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Sample records for algebraic specification language

  1. CASL, the Common Algebraic Specification Language

    DEFF Research Database (Denmark)

    Mossakowski, Till; Haxthausen, Anne Elisabeth; Sannella, Donald

    2008-01-01

    CASL is an expressive specification language that has been designed to supersede many existing algebraic specification languages and provide a standard. CASL consists of several layers, including basic (unstructured) specifications, structured specifications and architectural specifications...

  2. Banana Algebra: Compositional syntactic language extension

    DEFF Research Database (Denmark)

    Andersen, Jacob; Brabrand, Claus; Christiansen, David Raymond

    2013-01-01

    We propose an algebra of languages and transformations as a means of compositional syntactic language extension. The algebra provides a layer of high-level abstractions built on top of languages (captured by context-free grammars) and transformations (captured by constructive catamorphisms...... algebra as presented in the paper is implemented as the Banana Algebra Tool which may be used to syntactically extend languages in an incremental and modular fashion via algebraic composition of previously defined languages and transformations. We demonstrate and evaluate the tool via several kinds...

  3. Syntactic Language Extension via an Algebra of Languages and Transformations

    DEFF Research Database (Denmark)

    Andersen, Jacob; Brabrand, Claus

    2010-01-01

    We propose an algebra of languages and transformations as a means for extending languages syntactically. The algebra provides a layer of high-level abstractions built on top of languages (captured by context-free grammars) and transformations (captured by constructive catamorphisms). The algebra...... is self-contained in that any term of the algebra specifying a transformation can be reduced to a catamorphism, before the transformation is run. Thus, the algebra comes “for free” without sacrificing the strong safety and efficiency properties of constructive catamorphisms. The entire algebra...... as presented in the paper is implemented as the Banana Algebra Tool which may be used to syntactically extend languages in an incremental and modular fashion via algebraic composition of previously defined languages and transformations. We demonstrate and evaluate the tool via several kinds of extensions....

  4. Thought beyond language: neural dissociation of algebra and natural language.

    Science.gov (United States)

    Monti, Martin M; Parsons, Lawrence M; Osherson, Daniel N

    2012-08-01

    A central question in cognitive science is whether natural language provides combinatorial operations that are essential to diverse domains of thought. In the study reported here, we addressed this issue by examining the role of linguistic mechanisms in forging the hierarchical structures of algebra. In a 3-T functional MRI experiment, we showed that processing of the syntax-like operations of algebra does not rely on the neural mechanisms of natural language. Our findings indicate that processing the syntax of language elicits the known substrate of linguistic competence, whereas algebraic operations recruit bilateral parietal brain regions previously implicated in the representation of magnitude. This double dissociation argues against the view that language provides the structure of thought across all cognitive domains.

  5. Parallel object-oriented specification language

    NARCIS (Netherlands)

    Florescu, O.; Voeten, J.P.M.; Theelen, B.D.; Geilen, M.C.W.; Corporaal, H.; Burns, Alan

    2008-01-01

    The Parallel Object-Oriented Specification Language (POOSL) is an expressive modelling language for hardware/software systems [10]. It was originally defined in [7] as an object-oriented extension of process algebra CCS [6], supporting (conditional) synchronous message passing between

  6. An Algebraic Specification of the Semantic Web

    OpenAIRE

    Ksystra, Katerina; Triantafyllou, Nikolaos; Stefaneas, Petros; Frangos, Panayiotis

    2011-01-01

    We present a formal specification of the Semantic Web, as an extension of the World Wide Web using the well known algebraic specification language CafeOBJ. Our approach allows the description of the key elements of the Semantic Web technologies, in order to give a better understanding of the system, without getting involved with their implementation details that might not yet be standardized. This specification is part of our work in progress concerning the modeling the Social Semantic Web.

  7. Order-sorted Algebraic Specifications with Higher-order Functions

    DEFF Research Database (Denmark)

    Haxthausen, Anne Elisabeth

    1995-01-01

    This paper gives a proposal for how order-sorted algebraic specification languages can be extended with higher-order functions. The approach taken is a generalisation to the order-sorted case of an approach given by Mller, Tarlecki and Wirsing for the many-sorted case. The main idea in the proposal...

  8. A Relational Algebra Query Language for Programming Relational Databases

    Science.gov (United States)

    McMaster, Kirby; Sambasivam, Samuel; Anderson, Nicole

    2011-01-01

    In this paper, we describe a Relational Algebra Query Language (RAQL) and Relational Algebra Query (RAQ) software product we have developed that allows database instructors to teach relational algebra through programming. Instead of defining query operations using mathematical notation (the approach commonly taken in database textbooks), students…

  9. Language Analysis and Generation in Algebra Tutorial Dialogues for Language-Based Intelligent Tutoring Systems

    National Research Council Canada - National Science Library

    Kim, Jung

    2004-01-01

    The North Carolina A&T State University algebra tutoring dialogue project collects and analyzes algebra tutoring dialogues with the aim of describing tutoring strategies and language with enough rigor that they may...

