How many minutes are there between 12:27 PM and 4:41 PM? 254 How many minutes are there between 4:02 PM and 6:42 PM? 160 How many minutes are there between 5:40 AM and 9:51 AM? 251 How many minutes are there between 8:24 AM and 3:24 PM? 420 What is 82 minutes after 5:06 AM? 6:28 AM How many minutes are there between 6:55 PM and 2:42 AM? 467 What is 404 minutes before 5:52 PM? 11:08 AM How many minutes are there between 6:03 PM and 6:52 PM? 49 What is 60 minutes before 7:16 PM? 6:16 PM How many minutes are there between 8:02 PM and 2:42 AM? 400 What is 688 minutes before 10:50 PM? 11:22 AM What is 359 minutes after 2:07 PM? 8:06 PM What is 101 minutes before 3:07 AM? 1:26 AM How many minutes are there between 9:10 AM and 11:29 AM? 139 How many minutes are there between 4:28 AM and 9:48 AM? 320 What is 607 minutes before 1:18 AM? 3:11 PM How many minutes are there between 3:27 PM and 8:59 PM? 332 What is 158 minutes after 1:22 PM? 4:00 PM What is 596 minutes before 2:46 AM? 4:50 PM How many minutes are there between 8:20 PM and 2:15 AM? 355 How many minutes are there between 2:10 PM and 1:56 AM? 706 How many minutes are there between 7:02 AM and 12:55 PM? 353 How many minutes are there between 12:08 PM and 10:38 PM? 630 What is 607 minutes before 1:27 AM? 3:20 PM How many minutes are there between 11:43 AM and 6:31 PM? 408 What is 572 minutes before 12:40 AM? 3:08 PM What is 496 minutes before 4:37 PM? 8:21 AM What is 634 minutes before 10:14 PM? 11:40 AM How many minutes are there between 10:42 PM and 4:23 AM? 341 How many minutes are there between 2:36 PM and 7:06 PM? 270 How many minutes are there between 9:37 PM and 9:10 AM? 693 What is 194 minutes before 5:28 AM? 2:14 AM What is 669 minutes before 9:51 AM? 10:42 PM How many minutes are there between 6:27 PM and 11:42 PM? 315 How m
The spectator freely selects a card from a deck of cards and has it protrude from the center of the face down deck. The magician now squares up the deck and places it into the CRYSTAL CARD CASE. The deck of cards is imprisoned in the card case as the lid is closed. Suddenly the selected card seems to come to life, crawls out of the deck, pushes the lid open, revolves and rises completely out of the case! The card may then be handed out for inspection and the spectator may keep it as a momento. A moderate amount of practice is required, but well worth the effort. Complete instructions for different methods of performance are provided. USED, BUT GOOD CONDITION.	http://www.newplanetmagic.com/catalog/product_info.php?products_id=1534
It’s another cold blast for Saskatchewan as much of the province remains under an extreme cold warning. In Regina, wind chill values at -48 prompted both Regina Public Schools and Regina Catholic School divisions to cancel bus service. Schools, however, still remained opened. “I was actually late for work this morning,” Goodwin said. Another parent, Amanda Wood said she had to make alternate plans to get her daughter to and from school.” “I had to change, instead of walking. I had to change and get a ride cause of how cold it was,” she said. With the wind chill values, Regina felt like -48 on Wednesday. When temperatures dip as low as they did on Wednesday, Regina Public School’s Supervisor of Communications Terry Lazarou said it’s their policy to cancel service as it’s a matter of safety. “Not all students dress as well for the cold as they should. We don’t want our students waiting outside for a bus that might be late for whatever reason,” Lazarou said. READ MORE: Extreme cold warning issued for Regina; will feel like -40 with wind Lazarou said school buses sit idle when wind chill values drop below -45. The cold temperatures also put the brakes on outdoor recess and lunch as well. As per the school division’s policy, anytime wind chill values are below -25, students are advised to stay indoors. “The principals of the schools have the jurisdiction to decide whether it’s indoors or outdoor recess or lunch… Over the past few days when it’s been so cold, recess has been indoors,” Lazarou said. It’s another safety precaution for students, as frostbite can set in within minutes. “When you have skin that is exposed when you’re heading outside, and the windchill values are colder than -48 you can get frostbite within two to five minutes,” Lizée said. Classes at Payepot School on Piapot First Nation were closed Wednesday. Prairie School Division and South School Division also cancelled bus service Wednesday.	https://globalnews.ca/news/3175891/regina-parents-deal-with-school-bus-cancellations-due-to-cold-weather/
Nowadays, skin disease is a major problem among peoples worldwide. Different machine learning techniques are applied to predict the various classes of skin disease. In this research paper, we have applied six different machine learning algorithm to categorize different classes of skin disease using three ensemble techniques and then a feature selection method to compare the results obtained from different machine learning techniques. In the proposed study, we present a new method, which applies six different data mining classification techniques and then developed an ensemble approach using bagging, AdaBoost, and gradient boosting classifiers techniques to predict the different classes of skin disease. Further, the feature importance method is used to select important 15 features which play a major role in prediction. A subset of the original dataset is obtained after selecting only 15 features to compare the results of used six machine learning techniques and ensemble approach as on the whole dataset. The ensemble method used on skin disease dataset is compared with the new subset of the original dataset obtained from feature selection method. The outcome shows that the dermatological prediction accuracy of the test dataset is increased compared with an individual classifier and a better accuracy is obtained as compared with subset obtained from feature selection method. The ensemble method and feature selection used on dermatology datasets give better performance as compared with individual classifier algorithms. Ensemble method gives more accurate and effective skin disease prediction.	https://www.cheric.org/research/tech/periodicals/view.php?seq=1797081
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Though the presidential race is always the primary focus of every general election, it is only one of at least two dozen items that appear on the big ballot every four years. This is the time of the election cycle when everybody from elected officials to celebrities are urging voters to complete their civic duty and cast their ballots. In a year with fake drop-off boxes and efforts to suppress the vote are rampant, civic responsibility has never been more consequential. Those who have received their ballots in the mail (or have already voted early) know that the California ballot is extensive, and each item that needs a vote is just as crucial as the race to the White House. A majority “yes” vote approves these propositions while a majority “no” rejects them. Here’s a quick guide to the 11 ballot measures for California. The ones you’ve seen on TV Proposition 14: Stem Cell Research Institute Bond Initiative As expected from the title, this ballot measure, if approved, would send $5.5 billion in general obligation bonds for the state’s stem cell research institute, the California Institute for Regenerative Medicine (CIRM). The increased funds to the CIRM — which would come from investors who would be reimbursed over the next 30 years through taxpayers — would expand research capacity and allocate $1.5 billion for Alzheimer’s, Parkinson’s, stroke, epilepsy and other neurological and nervous system illnesses. The CIRM was established in 2004 as the first-of-its-kind state-sanctioned stem cell agency and was issued $3 billion in bonds. By October 2019, the CIRM had $132 million remaining and earlier in July 2019, the CIRM had seized applications for new projects because funds were drying up. Supporters — including the CIRM, Gov. Gavin Newsom and the University of California Board of Regents (UC labs and hospitals are a primary beneficiary of the CIRM) — maintain that stem cell research has led to increased understanding of diseases that affect millions of families, biotech jobs and careers and clinical trials over the last 16 years. But opponents of the bill — including the Los Angeles Times and San Francisco Chronicle editorial boards and Jeff Sheehy, board member of the CIRM — argued that the lack of advancement in stem cell research to find cures doesn’t warrant an increase in funding. California originally established the CIRM as a response to then-President George W. Bush’s ban on federal funding for stem cell research, and opponents also argue a state-funded institute is no longer necessary. As previously reported in the Asian Journal, the systems in which individuals donate stem cells is largely homogenous with ethnic groups — like Filipinos — vastly underrepresented, making it difficult for patients of color to successfully find matches needed for potentially life-saving transplants. Prop 16: Restoring affirmative action Prop 16 would allow universities, government offices and other public sectors to factor in a prospect’s race, ethnicity or gender in admissions, spending and hiring. In 1996, California voters approved a ballot proposition that prohibits affirmative action and put in place “race-neutral” policies. If passed, Prop 16 would reverse Prop 209. Prop 16 was inspired by the recent civil rights discourse following the killings of unarmed Black Americans, which catalyzed a national overview of whether or not systemic racism does exist within bureaucracies. Supporters of Prop 16 — which includes California Gov. Gavin Newsom and the Cal State University (CSU) and University of California (UC) systems argue that structural racism exists and it is propagated by color-blind approaches and philosophies. Examples of how Prop 16 may work, according to a recent virtual roundtable of Asian American business owners and experts: state offices would be allowed to establish goals for how many government contracts they grant to people of color-owned and women-owned businesses. In schools, principals of schools with a majority Black student body but majority white teaching pool may seek out Black teachers and teachers of color to more accurately represent the students they teach. Despite what opposers have argued, affirmative action would not induct quotas in university admissions since the U.S. Supreme Court banned those in 1978. But the opposition — which includes the California Republican Party and Chinese American Civic Action Alliance — still argues that allowing institutions to make decisions based on demographic identifiers is discrimination in itself. Prop 22: Protect-App-Based Drivers and Services Act One of the most advertised propositions to appear on this year’s ballot, Prop 22 would exclude gig companies — particularly ride-share and delivery companies like Uber, Lyft, DoorDash and Instacart — from a new state law that requires these companies to treat their workers as employees. The massive advertising comes from the combined $185 million spent by these companies to support Prop 22. These San Francisco-based companies have been fighting to keep their drivers and couriers as independent contractors, arguing it provides workers with flexible schedules and customers rides at low prices. In January, the state passed a law that required former contract workers in several industries to be categorized as employees which granted them the right to overtime pay, health care benefits, paid sick leave, unemployment insurance and worker’s compensation. Currently, drivers and couriers who work for gig companies are treated like independent contractors. If this measure passes, these companies would keep workers classified as contractors and grant them a tapered set of benefits, including a salary of at least 120% of minimum wage, health care subsidies and accident insurance. While proponents argue that such jobs were never meant to be full time positions, opponents argue that the measure would impede on job security during a time when unemployment is rampant. Opposers argue that the COVID-19 pandemic has upended the job market and further proved the necessity of the state law that would provide workers with paid sick leave and unemployment insurance. The fiscal impact of Prop 22 would be “minor increases in state income taxes paid by rideshare and delivery company drivers and investors.” Prop 23: Dialysis Clinic Requirements Initiative This ballot measure would “require chronic dialysis clinics to: have an on-site physician while patients are being treated; report data on dialysis-related infections; obtain consent from the state health department before closing a clinic and not discriminate against patients based on the source of payment.” In other words, this proposal promises a safeguard for clinics at risk of being closed, an increase in transparency between clinics and state health departments and networks and to be more inclusive regarding the payment of a patient’s treatment. The coronavirus pandemic has already made it difficult to access health care and specialized treatment, both of which are deemed essential services that have remained open throughout the various phases of safer-at-home policy. About 80,000 Californians receive dialysis treatment three days a week in 4-hour sessions, and missing a treatment could increase a patient’s risk of death by 30%, according to the National Kidney Foundation. Prop 23 supporters — which includes the California Democratic Party and California Labor Federation — argue that the measure ensures that clinics are inclusive to all budgets and protected from closures the same way hospitals are currently. (State approval is needed to close or reduce services of a hospital, and Prop 23 supporters say this measure will hold dialysis clinics “to the same standard.”) Opposers of Prop 23 — which includes the California Medical Association, California Hospital Association and the Renal Physicians Association — argue that the ballot measure is a special interest plan that does not require the on-site physician administrator “to have specialty training in kidney care of dialysis,” the No on Prop 23 campaign said. “Every dialysis patient is under the care of a physician kidney specialist, and dialysis treatments are administered by specially-trained nurses and technicians. It makes no sense to require physician administrators on site full-time,” said Dr. Jeffrey Perlmutter, president of the Renal Physicians Association. According to the ballot initiative’s text, the fiscal impact would be an increase in “state and local government costs likely in the low tens of millions of dollars annually.” The ones that would expand votership Prop 17: Voting Rights Restoration for Persons on Parole Amendment Allowing former convicts the right to vote has been among the most contentious issues in contemporary electoral discourse. Prop 17 would allow Californians on parole to vote. Supporters like Gov. Gavin Newsom, the American Civil Liberties Union (ACLU) and the League of Women Voters in California argue that civic engagement would reduce recidivism and give former convicts an opportunity to de-stigmatize their past. “Parole by definition is not punishment — it’s to help reintegrate people back into the mainstream,” Assemblymember Kevin McCarty (D-Sacramento) told CalMatters, adding that individuals who finish their sentences should be able to contribute to a democracy. The opposition, however, prefers a longer period of rehabilitation for parolees before they are granted the right to vote. Violent offenders must prove they’ve effectively evolved beyond their criminal past. Republican State Sen. Jim Nielsen of Yolo County said that the victims of these crimes “cannot so blithely put the crimes behind them.” The fiscal impact of Prop 17 would be an increase in county costs — estimated in the hundreds of thousands of dollars across California — for voter registration and ballot materials. There would also likely be a one-time cost (similarly in the hundreds of thousands) to update voter registration cards and the electoral system. Prop 18: Primary Voting for 17-Year-Olds Amendment As stated in the title, Prop 18 would allow 17-year-olds who turn 18 “at the time of the general election to vote in primary and special elections.” It would also allow 17-year-olds who are eligible to vote to seek office as current law states that only registered voters are allowed to run for elected office. Supporters of this proposition say that this could be a solution to the historically low voter turnout among 18 to 24 year olds. This could be a way to increase interest and excitement for civic participation at a young age and cultivate a more engaged young adult electorate. Gov. Gavin Newsom, the ACLU and the California Association of Student Councils all support the initiative. “Young people whose birthdays fall between the primary and general election are currently at a disadvantage to those who are permitted to vote in the primaries,” the California Association of Student Councils wrote. “Without full exposure to the electoral process, they are unable to submit their most educated vote in the general election.” However, opponents like the Election Integrity Project California, an academic non-profit group dedicated to “electoral integrity,” argue that 17-year-olds are still minors and are biologically not fully developed. They argue that 17-year-olds still need guardian approval for other legal contracts and certain activities and voting should be no different. “They are almost all still living at home and under the strong influence of their parents,” the Election Integrity Project California wrote in their argument. “This is not conducive to independent thought and voting without undue pressure from their immediate superiors. Just like Prop 17, if passed, the fiscal impact of Prop 18 would include a one-time cost in the hundreds of thousands to update voter registration systems. It would also likely lead to an increased cost for counties of up to $1 million every two years, which is needed to send and process voting materials to eligible 17-year-olds, the ballot measure said. The ones regarding criminal justice and privacy Prop 20: Criminal Sentencing, Parole and DNA Collection Initiative For those who have committed certain property crimes and repeatedly violated parole, Prop 20 would tighten the eligibility criteria for early parole and release from prison. Specifically, prosecutors would be allowed categorized property crimes of more than $250, crimes that would include “serial shoplifting” and car theft, as felonies rather than misdemeanors. It would also impose increased penalties to former convicts who violate their terms of release three times, increasing the frequency of recidivism. Police would also be required to collect DNA samples from those convicted of certain misdemeanors like shoplifting, forgery and illegal drug possession that would be kept in a state database. Supporters of this measure argue that the state has been lax on criminal justice, particularly when California downgraded many property crimes from felonies to misdemeanors, which they say led to an increase of car thefts and shoplifting. The bipartisan support for Prop 20 includes Assemblymembers Jim Cooper (D-Sacramento) and Vince Fong (R-San Joaquin Valley) who argue the state went too far when it increased opportunities for “non-violent felons.” Gov. Gavin Newsom, the ACLU, the California Teachers Association and the Chief Probation Officers of California all oppose Prop 20, arguing that the stringent “lock ‘em up and throw away the key” approach didn’t cut crime but instead inflated the state prison’s budget. The penal system disproportionately harms the overrepresented Black and Latino community, which presents a civil rights slant to the issue, supporters say. The costs of Prop 20 would include increased state and local correctional, court and law enforcement expenses in the tens of millions of dollars annually to support increases in county jail populations and community supervision. Prop 24: Consumer Personal Information Law and Agency Initiative This bill, in short, would tighten privacy law in California. Specifically, the bill would create a new state agency that enforces privacy law, conducts investigations into potential privacy violators and oversees penalties to violators. This bill would also give consumers the right to tell businesses to limit their use of sensitive data in their systems (like geographic location, demographic identifiers, health, etc) and prohibit businesses from storing this data for long periods of time. The government would also impose fines of up to $7,500 to companies that violate children’s privacy rights. Supporters of the bill argue that this gives consumers more agency over their personal data by limiting the use of location tracking and other sensitive information. However, the opposition posits that data privacy law, especially as it pertains to technology, is still in its infancy and should not be changed so hastily. They argue that parts of Prop 24 would hurt consumers, specifically through stifling a rule that allows workers to know what information employers are collecting about them. With the new state agency and the increased operations, the fiscal impact of Prop 24 would be at least $10 million annually and increased state costs for increased court and Dept. of Justice responsibilities. Prop 25: Replace Cash Bail with Risk Assessments Referendum Among the most talked-about issues during the primary election season, the cash bail system has been criticized for favoring criminal suspects who can afford to make bail and punishing those who cannot. After a suspect is arrested, they are held in jail. Sometimes, a cash bail is imposed upon them, and if they’re able to afford it, they are released from jail awaiting trial. But this system puts at a disadvantage poorer Californians who often either have to pay bail bond companies or sit in jail for the duration until their trial. Essentially, Prop 25 would uphold a 2018 law signed by then-Gov. Jerry Brown that would have replaced cash bail with a “risk-based algorithm” — or, a method to gauge a person’s risk for not appearing at trial. In essence, the higher the risk, the less likely they’ll be released from jail. Almost immediately, bail bonds companies challenged the law. Now, it’s up to voters to decide Supporters of Prop 25 — Gov. Gavin Newsom, the California Medical Association and Service Employees International Union — argue that the cash bail system is classist, unfair and, ultimately, racist. If two people charged with the same crime are put in jail, one who has generation wealth and one who is lower-income, the wealthier one who can afford to make bail will be able to go home that same night. The lower income one would likely not, even though they were charged with the same crime. The opposition to Prop 25 is varied. The California Peace Officers’ Association and the California Bail Agents Association both argue that the proposed alternative to cash bail is more costly and no better than the current system.They also warn that if more people are freed before trial, there could be an increase of crime. Civil rights organizations like the California State Conference of the NAACP and Human Rights Watch argue that the risk-based algorithm is flawed and the factors associated with this method could still put people of color at a disadvantage. The fiscal impact is estimated to be an increase of costs in the mid hundreds of millions of dollars annually for a new release-from-jail-prior-to-trial process. Likewise, jail costs would potentially decrease by tens of millions of dollars every year. The ones concerning housing and property taxes Prop 19: the Property Tax Transfers, Exemptions and Revenue for Wildfire Agencies and Counties Amendment Under Prop 19, Californians aged 55 or older would be granted a property tax break when purchasing a new home. In California, the cost of living is astronomical for new homeowners because property taxes are calculated based on the value of the home when it was bought, not on its current market value. So when Californians buy a new home, their property taxes skyrocket. That’s why Baby Boomers who bought homes in the 1970s to the 1990s pay lower property taxes than younger families who bought homes of the same size and quality in the last 10 years. Prop 19 would also do away with the inheritance tax break to allocate more funds to local and state fire departments and schools, the initiative says. According to the measure’s fiscal impact statement, local governments, schools and fire protection agencies could each gain tens of millions of dollars of property tax revenue each year. Prop 19 would allow the older homeowners to buy a new house and still pay relatively low property taxes. In addition to benefiting older homeowners, supporters say this actually benefits new homeowners because it provides an incentive for seniors to downsize, vacating an older home to younger owners. Supporters of the bill include Gov. Gavin Newsom, California Professional Firefighters and the California Association of Realtors, while opposers include Howard Jarvis Taxpayers Association. Prop 21: Local Rent Control Initiative Housing (or, difficult accessibility thereof) is one of the longest standing pressing issues plaguing California. The pandemic has upended this issue, leading to many families being evicted and losing their homes. Prop 21 is an effort to alleviate the many renters woes of the Golden State. This measure would allow cities to pass rent control measures on nearly all rental units as long as the properties are more than 15 years old. Last year, the state passed a law that capped rent increases at 8%, but that didn’t get rid of an older state law that prohibits cities from enacting their own, tighter rent control laws for rental units that were first occupied in the last 25 years. The law passed last year also didn’t prevent landlords from raising the rent for new tenants to keep up with the market. The fiscal impact would likely be a reduction in state and local revenues in the high tens of millions of dollars annually. This, according to the Legislative Analyst’s office, would be because landlords would pay lower property taxes. Supporters of this measure include the California Democratic Party and U.S. Sen. Bernie Sanders (who supports strict rent control laws) who say that cities should be able to enact their own limits to rent increases as a way to reduce homelessness and gentrification, particularly in California’s metro areas. But the opposition — including Gov. Gavin Newsom and California Apartment Association — argues that Prop 21 takes away an incentive for builders to construct more housing at a time when more housing is needed.	https://www.asianjournal.com/usa/california/a-quick-rundown-of-the-2020-california-ballot-measures/
--- abstract: 'A nonlocal vector calculus was introduced in [@dglz-nlc] that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A generalization is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green’s identities. The nonlocal vector calculus introduced in [@dglz-nlc] is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.' author: - \| Bacim Alali, Kuo Liu, and Max Gunzburger\ [^1] nocite: '[@]' title: A Generalized Nonlocal Calculus with Application to the Peridynamics Model for Solid Mechanics --- Keywords:* General nonlocal calculus, peridynamics, nonlocal diffusion, integral equations. Introduction ============ In recent years, nonlocal continuum models have been developed for several large-scale phenomena. Examples include the peridynamics formulation for solid mechanics [@Silling2000; @Silling2007] and nonlocal diffusion [@dglz-nld]. These nonlocal continuum models are described through integral equations in contrast to their classical local continuum counterparts which are given by partial differential equations. A key connection between the peridynamics model and classical elasticity and between the nonlocal diffusion model and classical diffusion is that these nonlocal models have been shown to converge, under certain conditions, to their local counterparts in the limit of vanishing nonlocality [@emmrich2007well; @dglz-ps; @dglz-nld]. Another connection between these local and nonlocal models is given through a [nonlocal vector calculus]{} that is introduced and developed in [@dglz-nlc]. The nonlocal vector calculus introduces integral operators that mimic the roles of the divergence, gradient, and other vector calculus operators. Specifically, the nonlocal divergence of a vector-valued function ${\boldsymbol\nu}({{\bf x}},{{\bf y}})$ is defined as [@dglz-nlc] $$\label{sdiv0} ({{\cal D}}_{{\boldsymbol\alpha}}{\boldsymbol\nu})({{\bf x}}) = \int\big({\boldsymbol\nu}({{\bf x}},{{\bf y}}) + {\boldsymbol\nu}({{\bf y}},{{\bf x}})\big)\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}},$$ where the kernel ${\boldsymbol\alpha}$ is an antisymmetric vector-valued function, i.e, ${\boldsymbol\alpha}({{\bf x}},{{\bf y}})=-{\boldsymbol\alpha}({{\bf y}},{{\bf x}})$. In addition, the action of the adjoint operator ${{\cal D}}^\ast_{{\boldsymbol\alpha}} $ on a scalar function $u({{\bf x}})$ is given by $$\label{sdivadj0} ({{\cal D}}_{{\boldsymbol\alpha}}^\ast u)({{\bf x}},{{\bf y}}) = -\big(u({{\bf y}}) - u({{\bf x}})\big){\boldsymbol\alpha}({{\bf x}},{{\bf y}}).$$ Moreover, for a scalar function $\eta({{\bf x}},{{\bf y}})$ and a vector-valued function ${{\bf u}}({{\bf x}})$, the nonlocal gradient operator ${{\cal G}}_{{\boldsymbol\alpha}}$ and its adjoint ${{\cal G}}_{{\boldsymbol\alpha}}^{\ast}$ are defined by $$\begin{aligned} \label{sgrad0} ({{\cal G}}_{{\boldsymbol\alpha}}\eta)({{\bf x}}) &=& \int\big(\eta({{\bf y}},{{\bf x}}) + \eta({{\bf x}},{{\bf y}})\big){\boldsymbol\alpha}({{\bf x}},{{\bf y}})\, d{{\bf y}},\\ \label{sgradadj0} ({{\cal G}}_{{\boldsymbol\alpha}}^* {{\bf u}})({{\bf x}},{{\bf y}}) & =& -\big({{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}}).\end{aligned}$$ Using these nonlocal operators, with specific choices of ${\boldsymbol\alpha}$, it is shown in [@dglz-nld] that $$\dot{u}+{{\cal D}}_{{\boldsymbol\alpha}}({{\cal D}}_{{\boldsymbol\alpha}}^\ast u)=b$$ is a nonlocal diffusion equation. In addition, the linear peridynamics equation [@Silling2007] $$\label{peridyn_0} \ddot{{{\bf u}}}=\mathcal{L}{{\bf u}}+{{\bf b}},$$ where $\mathcal{L}$ is given by , can be written, using nonlocal vector calculus operators [@dglz-ps], as $$\label{peridyn_L_old} \mathcal{L}{{\bf u}}=-{{\cal D}}_{{\boldsymbol\alpha}}(c_{1}' \omega \;({{\cal D}}_{{\boldsymbol\alpha}}^{\ast}{{\bf u}})^T)- {{\cal D}}_{{\boldsymbol\alpha}}^{\omega}(c_{2}' \mbox{tr} ({{{\cal D}}_{{\boldsymbol\alpha}}^{\omega}}^{\ast}{{\bf u}}) I),$$ where $I$ is the identity matrix, $c_1 ', c_2 '$ are material properties, $\omega$ a weight function, and ${{\cal D}}_{{\boldsymbol\alpha}}^{\omega}$, ${{{\cal D}}_{{\boldsymbol\alpha}}^{\omega}}^{\ast}$ are weighted versions of ${{\cal D}}_{{\boldsymbol\alpha}}$, ${{\cal D}}_{{\boldsymbol\alpha}}^{\ast}$, respectively; see [@dglz-ps] for details. In this work, we show that the linear peridynamics operator $\mathcal{L}$ has a simpler expression in terms of nonlocal vector calculus operators. In Theorem \[thmpdandno\], we show that, for an appropriate choice of the integral kernel ${\boldsymbol\alpha}$, the peridynamics operator $\mathcal{L}$ in can be cast as $$\label{peridyn_L_new} \mathcal{L}{{\bf u}}=-{{\cal G}}_{{\boldsymbol\alpha}}(c_{1} {{\cal G}}_{{\boldsymbol\alpha}}^{\ast}{{\bf u}})-{{\cal G}}_{{\boldsymbol\alpha}}(c_{2} \overline{{{\cal G}}_{{\boldsymbol\alpha}}^{\ast}}{{\bf u}}),$$ where $c_1, c_2$ are scalars, and $\overline{{{\cal G}}_{{\boldsymbol\alpha}}^{\ast}}$ is an average of ${{\cal G}}_{{\boldsymbol\alpha}}^{\ast}$ defined by $$(\overline{{{\cal G}}_{{\boldsymbol\alpha}}^} {{\bf u}})({{\bf x}}) = -\int \big({{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}})d{{\bf y}}.$$ This new expression for $\mathcal{L}$ given in bears a closer resemblance to the Navier operator of linear elasticity. Given the fact that the nonlocal calculus operators given by – mimic the differential calculus operators in the setting of nonlocal diffusion and peridynamics models, one may ask whether these operators are the only nonlocal integral operators that do so. In this work, we provide a general mathematical setting for the existence of nonlocal integral operators that resemble the differential calculus operators independent of particular nonlocal models. In Section \[gennlc\], we show that a nonlocal operator that resembles[^2] the divergence operator, for instance, must be of the general form $$\label{general_D} ({{\cal D}}{\boldsymbol\nu})({{\bf x}}) = \int\int{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}},$$ for some kernel ${\boldsymbol\kappa}$ that satisfies $$\label{div_cond} \int{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf x}}= 0 \qquad\mbox{for a.e. ${{\bf y}},{{\bf z}}$.}$$ We refer to the operator ${{\cal D}}$ in – as general nonlocal divergence. We introduce general nonlocal operators including a nonlocal gradient, nonlocal curl, and nonlocal Laplacian. General nonlocal calculus theorems and identities such as nonlocal integration by parts formulas and Green’s identities are developed. We show in Section \[sec\_special\] that the nonlocal divergence ${{\cal D}}_{{\boldsymbol\alpha}}$ in can be recovered from for a specialized kernel ${\boldsymbol\kappa}={\boldsymbol\kappa}({\boldsymbol\alpha})$. The other nonlocal operators in – are also shown to follow from the general formulation of the nonlocal calculus. In Section \[sec\_conclusion\], we provide a new example for nonlocal calculus operators. Specifically, we show that the operator defined by $$\label{sdiv_beta} ({{\cal D}}_{{\boldsymbol\beta}}{\boldsymbol\nu})({{\bf x}}) = \int\big({\boldsymbol\nu}({{\bf y}},{{\bf x}}) - {\boldsymbol\nu}({{\bf x}},{{\bf y}})\big)\cdot{\boldsymbol\beta}({{\bf x}},{{\bf y}})\,d{{\bf y}},$$ where the kernel ${\boldsymbol\beta}$ is a symmetric vector-valued function, is a nonlocal divergence operator. The operator ${{\cal D}}_{{\boldsymbol\beta}}$ is a special case of for a specific kernel ${\boldsymbol\kappa}={\boldsymbol\kappa}({\boldsymbol\beta})$. It is anticipated that nonlocal calculus operators, such as ${{\cal D}}_{{\boldsymbol\beta}}$ in , will be useful for the analysis of new nonlocal models. This article is organized as follows. Section \[gennlc\] introduces the general formulation for the nonlocal vector calculus. General nonlocal calculus theorems, identities, and regularity results for nonlocal operators are derived. Section \[sec\_special\] focuses on the special case of nonlocal calculus operators defined in –. An application to the peridynamics model of solid mechanics is discussed in Section \[sec\_peridynamics\]. Conclusion remarks and discussion of a new example of nonlocal calculus operators are provided in Section \[sec\_conclusion\]. A generalized nonlocal calculus {#gennlc} =============================== For the spaces ${{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}$ and ${{C_c^{\infty}({{\mathbb{R}^n}})}}$ and the corresponding dual spaces\ ${{[D'({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}$ and ${{D'({{\mathbb{R}^n}})}}$ with $k=1,2$ or $3$, we have the duality parings $$\begin{aligned} <{\boldsymbol\nu},{\boldsymbol\gamma}>_{{{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}},{{[D'({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}} &= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\nu}({{\bf z}},{{\bf y}})\cdot{\boldsymbol\gamma}({{\bf z}},{{\bf y}})\,d{{\bf z}}d{{\bf y}}, \\& \hspace{-1cm}\forall \,{\boldsymbol\nu}\in {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}},\,\,{\boldsymbol\gamma}\in {{[D'({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\end{aligned}$$ and $$<v,u>_{{{C_c^{\infty}({{\mathbb{R}^n}})}},{{D'({{\mathbb{R}^n}})}}} = \int_{{{\mathbb{R}^n}}}u({{\bf x}})v({{\bf x}})\,d{{\bf x}}\qquad\forall\, v\in {{C_c^{\infty}({{\mathbb{R}^n}})}},\,\,u\in {{D'({{\mathbb{R}^n}})}}.$$ For the product space ${{{{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\times {{C_c^{\infty}({{\mathbb{R}^n}})}}}}$ and its dual\ ${{\big({{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\times {{C_c^{\infty}({{\mathbb{R}^n}})}}\big)'}}$, the duality paring is given by $$\begin{aligned} &<{\boldsymbol\kappa},\,{\boldsymbol\sigma}>_{{{{{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\times {{C_c^{\infty}({{\mathbb{R}^n}})}}}}, {{\big({{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\times {{C_c^{\infty}({{\mathbb{R}^n}})}}\big)'}}} \\&\qquad\qquad= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\sigma}({{\bf x}},{{\bf y}},{{\bf z}})\cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}d{{\bf x}}, \\& \forall \, {\boldsymbol\sigma}\in {{\big({{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\times {{C_c^{\infty}({{\mathbb{R}^n}})}}\big)'}},\,\, {\boldsymbol\kappa}\in{{\big({{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\times {{C_c^{\infty}({{\mathbb{R}^n}})}}\big)'}}. \end{aligned}$$ Let ${{\cal D}}: {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\to {{D'({{\mathbb{R}^n}})}}$ denote a linear and continuous operator. Then, by the Schwartz Kernel Theorem, there exists a unique ${\boldsymbol\kappa}\in$\ ${{\big({{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\times {{C_c^{\infty}({{\mathbb{R}^n}})}}\big)'}}$ such that $$\begin{aligned} &<v,{{\cal D}}{\boldsymbol\nu}>_{{{C_c^{\infty}({{\mathbb{R}^n}})}},{{D'({{\mathbb{R}^n}})}}}\\ & \qquad\qquad= <v\otimes{\boldsymbol\nu},{\boldsymbol\kappa}>_{{{{{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\times {{C_c^{\infty}({{\mathbb{R}^n}})}}}},{{\big({{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\times {{C_c^{\infty}({{\mathbb{R}^n}})}}\big)'}}},\\ &\forall\,v\in {{C_c^{\infty}({{\mathbb{R}^n}})}},\,\,{\boldsymbol\nu}\in {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\end{aligned}$$ or, using the definitions of the duality pairings, $$\begin{aligned} \int_{{{\mathbb{R}^n}}}v({{\bf x}})({{\cal D}}{\boldsymbol\nu})({{\bf x}})\,d{{\bf x}}=\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} &v({{\bf x}}){\boldsymbol\nu}({{\bf y}},{{\bf z}})\cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}d{{\bf x}}\\& \forall\,v\in {{C_c^{\infty}({{\mathbb{R}^n}})}},\,\,{\boldsymbol\nu}\in {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}. \end{aligned}$$ The arbitrariness of $v\in {{C_c^{\infty}({{\mathbb{R}^n}})}}$ implies that ${{\cal D}}{\boldsymbol\nu}\in {{D'({{\mathbb{R}^n}})}}$ is given by $$\label{sktd} ({{\cal D}}{\boldsymbol\nu})({{\bf x}}) = \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\qquad\mbox{for almost all ${{\bf x}}\in {{\mathbb{R}^n}}$.}$$ We seek an operator ${{\cal D}}$ that satisfies a divergence-like theorem which we now describe. For ${\boldsymbol\nu}\in [L^1({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k$, let $\psi_{{\boldsymbol\nu}}\in[L^1({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k$ be such that \[psiass\] $$\begin{aligned} &\mbox{$\psi_{{\boldsymbol\nu}}$ is linear in ${\boldsymbol\nu}$}\label{psiassa}\\ &\mbox{$\psi_{{\boldsymbol\nu}}$ is antisymmetric, i.e., $\psi_{{\boldsymbol\nu}}({{\bf x}},{{\bf y}})=-\psi_{{\boldsymbol\nu}}({{\bf y}},{{\bf x}})$ for all ${{\bf x}},{{\bf y}}\in{{\mathbb{R}^n}}$}.\label{psiassb}\end{aligned}$$ For any ${{\bf x}}\in{{\mathbb{R}^n}}$ and $\widetilde\Omega\subset{{\mathbb{R}^n}}$, $\int_{\widetilde\Omega}\psi_{{\boldsymbol\nu}}({{\bf x}},{{\bf y}})\,d{{\bf y}}$ represents the nonlocal flux density at ${{\bf x}}$ into $\widetilde\Omega$; see [@dglz-nlc] for details. The operator ${{\cal D}}$ and the flux density $\int_{\widetilde\Omega}\psi_{{\boldsymbol\nu}}({{\bf x}},{{\bf y}})\,d{{\bf y}}$ are required to satisfy the nonlocal “divergence” theorem[^3] $$\label{divthm} \int_\Omega ({{\cal D}}{\boldsymbol\nu})({{\bf x}})\,d{{\bf x}}= \int_\Omega \int_{{\mathbb{R}^n}}\psi_{{\boldsymbol\nu}}({{\bf x}},{{\bf y}})\,d{{\bf y}}d{{\bf x}}\qquad \forall\,{\boldsymbol\nu}\in {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}},\,\, \Omega\subset{{\mathbb{R}^n}}.$$ From and the arbitrariness of $\Omega$, we obtain $$\label{divthm2} ({{\cal D}}{\boldsymbol\nu})({{\bf x}}) = \int_{{\mathbb{R}^n}}\psi_{{\boldsymbol\nu}}({{\bf x}},{{\bf y}})\,d{{\bf y}}\qquad\mbox{for a.e. ${{\bf x}}\in{{\mathbb{R}^n}}$.}$$ From and , we obtain $$\label{divthm3} \int_{{\mathbb{R}^n}}\psi_{{\boldsymbol\nu}}({{\bf x}},{{\bf y}})\,d{{\bf y}}=\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\qquad\mbox{for a.e. ${{\bf x}}\in{{\mathbb{R}^n}}$.}$$ Note that here ${\boldsymbol\kappa}$ is fixed whereas ${\boldsymbol\nu}$ is arbitrary. \[lemrho\] The kernel ${\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})$ satisfies $$\label{divthm4} \int_{{{\mathbb{R}^n}}}{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf x}}= 0 \qquad\mbox{for a.e. ${{\bf y}},{{\bf z}}\in{{\mathbb{R}^n}}$.}$$ [Proof.]{} From and the antisymmetry of $\psi_{{\boldsymbol\nu}}({{\bf x}},{{\bf y}})$, we have $$\label{divthm5} \int_{{\mathbb{R}^n}}({{\cal D}}{\boldsymbol\nu})({{\bf x}})\,d{{\bf x}}= \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}\psi_{{\boldsymbol\nu}}({{\bf x}},{{\bf y}})\,d{{\bf y}}d{{\bf x}}=-\int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}\psi_{{\boldsymbol\nu}}({{\bf y}},{{\bf x}})\,d{{\bf x}}d{{\bf y}}=0.