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Representation Theory Of Algebraic Groups
Representation may refer to: Law and politics *Representation (politics), political activities undertaken by elected representatives, as well as other theories ** Representative democracy, type of democracy in which elected officials represent a group of people * Representation, in contract law a pre-contractual statement that may (if untrue) result in liability for misrepresentation * Labor representation, or worker representation, the work of a union representative who represents and defends the interests of fellow labor union members * Legal representation, provided by a barrister, lawyer, or other advocate * Lobbying or interest representation, attempts to influence the actions, policies, or decisions of officials * "No taxation without representation", a 1700s slogan that summarized one of the American colonists' 27 colonial grievances in the Thirteen Colonies, which was one of the major causes of the American Revolution * Permanent representation, a type of diplomatic mission ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation (politics)
Political representation is the activity of making citizens "present" in public policy-making processes when political actors act in the best interest of citizens. This definition of political representation is consistent with a wide variety of views on what representing implies and what the duties of representatives are. For example, representing may imply acting on the expressed wishes of citizens, but it may alternatively imply acting according to what the representatives themselves judge is in the best interests of citizens. And representatives may be viewed as individuals who have been authorized to act on the behalf of others, or may alternatively be viewed as those who will be held to account by those they are representing. Political representation can happen along different units such as social groups and area, and there are different types of representation such as substantive representation and descriptive representation. Views of political representation Under the ''acc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation Theory (linguistics)
Representation theory (RT) is a theoretical linguistic framework in the generative Generative may refer to: * Generative actor, a person who instigates social change * Generative art, art that has been created using an autonomous system that is frequently, but not necessarily, implemented using a computer * Generative music, mus ... tradition, created and developed by Edwin S. Williams – chiefly in an eponymous monograph of 2003. Williams compares it with other frameworks such as Noam Chomsky's minimalist program, and argues that his proposal has significant descriptive and conceptual advantages over them. The substance of the proposal is that linguistic derivation is the result of mappings and mismappings between an open set of 'representations', which in one dimension correspond to increasingly larger Locality (linguistics), locality domains and in the other pair 'Syntax, syntactic' (sentential and sub-sentential) and 'Semantics, semantic' (as well as Pragmatics, pragmatic) le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Visualization
Data and information visualization (data viz or info viz) is an interdisciplinary field that deals with the graphic representation of data and information. It is a particularly efficient way of communicating when the data or information is numerous as for example a time series. It is also the study of visual representations of abstract data to reinforce human cognition. The abstract data include both numerical and non-numerical data, such as text and geographic information. It is related to infographics and scientific visualization. One distinction is that it's information visualization when the spatial representation (e.g., the page layout of a graphic design) is chosen, whereas it's scientific visualization when the spatial representation is given. From an academic point of view, this representation can be considered as a mapping between the original data (usually numerical) and graphic elements (for example, lines or points in a chart). The mapping determines how the attri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representative Sample
In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population in question. Sampling has lower costs and faster data collection than measuring the entire population and can provide insights in cases where it is infeasible to measure an entire population. Each observation measures one or more properties (such as weight, location, colour or mass) of independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design, particularly in stratified sampling. Results from probability theory and statistical theory are employed to guide the practice. In business and medical research, sampling is widely used for gathering information about a population. Acceptance sampling is used to determine if ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Representation
Social representations are a system of values, ideas, metaphors, beliefs, and practices that serve to establish social order, orient participants and enable communication among the members of groups and communities. Social representation theory is a body of theory within social psychology and sociological social psychology. It has parallels in sociological theorizing such as social constructionism and symbolic interactionism, and is similar in some ways to mass consensus and discursive psychology. Origin and definition The term ''social representation'' was originally coined by Serge Moscovici in 1961,Moscovici, S. (1961). ''La psychanalyse, son image et son public''. Paris: Presses Universitaires de France. in his study on the reception and circulation of psychoanalysis in France. It is understood as the collective elaboration "of a social object by the community for the purpose of behaving and communicating". They are further referred to as "system of values, ideas and practices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation (chemistry)