  10. LCM and MCM: Specification of a control system using dynamic logic and process algebra

    NARCIS (Netherlands)

    Wieringa, Roelf J.; Lewerentz, Claus; Lindner, Thomas

    1994-01-01

    LCM 3.0 is a specification language based on dynamic logic and process algebra, and can be used to specify systems of dynamic objects that communicate synchronously. LCM 3.0 was developed for the specification of object-oriented information systems, but contains sufficient facilities for the

  11. Prior knowledge of deaf students fluent in brazilian sign languages regarding the algebraic language in high school

    Directory of Open Access Journals (Sweden)

    Silvia Teresinha Frizzarini

    2014-06-01

    Full Text Available There are few researches with deeper reflections on the study of algebra with deaf students. In order to validate and disseminate educational activities in that context, this article aims at highlighting the deaf students’ prior knowledge, fluent in Brazilian Sign Language, referring to the algebraic language used in high school. The theoretical framework used was Duval’s theory, with analysis of the changes, by treatment and conversion, of different registers of semiotic representation, in particular inequalities. The methodology used was the application of a diagnostic evaluation performed with deaf students, all fluent in Brazilian Sign Language, in a special school located in the north of Paraná State. We emphasize the need to work in both directions of conversion, in different languages, especially when the starting record is the graphic. Therefore, the conclusion reached was that one should not separate the algebraic representation from other records, due to the need of sign language perform not only the communication function, but also the functions of objectification and treatment, fundamental in cognitive development.

  12. Linear algebra meets Lie algebra: the Kostant-Wallach theory

    OpenAIRE

    Shomron, Noam; Parlett, Beresford N.

    2008-01-01

    In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.

  13. CASL The Common Algebraic Specification Language Semantics

    DEFF Research Database (Denmark)

    Haxthausen, Anne

    1998-01-01

    This is version 1.0 of the CASL Language Summary, annotated by the CoFI Semantics Task Group with the semantics of constructs. This is the first complete but possibly imperfect version of the semantics. It was compiled prior to the CoFI workshop at Cachan in November 1998.......This is version 1.0 of the CASL Language Summary, annotated by the CoFI Semantics Task Group with the semantics of constructs. This is the first complete but possibly imperfect version of the semantics. It was compiled prior to the CoFI workshop at Cachan in November 1998....

  14. An introduction to algebraic geometry and algebraic groups

    CERN Document Server

    Geck, Meinolf

    2003-01-01

    An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type.The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups

  15. An embedded domain specific language for general purpose vectorization

    CERN Document Server

    Karpinski, Przemyslaw

    2017-01-01

    Portable SIMD code generation is an open problem in modern High Performance Computing systems. Performance portability can already be achieved, however it might fail when user-framework interaction is required. Of all portable vectorization techniques, explicit vectorization, using wrapper-class libraries, is proven to achieve the fastest performance, however it does not exploit optimization opportunities outside the simplest algebraic primitives. A more advanced language is therefore required, but the design of a new independent language is not feasible due to its high costs. This work describes an Embedded Domain Specific Language for solving generalized 1-D vectorization problems. The language is implemented using C++ as a host language and published as a lightweight library. By decoupling expression creation from evaluation a wider range of problems can be solved, without sacrificing runtime efficiency. In this paper we discuss design patterns necessary, but not limited, to efficient EDSL implementatio...

  16. Algebraic Specifications, Higher-order Types and Set-theoretic Models

    DEFF Research Database (Denmark)

    Kirchner, Hélène; Mosses, Peter David

    2001-01-01

    , and power-sets. This paper presents a simple framework for algebraic specifications with higher-order types and set-theoretic models. It may be regarded as the basis for a Horn-clause approximation to the Z framework, and has the advantage of being amenable to prototyping and automated reasoning. Standard......In most algebraic  specification frameworks, the type system is restricted to sorts, subsorts, and first-order function types. This is in marked contrast to the so-called model-oriented frameworks, which provide higer-order types, interpreted set-theoretically as Cartesian products, function spaces...... set-theoretic models are considered, and conditions are given for the existence of initial reduct's of such models. Algebraic specifications for various set-theoretic concepts are considered....

  17. Cylindric-like algebras and algebraic logic

    CERN Document Server

    Ferenczi, Miklós; Németi, István

    2013-01-01

    Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways:  as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.

