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Beckley Park is an English country house located near the village of Beckley, in Oxfordshire, England.
It was built in 1540 by Lord Williams of Thame, who also built a great house at Rycote, a few miles away. It was originally built as a lodge for use when the lord and a party hunted the great park | https://huggingface.co/datasets/fmars/wiki_stem |
A buttery was originally a large cellar room under a monastery, in which food and drink were stored for the provisioning of strangers and passing guests. Nathan Bailey's An Universal Etymological English Dictionary gives "CELLARIST – one who keeps a Cella, or Buttery; the Butler in a religious House or Monastery. " As the definition in John Stevens's The History of the Antient Abbeys shows, its initial function was to feed and water the guests rather than monks: "The Buttery; the Lodging for Guests" | https://huggingface.co/datasets/fmars/wiki_stem |
The Carbuncle Awards were architecture prizes, presented by the Scottish magazine Urban Realm (formerly Prospect) to buildings and areas in Scotland intermittently from 2000-2015. They were established following a discussion about why policy initiatives to improve the quality of the built environment seemed to be having so little impact beyond the centres of Scotland's key cities. The name of the awards was derived from a comment by Prince Charles, an outspoken critic of modern architecture, who in 1984 described Ahrends Burton Koralek's proposed extension of London's National Gallery as a "monstrous carbuncle on the face of a much-loved and elegant friend" | https://huggingface.co/datasets/fmars/wiki_stem |
Designation is the act of setting aside something, or devoting it to a particular purpose. In the legal planning context, it is also "the action of choosing a place for a special purpose or giving it a special status". The process of designation confers a legal status on a property by a specific law and provides a degree of legal protection (which varies by country) | https://huggingface.co/datasets/fmars/wiki_stem |
Dissenting Gothic is an architectural style associated with English Dissenters - Protestants not affiliated with the Church of England. It is a distinctive style in its own right within Gothic Revival architecture that emerged primarily in Britain, its colonies and North America, during the 19th century.
Definition
In contrast to the pure copying of English Gothic advocated for and promoted by some influential ecclesiologists during the early Gothic Revival period in Britain (most particularly by Augustus Welby Pugin and to an extent in the pages of the Camden Society's quarterly journal The Ecclesiologist (1841–68)), Dissenting Gothic provided a less Anglo-centric interpretation of the Gothic style, and purposely introduced modernising elements to meet clients' needs | https://huggingface.co/datasets/fmars/wiki_stem |
The great chamber was the second most important room in a medieval or Tudor English castle, palace, mansion, or manor house after the great hall. Medieval great halls were the ceremonial centre of the household and were not private at all; the gentlemen attendants and the servants would come and go all the time. The great chamber was at the dais end of the hall, usually up a staircase | https://huggingface.co/datasets/fmars/wiki_stem |
A great hall is the main room of a royal palace, castle or a large manor house or hall house in the Middle Ages, and continued to be built in the country houses of the 16th and early 17th centuries, although by then the family used the great chamber for eating and relaxing. At that time the word "great" simply meant big and had not acquired its modern connotations of excellence. In the medieval period, the room would simply have been referred to as the "hall" unless the building also had a secondary hall, but the term "great hall" has been predominant for surviving rooms of this type for several centuries, to distinguish them from the different type of hall found in post-medieval houses | https://huggingface.co/datasets/fmars/wiki_stem |
Grundy's Northern Pride is an ITV1 Tyne Tees/Granada series about architecture, presented by John Grundy. A follow-up to Grundy's Wonders, the series covers a wider area than that series (including north-west England as well as the north-east).
Beginning in early 2007, Northern Pride was broadcast on Tuesdays at 7 | https://huggingface.co/datasets/fmars/wiki_stem |
Grundy's Wonders is a Tyne Tees Television architecture programme presented by John Grundy, which began in 2000.
On the programme, Grundy explores buildings in north-east England, as well as Cumbria and Yorkshire. Each programme has a particular theme or type of building, and Grundy names his favourite piece of architecture (on the week's theme) his "Grundy's Wonder", and gives a "Big Boot" to things he dislikes | https://huggingface.co/datasets/fmars/wiki_stem |
These awards were created to celebrate design excellence in Kent and were first staged in 2003 and are usually held every two years. They were then renamed 'Kent Design and Development Awards' in 2012. Then have stayed as the 'Kent Design and Development Awards' in 2014 | https://huggingface.co/datasets/fmars/wiki_stem |
The "Magnificent Seven" is an informal term applied to seven large private cemeteries in London. They were established in the 19th century to alleviate overcrowding in existing parish burial grounds as London’s population grew during the Victorian era.