The structural formula of a chemical compound is a graphic representation of the molecular structure (determined by structural chemistry methods), showing how the atoms are possibly arranged in the real three-dimensional space. The chemical bonding within the molecule is also shown, either explicitly or implicitly. Unlike other chemical formula types, which have a limited number of symbols and are capable of only limited descriptive power, structural formulas provide a more complete geometric representation of the molecular structure. For example, many chemical compounds exist in different isomeric forms, which have different enantiomeric structures but the same molecular formula. There are multiple types of ways to draw these structural formulas such as: Lewis Structures, condensed formulas, skeletal formulas, Newman projections, Cyclohexane conformations, Haworth projections, and Fischer projections. Several systematic chemical naming formats, as in chemical databases, are used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation Of A Lie Group
In mathematics and theoretical physics, a representation of a Lie group is a linear action of a Lie group on a vector space. Equivalently, a representation is a smooth homomorphism of the group into the group of invertible operators on the vector space. Representations play an important role in the study of continuous symmetry. A great deal is known about such representations, a basic tool in their study being the use of the corresponding 'infinitesimal' representations of Lie algebras. Finite-dimensional representations Representations A complex representation of a group is an action by a group on a finite-dimensional vector space over the field \mathbb C. A representation of the Lie group ''G'', acting on an ''n''-dimensional vector space ''V'' over \mathbb C is then a smooth group homomorphism :\Pi:G\rightarrow\operatorname(V), where \operatorname(V) is the general linear group of all invertible linear transformations of V under their composition. Since all ''n''-dimension ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiple Representations (mathematics Education)
In mathematics education, a representation is a way of encoding an idea or a relationship, and can be both internal (e.g., mental construct) and external (e.g., graph). Thus multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate different mathematical features of the same object or operation, as well as connections between different properties. Multiple representations include graphs and diagrams, tables and grids, formulas, symbols, words, gestures, software code, videos, concrete models, physical and virtual manipulatives, pictures, and sounds. Representations are thinking tools for doing mathematics. Higher-order thinking The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills.S. Ainsworth, P. Bibby, and D. Wood, "Information technology and multiple representations: New opportunities – new problems, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Algebra Representation
In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vector space V together with a collection of operators on V satisfying some fixed set of commutation relations, such as the relations satisfied by the angular momentum operators. The notion is closely related to that of a representation of a Lie group. Roughly speaking, the representations of Lie algebras are the differentiated form of representations of Lie groups, while the representations of the universal cover of a Lie group are the integrated form of the representations of its Lie algebra. In the study of representations of a Lie algebra, a particular ring, called the universal enveloping algebra, associated with the Lie algebra plays an important role. The universa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules. Representations of groups are important because they allow many group-theoretic problems to be reduced to problems in linear algebra, which is well understood. They are also important in physics because, for example, they describe how the symmetry group of a physical system affects the solutions of equations describing that system. The term ''representation of a group'' is also used in a more general sense to mean any "description" of a group as a group of transformations of some mathematical o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation (mathematics)
In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures. Roughly speaking, a collection ''Y'' of mathematical objects may be said to ''represent'' another collection ''X'' of objects, provided that the properties and relationships existing among the representing objects ''yi'' conform, in some consistent way, to those existing among the corresponding represented objects ''xi''. More specifically, given a set ''Π'' of properties and relations, a ''Π''-representation of some structure ''X'' is a structure ''Y'' that is the image of ''X'' under a homomorphism that preserves ''Π''. The label ''representation'' is sometimes also applied to the homomorphism itself (such as group homomorphism in group theory). Representation theory Perhaps the most well-developed example of this general notion is the subfield of abstract algebra called representation theory, which studies the representing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knowledge Representation
Knowledge representation and reasoning (KRR, KR&R, KR²) is the field of artificial intelligence (AI) dedicated to representing information about the world in a form that a computer system can use to solve complex tasks such as diagnosing a medical condition or having a dialog in a natural language. Knowledge representation incorporates findings from psychology about how humans solve problems and represent knowledge in order to design formalisms that will make complex systems easier to design and build. Knowledge representation and reasoning also incorporates findings from logic to automate various kinds of ''reasoning'', such as the application of rules or the relations of sets and subsets. Examples of knowledge representation formalisms include semantic nets, systems architecture, frames, rules, and ontologies. Examples of automated reasoning engines include inference engines, theorem provers, and classifiers. History The earliest work in computerized knowledge represe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