  18. Realization Of Algebraic Processor For XML Documents Processing

    International Nuclear Information System (INIS)

    Georgiev, Bozhidar; Georgieva, Adriana

    2010-01-01

    In this paper, are presented some possibilities concerning the implementation of an algebraic method for XML hierarchical data processing which makes faster the XML search mechanism. Here is offered a different point of view for creation of advanced algebraic processor (with all necessary software tools and programming modules respectively). Therefore, this nontraditional approach for fast XML navigation with the presented algebraic processor may help to build an easier user-friendly interface provided XML transformations, which can avoid the difficulties in the complicated language constructions of XSL, XSLT and XPath. This approach allows comparatively simple search of XML hierarchical data by means of the following types of functions: specification functions and so named build-in functions. The choice of programming language Java may appear strange at first, but it isn't when you consider that the applications can run on different kinds of computers. The specific search mechanism based on the linear algebra theory is faster in comparison with MSXML parsers (on the basis of the developed examples with about 30%). Actually, there exists the possibility for creating new software tools based on the linear algebra theory, which cover the whole navigation and search techniques characterizing XSLT/XPath. The proposed method is able to replace more complicated operations in other SOA components.

  19. CASL - The CoFI Algebraic Specification Language - Semantics

    DEFF Research Database (Denmark)

    Haxthausen, Anne

    1999-01-01

    This is version 1.0 of the CASL Language Summary, annotated by the CoFI Semantics Task Group with the semantics of constructs. This is the second complete but possibly imperfect version of the semantics. It was compiled prior to the CoFI workshop in Amsterdam in March 1999.......This is version 1.0 of the CASL Language Summary, annotated by the CoFI Semantics Task Group with the semantics of constructs. This is the second complete but possibly imperfect version of the semantics. It was compiled prior to the CoFI workshop in Amsterdam in March 1999....

  20. On the PR-algebras

    International Nuclear Information System (INIS)

    Lebedenko, V.M.

    1978-01-01

    The PR-algebras, i.e. the Lie algebras with commutation relations of [Hsub(i),Hsub(j)]=rsub(ij)Hsub(i)(i< j) type are investigated. On the basis of former results a criterion for the membership of 2-solvable Lie algebras to the PR-algebra class is given. The conditions imposed by the criterion are formulated in the linear algebra language

  1. From CML to its Process Algebra

    DEFF Research Database (Denmark)

    Nielson, Flemming; Nielson, Hanne Riis

    1996-01-01

    and behaviours may lose prefixes as well as decrease. As the syntax of behaviours is rather similar to that of a process algebra, our main result may therefore be viewed as regarding the semantics of a process algebra as an abstraction of the semantics of an underlying programming language. This establishes...... a new kind of connection between "realistic" concurrent programming languages and "theoretical" process algebras...

  2. Quantization, Frobenius and Bi algebras from the Categorical Framework of Quantum Mechanics to Natural Language Semantics

    Science.gov (United States)

    Sadrzadeh, Mehrnoosh

    2017-07-01

    Compact Closed categories and Frobenius and Bi algebras have been applied to model and reason about Quantum protocols. The same constructions have also been applied to reason about natural language semantics under the name: ``categorical distributional compositional'' semantics, or in short, the ``DisCoCat'' model. This model combines the statistical vector models of word meaning with the compositional models of grammatical structure. It has been applied to natural language tasks such as disambiguation, paraphrasing and entailment of phrases and sentences. The passage from the grammatical structure to vectors is provided by a functor, similar to the Quantization functor of Quantum Field Theory. The original DisCoCat model only used compact closed categories. Later, Frobenius algebras were added to it to model long distance dependancies such as relative pronouns. Recently, bialgebras have been added to the pack to reason about quantifiers. This paper reviews these constructions and their application to natural language semantics. We go over the theory and present some of the core experimental results.

  3. A New Formalism for Relational Algebra

    DEFF Research Database (Denmark)

    Schwartzbach, Michael Ignatieff; Larsen, Kim Skak; Schmidt, Erik Meineche

    1992-01-01

    We present a new formalism for relational algebra, the FC language, which is based on a novel factorization of relations. The acronym stands for factorize and combine. A pure version of this language is equivalent to relational algebra in the sense that semantics preserving translations exist...

  4. Relational Algebra and SQL: Better Together

    Science.gov (United States)

    McMaster, Kirby; Sambasivam, Samuel; Hadfield, Steven; Wolthuis, Stuart

    2013-01-01

    In this paper, we describe how database instructors can teach Relational Algebra and Structured Query Language together through programming. Students write query programs consisting of sequences of Relational Algebra operations vs. Structured Query Language SELECT statements. The query programs can then be run interactively, allowing students to…

  5. Modular specifications in process algebra

    NARCIS (Netherlands)

    R.J. van Glabbeek (Rob); F.W. Vaandrager (Frits)

    1987-01-01

    textabstractIn recent years a wide variety of process algebras has been proposed in the literature. Often these process algebras are closely related: they can be viewed as homomorphic images, submodels or restrictions of each other. The aim of this paper is to show how the semantical reality,