Background
For hundreds of years, almost all London's dead were buried in small parish churchyards, which became dangerously overcrowded | https://huggingface.co/datasets/fmars/wiki_stem |
A mews is a row or courtyard of stables and carriage houses with living quarters above them, built behind large city houses before motor vehicles replaced horses in the early twentieth century. Mews are usually located in desirable residential areas, having been built to cater for the horses, coachmen and stable-servants of prosperous residents.
The word mews comes from the Royal Mews in London, England, a set of royal stables built 500 years ago on a former royal hawk mews | https://huggingface.co/datasets/fmars/wiki_stem |
Milford Hall is a privately owned 18th-century English country house at Milford, near Stafford. It is the family seat of the Levett Haszard family and is a Grade II listed building.
Association with Levett family
The estate passed to the Levett family in 1749 when Reverend Richard Levett, son of the Rector of Blithfield, Staffordshire, married Lucy Byrd, heiress of Milford and a descendant of the Byrd family of Cheshire | https://huggingface.co/datasets/fmars/wiki_stem |
The Southgate Estate was a modernist public housing project located in Runcorn New Town (Cheshire, England) and completed in 1977. The estate was designed by James Stirling, and comprised 1,500 residential units intended to house 6,000 people. The estate was demolished between 1990 and 1992 and replaced with another housing development, known as Hallwood Park, based around more traditional design principles | https://huggingface.co/datasets/fmars/wiki_stem |
Swarkestone Hall Pavilion, also known as Swarkestone Stand and The Grandstand, is a 17th-century pavilion 200 metres north of the ruins of Swarkestone Hall, Swarkestone, Derbyshire. It is a Grade I listed building south of Chellaston on the A514.
The pavilion was constructed between 1630 and 1632 | https://huggingface.co/datasets/fmars/wiki_stem |
Tower blocks are high-rise buildings for residential use. These blocks began to be built in Great Britain after the Second World War. The first residential tower block, "The Lawn", was constructed in Harlow, Essex, in 1951; it is now a Grade II listed building | https://huggingface.co/datasets/fmars/wiki_stem |
An urban heritage park is an unofficial designation for an inner-city area considered worthy of preservation because of its architectural or historic interest.
The term was first used to describe Castlefield in Manchester in 1982, inspired by examples of similar areas in Lowell, Massachusetts observed in 1975. After conservation area status was obtained for the area in Castlefield, a conservation committee representing the area's stakeholders was formed three years later, with three objectives:
To preserve and interpret the area's history
To influence future planning applications
To attract allocations of funds for improvements specially related to recreation and tourismThe group declared the area an "urban heritage park" later that year, and the term was heavily marketed | https://huggingface.co/datasets/fmars/wiki_stem |
The Wedgwood Institute is a large red-brick building that stands in Queen Street, in the town of Burslem, Stoke-on-Trent, Staffordshire, England. It is sometimes called the Wedgwood Memorial Institute, but it is not to be confused with the former Wedgwood Memorial College in Barlaston. It achieved listed building status (Grade II*) in 1972 | https://huggingface.co/datasets/fmars/wiki_stem |
A wool church is an English church financed primarily by donations from rich merchants and farmers who had benefitted from the medieval wool trade, hoping to ensure a place in heaven due to their largesse. Wool churches are common in the Cotswolds and in the "wool towns" of upland East Anglia, where enormous profits from the wool business spurred construction of ever-grander edifices. A wool church was often built to replace a smaller or less imposing place of worship, in order to reflect the growing prosperity of the community in which it was situated | https://huggingface.co/datasets/fmars/wiki_stem |
TV Time (formerly TVShow Time) is a tracking platform and social television network for TV and movies, available in app and desktop forms. Using TheTVDB as a data source, it allows users to store information about their media consumption and leave reviews.
History
Features
Every registered TV Time user has their own profile | https://huggingface.co/datasets/fmars/wiki_stem |
winnowTag is a web-based recommender system and news aggregator in which a person tags example items as belonging to a topic, thus training statistical text classification software to find more items on that same topic. Released as a publicly available web application in September 2010 by Mindloom, winnowTag uses Winnow content recommendation, a Naive Bayes text classifier evolved from SpamBayes. Users of winnowTag create and share tags, and use the shared tags of others to find on-topic content in real time | https://huggingface.co/datasets/fmars/wiki_stem |
The Association for Retail Technology Standards (ARTS) is an international standards organization dedicated to reducing the costs of technology through standards. Since 1993, ARTS has been delivering application standards exclusively to the retail industry. ARTS has four standards
The Standard Relational Data Model, UnifiedPOS, ARTS XML and the Standard RFPs | https://huggingface.co/datasets/fmars/wiki_stem |
An automated sales suppression device or zapper is a software program that falsifies the electronic records of point of sale (POS) systems for the purpose of tax evasion.