$$ Then, from , , and , we have $$\begin{aligned} \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}d{{\bf x}}= \int_{{\mathbb{R}^n}}(D{\boldsymbol\nu})({{\bf x}})\,d{{\bf x}}=0,\\ \quad\forall\,{\boldsymbol\nu}\in {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}.\end{aligned}$$ Therefore, $$\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\Big(\int_{{{\mathbb{R}^n}}}{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf x}}\Big)\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}=0, \qquad \forall\,{\boldsymbol\nu}\in {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}$$ which implies . $\Box$ We refer to a kernel ${\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})$ satisfying as a [divergence kernel.]{} From and , we are led to the following definition of a nonlocal divergence operator. \[ddiv\] The action of the [nonlocal divergence operator]{} ${{\cal D}}: {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\to {{D'({{\mathbb{R}^n}})}}$ on any vector-valued function ${\boldsymbol\nu}\in {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}$ is given by[^4] $$\label{divop} ({{\cal D}}{\boldsymbol\nu})({{\bf x}}) = \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\qquad\mbox{for a.e. ${{\bf x}}\in {{\mathbb{R}^n}}$,}$$ where ${\boldsymbol\kappa}\in{{\big({{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\times {{C_c^{\infty}({{\mathbb{R}^n}})}}\big)'}}$ satisfies . $\Box$ The adjoint operator ${{\cal D}}^\ast$ corresponding to the nonlocal divergence operator ${{\cal D}}$ is defined through the relation $$\label{adjdef} \begin{aligned} < u,{{\cal D}}{\boldsymbol\nu}>_{{{C_c^{\infty}({{\mathbb{R}^n}})}},{{D'({{\mathbb{R}^n}})}}} = <{\boldsymbol\nu}, &{{\cal D}}^\ast u>_{{{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}},{{[D'({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}} \\&\forall\, {\boldsymbol\nu}\in {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}},\,\,u\in {{C_c^{\infty}({{\mathbb{R}^n}})}}. \end{aligned}$$ \[propadj\] Corresponding to the nonlocal divergence operator ${{\cal D}}: {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\to {{D'({{\mathbb{R}^n}})}}$, we have the [adjoint operator]{} ${{\cal D}}^\ast: {{C_c^{\infty}({{\mathbb{R}^n}})}}\to {{[D'({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}$ whose action on any scalar-valued function $u\in {{C_c^{\infty}({{\mathbb{R}^n}})}}$ is given by[^5] $$\label{adjop} ({{\cal D}}^\ast u)({{\bf x}},{{\bf y}}) = \int_{{\mathbb{R}^n}}u({{\bf z}}) {\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\,d{{\bf z}}\qquad\mbox{for a.e. ${{\bf x}},{{\bf y}}\in {{\mathbb{R}^n}}$}.$$ [Proof.]{} From and we have $$\label{adjpf} \begin{aligned} \int_{{{\mathbb{R}^n}}}\Big(\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}&{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\Big) u({{\bf x}})\,d{{\bf x}}\\&= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} ({{\cal D}}^\ast u)({{\bf x}},{{\bf y}})\cdot{\boldsymbol\nu}({{\bf x}},{{\bf y}})\,d{{\bf y}}d{{\bf x}}. \end{aligned}$$ After switching the dummy variables ${{\bf x}}$ and ${{\bf z}}$ and then ${{\bf x}}$ and ${{\bf y}}$ in the left-hand side, we have $$\begin{aligned} \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}&{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}})u({{\bf x}})\,d{{\bf z}}d{{\bf y}}d{{\bf x}}\\&= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\kappa}({{\bf z}},{{\bf y}},{{\bf x}})\cdot{\boldsymbol\nu}({{\bf y}},{{\bf x}})u({{\bf z}})\,d{{\bf x}}d{{\bf y}}d{{\bf z}}\\&= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\cdot{\boldsymbol\nu}({{\bf x}},{{\bf y}})u({{\bf z}})\,d{{\bf y}}d{{\bf x}}d{{\bf z}}\\&= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\Big(\int_{{{\mathbb{R}^n}}}{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})u({{\bf z}})\,d{{\bf z}}\Big)\cdot{\boldsymbol\nu}({{\bf x}},{{\bf y}})\,d{{\bf y}}d{{\bf x}}. \end{aligned}$$ Then, because ${\boldsymbol\nu}\in {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}$ is arbitrary, we obtain from . $\Box$ Regularity of ${{\cal D}}$ and ${{\cal D}}^\ast$ ------------------------------------------------ In Definition \[ddiv\] and Proposition \[propadj\], we assume that ${\boldsymbol\nu}({{\bf x}},{{\bf y}})\in{{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}$, $u\in {{C_c^{\infty}({{\mathbb{R}^n}})}}$, and ${\boldsymbol\kappa}\in{{\big({{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\times {{C_c^{\infty}({{\mathbb{R}^n}})}}\big)'}}$. In fact, the nonlocal divergence operator ${{\cal D}}$ and its adjoint operator ${{\cal D}}^$ can be defined for functions having much less smoothness, as the next proposition shows. \[propreg\] Let $1\leq p \leq \infty$ and $1\leq q \leq \infty$ with $\frac{1}{p} + \frac{1}{q} = 1$ and assume that ${\boldsymbol\kappa}\in [L^p({{\mathbb{R}^n}}\times{{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k$. Then, $$\begin{aligned} {{\cal D}}&:\;{\boldsymbol\nu}\in [L^q({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k\longmapsto {{\cal D}}{\boldsymbol\nu}\in L^p({{\mathbb{R}^n}}) \label{drega} \\ {{\cal D}}^&:\; u\in L^q({{\mathbb{R}^n}})\longmapsto {{\cal D}}^u \in [L^p({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k.\label{dregb}\end{aligned}$$ In particular, $[L^2({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k \xmapsto{{{\cal D}}} L^2({{\mathbb{R}^n}}) \xmapsto{{{\cal D}}^} L^2[({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k$. Moreover, ${{\cal D}}$ and ${{\cal D}}^$ are bounded operators on $[L^2({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k$ and $L^2({{\mathbb{R}^n}})$, respectively. [Proof.]{} Letting ${\boldsymbol\nu}\in [L^q({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k$, by Minkowski’s integral inequality, we have $$\begin{aligned} \\|{{\cal D}}{\boldsymbol\nu}\\|_{L^p({{\mathbb{R}^n}})} &= \Big(\int_{{{\mathbb{R}^n}}} \Big\|\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\nu}({{\bf y}},{{\bf z}})\cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\Big\|^p d{{\bf x}}\Big)^{1/p} \\ &\leq \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} \Big( \int_{{{\mathbb{R}^n}}}\|{\boldsymbol\nu}({{\bf y}},{{\bf z}})\cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\|^p d{{\bf x}}\Big)^{1/p}\,d{{\bf z}}d{{\bf y}}\\ &\leq \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} \|{\boldsymbol\nu}({{\bf y}},{{\bf z}})\| \Big( \int_{{{\mathbb{R}^n}}}\|{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\|^p\,d{{\bf x}}\Big)^{1/p} d{{\bf z}}d{{\bf y}}. \end{aligned}$$ Applying the Hölder inequality to the last inequality, we have $$\label{dregc} \\|{{\cal D}}{\boldsymbol\nu}\\|_{L^p({{\mathbb{R}^n}})} \leq \\|{\boldsymbol\nu}\\|_{[L^q({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k} \\|{\boldsymbol\kappa}\\|_{[L^p({{\mathbb{R}^n}}\times{{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}$$ which completes the proof for . For , let $u\in L^q({{\mathbb{R}^n}})$. Then, using Minkowski’s integral inequality again, we have $$\begin{aligned} \\|{{\cal D}}^ u \\|_{[L^p({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k} &= \Big(\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} \Big\|\int_{{{\mathbb{R}^n}}} u({{\bf z}}){\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}}) d{{\bf z}}\Big\|^p d{{\bf y}}d{{\bf x}}\Big)^{1/p}\\ &\leq \int_{{{\mathbb{R}^n}}} \Big(\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\|u({{\bf z}}){\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\|^p d{{\bf y}}d{{\bf x}}\Big)^{1/p} d{{\bf z}}\\ &\leq \int_{{{\mathbb{R}^n}}} \|u({{\bf z}})\| \Big(\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\|{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\|^p\Big)^{1/p} d{{\bf z}}. \end{aligned}$$ Again, applying the Hölder inequality to the last inequality, we have $$\label{dregd} \\|{{\cal D}}^* u\\|_{[L^p({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k} \leq \\|u\\|_{L^q({{\mathbb{R}^n}})} \\|{\boldsymbol\kappa}\\|_{[L^p({{\mathbb{R}^n}}\times{{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}$$ which completes the proof for . The facts that ${{\cal D}}$ and ${{\cal D}}^$ are bounded operators on $L^2({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})^k$ and $L^2({{\mathbb{R}^n}})$, respectively, follow easily from and , respectively. $\Box$ Other nonlocal operators ------------------------ Other nonlocal operators that mimic the operators of the classical differential vector calculus can be defined. ### Nonlocal gradient and curl operators A nonlocal gradient operator can be defined in a manner similar to Definition \[ddiv\] for the nonlocal divergence operator. The action of the [nonlocal gradient operator]{} ${{\cal G}}: C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})\to [D'({{\mathbb{R}^n}})]^k$ on any scalar-valued function $\eta\in C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})$ is given by $$\label{adjgras} ({{\cal G}}\eta)({{\bf x}}) = \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\eta({{\bf y}},{{\bf z}}){\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\, d{{\bf z}}d{{\bf y}}\qquad\mbox{for a.e. ${{\bf x}}\in {{\mathbb{R}^n}}$}.$$ Corresponding to the nonlocal gradient operator\ ${{\cal G}}: C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})\to [D'({{\mathbb{R}^n}})]^k$, we have the [adjoint operator]{}\ ${{\cal G}}^\ast: [C_c^{\infty}({{\mathbb{R}^n}})]^k \to D'({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})$ whose action on any vector-valued function ${{\bf v}}\in [C_c^{\infty}({{\mathbb{R}^n}})]^k$ is given by $$\label{adjgra} ({{\cal G}}^\ast{{\bf v}})({{\bf x}},{{\bf y}}) = \int_{{{\mathbb{R}^n}}}{{\bf v}}({{\bf z}})\cdot{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}}) \,d{{\bf z}}\qquad\mbox{for a.e. ${{\bf x}},{{\bf y}}\in {{\mathbb{R}^n}}$}.$$ [Proof.]{} By definition, the adjoint operator ${{\cal G}}^\ast$ satisfies $$<{{\bf v}},{{\cal G}}\eta>_{[C_c^{\infty}({{\mathbb{R}^n}})]^k,D'({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})} = <\eta,{{\cal G}}^ {{\bf v}}>_{C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}}),[D'({{\mathbb{R}^n}})]^k}$$ for all $\eta\in C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})$ and ${{\bf v}}\in[ C_c^{\infty}({{\mathbb{R}^n}})]^k$. Then, the proof of follows along the same lines of the proof of Proposition .$\Box$ [Remark.]{} With ${{\cal G}}^\ast$ being the adjoint of the nonlocal gradient operator ${{\cal G}}$, one can identify $-{{\cal G}}^\ast$ as a nonlocal divergence operator.$\Box$ [Remark.]{} We now have the two nonlocal divergence operators ${{\cal D}}$ and $-{{\cal G}}^\ast$ and the two nonlocal gradient operators ${{\cal G}}$ and $-{{\cal D}}^\ast$. It is natural to have such pairs because of the two types of functions that are needed to describe nonlocality, i.e., functions of two points such as ${\boldsymbol\nu}({{\bf x}},{{\bf y}})$ and $\eta({{\bf x}},{{\bf y}})$ and functions of one point such as ${{\bf v}}({{\bf x}})$ and $u({{\bf x}})$. Thus, we have the nonlocal divergence and gradient operators ${{\cal D}}$ and ${{\cal G}}$ acting on functions of two points and the nonlocal divergence and gradient operators $-{{\cal G}}^\ast$ and $-{{\cal D}}^\ast$ acting on functions of one point.$\Box$ Similar to Proposition \[propreg\], one can prove the following proposition. \[propreg2\] Let $1\leq p \leq \infty$ and $1\leq q \leq \infty$ with $\frac{1}{p} + \frac{1}{q} = 1$ and assume that ${\boldsymbol\kappa}\in [L^p({{\mathbb{R}^n}}\times{{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k$. Then, $$\begin{aligned} {{\cal G}}&: \eta\in L^q({{\mathbb{R}^n}}\times{{\mathbb{R}^n}}) \longmapsto {{\cal G}}\eta\in [L^p({{\mathbb{R}^n}})]^k \\ {{\cal G}}^&: {{\bf u}}\in [L^q({{\mathbb{R}^n}})]^k \longmapsto {{\cal G}}^{{\bf u}}\in L^p({{\mathbb{R}^n}}\times{{\mathbb{R}^n}}) . \end{aligned}$$ In particular, $$L^2({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})\xmapsto{{{\cal G}}} [L^2({{\mathbb{R}^n}})]^k \xmapsto{{{\cal G}}^} L^2({{\mathbb{R}^n}}\times{{\mathbb{R}^n}}).$$ Moreover, ${{\cal G}}$ and ${{\cal G}}^$ are bounded operators on $L^2({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})$ and $[L^2({{\mathbb{R}^n}})]^k$, respectively.$\Box$ In the sequel, we will need the following averaging operator. \[dgbar\] The action of the [nonlocal averaging operator]{}\ $\overline{{{\cal G}}^} : [C_c^{\infty}({{\mathbb{R}^n}})]^k \longrightarrow C_c^{\infty}({{\mathbb{R}^n}})$ on a vector-valued function ${{\bf u}}\in [C_c^{\infty}({{\mathbb{R}^n}})]^k$ is given by $$\label{gbar} (\overline{{{\cal G}}^}{{\bf u}})({{\bf x}}) = \int_{{{\mathbb{R}^n}}}({{\cal G}}^* {{\bf u}})({{\bf x}},{{\bf z}})\, d{{\bf z}}.$$ [Remark.]{} A nonlocal curl operator ${{\cal C}}: [C_c({\mathbb{R}}^3\times{\mathbb{R}}^3)]^3\to [D'({\mathbb{R}}^3)]^3$ is given by its action action on any vector-valued function ${\boldsymbol\nu}\in [C_c^{\infty}({\mathbb{R}}^3\times{\mathbb{R}}^3)]^3$ as $$({{\cal C}}{\boldsymbol\eta})({{\bf x}}) = \int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3}{\boldsymbol\eta}({{\bf y}},{{\bf z}})\times{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\, d{{\bf z}}d{{\bf y}}\qquad\mbox{for a.e. ${{\bf x}}\in {\mathbb{R}}^3$}.$$ The corresponding nonlocal adjoint operator ${{\cal C}}^\ast: [C_c^{\infty}({\mathbb{R}}^3)]^3\to [D'({\mathbb{R}}^3\times{\mathbb{R}}^3)]^3$, which is also a nonlocal curl operator, is given by its action on any vector-valued function ${{\bf u}}\in [C_c^{\infty}({\mathbb{R}}^3)]^3$ as $$({{\cal C}}^\ast{{\bf v}})({{\bf x}},{{\bf y}}) = \int_{{\mathbb{R}}^3}{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\times{{\bf u}}({{\bf z}}) \,d{{\bf z}}\qquad\mbox{for a.e. ${{\bf x}},{{\bf y}}\in {\mathbb{R}}^3$}.$$ Regularity results similar to those proved in Propositions and for the nonlocal divergence and gradient operators hold for the nonlocal curl operator ${{\cal C}}$.$\Box$ ### Nonlocal divergence of a tensor and gradient of a vector The nonlocal divergence operator ${{\cal D}}$ can also be applied to a tensor-valued function yielding a vector-valued function. \[Nonlocal divergence of a tensor\] The action of the nonlocal divergence operator ${{\cal D}}:[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^{k\times k}\longrightarrow[D'({{\mathbb{R}^n}})]^k$ on the tensor-valued function ${\boldsymbol\Psi}\in [C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^{k\times k}$ is defined by $$\label{divten} ({{\cal D}}{\boldsymbol\Psi})({{\bf x}}) = \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\Psi}({{\bf y}},{{\bf z}}){\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\qquad\mbox{for a.e. ${{\bf x}}\in {{\mathbb{R}^n}}$}.$$ Here, ${\boldsymbol\Psi}{\boldsymbol\kappa}$ represents a matrix-vector product. The components of the vector ${{\cal D}}{\boldsymbol\Psi}$ are the nonlocal divergences of the corresponding rows of ${\boldsymbol\Psi}$. The action of the nonlocal adjoint operator\ ${{\cal D}}^:[C_c^{\infty}({{\mathbb{R}^n}})]^k\longrightarrow[D'({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^{k\times k}$ on the vector-valued function ${{\bf u}}\in [C_c^{\infty}({{\mathbb{R}^n}})]^k$ is given by $$\label{adjten} ({{\cal D}}^{{\bf u}}) ({{\bf x}},{{\bf y}}) = \int_{{{\mathbb{R}^n}}} {{\bf u}}({{\bf z}})\otimes{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}}) d{{\bf z}}\qquad\mbox{for a.e. ${{\bf x}},{{\bf y}}\in {{\mathbb{R}^n}}$}.$$ [Proof.]{} By the definition of adjoint operator, we have $$< {{\bf u}},{{\cal D}}{\boldsymbol\Psi}>_{[C_c^{\infty}({{\mathbb{R}^n}})]^k,[D'({{\mathbb{R}^n}})]^k} = <{\boldsymbol\Psi},\, {{\cal D}}^{{\bf u}}>_{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^{k\times k},[D'({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^{k\times k}}$$ for all ${\boldsymbol\Psi}\in C_c^{\infty}[{{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^{k\times k}$ and ${{\bf u}}\in[C_c^{\infty}({{\mathbb{R}^n}})]^k$. This is equivalent to $$\label{adjten2} \begin{aligned} \int_{{{\mathbb{R}^n}}} \Big(\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\Psi}({{\bf y}},{{\bf z}})&{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\Big)\cdot {{\bf u}}({{\bf x}})\, d{{\bf x}}\\&= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} {\boldsymbol\Psi}({{\bf x}},{{\bf y}}) : ({{\cal D}}^{{\bf u}})({{\bf x}},{{\bf y}}) \,d{{\bf y}}d{{\bf x}}. \end{aligned}$$ After switching ${{\bf x}}$ and ${{\bf z}}$ and then ${{\bf x}}$ and ${{\bf y}}$ in the left-hand side, we have $$\begin{aligned} \int_{{{\mathbb{R}^n}}} \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}&\big({\boldsymbol\Psi}({{\bf y}},{{\bf z}}){\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\big) \cdot {{\bf u}}({{\bf x}})\,d{{\bf z}}d{{\bf y}}d{{\bf x}}\\&= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\big({\boldsymbol\Psi}({{\bf y}},{{\bf x}}){\boldsymbol\kappa}({{\bf z}},{{\bf y}},{{\bf x}})\big) \cdot {{\bf u}}({{\bf z}})\,d{{\bf x}}d{{\bf y}}d{{\bf z}}\\&= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\big({\boldsymbol\Psi}({{\bf x}},{{\bf y}}){\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\big) \cdot{{\bf u}}({{\bf z}})\,d{{\bf y}}d{{\bf x}}d{{\bf z}}\\&= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\Psi}({{\bf x}},{{\bf y}}):\Big(\int_{{{\mathbb{R}^n}}} {{\bf u}}({{\bf z}}) \otimes{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\,d{{\bf z}}\Big)\,d{{\bf y}}d{{\bf x}}, \end{aligned}$$ where, for the last equality, we rearranged the tensor-vector products. Then, because ${\boldsymbol\Psi}\in [C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^{k\times k}$ is arbitrary, we obtain from .$\Box$ The nonlocal gradient operator ${{\cal G}}$ can also be applied to a vector-valued function yielding a tensor-valued function. \[Nonlocal gradient of a vector\] The action of the nonlocal gradient operator ${{\cal G}}:[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^{k}\longrightarrow[D'({{\mathbb{R}^n}})]^{k\times k}$ on the vector-valued function ${\boldsymbol\nu}\in [C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^{k}$ is defined by $$\label{gradvec} ({{\cal G}}{\boldsymbol\nu})({{\bf x}}) = \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\nu}({{\bf y}},{{\bf z}})\otimes{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\qquad\mbox{for a.e. ${{\bf x}}\in {{\mathbb{R}^n}}$}.$$ We then have that the action of the nonlocal adjoint operator ${{\cal G}}^:[C_c^{\infty}({{\mathbb{R}^n}})]^{k\times k}\rightarrow[D'({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^{k}$ on the tensor-valued function\ ${{\bf U}}\in [C_c^{\infty}({{\mathbb{R}^n}})]^{k\times k}$ is given by $$\label{adjten2} ({{\cal G}}^{{\bf U}}) ({{\bf x}},{{\bf y}}) = \int_{{{\mathbb{R}^n}}} {{\bf U}}({{\bf z}}){\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}}) d{{\bf z}}\qquad\mbox{for a.e. ${{\bf x}},{{\bf y}}\in {{\mathbb{R}^n}}$}.$$ ### Nonlocal Laplacian operators With ${{\cal D}}$ and $-{{\cal D}}^\ast$ denoting nonlocal divergence and gradient operators, respectively, their composition $-{{\cal D}}{{\cal D}}^\ast$ can be viewed as a nonlocal Laplacian operator. The following proposition provides the explicit form of this operator. The nonlocal Laplacian operator of a scalar-valued function $u({{\bf x}})$ is given by $$\label{nonlapa} -({{\cal D}}{{\cal D}}^\ast u)({{\bf x}})= -\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} u({{\bf w}}){\boldsymbol\kappa}({{\bf w}},{{\bf y}},{{\bf z}})\cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\, d{{\bf w}}d{{\bf z}}d{{\bf y}}$$ whereas the nonlocal Laplacian operator of a vector-valued function ${{\bf u}}({{\bf x}})$ is given by $$\label{nonlapb} -{{\cal D}}({{\cal D}}^\ast {\bf u}) = -\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{{\bf u}}({{\bf w}}){\boldsymbol\kappa}({{\bf w}},{{\bf y}},{{\bf z}}) \cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\, d{{\bf w}}d{{\bf z}}d{{\bf y}}$$ [Proof.]{} From and , we have that $$\begin{aligned} {{\cal D}}{{\cal D}}^\ast u &= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} ({{\cal D}}^\ast u)({{\bf y}},{{\bf z}}) \cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\\&= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} \Big[ \int_{{{\mathbb{R}^n}}} u({{\bf w}}){\boldsymbol\kappa}({{\bf w}},{{\bf y}},{{\bf z}})\, d{{\bf w}}\Big]\cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}. \end{aligned}$$ In the same manner, follows from and . $\Box$ ### Identities of the nonlocal calculus {#sec:ident} We begin with some identities that mimic those of the classical vector calculus. The first set of identities do not require any further conditions on the divergence kernel ${\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})$. \[ident1\] \[propident1\] [(i)]{} For $u({{\bf x}})=a$ and ${{\bf u}}({{\bf x}})={\bf a}$, where $a$ and ${\bf a}$ are scalar and vector constants, respectively, we have $$\label{ident1a} ({{\cal D}}^\ast a)({{\bf x}},{{\bf y}}) ={\bf 0},\qquad ({{\cal G}}^\ast{\bf a})({{\bf x}},{{\bf y}}) =0,\qquad\mbox{and}\qquad ({{\cal C}}^\ast{\bf a})({{\bf x}},{{\bf y}}) ={\bf 0}.$$ [(ii)]{} For the vector-valued functions ${{\bf u}}({{\bf x}})$ and ${\boldsymbol\nu}({{\bf x}},{{\bf y}})$, we have $$\label{ident1b} \begin{aligned} ({{\cal D}}{{\cal D}}^\ast {\bf u})({{\bf x}})&= ({{\cal C}}{{\cal C}}^\ast {\bf u})({{\bf x}})+ ({{\cal G}}{{\cal G}}^\ast {\bf u})({{\bf x}}) \\ ({{\cal G}}^\ast{{\cal G}}{\boldsymbol\nu})({{\bf x}},{{\bf y}}) &= ({{\cal C}}^\ast{{\cal C}}{\boldsymbol\nu})({{\bf x}},{{\bf y}})+({{\cal D}}^\ast {{\cal D}}{\boldsymbol\nu})({{\bf x}},{{\bf y}}). \end{aligned}$$ [(iii)]{} For the vector-valued functions ${{\bf u}}({{\bf x}})$ and ${\boldsymbol\nu}({{\bf x}},{{\bf y}})$, we have $$\label{ident1c} {{\cal D}}{\boldsymbol\nu}= \mbox{\em trace} ({{\cal G}}{\boldsymbol\nu}) \qquad\mbox{and}\qquad {{\cal G}}^\ast {{\bf u}}= \mbox{\em trace} ({{\cal D}}^\ast {{\bf u}}).$$ [Proof.]{} (i) Using , we have that $$({{\cal D}}^\ast a)({{\bf x}},{{\bf y}}) = \int_{{\mathbb{R}^n}}a{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\,d{{\bf z}}= a\int_{{\mathbb{R}^n}}{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\,d{{\bf z}}={\bf0} \qquad\forall\, a.$$ so that $({{\cal D}}^\ast a)({{\bf x}},{{\bf y}}) ={\bf0}$. The other two results in are proved in a similar manner. \(ii) We have that $$\begin{aligned} {{\cal D}}({{\cal D}}^\ast {\bf u})- {{\cal G}}({{\cal G}}^\ast {\bf u})& =\int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3}({{\cal D}}^\ast {\bf u})({{\bf y}},{{\bf z}}){\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\\& \qquad- \int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3}({{\cal G}}^\ast {\bf u})({{\bf y}},{{\bf z}}) {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\\& = \int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3}\Big( {{\bf u}}({{\bf w}})\otimes{\boldsymbol\kappa}({{\bf w}},{{\bf y}},{{\bf z}})\Big) {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\, d{{\bf w}}d{{\bf z}}d{{\bf y}}\\& \qquad- \int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3} \Big({{\bf u}}({{\bf w}})\cdot{\boldsymbol\kappa}({{\bf w}},{{\bf y}},{{\bf z}})\Big) {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf w}}d{{\bf z}}d{{\bf y}}\\&= \int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3}\Big[ {{\bf u}}({{\bf w}})\Big({\boldsymbol\kappa}({{\bf w}},{{\bf y}},{{\bf z}}) \cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\Big) \\& \qquad -\Big({{\bf u}}({{\bf w}})\cdot{\boldsymbol\kappa}({{\bf w}},{{\bf y}},{{\bf z}})\Big) {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\Big]\,d{{\bf w}}d{{\bf z}}d{{\bf y}}\\& =\int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3} \int_{{\mathbb{R}}^3} {\boldsymbol\kappa}({{\bf w}},{{\bf y}},{{\bf z}})\times{{\bf u}}({{\bf w}}) \times {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf w}}d{{\bf z}}d{{\bf y}}\\& =\int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3} \Big[\int_{{\mathbb{R}}^3} {\boldsymbol\kappa}({{\bf w}},{{\bf y}},{{\bf z}})\times{{\bf u}}({{\bf w}}) \,d{{\bf w}}\Big] \times {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\\& =\int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3} ({{\cal C}}^\ast {{\bf u}})({{\bf y}},{{\bf z}}) \times {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}={{\cal C}}({{\cal C}}^\ast{{\bf u}}) , \end{aligned}$$ where the first two equalities follow from the definitions of the operators ${{\cal D}}$, ${{\cal D}}^\ast$, ${{\cal G}}$, and ${{\cal G}}^\ast$, the third and fourth equalities follow from the standard vector identities $({\bf a}\otimes{\bf b})\cdot{\bf c} = {\bf a}({\bf b}\cdot{\bf c})$ and ${\bf a}\times({\bf b}\times{\bf c}) = {\bf b}({\bf a}\cdot{\bf c}) - {\bf c}({\bf a}\cdot{\bf b})$, respectively, the fifth equality is a tautology, and the last two inequalities follow from the definitions of the operators ${{\cal C}}^\ast$ and ${{\cal C}}$. The second identity in is proved in a similar manner. \(iii) The proofs of the identities in follow easily from the definitions of the operators and of the matrix trace, e.g., $$\begin{aligned} \mbox{trace} ({{\cal G}}{\boldsymbol\nu}) &= \mbox{trace}\Big(\int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} {\boldsymbol\nu}({{\bf y}},{{\bf z}})\otimes {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\Big) \\&= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} \mbox{trace}\Big({\boldsymbol\nu}({{\bf y}},{{\bf z}})\otimes {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\Big)\,d{{\bf z}}d{{\bf y}}\\& = \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} {\boldsymbol\nu}({{\bf y}},{{\bf z}})\cdot {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}={{\cal D}}{\boldsymbol\nu}\end{aligned}$$ with the proof of the second identity in following in a similar manner. $\Box$ Unlike the identities , the second set of identities do require additional conditions on the divergence kernel. \[ident2\] \[propident2\] [(i)]{} For $u({{\bf x}})=a$ and ${{\bf u}}({{\bf x}})={\bf a}$, where $a$ and ${\bf a}$ are scalar and vector constants, respectively, we have $$\label{ident2a} ({{\cal D}}{\bf a})({{\bf x}}) =0,\qquad ({{\cal G}}a)({{\bf x}}) ={\bf 0},\qquad\mbox{and}\qquad ({{\cal C}}{\bf a})({{\bf x}}) ={\bf 0}$$ if and only if $$\label{ident2b} \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}={\bf 0} \qquad \forall\,{{\bf x}}.$$ [(ii)]{} For any $v({{\bf x}})$ and ${{\bf u}}({{\bf x}})$, we have that $$\label{ident2c} {{\cal D}}\big({{\cal C}}^\ast{{\bf u}}\big)({{\bf x}})=0\qquad\mbox{and}\qquad {{\cal C}}\big({{\cal D}}^\ast v\big)({{\bf x}})={\bf0}$$ if and only if $$\label{ident2d} \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\times{\boldsymbol\kappa}({{\bf w}},{{\bf y}},{{\bf z}}) \,d{{\bf z}}d{{\bf y}}={\bf 0} \qquad\forall\,{{\bf x}},\,{{\bf w}}.$$ [(iii)]{} For any ${\boldsymbol\nu}({{\bf x}},{{\bf y}})$ and $\eta({{\bf x}},{{\bf y}})$ we have that $$\label{ident2e} {{\cal G}}^\ast \big({{\cal C}}{\boldsymbol\nu}\big)({{\bf x}},{{\bf y}})=0\qquad\mbox{and}\qquad {{\cal C}}^\ast\big({{\cal G}}\eta\big)({{\bf x}},{{\bf y}})=0$$ if and only if $$\label{ident2f} \int_{{\mathbb{R}^n}}{\boldsymbol\kappa}({{\bf z}},{{\bf w}},{{\bf r}})\times{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}}) \,d{{\bf z}}= {\bf0} \qquad\forall\,{{\bf x}},\,{{\bf y}},\,{{\bf w}},\,{{\bf r}}.$$ [Proof.]{} (i) For ${{\cal D}}{\bf a}$, we have $$({{\cal D}}{\bf a})({{\bf x}}) = \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}{\bf a}\cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf z}}={\bf a}\cdot\int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\qquad\forall\, {\bf a}$$ so that $({{\cal D}}{\bf a})({{\bf x}}) = 0$ if and only if holds. The other two results in are proved in a similar manner. [(ii)]{} From the definitions of the operators ${{\cal C}}$ and ${{\cal D}}^\ast$, we have that $$\begin{aligned} {{\cal D}}\big({{\cal C}}^\ast {{\bf u}}\big)({{\bf x}}) &=\int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3} ({{\cal C}}^\ast {{\bf u}})({{\bf y}},{{\bf z}})\cdot {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\\& =\int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3} \Big[ \int_{{\mathbb{R}}^3} {\boldsymbol\kappa}({{\bf w}},{{\bf y}},{{\bf z}}) \times{\bf u}({{\bf w}}) \,d{{\bf w}}\Big]\cdot {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\\& =\int_{{\mathbb{R}}^3} {{\bf u}}({{\bf w}})\cdot\Big[ \int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3} {\boldsymbol\kappa}({{\bf w}},{{\bf y}},{{\bf z}})\times {\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\Big]\,d{{\bf w}}. \end{aligned}$$ Because ${{\bf u}}({{\bf x}})$ is arbitrary, the first result in follows; the second results follows in a similar manner. [(iii)]{} From the definitions of the operators ${{\cal G}}^\ast$ and ${{\cal C}}$, we have that $$\begin{aligned} {{\cal G}}^\ast\big({{\cal C}}{\boldsymbol\nu}\big)({{\bf x}},{{\bf y}}) &=\int_{{\mathbb{R}}^3}({{\cal C}}{\boldsymbol\nu})({{\bf z}})\cdot{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\,d{{\bf z}}\\&= \int_{{\mathbb{R}}^3}\Big[ \int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3} {\boldsymbol\nu}({{\bf w}},{{\bf r}})\times{\boldsymbol\kappa}({{\bf z}},{{\bf w}},{{\bf r}}) \,d{{\bf w}}d{{\bf r}}\Big]\cdot{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\,d{{\bf z}}\\&= \int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3} {\boldsymbol\nu}({{\bf w}},{{\bf r}})\cdot\Big[\int_{{\mathbb{R}}^3} {\boldsymbol\kappa}({{\bf z}},{{\bf w}},{{\bf r}})\times{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}}) \,d{{\bf z}}\Big]\,d{{\bf w}}d{{\bf r}}. \end{aligned}$$ Because ${\boldsymbol\nu}({{\bf x}},{{\bf y}})$ is arbitrary, the first result in follows; the second results follows in a similar manner. $\Box$ ### Theorems of the nonlocal calculus We next consider the nonlocal analog of the divergence theorem of the classical vector calculus. \[divthmthm\] Let $\Omega\subseteq{{\mathbb{R}^n}}$. Then, $$\label{divthmnld} \int_\Omega ({{\cal D}}{\boldsymbol\nu})({{\bf x}})\,d{{\bf x}}= - \int_{{{\mathbb{R}^n}}\setminus\Omega} ({{\cal D}}{\boldsymbol\nu})({{\bf x}})\,d{{\bf x}}.$$ [Proof.]{} The proof of is basically a tautology because we defined the nonlocal operator ${{\cal D}}$ so that it satisfies a nonlocal divergence theorem. In fact, follows easily from .$\Box$ [Remark.]{} The integral of the classical local divergence of a vector over and arbitrary domain $\Omega$ is equal to the flux of that vector out of $\Omega$ which is given by an integral over the boundary of $\Omega$ of the normal component of the vector. Nonlocality results in the flux out of $\Omega$ to be given by a volume integral over the complement of $\Omega$ as is indicated in .$\Box$ [Remark.]{} Analogous theorems hold for the operators ${{\cal G}}$ and ${{\cal C}}$, i.e., $\int_\Omega ({{\cal G}}\eta)({{\bf x}})\,d{{\bf x}}= - \int_{{{\mathbb{R}^n}}\setminus\Omega} ({{\cal G}}\eta)({{\bf x}})\,d{{\bf x}}$ and $\int_\Omega ({{\cal C}}{\boldsymbol\eta})({{\bf x}})\,d{{\bf x}}= - \int_{{\mathbb{R}}^3 \setminus\Omega} ({{\cal D}}{\boldsymbol\eta})({{\bf x}})\,d{{\bf x}}$.$\Box$ Finally, we derive the nonlocal Green’s identities which again mimic the classical Green’s identities of the classical vector calculus. We begin with an integration by parts formula. \[greenide\] Given any functions $u({{\bf x}})$ and ${\boldsymbol\nu}({{\bf x}},{{\bf y}})$, we have that $$\label{greenibp} \int_{{\mathbb{R}^n}}u({{\bf x}}) {{\cal D}}({\boldsymbol\nu})({{\bf x}})\,d{{\bf x}}- \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}{\boldsymbol\nu}({{\bf x}},{{\bf y}})\cdot ({{\cal D}}^\ast u)({{\bf x}},{{\bf y}}) \, d{{\bf y}}d{{\bf x}}=0.$$ [Proof.]{} We have that $$\begin{aligned} 0 &= \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}u({{\bf x}}) {\boldsymbol\nu}({{\bf y}},{{\bf z}})\cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}d{{\bf x}}\\&\qquad - \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}u({{\bf x}}){\boldsymbol\nu}({{\bf y}},{{\bf z}})\cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}d{{\bf x}}\\&= \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}u({{\bf x}}) {\boldsymbol\nu}({{\bf y}},{{\bf z}})\cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}d{{\bf x}}\\&\qquad - \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}u({{\bf z}}){\boldsymbol\nu}({{\bf x}},{{\bf y}})\cdot{\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\,d{{\bf z}}d{{\bf y}}d{{\bf x}}\\&= \int_{{\mathbb{R}^n}}u({{\bf x}}) \Big[\int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}{\boldsymbol\nu}({{\bf y}},{{\bf z}})\cdot{\boldsymbol\kappa}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\Big]\,d{{\bf x}}\\&\qquad - \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}{\boldsymbol\nu}({{\bf x}},{{\bf y}})\cdot \Big[\int_{{\mathbb{R}^n}}u({{\bf z}}){\boldsymbol\kappa}({{\bf z}},{{\bf x}},{{\bf y}})\,d{{\bf z}}\Big]\, d{{\bf y}}d{{\bf x}}\\& = \int_{{\mathbb{R}^n}}u({{\bf x}}) {{\cal D}}({\boldsymbol\nu})({{\bf x}})\,d{{\bf x}}- \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}{\boldsymbol\nu}({{\bf x}},{{\bf y}})\cdot ({{\cal D}}^\ast u)({{\bf x}},{{\bf y}}) \, d{{\bf y}}d{{\bf x}}\end{aligned}$$ where the first equality is a tautology, the second equality follows from a cyclic replacement of the integration variables (${{\bf x}}$, ${{\bf y}}$, ${{\bf z}}$ $\to$ ${{\bf z}}$, ${{\bf x}}$, ${{\bf y}}$) in the second integral, the third equality is again a tautology, and the last follows from the definition of the operators ${{\cal D}}$ and ${{\cal D}}^$. Thus, is proven. $\Box$ \[greenidenthm\] Given functions $u({{\bf x}})$ and $v({{\bf x}})$, we have the [nonlocal Green’s first identity]{} \[greeniden\] $$\label{greeniden1} \int_{{\mathbb{R}^n}}u {{\cal D}}({{\cal D}}^\ast v)\,d{{\bf x}}- \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}({{\cal D}}^\ast v)\cdot ({{\cal D}}^\ast u) \, d{{\bf y}}d{{\bf x}}=0$$ the [nonlocal Green’s second identity]{} $$\label{greeniden2} \int_{{\mathbb{R}^n}}u {{\cal D}}({{\cal D}}^\ast v)\,d{{\bf x}}- \int_{{\mathbb{R}^n}}v {{\cal D}}({{\cal D}}^\ast u)\,d{{\bf x}}=0.$$ [Proof.]{} Setting ${\boldsymbol\nu}({{\bf x}},{{\bf y}}) = ({{\cal D}}^\ast v)({{\bf x}},{{\bf y}})$ in easily results in . Then, follows by reversing the roles of $u$ and $v$ in and then subtracting the result from . $\Box$ [Remark.]{} Analogous theorems hold for the pairs of operators ${{\cal G}}$ and ${{\cal G}}^\ast$ and ${{\cal C}}$ and ${{\cal C}}^\ast$. The following results are obvious consequences of and . Given a subdomain $\Omega\subseteq{{\mathbb{R}^n}}$ and functions $u({{\bf x}})$ and $v({{\bf x}})$, we have that \[greeniden\] $$\label{greeniden1aa} \int_\Omega u {{\cal D}}({{\cal D}}^\ast v)\,d{{\bf x}}- \int_{{\mathbb{R}^n}}\int_{{\mathbb{R}^n}}({{\cal D}}^\ast v)\cdot ({{\cal D}}^\ast u) \, d{{\bf y}}d{{\bf x}}= - \int_{{{\mathbb{R}^n}}\setminus\Omega} u {{\cal D}}({{\cal D}}^\ast v)\,d{{\bf x}}$$ and $$\label{greeniden2bb} \int_\Omega u {{\cal D}}({{\cal D}}^\ast v)\,d{{\bf x}}- \int_\Omega v {{\cal D}}({{\cal D}}^\ast u)\,d{{\bf x}}= - \int_{{{\mathbb{R}^n}}\setminus\Omega} u {{\cal D}}({{\cal D}}^\ast v)\,d{{\bf x}}+ \int_{{{\mathbb{R}^n}}\setminus\Omega} v {{\cal D}}({{\cal D}}^\ast u)\,d{{\bf x}}\hfill\Box.$$ Special case of the nonlocal operators {#sec_special} ====================================== The general forms of the nonlocal divergence operator and its adjoint operator are given in Definition \[ddiv\] and Proposition \[propadj\]. Here, we consider a simplified version of these operators which leads to the nonlocal vector calculus of [@dglz-nlc] and which has proven to be useful [@dglz-nld; @dglz-ps]. The simplification is effected by a special case of the Schwartz kernel given by $$\label{specker} {\boldsymbol\kappa}_{{\boldsymbol\alpha}}({{\bf x}},{{\bf y}},{{\bf z}}) = \delta({{\bf x}}-{{\bf z}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}}) + \delta({{\bf x}}-{{\bf y}}){\boldsymbol\alpha}({{\bf x}},{{\bf z}})$$ for an vector-valued function ${\boldsymbol\alpha}({{\bf x}},{{\bf y}})\in[L^1({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k$. Here, $\delta(\cdot)$ denotes the Dirac delta function. First, we verify that ${\boldsymbol\kappa}_\alpha$ satisfies . \[skdiv\] The specialized Schwartz kernel ${\boldsymbol\kappa}_{{\boldsymbol\alpha}}$ satisfies , i.e., $$\label{divthm4a} \int_{{{\mathbb{R}^n}}}{\boldsymbol\kappa}_{{\boldsymbol\alpha}}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf x}}= 0,$$ if and only if ${\boldsymbol\alpha}({{\bf x}},{{\bf y}})$ is antisymmetric, i.e., if and only if ${\boldsymbol\alpha}({{\bf x}},{{\bf y}}) = -{\boldsymbol\alpha}({{\bf y}},{{\bf x}})$ for all ${{\bf x}}$ and ${{\bf y}}$. [Proof.]{} We have $$\begin{aligned} \int_{{{\mathbb{R}^n}}}{\boldsymbol\kappa}_{{\boldsymbol\alpha}}({{\bf x}},{{\bf y}},{{\bf z}})\,d{{\bf x}}&= \int_{{{\mathbb{R}^n}}}\big(\delta({{\bf x}}-{{\bf z}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}}) + \delta({{\bf x}}-{{\bf y}}){\boldsymbol\alpha}({{\bf x}},{{\bf z}})\big)\,d{{\bf x}}\\&= {\boldsymbol\alpha}({{\bf z}},{{\bf y}}) + {\boldsymbol\alpha}({{\bf y}},{{\bf z}}) \end{aligned}$$ so that the result follows. $\Box$ [Remark.]{} In [@dglz-nld; @dglz-nlc; @dglz-ps], the antisymmetry of ${\boldsymbol\alpha}({{\bf x}},{{\bf y}})$ is [assumed.]{} Here, we have shown that this condition is necessary and sufficient for the operator ${{\cal D}}$ to be a nonlocal divergence operator in the sense that (and therefore ) is satisfied. $\Box$ \[thmsdiv\] For the specialized kernel ${\boldsymbol\kappa}_{{\boldsymbol\alpha}}$ given by , the action of the nonlocal divergence operator $({{\cal D}}_{{\boldsymbol\alpha}}{\boldsymbol\nu})({{\bf x}}):{{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}\rightarrow{{D'({{\mathbb{R}^n}})}}$ on a function ${\boldsymbol\nu}({{\bf x}},{{\bf y}})\in {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}$ is given by $$\label{sgrad} ({{\cal D}}_{{\boldsymbol\alpha}}{\boldsymbol\nu})({{\bf x}}) = \int_{{{\mathbb{R}^n}}}\big({\boldsymbol\nu}({{\bf x}},{{\bf y}}) + {\boldsymbol\nu}({{\bf y}},{{\bf x}})\big)\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}.$$ Moreover, the action of the adjoint operator $({{\cal D}}^\ast_{{\boldsymbol\alpha}} u)({{\bf x}},{{\bf y}}): {{C_c^{\infty}({{\mathbb{R}^n}})}}\rightarrow {{[D'({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}}$ on a function $u({{\bf x}})\in {{C_c^{\infty}({{\mathbb{R}^n}})}}$ is given by $$\label{sgradadj} ({{\cal D}}_{{\boldsymbol\alpha}}^\ast u)({{\bf x}},{{\bf y}}) = -\big(u({{\bf y}}) - u({{\bf x}})\big){\boldsymbol\alpha}({{\bf x}},{{\bf y}}) .$$ [Proof.]{} Setting ${\boldsymbol\kappa}={\boldsymbol\kappa}_{{\boldsymbol\alpha}}$ in , we have $$\begin{aligned} \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}{\boldsymbol\kappa}_{{\boldsymbol\alpha}}&({{\bf x}},{{\bf y}},{{\bf z}})\cdot\nu({{\bf y}},{{\bf z}})\,d{{\bf z}}d{{\bf y}}\\ &= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\Big(\delta({{\bf x}}-{{\bf z}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}}) + \delta({{\bf x}}-{{\bf y}}){\boldsymbol\alpha}({{\bf x}},{{\bf z}})\Big)\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}})\, d{{\bf z}}d{{\bf y}}\\ &= \int_{{{\mathbb{R}^n}}}{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\cdot{\boldsymbol\nu}({{\bf y}},{{\bf x}})\,d{{\bf y}}+ \int_{{{\mathbb{R}^n}}}{\boldsymbol\alpha}({{\bf x}},{{\bf z}})\cdot{\boldsymbol\nu}({{\bf x}},{{\bf z}})\,d{{\bf z}}\\ &=\int_{{{\mathbb{R}^n}}}\big({\boldsymbol\nu}({{\bf x}},{{\bf y}})+ {\boldsymbol\nu}({{\bf y}},{{\bf x}})\big) \cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}}) \,d{{\bf y}}, \end{aligned}$$ where the last equality follows by replacing the integration variable from ${{\bf z}}$ to ${{\bf y}}$ in the second integral preceding the equality. Thus, we have . Setting ${\boldsymbol\kappa}={\boldsymbol\kappa}_{{\boldsymbol\alpha}}$ in , we have $$\begin{aligned} \int_{{{\mathbb{R}^n}}}u({{\bf z}}){\boldsymbol\kappa}_{{\boldsymbol\alpha}}({{\bf z}},{{\bf x}},{{\bf y}})\,d{{\bf z}}&= \int_{{{\mathbb{R}^n}}}u({{\bf z}})\Big(\delta({{\bf z}}-{{\bf y}}){\boldsymbol\alpha}({{\bf z}},{{\bf x}}) + \delta({{\bf z}}-{{\bf x}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}})\Big)d{{\bf z}}\\ &= u({{\bf y}}){\boldsymbol\alpha}({{\bf y}},{{\bf x}}) + u({{\bf x}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}}) = -\big(u({{\bf y}}) - u({{\bf x}})\big){\boldsymbol\alpha}({{\bf x}},{{\bf y}}) , \end{aligned}$$ completing the proof of .$\Box$ [Remark.]