  6. Algebras of holomorphic functions and control theory

    CERN Document Server

    Sasane, Amol

    2009-01-01

    This accessible, undergraduate-level text illustrates the role of algebras of holomorphic functions in the solution of an important engineering problem: the stabilization of a linear control system. Its concise and self-contained treatment avoids the use of higher mathematics and forms a bridge to more advanced treatments. The treatment consists of two components: the algebraic framework, which serves as the abstract language for posing and solving the problem of stabilization; and the analysis component, which examines properties of specific rings of holomorphic functions. Elementary, self-co

  7. Quantization, Frobenius and Bi Algebras from the Categorical Framework of Quantum Mechanics to Natural Language Semantics

    Directory of Open Access Journals (Sweden)

    Mehrnoosh Sadrzadeh

    2017-07-01

    Full Text Available Compact Closed categories and Frobenius and Bi algebras have been applied to model and reason about Quantum protocols. The same constructions have also been applied to reason about natural language semantics under the name: “categorical distributional compositional” semantics, or in short, the “DisCoCat” model. This model combines the statistical vector models of word meaning with the compositional models of grammatical structure. It has been applied to natural language tasks such as disambiguation, paraphrasing and entailment of phrases and sentences. The passage from the grammatical structure to vectors is provided by a functor, similar to the Quantization functor of Quantum Field Theory. The original DisCoCat model only used compact closed categories. Later, Frobenius algebras were added to it to model long distance dependancies such as relative pronouns. Recently, bialgebras have been added to the pack to reason about quantifiers. This paper reviews these constructions and their application to natural language semantics. We go over the theory and present some of the core experimental results.

  8. Feature-Oriented Programming with Object Algebras

    NARCIS (Netherlands)

    B.C.d.S. Oliveira (Bruno); T. van der Storm (Tijs); A. Loh; W.R. Cook

    2013-01-01

    htmlabstractObject algebras are a new programming technique that enables a simple solution to basic extensibility and modularity issues in programming languages. While object algebras excel at defining modular features, the composition mechanisms for object algebras (and features) are still

  9. An Algebraic Programming Style for Numerical Software and Its Optimization

    Directory of Open Access Journals (Sweden)

    T.B. Dinesh

    2000-01-01

    Full Text Available The abstract mathematical theory of partial differential equations (PDEs is formulated in terms of manifolds, scalar fields, tensors, and the like, but these algebraic structures are hardly recognizable in actual PDE solvers. The general aim of the Sophus programming style is to bridge the gap between theory and practice in the domain of PDE solvers. Its main ingredients are a library of abstract datatypes corresponding to the algebraic structures used in the mathematical theory and an algebraic expression style similar to the expression style used in the mathematical theory. Because of its emphasis on abstract datatypes, Sophus is most naturally combined with object-oriented languages or other languages supporting abstract datatypes. The resulting source code patterns are beyond the scope of current compiler optimizations, but are sufficiently specific for a dedicated source-to-source optimizer. The limited, domain-specific, character of Sophus is the key to success here. This kind of optimization has been tested on computationally intensive Sophus style code with promising results. The general approach may be useful for other styles and in other application domains as well.

  10. A Simple and Practical Linear Algebra Library Interface with Static Size Checking

    Directory of Open Access Journals (Sweden)

    Akinori Abe

    2015-12-01

    Full Text Available Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime errors. While advanced type systems—specifically, dependent types on natural numbers—can ensure consistency among the sizes of collections such as lists and arrays, such type systems generally require non-trivial changes to existing languages and application programs, or tricky type-level programming. We have developed a linear algebra library interface that verifies the consistency (with respect to dimensions of matrix operations by means of generative phantom types, implemented via fairly standard ML types and module system. To evaluate its usability, we ported to it a practical machine learning library from a traditional linear algebra library. We found that most of the changes required for the porting could be made mechanically, and changes that needed human thought are minor.

  11. A Generalised Approach to Petri Nets and Algebraic Specifications

    International Nuclear Information System (INIS)

    Sivertsen, Terje

    1998-02-01

    The present report represents a continuation of the work on Petri nets and algebraic specifications. The reported research has focused on generalising the approach introduced in HWR-454, with the aim of facilitating the translation of a wider class of Petri nets into algebraic specification. This includes autonomous Petri nets with increased descriptive power, as well as non-autonomous Petri nets allowing the modelling of systems (1) involving extensive data processing; (2) with transitions synchronized on external events; (3) whose evolutions are time dependent. The generalised approach has the important property of being modular in the sense that the translated specifications can be gradually extended to include data processing, synchronization, and timing. The report also discusses the relative merits of state-based and transition-based specifications, and includes a non-trivial case study involving automated proofs of a large number of interrelated theorems. The examples in the report illustrate the use of the new HRP Prover. Of particular importance in this context is the automatic transformation between state-based and transitionbased specifications. It is expected that the approach introduced in HWR-454 and generalised in the present report will prove useful in future work on combination of wide variety of specification techniques

  12. Ada Linear-Algebra Program

    Science.gov (United States)

    Klumpp, A. R.; Lawson, C. L.