Function
Most jurisdictions levy a sales tax or a value added tax on commercial transactions such as sales in stores or food served in a restaurant. These transactions are now most often recorded by a POS system rather than a mechanical cash register | https://huggingface.co/datasets/fmars/wiki_stem |
EPAS (Electronic Protocols Application Software) is a non-commercial cooperation initiative launched in Europe which aims at developing a series of data protocols to be applied in a point of interaction (POI) environment.
The project intends to address the three following protocols; a terminal management protocol, a retailer application protocol and an acquirer protocol.
Project Development
The proposed initiative was structured along the three following main phases :
Phase I : development of technical specifications and issuance of standards (2006 - mid-2007)
Phase II : development of software and provision of test tools (2007 – 2008)
Phase III : construction of demonstrators (2008)
Participants
The EPAS Consortium is composed of 24 organisations | https://huggingface.co/datasets/fmars/wiki_stem |
Great Atlantic & Pacific Tea Co. v. Supermarket Equipment Corp | https://huggingface.co/datasets/fmars/wiki_stem |
JavaPOS (short for Java for Point of Sale Devices), is a standard for interfacing point of sale (POS) software, written in Java, with the specialized hardware peripherals typically used to create a point-of-sale system. The advantages are reduced POS terminal costs, platform independence, and reduced administrative costs. JavaPOS was based on a Windows POS device driver standard known as OPOS | https://huggingface.co/datasets/fmars/wiki_stem |
NewStore, Inc. provides Omnichannel-as-a-Service for enterprise retail brands worldwide. Its mobile-first, modular cloud platform includes point of sale (POS), order management (OMS), inventory, store fulfillment, clienteling, and native consumer app solutions | https://huggingface.co/datasets/fmars/wiki_stem |
NEXGO (also known as Shenzhen Xinguodu Technology Co. , Ltd. ) is a global manufacturer of high-tech payment terminals, PIN pads and point of sale hardware and software | https://huggingface.co/datasets/fmars/wiki_stem |
A payment terminal, also known as a point of sale (POS) terminal, credit card machine, PIN pad, EFTPOS terminal (or by the older term as PDQ terminal which stands for "Process Data Quickly"), is a device which interfaces with payment cards to make electronic funds transfers. The terminal typically consists of a secure keypad (called a PINpad) for entering PIN, a screen, a means of capturing information from payments cards and a network connection to access the payment network for authorization.
A payment terminal allows a merchant to capture required credit and debit card information and to transmit this data to the merchant services provider or bank for authorization and finally, to transfer funds to the merchant | https://huggingface.co/datasets/fmars/wiki_stem |
A Personal Shopping System (PSS) is a system designed to help customers with their purchases in a supermarket or any kind of self-service retailer. In this system, when the customer arrives at a supermarket, instead of picking a shopping cart, he/she picks an equipment (PDA or similar) which provides a friendly shopping interface.
Using some known technologies (barcode or RFID), the equipment is capable of showing on the screen all sort of information about any product available on the shelves | https://huggingface.co/datasets/fmars/wiki_stem |
The point of sale (POS) or point of purchase (POP) is the time and place at which a retail transaction is completed. At the point of sale, the merchant calculates the amount owed by the customer, indicates that amount, may prepare an invoice for the customer (which may be a cash register printout), and indicates the options for the customer to make payment. It is also the point at which a customer makes a payment to the merchant in exchange for goods or after provision of a service | https://huggingface.co/datasets/fmars/wiki_stem |
Revel Systems is an iPad-based point of sale system co-founded by Lisa Falzone and Christopher Ciabarra. It is now majority owned by private equity firm Welsh, Carson, Anderson & Stowe.
History
Revel Systems was founded in 2010 in San Francisco | https://huggingface.co/datasets/fmars/wiki_stem |
Global air-traffic management (GATM) is a concept for satellite-based Communication, navigation and surveillance and air traffic management. The Federal Aviation Administration and the International Civil Aviation Organization, a specialized agency of the United Nations, established GATM standards to keep air travel safe and effective in increasingly crowded worldwide air space. Efforts are being made worldwide to test and implement new technologies that will allow GATM to efficiently support air traffic control | https://huggingface.co/datasets/fmars/wiki_stem |
Social information processing is "an activity through which collective human actions organize knowledge. " It is the creation and processing of information by a group of people. As an academic field Social Information Processing studies the information processing power of networked social systems | https://huggingface.co/datasets/fmars/wiki_stem |
Social information processing theory, also known as SIP, is a psychological and sociological theory originally developed by Salancik and Pfeffer in 1978. This theory explores how individuals make decisions and form attitudes in a social context, often focusing on the workplace. It suggests that people rely heavily on the social information available to them in their environments, including input from colleagues and peers, to shape their attitudes, behaviors, and perceptions | https://huggingface.co/datasets/fmars/wiki_stem |
1000Memories was a website that let people organize, share, and discover old photos and memories and to set up family trees. It was shut down in late 2013 after an acquisition by Ancestry. com | https://huggingface.co/datasets/fmars/wiki_stem |
An adaptive website is a website that builds a model of user activity and modifies the information and/or presentation of information to the user in order to better address the user's needs.