{} For the kernel ${\boldsymbol\kappa}_{{\boldsymbol\alpha}}$, we have $$\label{mmmmmm} \begin{aligned} ({{\cal D}}_{{\boldsymbol\alpha}}{\boldsymbol\Psi})({{\bf x}}) &= \int_{{{\mathbb{R}^n}}}\big({\boldsymbol\Psi}({{\bf y}},{{\bf x}}) + {\boldsymbol\Psi}({{\bf x}},{{\bf y}})\big) {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}\\[1ex] ({{\cal D}}^_{{\boldsymbol\alpha}}{{\bf u}})({{\bf x}},{{\bf y}}) &= -\big({{\bf u}}({{\bf y}}) - {{\bf u}}({{\bf x}})\big)\otimes{\boldsymbol\alpha}({{\bf x}},{{\bf y}}) \\[1ex] ({{\cal G}}_{{\boldsymbol\alpha}}\eta)({{\bf x}}) &= \int_{{{\mathbb{R}^n}}}\big(\eta({{\bf y}},{{\bf x}}) + \eta({{\bf x}},{{\bf y}})\big){\boldsymbol\alpha}({{\bf x}},{{\bf y}})\, d{{\bf y}}\\[1ex] ({{\cal G}}_{{\boldsymbol\alpha}}^* {{\bf u}})({{\bf x}},{{\bf y}}) & = -\big({{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}}) = \mbox{trace}\, ({{\cal D}}^_{{\boldsymbol\alpha}} {{\bf u}}) \\[1ex] (\overline{{{\cal G}}^_{{\boldsymbol\alpha}}}{{\bf u}})({{\bf x}}) &= -\int_{{{\mathbb{R}^n}}}\big({{\bf u}}({{\bf z}}) - {{\bf u}}({{\bf x}})\big) \cdot {\boldsymbol\alpha}({{\bf x}},{{\bf z}}) \,d{{\bf z}}\\[1ex] ({{\cal C}}_{{\boldsymbol\alpha}}{\boldsymbol\nu})({{\bf x}}) &= \int_{{{\mathbb{R}}^3}}{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\times\big({\boldsymbol\nu}({{\bf y}},{{\bf x}}) + {\boldsymbol\nu}({{\bf x}},{{\bf y}})\big)\, d{{\bf y}}\\[1ex] ({{\cal C}}_{{\boldsymbol\alpha}}^* {{\bf u}})({{\bf x}},{{\bf y}}) & = -\big({{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\times{\boldsymbol\alpha}({{\bf x}},{{\bf y}}) \\[1ex] ({{\cal D}}_{{\boldsymbol\alpha}}{{\cal D}}_{{\boldsymbol\alpha}}^\ast u)({{\bf x}}) &=-2 \int_{{{\mathbb{R}^n}}} \big(u({{\bf y}}) - u({{\bf x}})\big) {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\cdot {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}\end{aligned}$$ for a tensor-valued ${\boldsymbol\Psi}({{\bf x}},{{\bf y}})$, a vector valued function ${{\bf u}}({{\bf x}})$, and a scalar-valued functions $\eta({{\bf x}},{{\bf y}})$. $\Box$ We now want to examine the identities of Section \[sec:ident\] in the context of the specialized kernel ${\boldsymbol\kappa}_{{\boldsymbol\alpha}}({{\bf x}},{{\bf y}},{{\bf z}})$. Instead of verifying the assumptions of Proposition \[propident2\], we directly examine those identities for the kernel . Of course, because of Propositions \[propident1\] and \[skdiv\], we have all the identities hold for the operators ${{\cal D}}_{{\boldsymbol\alpha}}$, ${{\cal D}}_{{\boldsymbol\alpha}}^\ast$, ${{\cal G}}_{{\boldsymbol\alpha}}$, etc. Thus, we need only address the identities . From the definitions of the relevant operators and the antisymmetry of ${\boldsymbol\alpha}({{\bf x}},{{\bf y}})$, we have that $$\begin{aligned} (&{{\cal D}}_{{\boldsymbol\alpha}} {{\cal C}}_{{\boldsymbol\alpha}}^\ast{{\bf u}})({{\bf x}}) \\&=\int_{{{\mathbb{R}}^3}} \Big({\boldsymbol\alpha}({{\bf x}},{{\bf y}}) \times \big( {{\bf u}}({{\bf x}}) - {{\bf u}}({{\bf y}}) \big) +{\boldsymbol\alpha}({{\bf y}},{{\bf x}}) \times \big( {{\bf u}}({{\bf y}}) - {{\bf u}}({{\bf x}}) \big)\Big) \cdot {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}\\&= 2\int_{{{\mathbb{R}}^3}} \Big({\boldsymbol\alpha}({{\bf x}},{{\bf y}}) \times \big( {{\bf u}}({{\bf x}}) - {{\bf u}}({{\bf y}}) \big) \Big) \cdot {\boldsymbol\alpha}({{\bf x}},{{\bf y}}) \,d{{\bf y}}= {\bf0}. \end{aligned}$$ Similarly, one can show that $({{\cal C}}_{{\boldsymbol\alpha}} {{\cal D}}_{{\boldsymbol\alpha}}^\ast{{\bf u}})({{\bf x}})={\bf 0}$. Also, we have that $$\begin{aligned} ({{\cal G}}_{{\boldsymbol\alpha}}^\ast &{{\cal C}}_{{\boldsymbol\alpha}}{\boldsymbol\nu})({{\bf x}},{{\bf y}}) \\&=-\int_{{{\mathbb{R}}^3}}\Big( {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\times\big({\boldsymbol\nu}({{\bf x}},{{\bf y}})+{\boldsymbol\nu}({{\bf y}},{{\bf x}})\big) \\& \qquad\qquad- {\boldsymbol\alpha}({{\bf y}},{{\bf x}})\times\big({\boldsymbol\nu}({{\bf y}},{{\bf x}})+{\boldsymbol\nu}({{\bf x}},{{\bf y}})\big) \Big)\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}\\&= -2\int_{{{\mathbb{R}}^3}}\Big( {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\times\big({\boldsymbol\nu}({{\bf x}},{{\bf y}})+{\boldsymbol\nu}({{\bf y}},{{\bf x}})\big) \Big)\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}={\bf0} \end{aligned}$$ and similarly that $({{\cal C}}^\ast{{\cal G}}\eta)({{\bf x}},{{\bf y}}) = {\bf 0}$. Finally, we have that, in general, $$({{\cal D}}{\bf a})({{\bf x}})= 2{\bf a}\cdot\int_{{{\mathbb{R}^n}}} {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}\ne0$$ and likewise $({{\cal G}}a)({{\bf x}})\ne0$ and $({{\cal C}}{\bf a})({{\bf x}})\ne{\bf 0}$. The following proposition summarizes these results. In general, for the specialized Schwartz kernel ${\boldsymbol\kappa}_{{\boldsymbol\alpha}}$, we have that , , , , and hold, but does not hold. $\Box$ The peridynamics model for solid mechanics {#sec_peridynamics} ========================================== We consider the state-based peridynamics model introduced in [@Silling2007] for the dynamics of isotropic heterogeneous solids. To simplify the presentation, we provide a direct description of this model without adhering to the notation used in [@Silling2007]. Our goal is to show how the peridynamics model can be expressed in terms of the nonlocal operators introduced and discussed in Section \[gennlc\]. The peridynamics model for solid mechanics {#peridyn} ------------------------------------------ Let $\Omega$ denote a domain in ${\mathbb{R}}^3$, ${{\bf u}}({{\bf x}},t)$ the displacement vector field, $\rho({{\bf x}})$ the mass density, and $b({{\bf x}},t)$ a prescribed body force density. Let $B_\varepsilon({{\bf x}})$ denote the ball centered at ${{\bf x}}$ having radius $\varepsilon$; here, $\varepsilon$ denotes the peridynamics horizon. Then, the peridynamic equation of motion is given by $$\label{pd1} \rho({{\bf x}}) \ddot{{{\bf u}}}({{\bf x}},t) = \int_{B_\varepsilon({{\bf x}})}\big( {{\bf T}}({{\bf x}},{{\bf y}}-{{\bf x}}) - {{\bf T}}({{\bf y}}, {{\bf x}}- {{\bf y}})\big) \,d{{\bf y}}+ {{\bf b}}({{\bf x}},t),$$ where $$\label{pd2} {{\bf T}}({{\bf x}},{{\bf y}}-{{\bf x}}) = {{\sigma}}({{\bf x}},{{\bf y}}){\boldsymbol\gamma}({{\bf x}},{{\bf y}})$$ with $$\label{pd3} {\boldsymbol\gamma}({{\bf x}},{{\bf y}}) = \frac{{{\bf u}}({{\bf y}}) + {{\bf y}}- ({{\bf u}}({{\bf x}}) + {{\bf x}})}{\|{{\bf u}}({{\bf y}}) + {{\bf y}}- ({{\bf u}}({{\bf x}}) + {{\bf x}})\|}$$ and $$\label{pd4} \begin{aligned} {{\sigma}}&({{\bf x}},{{\bf y}}) = \frac{3k({{\bf x}})}{m} w(\|{{\bf y}}-{{\bf x}}\|) \|{{\bf y}}-{{\bf x}}\| \theta({{\bf x}}) \\ &+ \frac{15\mu({{\bf x}})}{m} w(\|{{\bf y}}- {{\bf x}}\|)\Big(\|{{\bf u}}({{\bf y}}) + {{\bf y}}- ({{\bf u}}({{\bf x}}) + {{\bf x}})\| - \|{{\bf y}}-{{\bf x}}\| -\frac{1}{3}\|{{\bf y}}-{{\bf x}}\| \theta({{\bf x}}) \Big). \end{aligned}$$ In –, ${\boldsymbol\gamma}$ represents the direction of the force density that the particle at position ${{\bf y}}$ exerts on the particle at position ${{\bf x}}$ and ${{\sigma}}$ represents the magnitude of that force density. The first term in ${{\sigma}}$ is the hydrostatic (or isotropic) part whereas the second term represents the deviatoric part. The functions $k({{\bf x}})$ and $\mu({{\bf x}})$ denote the bulk and shear moduli, respectively, and $\theta({{\bf x}})$ denotes the volumetric change and is given by $$\theta({{\bf x}}) = \frac{3}{m} \Big( \int_{B_\varepsilon({{\bf x}})} w(\|{{\bf z}}-{{\bf x}}\|)\|{{\bf z}}-{{\bf x}}\|\, \|{{\bf u}}({{\bf z}}) + {{\bf z}}- ({{\bf u}}({{\bf x}}) + {{\bf x}})\| \,d{{\bf z}}-m\Big),$$ The radial function $w$ is given by $$w(\|\xi\|) = \left\{\begin{aligned} \frac{1}{\|{\boldsymbol\xi}\|^r} \qquad& \mbox{if $\|{\boldsymbol\xi}\|<\delta$} \\ 0 \qquad& \text{otherwise} \end{aligned} \right.$$ and $$m = \int_{\Omega} w(\|{\boldsymbol\xi}\|) \|{\boldsymbol\xi}\|^2 d\xi = \int_{B_{\delta}(0)} \|{\boldsymbol\xi}\|^{2-r} d{\boldsymbol\xi}= 4\pi\frac{\delta^{5-r}}{5-r} \qquad\text{for $r<5$}.$$ Note that when $r<5$, $m$ is finite. For example, when $r=2$, $m = \frac{4}{3}\pi\delta^3 = \|B_{\delta}(0)\|$. Let ${\boldsymbol\eta}({{\bf x}},{{\bf y}})={{\bf u}}({{\bf y}}) - {{\bf u}}({{\bf x}})$ denote the relative displacement. We linearize the peridynamic equation of motion with respect to small relative displacements, i.e., for $\|{\boldsymbol\eta}\|\ll1$, as discussed in [@Silling2010] . Observe that, in terms of ${\boldsymbol\eta}$, $$\theta({{\bf x}}) = \frac{3}{m}\int_{B_\varepsilon(0)} w(\|{\boldsymbol\zeta}\|)\|{\boldsymbol\zeta}\| (\|{\boldsymbol\eta}+{\boldsymbol\zeta}\|-\|{\boldsymbol\zeta}\|)\,d{\boldsymbol\zeta}$$ and thus $$\frac{\partial\theta}{\partial\eta_i}= \frac{3}{m}\int_{B_\varepsilon(0)} w(\|{\boldsymbol\zeta}\|)\|{\boldsymbol\zeta}\| \frac{\eta_i+\zeta_i}{\|{\boldsymbol\eta}+{\boldsymbol\zeta}\|}\,d{\boldsymbol\zeta}\qquad\mbox{for $i=1,2,3$}$$ so that $$\nabla_{{\boldsymbol\eta}}\theta\|_{{\boldsymbol\eta}={\bf0}} = \frac{3}{m}\int_{B_\varepsilon(0)} w(\|{\boldsymbol\zeta}\|) {\boldsymbol\zeta}\,d{\boldsymbol\zeta}.$$ Then, because $\theta=0$ when ${\boldsymbol\eta}={\bf0}$, we have that $$\theta_{lin}({{\bf x}}) = \frac{3}{m}\int_{B_\varepsilon(0)} w(\|{\boldsymbol\zeta}\|) {\boldsymbol\zeta}\cdot{\boldsymbol\eta}\,d{\boldsymbol\zeta}= \frac{3}{m}\int_{B_\varepsilon(0)} w(\|{{\bf z}}-{{\bf x}}\|) ({{\bf z}}-{{\bf x}})\cdot\big( {{\bf u}}({{\bf z}}) - {{\bf u}}({{\bf x}})\big)\,d{{\bf z}},$$ where $ \theta_{lin}$ denotes $\theta$ linearized about ${\boldsymbol\eta}={\bf 0}$. Similarly, we find that $$\label{siglin} \begin{aligned} {{\sigma}}_{lin}({{\bf x}},{{\bf y}}) = \frac{3}{m}k({{\bf x}})&w(\|{\boldsymbol\xi}\|)\|{\boldsymbol\xi}\| \frac{3}{m}\int_{B_\varepsilon(0)} w(\|{\boldsymbol\zeta}\|) {\boldsymbol\zeta}\cdot{\boldsymbol\eta}\,d{\boldsymbol\zeta}\\[1ex] &+ \frac{15}{m}\mu({{\bf x}}) w(\|{\boldsymbol\xi}\|) \Big( \frac{{\boldsymbol\xi}\cdot{\boldsymbol\eta}}{\|{\boldsymbol\xi}\|} - \frac{\|{\boldsymbol\xi}\|}{m} \int_{B_\varepsilon(0)} w(\|{\boldsymbol\zeta}\|) {\boldsymbol\zeta}\cdot{\boldsymbol\eta}\,d{\boldsymbol\zeta}\Big) \end{aligned}$$ and $$\label{betlin} \begin{aligned} {\boldsymbol\gamma}_{lin}({{\bf x}},{{\bf y}}) &= \frac{{\boldsymbol\xi}}{\|{\boldsymbol\xi}\|} + \Big(\frac{1}{\|{\boldsymbol\xi}\|} {\bf I} - \frac{{\boldsymbol\xi}\otimes{\boldsymbol\xi}}{\|{\boldsymbol\xi}\|^3}\Big){\boldsymbol\eta}\\&= \frac{{{\bf y}}-{{\bf x}}}{\|{{\bf y}}-{{\bf x}}\|} + \Big(\frac{1}{\|{{\bf y}}-{{\bf x}}\|} {\bf I} - \frac{({{\bf y}}-{{\bf x}})\otimes({{\bf y}}-{{\bf x}})}{\|{{\bf y}}-{{\bf x}}\|^3}\Big) \big( {{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big). \end{aligned}$$ Therefore, from , , and , and after ignoring higher-order terms in ${\boldsymbol\eta}$, the linearized force density is given by $$\label{lpd1} \begin{aligned} {{\bf T}}_{lin}({{\bf x}},{{\bf y}}) =\bigg[&\frac{15}{m}\mu({{\bf x}}) w(\|{{\bf y}}-{{\bf x}}\|)\frac{({{\bf y}}-{{\bf x}})\otimes({{\bf y}}-{{\bf x}})}{\|{{\bf y}}-{{\bf x}}\|^2}\bigg]\big( {{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big) \\& +\bigg[\frac{9}{m^2} w(\|{{\bf y}}-{{\bf x}}\|) \Big(k({{\bf x}})-\frac53\mu({{\bf x}})\Big) \\&\qquad \times\Big( \int_{B_\varepsilon({{\bf x}})} w(\|{{\bf z}}-{{\bf x}}\|) ({{\bf z}}-{{\bf x}})\cdot\big( {{\bf u}}({{\bf z}})-{{\bf u}}({{\bf x}})\big)\,d{{\bf z}}\Big)\bigg] ({{\bf y}}-{{\bf x}}). \end{aligned}$$ Let $$\label{lpd2} ({{\cal L}}{{\bf u}})({{\bf x}}) = \int_{B_\varepsilon({{\bf x}})} \Big({{\bf T}}_{lin}({{\bf x}},{{\bf y}})-{{\bf T}}_{lin}({{\bf y}},{{\bf x}}) \Big)\,d{{\bf y}}.$$ Then, the linearized peridynamic equation of motion for a heterogeneous, isotropic solid is given by $$\rho \ddot{{\bf u}}= {{\cal L}}{{\bf u}}+ {{\bf b}}.$$ The substitution of into yields $$\label{lpd3} \begin{aligned} (&{{\cal L}}{{\bf u}})({{\bf x}}) \\& = \int_{B_\varepsilon({{\bf x}})} \bigg[\frac{15}{m}\big(\mu({{\bf x}})+\mu({{\bf y}})\big) w(\|{{\bf y}}-{{\bf x}}\|)\frac{({{\bf y}}-{{\bf x}}) \otimes({{\bf y}}-{{\bf x}})}{\|{{\bf y}}-{{\bf x}}\|^2}\bigg]\big( {{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big) \,d{{\bf y}}\\&\qquad + \int_{B_\varepsilon({{\bf x}})}\int_{B_\varepsilon({{\bf x}})} \bigg[\frac{9}{m^2} \Big(k({{\bf x}})-\frac53\mu({{\bf x}})\Big) w(\|{{\bf y}}-{{\bf x}}\|)w(\|{{\bf z}}-{{\bf x}}\|) ({{\bf y}}-{{\bf x}}) \\&\qquad\qquad\qquad\qquad\qquad\qquad \otimes({{\bf z}}-{{\bf x}})\big( {{\bf u}}({{\bf z}})-{{\bf u}}({{\bf x}})\big)\Big] \,d{{\bf z}}d{{\bf y}}\\&\qquad + \int_{B_\varepsilon({{\bf x}})}\int_{B_\varepsilon({{\bf y}})} \bigg[\frac{9}{m^2} \Big(k({{\bf y}})-\frac53\mu({{\bf y}})\Big) w(\|{{\bf y}}-{{\bf x}}\|)w(\|{{\bf z}}-{{\bf y}}\|) ({{\bf y}}-{{\bf x}}) \\&\qquad\qquad\qquad\qquad\qquad\qquad \otimes({{\bf z}}-{{\bf y}})\big( {{\bf u}}({{\bf z}})-{{\bf u}}({{\bf y}})\big)\Big] \,d{{\bf z}}d{{\bf y}}. \end{aligned}$$ The following proposition shows that $({{\cal L}}{{\bf u}})({{\bf x}})$ can be written as an integral operator acting on the relative displacement ${{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})$ for some kernel ${{\bf C}}$. \[proplp\] The operator ${{\cal L}}$ given by can be written as $$\label{lpd4} ({{\cal L}}{{\bf u}})({{\bf x}})= \int_\Omega {{\bf C}}({{\bf x}},{{\bf y}}) \big( {{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\,d{{\bf y}},$$ where $${{\bf C}}({{\bf x}},{{\bf y}}) = {{\bf K}}({{\bf x}},{{\bf y}}) + {{\bf S}}({{\bf x}},{{\bf y}})$$ with $$\label{lpd5} {{\bf K}}({{\bf x}},{{\bf y}}) = \big(c_1({{\bf x}})+c_1({{\bf y}})\big) w(\|{{\bf y}}-{{\bf x}}\|)\frac{({{\bf y}}-{{\bf x}})\otimes({{\bf y}}-{{\bf x}})}{\|{{\bf y}}-{{\bf x}}\|^2} \chi_{B_\varepsilon({{\bf x}})}({{\bf y}})$$ and $$\label{lpd6} \begin{aligned} &{{\bf S}}({{\bf x}},{{\bf y}}) = \int_\Omega \Big[ c_2({{\bf z}}) w(\|{{\bf z}}-{{\bf x}}\|)w(\|{{\bf y}}-{{\bf z}}\|)({{\bf z}}-{{\bf x}})\otimes({{\bf y}}-{{\bf z}}) \chi_{B_\varepsilon({{\bf x}})}({{\bf z}})\chi_{B_\varepsilon({{\bf y}})}({{\bf z}}) \\&\qquad - c_2({{\bf y}}) w(\|{{\bf y}}-{{\bf x}}\|)w(\|{{\bf z}}-{{\bf y}}\|)({{\bf y}}-{{\bf x}})\otimes({{\bf z}}-{{\bf y}}) \chi_{B_\varepsilon({{\bf x}})}({{\bf y}})\chi_{B_\varepsilon({{\bf y}})}({{\bf z}}) \\&\qquad + c_2({{\bf x}}) w(\|{{\bf z}}-{{\bf x}}\|)w(\|{{\bf y}}-{{\bf x}}\|)({{\bf z}}-{{\bf x}})\otimes({{\bf y}}-{{\bf x}}) \chi_{B_\varepsilon({{\bf x}})}({{\bf y}})\chi_{B_\varepsilon({{\bf x}})}({{\bf z}}) \Big]\,d{{\bf z}}, \end{aligned}$$ where $$\label{lpd7} c_1({{\bf x}}) = \frac{15}{m}\mu({{\bf x}}),\qquad c_2({{\bf x}}) = \frac{9}{m^2} \Big(k({{\bf x}}) - \frac53\mu({{\bf x}})\Big),$$ and $\chi_{B_\varepsilon({{\bf x}})}$ denotes the indicator function of the set ${B_\varepsilon({{\bf x}})}$. [Proof.]{} It is obvious, with $c_1$ given by , that the first term in is equal to $\int_\Omega {{\bf K}}({{\bf x}},{{\bf y}}) \big( {{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\,d{{\bf y}}$. Thus, it remains to show that $\int_\Omega {{\bf S}}({{\bf x}},{{\bf y}})\big( {{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\,d{{\bf y}}$ is equal to the sum of the second and third terms in . We first write $$\label{lpd8} \int_\Omega {{\bf S}}({{\bf x}},{{\bf y}})\big( {{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\,d{{\bf y}}= \int_\Omega {{\bf S}}({{\bf x}},{{\bf y}}) {{\bf u}}({{\bf y}})\,d{{\bf y}}- \int_\Omega {{\bf S}}({{\bf x}},{{\bf y}}){{\bf u}}({{\bf x}})\,d{{\bf y}}.$$ For the first term in , we use to obtain $$\label{lpd9} \begin{aligned} &\int_\Omega {{\bf S}}({{\bf x}},{{\bf y}}){{\bf u}}({{\bf y}})\,d{{\bf y}}\\&\quad = \int_\Omega\int_\Omega \Big[ c_2({{\bf z}}) w(\|{{\bf z}}-{{\bf x}}\|)w(\|{{\bf y}}-{{\bf z}}\|)({{\bf z}}-{{\bf x}}) \\&\qquad\qquad\qquad\qquad\qquad \otimes({{\bf y}}-{{\bf z}}) \chi_{B_\varepsilon({{\bf x}})}({{\bf z}})\chi_{B_\varepsilon({{\bf y}})}({{\bf z}})\Big]{{\bf u}}({{\bf y}}) \,d{{\bf z}}d{{\bf y}}\\&\qquad - \int_\Omega\int_\Omega \Big[ c_2({{\bf y}}) w(\|{{\bf y}}-{{\bf x}}\|)w(\|{{\bf z}}-{{\bf y}}\|)({{\bf y}}-{{\bf x}}) \\&\qquad\qquad\qquad\qquad\qquad \otimes({{\bf z}}-{{\bf y}}) \chi_{B_\varepsilon({{\bf x}})}({{\bf y}})\chi_{B_\varepsilon({{\bf y}})}({{\bf z}})\Big]{{\bf u}}({{\bf y}}) \,d{{\bf z}}d{{\bf y}}\\&\qquad + \int_\Omega\int_\Omega \Big[ c_2({{\bf x}}) w(\|{{\bf z}}-{{\bf x}}\|)w(\|{{\bf y}}-{{\bf x}}\|)({{\bf z}}-{{\bf x}}) \\&\qquad\qquad\qquad\qquad\qquad \otimes({{\bf y}}-{{\bf x}}) \chi_{B_\varepsilon({{\bf x}})}({{\bf y}})\chi_{B_\varepsilon({{\bf x}})}({{\bf z}})\Big]{{\bf u}}({{\bf y}}) \,d{{\bf z}}d{{\bf y}}\\&\quad = \int_{B_\varepsilon({{\bf x}})}\int_{B_\varepsilon({{\bf y}})} \Big[ c_2({{\bf y}}) w(\|{{\bf y}}-{{\bf x}}\|)w(\|{{\bf z}}-{{\bf y}}\|)({{\bf y}}-{{\bf x}})\otimes({{\bf z}}-{{\bf y}}) \Big]{{\bf u}}({{\bf z}}) \,d{{\bf z}}d{{\bf y}}\\&\qquad - \int_{B_\varepsilon({{\bf x}})}\int_{B_\varepsilon({{\bf y}})}\Big[ c_2({{\bf y}}) w(\|{{\bf y}}-{{\bf x}}\|)w(\|{{\bf z}}-{{\bf y}}\|)({{\bf y}}-{{\bf x}})\otimes({{\bf z}}-{{\bf y}}) \Big]{{\bf u}}({{\bf y}}) \,d{{\bf z}}d{{\bf y}}\\&\qquad + \int_{B_\varepsilon({{\bf x}})}\int_{B_\varepsilon({{\bf x}})} \Big[ c_2({{\bf x}}) w(\|{{\bf y}}-{{\bf x}}\|)w(\|{{\bf z}}-{{\bf x}}\|)({{\bf y}}-{{\bf x}})\otimes({{\bf z}}-{{\bf x}}) \Big]{{\bf u}}({{\bf z}}) \,d{{\bf z}}d{{\bf y}}, \end{aligned}$$ where, for the last equality, ${{\bf y}}$ and ${{\bf z}}$ have been switched in the first and third integrals. Similarly, the second term in , after using and an appropriate change of variables, can be written as $$\label{lpd10} \begin{aligned} &\int_\Omega {{\bf S}}({{\bf x}},{{\bf y}}){{\bf u}}({{\bf x}})\,d{{\bf y}}\\&\quad = \int_{B_\varepsilon({{\bf x}})}\int_{B_\varepsilon({{\bf y}})} \Big[ c_2({{\bf y}}) w(\|{{\bf y}}-{{\bf x}}\|)w(\|{{\bf z}}-{{\bf y}}\|)({{\bf y}}-{{\bf x}})\otimes({{\bf z}}-{{\bf y}}) \Big]{{\bf u}}({{\bf x}}) \,d{{\bf z}}d{{\bf y}}\\&\qquad + \int_{B_\varepsilon({{\bf x}})}\int_{B_\varepsilon({{\bf x}})}\Big[ c_2({{\bf x}}) w(\|{{\bf y}}-{{\bf x}}\|)w(\|{{\bf z}}-{{\bf x}}\|)({{\bf y}}-{{\bf x}})\otimes({{\bf z}}-{{\bf x}}) \Big]{{\bf u}}({{\bf x}}) \,d{{\bf z}}d{{\bf y}}\\&\quad= \int_{B_\varepsilon({{\bf x}})}\int_{B_\varepsilon({{\bf x}})}\Big[ c_2({{\bf x}}) w(\|{{\bf y}}-{{\bf x}}\|)w(\|{{\bf z}}-{{\bf x}}\|)({{\bf y}}-{{\bf x}})\otimes({{\bf z}}-{{\bf x}}) \Big]{{\bf u}}({{\bf x}}) \,d{{\bf z}}d{{\bf y}}. \end{aligned}$$ The substitution of and into results in $$\begin{aligned} &\int_\Omega {{\bf S}}({{\bf x}},{{\bf y}})\big( {{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\,d{{\bf y}}\\ &= \int_{B_\varepsilon({{\bf x}})}\int_{B_\varepsilon({{\bf y}})} \Big[ c_2({{\bf y}}) w(\|{{\bf y}}-{{\bf x}}\|)w(\|{{\bf z}}-{{\bf y}}\|)({{\bf y}}-{{\bf x}})\otimes({{\bf z}}-{{\bf y}}) \Big]\big({{\bf u}}({{\bf z}})-{{\bf u}}({{\bf y}})\big) \,d{{\bf z}}d{{\bf y}}\\ &+ \int_{B_\varepsilon({{\bf x}})}\int_{B_\varepsilon({{\bf x}})}\Big[ c_2({{\bf x}}) w(\|{{\bf y}}-{{\bf x}}\|)w(\|{{\bf z}}-{{\bf x}}\|)({{\bf y}}-{{\bf x}})\otimes({{\bf z}}-{{\bf x}}) \Big]\big({{\bf u}}({{\bf z}})-{{\bf u}}({{\bf x}})\big) \,d{{\bf z}}d{{\bf y}}.\end{aligned}$$ which, with $c_2$ given by , is equal to the sum of the last two terms in .$\Box$ Relation between the peridynamics operator and the nonlocal operators {#pdandno} --------------------------------------------------------------------- Let $$\label{lpdw} w(\|{{\bf z}}\|) = \frac{1}{\|{{\bf z}}\|^2}$$ and $$\alpha({{\bf x}},{{\bf y}}) = ({{\bf y}}-{{\bf x}})w(\|{{\bf y}}-{{\bf x}}\|) \chi_{B_\varepsilon({{\bf x}})}({{\bf y}}) = \frac{{{\bf y}}-{{\bf x}}}{\|{{\bf y}}-{{\bf x}}\|^2}\chi_{B_\varepsilon({{\bf x}})}({{\bf y}}).$$ Note that $\alpha({{\bf x}},{{\bf y}}) = - \alpha({{\bf y}},{{\bf x}})$ and that the specialized Schwartz divergence kernel is given by $${\boldsymbol\rho}_{{\boldsymbol\alpha}}({{\bf x}},{{\bf y}},{{\bf z}}) = \delta({{\bf x}}-{{\bf z}}) \frac{{{\bf y}}-{{\bf x}}}{\|{{\bf y}}-{{\bf x}}\|^2}\chi_{B_\varepsilon({{\bf x}})}({{\bf y}}) + \delta({{\bf x}}-{{\bf y}}) \frac{{{\bf z}}-{{\bf x}}}{\|{{\bf z}}-{{\bf x}}\|^2}\chi_{B_\varepsilon({{\bf x}})}({{\bf z}}).$$ \[thmpdandno\] The linear peridynamic operator ${{\cal L}}$ is given it terms of the operators of the nonlocal vector calculus by $$\label{lpnc1} -{{\cal L}}u = {{\cal G}}_{{\boldsymbol\alpha}}(c_1{{\cal G}}^\ast_{{\boldsymbol\alpha}} u) +{{\cal G}}_{{\boldsymbol\alpha}}(c_2\overline{{{\cal G}}}^\ast_{{\boldsymbol\alpha}} u)$$ or, equivalently, by $$\label{lpnc2} -{{\cal L}}u = {{\cal D}}_{{\boldsymbol\alpha}}\big(c_1({{\cal D}}^\ast_{{\boldsymbol\alpha}} u)^T\big) +{{\cal G}}_{{\boldsymbol\alpha}}(c_2\overline{{{\cal G}}}^\ast_{{\boldsymbol\alpha}} u).$$ [Proof.]{} We observe that $$\label{lpnc3} \begin{aligned} {{\cal G}}_{{\boldsymbol\alpha}}(c_1{{\cal G}}^\ast_{{\boldsymbol\alpha}} {{\bf u}}) &= \int_{{\mathbb{R}}^3} \Big[c_1({{\bf y}})({{\cal G}}^\ast_{{\boldsymbol\alpha}}{{\bf u}})({{\bf y}},{{\bf x}}) +c_1({{\bf x}})({{\cal G}}^\ast_{{\boldsymbol\alpha}}{{\bf u}})({{\bf x}},{{\bf y}})\Big]{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}\\&= -\int_{{\mathbb{R}}^3} \Big[c_1({{\bf y}})\big({{\bf u}}({{\bf x}})-{{\bf u}}({{\bf y}})\big)\cdot{\boldsymbol\alpha}({{\bf y}},{{\bf x}}) \\& \qquad\qquad + c_1({{\bf x}})\big({{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\Big]{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}\\&= -\int_{{\mathbb{R}}^3} \big(c_1({{\bf x}})+c_1({{\bf y}})\big)\Big[\big({{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\Big] {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}\\&= - \int_{{\mathbb{R}}^3} \big(c_1({{\bf x}})+c_1({{\bf y}})\big) {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\otimes {\boldsymbol\alpha}({{\bf x}},{{\bf y}}) \big({{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\,d{{\bf y}}\\&= - \int_{B_\varepsilon({{\bf x}})} \big(c_1({{\bf x}})+c_1({{\bf y}})\big) \frac{({{\bf y}}-{{\bf x}})\otimes({{\bf y}}-{{\bf x}})}{\|{{\bf y}}-{{\bf x}}\|^4} \big({{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\,d{{\bf y}}. \end{aligned}$$ We next observe that $$\label{lpnc4} \begin{aligned} {{\cal G}}_{{\boldsymbol\alpha}}(c_2\overline{{{\cal G}}^\ast_{{\boldsymbol\alpha}}} {{\bf u}}) &= \int_{{\mathbb{R}}^3} \Big[c_2({{\bf y}})(\overline{{{\cal G}}^\ast_{{\boldsymbol\alpha}}}{{\bf u}})({{\bf y}}) +c_2({{\bf x}})(\overline{{{\cal G}}^\ast_{{\boldsymbol\alpha}}}{{\bf u}})({{\bf x}})\Big]{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}\\&= -\int_{{\mathbb{R}}^3} \bigg[c_2({{\bf y}})\int_{{\mathbb{R}}^3} \big({{\bf u}}({{\bf z}})-{{\bf u}}({{\bf y}})\big) \cdot {\boldsymbol\alpha}({{\bf y}},{{\bf z}})\,d{{\bf z}}\\& \qquad + c_2({{\bf x}})\int_{{\mathbb{R}}^3} \big({{\bf u}}({{\bf z}})-{{\bf u}}({{\bf x}})\big) \cdot {\boldsymbol\alpha}({{\bf x}},{{\bf z}})\,d{{\bf z}}\bigg]{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}\\&= -\int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3} c_2({{\bf y}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}})\otimes {\boldsymbol\alpha}({{\bf y}},{{\bf z}})\big({{\bf u}}({{\bf z}})-{{\bf u}}({{\bf y}})\big)\,d{{\bf z}}d{{\bf y}}\\& \qquad -\int_{{\mathbb{R}}^3}\int_{{\mathbb{R}}^3} c_2({{\bf x}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}})\otimes {\boldsymbol\alpha}({{\bf x}},{{\bf z}})\big({{\bf u}}({{\bf z}})-{{\bf u}}({{\bf x}})\big)\,d{{\bf z}}d{{\bf y}}\\&= -\int_{B_\varepsilon({{\bf x}})} \int_{B_\varepsilon({{\bf y}})} c_2({{\bf y}})\frac{({{\bf y}}-{{\bf x}})}{\|{{\bf y}}-{{\bf x}}\|^2}\otimes\frac{({{\bf z}}-{{\bf y}})}{\|{{\bf z}}-{{\bf y}}\|^2} \big({{\bf u}}({{\bf z}})-{{\bf u}}({{\bf y}})\big)\,d{{\bf z}}d{{\bf y}}\\& \qquad -\int_{B_\varepsilon({{\bf x}})}\int_{B_\varepsilon({{\bf x}})} c_2({{\bf x}})\frac{({{\bf y}}-{{\bf x}})}{\|{{\bf y}}-{{\bf x}}\|^2}\otimes\frac{({{\bf z}}-{{\bf x}})}{\|{{\bf z}}-{{\bf x}}\|^2} \big({{\bf u}}({{\bf z}})-{{\bf u}}({{\bf x}})\big)\,d{{\bf z}}d{{\bf y}}. \end{aligned}$$ Then, with ${{\cal L}}{{\bf u}}$ given by , $c_1({{\bf x}})$ and $c_2({{\bf x}})$ given by , and $w({{\bf x}})$ given by , follows from and . Finally, follows from the following proposition. $\Box$ The operators ${{\cal D}}$ and ${{\cal G}}$ satisfy $${{\cal D}}_{{\boldsymbol\alpha}}\big(c({{\cal D}}^\ast_{{\boldsymbol\alpha}} {{\bf u}})^T\big) ={{\cal G}}_{{\boldsymbol\alpha}}(c{{\cal G}}^\ast_{{\boldsymbol\alpha}} {{\bf u}})\qquad\mbox{for all ${{\bf u}}$}.$$ [Proof.]{} Using the definitions of ${{\cal D}}_{{\boldsymbol\alpha}}$, ${{\cal D}}^\ast_{{\boldsymbol\alpha}}$, ${{\cal G}}_{{\boldsymbol\alpha}}$, and ${{\cal G}}^\ast_{{\boldsymbol\alpha}}$, one finds $$\begin{aligned} {{\cal D}}_{{\boldsymbol\alpha}}\big(c&({{\cal D}}^\ast_{{\boldsymbol\alpha}} {{\bf u}})^T\big) = \int_{{{\mathbb{R}^n}}} \Big(c({{\bf y}})({{\cal D}}^\ast_{{\boldsymbol\alpha}}{{\bf u}})^T({{\bf y}},{{\bf x}}) +c({{\bf x}})({{\cal D}}^\ast_{{\boldsymbol\alpha}}{{\bf u}})^T({{\bf x}},{{\bf y}})\Big) {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\, d{{\bf y}}\\&= -\int_{{{\mathbb{R}^n}}} \Big[ c({{\bf y}}) \Big(\big({{\bf u}}({{\bf x}})-{{\bf u}}({{\bf y}})\big)\otimes{\boldsymbol\alpha}({{\bf y}},{{\bf x}})\Big)^T \\&\qquad\qquad +c({{\bf x}}) \Big(\big({{\bf u}}({{\bf y}})-{{\bf u}}({{\bf y}})\big)\otimes{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\Big)^T \Big]{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\, d{{\bf y}}\\&= -\int_{{{\mathbb{R}^n}}} \big( c({{\bf y}}) + c({{\bf x}})\big)\Big({\boldsymbol\alpha}({{\bf x}},{{\bf y}})\otimes\big({{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big) \Big) {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\, d{{\bf y}}\\&= -\int_{{{\mathbb{R}^n}}} \big( c({{\bf y}}) + c({{\bf x}})\big) \Big(\big({{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\Big) {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\, d{{\bf y}}\\&= -\int_{{{\mathbb{R}^n}}} \Big[ c({{\bf y}})\big({{\bf u}}({{\bf x}})-{{\bf u}}({{\bf y}})\big)\cdot{\boldsymbol\alpha}({{\bf y}},{{\bf x}}) \\&\qquad\qquad + c({{\bf x}})\big({{\bf u}}({{\bf y}})-{{\bf u}}({{\bf x}})\big)\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}}) \Big]{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}\\&= \int_{{{\mathbb{R}^n}}} \Big[ c({{\bf y}})({{\cal G}}^\ast_{{\boldsymbol\alpha}}{{\bf u}})({{\bf y}},{{\bf x}}) + c({{\bf x}})({{\cal G}}^\ast_{{\boldsymbol\alpha}}{{\bf u}})({{\bf x}},{{\bf y}}) \Big]{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\,d{{\bf y}}= {{\cal G}}_{{\boldsymbol\alpha}}(c{{\cal G}}^\ast_{{\boldsymbol\alpha}} {{\bf u}}). \,\hfill\Box \end{aligned}$$ Concluding remarks {#sec_conclusion} ================== We close the paper by briefly considering a second intriguing special case of the nonlocal operators and also briefly discussing, in general terms, the types of situations in which the generalized operators may be of use. Another special case of the nonlocal operators ---------------------------------------------- A different simplification of the nonlocal operators is effected by the Schwartz kernel given by $$\label{speckeraa} {\boldsymbol\kappa}_{{\boldsymbol\beta}}({{\bf x}},{{\bf y}},{{\bf z}}) = -\delta({{\bf x}}-{{\bf z}}){\boldsymbol\beta}({{\bf x}},{{\bf y}}) + \delta({{\bf x}}-{{\bf y}}){\boldsymbol\beta}({{\bf x}},{{\bf z}})$$ for a vector-valued function ${\boldsymbol\beta}({{\bf x}},{{\bf y}})\in[L^1({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k$. It is easy to show that ${\boldsymbol\kappa}_{{\boldsymbol\beta}}$ satisfies if and only if ${\boldsymbol\beta}({{\bf x}},{{\bf y}})$ is [symmetric]{}, i.e., we have ${\boldsymbol\beta}({{\bf x}},{{\bf y}}) = {\boldsymbol\beta}({{\bf y}},{{\bf x}})$. Note the contrasts with the simplified kernel ${\boldsymbol\kappa}_{{\boldsymbol\alpha}}$ given by for which ${\boldsymbol\alpha}$ is antisymmetric and the minus sign in is replaced by a plus sign. The specialized kernel ${\boldsymbol\kappa}_{{\boldsymbol\beta}}$ is a divergence kernel, i.e., it satisfies and, for that kernel, the nonlocal operator ${{\cal D}}$ is given by $$\label{cdb} ({{\cal D}}_{{\boldsymbol\beta}}{\boldsymbol\nu})({{\bf x}}) = \int_{{{\mathbb{R}^n}}}\big({\boldsymbol\nu}({{\bf y}},{{\bf x}}) - {\boldsymbol\nu}({{\bf x}},{{\bf y}}) \big)\cdot{\boldsymbol\beta}({{\bf x}},{{\bf y}})\,d{{\bf y}}.$$ and the adjoint operator ${{\cal D}}^\ast$ is given by $$({{\cal D}}_{{\boldsymbol\beta}}^\ast u)({{\bf x}},{{\bf y}}) = -\big(u({{\bf y}}) - u({{\bf x}})\big){\boldsymbol\beta}({{\bf x}},{{\bf y}}) .$$ Note the difference in a sign between ${{\cal D}}_{{\boldsymbol\alpha}}$ and ${{\cal D}}_{{\boldsymbol\beta}}$ but the similarity in sign between ${{\cal D}}_{{\boldsymbol\alpha}}^\ast$ and ${{\cal D}}_{{\boldsymbol\beta}}\ast$. The other operators of the nonlocal calculus, e.g., ${{\cal G}}$, ${{\cal C}}$, and their adjoined operators, have the obvious definitions resulting from making or not making the sign changes in the definitions of the corresponding operators engendered by the kernel ${\boldsymbol\kappa}_{{\boldsymbol\alpha}}$. In particular, the form of the nonlocal Laplacian operator remains unchanged, i.e., we have that $$\label{betalap} ({{\cal D}}_{{\boldsymbol\beta}}{{\cal D}}_{{\boldsymbol\beta}}^\ast u)({{\bf x}}) =-2 \int_{{{\mathbb{R}^n}}} \big(u({{\bf y}}) - u({{\bf x}})\big) {\boldsymbol\beta}({{\bf x}},{{\bf y}})\cdot {\boldsymbol\beta}({{\bf x}},{{\bf y}})\,d{{\bf y}}.$$ As was the case for the kernel ${\boldsymbol\kappa}_{{\boldsymbol\alpha}}$, for the specialized Schwartz kernel ${\boldsymbol\kappa}_{{\boldsymbol\beta}}$ we have that , , , , and hold. However, unlike the situation for ${\boldsymbol\kappa}_{{\boldsymbol\alpha}}$, for ${\boldsymbol\kappa}_{{\boldsymbol\beta}}$ we trivially have that also holds. On the other hand, the state-based peridynamic model of Section \[peridyn\] cannot be expressed in terms of the nonlocal operators corresponding to the kernel ${\boldsymbol\kappa}_{{\boldsymbol\beta}}$ as was done in Section \[pdandno\] for the kernel ${\boldsymbol\kappa}_{{\boldsymbol\alpha}}$. It would be of interest to explore what sort of mechanical model, if any, results from the use of the specialized operators ${{\cal G}}_{{\boldsymbol\beta}}$, ${{\cal D}}_{{\boldsymbol\beta}}$, etc., and to explore the differences between such a model and the state-based peridynamics model. Although beyond the scope of this work, this is a subject of current interest to the authors. However, an inkling of the differences can be gleaned by applying the operators ${{\cal D}}_{{\boldsymbol\alpha}}$ and ${{\cal D}}_{{\boldsymbol\beta}}$ to a scalar function. Conceptually, we do this by setting ${\boldsymbol\nu}({{\bf x}},{{\bf y}})={\bf a}u({{\bf x}})$ in and , where ${\bf a}$ denotes a constant vector, yielding $$({{\cal D}}_{{\boldsymbol\alpha}}u)({{\bf x}}) = \int_{{{\mathbb{R}^n}}} \big(u({{\bf y}}) + u({{\bf x}})\big)\widehat\alpha({{\bf x}},{{\bf y}})\,d{{\bf y}}$$ and $$\label{betalap2} ({{\cal D}}_{{\boldsymbol\beta}}u)({{\bf x}}) =\int_{{{\mathbb{R}^n}}} \big(u({{\bf y}}) - u({{\bf x}})\big)\widehat\beta({{\bf x}},{{\bf y}})\,d{{\bf y}},$$ where $\widehat\alpha({{\bf x}},{{\bf y}})={\bf a}\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}})$ is an antisymmetric function and $\widehat\beta({{\bf x}},{{\bf y}})={\bf a}\cdot{\boldsymbol\beta}({{\bf x}},{{\bf y}})$ is a symmetric function. Comparing the last equation in with after setting $\widehat\beta({{\bf x}},{{\bf y}})=-2{\boldsymbol\alpha}({{\bf x}},{{\bf y}})\cdot{\boldsymbol\alpha}({{\bf x}},{{\bf y}})$ and comparing with after setting $\widehat\beta({{\bf x}},{{\bf y}})=-2{\boldsymbol\beta}({{\bf x}},{{\bf y}})\cdot{\boldsymbol\beta}({{\bf x}},{{\bf y}})$, we that the direct action of the operator ${{\cal D}}_{{\boldsymbol\beta}}$ on a scalar function $u({{\bf x}})$ yields a nonlocal Laplacian of $u$. Modeling situations in which the general nonlocal operators can play a role --------------------------------------------------------------------------- Consider the specific Schwartz kernel given by $$\label{genkerab} {\boldsymbol\kappa}_{{\lambda{\boldsymbol\alpha}}}({{\bf x}},{{\bf y}},{{\bf z}}) = \lambda({{\bf x}},{{\bf z}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}}) + \lambda({{\bf x}},{{\bf y}}){\boldsymbol\alpha}({{\bf x}},{{\bf z}}),$$ where $\lambda({{\bf x}},{{\bf y}})$ and ${\boldsymbol\alpha}({{\bf x}},{{\bf y}})$ are scalar and vector-valued functions, respectively. This kernel can be viewed as a simplification of the general kernel ${\boldsymbol\kappa}$ or a generalization of the ${\boldsymbol\kappa}_{{{\boldsymbol\alpha}}}$ given by . Clearly, if we set $\lambda({{\bf x}},{{\bf y}})=\delta({{\bf x}}-{{\bf y}})$, then reduces to . Of course, we require the ${\boldsymbol\kappa}_{{\lambda{\boldsymbol\alpha}}}({{\bf x}},{{\bf y}},{{\bf z}})$ to satisfy which implies that $\lambda({{\bf x}},{{\bf y}})$ and ${\boldsymbol\alpha}({{\bf x}},{{\bf y}})$ must be such that $$\int_{{{\mathbb{R}^n}}}\Big(\lambda({{\bf x}},{{\bf z}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}}) + \lambda({{\bf x}},{{\bf y}}){\boldsymbol\alpha}({{\bf x}},{{\bf z}})\Big) d{{\bf x}}= {\bf 0}\qquad\forall\, {{\bf y}},{{\bf z}}\in{{\mathbb{R}^n}}.$$ For the kernel we have, from , the nonlocal divergence operator ${{\cal D}}_{{\lambda{\boldsymbol\alpha}}}$ such that $$\label{genkerab1} ({{\cal D}}_{{\lambda{\boldsymbol\alpha}}}{\boldsymbol\nu})({{\bf x}}) = \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} \Big(\lambda({{\bf x}},{{\bf z}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}}) + \lambda({{\bf x}},{{\bf y}}){\boldsymbol\alpha}({{\bf x}},{{\bf z}})\Big)\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}}) \,d{{\bf z}}d{{\bf y}}$$ and, from , the adjoint operator $$\label{genkerab2} ({{\cal D}}_{{\lambda{\boldsymbol\alpha}}}^\ast u)({{\bf x}},{{\bf y}}) = \int_{{{\mathbb{R}^n}}} u({{\bf z}}) \Big(\lambda({{\bf x}},{{\bf z}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}}) + \lambda({{\bf x}},{{\bf y}}){\boldsymbol\alpha}({{\bf x}},{{\bf z}})\Big)\, d{{\bf z}}.$$ Note that if $\lambda({{\bf x}},{{\bf y}})=\delta({{\bf x}}-{{\bf y}})$, then and reduce to and, respectively. From , we have that $$\begin{aligned} ({{\cal D}}_{{\lambda{\boldsymbol\alpha}}}&{\boldsymbol\nu})({{\bf x}}) \\&= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} \lambda({{\bf x}},{{\bf z}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}})\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}}) \,d{{\bf z}}d{{\bf y}}+ \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\lambda({{\bf x}},{{\bf y}}){\boldsymbol\alpha}({{\bf x}},{{\bf z}})\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}}) \,d{{\bf z}}d{{\bf y}}\\&= \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} \lambda({{\bf x}},{{\bf z}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}})\cdot{\boldsymbol\nu}({{\bf y}},{{\bf z}}) \,d{{\bf z}}d{{\bf y}}+ \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}}\lambda({{\bf x}},{{\bf z}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}})\cdot{\boldsymbol\nu}({{\bf z}},{{\bf y}}) \,d{{\bf z}}d{{\bf y}}\\& = \int_{{{\mathbb{R}^n}}}\int_{{{\mathbb{R}^n}}} \big({\boldsymbol\nu}({{\bf z}},{{\bf y}}) + {\boldsymbol\nu}({{\bf y}},{{\bf z}})\big)\cdot\lambda({{\bf x}},{{\bf z}}){\boldsymbol\alpha}({{\bf x}},{{\bf y}}) \,d{{\bf z}}d{{\bf y}}\end{aligned}$$ so that $$\label{genkerab3} ({{\cal D}}_{{\lambda{\boldsymbol\alpha}}}{\boldsymbol\nu})({{\bf x}}) = \int_{{{\mathbb{R}^n}}} {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\cdot \bigg( \int_{{{\mathbb{R}^n}}} \big({\boldsymbol\nu}({{\bf z}},{{\bf y}}) + {\boldsymbol\nu}({{\bf y}},{{\bf z}})\big)\lambda({{\bf x}},{{\bf z}}) \,d{{\bf z}}\bigg)d{{\bf y}}.$$ Recall, from Section \[gennlc\], that the right-hand side of is the total flux of ${\boldsymbol\nu}$ into the point ${{\bf x}}$ coming from all points ${{\bf y}}\in{{\mathbb{R}^n}}$. Note that for the specialized kernel , i.e., for $\lambda({{\bf x}},{{\bf y}})=\delta({{\bf x}}-{{\bf y}})$, the right-hand side reduces to the right-hand side of . To better explain the difference between and , it is instructive to consider the case of nonlocal interactions of finite extent, i.e., the case of $\lambda({{\bf x}},{{\bf z}})$ and ${\boldsymbol\alpha}({{\bf x}},{{\bf y}})$ having compact support. Specifically, we chose constants $\epsilon_\lambda$ and $\epsilon_{{{\boldsymbol\alpha}}}$ such that $0< \epsilon_\lambda<\infty$ and $0<\epsilon_{{{\boldsymbol\alpha}}} <\infty$ and then assume that $$\begin{aligned} &\lambda({{\bf x}},{{\bf z}}) = 0 \qquad\mbox{for ${{\bf z}}\not\in B_{\epsilon_\lambda}({{\bf x}})$} \\& {\boldsymbol\alpha}({{\bf x}},{{\bf y}})={\bf0} \qquad\mbox{for ${{\bf y}}\not\in B_{\epsilon_{{{\boldsymbol\alpha}}}}({{\bf x}})$}. \end{aligned}$$ Then, the right-hand sides of and become $$\label{genkerab4} \mbox{\em flux into ${{\bf x}}$} = \int_{B_{\epsilon_{{{\boldsymbol\alpha}}}}({{\bf x}})} {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\cdot\big({\boldsymbol\nu}({{\bf x}},{{\bf y}}) + {\boldsymbol\nu}({{\bf y}},{{\bf x}})\big) \,d{{\bf y}}$$ and $$\label{genkerab5} \mbox{\em flux into ${{\bf x}}$} = \int_{B_{\epsilon_{{{\boldsymbol\alpha}}}}({{\bf x}})} {\boldsymbol\alpha}({{\bf x}},{{\bf y}})\cdot \bigg( \int_{B_{\epsilon_\lambda}({{\bf x}})} \big({\boldsymbol\nu}({{\bf z}},{{\bf y}}) + {\boldsymbol\nu}({{\bf y}},{{\bf z}})\big)\lambda({{\bf x}},{{\bf z}}) \,d{{\bf z}}\bigg)d{{\bf y}},$$ respectively. Both and state that all points ${{\bf y}}$ in the ball centered at ${{\bf x}}$ and of radius $\epsilon_{{{\boldsymbol\alpha}}}$ contribute to the flux of ${\boldsymbol\nu}$ into the point ${{\bf x}}$. However, further states that the contribution to the flux of ${\boldsymbol\nu}$ into the point ${{\bf x}}$ coming from a particular point ${{\bf y}}\in B_{\epsilon_{{{\boldsymbol\alpha}}}}({{\bf x}})$ only depends on the value[^6] of ${\boldsymbol\nu}$ at the pair of points ${{\bf x}}$ and ${{\bf y}}$. On the other hand, states something quite different. We now have that the contribution to the flux of ${\boldsymbol\nu}$ into the point ${{\bf x}}$ coming from a particular point ${{\bf y}}\in B_{\epsilon_{{{\boldsymbol\alpha}}}}({{\bf x}})$ depends on the values of ${\boldsymbol\nu}$ at all point pairs ${{\bf y}}$ and ${{\bf z}}$ with ${{\bf z}}\in B_{\epsilon_{{{\boldsymbol\alpha}}}}({{\bf x}})$. It is also clear that reduces to in an appropriate limit as $\epsilon_\lambda\to0$ and for an appropriate $\lambda({{\bf x}},{{\bf z}})$, e.g., a Gaussian with variance and height depending $\epsilon_\lambda$ is such a way that it has unit area for all $\epsilon_\lambda$. We also know from previous work that, for appropriate $\alpha({{\bf x}},{{\bf y}})$, , or more precisely ${{\cal D}}_{{{\boldsymbol\alpha}}}$ given by , reduces, as $\epsilon_{{{\boldsymbol\alpha}}}\to0$, to the classical local differential divergence operator. We can interpret this limit as saying that only points in an infinitesimal ball centered at ${{\bf x}}$ contribute to the flux into ${{\bf x}}$, where an infinitesimal ball is needed so that one can be sure that derivatives are well defined. The sketches in Figure \[fig1\] are meant to illustrate this discussion. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- -- ![ Left: for the kernel , the contribution to the flux into a point ${{\bf x}}$ from a point ${{\bf y}}$ in an $\epsilon_{{{\boldsymbol\alpha}}}$-neighborhood of ${{\bf x}}$ is determined by ${{\bf z}}$ in an $\epsilon_\lambda$-neighborhood of ${{\bf x}}$. Middle: for the kernel , the contribution to the flux into a point ${{\bf x}}$ from a point ${{\bf y}}$ in an $\epsilon_{{{\boldsymbol\alpha}}}$-neighborhood of ${{\bf x}}$ is determined only by the point ${{\bf y}}$. Right: for local partial differential equation models, the contribution to the flux into a point ${{\bf x}}$ is determined from points in an infinitesimal neighborhood of ${{\bf x}}$.[]{data-label="fig1"}](nonlocal-nonlocal2.eps "fig:"){height="1.4in"} ![ Left: for the kernel , the contribution to the flux into a point ${{\bf x}}$ from a point ${{\bf y}}$ in an $\epsilon_{{{\boldsymbol\alpha}}}$-neighborhood of ${{\bf x}}$ is determined by ${{\bf z}}$ in an $\epsilon_\lambda$-neighborhood of ${{\bf x}}$. Middle: for the kernel , the contribution to the flux into a point ${{\bf x}}$ from a point ${{\bf y}}$ in an $\epsilon_{{{\boldsymbol\alpha}}}$-neighborhood of ${{\bf x}}$ is determined only by the point ${{\bf y}}$. Right: for local partial differential equation models, the contribution to the flux into a point ${{\bf x}}$ is determined from points in an infinitesimal neighborhood of ${{\bf x}}$.[]{data-label="fig1"}](nonlocal-local.eps "fig:"){height="1.4in"} --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- -- [5]{} Q. Du, M. Gunzburger, R. Lehoucq, and K. Zhou, Analysis and approximation of nonlocal diffusion problems with volume constraints; SIAM Review [54]{} 2012, 667-696. Q. Du, M. Gunzburger, R. Lehoucq, and K. Zhou, A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws, Math. Model. Meth. Appl. Sci. [ 23]{} 2013, 493-540. Q. Du, M. Gunzburger, R. Lehoucq, and K. Zhou, Analysis of the volume-constrained peridynamic Navier equation of linear elasticity; J. Elasticity [113]{} 2014, 193-217. S. Silling, Reformulation of elasticity theory for discontinuities and long-range forces, J. Mech. Phys. Solids [48]{} 2000, 175-209. S. Silling, Linearized theory of peridynamic states, J. Elasticity, [99]{} 2010, 85-111. S. Silling, M. Epton, O. Weckner, J. Xu, and E. Askari, Peridynamic states and constitutive modeling, J. Elasticity [88]{} 2007, 151-185. E. Emmrich and O. Weckner, On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity , Communications in Mathematical Sciences [5]{} 2007, 851-864. [^1]: Research and preparation of the paper was partially supported by the US Department of Energy grant number DE-SC0004970 and by the US National Science Foundation grant number DMS-1013845. [^2]: The resemblance of nonlocal divergence to local divergence is made precise in Section \[gennlc\]. [^3]: In words, states that the integral of the nonlocal divergence of ${\boldsymbol\nu}$ over any domain $\Omega\subset{{\mathbb{R}^n}}$ is equal to the flux of ${\boldsymbol\nu}$ exiting from $\Omega$ into the complement domain ${{\mathbb{R}^n}}\setminus\Omega$. This is made clear by noting that, due to the antisymmetry of $\psi_{{\boldsymbol\nu}}({{\bf x}},{{\bf y}})$, can be rewritten as $$\int_\Omega ({{\cal D}}{\boldsymbol\nu})({{\bf x}})\,d{{\bf x}}= \int_\Omega \int_{{{\mathbb{R}^n}}\setminus\Omega}\psi_{{\boldsymbol\nu}}({{\bf x}},{{\bf y}})\,d{{\bf y}}d{{\bf x}}\qquad \forall\,{\boldsymbol\nu}\in {{[C_c^{\infty}({{\mathbb{R}^n}}\times{{\mathbb{R}^n}})]^k}},\,\, \Omega\subset{{\mathbb{R}^n}}.$$ [^4]: A similar definition to was given in [@dglz-nlc]. However, there, the central requirement was not discussed nor was the development of the full nonlocal vector calculus associate with . [^5]: With ${{\cal D}}^\ast$ being the adjoint of the nonlocal divergence operator ${{\cal D}}$, one can identify $-{{\cal D}}^\ast$ as a nonlocal gradient operator. [^6]: It is clear from that only the symmetric part of ${\boldsymbol\nu}({{\bf x}},{{\bf y}})$ contributes to the flux so that there is actually no ambiguity between ${\boldsymbol\nu}({{\bf x}},{{\bf y}})$ and ${\boldsymbol\nu}({{\bf y}},{{\bf x}})$.