    1988-01-01

    Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

  13. An Improved Algorithm for Generating Database Transactions from Relational Algebra Specifications

    Directory of Open Access Journals (Sweden)

    Daniel J. Dougherty

    2010-03-01

    Full Text Available Alloy is a lightweight modeling formalism based on relational algebra. In prior work with Fisler, Giannakopoulos, Krishnamurthi, and Yoo, we have presented a tool, Alchemy, that compiles Alloy specifications into implementations that execute against persistent databases. The foundation of Alchemy is an algorithm for rewriting relational algebra formulas into code for database transactions. In this paper we report on recent progress in improving the robustness and efficiency of this transformation.

  14. Genetic algorithms in teaching artificial intelligence (automated generation of specific algebras)

    Science.gov (United States)

    Habiballa, Hashim; Jendryscik, Radek

    2017-11-01

    The problem of teaching essential Artificial Intelligence (AI) methods is an important task for an educator in the branch of soft-computing. The key focus is often given to proper understanding of the principle of AI methods in two essential points - why we use soft-computing methods at all and how we apply these methods to generate reasonable results in sensible time. We present one interesting problem solved in the non-educational research concerning automated generation of specific algebras in the huge search space. We emphasize above mentioned points as an educational case study of an interesting problem in automated generation of specific algebras.

  15. [Multilingualism and specific language impairment].

    Science.gov (United States)

    Arkkila, Eva; Smolander, Sini; Laasonen, Marja

    2013-01-01

    Specific language impairment is one of the most common developmental disturbances in childhood. With the increase of the foreign language population group an increasing number of children assimilating several languages and causing concern in language development attend clinical examinations. Knowledge of factors underlying the specific language impairment and the specific impairment in general, special features of language development of those learning several languages, as well as the assessment and support of the linguistic skills of a multilingual child is essential. The risk of long-term problems and marginalization is high for children having specific language impairment.

  16. Chiral algebras of class S

    CERN Document Server

    Beem, Christopher; Rastelli, Leonardo; van Rees, Balt C.

    2015-01-01

    Four-dimensional N=2 superconformal field theories have families of protected correlation functions that possess the structure of two-dimensional chiral algebras. In this paper, we explore the chiral algebras that arise in this manner in the context of theories of class S. The class S duality web implies nontrivial associativity properties for the corresponding chiral algebras, the structure of which is best summarized in the language of generalized topological quantum field theory. We make a number of conjectures regarding the chiral algebras associated to various strongly coupled fixed points.

  17. Matlab linear algebra

    CERN Document Server

    Lopez, Cesar

    2014-01-01

    MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Linear Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to

  18. Algebra Sets, Symbols, and the Language of Thought (Revised Edition)

    CERN Document Server

    Tabak, John

    2011-01-01

    Algebra, Revised Edition describes the history of both strands of algebraic thought. This updated resource describes some of the earliest progress in algebra as well as some of the mathematicians in Mesopotamia, Egypt, China, and Greece who contributed to this early period. It goes on to explore the many breakthroughs in algebraic techniques as well as how letters were used to represent numbers. New material has been added to the chapter on "modern" algebra, a type of mathematical research that continues to occupy the attention of many mathematicians today.

  19. A process algebra software engineering environment

    NARCIS (Netherlands)

    Diertens, B.

    2008-01-01

    In previous work we described how the process algebra based language PSF can be used in software engineering, using the ToolBus, a coordination architecture also based on process algebra, as implementation model. In this article we summarize that work and describe the software development process

  20. Q-systems as cluster algebras

    International Nuclear Information System (INIS)

    Kedem, Rinat

    2008-01-01

    Q-systems first appeared in the analysis of the Bethe equations for the XXX model and generalized Heisenberg spin chains (Kirillov and Reshetikhin 1987 Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Steklov. 160 211-21, 301). Such systems are known to exist for any simple Lie algebra and many other Kac-Moody algebras. We formulate the Q-system associated with any simple, simply-laced Lie algebras g in the language of cluster algebras (Fomin and Zelevinsky 2002 J. Am. Math. Soc. 15 497-529), and discuss the relation of the polynomiality property of the solutions of the Q-system in the initial variables, which follows from the representation-theoretical interpretation, to the Laurent phenomenon in cluster algebras (Fomin and Zelevinsky 2002 Adv. Appl. Math. 28 119-44)

  1. Method of computer algebraic calculation of the matrix elements in the second quantization language

    International Nuclear Information System (INIS)