Overview
An adaptive website adjusts the structure, content, or presentation of information in response to measured user interaction with the site, with the objective of optimizing future user interactions. Adaptive websites "are web sites that automatically improve their organization and presentation by learning from their user access patterns | https://huggingface.co/datasets/fmars/wiki_stem |
Ambient awareness (AmA) is a term used by social scientists to describe a form of peripheral social awareness through social media. This awareness is propagated from relatively constant contact with one's friends and colleagues via social networking platforms on the Internet. The term essentially defines the sort of omnipresent knowledge one experiences by being a regular user of these media outlets that allow a constant connection with one's social circle | https://huggingface.co/datasets/fmars/wiki_stem |
The Audience Engine is announced open-source, customizable suite of fundraising tools for public radio being developed by the Congera Corporation, a subsidiary of WFMU Radio. It was conceived by and is being developed under the supervision of WFMU management, but as of November 2020 no product has been announced, demoed or released thus rendering the project as effectively vaporware.
The platform is based on WFMU's own model of fundraising and listener-community relations, a project that began development in 1998 and WFMU claims helps raise 70% of its annual $2 | https://huggingface.co/datasets/fmars/wiki_stem |
In network science, a biased random walk on a graph is a time path process in which an evolving variable jumps from its current state to one of various potential new states; unlike in a pure random walk, the probabilities of the potential new states are unequal.
Biased random walks on a graph provide an approach for the structural analysis of undirected graphs in order to extract their symmetries when the network is too complex or when it is not large enough to be analyzed by statistical methods. The concept of biased random walks on a graph has attracted the attention of many researchers and data companies over the past decade especially in the transportation and social networks | https://huggingface.co/datasets/fmars/wiki_stem |
CiteULike was a web service which allowed users to save and share citations to academic papers. Based on the principle of social bookmarking, the site worked to promote and to develop the sharing of scientific references amongst researchers. In the same way that it is possible to catalog web pages (with Furl and delicious) or photographs (with Flickr), scientists could share citation information using CiteULike | https://huggingface.co/datasets/fmars/wiki_stem |
Collaborative filtering (CF) is a technique used by recommender systems. Collaborative filtering has two senses, a narrow one and a more general one. In the newer, narrower sense, collaborative filtering is a method of making automatic predictions (filtering) about the interests of a user by collecting preferences or taste information from many users (collaborating) | https://huggingface.co/datasets/fmars/wiki_stem |
Collaborative information seeking (CIS) is a field of research that involves studying situations, motivations, and methods for people working in collaborative groups for information seeking projects, as well as building systems for supporting such activities. Such projects often involve information searching or information retrieval (IR), information gathering, and information sharing. Beyond that, CIS can extend to collaborative information synthesis and collaborative sense-making | https://huggingface.co/datasets/fmars/wiki_stem |
Collaborative innovation is a process in which multiple players contribute towards creating new products with customers and suppliers. Collaboration can occur in all aspects of the business cycle, depending on the context:
Procurement and supplier collaboration
Research and development of new products, services, and technologies
Marketing, distribution, and commercializationCollaborative innovation network (CoIN) is a collaborative innovation practice that uses the internet platforms such as email, chat, social networks, blogs, and Wikis to promote communication and innovation within self-organizing virtual teams. The difference is that people collaborating in CoIN are so intrinsically motivated that they might not be paid nor get any advantage | https://huggingface.co/datasets/fmars/wiki_stem |
Collaborative intelligence characterizes multi-agent, distributed systems where each agent, human or machine, is autonomously contributing to a problem solving network. Collaborative autonomy of organisms in their ecosystems makes evolution possible. Natural ecosystems, where each organism's unique signature is derived from its genetics, circumstances, behavior and position in its ecosystem, offer principles for design of next generation social networks to support collaborative intelligence, crowdsourcing individual expertise, preferences, and unique contributions in a problem solving process | https://huggingface.co/datasets/fmars/wiki_stem |