TECHNICAL FIELD BACKGROUND ART PRIOR ART DOCUMENTS Patent Documents Patent Document 1: Japanese Unexamined Patent Publication No. 2015-015600 SUMMARY OF THE INVENTION Problem to be Solved by the Invention Means for Solving the Problem Advantageous Effect of the Invention EMBODIMENTS FOR IMPLEMENTING THE INVENTION First Embodiment Second Embodiment Third Embodiment Example DESCRIPTION OF THE REFERENCE NUMERALS The present invention relates to a temperature estimation system, a temperature estimation method, and a recording medium storing a temperature estimation program. A temperature at a location at which a user is located is useful information. There is a case in which a user may want to know the temperature, and a case in which a user may want to continuously obtain a temperature at a point at which the user is located for a predetermined time, for example, as environmental data related to skin. In recent years, many people hold and carry mobile terminal devices, such as smartphones. In such a mobile terminal device, various sensors, such as an acceleration sensor and a gyro sensor, are standardly installed. Further, for example, Patent Document 1 describes a temperature sensor for measuring a temperature of an object whose contact is detected by a contact sensor. Additionally, for example, for a smartphone operating on an Android (registered trademark) platform, various sensors are defined, such as an acceleration sensor (TYPE_ACCELEROMETER), a gyro sensor (TYPE_GYROSCOPE), and a temperature sensor (TYPE_TEMPERATURE, TYPE_AMBIENT_TEMPERATURE). Measured values by these sensors can be obtained by using an API, such as a sensor framework. A value measured by a temperature sensor, such as that described above, is, however, influenced by heating of a battery and a CPU, etc., installed inside a smartphone, so that an external temperature of the smartphone may not be accurately detected. As a result, when it is desirable to obtain the external temperature of the mobile terminal device, a user may be required to carry a thermometer separately and to measure the temperature with the thermometer. The present invention is achieved in view of the above-described circumstances, and an object is to provide a technique for accurately estimating an external temperature of a mobile terminal device using data that can be standardly obtained by the mobile terminal device, such as a smartphone. According to the present invention, there is provided a temperature estimation system including an internal temperature data obtainer that obtains internal temperature data of a user mobile terminal device carried by a user; an operation data obtainer that obtains operation data on an operation state of the user mobile terminal device; and a temperature estimator that calculates an estimated value of an external temperature in a vicinity of the user mobile terminal device from the internal temperature data and the operation data of the user mobile terminal device, based on correlation among internal temperature data of a mobile terminal device for measurement, operation data on an operation state of the mobile terminal device for measurement, and actual temperature data that represents an actual environmental temperature in a vicinity of the mobile terminal device for measurement. An external temperature of a mobile terminal device can be accurately estimated using data that can be standardly obtained by the mobile terminal device, such as a smartphone. Embodiments of the present invention are described below using the drawings. Note that, in all the drawings, similar reference numerals are attached to similar components, and the description is omitted as appropriate. In the embodiments, an object is to accurately estimate a temperature at a point at which a user is located (an external temperature of the mobile terminal device) only by using a mobile terminal device, such as a smartphone, carried by the user. In general, a battery and a CPU are installed inside a mobile terminal device, such as a smartphone, and some temperature sensors for detecting overheating, etc., of the battery and the CPU are also installed inside. Accordingly, it is considered that the temperature measured by the temperature sensors installed inside the mobile terminal device can be detected. However, if, for example, a high load process is performed by a mobile terminal device, a temperature of the battery and the CPU rises, and the temperature measured by the temperature sensors installed inside the mobile terminal device becomes higher than the actual external temperature. Consequently, the external temperature of the mobile terminal device may not be accurately detected by the temperature sensors installed inside the mobile terminal device. In the embodiments, a temperature (internal temperature data) measured by temperature sensors that are installed inside a predetermined mobile terminal device (a mobile terminal device for measurement), operation data on an operation state of the mobile terminal device, and actual temperature data representing an actual environmental temperature in a vicinity of the mobile terminal device are obtained, and correlation among these is calculated in advance. Then, internal temperature data measured by temperature sensors installed inside a mobile terminal device carried by a user (a user mobile terminal device) and operation data on an operation state of the mobile terminal device are obtained, and an estimation value of the external temperature in a vicinity of the mobile terminal device is calculated from the internal temperature data and the operation data, based on the correlation calculated in advance. In the following embodiments, a case is described as an example, in which the mobile terminal device is a smartphone. FIG. 1 100 is a block diagram illustrating an example of a functional configuration of a temperature estimation system in the embodiment. 100 200 300 100 110 112 114 116 130 132 300 110 112 116 a a a. In the embodiment, the functional configuration of the temperature estimation system can be a configuration that is embedded in a server apparatus that is connected to a smartphone through a network. The temperature estimation system includes an internal temperature data obtainer ; an operation data obtainer ; a temperature estimator ; an estimated temperature output ; an estimation formula storage ; and an estimated temperature storage . The smartphone includes, as functions, an internal temperature obtainer ; an operation data obtainer ; and an estimated temperature output FIG. 2 300 is a block diagram illustrating an example of a hardware configuration of the smartphone according to the embodiment. 300 302 304 306 308 310 312 314 316 The smartphone includes an input unit ; an output unit ; a CPU (Central Processing Unit) ; a memory ; a storage ; a network I/C ; a battery ; and a sensor . 302 302 304 302 304 The input unit may be, for example, a button, a keyboard, etc., that are operated by a user, etc. The input unit may be, for example, an audio input device that enables inputting through a voice, such as a microphone. The output unit may be a speaker, a display, etc. The input unit and the output unit may be configured such that an input configuration and an output configuration are integrated, such as a touch panel. 308 308 310 The memory stores a control program, such as an OS (Operating System), an execution program, etc. Here, the memory is a ROM (Read Only Memory), a RAM (Random Access Memory), etc. The storage may be a built-in storage, etc. 306 308 The CPU implements a temperature estimation process according to the embodiment by controlling a process by the entire computer, such as various types of operations, inputting/outputting of data to/from each hardware component, etc., based on the control program and the execution program stored in the memory . 312 200 The network I/C communicates data with another device, such as the server apparatus , by establishing a connection to a network, such as the Internet, a LAN, etc. 314 The battery may be, for example, a lithium ion battery, etc., that may be generally installed inside a smartphone. 316 316 316 316 316 300 316 314 306 300 a a a a The sensor includes various types of sensors that may be generally installed inside a smartphone, such as an acceleration sensor, a gyro sensor, etc. In the embodiment, the sensor includes at least a temperature sensor . The temperature sensor is not particularly limited, provided that the temperature sensor is installed inside the smartphone . For example, the temperature sensor may be a temperature sensor for measuring a temperature (overheating) of the battery and the CPU installed inside the smartphone . 200 300 200 200 FIG. 2 Note that the hardware configuration of the server apparatus is also the same as the hardware configuration of the smartphone illustrated in . However, the configuration of the server apparatus may not include a temperature sensor. In the server apparatus , the storage may be an HDD (Hard Disk Drive), for example. FIG. 1 110 300 300 110 200 300 110 316 300 110 a a a Referring back to , the internal temperature data obtainer of the smartphone obtains internal temperature data of the smartphone . The internal temperature data obtainer of the server apparatus retrieves, through a network, the internal temperature data of the smartphone obtained by the internal temperature data obtainer . The internal temperature data may represent the temperature measured by the temperature sensor that is installed inside the smartphone . The internal temperature data obtainer is capable of retrieving, for a predetermined time period, internal temperature data every constant time interval. 112 300 300 112 200 300 112 306 300 314 112 110 112 a a a a The operation data obtainer of the smartphone obtains operation data on an operation state of the smartphone . The operation data obtainer of the server apparatus retrieves, through a network, the operation data of the smartphone that is obtained by the operation data obtainer . The operation data may be, for example, an operation state of the CPU installed inside the smartphone , a voltage of the battery , etc. The operation data obtainer is capable of retrieving, for a predetermined time period, operation data every constant time interval. The procedure for the internal temperature data obtainer to obtain the internal temperature data and the procedure for the operation data obtainer to obtain the operation data are described below. 130 300 300 114 300 300 130 The estimation formula storage stores an estimation formula far calculating an estimated value of the external temperature in a vicinity of the smartphone based on the internal temperature data and the operation data of the smartphone . The temperature estimator calculates an estimated value of the external temperature in the vicinity of the smartphone by applying the internal temperature data and the operation data of the smartphone to an estimation formula stored in the estimation formula storage . 114 132 116 300 114 300 316 a The temperature estimator stores the calculated estimated value of the external temperature in the estimated temperature storage . The estimated temperature output provides, through a network, the smartphone with the estimated value of the external temperature calculated by the temperature estimator . In the smartphone , the temperature sensor outputs the obtained estimated value of the external temperature, for example, by displaying the obtained estimated value of the external temperature on a display. 130 Next, a procedure for calculating the estimation formula stored in the estimation formula storage is described. In the embodiment, the estimation formula may represent correlation among the internal temperature data of the smartphone for measurement, the operation data on an operation state of the smartphone for measurement, and actual temperature data representing an actual environmental temperature in the vicinity of the smartphone for measurement. Specifically, the estimation formula may be obtained by multiple regression analysis, where an outcome variable (a dependent variable) is the “actual temperature data” and predictor variables are the “internal temperature data” and the “operation data.” The actual temperature data may be the data obtained by measuring the actual environmental temperature by a thermometer. Alternatively, the actual temperature data may be a controlled temperature under a condition in which the temperature is controlled, such as a thermostatic chamber. FIG. 3 FIG. 4 is a flowchart illustrating an example of a procedure for calculating an estimation formula by multiple regression analysis in the embodiment. is a diagram illustrating the example of the procedure for calculating the estimation formula in the embodiment. FIG. 3 FIG. 4 100 500 510 510 510 500 510 As illustrated in , first, actual temperature data, internal temperature data, and operation data are obtained (step S). Specifically, as illustrated in , a measurer carries a smartphone for measurement and a digital thermometer . As an example, the measurer may carry the digital thermometer while putting the digital thermometer in a chest pocket, etc., or in a pocket in a bag. Then, for a predetermined time period, internal temperature data and operation data of the smartphone for measurement and actual temperature data measured by the digital thermometer are obtained every constant time interval. 510 510 510 510 510 510 200 a It suffices if the digital thermometer is capable of measuring an actual ambient temperature on the spot, and a commercially available one can be used. The digital thermometer has a function for measuring a temperature every constant time interval to obtain the measured temperature while associating the measured temperature with time. A configuration may be adopted such that the temperature and the time obtained by the digital thermometer are stored in an actual temperature data storage , which is formed of an internal memory of the digital thermometer , for example. Alternatively, a configuration may be adopted such that the temperature and the time obtained by the digital thermometer are sequentially transmitted to a server apparatus, such as the server apparatus . 500 300 500 500 300 FIG. 2 A hardware configuration of the smartphone for measurement may be the same as the hardware configuration of the smartphone , which is described by referring to . Here, for the purpose of explanation, the smartphone for measurement is denoted as the “smartphone for measurement.” However, the smartphone for measurement may be the same smartphone as the smartphone . 500 As described above, for example, for a smartphone operating on an Android (registered trademark) platform, various sensors are defined, such as an acceleration sensor (TYPE_ACCELEROMETOR), a gyro sensor (TYPE_GYROSCOPE), and a temperature sensor (TYPE_TEMPERATURE, TYPE_AMBIENT_TEMPERATURE). Values measured by these sensors can be obtained using an API, such as a sensor framework. The internal temperature data of the smartphone for measurement can be obtained by using an API, such as the sensor framework. Additionally, in a smartphone operating on an Android (registered trademark) platform, a battery voltage (voltage) and a temperature (temperature) can be obtained using, for example, a predetermined source code using a BroadcastReceiver class and a BatteryManager class. 500 The internal temperature data and the battery voltage, as the operation data, of the smartphone for measurement can be obtained by such a source code. 1 Additionally, in a smartphone operating on an Android (registered trademark) platform, CPU information can be obtained using a predetermined source code for reading out/proc/cupinfo and/proc/stat on a file system. Here, as the CPU information, data of/proc/stat may be used, and a plurality of data items may be obtained (which are referred to as CPU through CPUn below (n is an integer greater than or equal to 2)). 500 The CPU information, as the operation data of the smartphone for measurement , can be obtained by such a source code. 300 500 110 112 110 112 a a a a Similar to the smartphone , the smartphone for measurement includes, as functional components, the internal temperature data obtainer and the operation data obtainer . The internal temperature data obtainer obtains, for a predetermined time period, the internal temperature data every constant time interval using the above-described API, a predetermined source code, etc.; and the operation data obtainer obtains, for the predetermined time period, the operation data every constant time interval using the above-described API, a predetermined source code, etc. 200 200 200 510 110 200 110 500 500 112 200 112 500 500 200 200 230 200 FIG. 9 FIG. 10 FIG. 9 FIG. 10 a a Here, the process of calculating the estimation formula by multiple regression analysis is described by exemplifying a case in which the process is executed by the server apparatus , though the process is not necessarily executed by the server apparatus . The data obtainer (see and ) of the server apparatus obtains the actual temperature data associated with the date and time from the digital thermometer . Additionally, the internal temperature data obtainer of the server apparatus obtains, from the internal temperature data obtainer of smartphone for measurement , the internal temperature data of the smartphone for measurement that is associated with the date and time; and the operation data obtainer of the server apparatus obtains, from the operation data obtainer of the smartphone for measurement , the operation data of the smartphone for measurement that is associated with the date and time. The actual temperature data, the internal temperature data, and the operation data, which are obtained by the server apparatus , are stored in a storage of the server apparatus (e.g., the data accumulator of the server apparatus (see and ) described below). In the following, the data collected for calculating the estimation formula is also referred to as “estimation formula calculation data.” FIG. 5 510 is a diagram illustrating an example of the actual temperature data obtained by the digital thermometer . The actual temperature data associated with date and time is obtained. FIG. 6 500 1 3 is a diagram illustrating an example of the internal temperature data and the operation data, which are obtained for the smartphone for measurement . The internal temperature data and the operation data (CPU through CPU , VOLT) associated with date and time are obtained. FIG. 3 104 Referring back to , at step S, an estimation formula for calculating an estimated value of the external temperature in the vicinity of the smartphone is calculated using the actual temperature data, the internal temperature data, and the operation data. As described above, in the embodiment, the estimation formula can be calculated by multiple regression analysis with the “actual temperature data” as the outcome variable (the dependent variable), and the “internal temperature data” and the “operation data” as the predictor variables. 102 Additionally, as described in the embodiment, if there are multiple types of operation data, data with a high correlation coefficient with the actual temperature data can be selected to be used (step S). 1 1 As described above, when the battery voltage and the CPU information are obtained in the smartphone operating on the Android (registered trademark) platform by using the predetermined source code, a plurality of data items, such as VOLT, and CPU through CPUn (n is an integer greater than or equal to 2), is obtained as the operation data. Here, the implication of the values that are obtained as the CPU information, such as CPU through CPUn (n is an integer greater than or equal to 2), is not clarified. However, by selectively using the operation data that is highly likely to affect the “actual temperature data,” an estimation formula can be obtained with which an estimated value of the external temperature can be accurately calculated. Various types of existing statistical analysis software can be used for calculating the estimation formula (multiple regression analysis) and for calculating correlation coefficients. For example, the statistical analysis software “R,” SPSS, etc., can be used. 102 103 In the process of step S, prior to performing the multiple regression analysis of step S, correlation coefficients between the operation data items and the actual temperature data may be calculated, and the operation data item with a high correlation coefficient with the actual temperature data may be selected; or a predetermined number of the operation data items may be selected in a descending order of the correlation coefficients. 102 103 As another example, the process at step S and the process at step S may be simultaneously performed. Namely, first, preliminary multiple regression analysis may be performed with the obtained all the operation data items and the internal temperature data as the predictor variables and the actual temperature data as the outcome variable. Based on the result, for example, based on the correlation coefficients and the significance levels, an operation data item that causes large effect on the actual temperature data is selected from the operation data items. Subsequently, an estimation formula can be calculated by performing, again, the multiple regression analysis with the selected operation data item and the internal temperature data as the predictor variables and the actual temperature data as the outcome variable. The process of selecting an appropriate operation data item from the plurality of types of operation data items may be appropriately performed based on the statistical analysis. 1 2 Furthermore, in addition to using, as the operation data items, for example, the values of the above-described CPU information and the battery voltage as they are, for example, differences, etc., among different types of operation data items may be used as the operation data items. Specifically, for example, a value obtained as (CPU-CPU) may be used as a type of the operation data item. In this case, considering the correlation coefficients with the actual temperature data, an operation data item that causes large effect on the actual temperature data may be used as the operation data. As described above, for example, when a process with a high load is executed in the smartphone, the temperature of the battery and the CPU rises, and the temperature measured by the temperature sensor installed inside the smartphone may become higher than the actual external temperature. In the embodiment, the estimation formula is calculated by adding, to the predictor variables, the CPU information, the battery voltage, etc., as the operation data on the operation state of the smartphone. As a result, according to the estimation formula in the embodiment, even if, for example, the operation state of the smartphone is highly busy and the internal temperature of the smartphone rises above the external temperature, an estimated value of the external temperature can be calculated which reflects the operation state of the smartphone and which is lower than the internal temperature. FIG. 7 FIG. 7 500 is a diagram illustrating an example of the estimation formula calculation data for calculating the estimation formula. As illustrated in , the estimation formula can be calculated based on the relation among the internal temperature data, the operation data, and the actual temperature data that are obtained over a period including a plurality of states respectively corresponding to different operation states of the smartphone for measurement . Additionally, the estimation formula can be calculated based on the relation among the internal temperature data, the operation data, and the actual temperature data that are obtained for a plurality of time periods respectively corresponding to different environmental states, which correspond to different average temperatures, such as different seasons. FIG. 4 500 510 500 As described by referring to , a measurer carries the smartphone for measurement and the digital thermometer to obtain the internal temperature data, the operation data, and the actual temperature data. The measurer can obtain the internal temperature data, the operation data, and the actual temperature data, for example, during a low load state in which no application of the smartphone for measurement is used, and during a high load state in which predetermined application (movie playback application, music playback application, net radio application, etc.) with a large load is used. The estimation formula can be calculated using these data items as the estimation formula calculation data. Additionally, the internal temperature data, the operation data, and the actual temperature data can be obtained during a plurality of time periods respectively corresponding to different environmental states, such as a high temperature environment with high temperature in summer and a low temperature environment with low temperature in winter. The estimation formula can be calculated using these data items as the estimation formula calculation data. Here, the data items under such different environmental conditions may also be obtained under a condition in which the temperature and humidity can be controlled, such as a thermostatic chamber in a laboratory. At this time, the controlled temperature can be used as the actual temperature data. As described above, the accuracy of the estimation formula can be enhanced by calculating the estimation formula using the data items that are obtained under different conditions, as the estimation formula calculation data, and estimated values of the external temperature can be accurately calculated under various conditions. FIG. 1 110 300 300 110 300 a a Referring back to , in the embodiment, the internal temperature data obtainer of the smartphone can obtain the internal temperature data of the smartphone using the above-described predetermined source code, for example. Additionally, the internal temperature data obtainer may obtain the internal temperature data of the smartphone using an API, such as the above-described sensor framework. 112 300 300 112 300 a a In the embodiment, the operation data obtainer of the smartphone can obtain the battery voltage (VOLT) as the operation data of the smartphone using the above-described predetermined source code, for example. Additionally, the operation data obtainer can obtain the CPU information as the operation data of the smartphone using the above-described predetermined source code, for example. FIG. 8 100 is a flowchart illustrating an example of a process by the temperature estimation system according to the embodiment. 110 112 120 114 130 114 300 122 The internal temperature data obtainer obtains the internal temperature data while associating the internal temperature data with the date and time; and the operation data obtainer obtains the operation data while associating the operation data with the date and time (step S). The temperature estimator sequentially applies the internal temperature data and the operation data that are associated with the same date and time to the estimation formula stored in the estimation formula storage , and the temperature estimator calculates an estimated value of the external temperature in the vicinity of the smartphone at that date and time (step S). 116 300 114 300 316 124 120 124 114 122 The estimated temperature output provides, through a network, the smartphone with the estimated value of the external temperature calculated by the temperature estimator . In the smartphone , the sensor outputs the obtained estimated value of the external temperature, for example, by displaying the obtained estimated value of the external temperature on a display (step S). The process from step S to step S can be executed substantially in real time. As a result, the user can be aware of the temperature at a point at which the user is located. Additionally, the temperature estimator may store the estimated values of the external temperature that are continuously calculated at step S for a predetermined time period, while associating the estimated values of the external temperature with the date and time. With such a configuration, the estimated values of the external temperature at the point at which the user is located can be continuously stored for a predetermined time, and the estimated values of the external temperature can be used as environmental data on the skin, for example. FIG. 1 300 200 200 300 116 300 300 300 132 300 300 Note that, in , only one smartphone is depicted. However, the server apparatus may be configured such that the server apparatus is connected to a plurality of smartphones through a network. Additionally, the estimated temperature output can calculate, for each of the plurality of smartphones , an estimated value of the external temperature. The process related to each smartphone is performed while associating the process with identification information (ID) of the smartphone . In this case, the estimated temperature storage stores the estimated value of the external temperature calculated for each of the plurality of smartphones while associating the estimated value of the external temperature with the identification information of the smartphone . 100 200 300 200 300 300 Though it is not depicted, the temperature estimation system (the server apparatus ) may further include a location information obtainer for obtaining location information of each smartphone . With such a configuration, in the server apparatus , an estimated value of the external temperature at a specific location can be detected based on the estimated value of the external temperature and the location information of each smartphone . Additionally, by detecting the estimated value of the external temperature of each of the plurality of smartphones while associating the estimated value of the external temperature and the location information, the estimated values of the external temperature at a plurality of locations can be used. FIG. 9 100 Furthermore, the estimation formula calculation data for calculating the estimation formula can be sequentially accumulated, and, based on the accumulated estimation formula calculation data, the estimation formula can be sequentially updated. is a block diagram illustrating an example of a functional configuration of the temperature estimation system according to the embodiment. 100 200 210 212 230 FIG. 1 In the embodiment, the temperature estimation system (the server apparatus ) further includes, in addition to the functional configuration illustrated in , the data obtainer ; an estimation formula calculator ; and a data accumulator . 210 510 300 510 210 510 210 230 FIG. 4 The data obtainer obtains the estimation formula calculation data. The estimation formula calculation data can be obtained, for example, by the following procedure. Digital thermometers , such as that described by referring to in the first embodiment, are distributed to a plurality of users. Each user carries the user's smartphone (e.g., the smartphone ) and the digital thermometer to obtain the estimation formula calculation data. The data obtainer obtains, from the digital thermometer and the smartphone, etc., of each user, the actual temperature data, the internal temperature data, and the operation data. The data obtainer stores the obtained estimation formula calculation data in the data accumulator . 212 230 210 212 212 130 130 The estimation formula calculator calculates (updates) the estimation formula based on the estimation formula calculation data stored in the data accumulator . Upon detecting that the data obtainer obtains new estimation formula calculation data, the estimation formula calculator calculates the estimation formula again by adding the newly obtained estimation formula calculation data to update the estimation formula. The estimation formula calculator stores the calculated estimation formula in the estimation formula storage . As a result, the estimation formula in the estimation formula storage is updated. 100 In general, accuracy of statistical data increases, as the sample size increases. According to the configuration of the temperature estimation system according to the embodiment, the estimation formula can be updated by increasing the sample size, and the accuracy of the estimation formula can be enhanced. 300 300 100 FIG. 10 The estimation formula can be prepared for each state of the smartphone, such as the operation state and the environmental state of the smartphone. Depending on the state of the smartphone , such as the operation state and the environmental state of the smartphone , an estimated value of the external temperature can be calculated using the corresponding estimation formula. is a block diagram illustrating an example of the functional configuration of the temperature estimation system according to the embodiment. 100 122 122 300 300 110 112 300 300 112 FIG. 9 In the embodiment, the temperature estimation system further includes, in addition to the functional configuration illustrated in , a state determiner . The state determiner determines the state of the smartphone , such as the operation state and the environmental state of the smartphone , for estimating the external temperature, based on the data obtained by the internal temperature data obtainer and the operation data obtainer . The operation state of the smartphone may be, for example, a high load state or not, and the operation state of the smartphone can be determined, for example, based on whether predetermined application is used. Additionally, the operation state can be determined based on a value of a predetermined operation data item of the operation data that is obtained by the operation data obtainer . The environmental state can be determined, for example, based on whether the season is summer or winter. FIG. 11 230 230 1 3 In the embodiment, the estimation formula calculation data may be configured to include a state, such as an operation state and an environmental state of the smartphone at a time of obtainment. is a diagram illustrating an example of an internal structure of the data accumulator in which the estimation formula calculation data is stored. In the data accumulator , the estimation formula calculation data includes the date and time; the actual temperature data; the internal temperature data; and the operation data (CPU through CPU, VOLT), and a state, such as the operation state and the environmental state, is associated with the estimation formula calculation data. FIG. 3 FIG. 6 In the embodiment, the estimation formula can be calculated for each state using the estimation formula calculation data for the corresponding state. For example, the estimation formula for high-load/high-temperature can be calculated by performing multiple regression analysis similar to that described by referring to through using the actual temperature data, the internal temperature data, and the operation data that are associated with high-load/high-temperature. Similarly, for example, the estimation formula for low-load/high-temperature, the estimation formula for high-load/low-temperature, the estimation formula for low-load/low-temperature, etc., can be calculated. Additionally, the estimation formula can be calculated by separating, for example, the estimation formula for high-load from the estimation formula for low-load; or the estimation formula for high-temperature from the estimation formula for low-temperature. FIG. 12 130 130 is a diagram illustrating an example of the internal structure of the estimation formula storage . In the estimation formula storage , a plurality of estimation formulas X1, X2, etc., are stored while the estimation formulas are associated with respective states. Additionally, the operation data used for each estimation formula can be stored while associating the operation data with the estimation formula. FIG. 13 100 is a flowchart illustrating an example of a process by the temperature estimation system according to the embodiment. 110 112 140 122 300 110 112 142 114 122 144 114 300 146 The internal temperature data obtainer obtains the internal temperature data while associating the internal temperature data with date and time, and the operation data obtainer obtains the operation data while associating the operation data with the date and time (step S). The state determiner determines the operation state and the environmental state, etc., of the smartphone at the date and time of the internal temperature data and the operation data obtained by the internal temperature data obtainer and the operation data obtainer (step S). The temperature estimator selects an estimation formula corresponding to the state determined by the state determiner (step S), and the temperature estimator calculates, using the estimation formula, an estimated value of the external temperature in the vicinity of the smartphone at the corresponding date and time (step S). 140 142 Note that the process at step S and step S can be executed substantially in real time. 100 With the configuration of the temperature estimation system according to the embodiment, the estimation formulas can be selectively used depending on the state, and the estimated value of the external temperature can be more accurately calculated. FIG. 4 The estimation formula calculation data was collected by actually using the smartphone (GALAXY Note) and the digital thermometer in accordance with the procedure described by referring to during five days between March 2016 and May 2016. Here, for each of the high load state in which application, such as Youtube and TuneInradio, was used and the low load state in which no application was used, the estimation formula calculation data was collected at a room temperature and at a low temperature environment in which the smartphone was placed in a refrigerator. 1 7 1 4 6 7 As the operation data, the battery voltage (VOLT) and the CPU information (CPU through CPU) were obtained. Among these, the five types with high correlation coefficients with the actual temperature data, namely, the battery voltage (VOLT) and the CPU information (CPU, CPU, CPU, CPU), were used for the calculation of the estimation formula. The calculation of the correlation coefficients and the multiple regression analysis were performed using statistical analysis software “R.” As a result, the following estimation formula was obtained. (Estimated value of the external temperature)=−1.88E+01+3.40E−01×(the internal temperature data)+8.69E−03×(VOLT)−1.56E−05×(CPU1)−1.72E−07×(CPU4)+1.02E−01×(CPU6)+3.01E−05×(CPU7) (1) 1 4 6 7 Additionally, separately from the collection of the estimation formula calculation data, the internal temperature data, the operation data, and the actual temperature data were collected using the same smartphone (GALAXY Note) and the digital thermometer. Here, the data collection was performed at a room temperature for each of the high load state in which application, such as Youtube and TuneInradio, was used in the smartphone and the low load state in which no application was used. The estimated value of the external temperature was calculated by applying the collected internal temperature data and the operation data (VOLT, CPU, CPU, CPU, and CPU) to the formula (1). FIG. 14 FIG. 14 is a diagram illustrating the estimated values of the external temperature, which are calculated from the collected internal temperature data, the collected actual temperature data, and the formula (1). As shown in , even if the smartphone is in the high load state, the estimated value of the external temperature is approximately equal to the actual temperature, and the external temperature of the smartphone can be accurately estimated. 100 With the temperature estimation system in the embodiment, the external temperature of the mobile terminal device can be accurately estimated using data that can be standardly obtained by the mobile terminal device, such as the smartphone. The embodiments of the present invention are described above by referring to the drawings. However, these are exemplification of the present invention, and various configurations other than the above-described configurations may be adopted. 100 100 FIG. 1 FIG. 9 FIG. 10 Each component of the temperature estimation system illustrated in , , and shows a functional unit block, which is not a hardware unit configuration. Each components of the temperature estimation system is implemented by a combination of hardware and software, which mainly include one or more computer CPUs; a memory; a program loaded on the memory for implementing a component of the drawings; a storage unit, such as a hard disk for storing the program; and an interface for network connection. A person ordinarily skilled in the art will appreciate that there are various modifications to the implementation methods and the devices. FIG. 1 FIG. 1 100 200 100 300 100 300 200 For example, in , the configuration is illustrated as the example in which the functional configuration of the temperature estimation system is embedded in the server apparatus . However, the functional configuration of the temperature estimation system illustrated in may be provided in the smartphone . A part of the functional configuration of the temperature estimation system described in the embodiments above may be provided in the smartphone , and the remainder may be provided in the server apparatus . 300 114 130 300 300 140 130 200 300 200 300 300 300 200 132 300 300 For example, the smartphone may be configured to include the temperature estimator and the estimation formula storage , and the configuration may be such that the estimated value of the external temperature is calculated by the smartphone . Alternatively, for example, the smartphone may include the temperature estimator , and the configuration may be such that, depending on necessity, the estimation formula stored in the estimation formula storage is retrieved from the server apparatus , and the estimated value of the external temperature is calculated by the smartphone . In this case, the server apparatus may retrieve, for each of the plurality of smartphones , the estimated value of the external temperature of the smartphone while associating the estimated value of the external temperature of the smartphone with the corresponding identification information, and the server apparatus may store, in the estimated temperature storage , the estimated value of the external temperature of each smartphone while associating the estimated value of the external temperature of the smartphone with the corresponding identification information. 110 112 300 300 110 316 a a a a. Furthermore, the configuration of the internal temperature data obtainer and the operation data obtainer of the smartphone to obtain the internal temperature data and the operation data of the smartphone is not limited to the above-described procedure using the API, the predetermined source code, etc., and various configurations may be adopted, such as a configuration in which the internal temperature data obtainer directly obtains the internal temperature data measured by the temperature sensor 300 110 112 200 300 Furthermore, a configuration may be such that, if the internal temperature data and the operation data of the smartphone are accumulated in a predetermined external server, the internal temperature data obtainer and the operation data obtainer of the server apparatus directly obtain the internal temperature data and the operation data of the smartphone using the above-described API, the predetermined source code, etc. In the embodiments above, the smartphone operating on the Android (registered trademark) platform is described as the example. However, if a mechanism is provided with which the internal temperature data and the operation data can be obtained in the same manner, the internal temperature data and the operation data can be obtained by a similar process by a smartphone with another OS as a platform. In the embodiments above, the examples are illustrated in which the estimation formula is calculated using the multiple regression analysis. However, the embodiments are not limited to the multiple regression analysis, and the correlation among the internal temperature data, the operation data, and the actual temperature data can be represented by formulas or models using various statistical analysis methods, etc. In the third embodiment, an example is illustrated in which an estimation formula is prepared for each state, and an estimation formula is selected depending on a state. Similarly, an estimation formula may be prepared for each type and for each model of the mobile terminal device, and an estimation formula to be used may be selected depending on the type and the model of the mobile terminal device. This international application is based on and claims priority to Japanese Patent Application No. 2016-172246, filed on Sep. 2, 2016, and the entire content of which is hereby incorporated by reference. 100 temperature estimation system 110 internal temperature data obtainer 112 operation data obtainer 114 temperature estimator 116 estimated temperature output 116 a estimated temperature output 122 state determiner 130 estimation formula storage 132 estimated temperature storage 200 server apparatus 210 data obtainer 212 estimation formula calculator 230 data accumulator 300 smartphone 314 battery 316 a temperature sensor 500 smartphone for measurement 510 digital thermometer BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram illustrating an example of a functional configuration of a temperature estimation system according to an embodiment; FIG. 2 is a block diagram illustrating an example of a hardware configuration of a smartphone according to an embodiment; FIG. 3 is a flowchart illustrating an example of a procedure for calculating an estimated formula according to an embodiment; FIG. 4 is a diagram illustrating the example of the procedure for calculating the estimated formula according to the embodiment; FIG. 5 is a diagram illustrating an example of actual temperature data stored in an actual temperature data storage of a digital thermometer; FIG. 6 is a diagram illustrating an example of data stored in a measured data storage of a smartphone for measurement; FIG. 7 is a diagram illustrating an example of estimated formula calculation data for calculating the estimated formula; FIG. 8 is a flowchart illustrating an example of a process by the temperature estimation system according to an embodiment; FIG. 9 is a block diagram illustrating an example of a functional configuration of the temperature estimation system according to an embodiment; FIG. 10 is a block diagram illustrating an example of a functional configuration of the temperature estimation system according to the embodiment; FIG. 11 is a diagram illustrating an example of the estimation formula calculation data according to an embodiment; FIG. 12 is a diagram illustrating an example of an internal structure of an estimation formula storage; FIG. 13 is a flowchart illustrating an example of a process by the temperature estimation system according to an embodiment; and FIG. 14 is a diagram showing external temperature estimation values calculated in an embodiment.