    Gotoh, Masashi; Mori, Kazuhide; Itoh, Reikichi

    1995-01-01

    An automated method by the algebraic programming language REDUCE3 for specifying the matrix elements expressed in second quantization language is presented and then applied to the case of the matrix elements in the TDHF theory. This program works in a very straightforward way by commuting the electron creation and annihilation operator (a † and a) until these operators have completely vanished from the expression of the matrix element under the appropriate elimination conditions. An improved method using singlet generators of unitary transformations in the place of the electron creation and annihilation operators is also presented. This improvement reduces the time and memory required for the calculation. These methods will make programming in the field of quantum chemistry much easier. 11 refs., 1 tab

  2. ASYS: a computer algebra package for analysis of nonlinear algebraic equations systems

    International Nuclear Information System (INIS)

    Gerdt, V.P.; Khutornoj, N.V.

    1992-01-01

    A program package ASYS for analysis of nonlinear algebraic equations based on the Groebner basis technique is described. The package is written in REDUCE computer algebra language. It has special facilities to treat polynomial ideals of positive dimension, corresponding to algebraic systems with infinitely many solutions. Such systems can be transformed to an equivalent set of subsystems with reduced number of variables in completely automatic way. It often allows to construct the explicit form of a solution set in many problems of practical importance. Some examples and results of comparison with the standard Reduce package GROEBNER and special-purpose systems FELIX and A1PI are given. 21 refs.; 2 tabs

  3. Several complex variables and Banach algebras

    International Nuclear Information System (INIS)

    Allan, G.R.

    1976-01-01

    This paper aims to present certain applications of the theory of holomorphic functions of several complex variables to the study of commutative Banach algebras. The material falls into the following sections: (A) Introcution to Banach algebras (this will not presuppose any knowledge of the subject); (B) Groups of differential forms (mainly concerned with setting up a useful language); (C) Polynomially convex domains. (D) Holomorphic functional calculus for Banach algebras; (E) Some applications of the functional calculus. (author)

  4. Emphasizing Language and Visualization in Teaching Linear Algebra

    Science.gov (United States)

    Hannah, John; Stewart, Sepideh; Thomas, Mike

    2013-01-01

    Linear algebra with its rich theoretical nature is a first step towards advanced mathematical thinking for many undergraduate students. In this paper, we consider the teaching approach of an experienced mathematician as he attempts to engage his students with the key ideas embedded in a second-year course in linear algebra. We describe his…

  5. Domain-specific languages in perspective

    NARCIS (Netherlands)

    J. Heering (Jan); M. Mernik (Marjan)

    2007-01-01

    textabstractDomain-specific languages (DSLs) are languages tailored to a specific application domain. They offer substantial gains in expressiveness and ease of use compared with general-purpose languages in their domain of application. Although the use of DSLs is by no means new, it is receiving

  6. Algebraic computability and enumeration models recursion theory and descriptive complexity

    CERN Document Server

    Nourani, Cyrus F

    2016-01-01

    This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic type...

  7. Vertex algebras and mirror symmetry

    International Nuclear Information System (INIS)

    Borisov, L.A.

    2001-01-01

    Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly vertex algebras that correspond to holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in toric varieties. We establish the relation between these vertex algebras for mirror Calabi-Yau manifolds. This should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras. Our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra, as well as some basic results of the theory of vertex algebras. Ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties.This paper could also be of interest to physicists, because it contains explicit description of holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in terms of free bosons and fermions. (orig.)

  8. Polymorphism and Module-Reuse Mechanisms for Algebraic Petri Nets in CoopnTools

    OpenAIRE

    Buffo, Mathieu; Buchs, Didier; Donatelli, S.; Kleijn, J.

    1999-01-01

    This paper introduces CoopnTools, a tool set allowing the support of object-oriented specifications written by means of the language CO-OPN/2, based on synchronised algebraic Petri nets. In particular, this paper shows how concrete mechanisms dealing with polymorphism and module-reuse are implemented in CoopnTools.

  9. XAL: An algebra for XML query optimization

    NARCIS (Netherlands)

    Frasincar, F.; Houben, G.J.P.M.; Pau, C.D.; Zhou, Xiaofang

    2002-01-01

    This paper proposes XAL, an XML ALgebra. Its novelty is based on the simplicity of its data model and its well-defined logical operators, which makes it suitable for composability, optimizability, and semantics definition of a query language for XML data. At the heart of the algebra resides the

  10. Parsing with Regular Expressions & Extensions to Kleene Algebra

    DEFF Research Database (Denmark)

    Grathwohl, Niels Bjørn Bugge

    . In the second part of this thesis, we study two extensions to Kleene algebra. Chomsky algebra is an algebra with a structure similar to Kleene algebra, but with a generalized mu-operator for recursion instead of the Kleene star. We show that the axioms of idempotent semirings along with continuity of the mu......-operator completely axiomatize the equational theory of the context-free languages. KAT+B! is an extension to Kleene algebra with tests (KAT) that adds mutable state. We describe a test algebra B! for mutable tests and give a commutative coproduct between KATs. Combining the axioms of B! with those of KAT and some...