Corporate social media is the use of social media platforms, social media communications and social media marketing techniques by and within corporations, ranging from small businesses and tiny entrepreneurial startups to mid-size businesses and huge multinational firms. Within the definition of social media, there are different ways corporations utilize it. Although there is no systematic way in which social media applications can be categorized, there are various methods and approaches to having a strong social media presence | https://huggingface.co/datasets/fmars/wiki_stem |
Crowdreviewing is the practice of gathering opinion or feedback from a large number of people, typically via the internet or an online community; a portmanteau of "crowd" and "reviews". Crowdreviewing is also often viewed as a form of crowd voting which occurs when a website gathers a large group's opinions and judgment. The concept is based on the principles of crowdsourcing and lets users submit online reviews to participate in building online metrics that measure performance | https://huggingface.co/datasets/fmars/wiki_stem |
Datafication is a technological trend turning many aspects of our life into data which is subsequently transferred into information realised as a new form of value. Kenneth Cukier and Viktor Mayer-Schönberger introduced the term datafication to the broader lexicon in 2013. Up until this time, datafication had been associated with the analysis of representations of our lives captured through data, but not on the present scale | https://huggingface.co/datasets/fmars/wiki_stem |
The dead Internet theory is an online conspiracy theory that asserts that the Internet now consists almost entirely of bot activity and automatically generated content that is manipulated by algorithmic curation, marginalizing organic human activity. These intelligent bots are assumed to have been made, in part, to help manipulate algorithms and boost search results in order to ultimately manipulate consumers. Further, proponents of the theory accuse government agencies of using bots to manipulate public perception | https://huggingface.co/datasets/fmars/wiki_stem |
Dgroups is a partnership of international development organisations working together towards a common vision: A world where every person is able to contribute to dialogue and decision-making for international development and social justice. The platform is administered by the Partner Members of the Dgroups Foundation (below).
Brief history
Dgroups - Development through dialogue - was set up in 2002 as an online platform offering tools and services that bring individuals and organisations together in the international development community | https://huggingface.co/datasets/fmars/wiki_stem |
Eardex. com (short for Earth Index) was a free website to find, share and compare information on cost of living worldwide. It worked like a wiki for prices in all the towns and cities, regions and countries of the world | https://huggingface.co/datasets/fmars/wiki_stem |
An editorial calendar, or publishing schedule, is used by bloggers, publishers, businesses, and groups to control publication of content across different media, for example, newspaper, magazine, blog, email newsletters, and social media outlets.
Publishers also extract some of their editorial calendar data and make the data publicly available to attract advertisers. Public relations professionals also use these abbreviated editorial calendars to try to place stories for their clients | https://huggingface.co/datasets/fmars/wiki_stem |
Eng-Tips Forums is an English-language knowledge market website that allows users to post engineering-related questions to be answered and answer questions asked by other users. The targeted audience of Eng-Tips is engineering professionals. The website's content is primarily composed of engineering forums | https://huggingface.co/datasets/fmars/wiki_stem |
Enterprise bookmarking is a method for Web 2. 0 users to tag, organize, store, and search bookmarks of both web pages on the Internet and data resources stored in a distributed database or fileserver. This is done collectively and collaboratively in a process by which users add tag (metadata) and knowledge tags | https://huggingface.co/datasets/fmars/wiki_stem |
Enterprise social networking focuses on the use of online social networks or social relations among people who share business interests and/or activities. Enterprise social networking is often a facility of enterprise social software (regarded as a primary component of Enterprise 2. 0), which is essentially social software used in "enterprise" (business/commercial) contexts | https://huggingface.co/datasets/fmars/wiki_stem |
Foo Camp is an annual hacker event hosted by publisher O'Reilly Media. O'Reilly describes it as "the wiki of conferences", where the program is developed by the attendees at the event, using big whiteboard schedule templates that can be rewritten or overwritten by attendees to optimize the schedule; this type of event is sometimes called an unconference.