--- abstract: 'We evaluate the density matrix of an arbitrary quantum mechanical system in terms of the quantities pertinent to the solution of the time-dependent density functional theory (TDDFT) problem. Our theory utilizes the adiabatic connection perturbation method of Görling and Levy, from which the expansion of the many-body density matrix in powers of the coupling constant $\lambda$ naturally arises. We then find the reduced density matrix $\rho_\lambda(\rv,\rv'',t)$, which, by construction, has the $\lambda$-independent diagonal elements $\rho_\lambda(\rv,\rv,t)=n(\rv,t)$, $n(\rv,t)$ being the particle density. The off-diagonal elements of $\rho_\lambda(\rv,\rv'',t)$ contribute importantly to the processes, which cannot be treated via the density, directly or by the use of the known TDDFT functionals. Of those, we consider the momentum-resolved photoemission, doing this to the first order in $\lambda$, i.e., on the level of the exact exchange theory. In illustrative calculations of photoemission from the quasi-2D electron gas and isolated atoms, we find quantitatively strong and conceptually far-reaching differences with the independent-particle Fermi’s golden rule formula.' author: - 'Vladimir U. Nazarov' title: 'Many-body quantum dynamics by the reduced density matrix based on the time-dependent density functional theory' --- Time-dependent (TD) density functional theory (TDDFT) [@Zangwill-80; @Runge-84; @Gross-85] is a widely used powerful method to study the time-evolution and the excitation processes in quantum mechanical systems. Its success is due to the crucial simplification arising from the substitution of the prohibitively complicated many-body problem with the reference single-particle one, keeping (apart from approximations possibly invoked) the exact TD electron density of the original many-body system. The description of a number of physical processes (e.g., optical absorption [@Kim-02; @Botti-04], slowing of ions in matter [@Echenique-81; @Nazarov-05], impurity resistivity of metals [@Nazarov-14-2], [etc.]{}) can be rigorously reduced to finding the TD electron density, making TDDFT the method of choice for studying those classes of phenomena. There exist, at the same time, fundamental processes and the corresponding experimental methods, the theory of which cannot, on the very general physical grounds, be formulated explicitly in terms of the particle density. For a clear example, the momentum-resolved photoemission requires the knowledge of the probability in the [momentum space]{}, which, as long as we remain within the framework of the consistent quantum mechanics, cannot be found directly from the probability in the [coordinate space]{}, the latter giving the particle density. The necessary information is, in this case, contained in the reduced density matrix (DM) $\rho$ [@Landau-81]. The real space $\rho(\rv,\rv',t)$ and the momentum space $\rho(\pv,\pv',t)$ representations of $\rho$ are related by the double Fourier transform, while the diagonal elements in the corresponding representations (probabilities) cannot be related directly [^1]. To find the reduced DM is a complicated problem, generally speaking, taking us back to the many-body theory. In this Letter we come up with the observation that the solution of this task can be greatly facilitated if the TDDFT problem for the same system has been already solved. We use the power of the adiabatic connection perturbation method [@Gorling-94; @Gorling-97] and show that, changing the electron-electron ($e$-$e$) interaction constant $\lambda$ continuously from zero (for the reference system) to one (for the physical system), while keeping the particle density $n_\lambda(\rv)=n(\rv)$ unchanged, we determine not only the Kohn-Sham (KS) [@Kohn-65] potential $v_s(\rv,t;\lambda)$, but also the many-body DM $\hat{\rho}_\lambda$. The latter can be readily reduced to the one-DM $\rho_\lambda(\rv,\rv',t)$ expressed through the KS TDDFT quantities. We emphasize, and this is the motivation of this work, that $\rho_{\lambda=1}(\rv,\rv',t)$ is, while the KS DM is not, the true reduced DM of the physical system (c.f., Ref. [@Casida-95]). Practically, the above program can so far be implemented to the first order in $\lambda$ only, which results in the construction of the TD exact-exchange (TDEXX)-based theory of the DM. We apply this theory to the problem of the momentum-resolved photoemission, finding quantitative and qualitative differences with the Fermi’s golden rule. We use atomic units ($e^2=m_e=\hbar=1$). [Real-time formalism for DM to the first order in the interaction.]{}–We write the adiabatic connection Hamiltonian for an $N$-particle system [@Gorling-94; @Gorling-97] $$\hat{H}(t;\lambda) \! = \! \sum\limits_{i=1}^N \! \left[ -\frac{1}{2} \Delta_i \! + \! v_{ext}(\rv_i,t) \! + \! \tilde{v}(\rv_i,t;\lambda) \right] + \sum\limits_{i<j}^N \frac{\lambda}{\|\rv_i \! -\! \rv_j\|}, \label{Hac}$$ where $\lambda\in[0,1]$, $\tilde{v}(\rv,t;0)=v_s(\rv,t) -v_{ext}(\rv,t)$, $v_{ext}$ and $v_s$ being the external and KS potentials, respectively, and we keep the particle density $\lambda$-independent [@Gorling-94; @Gorling-97]. The corresponding $N$-body DM obeys the Liouville’s equation $$i \frac{\pa \hat{\rho}(t;\lambda)}{\pa t}= [\hat{H}(t;\lambda),\hat{\rho}(t;\lambda)]. \label{l}$$ Expanding to the first order in $\lambda$ (but making, so far, no assumption regarding the strength of the external TD field), we write $$\left[ \begin{array}{l} \hat{H}(t;\lambda)\\ \hat{\rho}(t;\lambda)\\ \tilde{v}(t;\lambda) \end{array} \right] = \left[ \begin{array}{l} \hat{H}_0(t)\\ \hat{\rho}_0(t)\\ \tilde{v}_0(t) \end{array} \right]+ \lambda \left[ \begin{array}{l} \hat{H}_1(t)\\ \hat{\rho}_1(t)\\ \tilde{v}_1(t) \end{array} \right], \label{v01}$$ where $$\begin{aligned} &\hat{H}_0(t) = \sum\limits_{i=1}^N \left[ -\frac{1}{2} \Delta_i +v_{ext}(\rv_i,t) + \tilde{v}_0(\rv_i,t) \right],\\ &\hat{H}_1(t) = \sum\limits_{i=1}^N \tilde{v}_1(\rv_i,t) + \sum\limits_{i<j}^N \frac{1}{\|\rv_i-\rv_j\|},\label{H1}\end{aligned}$$ and the corresponding density matrices evolve as $$\begin{aligned} &i \frac{\pa \hat{\rho}_0(t)}{\pa t}= [\hat{H}_0(t),\hat{\rho}_0(t)], \label{0}\\ &i \frac{\pa \hat{\rho}_1(t)}{\pa t}= [\hat{H}_0(t),\hat{\rho}_1(t)]+[\hat{H}_1(t),\hat{\rho}_0(t)]\label{l1}.\end{aligned}$$ Let for $t\le 0$ the system be in its ground-state with the KS wave-function $\|0\rangle$, where $\|\alpha\rangle$ is the orthonormal complete set of the Slater-determinant eigenfunctions of $\hat{H}_0(0)$. Let at $t=0$ the TD potential be switched on. Then, since $\hat{H}_0(t)$ is self-conjugate, $\|\alpha(t)\rangle$, which satisfy $$i \frac{\pa \|\alpha(t)\rangle}{\pa t}= \hat{H}_0(t) \|\alpha(t)\rangle, \, \|\alpha(0)\rangle=\|\alpha\rangle, \label{ts}$$ constitute also an orthonormal complete set at each $t$. From Eqs. (\[0\]) and (\[l1\]) we obtain [Ref. @Note1 Sec. I] $$\begin{aligned} &\langle \alpha(t)\| \hat{\rho}_0(t)\| \beta(t) \rangle = \delta_{\alpha 0} \delta_{\beta 0}, \label{mat0} \\ &\langle \alpha(t)\| \hat{\rho}_1(t)\| \beta(t) \rangle \! = \! i (\delta_{\alpha 0}-\delta_{\beta 0}) \! \! \! \int\limits_{-\infty}^t \! \! \langle \alpha(t')\| \hat{H}_1(t')\| \beta(t')\rangle d t', \label{mat}\end{aligned}$$ where $\delta_{\alpha \beta}$ is the Kronecker symbol. Transforming Eqs. (\[mat0\]) and (\[mat\]) to real space and reducing to the one-DM, we find $$\begin{aligned} &\rho_0(\rv,\rv',t) \! = \sum\limits_{i\in occ} \phi_i(\rv,t) \phi_i^(\rv',t), \label{rho0000} \\ &\rho_1(\rv,\rv',t) \! = \! \! \! \! \! \! \sum\limits_{\substack{i\in occ\\ j\in unocc}} \! \! \! \! \! \langle 0(t) \| \hat{\rho}_1(t)\| 0_{ij}(t)\rangle \phi_i(\rv,t) \phi_j^(\rv',t) + (\rv \! \leftrightarrow \! \rv')^, \label{rho1000}\end{aligned}$$ where $\phi_i$ are KS orbitals, $0_{ij}(t)$ is the propagated ground-state Slater-determinant $0(t)$ with the $i$-th orbital replaced with the $j$-th one \[$\langle 0(t) \| \hat{\rho}_1(t)\| 0_{ij}(t)\rangle$ are the only matrix elements that survive the integration\]. Equation (\[rho1000\]) reduces to $$\begin{split} &\rho_1(\rv,\rv',t) \! = \! -i \! \! \! \! \sum\limits_{\substack{i\in occ\\ j\in unocc}} \! \! \! \int_{-\infty}^t \! \! \! \! d t' \left[ \int \! \! v_x(\rv_1,t') \phi_i^(\rv_1,t') \phi_j(\rv_1,t') d\rv_1 \right. \\ &\left. + \int \frac{ \phi_i^(\rv_1,t') \rho_0(\rv_1,\rv_2,t') \phi_j(\rv_2,t')}{\|\rv_1-\rv_2\|} d\rv_1 d\rv_2 \right] \phi_i(\rv,t) \phi_j^(\rv',t) \\ & + (\rv \leftrightarrow \rv')^, \end{split} \label{rho1}$$ where $v_x=v_s-v_{ext}-v_H$, and $v_H$ are the exchange and the Hartree potentials, respectively. Setting $\rv'=\rv$ in Eq. (\[rho1\]) and equating to zero (the density must be $\lambda$-independent), we retrieve the TD version of the optimized effective potential equation [@Sharp-53; @Talman-76] for $v_x(\rv,t)$. On the other hand, if above we allowed for nonlocal effective potentials, then Eq. (\[rho1\]) would reproduce the long-known result [@Moller-34] that the Hartree-Fock (HF) potential nullifies $\rho_1$. Consequently, the (TD)HF reduced DM is the first-order approximation to the physical one. As discussed above, this is not the case within TDDFT. It is verifiable by the direct substitution that $\rho_0$ of Eq. (\[rho0000\]) and $\rho_1$ of Eq. (\[rho1\]) satisfy the Liouville-type equations $$\begin{aligned} &i \frac{\pa \rho_0(\rv,\rv',t)}{\pa t} = [\hat{h}_s(t),\rho_0(t)] , \label{Li0}\\ \begin{split} &i \frac{\pa \rho_1(\rv,\rv',t)}{\pa t} = [\hat{h}_s(t),\rho_1(t)] -[ v_x(t), \rho_0(t)] + \\ & \int \! \rho_0(\rv,\rv_1,t) \rho_0(\rv_1,\rv',t) \left[ \frac{1}{\|\rv_1-\rv'\|} -\frac{1}{\|\rv_1-\rv\|}\right]d\rv_1 , \end{split} \label{Li1}\end{aligned}$$ where $\hat{h}_s(t)$ is the KS Hamiltonian. Equation (\[rho1\]) or, alternatively, (\[Li1\]) determine the time-evolution of the reduced DM to the first order in the interaction, and they are expected to be useful in the nonlinear dynamics. We, however, turn now to the linear response regime and focus on the photoemission spectroscopy (PES) application. [Linear-response theory.]{}–From now on we assume the TD external potential $$v_{ext}^{(1)}(\rv,t) = \frac{1}{2} \left[ v_{ext}^{(1)}(\rv,\omega) e^{-i \omega t} + c.c. \right]. \label{extp}$$ to be weak. We expand $\rho(t)=\rho^{(0)}+\rho^{(1)}(t)+\rho^{(2)}(t) + \dots$, where the superscripts stand for the orders in the strength of the TD perturbation, while the subscripts remain reserved for the orders in the $e$-$e$ interaction. To the zeroth order in the latter, we obtain for the probability per unit time for an electron to be emitted into the state $\phi_f(\rv)$ [Ref. @Note1 Sec. II] [^2] $$\lim\limits_{t\to \infty} \! \! \frac{\langle \phi_f\| \rho_0^{(2)}(t)\|\phi_f\rangle}{t} \! = \! \sum\limits_{i\in occ} A_{f i}(\omega) \delta(\omega-\epsilon_f+\epsilon_i), \label{ph0}$$ where $$A_{f i}(\omega)= \frac{\pi }{2} \|\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_i\rangle\|^2, \label{def0}$$ which reproduces the conventional Fermi’s golden rule. To the [first]{} order in the interaction, Eq. (\[Li1\]) leads to [Ref. @Note1 Sec. III] $$\lim\limits_{t\to \infty} \frac{ \langle \phi_f\| \rho_1^{(2)}(t)\|\phi_f\rangle}{t} = \sum\limits_{i\in occ} \Delta A_{f i}(\omega) \delta(\omega-\epsilon_f+\epsilon_i) + \Delta B_{f i}(\omega) \delta'(\omega-\epsilon_f+\epsilon_i) , \label{ph1}$$ $$\begin{split} & \Delta A_{f i}(\omega) = -\pi \, {\rm Re} \left \{ \langle \phi_f\|v_s^{(1)}(\omega)\|\phi_i\rangle^ \left[ \langle \phi_f\|v_x^{(1)}(\omega)\|\phi_i\rangle + \sum\limits_{k\ne i} C_{k i} \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle }{\epsilon_i-\epsilon_k} \right. \right. \\ & \left. \left. + \sum\limits_{k\ne f} C_{f k} \frac{ \langle \phi_k\|v_s^{(1)}(\omega)\|\phi_i\rangle }{\epsilon_f-\epsilon_k} + \sum\limits_{kl} (f_k-f_l) \, \frac{ \langle \phi_k\|v_s^{(1)}(\omega)\|\phi_l\rangle}{\epsilon_k-\epsilon_l-\omega-i\eta} \int \frac{\phi_i(\rv) \phi_f^(\rv') \phi_l^(\rv) \phi_k(\rv') }{\|\rv-\rv'\|} d\rv d\rv' \right] \right\}, \end{split} \label{def1}$$ $$\Delta B_{f i} (\omega) = - \frac{\pi}{2} \|\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_i\rangle\|^2 C_{i i}, \label{def2}$$ where $$C_{k m} \! = \! \langle\phi_k\|v_x^{(0)} \|\phi_m\rangle + \! \int \! \rho_0^{(0)}(\rv,\rv') \frac{\phi_k^(\rv) \phi_m(\rv')}{\|\rv-\rv'\|}d\rv d\rv' , \label{def3}$$ and $f_k$ are the orbitals’ occupancies. Equations (\[ph1\])-(\[def3\]) generalize the Fermi’s golden rule, including interaction to the first order. The two terms in Eq. (\[ph1\]) have distinct physical meaning: The one with the delta-function accounts for the change in the [amplitude]{} of the emission due to the $e$-$e$ interaction. The one with the delta-function derivative accounts for the [excitation energies shifts]{}, due to the same reason. To demonstrate this, we combine Eqs. (\[ph0\]) and (\[ph1\]) as $$\begin{split} \lim\limits_{t\to \infty} \frac{ \langle \phi_f\| \rho^{(2)}(t)\|\phi_f\rangle}{t} & = \sum\limits_{i\in occ} \left[ A_{f i}(\omega) \! + \! \Delta A_{f i}(\omega)\right] \delta(\omega -\epsilon_f + \epsilon_i) + \Delta B_{f i}(\omega) \delta'(\omega-\epsilon_f+\epsilon_i) \label{ph} \\ &= \sum\limits_{i\in occ} \left[ A_{f i}(\omega) + \Delta A_{f i}(\omega)\right] \delta\left[\omega - \epsilon_f + \epsilon_i +\Delta \omega_i\right] , \end{split}$$ where $$\Delta \omega_i =\frac{\Delta B_{f i}(\omega)}{A_{f i}(\omega)}= - C_{i i}. \label{dw}$$ We note that the energy-shift (\[dw\]) is a ground-state property of the KS system. We now turn to illustrative calculations. [Photoemission from quasi-2D electron gas with one filled subband.]{}–For quasi-2D electron gas (Q2DEG) with one filled subband and normally applied electric field (schematized in Fig. \[sys\]) the analytical solution to the TDEXX problem exists [@Nazarov-17], which makes it ideally suited for the illustration of our theory by a simple calculation. Then $$\begin{split} v_x(z,t) = -\frac{1}{n_s} \int \frac{F_2(k_F\|z - z'\|)}{\|z - z'\|} n(z',t) d z' , \end{split} \label{main152}$$ where $F_2(u)=1+[L_1(2 u)-I_1(2 u)]/u$, $L_1$ and $I_1$ are the 1st-order modified Struve and Bessel functions, $n_s=\int_{-\infty}^\infty n(z,t) d z$ is the time-independent 2D density, and $k_F$ is the corresponding 2D Fermi radius. From equations (\[def0\]), (\[def1\])-(\[def2\]), we find $A_{f 0}(\omega)$, $\Delta A_{f 0}(\omega)$, and $\Delta \omega$ [Ref. @Note1 Sec. IV]. In particular, $$\Delta \omega(k_\\|) = - \int \|\mu_0(z)\|^2 G_{k_\\|}(z)d z, \label{shift2D}$$ where $\kv_\\|$ is the conserving in-plane momentum, $$\begin{aligned} &G_{k_\\|}(z)=v_x^{(0)}(z)+ k_F \int \|\mu_0(z')\|^2 S_{k_\\|}(k_F\|z-z'\|) d z',\\ &S_{k_\\|}(u)= \int\limits_0^\infty \frac{J_1(x) J_0(\frac{k_\\|}{k_F} x)}{\sqrt{x^2+u^2}} d x , \label{SSS} \end{aligned}$$ and $J_n(x)$ are Bessel functions [see Ref. @Note1 Sec. IV for the plot of $S_{k_\\|}(u)$]. In Fig. \[dB\] we plot the ionization potential (IP) of an electron with the momentum $k_\\|$. The IP with the interactions included (the solid curve for the EXX calculation) depends on $k_\\|$. This dependence signifies a fundamental difference between the KS and the many-body dynamics: Our system is uniform in the $xy$-plane and, therefore, $xy$ and $z$ coordinates separate in the KS equations, resulting in the motion of a KS electron in the $z$-dimension being unaffected by the value of its in-plane momentum. In particular, the IP in the KS dynamics is $k_\\|$-independent (shown with horizontal lines). Secondly, depending on $k_\\|$, the energy shift can be either positive or negative. Therefore, for larger $k_\\|$, we can emit an electron with the photon energy $\omega$ less than the KS work function $-\epsilon_0$. We stress that these results are not in contradiction to the theorem stating that the minus highest occupied KS orbital energy is IP [@Perdew-82] (IP-theorem), since the latter has been proven for finite number of particles (and then $k_\\|$ is not defined), while our case is of infinite number of electrons [^3]. Expansion of DM in $\lambda$, leading to Eq. (\[rho1\]), may not necessarily be based on TDEXX. While the latter ensures that $\rho(\rv,\rv,t)$ is the physical density to the 1st order, we could have used other TDDFT schemes as well. Then the resulting series could, likewise, be expected to converge to the physical DM. In Fig. \[dB\] we, therefore, compare EXX results to those of the local density approximation (LDA) (dashed lines). An eloquent conclusion is that, while the KS eigenvalues, being auxiliary quantities, are completely different in the respective approximations (horizontal lines), the IPs we obtain, being approximations to physical quantities, are found close to each other in EXX and LDA. Obviously, the latter is of great practical consequence, since it shows that inexpensive local functionals can be successfully used in the framework of this theory. In Fig. \[MF\], we plot the interacting electrons’ emission intensity and compare it with its Fermi’s golden rule counterpart. It must be noted that the golden rule is overwhelmingly often used in the literature with the KS field in the matrix element replaced with the bare external one (dipole approximation), while the screening has been included only rather recently [@Krasovskii-10]. It is, therefore, instructive to compare our results to the both variants of the conventional formula. Without interaction, the threshold of the photoemission lies at $-\epsilon_0$, shown in Fig. \[MF\] with a long vertical dotted line, and it is the same for all values of $k_\\|$. As discussed above, this is not the case with the interaction included, and the corresponding thresholds for three values of $k_\\|$ are shown by short vertical dotted lines. The spectra at different $k_\\|$ are very different from each other, signifying the important quantitative role of the interaction effect. The case of $k_\\|=k_F$ deserves special attention: Here $\Delta \omega >0$, which makes emission possible at $\omega<-\epsilon_0$. In this energy range, the spectrum is strongly affected by the transitions between the ground and discreet excited states, resulting in resonances at the corresponding energies. Since within TDEXX these transitions are undamped [@Nazarov-17], the amplitudes of the corresponding peaks are not in the same scale with the rest of the spectra. [Isolated atoms.]{}– Our second example concerns photoemission from atoms. In Table \[table1\] we list the KS EXX eigenvalues, the energy shifts, and the total IP according to the present theory. The following important observations can be made. Firstly, for the highest energy levels, the shifts $\Delta \omega$ disappear, which is in agreement with the IP-theorem. atom $-\epsilon_i$ $-\Delta \omega_i$ $-(\epsilon_i\! + \! \Delta \omega_i$) $-\epsilon_i^{exp}$ $-\epsilon_i^{HF}$ -------- --------------- ------------------------ ---------------------------------------- --------------------- -------------------- He(1s) 0.9179 -9.6$\times$10$^{-14}$ 0.9179 0.9036 0.9179 Be(1s) 4.1147 0.6169 4.7316 4.384 4.7327 (2s) 0.3091 -2.7$\times$10$^{-6}$ 0.3091 0.3425 0.3093 Ne(1s) 30.767 1.9951 32.762 31.985 32.772 (2s) 1.7054 0.2187 1.9241 1.781 1.9304 (2p) 0.8478 -5.4$\times$10$^{-5}$ 0.8477 0.7960 0.8504 Mg(1s) 46.267 2.7567 49.024 48.174 49.032 (2s) 3.0927 0.6697 3.7624 3.454 3.7677 (2p) 1.8696 0.4114 2.2811 2.0212 2.2822 (3s) 0.2526 3.2$\times$10$^{-5}$ 0.2526 0.2811 0.2531 : KS EXX orbital eigenvalues $\epsilon_i$, the energy shifts $\Delta \omega_i$ of Eq. (\[dw\]), and the corresponding interaction-corrected IP $-(\epsilon_i + \Delta \omega_i)$ for several spherically symmetric spin neutral atoms, compared to the experimental [@Shirley-77] and the HF [@Saito-09] values. \[table1\] Secondly, for inner levels, $\Delta \omega$ are large and they change the KS eigenvalues in the right direction to the experimental IP. These shifts are, however, too big, making the theoretical IP to overestimate the experimental ones, while the KS values underestimate them. Obviously, further terms in the series in $\lambda$ are necessary to improve the agreement with experiment. Thirdly, our $\epsilon_i+\Delta \omega_i$ are found very close to the HF eigenvalues. This has a fundamental reason: As follows from the discussion after Eq. (\[rho1\]), the latter give physical IP to the first order in the interaction, which also $\epsilon_i+\Delta \omega_i$ do, but not $\epsilon_i$. atom $-\epsilon_i^{LDA}$ $-\epsilon_i^{EXX}$ $-(\epsilon_i^{LDA} \! + \! \Delta \omega_i^{LDA}$) $-(\epsilon_i^{EXX} \! + \! \Delta \omega_i^{EXX}$) -------- --------------------- --------------------- ----------------------------------------------------- ----------------------------------------------------- -- He(1s) 0.5170 0.9179 0.9354 0.9179 Be(1s) 3.7956 4.1147 4.7547 4.7316 (2s) 0.1736 0.3091 0.3123 0.3091 Ne(1s) 30.229 30.767 32.849 32.762 (2s) 1.2656 1.7054 1.9741 1.9241 (2p) 0.4428 0.8478 0.8958 0.8477 Mg(1s) 45.890 46.267 49.090 49.024 (2s) 2.8454 3.0927 3.7874 3.7624 (2p) 1.6615 1.8696 2.3102 2.2811 (3s) 0.1423 0.2526 0.2542 0.2526 : KS LDA and EXX orbital eigenvalues and the corresponding interaction-corrected IP of the atoms in Table \[table1\]. \[table2\] As seen from Table \[table2\], similarly to the case of Q2DEG, the use of LDA instead of EXX does not change the IP significantly: while the orbital eigenvalues differ largely in the corresponding approximations, adding $\Delta \omega$ brings them close together. In conclusions, assuming a solution to the TDDFT problem for a quantum mechanical system known, we have evaluated the reduced density matrix $\rho(\rv,\rv',t)$ to the first order in the $e$-$e$ interaction, at the fixed particle density, as stipulated by TDDFT. The knowledge of $\rho(\rv,\rv',t)$ extends the theory to phenomena, which are now beyond the reach of the pure TDDFT with the existing observable functionals. As a particular application, we have derived an extension to the Fermi’s golden rule for the momentum-resolved stationary photoelectron spectroscopy, which accounts for the interparticle interaction. Our calculations for the quasi-2D electron gas with one filled subband and for isolated atoms manifest an important role of the $e$-$e$ interactions in the TDDFT of PES. In particular, our theory captures a remarkable effect of the correlation between the in-plane and the normal motion in a laterally uniform system, which is a feature due to the many-body interactions. Going beyond the bare exchange remains the main challenge in the future development of the theory. Although, on the formal level, our method contains all the correlations at $\lambda^n, n\ge 2$, at present only the inclusion of the $\lambda^2$ term looks feasible. Since this method involves the TDDFT calculation followed by the construction of the reduced DM, it comes very encouraging that, as both our examples show, the inaccuracies of the former are compensated by the latter. This opens the way to use the inexpensive local TDDFT functionals without compromising the accuracy of the final results, which greatly contributes to the practicability of this method. Among other extensions of the theory, we note that the nonlinear dynamics using our Eq. (\[Li1\]) provides a natural pathway to the quantum-mechanically consistent inclusion of interactions in the theory of photoemission in the time-domain [@Pohl-00; @DeGiovannini-12; @Dinh-13; @Dauth-16; @Wopperer-17; @DeGiovannini-17], presently this theory relying on the [ansatz]{} of the identification of the KS particles with physical electrons [@Dauth-16]. Finally, we anticipate it conceptually feasible to extend the theory to evaluate the two-electron density matrix, with an immediate application to the double photoelectron spectroscopy. Author acknowledges support from the Ministry of Science and Technology, Taiwan, Grants 106–2923–M-001–002–MY3 and 107–2112–M–001–033. [31]{}ifxundefined \[1\][ ifx[\#1]{} ]{}ifnum \[1\][ \#1firstoftwo secondoftwo ]{}ifx \[1\][ \#1firstoftwo secondoftwo ]{}““\#1””@noop \[0\][secondoftwo]{}sanitize@url \[0\][‘\ 12‘\$12 ‘&12‘\#12‘12‘\_12‘%12]{}@startlink\[1\]@endlink\[0\]@bib@innerbibempty [*, ()](https://doi.org/10.1103/PhysRevA.21.1561) @noop [, ()]{} @noop [, ()]{} @noop [, ()]{} @noop [, ()]{} [, ()](https://doi.org/https://doi.org/10.1016/0038-1098(81)91173-X) [, ()](https://doi.org/10.1103/PhysRevB.71.121106) [, ()](https://doi.org/10.1103/PhysRevB.89.241108) @noop []{} (, , ) @noop [**, ()]{} @noop [, ()]{} @noop [, ()]{} , in [](https://doi.org/10.1142/9789812830586_0005) () pp. [**, ()](https://doi.org/10.1103/PhysRev.90.317) @noop [, ()]{} [, ()](https://doi.org/10.1103/PhysRev.46.618) [, ()](https://doi.org/10.1103/PhysRevLett.118.236802) [, ()](https://doi.org/10.1103/PhysRevLett.49.1691) [, ()](https://doi.org/10.1103/PhysRevB.82.125102) [, ()](https://doi.org/10.1103/PhysRevB.15.544) [, ()](https://doi.org/https://doi.org/10.1016/j.adt.2009.06.001) [, ()](https://doi.org/10.1103/PhysRevLett.84.5090) [, ()](https://doi.org/10.1103/PhysRevA.85.062515) [, ()](https://doi.org/10.1103/PhysRevA.87.032514) [, ()](https://doi.org/10.1103/PhysRevA.93.022502) [, ()](https://doi.org/10.1140/epjb/e2017-70548-3) [, ()](https://doi.org/10.1021/acs.jctc.6b00897) SUPPLEMENTAL MATERIAL {#supplemental-material .unnumbered} ===================== to the paper by Vladimir U. Nazarov\ \ [Many-body quantum dynamics by the TDDFT-based theory of the reduced density matrix*]{} (I) Derivation of Eqs. (\[mat0\]) and (\[mat\]). ================================================ \(a) Taking a matrix element of Eq. (\[0\]), we have $$i \langle \alpha(t)\| \frac{\pa \hat{\rho}_0(t)}{\pa t}\| \beta(t)\rangle= \langle \alpha(t)\| [\hat{H}_0(t),\hat{\rho}_0(t)] \| \beta(t)\rangle,$$ which, with account of Eq. (\[ts\]) leads to $$i \langle \alpha(t)\| \frac{\pa \hat{\rho}_0(t)}{\pa t}\| \beta(t)\rangle= \langle i \frac{\pa \alpha(t)}{\pa t} \| \hat{\rho}_0(t) \| \beta(t)\rangle- \langle \alpha(t)\| \hat{\rho}_0(t) \| i \frac{\pa \beta(t)}{\pa t}\rangle,$$ and, therefore, to $$\frac{\pa}{\pa t} \langle \alpha(t)\| \hat{\rho}_0(t)\| \beta(t) \rangle = 0.$$ Hence $$\langle \alpha(t)\| \hat{\rho}_0(t)\| \beta(t) \rangle = \langle \alpha\| \hat{\rho}_0(0)\| \beta \rangle,$$ and Eq. (\[mat0\]) is proven with account of the fact that at $t=0$ our system is in its ground KS state. \(b) Similarly, taking a matrix element of Eq. (\[l1\]), we have $$i \langle \alpha(t)\| \frac{\pa \hat{\rho}_1(t)}{\pa t}\| \beta(t)\rangle= \langle \alpha(t)\| [\hat{H}_0(t),\hat{\rho}_1(t)] \| \beta(t)\rangle+ \langle \alpha(t)\| [\hat{H}_1(t),\hat{\rho}_0(t)]\| \beta(t)\rangle,$$ which, with account of Eq. (\[ts\]) and of the equation $$\hat{\rho}_0(t)\| \alpha(t)\rangle=\delta_{\alpha 0} \|\alpha(t)\rangle$$ leads to $$i \langle \alpha(t)\| \frac{\pa \hat{\rho}_1(t)}{\pa t}\| \beta(t)\rangle= \langle i \frac{\pa \alpha(t)}{\pa t} \| \hat{\rho}_1(t) \| \beta(t)\rangle- \langle \alpha(t)\| \hat{\rho}_1(t) \| i \frac{\pa \beta(t)}{\pa t}\rangle +(\delta_{\beta 0}-\delta_{\alpha 0}) \langle \alpha(t)\| \hat{H}_1(t)\| \beta(t)\rangle,$$ and, therefore, to $$i \frac{\pa}{\pa t} \langle \alpha(t)\| \hat{\rho}_1(t)\| \beta(t) \rangle = (\delta_{\beta 0}-\delta_{\alpha 0}) \langle \alpha(t)\| \hat{H}_1(t)\| \beta(t)\rangle. \label{lll}$$ Equation (\[mat\]) is obtained by the time integration of Eq. (\[lll\]). (II). Derivation of Eqs. (\[ph0\])-(\[def0\]). ============================================== We apply the time-dependent perturbation $$v_{ext}^{(1)}(t) = \frac{1}{2} \left[ v_{ext}^{(1)}(\omega) e^{-i (\omega+i\eta) t}+ v_{ext}^{(1)}(-\omega) e^{i (\omega-i\eta) t} \right],$$ where $\eta$ is a positive infinitesimal, ensuring the perturbation to be zero at $t\to -\infty$. Within the linear response, the same holds for the KS potential $$v_s^{(1)}(t) = \frac{1}{2} \left[ v_s^{(1)}(\omega) e^{-i (\omega+i\eta) t}+ v_s^{(1)}(-\omega) e^{i (\omega-i\eta) t} \right]. \label{Svs}$$ Expanding Eq. (\[Li0\]) to the second order in the perturbation, we have $$\begin{aligned} &i\frac{\pa \rho_0^{(1)}(t)}{\pa t}=[\hat{h}_s^{(0)},\rho_0^{(1)}(t)]+[v_s^{(1)}(t),\rho_0^{(0)}], \label{Li01}\\ &i\frac{\pa \rho_0^{(2)}(t)}{\pa t}=[\hat{h}_s^{(0)},\rho_0^{(2)}(t)]+[v_s^{(1)}(t),\rho_0^{(1)}(t)]+[v_s^{(2)}(t),\rho_0^{(0)}]. \label{Li02}\end{aligned}$$ By Eq. (\[Li02\]) we have $$i\frac{\pa \langle \phi_f\|\rho_0^{(2)}(t)\|\phi_f\rangle}{\pa t}= \langle\phi_f\|[v_s^{(1)}(t),\rho_0^{(1)}(t)]\|\phi_f\rangle = 2 i \, {\rm Im} \langle\phi_f\|v_s^{(1)}(t) \rho_0^{(1)}(t)\|\phi_f\rangle, \label{22}$$ where $\phi_f$ is the orbital of the emitted electron, and the contributions from the first and the third terms in the right-hand side of Eq. (\[Li02\]) disappear, $\phi_f$ being empty in the ground-state. Equation (\[Li01\]) gives us $$\langle \phi_f\|\rho_0^{(1)}(t)\|\phi_m\rangle= \frac{f_f-f_m}{2} \left[ \langle \phi_f\|v_s^{(1)}(\omega)\|\phi_m\rangle \frac{e^{-i( \omega+i\eta) t}}{\epsilon_f-\epsilon_m-\omega-i\eta} + \langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_m\rangle \frac{e^{i(\omega -i\eta) t}}{\epsilon_f-\epsilon_m+\omega-i\eta} \right] . \label{rho01m}$$ Combining Eqs. (\[22\]), (\[Svs\]), and (\[rho01m\]), we can write $$\begin{split} &\frac{\pa \langle \phi_f\|\rho_0^{(2)}(t)\|\phi_f\rangle}{\pa t} = 2 \, {\rm Im} \sum\limits_i \langle\phi_f\|v_s^{(1)}(t)\|\phi_i\rangle \langle \phi_i\|\rho_0^{(1)}(t)\|\phi_f\rangle = \\ &\frac{1}{2} \, {\rm Im} \! \sum\limits_i (f_i \! - \! f_f) \! \left[ \langle \phi_f\|v_s^{(1)}(\omega)\|\phi_i \rangle e^{-i (\omega+i\eta) t} \! + \! \langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_i \rangle e^{i (\omega-i\eta) t} \right] \! \left[ \! \frac{\langle \phi_i\|v_s^{(1)}(\omega)\|\phi_f\rangle e^{-i( \omega+i\eta) t}}{\epsilon_i-\epsilon_f-\omega-i\eta} \! + \! \frac{\langle \phi_i\|v_s^{(1)}(-\omega)\|\phi_f\rangle e^{i(\omega -i\eta) t}}{\epsilon_i-\epsilon_f+\omega-i\eta} \! \right] \\ &=\! \frac{e^{2 \eta t}}{2} \, {\rm Im} \! \! \sum\limits_{i\in occ} \! \frac{\|\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_i \rangle\|^2 }{\epsilon_i-\epsilon_f+\omega-i\eta} \! + \! \frac{\|\langle \phi_i\|v_s^{(1)}(\omega)\|\phi_f\rangle \|^2}{\epsilon_i-\epsilon_f-\omega-i\eta} \! = \! \frac{\pi}{2} \! \sum\limits_{i\in occ} \! \|\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_i \rangle\|^2 \delta(\epsilon_i \! - \! \epsilon_f \! +\! \omega) \! + \! \|\langle \phi_i\|v_s^{(1)}(\omega)\|\phi_f\rangle \|^2 \delta(\epsilon_i \! - \! \epsilon_f \! - \! \omega). \end{split} \label{222}$$ In the third line of Eq. (\[222\]) we have kept the non-oscillating terms only, and after the last equality sign we have taken the $\eta\to$ limit. Assuming $\omega>0$ and noting that $\epsilon_f>\epsilon_i$, we conclude the proof of Eqs. (\[ph0\])-(\[def0\]). (III). Derivation of Eqs. (\[ph1\])-(\[def3\]). =============================================== We write down the second-order term in the expansion of Eq. (\[Li1\]) in powers of the perturbation $$\begin{split} &\frac{\pa \langle \phi_f\| \rho_1^{(2)}(t)\|\phi_f\rangle }{\pa t} \! = 2 \, {\rm Im} \left\{ -\langle \phi_f\| \rho_1^{(1)}(t) v_s^{(1)}(t) \|\phi_f\rangle+ \langle \phi_f\| v_s^{(2)}(t) \rho_1^{(0)} \|\phi_f\rangle + \langle \phi_f\| \rho_0^{(1)}(t) v_x^{(1)}(t)\|\phi_f\rangle \right. \\ & \left. + \sum\limits_{m} \langle \phi_f\|\rho_0^{(2)}(t)\|\phi_m\rangle \left[ \langle \phi_m\|v_x^{(0)}\|\phi_f\rangle +\int \frac{\phi_m^(\rv) \phi_f(\rv') \rho_0^{(0)}(\rv,\rv')} {\|\rv-\rv'\|} d\rv d\rv'\right] \right. \\ & \left. + \sum\limits_{mkl} \langle \phi_f\|\rho_0^{(1)}(t)\|\phi_m\rangle \langle \phi_k\|\rho_0^{(1)}(t)\|\phi_l\rangle \int \frac{\phi_m^(\rv) \phi_f(\rv') \phi_k(\rv) \phi_l^(\rv') }{\|\rv-\rv'\|} d\rv d\rv' \right\}. \end{split} \label{IIIstart}$$ In the following, we evaluate term by term in Eq. (\[IIIstart\]). In resulting expressions, we retain the non-oscillating terms only, keeping in view that the oscillating ones do not give a contribution to the final result. Accordingly, we use the $\sim$ (tilde) sign to denote the right-hand sides with the oscillating parts dropped. A caution should, however, be exercised to omit an oscillating term only when it would not be further multiplied by another oscillating one, yielding a non-oscillating result. For example, in Eq. (\[T1\]), oscillating expressions are omitted, while it would be incorrect to omit such parts in $\rho_1^{(1)}(t)$ before evaluating its product with $v_s^{(1)}(t)$. All the quantities below are obtained by expanding Eqs. (\[Li0\]) or (\[Li1\]) to the corresponding orders in the time-dependent perturbation. We arrive at $$\begin{split} &\langle \phi_f\| \rho_1^{(1)}(t) v_s^{(1)}(t) \|\phi_f\rangle \sim \frac{1}{4} \sum\limits_{m\in occ} \left[ \frac{\langle \phi_f\|v_x^{(1)}(\omega)\|\phi_m\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m-\omega-i\eta} + \frac{\langle \phi_f\|v_x^{(1)}(-\omega)\|\phi_m\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle}{\epsilon_f-\epsilon_m+\omega-i\eta} \right] + \\ & \! \! \! \! \! \! \! \! \! \! \! \frac{1}{4} \! \sum\limits_{m k} \! \frac{f_k \! - \! f_m}{\epsilon_k \! - \! \epsilon_m} \! \! \left[ \! \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m-\omega-i\eta} \! + \! \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m+\omega-i\eta} \! \right] \! \! \left[ \! \langle\phi_k\|v_x^{(0)} \|\phi_m\rangle \! + \! \! \int \! \! \! \rho_0^{(0)}(\rv,\rv') \frac{\phi_k^(\rv) \phi_m(\rv')}{\|\rv'-\rv\|}d\rv' d\rv \right] \! \! - \\ & \! \! \! \! \! \! \! \! \! \! \! \frac{1}{4} \! \sum\limits_{m k} \frac{f_f \! - \! f_k}{\epsilon_f \! - \! \epsilon_k} \! \left[ \! \langle\phi_f\|v_x^{(0)} \|\phi_k\rangle \! + \! \! \int \! \! \! \rho_0^{(0)}(\rv,\rv') \frac{\phi_f^(\rv) \phi_k(\rv')}{\|\rv'-\rv\|}d\rv' d\rv \right] \! \! \left[ \! \frac{\langle \phi_k\|v_s^{(1)}(\omega)\|\phi_m\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m-\omega-i\eta} \! + \! \frac{\langle \phi_k\|v_s^{(1)}(-\omega)\|\phi_m\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m+\omega-i\eta} \! \right] \! \! - \\ & \! \! \! \! \! \! \! \! \! \! \! \sum\limits_{\substack{m\in occ \\ k l}} \frac{f_l-f_k}{4} \left[ \frac{\langle \phi_k\|v_s^{(1)}(\omega)\|\phi_l\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{(\epsilon_f \! - \! \epsilon_m \! - \! \omega \! - \! i\eta)(\epsilon_k \! - \! \epsilon_l \! - \! \omega \! - \! i\eta)} + \frac{\langle \phi_k\|v_s^{(1)}(-\omega)\|\phi_l\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle }{( \epsilon_f \! - \! \epsilon_m \! + \! \omega \! - \! i\eta) (\epsilon_k \! - \! \epsilon_l \! + \! \omega \! - \! i\eta)} \right] \int \frac{\phi_k(\rv') \phi_l^(\rv) \phi_f^(\rv') \phi_m(\rv) }{\|\rv'-\rv\|} d\rv' d\rv \, + \\ & \! \! \! \! \! \! \! \! \! \! \! \sum\limits_{m k} \! \frac{f_k\! - \! f_f}{4} \! \! \left[ \! \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{(\epsilon_f \! - \!\epsilon_m \! - \! \omega \! - \! i\eta) (\epsilon_f \! - \! \epsilon_k \! - \! \omega \! - \! i\eta)} \! + \! \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle}{(\epsilon_f \! - \! \epsilon_m \! + \! \omega \! - \! i\eta)(\epsilon_f \! - \! \epsilon_k \! + \! \omega \! - \! i\eta)} \! \right] \! \! \left[ \! \langle\phi_k\|v_x^{(0)} \|\phi_m\rangle \! + \! \! \int \! \! \rho_0^{(0)}(\rv,\rv') \frac{\phi_k^(\rv) \phi_m(\rv')}{\|\rv'-\rv\|} d\rv' d\rv \right] \! \! - \\ & \! \! \! \! \! \! \! \! \! \! \! \sum\limits_{m k} \! \frac{f_m \! - \! f_k}{4} \! \! \left[ \frac{ \langle \phi_k\|v_s^{(1)}(\omega)\|\phi_m\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{(\epsilon_f \! - \! \epsilon_m \! - \! \omega \! -i\eta)(\epsilon_k \! - \! \epsilon_m \! - \! \omega \! - \! i\eta)} \! + \! \frac{\langle \phi_k\|v_s^{(1)}(-\omega)\|\phi_m\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle }{(\epsilon_f \! - \! \epsilon_m \! + \! \omega \! - \! i\eta) (\epsilon_k \! - \! \epsilon_m \! + \! \omega \! - \! i\eta)} \right] \! \! \left[ \! \langle\phi_f\|v_x^{(0)} \|\phi_k\rangle \! + \! \! \int \rho_0^{(0)}(\rv,\rv') \frac{\phi_f^(\rv) \phi_k(\rv') }{\|\rv'-\rv\|} d\rv' d\rv \right] \! , \end{split} \label{T1}$$ $$\langle \phi_f\| v_s^{(2)}(t) \rho_1^{(0)} \|\phi_f\rangle\sim \sum\limits_{m\in occ} \frac{\langle \phi_f\| v_s^{(2)}(0) \|\phi_m\rangle}{\epsilon_f-\epsilon_m} \left[ \langle\phi_m\|v_x^{(0)} \|\phi_f\rangle + \int \rho_0^{(0)}(\rv,\rv') \frac{\phi_m^(\rv) \phi_f(\rv')}{\|\rv-\rv'\|}d\rv d\rv' \right], \label{T2}$$ where we have used the following two equations $$v_s^{(2)}(t) = v_s^{(2)}(2 \omega) e^{2 (-i \omega+ \eta) t}+ v_s^{(2)}(0) e^{2\eta t}+ v_s^{(2)}(-2 \omega)e^{2 (i \omega+\eta) t} ,$$ $$\begin{split} & \langle\phi_n\|\rho_1^{(0)}\|\phi_m\rangle = \frac{f_m-f_n}{\epsilon_n-\epsilon_m} \left[ \langle\phi_n\|v_x^{(0)} \|\phi_m\rangle \! + \! \int \rho_0^{(0)}(\rv,\rv_1) \frac{\phi_n^(\rv) \phi_m(\rv_1)}{\|\rv_1-\rv\|}d\rv_1 d\rv \right]. \end{split}$$ $$\langle \phi_f\| \rho_0^{(1)}(t) v_x^{(1)}(t)\|\phi_f\rangle \sim - \frac{1}{4} \sum\limits_{m\in occ} \left[ \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_m\rangle \langle \phi_m\|v_x^{(1)}(-\omega)\|\phi_f\rangle}{\epsilon_f-\epsilon_m-\omega-i\eta} + \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_m\rangle \langle \phi_m\|v_x^{(1)}(\omega)\|\phi_f\rangle}{\epsilon_f-\epsilon_m+\omega-i\eta} \right],$$ $$\begin{split} \langle \phi_f\|\rho_0^{(2)}(t)\|\phi_m\rangle \sim \frac{1}{4} \sum\limits_k \left[ (f_m-f_k) \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_k\|v_s^{(1)}(-\omega)\|\phi_m\rangle}{(\epsilon_f-\epsilon_m-2 i\eta)(\epsilon_k-\epsilon_m+\omega-i\eta)} + (f_m-f_k) \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_k\|v_s^{(1)}(\omega)\|\phi_m\rangle}{(\epsilon_f-\epsilon_m-2 i\eta) (\epsilon_k-\epsilon_m-\omega-i\eta)} \right. \\ \left. - (f_k-f_f) \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_k\|v_s^{(1)}(-\omega)\|\phi_m\rangle}{(\epsilon_f-\epsilon_m-2i\eta) (\epsilon_f-\epsilon_k-\omega-i\eta)} - (f_k-f_f) \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_k\|v_s^{(1)}(\omega)\|\phi_m\rangle}{(\epsilon_f-\epsilon_m -2 i\eta)(\epsilon_f-\epsilon_k+\omega-i\eta)} \right] +(f_f-f_m) \frac{\langle \phi_f\|v_s^{(2)}(0)\|\phi_m\rangle}{\epsilon_f-\epsilon_m-i\eta}, \end{split} \label{T4}$$ $$\sum\limits_{mkl} \langle \phi_f\|\rho_0^{(1)}(t)\|\phi_m\rangle \langle \phi_k\|\rho_0^{(1)}(t)\|\phi_l\rangle \! \sim \! \frac{1}{4}\sum\limits_{\substack{m\in occ \\ k l}} \! (f_l-f_k) \! \left[ \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_m\rangle \langle \phi_k\|v_s^{(1)}(-\omega)\|\phi_l\rangle}{(\epsilon_f \! - \! \epsilon_m \! - \! \omega \! - \! i\eta)(\epsilon_k \! - \! \epsilon_l \! + \! \omega \! - \! i\eta)} \! + \! \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_m\rangle \langle \phi_k\|v_s^{(1)}(\omega)\|\phi_l\rangle}{(\epsilon_f \! - \! \epsilon_m \! +\! \omega \! - \! i\eta)(\epsilon_k \! - \! \epsilon_l \! - \! \omega \! - \! i\eta)} \right]. \label{T5}$$ After Eqs. (\[T1\])-(\[T5\]) are substituted into Eq. (\[IIIstart\]), a number of simplifications occur, and, remembering that $\eta$ is a positive infinitesimal, we arrive at Eqs. (\[ph1\])-(\[def3\]). The most part of the transformations being straightforward, we mention only the two keypoints: \(I) The two instances of the quadratic KS potential $v_s^{(2)}$, which are present in Eqs. (\[T2\]) and (\[T4\]), cancel each other (note, that $\epsilon_f>\epsilon_m$ in the last term of Eq. (\[T4\]), so that $ i \eta$ can be dropped from its denominator). The latter is a very fortunate development, since the evaluation of the quadratic response would have presented an insurmountable difficulty for nontrivial systems; \(II) The demonstration of the emergence of the delta-function derivative in Eq. (\[ph1\]) is nontrivial, and we, therefore, give some additional details. The origin lies in the second and the fifth terms in Eq. (\[T1\]). We write $$\begin{split} & \! \! \! \! \! \! \! \! \! \! \! Q=\frac{1}{4} \! \sum\limits_{m k} \! \frac{f_k \! - \! f_m}{\epsilon_k \! - \! \epsilon_m \pm i \eta} \! \! \left[ \! \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m-\omega-i\eta} \! + \! \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m+\omega-i\eta} \! \right] C_{k m} + \\ & \! \! \! \! \! \! \! \! \! \! \! \frac{1}{4} \sum\limits_{m k} (f_k\! - \! f_f)\! \! \left[ \! \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{(\epsilon_f \! - \!\epsilon_m \! - \! \omega \! - \! i\eta) (\epsilon_f \! - \! \epsilon_k \! - \! \omega \! - \! i\eta)} \! + \! \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle}{(\epsilon_f \! - \! \epsilon_m \! + \! \omega \! - \! i\eta)(\epsilon_f \! - \! \epsilon_k \! + \! \omega \! - \! i\eta)} \! \right] C_{k m}, \end{split}$$ where $C_{k m}$ is given by Eq. (\[def3\]). Then $$\begin{split} & Q=\frac{1}{4} \! \sum\limits_{m k} \! \frac{f_k \! - \! f_f}{\epsilon_k \! - \! \epsilon_m \pm i \eta} \! \! \left[ \! \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m-\omega-i\eta} \! + \! \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m+\omega-i\eta} \! \right] C_{k m} + \\ & \frac{1}{4} \! \sum\limits_{m k} \! \frac{f_f \! - \! f_m}{\epsilon_k \! - \! \epsilon_m \pm i \eta} \end{split}$$ Summing up the first and the third terms, we have $$\begin{split} & Q=\frac{1}{4} \sum\limits_{m k} \! \frac{f_k \! - \! f_f}{\epsilon_k \! - \! \epsilon_m \pm i \eta} \! \! \left[ \! \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_k-\omega-i\eta} \! + \! \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_k+\omega-i\eta} \! \right] C_{k m} + \\ &\frac{\pm i\eta}{4} \sum\limits_{m k} \! \frac{f_k \! - \! f_f}{\epsilon_k \! - \! \epsilon_m \pm i \eta} \! \! \left[ \! \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{(\epsilon_f-\epsilon_k-\omega-i\eta) (\epsilon_f-\epsilon_m-\omega-i\eta)} \! + \! \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle }{(\epsilon_f-\epsilon_k+\omega-i\eta)(\epsilon_f-\epsilon_m+\omega-i\eta)} \! \right] C_{k m} + \\ & \frac{1}{4} \sum\limits_{m k} \! \frac{f_f \! - \! f_m}{\epsilon_k \! - \! \epsilon_m \pm i \eta} \! \! \left[ \! \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m-\omega-i\eta} \! + \! \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m+\omega-i\eta} \! \right] C_{k m}. \end{split}$$ Interchanging the dummy $k$ and $m$ indices in the first term, we have $$\begin{split} & Q=\frac{1}{4} \sum\limits_{m k} \! \frac{f_f \! - \! f_m}{\epsilon_k \! - \! \epsilon_m \mp i \eta} \! \! \left[ \! \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_m\rangle \langle \phi_k\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m-\omega-i\eta} \! + \! \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_m\rangle \langle \phi_k\|v_s^{(1)}(\omega)\|\phi_f\rangle }{\epsilon_f-\epsilon_m+\omega-i\eta} \! \right] C_{m k} + \\ \end{split}$$ or $$\begin{split} & Q= \frac{\pm i\eta}{4} \sum\limits_{m k} \! \frac{f_k \! - \! f_f}{\epsilon_k \! - \! \epsilon_m \pm i \eta} \! \! \left[ \! \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle }{(\epsilon_f-\epsilon_k-\omega-i\eta) (\epsilon_f-\epsilon_m-\omega-i\eta)} \! + \! \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle }{(\epsilon_f-\epsilon_k+\omega-i\eta)(\epsilon_f-\epsilon_m+\omega-i\eta)} \! \right] C_{k m} + \\ & \frac{1}{2} \sum\limits_{m k} \! (f_f \! - \! f_m) {\rm Re} \left[ \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle C_{k m}}{\epsilon_k \! - \! \epsilon_m \pm i \eta } \right] \frac{1}{\epsilon_f-\epsilon_m-\omega-i\eta} + \\ & \frac{1}{2} \sum\limits_{m k} \! (f_f \! - \! f_m) {\rm Re} \left[ \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle C_{k m}}{\epsilon_k \! - \! \epsilon_m \pm i \eta } \right] \frac{1}{\epsilon_f-\epsilon_m+\omega-i\eta}. \end{split}$$ Then $$\begin{split} & {\rm Im \, Q}= \frac{1}{4} {\rm Im} \sum\limits_{m } (f_m \! - \! f_f) \! \! \left[ \! \frac{\|\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_m\rangle\|^2 }{ (\epsilon_f-\epsilon_m-\omega-i\eta)^2} \! + \! \frac{\| \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle\|^2 }{(\epsilon_f-\epsilon_m+\omega-i\eta)^2} \! \right] C_{m m} + \\ & \frac{1}{2} {\rm Im} \sum\limits_{m k} \! (f_f \! - \! f_m) {\rm Re} \left[ \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle C_{k m}}{\epsilon_k \! - \! \epsilon_m \pm i \eta } \right] \frac{1}{\epsilon_f-\epsilon_m-\omega-i\eta} + \\ & \frac{1}{2} {\rm Im} \sum\limits_{m k} \! (f_f \! - \! f_m) {\rm Re} \left[ \frac{\langle \phi_f\|v_s^{(1)}(-\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(\omega)\|\phi_f\rangle C_{k m}}{\epsilon_k \! - \! \epsilon_m \pm i \eta } \right] \frac{1}{\epsilon_f-\epsilon_m+\omega-i\eta}, \end{split}$$ or $$\begin{split} & {\rm Im \, Q}= -\frac{\pi}{4} {\rm Im} \sum\limits_{m } (f_m \! - \! f_f) \|\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_m\rangle\|^2 C_{m m} \delta' (\epsilon_f-\epsilon_m-\omega)+ \\ & \frac{\pi}{2} \sum\limits_{m \ne k} \! (f_f \! - \! f_m) {\rm Re} \left[ \frac{\langle \phi_f\|v_s^{(1)}(\omega)\|\phi_k\rangle \langle \phi_m\|v_s^{(1)}(-\omega)\|\phi_f\rangle C_{k m}}{\epsilon_k \! - \! \epsilon_m } \right] \delta(\epsilon_f-\epsilon_m-\omega) , \end{split}$$ where we have used the relations $$\begin{aligned} &\lim\limits_{\eta\to 0} {\rm Im} \, \frac{1}{x- i\eta} =\pi \delta(x),\\ &\lim\limits_{\eta\to 0} {\rm Im} \, \frac{1}{(x- i\eta)^2} =-\pi \delta'(x),\end{aligned}$$ and dropped the terms with $\delta(\epsilon_f-\epsilon_m+\omega)$ and $\delta'(\epsilon_f-\epsilon_m+\omega)$, since $\epsilon_f \in unocc$ and, hence, $\epsilon_m\in occ$, and $\omega$ is assumed positive. (IV). Reduction of Eqs. (\[def0\]), (\[def1\])-(\[def2\]) in the case of the Q2DEG with one filled subband. =========================================================================================================== As shown below, in the specific case of the Q2DEG with one subband filled, equations (\[def0\]), (\[def1\])-(\[def2\]) reduce to $$A_{f 0}(\omega) =\frac{\pi}{2} H(k_F-k_\\|) \left\|\langle \mu_f \|v_s^{(1)}(\omega)\|\mu_0)\rangle\right\|^2 \label{FGRS}$$ and $$\begin{split} &\Delta A_{f 0}(\omega)= -\pi H(k_F-k_\\|) \, {\rm Re} \left\{ \langle \mu_f\|v_s^{(1)}(\omega)\|\mu_0\rangle^* \left[ \frac{k_F}{n_s} \! \int \mu_0(z') \mu_n^(z') n^{(1)}(z,\omega) S_{k_\\|}(\|z-z'\|) d z d z' \right. \right. \\ & \left. + \langle \mu_f\|v_x^{(1)}(\omega)\|\mu_0\rangle + \frac{1}{2 n_s} \int \frac{\mu_n^(z)}{\mu_0(z)} v_s^{(1)}(z, \omega) \chi_s(z,z') G_{k_\\|}(z') d z d z' + \frac{1}{\omega}\langle \mu_0\|v_s^{(1)}(\omega)\|\mu_0\rangle \langle\mu_f\|G_{k_\\|} \|\mu_0\rangle \right. \\ & \left. \left. + \frac{1}{2 n_s} \int \frac{\mu_n^(z) }{\mu_0(z)} n^{(1)}(z,\omega) G_{k_\\|}(z) d z - \frac{\omega}{(2 n_s)^2} \int \frac{ \mu_n^(z') }{\|\mu_0(z)\|^2 \mu_0(z')} \chi_s(z,z') n^{(1)}(z,\omega) G_{k_\\|}(z') d z d z' \right] \right\}, \end{split} \label{amp1S}$$ $$\Delta \omega(k_\\|) = - \int \|\mu_0(z)\|^2 G_{k_\\|}(z)d z, \label{shift2DS}$$ where $H(k)$ is the Heaviside step function, $n^{(1)}(z,\omega)$ is the density fluctuation, $\mu_m(z)$ are the orbitals of the perpendicular motion, $\lambda_m$ are the corresponding eigenenergies, $\kv_\\|$ is the conserving parallel wave-vector, common for the initial and final KS states, $\chi_s(z,z')$ is the static KS density response function. The derivation of Eqs. (\[FGRS\]), (\[amp1S\]), and (\[shift2DS\]) is as follows. KS orbitals are (for brevity, we omit the ‘parallel’ index in $\pv_\\|$) $$\phi_{m \pv}(\rv)= \frac{1}{\sqrt{\Omega}} e^{i \pv\cdot \rv_\\|} \mu_m(z),$$ where $\Omega$ is the normalization area, and the eigenenergies corresponding to $\mu_m(z)$ will be denoted by $\lambda_m$. Only the orbitals $$\phi_{0 \pv}(\rv)= \frac{1}{\sqrt{\Omega}} e^{i \pv \cdot \rv_\\|} \mu_0(z), \ \ \|\pv \| \le k_F,$$ are occupied. We then evaluate in a straightforward manner $$\begin{split} C_{\pv k, \pv' m}= \delta_{\pv \pv'} \left[ \langle \mu_k\|v_x^{(0)}\| \mu_m\rangle+ k_F \int \mu_0(z) \mu_0^(z') \mu_k^(z) \mu_m(z') S_p(k_F \|z-z'\|) dz dz' \right], \end{split}$$ where the function $S$ is given by Eq. (\[SSS\]). Furthermore, remembering that $i\in occ$ and $f\in unocc$, we find $$\begin{split} &\sum\limits_{l=1}^\infty C_{l 0} \frac{\langle \mu_f\|v_s^{(1)}(\omega)\|\mu_l\rangle }{\lambda_0-\lambda_l} = \sum\limits_{l=1}^\infty \frac{\langle \mu_f\|v_s^{(1)}(\omega)\|\mu_l\rangle }{\lambda_0-\lambda_l} \langle \mu_l\|G_{k_\\|}\| \mu_0\rangle= \\ & \int \sum\limits_{l=1}^\infty \frac{\mu_f^(z') v_s^{(1)}(z',\omega) \mu_l(z')\mu_l(z) G_{k_\\|}(z) \mu_0(z)} {\lambda_0-\lambda_l} d z d z'= \frac{1}{2 n_s} \int \frac{\mu_f^(z') }{\mu_0(z')} v_s^{(1)}(z',\omega) \chi_s(z',z) G_{k_\\|}(z) d z d z', \end{split} \label{N10}$$ $$\begin{split} & \sum\limits_{kl} (f_k \! - \! f_l) \frac{ \langle \mu_k\|v_s^{(1)}(\omega)\|\mu_l\rangle}{\epsilon_k \! - \! \epsilon_l \! - \! \omega \! - \! i\eta} \! \int \! \frac{\phi_i(\rv) \phi_f^(\rv') \phi_l^(\rv) \phi_k(\rv') }{\|\rv-\rv'\|} d\rv d\rv' \! = \! k_F \! \sum\limits_{l=1}^\infty \! \left[ \frac{ \langle \mu_0\|v_s^{(1)}(\omega)\|\mu_l\rangle}{\lambda_0 \! - \! \lambda_l \! -\omega \! -i\eta} \! \int \! \! S_{k_\\|}(k_F \|z \! - \! z'\|) \mu_0(z) \mu_f^(z') \mu_l(z) \mu_0(z') d z d z' \right. \\ & \left. - \frac{ \langle \mu_l\|v_s^{(1)}(\omega)\|\mu_0\rangle}{\lambda_l \! -\lambda_0 \! -\omega \! -i\eta} \! \int \! \! S_{k_\\|}(k_F \|z \! - \! z'\|) \mu_0(z) \mu_f^(z') \mu_l(z') \mu_0(z) d z d z' \right], \end{split} \label{N11}$$ $$\begin{split} \sum\limits_l C_{f l} \frac{ \langle \mu_l\|v_s^{(1)}(\omega)\|\mu_0\rangle }{\omega+i\eta +\lambda_0-\lambda_l} = \sum\limits_l \left[ \langle \mu_f\|v_x^{(0)}\|\mu_l\rangle+k_F \int \mu_0(z) \mu_0^(z') \mu_f^(z) \mu_l(z') S_p(k_F \|z-z'\|) dz dz' \right] \frac{ \langle \mu_l\|v_s^{(1)}(\omega)\|\mu_0\rangle }{\omega+i\eta +\lambda_0-\lambda_l}. \label{N12} \end{split}$$ From Eqs. (\[N11\]) and (\[N12\]) we have $$\begin{split} & \sum\limits_{kl} (f_k-f_l) \, \frac{ \langle \mu_k\|v_s^{(1)}(\omega)\|\mu_l\rangle}{\epsilon_k-\epsilon_l-\omega-i\eta} \int \frac{\phi_i(\rv) \phi_f^(\rv') \phi_l^(\rv) \phi_k(\rv') }{\|\rv-\rv'\|} d\rv d\rv' +\sum\limits_l C_{f l} \frac{ \langle \mu_l\|v_s^{(1)}(\omega)\|\mu_0\rangle }{\omega+i\eta +\lambda_0-\lambda_l} = \\ & \frac{k_F}{n_s} \! \int \! S_{k_\\|}(k_F\|z \! - \! z'\|) \chi_s(z,z'',\omega) v_s^{(1)}(z'',\omega) \mu_f^(z') \mu_0(z') d z d z' dz'' \! + \! \sum_l \frac{ \langle \mu_l\|v_s^{(1)}(\omega)\|\mu_0\rangle }{\omega\! + \! i\eta \! + \! \lambda_0 \! - \! \lambda_l} \langle \mu_f\|G_{k_\\|}\|\mu_l\rangle = \\ & \frac{k_F}{n_s} \int S_{k_\\|}(k_F\|z - z'\|) n^{(1)}(z,\omega) \mu_f^(z') \mu_0(z') d z d z' = \\ + \frac{ \langle \mu_0\|v_s^{(1)}(\omega)\|\mu_0\rangle }{\omega} \langle \mu_f\|G_{k_\\|}\|\mu_0\rangle + \sum_{l=1}^\infty \frac{ \langle \mu_l\|v_s^{(1)}(\omega)\|\mu_0\rangle }{\omega + i\eta + \lambda_0 - \lambda_l} = \\ \! + \! \frac{1}{n_s} \! \int \! \frac{\mu_f^*(z)}{\mu_0(z)} G_{k_\\|}(z) \tilde{\chi}(z,z',\omega) v_s^{(1)}(z',\omega) d z d z', \label{N13} \end{split}$$ where $$\chi_s(z,z',\omega) = n_s \mu_0(z) \mu_0(z') \sum\limits_{l=1}^\infty \left( \frac{1}{\omega+i\eta+\lambda_0-\lambda_l} + \frac{1}{-\omega-i\eta+\lambda_0-\lambda_l} \right) \mu_l(z) \mu_l(z'), \label{chis}$$ is the density-response function of the Q2DEG with one filled subband [@Nazarov-17], and in the last line of Eq. (\[N13\]) we have introduced the notation $$\tilde{\chi}_s(z,z',\omega) = n_s \mu_0(z) \mu_0(z') \sum\limits_{l=1}^\infty \frac{\mu_l(z) \mu_l(z')}{\omega+i\eta+\lambda_0-\lambda_l}.$$ The proof of Eq. (\[amp1S\]) is concluded by summing up Eqs. (\[N10\]) and (\[N13\]) and noting that $$\tilde{\chi}_s(z,z',\omega) = \frac{1}{2} \chi_s(z,z',\omega) -\frac{\omega}{4 n_s} \int \frac{\chi_s(z,z'') \chi_s(z'',z',\omega)}{\|\mu_0(z'')\|^2} d z''.$$ Finally, the latter equality is proven by the direct substitution of Eq. (\[chis\]) into the second term on its right-hand side and the integration, taking into account the orthonormality of $\mu_l(z)$. Function $S_{k_\\|}(u)$ of Eq. (\[SSS\]) is plotted in Fig. \[FSSS\]. [^1]: According to the general principles of TDDFT, all physical quantities, including the momentum distribution, are determined by the particle density. The corresponding functionals are not, however, known, which necessitates such studies as ours. [^2]: The contribution from $\rho^{(1)}$ term is zero identically. [^3]: Interestingly, the IP-theorem holds, in this case, ‘on average’, i.e., IP($k_{\\|}$), averaged over $\kv_{\\|}$, equals the minus KS eigenvalue, since $ \int_{k_{\\|} \le k_F} \Delta \omega(k_{\\|}) d \kv_{\\|}=0$, as can be verified by Eqs. (\[shift2D\])-(\[SSS\]) and (\[main152\]).