  11. Linear algebra

    CERN Document Server

    Edwards, Harold M

    1995-01-01

    In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject

  12. Learning abstract algebra with ISETL

    CERN Document Server

    Dubinsky, Ed

    1994-01-01

    Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics...

  13. Syntax and Meaning as Sensuous, Visual, Historical Forms of Algebraic Thinking

    Science.gov (United States)

    Radford, Luis; Puig, Luis

    2007-01-01

    Before the advent of symbolism, i.e. before the end of the 16th Century, algebraic calculations were made using natural language. Through a kind of metaphorical process, a few terms from everyday life (e.g. thing, root) acquired a technical mathematical status and constituted the specialized language of algebra. The introduction of letters and…

  14. Basic algebraic topology and its applications

    CERN Document Server

    Adhikari, Mahima Ranjan

    2016-01-01

    This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. T...

  15. L_∞ algebras and field theory

    International Nuclear Information System (INIS)

    Hohm, Olaf; Zwiebach, Barton

    2017-01-01

    We review and develop the general properties of L_∞ algebras focusing on the gauge structure of the associated field theories. Motivated by the L_∞ homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the L_∞ structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an L_∞ algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full L_∞ algebra for the interacting theory. The analysis suggests that L_∞ algebras provide a classification of perturbative gauge invariant classical field theories. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  16. Algebraic Systems and Pushdown Automata

    Science.gov (United States)

    Petre, Ion; Salomaa, Arto

    We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.

  17. Aberration studies and computer algebra

    International Nuclear Information System (INIS)

    Hawkes, P.W.

    1981-01-01

    The labour of calculating expressions for aberration coefficients is considerably lightened if a computer algebra language is used to perform the various substitutions and expansions involved. After a brief discussion of matrix representations of aberration coefficients, a particular language, which has shown itself to be well adapted to particle optics, is described and applied to the study of high frequency cavity lenses. (orig.)

  18. Clojure for domain-specific languages

    CERN Document Server

    Kelker, Ryan D

    2013-01-01

    An example-oriented approach to develop custom domain-specific languages.If you've already developed a few Clojure applications and wish to expand your knowledge on Clojure or domain-specific languages in general, then this book is for you. If you're an absolute Clojure beginner, then you may only find the detailed examples of the core Clojure components of value. If you've developed DSLs in other languages, this Lisp and Java-based book might surprise you with the power of Clojure.

  19. Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C Language

    OpenAIRE

    Blaha, Stephen

    2002-01-01

    We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.

  20. Regular algebra and finite machines

    CERN Document Server

    Conway, John Horton

    2012-01-01

    World-famous mathematician John H. Conway based this classic text on a 1966 course he taught at Cambridge University. Geared toward graduate students of mathematics, it will also prove a valuable guide to researchers and professional mathematicians.His topics cover Moore's theory of experiments, Kleene's theory of regular events and expressions, Kleene algebras, the differential calculus of events, factors and the factor matrix, and the theory of operators. Additional subjects include event classes and operator classes, some regulator algebras, context-free languages, communicative regular alg

  1. Abstract algebra

    CERN Document Server

    Garrett, Paul B

    2007-01-01

    Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal

  2. L{sub ∞} algebras and field theory

    Energy Technology Data Exchange (ETDEWEB)

    Hohm, Olaf [Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY (United States); Zwiebach, Barton [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA (United States)

    2017-03-15

    We review and develop the general properties of L{sub ∞} algebras focusing on the gauge structure of the associated field theories. Motivated by the L{sub ∞} homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the L{sub ∞} structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an L{sub ∞} algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full L{sub ∞} algebra for the interacting theory. The analysis suggests that L{sub ∞} algebras provide a classification of perturbative gauge invariant classical field theories. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  3. The language of mathematics: investigating the ways language counts for children's mathematical development.

    Science.gov (United States)

    Vukovic, Rose K; Lesaux, Nonie K

    2013-06-01

    This longitudinal study examined how language ability relates to mathematical development in a linguistically and ethnically diverse sample of children from 6 to 9 years of age. Study participants were 75 native English speakers and 92 language minority learners followed from first to fourth grades. Autoregression in a structural equation modeling (SEM) framework was used to evaluate the relation between children's language ability and gains in different domains of mathematical cognition (i.e., arithmetic, data analysis/probability, algebra, and geometry). The results showed that language ability predicts gains in data analysis/probability and geometry, but not in arithmetic or algebra, after controlling for visual-spatial working memory, reading ability, and sex. The effect of language on gains in mathematical cognition did not differ between language minority learners and native English speakers. These findings suggest that language influences how children make meaning of mathematics but is not involved in complex arithmetical procedures whether presented with Arabic symbols as in arithmetic or with abstract symbols as in algebraic reasoning. The findings further indicate that early language experiences are important for later mathematical development regardless of language background, denoting the need for intensive and targeted language opportunities for language minority and native English learners to develop mathematical concepts and representations. Copyright © 2013. Published by Elsevier Inc.