The event started as a joke between Tim O'Reilly and Sara Winge, O'Reilly's VP of Corporate Communications | https://huggingface.co/datasets/fmars/wiki_stem |
FriendFeed was a real-time feed aggregator that consolidated updates from social media and social networking websites, social bookmarking websites, blogs and microblogging updates, as well as any type of RSS/Atom feed. It was created in 2007 by Bret Taylor, Jim Norris, Paul Buchheit and Sanjeev Singh. It was possible to use this stream of information to create customized feeds to share, as well as originate new posts-discussions, (and comment) with friends | https://huggingface.co/datasets/fmars/wiki_stem |
Government by algorithm (also known as algorithmic regulation, regulation by algorithms, algorithmic governance, algocratic governance, algorithmic legal order or algocracy) is an alternative form of government or social ordering where the usage of computer algorithms, especially of artificial intelligence and blockchain, is applied to regulations, law enforcement, and generally any aspect of everyday life such as transportation or land registration. The term "government by algorithm" appeared in academic literature as an alternative for "algorithmic governance" in 2013. A related term, algorithmic regulation, is defined as setting the standard, monitoring and modifying behaviour by means of computational algorithms – automation of judiciary is in its scope | https://huggingface.co/datasets/fmars/wiki_stem |
In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics. It was developed by many scientists and mathematicians during the 18th century and onward, after Newtonian mechanics. Since Newtonian mechanics considers vector quantities of motion, particularly accelerations, momenta, forces, of the constituents of the system, an alternative name for the mechanics governed by Newton's laws and Euler's laws is vectorial mechanics | https://huggingface.co/datasets/fmars/wiki_stem |
In relativistic quantum mechanics and quantum field theory, the Bargmann–Wigner equations describe free particles with non-zero mass and arbitrary spin j, an integer for bosons (j = 1, 2, 3 . . | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematical physics, the Berezin integral, named after Felix Berezin, (also known as Grassmann integral, after Hermann Grassmann), is a way to define integration for functions of Grassmann variables (elements of the exterior algebra). It is not an integral in the Lebesgue sense; the word "integral" is used because the Berezin integral has properties analogous to the Lebesgue integral and because it extends the path integral in physics, where it is used as a sum over histories for fermions.
Definition
Let
Λ
n
{\displaystyle \Lambda ^{n}}
be the exterior algebra of polynomials in anticommuting elements
θ
1
,
…
,
θ
n
{\displaystyle \theta _{1},\dots ,\theta _{n}}
over the field of complex numbers | https://huggingface.co/datasets/fmars/wiki_stem |
In applied mathematics, bred vectors are perturbations related to Lyapunov vectors, that capture fast-growing dynamical instabilities of the solution of a numerical model. They are used, for example, as initial perturbations for ensemble forecasting in numerical weather prediction. They were introduced by Zoltan Toth and Eugenia Kalnay | https://huggingface.co/datasets/fmars/wiki_stem |
In algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry. Their name was coined by Candelas et al | https://huggingface.co/datasets/fmars/wiki_stem |
In quantum mechanics, the canonical commutation relation is the fundamental relation between canonical conjugate quantities (quantities which are related by definition such that one is the Fourier transform of another). For example,
between the position operator x and momentum operator px in the x direction of a point particle in one dimension, where [x , px] = x px − px x is the commutator of x and px , i is the imaginary unit, and ℏ is the reduced Planck's constant h/2π, and
I
{\displaystyle \mathbb {I} }
is the unit operator. In general, position and momentum are vectors of operators and their commutation relation between different components of position and momentum can be expressed as
where
δ
i
j
{\displaystyle \delta _{ij}}
is the Kronecker delta | https://huggingface.co/datasets/fmars/wiki_stem |
The theory of causal fermion systems is an approach to describe fundamental physics. It provides a unification of the weak, the strong and the electromagnetic forces with gravity at the level of classical field theory. Moreover, it gives quantum mechanics as a limiting case and has revealed close connections to quantum field theory | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.
Change of variables is an operation that is related to substitution | https://huggingface.co/datasets/fmars/wiki_stem |
In particle physics, chiral symmetry breaking is the spontaneous symmetry breaking of a chiral symmetry – usually by a gauge theory such as quantum chromodynamics, the quantum field theory of the strong interaction. Yoichiro Nambu was awarded the 2008 Nobel prize in physics for describing this phenomenon ("for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics").
Overview
Quantum chromodynamics
Experimentally, it is observed that the masses of the octet of pseudoscalar mesons (such as the pion) are much lighter than the next heavier states such as the octet of vector mesons, such as rho meson | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed with a metric, allowing distances to be measured on that surface. In differential geometry, an affine connection can be defined without reference to a metric, and many additional concepts follow: parallel transport, covariant derivatives, geodesics, etc | https://huggingface.co/datasets/fmars/wiki_stem |
In the theory of random matrices, the circular ensembles are measures on spaces of unitary matrices introduced by Freeman Dyson as modifications of the Gaussian matrix ensembles. The three main examples are the circular orthogonal ensemble (COE) on symmetric unitary matrices, the circular unitary ensemble (CUE) on unitary matrices, and the circular symplectic ensemble (CSE) on self dual unitary quaternionic matrices.
Probability distributions
The distribution of the unitary circular ensemble CUE(n) is the Haar measure on the unitary group U(n) | https://huggingface.co/datasets/fmars/wiki_stem |
A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories. In most contexts, 'classical field theory' is specifically intended to describe electromagnetism and gravitation, two of the fundamental forces of nature.