Every person loves to do something or other during his or her pass time in order to relax one’s mind as well as the soul. There are some things in life which you do which give you immense joy and satisfaction. Such a thing integral to one’s happiness is what we call a hobby. It may be anything from reading books to travelling; no person in this world is immune to a hobby. Since hobby is such a general topic, we have come up with short essays for students along with some longer ones so as to tell them what having a hobby feels like. The essays have been written in a simple yet crisp language and shall prove beneficial to the students. - List of Essays on My Hobby in English - Essay on My Hobby Reading Books – Essay 1 (250 Words) - Essay on My Hobby Reading Books – Essay 2 (250 Words) - Essay on My Hobby Playing Cricket – Essay 3 (250 Words) - Essay on My Hobby Drawing – Essay 4 (250 Words) - Essay on My Hobby Dancing – Essay 5 (250 Words) - Essay on My Hobby – Sewing – Essay 6 (500 Words) - Essay on My Hobby – Essay 7 (750 Words) - Essay on My Hobby Cooking – Essay 8 (1000 Words) List of Essays on My Hobby in English Essay on My Hobby Reading Books – Essay 1 (250 Words) My hobby is reading books. Reading a book is one of my favorite pass times and since I work with words for a living it is also one of my favorite work tasks. There are no words that can describe my admiration and respect for the written word and the modest book that houses them. Even though great thinker of antiquity like Socrates despised the written word calling it unresponsive and dead we have to give out thanks to its ability to conserve knowledge for generations. My hobby reading books is the best way to escape from the torment of the world and to rest in a world of imagination. Undisturbed by the troubles of my life, my mind can rest from all the stress it goes through every day and find comfort in the words of wise writers or happiness in those that like more light-hearted topics. Not only do I read books but I also collect them and spend endless hours searching for the right edition for their collection. I even save up money so that I can buy books and extend my library or spend fortunes on rare historic manuscripts. The fact of the matter is that there is no better way for me to rest and at the same time practice my brain by reading a book, so as far as my hobby reading books goes this way, it is the best pass time I can have. Believe me, once you start exploring the sea of stories written on paper you will never want to stop exploring. Essay on My Hobby Reading Books – Essay 2 (250 Words) Hobby is something that is of our interest and keeps us engaged in our free time with a free mind. A good habit will not only help us to escape from our daily cores but also keeps us peaceful. Studies prove that practicing a good hobby will keep us away from many mind related problems and loneliness as well. Reading books as My Hobby: Hobby is something that develops with us from an early age. I find happiness in reading books in my lonely time to free my mind of stress and study pressures. My hobby is reading books. Reading books is the best knowledge gaining hobby. My hobby reading books has helped me to improve my language too. When I start reading, I create my own imaginary and creative world to travel with the story. Reading thriller novels will help me to travel to that world with mystery and stories with adventures will improve my creative side, as I am constantly imagining the scenario that’s happening in the story and so on. Thus my hobby reading books interest me the most, has helped me to understand the language better, create noble and ideal thoughts in me and more. Inspirational and instructive books have always inspired my growing mind to follow the better path to achieve my life goal. By reading books I can be updated on the present world. A person with understandability towards anything will be able to acquire their desired heights more easily and books are molding me to be one. Living amidst books makes me feel happier and loneliness has never touched me at any point in my life. Books have become my best friend since childhood and I can feel the positive changes they create in me. Essay on My Hobby Playing Cricket – Essay 3 (250 Words) “All work and no play makes Jack a dull boy.” We have all heard of this adage time and again and it also throws light on how important it truly is to make sure that we all have a hobby. The game of cricket: Well, my hobby is cricket as I have been enjoying this sport since a very tender age. I remember gazing from the winnow of my room and watching the grown-ups immerse themselves in a game of cricket. I would spend hours watching them and remembering the different shots, the way the bowlers threw the ball at different angles and even imagined myself excelling at cricket. The need for passion: I believe that regardless of what we choose, it is important for each one of us to have a hobby. My hobby is something which keeps me going and it adds to my verve and energy. If you develop a good hobby, it will make sure that you would have something to unwind your mind. When I go out to play cricket, in that moment, I do not think of anything else as I am cool, composed and nothing else matters. So, if you have not yet found your thing which you can truly call as a hobby, I suggest you do so. I knew my hobby since a tender age and it soon grew into my passion and I can say with utmost pride that I am quite good at cricket. When you truly love something, your zest will give you the kick to excel in it too. Essay on My Hobby Drawing – Essay 4 (250 Words) I have a lot of hobbies to pass my time. One of such things is drawing. Even when I was a little child, drawing has always made me happy. Sitting quietly in a place, I can draw for hours. It keeps me busy and relaxes my mind. There is a little secret to why I love drawing so much. As a person, I am less talkative. Because of that, there are very few friends in my life. The thing is that, instead of speaking out everything, I prefer to express my emotions silently. And drawing just helps me do that. Sketching is not merely a pass time to me. God has given me a beautiful way to share my thoughts and feelings through drawing. It is an art that becomes my voice when I wish to be quiet. Moreover, drawing also helps me connect more with nature. Trees, birds, animals, rivers, clouds are some of the favorite things that I like to draw. My art teacher praises the passion I have for drawing. She also appreciates the blending of shades and strokes of brushes when I paint something. My parents and friends always encourage me for the same. I wish to pursue drawing for the rest of my life. It is my dream to become a true artist one day and that is only possible with regular practice and devotion. Essay on My Hobby Dancing – Essay 5 (250 Words) Introduction: My hobby is dancing. Dancing is the art of performing purposefully selected sequence of movements by humans. Dance is a beautiful hobby that slowly builds in an individual. Dancing becomes a hobby to people who like to listen to music because as they listen, they tend to accompany the beats with dance moves. Although some people might be enjoying music but they are unable to dance because dancing is a performance that requires a skill that not everyone can master. How it began: Ever since I was a child, I have been chubby and so my parents had to sign me up for dancing lessons so that I can get physically fit. The dancing lessons seemed enjoyable but when I joined the first class I was unable to dance. I developed a strong determination to learn how to dance because by nature I do not like to accept failure. Within a few weeks, I had learned how to dance and it grew in me and dancing became my hobby. I would dance everywhere and that is how I grew fond of my hobby dancing. Benefits of My Hobby Dancing: Through my hobby dancing, I was able to lose weight and my chubbiness was gone. The regular dancing that I have been doing has kept me fit. Sometimes I make money from dancing especially during the holidays. Dancing at events or festivals earns me money. At school, I have won awards because I participate in dance as an extracurricular activity. It is a great feeling to have dancing as my hobby because it is what I love and enjoy. Essay on My Hobby – Sewing – Essay 6 (500 Words) Introduction: Who are we without our hobbies? Apart from our physical appearances, the collection of the things we do is what makes us distinct from the next person. While there are things we do simply because we have to, we do others because we love to. Hobbies are things we do because we have a natural inclination to do so. They give us so much pleasure that we would spend our life time doing it. This is why people try to build their respective professions around their hobbies. By so doing, an ordinarily difficult task suddenly becomes simple. My love for sewing: Though I have a lot of hobbies, my love for sewing stands out from the crowd. It all started when my mother bought a sewing machine when I was younger. I was immediately fascinated by the mechanical excellence of the equipment. First, it was the way the machine rolled. Then I was puzzled about the thread movement and how it miraculously turned torn pieces into masterpieces. Subsequently, my curiosity became a source of entertainment. I would play around the machine and time would disappear while I do so. I would cut my old clothing and run it through the machine just to see it move. Slowly and surely, I became enchanted with sewing so much that it dominated my thought and became my hobby. Now, I would not leave a single week without creating something adorable with the sewing machine. A few moments spent away from this intriguing environment feels like an eternity. What’s more, I have found that sewing has a therapeutic effect on me. It helps clear my thought and keeps me focused on a single task. Though there is financial gain in this endeavor I do it simply for the thrill. Me and my hobby: Sewing is my hobby and it is refreshing to me but over time I realized that by virtue of my love for this craft I became interested in related fields. First, I have to create a sketch of what to sew. This process is a purely creative one. As I draw, I can picture what I would do to the real fabric when I eventually get on the machine. I also visualize what the eventual dress would look like on me or whoever would eventually wear it. Then, I cut pieces of the fabric as outlined in my drawings. The cutting stage is mainly about precision. The materials have to be systematically shaped in such a way that it fits the measurement taken. Any deviation from this would lead to undesired results. Finally, the pieces are carefully held together by the automated needle of the machine. This is the most fulfilling part of the process. This is so because seeing the conceptualized idea come to bare serves as an icing on the cake. However, the feeling of excitement I experience after the cloth is made quickly evaporates. I am immediately left with the desire to start over again. Though the process might seem mechanical or even uninspiring to an onlooker, I wouldn’t trade my hobby of sewing for anything else in the world. Essay on My Hobby – Essay 7 (750 Words) Any activity which one does for pleasure is called as a hobby. It can anything ranging from reading books, spending time with your pets, travelling around, talking to new people, just anything which gives immense pleasure to a person and relieves a person of the tensions of daily life. I too have a hobby which is quite common in the world as so many people do it. My Hobby, My Pleasure: My hobby is reading anything knowledgeable be it the newspapers, magazines, short story books or the novel series. I just love to read. In fact, I have this good collection of books at home which I feel is the biggest treasure I have. How it all started: When I was in school we were asked to read the newspaper every day and come up with three national, three international and three sports news in the class. This was a sort of regular activity for us. It is from here that I gathered interest in reading newspapers. Slowly as we all grew up this hobby of reading newspapers in the morning developed into a full-time activity of reading which came around. Overall these years, I have the pleasure of reading the Harry Potter series, which still remain the best, The Shiva Trilogy from Amish Tripathi, books from good authors both from India and abroad. Books, Our best friends: Life isn’t anything but difficult to live without friends. With regards to Books, they can be our closest friends ever. Great Books advances our brain with great contemplations and information simply like a decent friend. We can’t feel alone in the vicinity of books. We can learn numerous beneficial things while perusing a decent book. Books composed by well-known and experienced authors causes us to improve as a person and furthermore show us how to serve the general public in the most ideal way. When we are separated from everyone else, we can generally get a book and begin perusing to feel unwind. Books are our closest companions since they rouse us to do incredible things throughout everyday life and conquer our disappointments. Books can be great or terrible, however, it is our duty to pick them wisely. Kinship with Good books makes you Good individual and companionship with Bad books make you a terrible individual. Books will dependably be there for you in your terrible occasions. Books motivate us to have dreams. Moreover, books convey a positive incentive to our life and make us a better human being. Advantages of Having a Hobby: Having a hobby is really basic for a solid character and body. In addition to the fact that they are fun, a hobby can revive one completely, help with remaining solid, dynamic and cheerful. Spending time doing the things that we appreciate can help postpone maturing and prompt positive emotions that assistance battle against specific diseases. A hobby makes you more joyful and more substance as a human being. In addition to the fact that this is useful for your general wellbeing and prosperity, it likewise expands your fulfilment with life and brings you harmony, joy and energy. What’s more, makes you simpler to live with! On the off chance that your days are loaded up with only customer gatherings, ventures and constant work, a hobby can help facilitate a portion of that pressure and take your brain off work. In fact, a few research studies have demonstrated that individuals who take part in leisure activities are more averse to creative memory issues. Hobbies are additionally known to fight off sadness and lower circulatory strain. So in addition to the fact that hobbies help you mentally, they are useful for your body as well. Conclusion: Having a hobby that we enjoy doing brings us joy and advances our lives. It gives us something enjoyable to do amid our recreation time and gives us the chance to learn new aptitudes. We are exceptionally lucky to have such a large number of various choices out there today. Actually, there are whole sites committed to diversions and interests. The most ideal approach to developing another hobby is to take a stab at something new. The world is loaded with magnificent, energizing exercises that we can investigate and embrace as our own. Obviously, we all are one of a kind and, accordingly, our interests and leisure activities change. In any case, when we discover an interest that we really appreciate and are enthusiastic about, we end up snared. It turns out to be a piece of our lives and encourages us in an exceptionally close to home way. Last, but not the least, hobby help us live our dreams which usually get ignored due to our busy lives. Essay on My Hobby Cooking – Essay 8 (1000 Words) Introduction: A hobby is one’s favourite habit, activity or what a person chooses to do or what the person does usually for enjoyment and pleasure in his/her available leisure time. Having a hobby is a very good thing that can be developed at a point in one’s life from childhood all the way to adulthood but it is sometimes best to have a hobby from childhood. We all participate in some kind of activity in line with our interests that we derive joy and happiness from; this activity is our hobby. We all have different hobbies based on our interests, dislikes and likes. Types of Hobbies: There are a lot of different types of hobbies that we can show interest in and develop, examples of hobbies are singing, dancing, playing outdoor or indoor games, drawing, collecting antiques, bird watching, writing, photography, reading, eating, playing, sports, music, gardening, cooking, watching TV, talking and any other activity you can think of. Our different hobbies that become a source of earning money and a means of livelihood and we can build a very successful career out of our hobbies. A hobby is meant to be enjoyed in our leisure time but it can become a lot more than that. My Hobbies: One popular misconception is that we can have only one hobby; this is totally not true. As a child growing up, I loved and enjoyed cooking and I would spend hours watching cooking programmes and watching my parents cook. Sooner rather than later, I also started trying out different recipes and dishes I had seen on TV and sometimes even tweaked a few things and made delicacies of my own. Cooking gave my childhood so much joy and bliss which made it one of my hobbies, I could cook all day and I get just happy at the thought of trying out a new recipe. Another hobby of mine is soccer which is kind of an accidental hobby (if there is anything like that). I had always loved watching football (or soccer) and was pretty good at analysis and understanding of the game but I never really tried playing the sport because of my first hobby that is cooking which meant I was more of the indoor person. Fate would have it that one of my close friends was on the varsity soccer team and all the goalkeepers got injured so he told me about an open audition for the position of goalkeeper and I just decided to try out. I was wonderful at the try outs and got a spot on the varsity soccer team, I became a pretty brilliant goalkeeper and I look forward to every opportunity to get on the field of play. There is this feeling of fulfilment and satisfaction I get anytime I am on the field of play. It is very possible to have more than one hobby so open yourself to the possibilities of all the different activities and interesting things around us. My Favourite Hobby: My favourite hobby is gardening. I spend most of my leisure time when I am not cooking or playing soccer in gardening. Gardening has been a huge source of knowledge, education, delight and entertainment to me. I have had the opportunity to learn a lot of new things on flowers, plants, vegetables, butterflies and even birds from gardening. My parents have a little plot of land where I pursue and practice this hobby. I have different varieties of vegetables, flowers and a few fruit trees in my garden. Some of the vegetables I grow are carrots, tomatoes, cauliflower, cabbage, spinach, radish, chillies, bitter gourd, etc. I also grow flowers like jasmine, roses, lilies, merry gold, carnation, poppies, flux and forget-me-not. These flowers make the garden a delight to behold and give the garden a soothing fragrance. There are a few fruit-trees in the garden including banana, mango, guava and pomegranate. The garden is visited often by quite a number of birds and there are even some birds are live permanently on the fruit trees. The chirping sound made by the birds and their sweet music gives the garden the perfect condition and makes it the ideal place to be. Gardening has also helped my other hobby (soccer) by keeping me mentally alert, physically fit and very fresh. The ambience of the garden is highly invigorating, fresh and soothing; there is calmness to the atmosphere of the garden. The processes and activities involved in gardening include weeding, digging, grafting, cutting, maturing, watering and the tilling of the soil. All of these activities get me the needed physical exercise I need to make my body fit and keep me sharp mentally. A lot of family members and friends appreciate my hobby gardening. Over the years, I have been able to develop skills needed in gardening, sometimes; my father also helps me maintain the garden. I have a worthy and wonderful collection of magazines and books on vegetables, flowers, fruit trees and also gardening overall. It is quite a wonderful experience to watch plants grow, develop and blossom. I am not full of knowledge in gardening; sometimes, I get advice and help from a professional gardener so as to know the right thing to do. I spend a large chunk of my money purchasing manure, seeds, fertilisers, books on gardening and gardening tools and implements. I try to catch all the programmes on television about gardening, I visit plant and flower shows and also fruit and vegetable exhibition. I try my possible best to balance all my hobbies, studies and other engagements without hurting any one of them for the others. Gardening motivates me and gives me a sense of purpose about what I can achieve with my life. Once I am gardening, I forget about all of my worries, troubles and problems of the world. I am my happiest when I am working in the garden or when I get to give my friends and my family members fruits from the garden.	https://www.thewisdompost.com/essay/my-hobby-essay/3277
The formation of the folk dance culture of the Circassians over the centuries was not easy and in constant search. The historical and social sources of the appearance of their own folk choreography in Adygea were folk traditions, psychology and creative thinking of the people. Self-expression in dance acquired over time special forms, techniques and character, and became part of the rich cultural heritage of the republic. It is believed that the impetuousness of the dancers and the speed of folk dances completely shifted from the Adyghe warriors who participated in numerous Caucasian wars. Syncopic rhythm is a consequence of the running of a horse translated into dance movements and the perception of it by riders - warriors. In these dances there are also the best qualities of the Circassians - pride, modesty, heroism and fortitude. Dance for Adyghe is a manifestation of life principles, a peculiar model of his life. Dancing was always a favorite entertainment in Adygea: at holidays, weddings, any solemn and joyful occasions music, singing, clapping and, of course, the dance with jumps and unusual sharp movements sounded. For a long time, Circassians have preserved original dance tunes and theatrical pantomimes with dance performances (dzheguaco, ajgafy). Improvisation and acting finds are a hallmark of such representations. Adyghe dances are always emotional due to the dancer’s noticeable readiness for action, his openness, but at the same time - inner peace and attentiveness. At the heart of many Adyghe dances there are mythological concepts: "Dygye" or the sun - this is a kind of code of national dance. So, the shape of the sun contributed to the appearance of circular dances. But the biggest source of the content of Adyghe dances is the Nart epic: “Once the brave sleds gathered on the black mountain and started dancing, competing in dances with sleds. Shabotnuko jumped onto a three-legged round table and started to dance, without spilling even a drop of seasoning and without disturbing the order ... ” The most characteristic features of Adyghe national dances The first feature: the head, shoulders, torso, arms and legs of the dancer are synchronized in movements and take those positions that correspond to the specific elements of a particular dance. So there is a deep disclosure of the content of the dance. Second: the head of the dancer is usually directed towards the partner. The girls in dance bow their heads to one of the shoulders and, if necessary, turn it in one direction or another, modestly lower your eyes. The young men always hold their heads high, they turn in the necessary direction more abruptly and impetuously. Facial expression. Usually it is restrained smiles and a calm face in general in girls and more expressive in boys. The shoulders of the dancers. Turning synchronously with the body, emphasizing the severity, restraint and pride. During turns, the corresponding shoulder first slowly begins to move in the desired direction. The girls lower their shoulders a little, and the young men hold them straight, and unroll them slightly. The positions and movements of the arms and legs of the dancers are diverse and complex. In them, a number of characteristic positions of the hands are more common, and especially in the dance movements of girls. But to describe such movements in words is extremely difficult. Therefore, let us leave a specific topic to professional choreographers and visitors to the Adyghe folk dance studios. There are many dances in Adygea that require skill and perfection. Such ones as lezginka, hasht, lo-kuazhe, cafe, udzh are at the same time complex, stately and beautiful. But for any Circassian dance is a show of fortitude when the impossible becomes possible. And this is art. A kind of gratitude for the mercies received from the ancient gods, this is a reflection of life in all its many-faceted beauty, this is the path to the knowledge of the vast and substantial world of human feelings. Devoid of its emotional content, dance ceases to be art.	https://zvuk-m.com/en/adygejskie-narodnye-tancy.html
The Logistical Importance of Waterways of the World Water has been a critical part of man’s existence, and not just for sustenance. Ever since the inception of even crudest of boats, man has used various bodies of water for transportation, travel, luxury, business, food, and more. What we’ll be looking at in this article as some of the waterways, whether artificial or natural, used for the shipment of goods. Shipping goods is all about making sure the load gets from point A to point B in the shortest time possible with the least amount of risk. When shipping by water, navigating around landmasses adds a massive amount of time to any journey. To this end, man has constructed various canals to serve as alternate routes. Whether it’s to save time or avoid dangerous waters, the following canals have served a critical role in shipping goods over the course of their existence. Beijing-Hangzhou Grand Canal The canal popularly known as the Grand Canal is the longest and oldest canal in the world. This UNESCO World Heritage Site contributes heavily to China’s economy, linking the northern and southern parts of the country. The canal connects the Yellow and Yangtze rivers, going through several provinces and even connecting with several other rivers. The logistical significance of this canal is clear; the connectivity it provides allows for shipping opportunities that may otherwise cost far more. About 100,000 river vessels transit on the canal each year, carrying about 260 million tons, mostly construction material. That is three times as much cargo as is carried on the Beijing-Shanghai railway; the canal not only connects the north and south parts of the country, but offers an alternative for a scale of goods that couldn’t be accommodated by other transportation methods. Suez Canal The Suez Canal links the Mediterranean Sea with the Gulf of Suez. It provides the shortest maritime route between Europe and the regions which share a border with the Indian Ocean and the Western Pacific Ocean. This extremely crucial shipping canal is one of the most heavily used shipping routes in the world. The Suez Canal, located in Egypt, has been recognized as a maritime route to remain open at all times, irrespective of global conflicts. In 2020, nearly 19,000 ships transited the Suez Canal, averaging 51.5 per day. It saves thousands of nautical miles in travel; up to 9,891 in the case of the Jeddah to Piraeus. Corinth Canal The Corinth Canal Connects the Gulf of Corinth and the Saronic Gulf in the Aegean Sea. Although it is less important in modern times, due to its incapability to accommodate modern ships, it still serves a purpose in aiding seafarers to avoid the dangers of sailing 700 KM around the treacherous southern capes. The canal does serve 15,000 ships from 50 countries. Panama Canal The Panama Canal is a critical waterway for the US. In 2020, it saw 13,369 vessels carrying 475.2 million tons of cargo. It Connects the Pacific and Atlantic Oceans through the Pana isthmus, a narrow strip that separates the Caribbean Sea from the Pacific Ocean. The Panama Canal eliminates the need for ships to take the much longer, and more dangerous, route around the tip of South America, essentially saving a continent’s worth of travel. The journey is shortened by about 15,000 KM. Such a distance can make or break logistics operations, and would make many previously impossible endeavors easily feasible. Kiel Canal The Kiel Canal is another waterway that saves a lot of time and distance. Connecting the Baltic Sea with the North Sea, the Kiel Canal passes through the German province of Schleswig-Holstein. As of 2019, this canal has seen annual traffic of about 30,000 ships, saving them from taking the alternative route that passes via Denmark; a route that is not only considered unstable, but being able to bypass it also saves an average of 250 nautical miles. There is a common theme with the canals we have mentioned, as well as the many more that exist globally: they give us efficient shipping routes. Logistics companies, whether dealing with land or naval routes, are always on the lookout for ways to cut distances and minimize risks, and canals serve both purposes, allowing for more effective bulk shipping by boat. On the other hand, the heavy reliance on these canals was highlighted recently by the Suez Canal’s blockage, caused by the massive Ever Given. It is estimated the it caused e-commerce firms globally about 4 billion pounds because of the disruption to supply chains and increased shipping costs. Busy ports and terminals elsewhere, to where traffic may have been redirected, may not have berths for ships arriving outside their originally scheduled windows. Although the fault of the incident can be placed on the Ever Given’s massive size rather than the Canal itself, we are shown just how invested the logistics industry is in to shipping by boat. Despite this incident, canals are unlikely to be shunned, as the routes they provide are far too valuable. Throughout history they have seen heavy use, and will continue to do so in the foreseeable future.	https://www.technologytimes.pk/2021/07/27/the-logistical-importance-of-waterways-of-the-world/
Welcome to My Personal Page From Sunday, June 13 - Friday, June 18, 2021 I will be participating in the PJ Walk for Love in support of Ronald McDonald House Charities® Atlantic and the more than 2,000 Maritime families they support each year. All donations will go directly to the charity and donations over $20 will receive an official tax receipt. My personal fundraising goal will support Maritime families. Please consider sponsoring me to help raise funds for this great cause! Achievements 1 Night of Comfort $140 Raised - 1 Night of Comfort Personal Progress: of Goal $150 Raised $140.00 Fundraising Honor Roll Mrs. Lisa Vienneau $150 If you think this page contains objectionable content, please inform the system administrator.	http://support.rmhatlantic.ca/site/TR/Events/General?px=1001490&pg=personal&fr_id=1107
Admiral Black Harry, We are pleased to accept Lord Otto Spilman into our Navy as Captain of the Prinz Retter der Meere. He has truly undergone great travails to reach our shores, and we have every faith that he and his crew, along with the other ships of the Navy, will secure our shores against the dreadful pirate scourge, and prevent the same misfortune from befalling any other ships in our waters. (Any, that is, except those of our enemies!) Thank you also for the gentle reminder that the seas around Golden Playne remain undefended. Although the Canton's nascent army is mighty, we do indeed need at least one ship to secure our Baronial and Canton waters from the dreadful pirates of the south. We will put this question before the populace of Golden Playne so that they might begin construction of an appropriate vessel. In service, Abe Akirakeiko, Palatine Baroness Ii Katsumori, Baron Original Message ---- From: Howard Re: The Baronial Navy of the Far West My Lord Captain, I am hard pressed to recall a more terrifying tale. You are truly blessed to be among us this day. With your skill of survival an unique soul of having the strength of a warrior and heart of a poet, we would be honored by your service to the Navy. My Beloved Excellencies, I submit an recommend my Lord Captain Spilman for service in your Navy. His pure spirit coupled with his determination make him no only welcome...but very needed. This will secure 3 corners of your Barony. But humbly submit we need to secure Golden Playne soon. We await your your kind consideration. Yours In Service, Black Harry Admiral Baronial Navy of the Far West Sent from my iPhone On May 7, 2010, at 11:25 AM, "otto_spilman" wrote: My Letter of Request Unto Black Harry, Captain of the Aswang and Admiral of the Far West Navy, Greetings, I, Lord Otto Spilman write to you this day, with story of grave strife. My Warship, the Prinz Retter der Meere set sail many full moons ago, from a kingdom far from this place. I was a lone Spielmann, artisan and swordsmen sent to entertain the likes of the captain and Landsknecht Fahnlein aboard our mighty ship. The night turned grey and you couldn't see from brow to stern, our ship was separated from the fleet. 3 moons passed with little supplies, when we were struck at night by a band of pirate ships. A might battle took place that required I lay down my lute, and pull out my sword. All though we were able to fight of the attack, Our Captain was killed, and all were injured, save me. The small remainder of survivors sailed the mighty Prinz Retter der Meere for what seemed eternity. Hungry and parched we pushed forward, fighting off many attacks on our journeys. The tolls of previous battles were weighing heavy on the shoulders of the remaining men. The stench of infection of wounds filled the air. The sea became angry, thrashing our ship to and fro for 4 moons. Our sails were ripped to shreds by the breath of the gods and the injured men, too weak to hold on, were swallowed by the ravenous sea. I became the lone Captain and sailor to a ship with ripped sails, left to the whims of the sea. 2 moons passed when I saw land for the very first time. I ported my ship off the coast of what appeared to be a small island. All though months have passed since this ordeal, I have been commissioned by many nobles and have earned enough to make the needed repairs to the Prinz Retter der Meere. She is sea worthy once again. With no hopes to find home, I have declared the Barony known as the Far West as my new home. I have heard rumors of the start of a Far West Navy and as the self proclaimed Captain of the Prinz Retter der Meere, I Humbly offer myself and my ship to the service of Far West and The Admiral, Black Harry. I proven myself worthy in combat and hope that my prowlness and commitment to live, can further protect all that falls under the Barony of the Far West. With your approval, I give my oath as Captain, to acquire a ship and battle worthy crew, to promote the arts of the sword, and to protect the seas of the Far West. To Translate my ship name into your toungue, it would be "Prince Savior of Seas".	http://scabattlerock.wikia.com/wiki/User_blog:Stevenyuko/Appointment_Letter_Far_West_Navy_-_Prinz_Retter_Der_Meere
A young girl who has benefited from donations will set up a lemonade stand today in Statesboro to benefit a young boy whose health is worse than hers. Anna Hays and her friends will sell lemonade at the stand from 2:30-5:30 p.m. in front of 911 Pointer Road in the Hunters Pointe subdivision. That subdivision is off Akins Pond Road and U.S. Highway 80 West just north of William James Middle School. Anna has cancer and has been the beneficiary of several fundraisers. She wants to help a young boy named Silas, who also has cancer and whose condition is even more serious. Lemonade will be sold for any amount the buyer wishes to donate.	https://www.statesboroherald.com/local/lemonade-stand-to-benefit-boy-with-cancer/
Good Morning P1L, I hope you had a lovely day of learning yesterday! It was great to see so many of you in our small group sessions. I hope you have a lovely day, Miss McGillivray Morning Routine: Wake up, shake up Start your day like we always do in school! Here is the challenge – get someone in your family to do it with you! Say hello in French to someone like we do during the register! Morning Workout: Start your morning with some Joe Wicks! Literacy Activities Sounds Learning Intention (What we are learning today): - I am learning that two letters together make one sound. - I am learning to recognise the diagraph th - I am learning to segment, world-build and blend using th Success Criteria (How can I show that I have learned and understood) • I can identify that t and h together make the sound th (two letters make one sound) • I can read words that have the sound th • I can write words that have the sound th • I can identify words that contain the sound th Please revise the th sound from yesterday. Also continue to work on all the sounds worked so far and make words. Ask your child to make words and read them. Th sound games: Here are some examples: Words: thick, bath, path, moth, that, then, this, Beth, Cath, with Use the words above to make flash cards! Here are 2 more games for you to play to practise these sounds. These games can be played with 1 child and an adult at home Please have a look at the Alphablocks website it is great! https://www.bbc.co.uk/cbeebies/shows/alphablocks Handwriting: Letters a and o. Look at the video below. You can use a white board or a paper. It is useful for the children to have lines, so they have a reference and they can do all the letters the same size. Look carefully. - We always start where the dot is, we go from the low left corner of the square to the top right corner of the square. - We use the lines on the paper to help us to follow. - o: we go from the low left corner of the square to the middle if the top of the next square we go round anti clockwise all the way the top again. Squares. https://teachhandwriting.co.uk/continuous-cursive-beginners-choice-2.html Tricky words this week are: be and she. Please practise spelling and reading these words. - To practise recognising these words make tricky word flash cards and test each other on reading them! https://www.spellingcity.com/users/P1Lionsandtigers Reading Focus: comprehension Today try to read the reading book without support. Take your time, it doesn’t matter if there are words that you find tricky and adult will be able to support you. After reading the book use your ‘Reading Caterpillar’ (given at school): Ask an adult to make up a question from each colour section for you to answer or you could make up questions for them to answer! Remember the higher up the rocket you go, the more brain power you are using! Numeracy: Today’s Key Task Learning intention - To develop strategies including counting on and counting back Success criteria - I can count the total number two screened collections - I can count on from the largest number You will need - 2 collections different small items such as counters, buttons, cheerios or raisins ( approx up to 20 each) of two types - two pieces of paper to cover/screen the collections adult :Here are x cheerios. I’m going to cover them these counters with this piece of paper, Now here are y raisins. I’m going to cover them with this other piece of paper X and Y – how many altogether ?…. Would you like to check ? In this video example, the pupil counts from one to find the total , but we should aim to encourage a counting on strategy, where the largest number is retained in the head and the smaller number counted on, Repeat with different quantities under the screens, varying the level of difficulty as appropriate. Challenge. If you wish further challenge you can replace the first collection with a higher number card from yesterday’s activity and then screen a collection of items to add on. E.g – Under this piece of paper is a card saying 28, and under this one there are 6 raisins…. You may wish to try this fruit splat addition game. Choose your level of challenge. French Today we would like you to think about different languages. Are there any languages other than English spoken in your family? Have you ever been on holiday to a country where people speak a different language to your own ? Watch this clip of some French children playing a game like hopscotch. Can you hear them counting to ten? - Did you recognise some of these numbers already? - Can you practise counting to 10 in French? - Do you know how to count to 10 in any other languages? - Can you guess what ‘Manqué’ means ? You can also hear the pronunciation of the numbers one at a time on this website Challenge:- Play a game of hopscotch and do all the counting in French ( or Spanish, or any other language other than English) Further suggestions and learning links Here you will find some additional links and ideas for Literacy, Numeracy and Maths activities should you wish to use them. Literacy - To help you with handwriting and review letter formation that we have already done you could use this: https://www.ictgames.com/mobilePage/writingRepeater/index.html - This game is good for tricky words: https://www.ictgames.com/littleBirdSpelling/ - You could use this game to make and read sentences: https://www.ictgames.com/mobilePage/sentenceSub/index.html You don’t need a computer to do this game: write words that we have worked on and tricky words (some with capital at the beginning) and full stops. Ask your child to make sentences with them. Numeracy Warm up your counting forward and backward skills by playing this game. You, or your adult, can choose the starting number and whether you are counting forwards or backwards by adjusting the yellow sliders in the screen.	https://buckstoneprimary.com/2021/01/19/learning-together-at-home-19-01-21/
- is the type of the matrix. - is the order of the Anti diagonal matrix. Description - This function gives the matrix satisfying the anti diagonal properties. - An anti-diagonal matrix is a matrix where all the entries are zero except those on the diagonal going from the lower left corner to the upper right corner (), known as the anti-diagonal. - So here we are getting all entries are 0 except from the opposite of main diagonal as 1. - The properties of anti diagonal matrix are: - 1.The product of two anti-diagonal matrices is a diagonal matrix. - 2. If A and D are n×n anti-diagonal and diagonal matrices, respectively, then AD,DA are anti-diagonal. - 3.All anti-diagonal matrices are also persymmetric. - To display the different order of matrices then the syntax is MATRIX("anti-diagonal",5).	http://wiki.zcubes.com/index.php?title=Manuals/calci/ANTIDIAGONAL&oldid=211977
This is a response to ‘The Spirit Level’ and the response to it, with discussion of the implications to be drawn for tackling inequality. You can also download it as a pdf (67kb). This article is on 5 pages, and you can go to the next page you want by clicking on the relevant number at the bottom of each page. Introduction – Selling Equality to the Rich ‘The Spirit Level’ is a book-length distillation of the work of Richard Wilkinson and Kate Pickett on the statistical relationship between standard measures of economic inequality and various social ills, such as ill-health, lack of social trust and crime. Its importance, and the controversy surrounding it, derives from its apparent ‘scientific’ justification of what might otherwise be instinctive or ‘moral’ beliefs in the desirability of equality. The significance of the work is in the prospect it raises of a new dimension to the clash between rich and poor – clear-cut evidence showing that social factors affecting the whole population (rich and poor alike) are beneficially affected by a smaller spread between the highest and lowest incomes. These benefits come over and above the individual advantage of a higher rather than lower income. While not necessarily disputing their conclusion, in this essay I point out the potential weaknesses that cast doubt on their particular analysis, and so render it a less than potent political weapon for egalitarians. At the same time I emphasise the importance of tackling overall inequality, not just inequality of income and wealth, for the benefit of the vast majority who would certainly gain. Inequality as ‘Social Pollution’ From the point of view of those with high incomes, if greater equality improves their absolute welfare no intrinsic social conscience is necessary to see this as desirable. This clearly broadens the potential appeal of egalitarian policies that involve the redistribution of incomes and wealth. We can illustrate the argument diagrammatically. Figure 1 above shows the share of incomes (and assuming a direct relationship between the level of income and welfare, the latter also) plotted on the vertical axis, against the population ordered from lowest to highest income on the horizontal axis. The red curve shows the income level rising slowly from person to person for those with lower incomes, then much more rapidly for those with higher incomes. The total income is given by the area under the curve, and the total income received by any group is indicated by the area under the part of the curve on which that group is situated. Under the red curve the area belonging to the poorer half of the population (on the left of the graph) is much less than that belonging to the richer half (on the right of the graph). This red curve therefore represents a high level of inequality of income, and consequently of welfare. The blue curve on the diagram represents a more equal distribution of the same total income. Assuming no direct effect of the reduction of equality, the welfare levels would also be distributed according to the blue curve. While the majority of the population are therefore better off with the blue curve – since their welfare levels lie above what they would have been with the red curve – there are a small number of the rich who are now worse off. This is likely to be a block to motivating political support for inequality reduction, firstly because the economic power of the rich can be translated into political power in disproportion to their numbers, and secondly perhaps because of aspirational beliefs of some of those who would currently be better off but calculate according to a positive probability of one day being among the rich. The extent to which these beliefs are fostered by organisations and media outlets controlled by the rich serves their current interest in maintaining the red curve.	http://www.futureeconomics.org/2012/07/beyond-the-spirit-level/
Start at the CVC gate in Hill Street or at the end of Ridge Road. Walk around the dam or take the turn-off into the Kloof at the far side of the dam wall. Take a rest on the bench overlooking the dam with mount Horeb in the background. Fishing in the dam is allowed, and the map serves as a fishing permit. This walk is also the starting point for the SPRUIT WALK, the CLARENS MOUNTAIN TRAIL, the PORCUPINE TRAIL and the CARACAL CONTOUR. Spruit Walk (light blue) 2.5km/1 hour Take the DAM WALK over the dam wall, turn right and turn right again following the blue marker. This is a lovely, mostly shady route along a crystal clear mountain stream (in summer). Cross a few wooden bridges until you reach Le Roux Street. Here the trail splits into two options (left, along the same Kloof Spruit, or right past the log cabin to the Eastern Spruit). Both join up again at the bridge in Van Zyl Street. From here, continue alongside the spruit until you reach Lake Clarens. Clarens Mountain Trail (light red) 3.4km/2.5 hours Start with the DAM WALK. After crossing the dam wall, turn right and follow the path with red markers up the mountain side. On the left are sandstone cliffs with a beautiful little waterfall (summers only). Follow the red markers further and traverse the Clarens Mountain on a contour path. You can choose the higher or lower route. This trail offers beautiful views over the Clarens Village, the Little Caledon River Valley, and the Red Mountains up to Golden Gate National Park. Descend the mountain above Berg Street, or continue on the Sky Contour Trail. Scilla Walk (light green) 2.4km/30 min This trail is named after the BLUE SCILLA (Afr: Blouberg-lelie), a protected plant species with a beautiful blue flower which flowers during October. Start at the CVC gate at the top of Main Street, and follow the green markers straight ahead. You will find a bench on the left. From there you have a lovely view of the village and Mount Horeb. This route can be walked as a circular route in either direction or you can continue on the DAM & KLOOF walks. Maluti View Route (yellow) 700m/15 min This route is a short deviation on the SCILLA TRAIL, onto a solid sandstone ridge from where you have a perfect view of the Maluti Mountain range in Lesotho, sometimes snow-capped during the winter months. This is an ideal vantage point to watch a golden sunset over the Red Mountains. Porcupine Trail (black) 3.5km/1. hour This is for the hiker that wants to go a little further and really wants to be in the middle of nature. Bikers can follow this route coming from the SKY CONTOUR and CLARENS MOUNTAIN TRAILS. Follow the dam trail from the CVC gate in Hill Street, then continue up the mountain with the CLARENS MOUNTAIN TRAIL (Blue Mark-ers). Once higher up, turn left at the black marker. Follow the contour path until it joins the DAM AND KLOOF WALK above the inflow of the dam. From here, you can choose your return route. Caracal Contour (yellow with black) 5.2km/2.5 hours walk and 20 min cycling The best views of Clarens and surrounding landscape, given its high elevation. The vistas from this trail are stunning. The trail has been carefully designed with conservation in mind, and is suitable for mountain bikers and hikers. Use the DAM AND KLOOF walks to get onto the PORCUPINE trail above the dam inflow. Follow the PORCUPINE TRAIL for a short distance, then turn towards the bench on the sandstone outcrop. Pass the bench up the mountain via a few switchbacks, then follow the contour path. Walk until the trail joins the CLARENS MOUNTAIN TRAIL. Mallen Walk (pink) 1.1km/30 min A lovely and easy walk on the Clarens Mountain slope above the SPRUIT WALK. Start in Berg Street close to the junction with Van Zyl Street and follow the path towards the mountain side. Turn left on MALLEN WALK (the right-hand path is the CLARENS MOUNTAIN TRAIL). The path eventually joins the SPRUIT WALK close to Steyn Street. You can also walk any half of the trail by crossing the wooden bridge at the lower end of Le Roux Street, and turn left or right at the T-junction. Titanic Trail (magenta) 2km/1.5 hours The Titanic rock is a large sandstone cliff which has the shape of a ship’s bow. It is named after the well-known passenger steamer that sank in the Atlantic in 1912. This trail takes you past Titanic and then up on the northern slope where it ends above this beautiful rock formation. From here, you can also enjoy a lovely view of the village. Start in Naauwpoort Street just north from the Maluti Lodge Hotel and follow the trail markers. A few switch-backs on the North slope of the mountain will take you to the top. Return on the same Trail, or continue on the SKY CONTOUR. Sky Contour (blue) 3.5 km/2 hours The SKY CONTOUR is a 3,5km trail, joining the TITANIC TRAIL and the CLARENS MOUNTAIN TRAIL. Start with the TITANIC TRAIL and walk North to South following the blue route markers, or the other way starting with the CLARENS MOUNTAIN TRAIL. The Clarens Golf Course Walks Mount Horeb Climb Report at THE CLARENS golf estate club house on the Fouriesburg Road and choose your route. You will see many Springbuck grazing on the lower side. The Mount Horeb Climb is not a CVC trail, but is listed here for those interested in a more challenging hike, and a better view. Book your hike up Mount Horeb with Clarens Xtreme at 530 Sias Oosthuizen Street (082-563-6242).Note that you will also have to notify two farm owners of your hike (other- wise you may just be mistaken for cattle rustlers): Neil van Schalkwyk (082-774-8814) and Daan Viljoen (083-630-8302). Elevation at start point is approximately 1850m. Mount Horeb elevation is 2449m. Plan for 5-6 hours up and down, and take enough drinking water.	https://clarensvillageconservancy.com/hiking/
If you can, please help clean this up by fixing the links or creating the missing pages. A writing system, also called a script, is a type of symbolic system used to represent elements or statements expressible in language. Contents - 1 General properties - 2 Basic terminology - 3 History of writing systems - 4 Types of writing systems - 5 Directionality - 6 See also - 7 External links - 8 References General properties Writing systems are distinguished from other possible symbolic communication systems in that one must usually understand something of the associated language in order to successfully read and comprehend the text. Contrast this with other possible symbolic systems such as information signs, painting, maps, and mathematics, which do not necessarily depend upon prior knowledge of a given language in order to extract their meaning. Every human community possesses language, a feature regarded by many as an innate and defining condition of humankind. However, the development and adoption of writing systems has occurred only sporadically. Once established, writing systems are on the whole modified more slowly than their spoken counterparts, and often preserve features and expressions which are no longer current in the discourse of the speech community. The great benefit conferred by writing systems is their ability to maintain a persistent record of information expressed in a language, which can be retrieved independently of the initial act of formulation. All writing systems require: - a set of defined base elements or symbols (termed characters or graphemes); - a set of rules and conventions understood and shared by a community, which arbitrarily assign meaning to the base elements, their ordering, and relations to one another; - a language (generally a spoken language) whose constructions are represented and able to be recalled by the interpretation of these elements and rules; - some physical means of distinctly representing the symbols by application to a permanent or semi-permanent medium, so that they may be interpreted (usually visually, but tactile systems have also been devised). Basic terminology The study of writing systems has developed along partially independent lines in the examination of individual scripts, and as such the terminology employed differs somewhat from field to field. The generic term text may be used to refer to an individual product of a writing system. The act of composing a text may be referred to as writing, and the act of interpreting the text as reading. In the study of writing systems, orthography refers to the method and rules of observed writing structure (literal meaning, "correct writing"), and in particular for alphabetic systems, includes the concept of spelling. A grapheme is the technical term coined to refer to the specific base or atomic units of a given writing system. Graphemes are the minimally significant elements which taken together comprise the set of "building blocks" out of which texts of a given writing system may be constructed, along with rules of correspondence and use. The concept is similar to that of the phoneme used in the study of spoken languages. For example, in the Latin-based writing system of standard contemporary English, examples of graphemes include the majuscule and minuscule forms of the twenty-six letters of the alphabet (corresponding to various phonemes), marks of punctuation (mostly non-phonemic), and a few other symbols such as those for numerals (logograms for numbers). Note that an individual grapheme may be represented in a wide variety of ways, where each variation is visually distinct in some regard, but all are interpreted as representing the "same" grapheme. These individual variations are known as allographs of a grapheme (compare with the term allophone used in linguistic study). For example, the minuscule letter a has different allographs when written as a cursive, block, or typed letter. The selection between different allographs may be influenced by the medium used, the writing instrument, the stylistic choice of the writer, and the largely unconscious features of an individual's handwriting. The terms glyph, sign and character are sometimes used to refer to a grapheme. Common usage varies from discipline to discipline; compare cuneiform sign, Maya glyph, Chinese character. The glyphs of most writing systems are made up of lines (or strokes) and are therefore called linear, but there are glyphs in non-linear writing systems made up of other types of marks, such as Cuneiform and Braille. Writing systems are conceptual systems, as are the languages to which they refer. Writing systems may be regarded as complete according to the extent to which they are able to represent all that may be expressed in the spoken language. History of writing systems - Main article: History of writing Proto-writing Before there was writing, there was proto-writing. However, few examples survive, and some experts question whether the inscriptions are early writing at all. Some believe them to have been some kind of ideographic and/or early mnemonic devices that may have been invented by creative prehistoric individuals. The best known examples are: - Symbols on tortoise shells in Jiahu, ca. 4600 BC - Vinca script (Tărtăria tablets), ca. 4500 BC - Early Indus script, ca. 3500 BC Invention of writing The invention of the first writing systems is roughly contemporary with the beginning of the Bronze Age in the late Neolithic of the late 4th millennium BC. The first writing system is generally believed to have been the Sumerian script, which developed into cuneiform. Egyptian hieroglyphs, and the undeciphered Proto-Elamite script and Indus Valley script also date to this era; though a few scholars have questioned the Indus Valley script's status as a writing system. The Chinese script may have originated independently of the Middle Eastern scripts, around 1200 BC. The pre-Columbian writing systems of the Americas (including among others Olmec and Mayan) are also generally believed to have had independent origins. The first pure alphabets emerged around 2000 BC in Ancient Egypt, but by then alphabetic principles had already been inculcated into Egyptian hieroglyphs for a millennium (see Middle Bronze Age alphabets). Types of writing systems The oldest-known forms of writing were primarily logographic in nature, based on pictographic and ideographic elements. Most writing systems can be broadly divided into three categories: logographic, syllabic and alphabetic (or segmental); however, all three may be found in any given writing system in varying proportions, often making it difficult to categorise a system uniquely. The term complex system is sometimes used to describe those where the admixture makes classification problematic. \|Type of writing system\|\|What each symbol represents\|\|Example\| \|Logographic\|\|morpheme\|\|Chinese hanzi\| \|Syllabic\|\|syllable\|\|Japanese kana\| \|Alphabetic\|\|phoneme (consonant or vowel)\|\|Latin\| \|Abugida\|\|phoneme (consonant+vowel)\|\|Indian devanagari\| \|Abjad\|\|phoneme (consonant)\|\|Arabic\| \|Featural\|\|phonetic feature\|\|Korean hangul\| See also: phonemic and phonetic orthography. Logographic writing systems Main article: Logogram A logogram is a single written character which represents a complete grammatical word. Most Chinese characters are classified as logograms. As each character represents a single word (or, more precisely, a morpheme), many logograms are required to write all the words of language. The vast array of logograms and the memorization of what they mean are the major disadvantage of the logographic systems over alphabetic systems. However, since the meaning is inherent to the symbol, the same logographic system can theoretically be used to represent different languages. In practice, this is only true for closely related languages, like the Chinese languages, as syntactical constraints reduce the portability of a given logographic system. Both Korean and Japanese use Chinese logograms in their writing systems, with most of the symbols carrying the same or similar meanings. However, the semantics, and especially the grammar, are different enough that a Chinese text is not readily understandable to a Japanese or Korean reader. While most languages do not use wholly logographic writing systems many languages use some logograms. A good example of modern western logograms are the Hindu-Arabic numerals — everyone who uses those symbols understands what 1 means whether he or she calls it one, eins, uno, or ichi. Other western logograms include the ampersand &, used for and, and the at sign @ , used in many contexts for at. Logograms are sometimes called ideograms, a word that refers to symbols which graphically represent abstract ideas, but linguists avoid this use, as Chinese characters are often semantic–phonetic compounds, symbols which include an element that represents the meaning and element that represents the pronunciation. Some nonlinguists distinguish between lexigraphy and ideography, where symbols in lexigraphies represent words, and symbols in ideographies represent words or morphemes. The most important (and, to a degree, the only surviving) modern logographic writing system is the Chinese one, whose characters are used, with varying degrees of modification, in Chinese, Japanese, Korean, Vietnamese, and other east Asian languages. Ancient Egyptian hieroglyphics and the Mayan writing system are also systems with certain logographic features, although they have marked phonetic features as well, and are no longer in current use. See List of writing systems for a list of predominantly-logographic writing systems. Syllabic writing systems Main article: Syllabary As logographic writing systems use a single symbol for an entire word, a syllabary is a set of written symbols that represent (or approximate) syllables, which make up words. A symbol in a syllabary typically represents a consonant sound followed by a vowel sound, or just a vowel alone. In a true syllabary there is no systematic graphic similarity between phonetically related characters (though some do have graphic similarity for the vowels). That is, the characters for "ke", "ka", and "ko" have no similarity to indicate their common "k"-ness. Compare abugida, where each grapheme typically represents a syllable but where characters representing related sounds are similar graphically (typically, a common consonantal base is annotated in a more or less consistent manner to represent the vowel in the syllable). Syllabaries are best suited to languages with relatively simple syllable structure, such as Japanese. The English language, on the other hand, allows complex syllable structures, with a relative large inventory of vowels and complex consonant clusters, making it cumbersome to write English words with a syllabary. To write English using a syllabary, every possible syllable in English would have to have a separate symbol, and whereas the number of possible syllables in Japanese is no more than one hundred or so, in English there are many thousands. Other languages that use syllabic writing include Mycenaean Greek (Linear B) and Native American languages such as Cherokee. Several languages of the Ancient Near East used forms of cuneiform, which is a syllabary with some non-syllabic elements. See List of writing systems for a list of syllabaries. Alphabetic writing systems Main article: Alphabet An alphabet is a small set of letters — basic written symbols — each of which roughly represents or represented historically a phoneme of a spoken language. The word alphabet is derived from alpha and beta, the first two symbols of the Greek alphabet. In a perfectly phonological alphabet, the phonemes and letters would correspond perfectly in two directions: a writer could predict the spelling of a word given its pronunciation, and a speaker could predict the pronunciation of a word given its spelling. Each language has general rules that govern the association between letters and phonemes, but, depending on the language, these rules may or may not be consistently followed. Perfectly phonological alphabets are very easy to use and learn, and languages that have them (for example, Finnish) have much lower barriers to literacy than languages such as English, which has a very complex and irregular spelling system. As languages often evolve independently of their writing systems, and writing systems have been borrowed for languages they were not designed for, the degree to which letters of an alphabet correspond to phonemes of a language varies greatly from one language to another and even within a single language. In modern times, when linguists invent a writing system for a language that didn't previously have one, the goal is usually to make perfectly phonological alphabet. An example of such writing systems is the "IPA" (International Phonetic Alphabet). See alphabet for more information about alphabets. See List of writing systems for a list of alphabetic writing systems. Abjads Main article: Abjad The first type of alphabet that was developed was the abjad. An abjad is an alphabetic writing system where there is one symbol per consonant. Abjads differ from regular alphabets in that they only have characters for consonantal sounds. Vowels are not usually marked in abjad. All known abjads (except maybe Tifinagh) belong to the Semitic family of scripts, and derive from the original Northern Linear Abjad. The reason for this is that Semitic languages and the related Berber languages have a morphemic structure which makes the denotation of vowels redundant in most cases. Some abjads (like Arabic and Hebrew) have markings for vowels as well, but only use them in special contexts, such as for teaching. Many scripts derived from abjads have been extended with vowel symbols to become full alphabets, the most famous case being the derivation of the Greek alphabet from the Phoenician abjad. This has mostly happened when the script was adapted to a non-Semitic language. The term abjad takes its name from the old order of the Arabic alphabet's consonants Alif, Bá, Jim, Dál, though the word may have earlier roots in Phoenician or Ugaritic. Abjad is still the word for alphabet in Arabic and Indonesian. See List of writing systems for a list of abjad-based writing systems. Abugidas Main article: Abugida An abugida is an alphabetic writing system whose basic signs denote consonants with an inherent vowel and where consistent modifications of the basic sign indicate other following vowels than the inherent one. Thus, in an abugida there is no sign for "k", but instead one for "ka" (if "a" is the inherent vowel), and "ke" is written by modifying the "ka" sign in a way that is consistent with how one would modify "la" to get "le". In many abugidas the modification is the addition of a vowel sign, but other possibilities are imaginable (and used), such as rotation of the basic sign, addition of diacritical marks, and so on. The obvious contrast is with syllabaries, which have one distinct symbol per possible syllable, and the signs for each syllable have no systematic graphic similarity. The graphic similarity comes from the fact that most abugidas are derived from abjads, and the consonants make up the symbols with the inherent vowel, and the new vowel symbols are markings added on to the base symbol. The Ethiopic script is an abugida, although the vowel modifications in Ethiopic are not entirely systematic. Canadian Aboriginal Syllabics can be considered abugidas, although they are rarely thought of in those terms. The largest single group of abugidas is the Brahmic family of scripts, however, which includes nearly all the scripts used in India and Southeast Asia. The name abugida is derived from the first four characters of an order of the Ge'ez script used in some religious contexts. The term was coined by Peter T. Daniels. See List of writing systems for a list of abugida-based writing systems. Featural writing systems A featural script represents finer detail than an alphabet. Here symbols do not represent whole phonemes, but rather the elements (features) that make up the phonemes, such as voicing or its place of articulation. Theoretically, each feature could be written with a separate letter; and abjads or abugidas, or indeed syllabaries, could be featural, but the only prominent system of this sort is Korean Hangul. In Hangul, the featural symbols are combined into alphabetic letters, and these letters are in turn joined into syllabic blocks, so that the system combines three levels of phonological representation. See List of writing systems for a list of featural writing systems. Directionality Different scripts are written in different directions. The early alphabet could be written in any direction: either horizontal (left-to-right or right-to-left) or vertical (up or down). It could also be written boustrophedon: starting horizontally in one direction, then turning at the end of the line and reversing direction. Egyptian hieroglyph is one such script, where the beginning of a line written horizontally was to be indicated by the direction in which animal and human ideograms are looking. The Greek alphabet and its successors settled on a left-to-right pattern, from the top to the bottom of the page. Other scripts, such as Arabic and Hebrew, came to be written right-to-left. Scripts that incorporate Chinese characters have traditionally been written vertically (top-to-bottom), from the right to the left of the page, but nowadays are frequently written left-to-right, top-to-bottom, due to Western influences, a growing need to accommodate terms in the Roman alphabet, and technical limitations in popular electronic document formats. The Mongolian alphabet is unique in being the only script written top-to-bottom, left-to-right; this direction originated from an ancestral Semitic direction by rotating the page 90° counter-clockwise to conform to the appearance of Chinese writing. Scripts with lines written away from the writer, from bottom to top, also exist, such as several used in the Philippines and Indonesia. See also - Artificial script - Calligraphy - Genealogy of scripts derived from Proto-Sinaitic - ISO 15924 - list of "codes for the representation of names of scripts" - List of writing systems - List of inventors of writing systems - Majuscule - Minuscule - Nü Shu - Official script - Orthography - Pasigraphy - Penmanship - Shorthand - Spelling - Transliteration - Written language In computers and telecommunication systems, graphemes and other grapheme-like units required for text processing are represented by "characters" that typically manifest in encoded form. For technical aspects of computer support for various writing systems, see the articles CJK (Chinese, Japanese, Korean) and Bi-directional text, as well as Category:Character encoding. External links - About African writing systems by the John Henrik Clarke Africana Library at Cornell University: - General about writing systems - Alphabetic Writing Systems - Michael Everson's Alphabets of Europe - The Unicode Consortium - A Typographic Outcry: a curious perspective References - Coulmas, Florian. 1996. The Blackwell encyclopedia of writing systems. Oxford: Blackwell. - Daniels, Peter T., and William Bright, eds. 1996. The world's writing systems. ISBN 0-19-507-993-0. - DeFrancis, John. 1990. The Chinese Language: Fact and Fantasy. Honolulu: University of Hawaii Press. ISBN 0824810686 - Hannas, William. C. 1997. Asia's Orthographic Dilemma. University of Hawaii Press. ISBN 082481892X (paperback); ISBN 0824818423 (hardcover) - Rogers, Henry. 2005. Writing Systems: A Linguistic Approach. Oxford: Blackwell. ISBN 0-631-23463-2 (hardcover); ISBN 0-631-23464-0 (paperback) - Sampson, Geoffrey. 1985. Writing Systems. Stanford, California: Stanford University Press. ISBN 0-8047-1756-7 (paper), ISBN 0-8047-1254-9 (cloth). - Smalley, W.A. (ed.) 1964. Orthography studies: articles on new writing systems, United Bible Society, London. This article incorporates text from Wikipedia, and is available under the GNU Free Documentation License. For the original article please see the "external links" section.	http://www.frathwiki.com/Writing_system
This modeling method provides a more accurate analysis than trying to use a plateshell element with a. All these economical clear span structures permit unsurpassed flexibility in use of interior space. Framed buildings are building structures formed by the framed elements usually in the form of columns and beams, as well as further strengthened as necessary by the introduction of rigid floor membranes and external walls. Report on rigid frame structures linkedin slideshare. Its members can take bending moment, shear, and axial loads. This framing system clears spans up to 300 or more. Rigid frame analysis as highly redundant structures, rigid frames are designed initially on the basis of approximate analysis, after that a detailed analysis and checks are made. This frame type is economical with individual spans of 40 feet to 80 feet and building widths from 80 feet to 300 feet plus. In some building frame structures, the diagonal braces or walls form an inherent and evident part of the building design as is the case for the highrise building in san francisco shown in figure 24. A fairly simple work around is to use rigid links to transfer the bending moment from the joint at the wall as shear force to the surrounding joints in the wall. Commercial building structural design and analysis major. Solidmass structures solid structures rely heavily on solid. Shell structures a shell structure is more enclosing than a frame structure it surrounds and encloses something. Frames and machines indian institute of technology guwahati. The rigid plastic analysis presented has been formulated in a way that it circumvents the need of subdividing the beams, whereby, nevertheless, completely arbitrary loads can be accomodated. The related join method, uses merge internally for the indexonindex by default. Rigid connections are more ductile and therefore the structure performs better in load reversal situations or in earthquakes. The rigid outrigger approach was utilized to develop a program called outrigger program to analyze multioutrigger braced tall buildings. This presentation focuses on braced frames left and rigid frames right. This type of frame structures resists shear, moment and torsion more effectively than any other type of frame. Workbook for rigid frames using kleinlogel formula miscion. Recommending the rigid frame design for use where vertical supports of the bridge are elastic, as in viaducts, the authors enumerated several advantages of rigid frame bridges over simply supported girder spans. A rigid frame bridge is a bridge in which the superstructure and substructure are rigidly connected to act as a continuous unit. They provide more stability and resist rotations effectively. Frame is an assembly of several flexural members oriented in different directions and connected by rigid joints. The word rigid implies the ability to stand the deformation. Rigid frame formulas explicit formulas of all statical quantities for those singlepanel frames which occur in practical steel, reinforced concrete, and timber construction by kleinlogel, adolf and a great selection of related books, art and collectibles available now at. Semi rigid timber frame and space structure connections by. Optimal design of frame structures with semi rigid joints. There are several options for ordinary steel moment frames found in standard table 15. Rigid frame structure which are further subdivided into. Rigid frame systems for resisting lateral and vertical loads have long been accepted for the design of the buildings. Therefore, the axial force, shear force and bending moment diagrams of frame. Pdf optimal design of frame structures with semirigid. The solution to this problem requires consideration of the stressdeformation. Rigid frame steel buildings worldwide steel buildings. These structures are usually used to overcome the large moments developing due to the applied loading. These structures are usually used to overcome large moments developing due to the applied loading. We point out this fact, because we have to combine the method we. Now, the same example with frame generator end treatments is simulated again. Concrete reinforcing steel institute, a manual of standard. A rigid frame is a structural configuration consisting of a frame in which the connections between all of the frame pieces are fixed at particular angles that do not change. Pdf a study of the various structural framing systems subjected. By combining the two systems, reduced deflections can be realized. The evaluation of upper and lower bounds of the plastic limit state of frame structures using the upper bound theorem 1 chapter 1 introduction 1. If the frame is rigid or nonrigid, the floors can be a plate or slab which has drop panels around columns. Ieee 605 is a great source for substation rigid bus design. This means its the only choice for buildings larger than a story, which basically cant be built using arched style. With this system the joints of two studs and two rafters are made rigid by gluing and nailing plywood gussets on each side of each joint, doing away with the need for posts and ties. Rigidframe construction may require a slightly greater amount of steel than a truss column frame. Nov 07, 2016 a rigid frame in high rise structure typically consists of parallel or orthogonally arranged bents consisting of columns and beams with momentresistant joints. Rigid frames come forth as structural expressions of designers. Structural steel framing options for mid and high rise buildings i. Rigidframe construction may require a slightly greater amount of steel than a truss. Rigid frame the vp rigid frame is the ideal system when economical, columnfree interior space is desired. For a rigid frame, with known loads and support conditions, determination of reactions, internal forces, and bending moments is a statically indeterminate problem. Basis for the designs for your next farm building, consider using the lumber rigid frame system of construction. The new wbl and ebl structures are single span concrete rigid frame structures carrying two 3. For the simple beam moments it is necessary to combine the moments due to the. Rigid frame buildings are constructed with a skeletal primary structural steel design to carry the structural loading of the building. Description analysis of rigid frames using kleinlogel formula. These links are automatically created and join the disconnected beams, due to trimming. Frame structures are the structures having the combination of beam, column and slab to resist the lateral and gravity loads. While not being a popular building system for tall buildings today, many tall buildings comprise rigid frames in. A line constraint, also known as an edge constraint, may be applied to the edge of a shell or solid object. Typically, the structure is cast monolithically, making the structure continuous from deck to foundation. What structural engineers should know about substation. Pdf effect of semirigid connection in optimal design of. When any frame is loaded, it deflects and its shape under load is different from. As a result of these connectors, the rigid steel building structure can resist movement and have an improved overall stable design. Detailed design of portal frames 4 3 2 second order effects in portal frames 2. Rigid frames why do these structures better support loads. The straight column rigid frame is ideal for maximum. Chapter 16 analysis of statically indeterminate structures. Design of deployable structures using limit analysis of. The two common assumptions as to the behavior of a building frame are 1 that its beams are free to rotate at their. Arigidunbracedframeshouldbecapableofresistinglateralloadswithoutrelyingonanadditional bracing system for stability. The results of the hybrid simulation and the parametric studies are used to quantify various fundamental code parameters needed for the seismic design of structures. Column a structural element that usually carries its primary loads in compression or tension parallel its axis. All these economical clearspan structures permit unsurpassed flexibility in use of interior space. Architectural structures iii arch 631 f2008abn rigid frames moments get redistributed deflections are smaller effective column lengths are shorter rigid frames 6 lecture 7 architectural structures iii arch 631 f2008abn rigid frames resists lateral loadings shape depends on stiffness of beams and columns 90 maintained rigid frames 7 lecture 7. The immediate difference, even before we run the analysis, is the creation of the red rigid links. Oncenter and offcenter ridges and singleslope designs are also available. Structural steel framing options for mid and high rise buildings by jason a. Rigid frames are considered economical for buildings of up to about 25 stories, above. Structural steel framing options for mid and high rise buildings. Clear spans up to 300 or more are available, along with oncenter and offcenter ridges and singleslope designs. These joints will then displace, along those dof selected, as a function of interpolation between the two master joints which govern constraint behavior. In a beam or rigid frame external reactions are provided by either hinge or roller supports or by a fixed end, as shown in figure 3. These elements behave differently depending on their supports and the ratio of the sides. Rigid frame structures offer up to 300 feet of clear span space, with a completely columnfree interior. The word rigid means ability to resist the deformation. Rigid frame buildings have only columns in the plane, making the placement of openings, walls and windows very. The frame, by itself, has to resist all the design forces, including gravity as well as. What structural engineers should know about substation rigid bus design. Plastic limit analysis problem with quadratic yield function with respect to memberend moments is solved to generate hinges in arbitrary directions of a partially rigid frame. The evaluation of upper and lower bounds of the plastic limit state of frame structures using the upper. For the design of structural steel elements, the aisc steel manual 2 was used. Frames are structures with at least one multi force member, i external reactions frame analysis involves determining. Frame is a spreadsheet program written in msexcel for the purpose of plane frame analysis of portal and gable rigid plane frames subjected to various types of loading. Rigid frame systems are utilized in both steel and reinforced concrete construction. Benefits of michie corporations rigid frame bridges. The clear span rigid frame is the ideal system when economical, column free interior space is desired. Save my name, email, and website in this browser for the. The specimen was placed on floor for the easier manipulation. In rigid frame structures, the interaction of the walls o r legs and slab or beams generates positive and negative moments throughout the structure. Rigid frame building as a manufacturer and supplier of steel buildings, triad corrugated metal is dedicated to providing our customers with the highest standard for their building demands. Frames that are not internally rigid when a frame is not internally rigid, it has to be provided with additional external supports to make it rigid. In this paper, a genetic algorithm is pr oposed for discrete minimal we ight design of steel planar frames with semi rigid beamt o column connections. The linear programming approach to generating deployable structures is extend to allow a hinge rotating around an axis in arbitrary direction. Chapter 4 buildings, structures, and nonstructural. The related join method, uses merge internally for the indexonindex by default and columnsonindex join. Rigid framing, namely moment framing, is based on the fact that beamtocolumn connections have enough rigidity to hold the nearly unchanged original angles between. Pdf the objective of this study is to investigate the seismic behavior of the structure having various structural configurations. Rigid and semi rigid frames are often used as important elements of building structures. Rigid plastic analysis of plane frame structures sciencedirect. Its unobstructed arrangement, clear of structural walls, allows freedom internally for the layout. Pros and cons of rigid frame buildings wasatch steel. Three frames were tested, first had only glued joint with rods and two other frames had steel assembled joints. Dealing with continuous bridges, moment distribution method is best suited for practical design because the sections of the structures vary at different points for which other methods are laborious and therefore, unsuitable. Since three components of reaction are required for static equilibrium the total number of unknowns is equal to. Plane frames are twodimensional structures constructed with straight elements connected together by rigid andor hinged connections. In most buildings, the braces or walls may be hidden behind exterior. There are basically two types of frame to consider. Steel structural pieces are most common, but other types of frame pieces may also be used, including concrete structural pieces in bridges. Feb 22, 2017 introduction rigid frame structure can be defined as the structures in which beams and columns are made monolithically and act collectively t resist the moments which are generating due to applied load. Enter the rigid frame building system, a complete package from start to finish. They are purpose built structures with a variety of wall and roof systems to meet a wide range of unique project requirements. While there are pros and cons to each system, one advantage of rigid frames is that they may be engineered to safely support loads, including loads from collateral systems such as conveyors. The solid web rigid frame with interior columns provides multiple spans on wider buildings. Even though the detailing of the rigid connections results in a less economic structure, rigid unbraced frame systems have the following bene. Live load distribution on rigid frame concrete bridge. Large fabric structures are available with two framing types. The rigid frame system has several features to recommend it. The depth of the rigid frame deck slab is 500mm at midspan and mm at the legs. Modular design fast, easy installation, and standardized units result in lower project costs and less jobsite delays. The statical indeterminacy of a ring is known and hence. Nov 09, 2015 why do rigid frame structures better support loads. Rigid jointed frames are framed structures in which the members transmit applied loads by axial, shear, and bending effects. Structural steel framing options for mid and high rise. Numerous studies related to the stability of rigid or semi rigid frame structures have been performed and described in the form of journal articles. Rigid frames are highly interdependent structures, where the presence of a moment connection between beam and column presents an additional complexity to the distribution and resolution of bending moment. In addition, a program called frame tube was developed which allows analysis of single and quadbundled framed tube structures. Under the action of external loads, the elements of a plane frame are subjected to axial forces similar to truss members as well as. Major parts of reinforced concrete buildings framed. See rigid links in the modeling tips section to learn how to create rigid links. Frame structures a frame structure is a structure made up of many rigid parts joined together to form a framework. Common forms of framed building structure subdivided into 2 main types. Rigid frame calculations gravity and lateral loads consider the following loading scenarios. Frame portal and gable rigid plane frame analysis spreadsheet. Frame structures types of frame structures rigid frame. These frames are built at the site which may or may not be poured monolithically. Column base usually a thick plate at the bottom of a column through which anchor bolts mechanically connect the column and transfer forces to the. All structures are analyzed using threedimensional static or dynamic methods. Pdf live load distribution on rigid frame concrete bridge. Chapter 6 rigid frame analysis bending beam structure. Analysis of plane frames cleveland state university. The connections between members are rigid connections which transfer bending moment, axial forces, and shear. The advantage of rigid frame is that they feature positive and negative bending moments throughout the structure due to interaction of walls, beams and slabs. The procedure may typically include the following stages. A rigid frame is an unbraced frame, that is capable of resisting both vertical and lateral loads by the bending of beams and columns. Frames are subjected to loads and reactions that lie in the plane of the structure. Custom designs architectural form liners offer rustic, natural looking structures that blend with the local landscape. Rigid frame buildings are known for their loadresisting structures, consisting of straight or curved members interconnected with mostly rigid connections. Pdf geometric nonlinear approach to stiffness state of. Stability analysis of frames pennsylvania state university. Geometric nonlinear approach to stiffness state of semi rigid structures article pdf available march 2016 with 55 reads how we measure reads.	https://stufenfasto.web.app/527.html
The Reylomons are an alien species in the New Fantendoverse. They are widely recognized as galactic nomads, and can be found on almost any planet in the galaxy, although they usually prefer humid planets with jungles and similar biomes. History Long ago, there was a planet called Reyloma, a large jungle planet with raging rivers and colorful varieties of wildlife. The dominant species was the Reylomon race, who had established a feudal system of government in which property was divided among lords, barons, etc. One Reylomon, the Empress, ruled over the whole planet, and was even treated like an almighty goddess by her subjects. The planet thrived for centuries until it was finally shattered by a giant comet around 1684 (in Earth years), and the Reylomons decided to spread out as a society of nomads, with the Empress continuing to establish guidelines for them to follow. They also began inhabiting other planets similar to the now-destroyed Reyloma, so that their species could continue to survive and evolve. Appearance The Reylomons greatly resemble Earth pandas. The males are generally muscular with black and white fur and a bright red tuft on their forehead, and the females are slender with shiny brown fur, complete with silvery highlights, and a series of golden feather-like appendages for a tail, resembling a male peacock's feathers. Reylomons also have razor-sharp fangs, which they use to catch prey and in combat. Under their fur, their skin is rather tough, protecting them from most cuts and punctures. Abilities In terms of superpowers, Reylomons are usually able to change the size of their limbs. This can be very useful for running, climbing, swimming, and in some cases combat. Reylomons are also skilled with machines. They usually search through piles of garbage to find useful objects, such as aluminum, glass, and plastic, to use for building. One of the Reylomon race's most notable creations is the Havanobans, a line of robots designed for stealth, warfare, and security. The Havanobans are small robots with rounded edges, ergonomic limbs, and a wide variety of weapons and tools stored in their shells, from wrist blasters to rocket boots and everything in between. Trivia - The Reylomons' resemblance to pandas and tendency to dig through trash for tools, when put together, are inspired by one of Rocket Raccoon's nicknames in the Marvel Cinematic Universe -- "trash panda". - Their robots, the Havanobans, are inspired by the cartoon character Robotboy and the battle droids from the Star Wars franchise. - The idea of the Reylomons becoming nomads was inspired by the ending of Thor: Ragnarok, where Asgard was destroyed by Surtur and the Asgardians decided to travel the galaxy so their culture would survive.	https://fantendo.fandom.com/wiki/Reylomons
CHRIS COTE a bit shabby, yet charming guy in his fifties with grey curly hair and mediterranean looks is sitting in a plane. He is scrolling through photos on his computer. The lady sitting beside him gets interested after Chris reveals that all the pictures are from Finland. Chris starts to tell the stories behind the pictures. Episode 1, ”The Lonely King” Chris has hitched a ride and ended up to an odd place called AAVARANTA, where the interesting chain of events later takes place. Every year Finland holds a competition for upcoming tango singers. The winners are crowned as Tango King and Queen. Surprisingly often they end up getting romantically involved. This year the romance of these two has ended in a tragic way. The new Queen was shot dead by her jealous, soon-to-be ex husband. The heartbroken King was taken to hospital, badly injured. After a recovery period the King, still in misery, arrives into the VILLAGE of Tango Kings and Queens, Aavaranta. In Aavaranta the former tango royalties are all happily married together, making the new King the odd one; pitied by some, feared by others. There is a welcoming ceremony during which the new King meets all the villagers, among them also Chris and the mysterious femme fatale, YVONNE HELSINGIUS. Soon the King lives similar life to the others; early evening heading for the gig in one of the dance halls, getting back in the early hours of the morning. The hard work at the struggling tango scene takes its toll. (Because the ongoing free jazz boom in Finland the popularity of traditional Finnish tango has declined dramatically.) The new king feels miserable and he is longing for true love. One day he meets a girl of his dreams. The girl lives on a small island across the lake, opposite of Aavaranta. They fall in love. But the villagers don´t accept the relationship between The King and the girl, an outsider, a nobody. They decide to take action. While the king is away on a gig, the women of the village take the girl out on the lake on a ”kirkkovene”, a very big rowing boat. They make the girl ”accidentally” drop into the lake and leave her to drown. When the King comes home, he finds the girl washed ashore. Thinking the girl is dead, the King decides to drown himself to be together with his loved one. But the girl wakes up. And when she finds out the King is dead, she jumps into the lake. Last thing we see is her swimming towards the sunrise. Interlude Chris and the lady are still sitting in the plane. After hearing the first part of the story, the lady gets even more interested in Chris and his reasons for going to Finland in the first place. Chris tells about his troubled relationship back home and the lack of job opportunities for a free jazz guitar player in U.S. Chris continues his story. Now he tells what happened before he came to Aavaranta. Episode 2, “The Cage of Freedom” There has been a huge free jazz boom going on in Finland for several years. Free jazz musicians are teen idols, records top the charts and the bands fill up huge venues all around the country. The brightest star of them all is IDIOM, the band Chris plays guitar in. The leader of Idiom, ASEL, is a career oriented, determined and a little pompous sax player. The bass player VARKKI, is mostly interested in pleasing the crowds and thus generating as much money as possible. The drummer, HANSKI, is a mellow boozy dude, who secretly loves Finnish tango. Chris also has been digging into history of Finnish tango, and he is impressed. The band starts to feel trapped by the massive free jazz phenomenon and begins to divide. At the top of their game they are faced with the classic dilemma; to follow their hearts and risk losing it all or continue on the steady path of fame and fortune. After a successful gig Chris and Hanski decide to go see a classic tango band in nearby restaurant and force the others to join them. Due the lack of popularity and untrendiness of the finnish tango the band is performing in a nearly empty restaurant. Idiom is pretty impressed by the professionalism of the band and end up having a boozy night of laughter and brotherhood with the tango guys. The following night hangoverish Idiom perform a set of their top free jazz hits, including “The Golden Moose”, their current number one single on the charts. As they play the last song of the set, Chris and Hanski start experimenting with tango beats and little by little the others are forced to join them. Eventually the free jazz turns into a classic, all Finnish tango and Chris starts to sing. The booing crowd starts leaving the concert, disappointed. Only a few young girls remain, staring Chris, bewildered. And at the back of the restaurant Chris sees the femme fatale, Yvonne Helsingius. Their eyes meet. There is an instant connection. Next morning the band packs up their van and head towards their uncertain, but joyfully open future. Interlude Back on the plane Chris tells about his enthusiasm about the band’s future. But he also mentions that life often offers surprises. The story continues. Episode 3, “Tango Nazis F**k Off” Chris gets fired from the band for being already too “Finnish”, meaning his drinking has gotten out of hands. Band recommends him to find a tango orchestra to play with, because “they’ll tolerate anything.” Chris is left in a hotel somewhere in the middle of Finland and tries to hitch a ride. A former Tango Queen picks him up and after trying to seduce him, takes him to Aavaranta, the village of Tango Royalty. (And right here we are back in the beginning of the first episode.) Being a guitar player, Chris immediately makes friends among the villagers. Chris takes part in the welcoming ceremony of the new Tango King and sets his eyes on the mysterious femme fatale, Yvonne Helsingius. Chris finds out that Yvonne´s late dad was not only the “Father of the Finnish tango”, a famous composer but also the founder of Aavaranta. Chris gets obsessed with Yvonne, borrows a rowboat and follows the recluse beauty to her cottage on an island opposite of Aavaranta. When Chris confronts Yvonne, they connect immediately and he gains her trust. She tells about her dad and her past. She takes Chris to her studio where she has been editing her new documentary. The documentary tells the Real Story of Finnish tango: When the nazis fled from Finland on submarines on the last days of world war II they took bunch of 78 rpm records of original Finnish tango with them. Once they arrived in Argentina, those records immediately gained a huge popularity among Juan Peron´s corrupted elite and their nazi comrades. Wild, sometimes perverted parties were thrown. During those decadent orgies the great Finnish records caught the attention of the local composer and political strategists. They decided that this new musical style was just perfect for boosting the patriotism and national pride. Composer stole Yvonne´s father´s song and wrote highly patriotic lyrics that were borderline fascist. The patriotic song soon became an international hit and the translated versions of it were recorded all around the world, even in Finland. Yvonne plays the Finnish translated version of the song to Chris. The lyrics are almost identical to the original nationalist Argentinian one. Then she gets another 78 rpm record from her vault. It was released way earlier, before the war. Credited to her father the lyrics of the song embrace the world and praises internationalism, freedom and the brotherhood of man. Right here and now Chris realizes how the worldwide musical phenomenon really was born. A huge success story, nowadays falsely known as Argentinian tango. It all roots back to those records that nazis brought with them. From Finland to Argentina. Romantic feelings arise between Chris and Yvonne. Chris realizes that Yvonne´s daughter MAYA, is the girl who the villagers tried to drown earlier. Maya suggests that Chris could stay with them on the island. Interlude On a plane Chris tells the lady that he´s not the kind of guy who sneaks out of relationship, so he had to get back home… Chris notices that the lady is fast asleep and the plane starts landing. After the customs we see Yvonne and Maya waving at Chris and we realize that he was already on his way back to Finland. Epilogue Yvonne´s father´s beautiful tango plays with a full orchestra and Chris is singing the original humanistic lyrics. We see Chris playing the song on the beach of the island. Across the lake, In Aavaranta, there are police cars and cops arresting the villagers, who had tried to drown Maya. Chris keeps on playing the song and little by little the sound of the orchestra fades. Now there is only Chris singing. Last thing we see is Chris, Yvonne and Maya gathered around the bonfire in the still of the night. Chris playing guitar and singing about the eternal beauty of life, friendship and love that conquers all. The end UPDATE April 4th: 4th version of the script is complete.	https://www.mufarang.fi/jossakin-on-maa
Image-Guided Radiation Therapy This page has been fact-checked by a Doctor of nursing practice specializing in Oncology and has experience working with mesothelioma patients. Sources of information are listed at the bottom of the article. We make every attempt to keep our information accurate and up-to-date. Please Contact Us with any questions or comments. Image-guided radiation therapy (IGRT) is a treatment for cancers including mesothelioma. It uses imaging scans to direct and guide radiation to the tumor and is often used along with chemotherapy or surgery. What Is IGRT? IGRT uses images to guide radiation treatment. This treatment is a type of external beam radiation therapy, meaning the radiation beam is created by a linear accelerator machine. That beam is then directed to a point, or points, on the outside of the patient’s body. Then the radiation penetrates the skin and other tissue to kill cancer cells in an underlying tumor. Before beginning IGRT a patient must undergo several imaging scans. These scans are used by the medical team to create a specific radiation plan for the patient. Images may also be taken and used during radiation treatment to change the dosing and the focus of the beam. The result is radiation therapy that more precisely targets the tumor. It also allows for higher radiation doses and better protection of healthy tissue. IGRT is often used for mesothelioma or asbestos-related lung cancer. These types of cancer tumors are close to vital organs; therefore, having a targeted and precise type of radiation therapy is important to avoid serious side effects and minimize damage. Types of Images Used in IGRT Types of imaging scans for IGRT depend on the medical team and the equipment available: - CT scans (computer tomography scans) use several X-ray images to create a cross-sectional image or a three-dimensional image of the tumor. - PET scans (positron emission tomography) scan a radioactive material that has been injected into the body. As the radioactive material collects in cancer tumors, it allows it to appear clearly in imaging scans. - MRI (magnetic resonance imaging) uses magnetic fields to create a three-dimensional image. - Ultrasound uses sound waves to create a two- or three-dimensional image of soft tissues, like tumors. Preparation for IGRT IGRT begins with a preparatory session, sometimes called a simulation. The patient is imaged with one or more imaging scans during the planning stage. These images are fed into the computer that will direct the radiation treatment. The medical team creates a plan for treatment using the computer and the images taken of the tumors. Images may also be taken during treatment to change the direction or dosage of the radiation as necessary. The technicians may insert metal markers near the tumor to help identify it on imaging scans. Preparation may also include fitting molds or masks for the patient to wear or be situated with during the treatment. These molds are designed to keep the patient properly positioned, protect healthy tissue, and help guide the radiation beam. During Treatment Preparation for IGRT often takes longer than the actual treatment. Once planning is complete, the patient is positioned on a table or bed, with molds placed if necessary. The technicians and doctors then retreat to another room to avoid radiation exposure during treatment. The procedure takes about fifteen to thirty minutes and is not painful. A patient may require several treatment sessions. Benefits of Using IGRT Using images to guide radiation therapy is beneficial in multiple ways: - One important benefit is increased accuracy. Without image guidance, there is a greater risk of the beam missing cancerous tissue and harming healthy cells. Using multiple images improves the definition and monitoring of the shape, size, and location of the tumor. - Because this technique is more accurately directed, it allows for a larger and more powerful dose of radiation. This increased dosage can improve treatment effectiveness. - Because radiation treatment harms healthy tissue, patients often experience painful or uncomfortable side effects. With image-guided radiation, this harm is minimized as are side effects for most patients. Risks and Side Effects Radiation therapy often causes side effects; however, IGRT causes fewer and milder side effects than non-guided radiation. This is because radiation in IGRT is focused precisely on the shape and size of individual tumors. Because of this increased focus, healthy tissue is less likely to be affected. Side effects are still possible, including irritation, swelling, or hair loss at the beam site. Fatigue is also a common side effect that occurs with radiation therapy, though it improves after the completion of treatment. For mesothelioma patients, there may be other side effects due to treatment location. For example, with pleural mesothelioma, radiation is aimed at the chest. This may cause swelling or inflammation in the heart or lungs. This inflammation can cause difficulty breathing which may be temporary and mild or permanent and more severe. For peritoneal mesothelioma, potential side effects are caused by damage to the bowels and bladder, resulting in digestive issues or incontinence. Image-guided radiation therapy is an important treatment for many patients with mesothelioma. IGRT protects healthy organs and tissue while attacking tumors in sensitive locations. It can be used before surgery to shrink tumors or after surgery to reduce the chances that tumors will return.Get Your FREE Mesothelioma Packet Page Medically Reviewed and Edited by Anne Courtney, AOCNP, DNP Anne Courtney has a Doctor of Nursing Practice degree and is an Advanced Oncology Certified Nurse Practitioner. She has years of oncology experience working with patients with malignant mesothelioma, as well as other types of cancer. Dr. Courtney currently works at University of Texas LIVESTRONG Cancer Institutes.	https://mesothelioma.net/image-guided-radiation-therapy/
Warrior (56 x 74 cm) In this abstract painting the artist has once again used red-violet colours. They dominate the canvas. The composition is in vertical format, and there has been cropping and foreshortening of the subject, the warrior. He appears quite close to the viewer. His spear has been placed slightly left of centre so that the painting is balanced, and the viewer can find it easier to focus on points of interest. The first focal connection is the folded fingers on the spear. Then the eye travels anti-clockwise around the canvas, but returns to connect with the warrior’s blue eye. Light comes from the left, and the shadow behind the warrior highlights his shape. The warrior’s head shape is interesting and invites comment. A mixture of angles, straight and curved lines make the painting interesting. Brush strokes are deliberate and controlled. The ‘eye’ appears in many of the artist’s works and had special significance for him. Perhaps the ‘all seeing’ eye has a presence in this painting. Warrior takes the viewer out of the real world, and one may assume the artist was influenced by the surrealist artist Dali (1904 – 1989). The mood of the painting is slightly threatening.	https://philwhatmore.com.au/warrior-56-x-74-cm/
Imagine being in a collaboration – perhaps between departments in the same company, or perhaps between companies in an alliance. Do you feel all the weight of your department’s culture behind you, pressing you to behave in ‘our’ way? Perhaps you feel frustrated with the other team? Frustrated at ‘their’ way of approaching tasks? You know, intellectually, that you need to take a different approach so that you can work better with them: - Seeing the world through their eyes - ‘Walking in their shoes’ - Flexing your organization’s standard approach Having such an awareness is one thing; being willing to flex your behaviour to others is another. The Unexpected Benefits from Skill Training As a third party, we’ve coached, mediated and facilitated many collaborations between teams with good success. Supported in this way, some of the department leaders we had worked with, realised there were some skills we had that they wanted, and these could be be taught and practised. They asked us to develop and lead a Skills Masterclass to do this. We’ve led a number of tailored Collaboration Skill Masterclasses in this kind of situation. Each one tailored to the client’s needs, although always having: - Rackham’s Communicating Behaviours - A mixture of group exercises and real scenario simulations We have been surprised how effective this has been at helping leaders to lift a mirror up to themselves to clearly see their unique patterns, e.g. - For one department: they realised they spent so much time ‘perfecting’ the process that then they didn’t have time to get into the actual content - For another department: choosing to take everything ‘personally’, instead of problem-solving together - For another company: being too polite to disagree, losing time on dead-ends, rather than investing it where there was more likelihood of success How Is This Helpful for the Future? In each case, we asked how this impacted them in their collaborations. As they discussed this, they stepped from - an intellectual awareness - to having empathy - to being motivated to manage this behaviour consciously when working with the other department - to being an even more successful collaborator. As a collaborator, how aware and willing are you to flex your behaviour?	https://www.red10dev.com/collaboration-know-yourself-flex-accordingly/
- Harden off before planting outdoors. Set outdoors only after all danger of frost has passed and the nighttime temperatures are consistently above 45 F. - Space transplants 1 to 2 feet apart for determinate varieties - Indeterminate varieties should be spaced 14 to 20 inches apart when staked and 2 to 3 feet apart when unstaked - Tomatoes perform better when planted deep or trenched. Place in the ground so that the lowest set of leaves is just above the soil surface. Roots will form from along the buried stem. - Place any plant supports at the time of planting to avoid damaging developing roots - Mulch the soil around the plants to retain moisture and to suppress weeds - Tomatoes require adequate, even moisture to flower and fruit properly. Ideally 1 inch of rain a week or supplemental watering may be required to provide consistent moisture.	https://www.melindamyers.com/plants/fruits-vegetables/tomato?ccm_paging_p=19
Match 4 game inspired by Puyo Puyo Tetris and Spirits of Metropolis. Press on any gem on the board to change to the new color that you have selected from the allowed color. Try to create 4 or more of the same color to start a combo chain. Your score is the number of combo chains that is happening and not on the number of gems cleared. If you didn't fire any combo in 5 moves you lose the game so try to start one soon. Try to have fun and get the maximum score in the number of turns that you have. To mute the music press M. Game: by Ahmed Khalifa Music: "Inspired" by Kevin Macleod. Made: by allegrojs. Comments Log in with itch.io to leave a comment.	https://amidos2006.itch.io/macha4