A physical field can be thought of as the assignment of a physical quantity at each point of space and time | https://huggingface.co/datasets/fmars/wiki_stem |
Classical Mechanics is a well-established textbook written by Thomas Walter Bannerman Kibble and Frank Berkshire of the Imperial College Mathematics Department. The book provides a thorough coverage of the fundamental principles and techniques of classical mechanics, a long-standing subject which is at the base of all of physics.
Publication history
The English language editions were published as follows:
The first edition was published by Kibble, as Kibble, T | https://huggingface.co/datasets/fmars/wiki_stem |
In differential geometry and theoretical physics, the classification of electromagnetic fields is a pointwise classification of bivectors at each point of a Lorentzian manifold. It is used in the study of solutions of Maxwell's equations and has applications in Einstein's theory of relativity.
The classification theorem
The electromagnetic field at a point p (i | https://huggingface.co/datasets/fmars/wiki_stem |
Coherent states have been introduced in a physical context, first as quasi-classical states in quantum mechanics, then as the backbone of quantum optics and they are described in that spirit in the article Coherent states (see also). However, they have generated a huge variety of generalizations, which have led to a tremendous amount of literature in mathematical physics.
In this article, we sketch the main directions of research on this line | https://huggingface.co/datasets/fmars/wiki_stem |
A purely combinatorial approach to mirror symmetry was suggested by Victor Batyrev using the polar duality for
d
{\displaystyle d}
-dimensional convex polyhedra. The most famous examples of the polar duality provide Platonic solids: e. g | https://huggingface.co/datasets/fmars/wiki_stem |
Common integrals in quantum field theory are all variations and generalizations of Gaussian integrals to the complex plane and to multiple dimensions. Other integrals can be approximated by versions of the Gaussian integral. Fourier integrals are also considered | https://huggingface.co/datasets/fmars/wiki_stem |
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified.
Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory | https://huggingface.co/datasets/fmars/wiki_stem |
In differential geometry, a field in mathematics, Darboux's theorem is a theorem providing a normal form for special classes of differential 1-forms, partially generalizing the Frobenius integration theorem. It is named after Jean Gaston Darboux who established it as the solution of the Pfaff problem. It is a foundational result in several fields, the chief among them being symplectic geometry | https://huggingface.co/datasets/fmars/wiki_stem |
In the theory of Lie groups, the exponential map is a map from the Lie algebra g of a Lie group G into G. In case G is a matrix Lie group, the exponential map reduces to the matrix exponential. The exponential map, denoted exp:g → G, is analytic and has as such a derivative d/dtexp(X(t)):Tg → TG, where X(t) is a C1 path in the Lie algebra, and a closely related differential dexp:Tg → TG | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are differentiable.
Definition
Given two manifolds
M
{\displaystyle M}
and
N
{\displaystyle N}
, a differentiable map
f
:
M
→
N
{\displaystyle f\colon M\rightarrow N}
is called a diffeomorphism if it is a bijection and its inverse
f
−
1
:
N
→
M
{\displaystyle f^{-1}\colon N\rightarrow M}
is differentiable as well | https://huggingface.co/datasets/fmars/wiki_stem |
In physics and mathematics, in the area of dynamical systems, a double pendulum also known as a chaos pendulum is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. The motion of a double pendulum is governed by a set of coupled ordinary differential equations and is chaotic.
Analysis and interpretation
Several variants of the double pendulum may be considered; the two limbs may be of equal or unequal lengths and masses, they may be simple pendulums or compound pendulums (also called complex pendulums) and the motion may be in three dimensions or restricted to the vertical plane | https://huggingface.co/datasets/fmars/wiki_stem |
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a constant factor when that linear transformation is applied to it. The corresponding eigenvalue, often represented by
λ
{\displaystyle \lambda }
, is the multiplying factor.
Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon | https://huggingface.co/datasets/fmars/wiki_stem |
In differential geometry and mathematical physics, an Einstein manifold is a Riemannian or pseudo-Riemannian differentiable manifold whose Ricci tensor is proportional to the metric. They are named after Albert Einstein because this condition is equivalent to saying that the metric is a solution of the vacuum Einstein field equations (with cosmological constant), although both the dimension and the signature of the metric can be arbitrary, thus not being restricted to Lorentzian manifolds (including the four-dimensional Lorentzian manifolds usually studied in general relativity). Einstein manifolds in four Euclidean dimensions are studied as gravitational instantons | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, especially the usage of linear algebra in mathematical physics, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving brevity. As part of mathematics it is a notational subset of Ricci calculus; however, it is often used in physics applications that do not distinguish between tangent and cotangent spaces. It was introduced to physics by Albert Einstein in 1916 | https://huggingface.co/datasets/fmars/wiki_stem |
In physics and mathematics, in the area of dynamical systems, an elastic pendulum (also called spring pendulum or swinging spring) is a physical system where a piece of mass is connected to a spring so that the resulting motion contains elements of both a simple pendulum and a one-dimensional spring-mass system. The system exhibits chaotic behaviour and is sensitive to initial conditions. The motion of an elastic pendulum is governed by a set of coupled ordinary differential equations | https://huggingface.co/datasets/fmars/wiki_stem |
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
where
is the speed of light (i | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics and physics, an equipotential or isopotential refers to a region in space where every point is at the same potential. This usually refers to a scalar potential (in that case it is a level set of the potential), although it can also be applied to vector potentials. An equipotential of a scalar potential function in n-dimensional space is typically an (n − 1)-dimensional space | https://huggingface.co/datasets/fmars/wiki_stem |
Within mathematics, an N×N Euclidean random matrix  is defined with the help of an arbitrary deterministic function f(r, r′) and of N points {ri} randomly distributed in a region V of d-dimensional Euclidean space. The element Aij of the matrix is equal to f(ri, rj): Aij = f(ri, rj).