The North West Swan Study was formed in 1988 to study the Mute Swan (Cygnus olor) population of the North West of England. This area encompasses Greater Manchester, Lancashire, Cumbria, Merseyside (north of the River Mersey) and the Isle of Man, a total of approximately 12,250 sq km. The method employed is to mark ( or "ring" ) individual birds with uniquely numbered leg rings so that they may be identified on future occasions. The Study Group The group consists of several bird ringers who are licensed by the British Trust for Ornithology. The main ringers currently involved are Wes Halton (Bolton), Jack Sheldon (Barrow in Furness), Dr Steve Christmas (Manchester), Charlie Findley (The Fylde) and Dave Sharpe (Isle of Man). In addition other interested individuals assist in recording ring numbers and on ringing expeditions. The ringers are rigorously trained and operate under strict guidelines to ensure that the birds are neither harmed in any way or subjected to excess disturbance during the ringing process. The study, which is one of several in Great Britain, is assisted by The Wildfowl and Wetlands Trust and affiliated to the International Wildfowl Research Bureau. The Ringing Process Swans are caught by several methods, but most often by simply feeding and then grabbing hold of them by hand or with a swan hook, which is similar to a small shepherd's crook. The swan's legs and wings are then restrained using elasticated bandage to protect both it and the ringer before the ringing process takes place. Each swan is fitted with two rings, one is a metal ring issued by the British Trust for Ornithology with a unique number and normally lasts for the bird's lifetime. The second is a large plastic ring (various colours are in use nationally but the North West Study use a blue ring with white characters).The latter can be easily read in the field and alleviates the need to re-catch the swan to identify it on subsequent occasions and allows the public to record any swans that they may see. After the actual ringing the swan's age and sex is assessed and various measurements along with its weight are recorded . The swan is then immediately released. The original ringing information is stored on a computer database, to which is added all further sightings of ringed birds, breeding successes, causes of death etc. This database now contains a large amount of information on over 4300 individual swans, and is regularly analysed to monitor trends in movements and sudden increases in the death rate etc. The group welcome reports of sightings of swans from members of the public. A full copy of the information on each swan seen is sent to people who report details of ringed birds seen to the group. Reporting Swan Sightings If you wish to assist the group with any sightings of swans please include the following details:- Date, Location (with OS grid reference if possible); number of swans present (ringed and unringed); a contact phone number if possible If you require further information or wish to submit records of ringed swans please contact :- Wes Halton, 6 Hilary Grove, Farnworth, Bolton, Lancs. BL4 9NA.	https://northwestswanstudy.org.uk/swanstud.htm
HIGH TORQUE rear Platinium motor (for cargo or tricycles) 250 watts rated power / 504 max. Torque of 40 Nm Speed 15 km / h Efficiency> 80% Compatible 6-bolt disc brake and threaded pinions. Cable length: 90 cm. Weight: 2.2 Kg. It is lightest and smallest in its category. Spokes: 2.25mm reinforced, silver Rim type: Double wall: black and silver Platinium e-bike Motor 250 watt. 24"	https://ciclotek.com/gb/ebike-motors/9386-platinium-e-bike-motor-250-watt-front-20-high-torque.html
By Mark Timm, CEO Ziglar Family Ahhh… summer! It may not have technically arrived according to the calendar, but with school out and kids home all day it’s most definitely summer time in our household! There are so many things to love about summer, from the relaxed schedule and pace of life, to the hours spent fishing and swimming at the lake, to the seemingly endless supply of garden-fresh produce — it’s pretty much unanimously our family’s favorite time of year. So yes, it’s a time to relax, slow down, and really enjoy the long summer days. But one thing my wife and I have learned as parents is that relaxed doesn’t mean a complete absence of any schedule or structure. Kids are kids, and even in the summer, they do better with some direction for their days. How little or much structure you provide for your kids is a personal choice, and it depends on your unique family dynamics. Some families find that just having two or three general guidelines works well enough (like limiting screen time or requiring some help around the house) while other families find that having a daily checklist of responsibilities is more effective. One idea that has worked well for us is to have a small whiteboard for each kid (or one large whiteboard divided into sections for each kid) with a daily checklist of tasks to accomplish. We start by giving them freedom to choose when to take care of the tasks, but if they start to neglect some items, or save them until right before bed and then do a quick, less-than-thorough job, we might set some time limits on when things have to be completed. Another possibility is to prohibit all electronics until tasks are done, and that is definitely something we deploy if screen time seems to be taking up too much daily time. Here’s a look at what a typical daily checklist for our kids might look like, keeping in mind that we have all teenagers! - Pick-up your bedroom and bathroom - Put away your laundry - Exercise 30 minutes (can be anything active, preferably outdoors) - Read two chapters in your summer reading book - Write a thank-you note to your grandma for the birthday gift. - Ask Mom what one chore she needs your help on today We keep it short and sweet, and as simple as possible, so that nobody feels like the list is overwhelming. On any given day, 5 – 6 items is the most we would assign. What’s on Your Bucket List? Another tactic we employ to keep the kids from slipping into the dreaded “I’m bored” mode is to post a summer bucket list. This list has tons of ideas for the kids to try, and after completing each one, they put a check-mark with their initials. It becomes somewhat of a contest to see who can complete the most items before the end of summer, and we’ll even give some prizes to our top finishers! Here is a sample of what a summer bucket list could look like for teens, and this can be easily modified for younger kids: - Watch fireworks - Play BINGO - Fly a kite - Wash the car - Go to a concert - Make homemade pizza - Go camping - Go to a movie - Catch a fish - Find 3 constellations - Make a tie-dye shirt - Play a board game with your siblings - Got to a parade - Make a watercolor painting - Make s’mores - Play flashlight tag - Volunteer somewhere for at least 3 hours - Water balloon fight - Watch the sunrise and sunset in the same day - Create a photo album - Read a whole book in one day The possibilities are endless, and you can find tons more ideas with a quick Google search. The best idea is for your family to create the list together, then post it in a common area for easy access and reference. Then, get busy having fun! What ideas do you have for keeping kids from turning into couch potatoes over the summer? Share them below!	https://www.ziglarfamily.com/cool-ideas-for-kids-during-the-hot-summer-months/
Sir Max Hugh Macdonald Hastings (born 28 December 1945) is a British journalist, who has worked as a foreign correspondent for the BBC, editor-in-chief of The Daily Telegraph, and editor of the Evening Standard. He is also the author of numerous books, chiefly on defence matters, which have won several major awards. Hastings' parents were Macdonald Hastings, a journalist and war correspondent and Anne Scott-James, sometime editor of Harper's Bazaar. He was educated at Charterhouse School and University College, Oxford, which he left after a year. He then moved to the United States, spending a year (1967–68) as a Fellow of the World Press Institute, following which he published his first book, America, 1968: The Fire This Time, an account of the US in its tumultuous election year. He became a foreign correspondent and reported from more than sixty countries and eleven wars for BBC TV's Twenty-Four Hours current affairs programme and for the Evening Standard in London. Hastings was the first journalist to enter Port Stanley during the 1982 Falklands War. After ten years as editor and then editor-in-chief of The Daily Telegraph, he returned to the Evening Standard as editor in 1996 until his retirement in 2002. Hastings was appointed Knight Bachelor in the 2002 Birthday Honours for services to journalism. He was elected a member of the political dining society known as The Other Club in 1993. He has presented historical documentaries for the BBC and is the author of many books, including Bomber Command, which earned the Somerset Maugham Award for non-fiction in 1980. Both Overlord and The Battle for the Falklands won the Yorkshire Post Book of the Year prize. He was named Journalist of the Year and Reporter of the Year at the 1982 British Press Awards, and Editor of the Year in 1988. In 2010 he received the Royal United Services Institute's Westminster Medal for his "lifelong contribution to military literature", and the same year the Edgar Wallace Award from the London Press Club. Hastings writes a column for the Daily Mail and often contributes articles to other publications such as The Guardian, The Sunday Times and The New York Review of Books.	https://iztok-zapad.eu/en/maks-heystings
Take two of Tinkertown Pies’ Cherry Rosemary Pie and I think I nailed it this time, you guys! Tinkertown Pies’ Vegan Cherry Rosemary Pie Recipe + Three Days in Atlanta I spent a couple days in Atlanta where I ate one biscuit per day and learned how to make this pie! Vegan Cooking in Your Air Fryer: Carrot Cake in a Mug Recipe If you thought your air fryer was just a glorified tater tot machine, Kathy Hester has a new cookbook that’s going to blow your mind. The New Vegan: Gluten-free Orange Polenta Cake Recipe This recipe features my two favorite food groups: corn and frosting.	http://bakeanddestroy.net/recipes/cakes-pies/
Hello Asbed, Happy 5th! I sat one day in front of a bird feeder trying for this same shot, with a squirrel jumping to the feeder, and I wasn't happy with any of my shots, so I know how difficult this was to capture. Very well done. The detail captured on this guy is excellent. There is a busy background behind him but with your selection of aperture, he is still very clear and defined separately from this background. Thanks, John The Hill's Alive (30) waylim (1765) Hello Way, I like the "pop" you get in this shot of yours. The colour and sharpening of the front flowers and the guanacos really stand out. The mountain with the Jacobs ladder effect from the sun really back this up nicely. It would be interesting to see your processing on this one. Thanks, enjoyed! John Difficult but nice shot Mark. With the backlighting, getting the exposure right on the front of the trunks is tough, but you have good detail here. You have some burn on the top right, but there is still sufficient detail seen with the backlit leaves here to leave a pleasing photograph. Thanks, John battle scars (6) MarkRLids (8) Hello Mark, and welcome to TN. This is a great first shot. I like the colour and detail you've captured on this guy with great use of your depth of field to isolate the monarch from his background and the other butterfly. Ram's right the shot might be a bit larger for the presentation. Thanks, John Today I am green (30) jusninasirun (14660) Hello Jusni, judging from your exif data, this guy was kind enough to give you this great display in the late afternoon, as opposed to those Florida types that only come out at night. Nice shot with very nice contrast seen between your lizard and his surroundings. Very nice use of your flash, good light while not overdoing it. Thanks, John Actitis hypoleucos (58) chrimakris (26007) Hello Christodoulos, good crisp shot of this Sandpiper, well composed with excellent detail and exposure. The pose of the hunt is well captured in this shot. Thanks, John Eastern Water Dragon (14) mlines (3116) Hi Murray, I would have to agree with you about the Spit to Manly walk. It was one of my favourites, or a close second to the Bondi to Bronte walk. The good thing about this walk was the beer at the end, in Manly, at the Bavarian Cafe. Anyway, I like the positioning you have on this guy. This is a very tough environment to capture these guys with the light and shadows. In this capture you got him, complete with a nice capture of the eye, but it looks like you ran into a bit of trouble with over exposure of the highlights on the rock, and a bit of loss of detail in the shadows. Thanks, John Three Jolly Fellas (26) delpeoples (58) Hello Lisa, and welcome to TN. This is a good start to shooting on the natural side. You've presented these 3 very well on their angled ledge. Colour and detail is good with good focus. I like the use of your depth of field here with the farther one just starting to fade out in the background. You must have been pretty close to capture these guys like this with a 105. I agree with you about their call. This is one I really miss. Say hi to the "school boys" for me. Thanks, John Ibis landing (28) fthsm (3689) Hello Fatih, you continue to produce very good work on TN, with the capture of this Ibis. Your timing was perfect here, with great positioning of the bird in the frame, and great exposure of the bird itself. Notes about the bird are probably a little redundant at this point; we've read it all a few times. Some notes about the shot would have been nice however. Thanks, John Platypus (104) JoseMiguel (5658) Hola Jose Miguel, very nice capture of this elusive creature. I am so jealous. The only time I saw one of these guys was at the Sydney Aquarium, and we bought one (a door stop) from Australian Geographic. These are for sure one of the more interesting animals to be encountered in Australia, and you've placed him into a very excellent presentation. Great shot, excellent notes. Very excellent work on your part!	https://i1.treknature.com/critiques.php@filter=JPlumb.html
The State Department has made a determination approving a possible Foreign Military Sale to Turkey of eighty (80) Patriot MIM-104E Guidance Enhanced Missiles (GEM-T) missiles, sixty (60) PAC-3 Missile Segment Enhancement (MSE) missiles and related equipment for an estimated cost of $3.5 billion. The Defense Security Cooperation Agency delivered the required certification notifying Congress of this possible sale today. Turkey has requested the possible sale of four (4) AN/MPQ-65 Radar Sets, four (4) Engagement Control Stations, ten (10) Antenna Mast Groups (AMGs), twenty (20) M903 Launching Stations, eighty (80) Patriot MIM-104E Guidance Enhanced Missiles (GEM-T) missiles with canisters, sixty (60) PAC-3 Missile Segment Enhancement (MSE) missiles, and five (5) Electrical Power Plant (EPP) III. Also included with this request are communications equipment, tools and test equipment, range and test programs, support equipment, prime movers, generators, publications and technical documentation, training equipment, spare and repair parts, personnel training, Technical Assistance Field Team (TAFT), U.S. Government and contractor technical, engineering, and logistics support services, Systems Integration and Checkout (SICO), field office support, and other related elements of logistics and program support. The total estimated program cost is $3.5 billion. The prime contractors will be Raytheon Corporation in Andover, Massachusetts, and Lockheed-Martin in Dallas, Texas. The purchaser requested offsets. At this time offset agreements are undetermined and will be defined in negotiations between the purchaser and contractors. Implementation of this proposed sale will require approximately 25 U.S. Government and 40 contractor representatives to travel to Turkey for an extended period for equipment de-processing/fielding, system checkout, training, and technical and logistics support.	http://www.asdnews.com/news/defense/2018/12/19/turkey-patriot-missile-system-related-support-equipment
Rent A Car in Karpathos There are many car rental agencies in Karpathos, so you can easily discover the island. There are some main rules for renting a car: Minimum age are mostly 21 years old by the driver, and holder of the licence for at least 1 or 2 years. The cost of the rental must be payed at takeover. Renter pays for gasoline consumed during the rental period. Tickets and subsequent administrative sanctions resulting from traffic violations during the rental period are at renter’s expenses. Vehicles shall not be used against greek law. While the driver is under the influence of alcohol, driving of the car is forbidden. More information is coming soon!	https://karpathosinfo.com/index.php/travel-to-karpathos/karpathos-rent-a-car
Q: Changing the height of a dynamic-height UITableViewCell after it's already appeared I followed this tutorial to create a dynamic height UITableViewCell. My prototype cell has 1 label (pretty simple). That label has constraints set to "0" for all sides of the cell edges. That label has numberOfLines = 0 and wraps the word. In my UITableView setup, I do this: self.tableView.rowHeight = UITableViewAutomaticDimension self.tableView.estimatedRowHeight = 100.0 //some random number Basically, everything works. Each cell has its own different height. The problem arises when I update that label with different text. The height of the cell stays the same, and the text just gets truncated OR white space appears. Is there a way to tell the cell to "redraw" itself so that it calculates the height again? Ideally, I'd like to do this inside the UITableViewCell class, since that's where it receives a notification to update the label text. A: You have to implements estimatedHeightForRowAtIndexPath and calculate your label's size. for example : override func tableView(tableView: UITableView, estimatedHeightForRowAtIndexPath indexPath: NSIndexPath) -> CGFloat { let model = YourModelArray[indexPath.row] // Label fontName and size let attributes = [ NSFontAttributeName : UIFont(name: "FontName-Regular", size: 16) as! AnyObject] let nsStringText = model.text as! NSString // Calculate the size here //--------------------// //--10--UILabel--10--// //-----Element------// //------------------// let size = nsStringText. boundingRectWithSize(CGSize(width: self.tableView.frame.width - 20, height: 1000), options:[NSStringDrawingOptions.UsesLineFragmentOrigin, NSStringDrawingOptions.UsesFontLeading], attributes: attributes, context: nil) // Basically add other elements heights and vertical Spacing between them return size.height + element.frame.height + verticalSpacingBetweenLabelAndElement }
Aroma Hotel established in 1967 is located in the tranquil woods of Ayarpata Nainital (approx. 300 mtrs from the Naini Lake). Surrounded by tall pine & oak trees, the hotel gives you a true feel of a vacation in hill station. The hotel caters exclusively to the taste of a traveler seeking the serine beauty in the Himalayan foothill. It's a preferred accommodation of every traveler visiting Nainital for its natural beauty. The ambience and customer service has been specially designed to suit the tastes and requirements of budget mind leisure travelers with great hospitality. The multi cuisine restaturent of the Hotel lounge serves gourmets delight delicious food in Anamika Hotel.The culinary experties of the Chef makes each meal a special occasio for the guest. Facilities: • Well Appointed rooms. • Multi cuisine restaurant. • Doctor on Call • Courtesy car to and from the hotel on phone call.	http://www.nainital-hotels.com/nainital/hotels/aromahotel
The now quiet road that led to Bellechulish was slowly absorbed back into nature as grass, flowers and small shrubs reclaimed what they can as fast as they can. Dry grass, dying bushes and withering flowers are all that’s left of the once well kept gardens. Most doors were either completely gone or mere remnants of rotten wood and rusty metal. The open doorways looked eerie as only darkness showed within. Broken roof tiles lay in the streets and gardens and crusty, dry paint faded from walls and fences. Bellechulish, once a growing town on the rise to a better future had been forsaken and left to rot alone. Silence had taken the place of the sound of playing children, talking neighbors and the sounds of a working community. The silence was deafening. The police station once offered those in need and danger the protection they needed, but all this station can offer now is a home to animals and a shelter from the rain. On the bright side at least the cells were empty. No matter how many animals made their home in this town now you couldn’t help but be overcome with loneliness. Life had not just come to a halt, it had completely disappeared. But even with all the animals that lived here now and made this town their new home you couldn’t escape the feeling that so much had been lost forever. What was once a wide avenue that led to Arbington was barely discernible through the weeds and grasses that had reclaimed it. Dry grass, dying bushes and withering flowers are all that’s left of the once well kept gardens. Doors were boarded up tightly and some showed signs of painted symbols with meanings known only to those who put them there, but whoever put them there’s long gone too. Dry rot, vines and other undesired vegetation had taken the place of paint on most buildings and created their own kind of decoration. Arbington, once a hub of modern housing and technological developments was now a mere distant memory of better times. Bird songs, animals rustling in the bushes and trees and the various animal sounds from stray pets and other wild animals had taken the place of the sounds of a bustling community. The lighthouse was once a beacon in multiple senses of the word. The once bright light on the outskirts of town was now merely a broken pillar and the perfect spot for nesting birds who gladly took advantage of this. Street after street of abandoned homes made for a terrifying thought. Each house was once a home, a home belonging to a family and now there was only emptiness. But despite all the decay and destruction at least there was happiness among the animals. Most had found a relatively safe haven to live in.	https://articlepedia.xyz/depraved-posseddssdsd/
We’ve had the cabling company that works with Bogons, our preferred supplier, out to look at the glen and they’ve now been commissioned to come back and carry out the necessary detailed survey (taking 4/5 days) to fully cost what’s needed. That’s happening from 8 March. We’ve asked them to provide us with a menu of costs for each part of the network: the 13km that gets to all bar 22 of the 178 properties in our area and for each segment beyond that (totalling another 13km). This will let us work out just how much of the work we need to do ourselves to get to all parts of the glen: we know that the only way we will be able to provide fibre to every house or business in the area will through significant community effort as part of the lay. The rest of our costs are now fairly firm, so we’re awaiting the survey results that will let us know just where we stand. We’re including in that survey the costs of crossing both the glen road where needed and the A84 where we’re serving Balquhidder Station.	https://balquhidder.net/2016/02/
rubber, cork, glass, or plasticused to close off a glasstube, piece of laboratory glassware, a wine bottleor barrel and other containers with orifices. A rubber stopper is sometimes called a rubber bung, and a cork stopper is called a cork. Ground glass stoppers and rubber stoppers are commonly used with laboratory glassware, mainly because of their nonreactivity. Some stoppers used in labs have holes in them to allow the insertion of glass or rubber tubing. This is often used when a reaction is taking place in the flask or test tube and the byproduct or result of the reaction is desired to be collected. For instance, if one were to boil water in a test tube in an attempt to collect the water vapor, one can seal the test tube with a stopper with holes in it. Upon inserting tubing into the hole(s) and exposing the tube to heat, the water vapor will rise through the hole, make its way through the tubing, and into the collection chamber of choice. The water vapor would not be able to escape into the air, because the stopper and the tubing, if set up correctly, should be airtight. Wikimedia Foundation. 2010. Look at other dictionaries:	https://enacademic.com/dic.nsf/enwiki/431679
By collaborating with socially responsible developers, Mercy Community Capital has helped finance the development of single and multifamily homes for rental and homeownership. These developments help underserved communities, including people with low-incomes, seniors, farm workers, people who have experienced homelessness, and people with disabilities. Our mission is to create stable, vibrant, and healthy communities by developing, financing, and operating affordable, program-enriched housing for families, seniors, and people with special needs who lack the economic resources to access quality, safe housing opportunities. - - Number of Loans: 596 - Total Amount Loaned: $427 million - Total Amount Leveraged: $4.5 billion - Number of States: 41 plus Puerto Rico - Number of Communities: 248 - Number of Units Preserved or Created: 33,151 - Number of Residents Housed: 82,187 - Percent of Units to Low-Income Residents in 2020: 100% - Number of residents with onsite services available to them in 2020 (includes financial counseling, health and wellness programs, job training, and after-school programs): 2,063 - 2020 Total Household Savings in Rent: $20 million - 2020 Total Homeownership Savings: $8 million Calculated as the difference between the average annual market rent and the average annual restricted rent.	https://www.mercyhousing.org/partner-with-us/mercy-community-capital/our-impact/
I recently needed to brush up on WPF and had the idea of adding a Clipping Plane to Rod Stephens' excellent WPF Menger Sponge. While I was at it, I added some other features which I will describe via the following links: Download the MengerSpongeClipping.zip file and extract it. Open the MengerSpongeClipping project with Visual Studio. Build it by pressing F6; the project should build successfully with no errors. Press F5 to run the MengerSpongeClipping project in debug mode. MengerSpongeClipping To clip the Menger Sponge, simply click the "Clip" button. You can orient the clipping plane using the sliders as illustrated in the above image. You can rotate the clipping plane about the x, y, or z axes using the "Rotate Plane" Sliders, and you can translate it along the x, y, or z axes using "Translate Plane" sliders. For this version, the Clipping Plane is assumed to be infinite in all directions, so the translation is for demonstration purposes and does not affect the actual clipping. (In a future version, I plan on having the clipping algorithm assume a finite Clipping Plane, and therefore take into account the translation of the Clipping Plane, so parts of the Sponge that are outside are not clipped.) The positive side of the Clipping Plane is an opaque green; the negative side is an opaque blue. My implementation of the clipping plane is simple: the distance from the plane to each rectangle center is computed, and rectangles with distance values less than zero (that is, behind the opaque blue side) are discarded. The method DrawClippingPlane() performs the following steps: DrawClippingPlane() The method DistanceFromPlaneToPoint() uses the Equation of the Clipping Plane to determine the distance to the rectangle's center. The method RemoveClippedRectangles() (described below) computes the distance and removes clipped rectangles from RectanglesMade. The method DrawClippedSponge() (also described below) redraws the Menger Sponge. DistanceFromPlaneToPoint() RemoveClippedRectangles() RectanglesMade DrawClippedSponge() I used Mr. Stephens' WPF Cylinder code to draw the x, y, z axes. You can toggle them on and off by pressing the "A" (the Axis Toggle Key), or by using "View" from the Menu Bar. To label the axes, I used Eric Sink's fantastic CreateTextLabel3D() method; I added another parameter, a Transform3DGroup transform. See TextLabel3D.cs for details. CreateTextLabel3D() Transform3DGroup transform In WPF (and DirectX and OpenGL), a directional light is a light that projects its effect along a specified vector. The Vector3D lightVector1, Vector3D lightVector2, Color lightColor1 and Color lightColor2 are inputs to the DirectionalLight() constructor. Since it can sometimes be hard to visualize where the light is pointing by specifying a vector, I used Mr. Stephens' WPF Cone code to draw "flashlights" (a flashlight is known as a torch in the UK) that shows where the directional light is pointing. There are two directional lights named appropriately enough Light 1 and Light 2. The flashlights are disabled (not displayed) by default for clarity. To enable (display) them, press the "F" key (the Flashlight Toggle Key) or use "View" from the Menu Bar. Whether the flashlights are enabled or not does not affect the actual lighting; in other words, they are only used for making the lighting vectors easier to visualize. Vector3D lightVector1 Vector3D lightVector2 Color lightColor1 Color lightColor2 DirectionalLight() You can experiment with the two lights by setting the sliders for the direction vectors and combo box for the colors. If you select "None" from the colors combo box, the corresponding DirectionalLight() is turned off, and the flashlight is displayed in wireframe code supplied by Mr. Stephens. (I spent some time trying to use 3D Tools wireframe, but to no avail.) In the illustration below, I've enabled the flashlights, zoomed out a little (using the minus key) and disabled the Clipping Plane (for clarity) by pressing the "P" key (the Clipping Plane Toggle Key). Next, I set the direction vectors as shown, set Light 1 (in the background) to blue and Light 2 (in the foreground) to red. Note how the red light illuminates the X and Z faces of the Menger Sponge to red, and the Y face is a shade of purple due to the combination of blue and red: In the next illustration, after I rotate the scene 195 degrees using the arrow keys (note how theta goes from 60° to 255°), and tilt it from phi=30 degrees to phi=40 degrees, the effect of the Light 1, the blue light (now in the foreground) can be seen illuminating the -X and -Z faces of the Menger Sponge to blue: You can add textures to the Menger Sponge by selecting an image file from the "Texture" combo box as shown below. In order to use this feature, you first need to modify app.config to point to the image files, for example: <setting name="ImageFileLocation" serializeAs="String"> <value>C:\MyProjects\MengerSponge\MengerSpongeClipping\MengerSpongeClipping\Images\</value> </setting> The code for this is from yet another useful article by Mr. Stephens on textures. Since the number of rectangles drawn is determined by the SpongeDepth, I added a WPF Progress Bar to show the progress of re-drawing the clipped Menger Sponge, as illustrated below. The code demonstrates the use of a BackgroundWorker object. To get the full effect if you're running on a fast machine, you might want to run the program in Debug mode by pressing F5 since there is some console output in debug mode which slows the process somewhat. SpongeDepth BackgroundWorker When you click the "Clip" button, the BtnClip_Click() callback creates the BackgroundWorker object in order to perform the clipping operation on a separate thread. Note the use of Dispatcher.Invoke in RemoveClippedRectangles() which is needed since the method DrawClippedSponge() accesses the spongeMesh object which is owned by a different thread. The method RemoveClippedRectangles() calculates the progress. BtnClip_Click() BackgroundWorker Dispatcher.Invoke spongeMesh The Menu Bar has "File", "View" and "Help" menu items. "File->Save As..." allows you to save your settings to a text file, and "File->Open" allows you to retrieve them. File->Reset will reset the Clipping Plane rotations and translations, Camera movements, lighting settings, and textures to their initial values (as will pressing the Escape key). "View" allows you to toggle the Axes, Clipping Plane, Sponge, and Plane Normal. You can also use the "A", "P", "S", and "N" toggle keys, respectively. Since the Plane Normal is small (a unit vector), you will have to turn off the Sponge (and Axes, if the Plane Normal is aligned with an axis) in order to see it.	https://www.codeproject.com/Articles/1256458/Clipping-Plane-in-WPF-3D
Damages to doors can happen quite often, whether they're interior or exterior doors. Instead of replacing the entire door, which can be expensive, it's best to know how to fix the hole yourself. But how do you do this? We've researched the best way to fix a hole in the door, and in this post, we will share it with you. Here are the steps to fix a hole in a door: - Sand the surrounding area - Apply wood filler - Sand the filler material - Wipe down the sanded area - Prime the door - Paint the door - Apply additional paint coats A hole in your door can be aesthetically jarring. You'll be happy to know that they are relatively easy to fix, however. Continue reading to learn about the quickest and easiest method to fix a hole in the door. Steps To Fix Hole In Door Before starting the project to fix the hole in your door, it's important to first note the material on the door. You'll need to find the correct filler material to cover up the hole. Things you'll need: - Workmans's gloves - 200- and 300-grit sandpaper - Putty knife - Wood filler - Damp paper towel or sponge - Hammer - Wood filler - Wood paint - Paintbrush - Screwdriver 1. Sand the surrounding area Before sanding the door, be sure to lay down a drop cloth to avoid getting wood dust and paint on the floor beneath it. Next, while wearing a pair of workman's gloves, take your 200-grit sandpaper and sand down the hole and the surrounding area. Make sure to remove any splintering and sand down areas where the paint is peeling. Inspect the entire door to determine if other areas need repair at this time. Afterward, take a damp paper towel or sponge and wipe down the area that you've sanded. Check out these sanding blocks on Amazon. 2. Apply wood filler Next, take your wood filler and squeeze one or two beads of the filler onto a putty knife. Then, use the knife to spread the filler over the hole and the area surrounding it. Take your time while spreading the filler, as you want to achieve an even and smooth finish. Keep in mind that the area where the filter is applied should be flush with the rest of the door's surface. Next, let the filler dry for the allotted time according to the directions on the bottle. Typically, the filler will need to drive for at least 15 to 30 minutes---though this may be longer for larger holes. Learn more about this putty knife on Amazon. 3. Sand the filler material Next, take your 300-grit sandpaper and sand down the patched-up area. Be sure to sand down any humps or uneven areas where the filler is not flush with the door. Also, be careful not to sand the filler down too much where it creates an indentation in the surface of the door, or you'll have to re-apply it. Take your hand and run it over the surface of the door to make sure that it is smooth and even. If it isn't, you need to sand it down more. Learn more about this wood filler on Amazon. 4. Wipe down the sanded area Next, take your damp cloth or rag and wipe down the area that you have sanded. Sanding creates a lot of wood dust, and this will make your final finish gritty and bumpy. Be sure not to add too much water to the cloth, as you don't want the door to be wet. The sanding will also help the paint and primer to adhere better to the surface of the wood. Check out this microfiber cloth on Amazon. 5. Prime the door Use your paintbrush to apply the primer to the patched-up hole. Apply a thin, even layer of primer and make sure that it covers the surrounding areas of the patchwork. If you repair a relatively large hole, you may want to use a roller for a quick paint job. Check out this paintbrush set on Amazon. 6. Paint the door Once the primer has dried, go over the patched-up area and the surrounding area again using the paint. Make sure to cover any grooves, panels, and crevices within the door using long even strokes. This will help you avoid leaving paint lines on the final finish. If you plan to spray paint the door, be sure to hold the can at least 8 to 10 inches away to avoid dripping. You may also want to consider painting the entire door instead of having the patch job stand out, which can be an issue if the door hasn't been painted in years. 7. Apply additional paint coats Once the first coat of paint dries, apply additional codes as needed. How Much Does It Cost To Fix A Hole In The Door? The cost of repairing a door depends on a few things. The biggest factor is the size of the hole and the type of material that the door is made of. For example, reinforced steel or glass doors will typically cost more to repair than hardwood doors. A typical door repair can cost anywhere from $100 to $400 for parts and labor. And, of course, your location will always be another contributing factor to the average cost for this service. How Do You Fill A Hole In A Hollow Metal Door? Fixing a hole in a metal door is somewhat similar to fixing that in a wood door. Let's take a look at the steps to get it done. Things you'll need: - Paintbrush - Plastic drop sheet - Multi-grit sanding block - Wire brush - Metal filler or bonding autobody filler - Putty knife - Sandpaper - Paint - Primer 1. Prepare and sand the area Start by laying down a drop cloth or newspapers around the door. Next, take your sanding block and sand in the area around the hole until you reach the layer of unsheathed metal. Then, sand down any surrounding paint that may have peeled away. If you notice any other splits or dents in the wood, be sure to attend to them as well. After you have finished sanding the door, use a damp sponge or rag to wipe down the area. Take a look at this drop cloth on Amazon. 2. Treat the rusted areas Next, take your rust remover and apply it to the hole in the surrounding areas to remove any traces of corrosion and rust. You may also need to use your wire brush for this step as well if the rust proves difficult to remove. You can clean the metal surface using dishwashing liquid or CLR. 3. Apply the metal filler Next, take out your metal filler and apply it to the door. Keep in mind that some metal fillers come with a compound and an activator which will need to be combined before applying them to metal surfaces. Use your putty knife to apply a small amount of the filler to the door according to the manufacturer's directions. Be sure to smooth over the surface using the putty knife as much as possible. When you're done, the hole should be completely filled. 4. Sand down the metal filler Take the coarse side of your sanding block and sand down the metal filler until the hole and surrounding area are flush with the rest of the door. After sanding the area, take a damp cloth and wipe down any sanding dust from the door. Next, take the fine side of the sanding block and go over the area once again, but lightly. This will help create a better surface for the paint application. 5. Apply a primer Next, take a rust-inhibiting primer and apply it to the door using a paintbrush or roller. Be sure that the door is dried completely before applying a primer. Learn more about this metal primer on Amazon. 6. Paint the door Once the primer has dried, apply the paint to the patched-up area or the entire door if needed. After that, apply any additional coats as needed, but first, make sure that the previous coat has dried completely. It's also helpful to sand the area again between each paint coat. Learn more about this metal paint on Amazon. Can You Plaster A Hole In A Door? This is typically not recommended. Most doors are either made of wood, metal, or fiberglass. Repairing holes in these doors is typically done with a wood filler, bonding metal, or fiberglass filler. Plastering is typically done with a plaster bonder and used on drywall products, which interior and exterior doors aren't made of. Wrapping Things Up We hope that this post has been helpful and illustrating how to repair a hole in a door. Remember, always be sure of the material the door is made up of before repairing any damage to it. Before you go, be sure to check out our other posts:	https://uooz.com/how-to-fix-hole-in-door/
We are seeing damage from bermudagrass stem maggot (BSM) at this time and will have to start treating fields. I looked at this hay field in Boston last week. Colquitt County Agent Jeremy Kichler is reporting BSM in Alicia plots at the Expo. The hay field will have a frosted appearance after the larvae (maggot) of the fly feed inside the shoot affecting only the top shoots (usually top 2). The lower shoots are not affected. The shoots stop elongating after feeding occurs. In the U.S., only bermudagrass is a host of BSM. Below are points I try to summarize from Biology & Management of Bermudagrass Stem Maggot. Click that link to read more detail. Identification The fly is small and yellow colored with dark eyes. The fly lays its eggs on the bermudagrass stem near a node. The maggot is yellowish in color and grows to be about 1/8 inch long. It may be hard to find the maggots, because they have usually left the stem by the time the plant shows symptoms of damage. There are multiple generations each summer. The fly has a life cycle that usually lasts about 3 weeks, but can be as short as 12 days. Management One cultural option we have is to go ahead and cut the hay. UGA Extension Specialists Dr. Will Hudson and Dr. Dennis Hancock say if damage is found within 1 week of the normal harvest stage, go ahead and harvest the crop as soon as weather conditions allow. Once the damage becomes apparent, the crop is unlikely to add a significant amount of yield. If damage is observed within 1 to 3 weeks after the previous harvest, it is also likely that the crop will not add a significant amount of yield. The damaged crop should be cut and (if the yields are substantial enough to warrant) baled and removed from the field as soon as weather conditions allow. Leaving the damaged crop in the field will only compete with any attempts by the plant to regrow and decrease the opportunity that the next cutting will have to accumulate mass. Control The most important insecticide spray is the first one which should occur 7 – 10 days after cutting. We then follow up with another application 7 days following this. Below is from Dr. Hancock: We still do not have an insecticide that can successfully eradicate the invasive bermudagrass stem maggot (BSM). However, we have been able to suppress the fly population and the associated damage by the maggot when affected bermudagrass fields received two applications: 1) applying a pyrethroid (any labeled pyrethroid seems to work) as soon as the harvested bermudagrass begins to regrow (7 – 10 days after cutting) and 2) a second application 5-7 days later. Because of the expense of these treatments, these applications should only be made if a history of BSM damage would suggest that greater than 25% yield loss from the BSM is to be expected.	https://thomascountyag.com/2016/06/21/bermudagrass-stem-maggot/
Tessa has always been very protective of her loved ones and at 20 years old, that hasn’t changed. The terrier mix is devoted to her mom, but nothing beats her toy banana. It might just be padding and yellow fabric, but it's special to Tessa—and she's making sure everyone else admits it's special too. Tessa's mother Shanna Loren bought the banana five years ago after a dog destroyed Tessa's favourite toy. "I found it in a trash can at a pet store, but I knew it was the size of a toy she liked," Loren told The Dodo. "As soon as I gave her the banana, she took it." Now, when people visit, Tessa proudly shows off her bananas and insists guests pay tribute to her prized toy. "She wants people to acknowledge it before she puts it down," Loren said. "When she puts it down, she puts it in what she thinks is the best bed." Puppies are stubborn about bananas - don't let age or hearing loss get in the way of their mission. "We instructed the guests to tell her they saw her bananas so she could lie down," Loren said. "It's funny that now that she's deaf, our friends are yelling at her, 'I love your bananas, Tessa!'" With Tessa, you're never too old to fall asleep with your favorite plush toy. "She never made it a 'toy,'" Loren said. "It's her only small possession, and it's her life."	https://www.embounce.net/2022/10/20-year-old-dog-still-loves-to-snuggle.html
A Polish woman has wowed the Internet with her TikTok videos, in which she shows off her on-point Singaporean accent. In a video posted on November 25, TikTok user Mamiko shared how her accent has changed after one day, one week, one month and one year in Singapore. "Aiya, I tell you ah, the bak kut teh is very shiok!" she says in the video, which has garnered over 1.4 million views to date. Mamiko, who has 665,000 followers on the social media platform, also uploaded a video of her ordering ice cream bread from an ice cream uncle along Orchard Road and digging into the uniquely Singaporean snack.
Nausea with or without vomiting, and occasionally vomiting without nausea, can occur at any stage of HIV infection. Nausea is a common adverse effect of many antiretroviral (ARV) and other medications, and it often occurs within weeks of starting new medications. In some cases, nausea causes significant discomfort and may interfere with medication adherence. Nausea and vomiting also may be symptoms of a serious complication of ARV therapy, or signs of an opportunistic infection or neoplasm in patients with late-stage AIDS. Clinicians must identify the cause of nausea and vomiting and initiate appropriate treatment. S: Subjective The patient experiences nausea with or without vomiting, or vomiting without nausea. Ascertain the following during the history: - Duration of symptoms - Characteristics, timing, and precipitating factors - Vomiting, including hematemesis - Diarrhea - Abdominal pain - Fever - Jaundice - Lightheadedness, dizziness, vertigo, or orthostatic symptoms - Polyuria - Polydipsia - Headache - Changes in vision - Neck stiffness - Pruritus - Medications, new and ongoing - Nutritional supplements and non-prescription medications - Possibility of pregnancy (for women) (e.g., missed menses) - Alcohol intake, substance use or abuse - History of: - Hepatitis - Kidney disease - Pancreatitis - Cytomegalovirus - Central nervous system (CNS) infections, including toxoplasmosis, cryptococcosis, chronic meningitis - CNS lymphoma O: Objective Check vital signs, including orthostatic blood pressure and heart rate measurements. Conduct a thorough physical examination, including evaluation of the following: - Skin turgor - Eyes and fundi (retinal abnormalities such as papilledema) - Oropharynx (dryness of oral mucosa, thrush, ulcerations) - Neck (stiffness or other signs of meningeal irritation) - Abdomen (tenderness, distention, masses, organomegaly) - Pelvis (tenderness, masses) - Neurologic system (mental status, focal neurologic abnormalities) Review recent CD4 measurements, if available, to determine the patient's risk of opportunistic illnesses. A: Assessment A partial differential diagnosis includes the following conditions: - Medication effect or reaction - Foodborne illness - Viral or other infectious gastroenteritis - Pancreatitis - Hepatitis, infectious or drug related (see chapters Hepatitis B Infection and Hepatitis C Infection) - Appendicitis - Esophagitis (see chapter Esophageal Problems) - Lactic acidosis attributable to nucleoside analogues - Pregnancy - Adrenal insufficiency - CNS lymphoma - Meningitis - Uremia - Diabetic ketoacidosis - Influenza - Pelvic inflammatory disease (see chapter Pelvic Inflammatory Disease) - Myocardial infarction P: Plan Diagnostic Evaluation Perform laboratory work and other diagnostic studies as suggested by the history, physical examination, and differential diagnosis. Tests may include the following: - Complete blood count with differential - Electrolytes, creatinine, blood urea nitrogen - Glucose - Amylase and lipase if symptoms of pancreatitis are present - Liver function tests and hepatitis serologies for possible acute or chronic hepatitis - Blood cultures and other fever workup as needed (see chapter Fever) - Computed tomography scan of the brain if neurologic symptoms are present (see chapter Neurologic Symptoms) - Cortisol and cosyntropin stimulation test if indicated (e.g., fatigue, weakness, unexplained abdominal pain, weight loss, orthostasis; usually in late-stage AIDS) - If odynophagia or dysphagia is present, see chapter Esophageal Problems - Lactic acid levels if lactic acidosis is suspected - Pregnancy test if indicated - Electrocardiogram if patient has chest pain or suspicious symptoms Consult with an HIV expert to determine whether hospitalization or other laboratory tests are needed. Treatment Once the diagnosis is made, appropriate treatment should be initiated. In seriously ill patients, presumptive treatment may be started while diagnostic test results are pending. See appropriate chapters in section Comorbidities, Coinfections, and Complications and relevant guidelines. In the case of significant adverse effects from ARVs or other medications, substitute a less-emetogenic ARV for the problematic medication, if possible (without compromising the efficacy of the treatment regimen). In the case of serious or life-threatening medication toxicities (e.g., lactic acidosis or abacavir hypersensitivity reaction), discontinue the problematic medication (see chapter Adverse Reactions to HIV Medications). After the workup and exclusion of life-threatening illness, symptomatic treatment can be considered. If nausea and vomiting are attributable to medications that are vital to the patient, and these complications are not life-threatening, antiemetic therapy may be the best treatment. Chronic therapy is not always necessary. Some patients obtain adequate relief by breaking the "nausea cycle" with effective antiemetics for 1-2 days and then establishing meals or snacks with medications. Patients with dehydration may require administration of fluids (PO or IV) to relieve nausea. For patients with chronic nausea resulting in weight loss, refer to a nutritionist for assessment and nutritional support. Symptomatic treatment Consider the following strategies for symptomatic treatment: - For nausea that occurs in relation to an event or action (e.g., after taking ARVs) antiemetics may be given preemptively (e.g., 30 minutes beforehand). - Ginger capsules have proven effective in clinical trials for the management of pregnancy-related and chemotherapy-related nausea. Foods and beverages containing ginger (e.g., tea, cookies, ginger ale, candies) may help provide relief. - Promethazine (Phenergan) may be given as a 12.5-25 mg PO tablet Q4-6H as needed. For patients unable to tolerate the PO formulation, promethazine suppositories (12.5 or 25 mg) may be used. - Prochlorperazine (Compazine) may be given as a 5 mg or 10 mg PO tablet, or a 25 mg rectal suppository, Q6-8H as needed. Extended-release spansule, 10 mg Q12H or 15 mg QAM, also can be considered. - Lorazepam (Ativan) may be given as a 0.5 mg PO tablet 30 minutes before taking medications for symptoms of anticipatory nausea. Patients with anticipatory nausea develop significant nausea or vomiting when even thinking about medications or reaching for the medications. - Dronabinol (Marinol) may relieve nausea, especially when nausea is accompanied by a loss of appetite. This remedy is best tolerated by patients who have tolerated inhaled marijuana. The starting dosage is 2.5 to 5 mg BID or TID. - 5-Hydroxytryptamine (5-HT3) receptor antagonists such as dolasetron 50 mg and 100 mg, granisetron 1 mg, and ondansetron 4 mg and 8 mg are highly effective are highly effective in relieving severe nausea and vomiting resulting from chemotherapy and other causes. However, access to these medications is limited by their cost. Their use should be considered a short-term strategy or reserved for cases of nausea/vomiting refractory to other antiemetics. - Metoclopramide (Reglan) may be used to enhance gastrointestinal motility in patients who experience nausea and vomiting caused by gastroparesis. The typical PO dose is 5-10 mg Q4-6H, or it can be taken TID with meals if the nausea or vomiting is associated with eating. - H2 antagonists or proton pump inhibitors may be helpful in treating nausea/vomiting related to gastritis or acid reflux (caution: these agents interfere with absorption of atazanavir and rilpivirine; consult dosing recommendations); see chapter Esophageal Problems and relevant tables in the U.S. Department of Health and Human Services Guidelines for the Use of Antiretroviral Agents in HIV-1-Infected Adults and Adolescents (see Appendix). Patient Education - Nausea and vomiting can have many different causes. Patients should let their health care provider know if they are having these symptoms so that the most likely cause can be determined. - Patients should stay nourished and well hydrated even if they are experiencing nausea and vomiting. Eating small, frequent meals may be best tolerated, while avoiding dairy products, spicy or greasy foods, and high-fat meals. Taking medications with food may reduce symptoms of nausea (note that some medications must be taken on an empty stomach). - Patients should not stop taking any of their medications without first discussing it with their health care provider. Many medications must be continued despite nausea. Nausea and vomiting owing to ARVs may resolve or become tolerable over time. - Many patients wonder whether they should take their medicines again if they vomit after taking a dose. Generally, the medicines are still in the body unless the pills actually come back up. Patients should call their health care provider if they have any questions. - Ginger may help to relieve nausea. Ginger can be taken in a variety of ways, including ginger ale, tea, cookies, candies, and ginger capsules. Patients can choose the form of ginger that works best for them. References - Chubineh S, McGowan J. Nausea and vomiting in HIV: a symptom review. Int J STD AIDS. 2008 Nov;19(11):723-8. - Hill A, Balkin A. Risk factors for gastrointestinal adverse events in HIV treated and untreated patients. AIDS Rev. 2009 Jan-Mar;11(1):30-8. - Sulkowski MS, Chaisson RE. Gastrointestinal and Hepatobiliary Manifestations of HIV Infection. In: Mandell GL, Bennett JR, Dolin R, eds. Principles and Practice of Infectious Diseases, 6th ed. Philadelphia: Churchill Livingstone, 2005;1575-80.	https://aidsetc.org/guide/nausea-and-vomiting
After waking my computer (Acer Aspire with the factory default Windows 7 install and divers, Windows update running) from hibernation, it is a pain to type, since on average 5-10 keypresses are missing per 100 presses, using the laptop's keyboard. Steps to reproduce: - Power off - Power on, wait for system to become usable Open Notepad, for five times enter 10x the same character. This gives a similar pattern of 50 characters total: xxxxxxxxxxyyyyyyyyyyaaaaaaaaaassssssssssdddddddddd Optionally repeat. Everything is fine this far. - Hibernate - Power on and resume - Repeat steps 3-4. This time approximately 3-5 character will be missing from each 50 characters What I ruled out: - putting to Sleep or just Locking and resuming from there does not cause problem battery / AC usage does not matter - Internet connection does not matter - running processes seem to be the same before and after hibernation - keypress speed doesn't really matter. For the test I use a nominal 3-5 strokes/second beat. - plugging in an external USB keyboard works fine, but the built-in one still misbehaves What could be the problem? How could I diagnose if the keypresses arrive in, but get swallowed at some point? (maybe some nasty keyboard handler hook misbehaves?). Pushing the PowerSmart button and toggling to power saving state fixes the problem. Also, toggling it again back to the original state keeps it fixed. So this may be a fine workaround, but is not a conforming solution.	https://superuser.com/questions/246962/windows-7-misses-keystrokes-from-internal-keyboard-after-hibernation-on-acer-asp

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