History
Euclidean random matrices were first introduced in 1999 | https://huggingface.co/datasets/fmars/wiki_stem |
In physics, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. For example, on a weather map, the surface temperature is described by assigning a number to each point on the map; the temperature can be considered at a certain point in time or over some interval of time, to study the dynamics of temperature change. A surface wind map, assigning an arrow to each point on a map that describes the wind speed and direction at that point, is an example of a vector field, i | https://huggingface.co/datasets/fmars/wiki_stem |
In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, as functions of time and space. Since the field equation is a partial differential equation, there are families of solutions which represent a variety of physical possibilities | https://huggingface.co/datasets/fmars/wiki_stem |
Five Equations That Changed the World: The Power and Poetry of Mathematics is a book by Michael Guillen, published in 1995.
It is divided into five chapters that talk about five different equations in physics and the people who have developed them.
The scientists and their equations are:
Isaac Newton
F
=
G
M
m
/
r
2
{\displaystyle F=GMm/r^{2}}
(Universal Law of Gravity)
Daniel Bernoulli (Law of Hydrodynamic Pressure)
Michael Faraday (Law of Electromagnetic Induction)
Rudolf Clausius (Second Law of Thermodynamics)
Albert Einstein (Theory of Special Relativity)The book is a light study in science and history, portraying the preludes to and times and settings of discoveries that have been the basis of further development, including space travel, flight and nuclear power | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. Floer homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. Andreas Floer introduced the first version of Floer homology, now called Lagrangian Floer homology, in his proof of the Arnold conjecture in symplectic geometry | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer.
The subject of Fourier analysis encompasses a vast spectrum of mathematics | https://huggingface.co/datasets/fmars/wiki_stem |
In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, Fredholm theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation. In a broader sense, the abstract structure of Fredholm's theory is given in terms of the spectral theory of Fredholm operators and Fredholm kernels on Hilbert space | https://huggingface.co/datasets/fmars/wiki_stem |
Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions. Functional integrals arise in probability, in the study of partial differential equations, and in the path integral approach to the quantum mechanics of particles and fields.
In an ordinary integral (in the sense of Lebesgue integration) there is a function to be integrated (the integrand) and a region of space over which to integrate the function (the domain of integration) | https://huggingface.co/datasets/fmars/wiki_stem |
In physics, a gauge theory is a field theory in which the Lagrangian is invariant under local transformations according to certain smooth families of operations (Lie groups).
The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, and especially differential geometry and mathematical physics, gauge theory is the general study of connections on vector bundles, principal bundles, and fibre bundles. Gauge theory in mathematics should not be confused with the closely related concept of a gauge theory in physics, which is a field theory which admits gauge symmetry. In mathematics theory means a mathematical theory, encapsulating the general study of a collection of concepts or phenomena, whereas in the physical sense a gauge theory is a mathematical model of some natural phenomenon | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematical physics higher gauge theory is the general study of counterparts of gauge theory that involve higher-degree differential forms instead of the traditional connection forms of gauge theories.
Frameworks for higher gauge theory
There are several distinct frameworks within which higher gauge theories have been developed. Alvarez et al | https://huggingface.co/datasets/fmars/wiki_stem |
The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics.
They span the Lie algebra of the SU(3) group in the defining representation.
Matrices
Properties
These matrices are traceless, Hermitian, and obey the extra trace orthonormality relation (so they can generate unitary matrix group elements of SU(3) through exponentiation) | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics and physics, in particular quantum information, the term generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices. Here, a few classes of such matrices are summarized.
Multi-qubit Pauli matrices (Hermitian)
This method of generalizing the Pauli matrices refers to a generalization from a single 2-level system (qubit) to multiple such systems | https://huggingface.co/datasets/fmars/wiki_stem |
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