  4. Towards Domain-specific Flow-based Languages

    DEFF Research Database (Denmark)

    Zarrin, Bahram; Baumeister, Hubert; Sarjoughian, Hessam S.

    2018-01-01

    describe their problems and solutions, instead of using general purpose programming languages. The goal of these languages is to improve the productivity and efficiency of the development and simulation of concurrent scientific models and systems. Moreover, they help to expose parallelism and to specify...... the concurrency within a component or across different independent components. In this paper, we introduce the concept of domain-specific flowbased languages which allows domain experts to use flow-based languages adapted to a particular problem domain. Flow-based programming is used to support concurrency, while......Due to the significant growth of the demand for data-intensive computing, in addition to the emergence of new parallel and distributed computing technologies, scientists and domain experts are leveraging languages specialized for their problem domain, i.e., domain-specific languages, to help them...

  5. Hand Specific Representations in Language Comprehension

    Directory of Open Access Journals (Sweden)

    Claire eMoody-Triantis

    2014-06-01

    Full Text Available Theories of embodied cognition argue that language comprehension involves sensory-motor re-enactments of the actions described. However, the degree of specificity of these re-enactments as well as the relationship between action and language remains a matter of debate. Here we investigate these issues by examining how hand-specific information (left or right hand is recruited in language comprehension and action execution. An fMRI study tested right-handed participants in two separate tasks that were designed to be as similar as possible to increase sensitivity of the comparison across task: an action execution go/no-go task where participants performed right or left hand actions, and a language task where participants read sentences describing the same left or right handed actions as in the execution task. We found that language-induced activity did not match the hand-specific patterns of activity found for action execution in primary somatosensory and motor cortex, but it overlapped with pre-motor and parietal regions associated with action planning. Within these pre-motor regions, both right hand actions and sentences elicited stronger activity than left hand actions and sentences - a dominant hand effect -. Importantly, both dorsal and ventral sections of the left pre-central gyrus were recruited by both tasks, suggesting different action features being recruited. These results suggest that (a language comprehension elicits motor representations that are hand-specific and akin to multimodal action plans, rather than full action re-enactments; and (b language comprehension and action execution share schematic hand-specific representations that are richer for the dominant hand, and thus linked to previous motor experience.

  6. Hand specific representations in language comprehension.

    Science.gov (United States)

    Moody-Triantis, Claire; Humphreys, Gina F; Gennari, Silvia P

    2014-01-01

    Theories of embodied cognition argue that language comprehension involves sensory-motor re-enactments of the actions described. However, the degree of specificity of these re-enactments as well as the relationship between action and language remains a matter of debate. Here we investigate these issues by examining how hand-specific information (left or right hand) is recruited in language comprehension and action execution. An fMRI study tested self-reported right-handed participants in two separate tasks that were designed to be as similar as possible to increase sensitivity of the comparison across task: an action execution go/no-go task where participants performed right or left hand actions, and a language task where participants read sentences describing the same left or right handed actions as in the execution task. We found that language-induced activity did not match the hand-specific patterns of activity found for action execution in primary somatosensory and motor cortex, but it overlapped with pre-motor and parietal regions associated with action planning. Within these pre-motor regions, both right hand actions and sentences elicited stronger activity than left hand actions and sentences-a dominant hand effect. Importantly, both dorsal and ventral sections of the left pre-central gyrus were recruited by both tasks, suggesting different action features being recruited. These results suggest that (a) language comprehension elicits motor representations that are hand-specific and akin to multimodal action plans, rather than full action re-enactments; and (b) language comprehension and action execution share schematic hand-specific representations that are richer for the dominant hand, and thus linked to previous motor experience.

  7. Geometric algebra with applications in science and engineering

    CERN Document Server

    Sobczyk, Garret

    2001-01-01

    The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer­ ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar­ ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math­ ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling ...

  8. MATLAB matrix algebra

    CERN Document Server

    Pérez López, César

    2014-01-01

    MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Matrix Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at symbolic and numeric variables, with an emphasis on vector and matrix variables, you will go on to examine functions and operations that support vectors and matrices as arguments, including those based on analytic parent functions. Computational methods for finding eigenvalues and eigenvectors of matrices are detailed, leading to various matrix decompositions. Applications such as change of bases, the classification of quadratic forms and ...

  9. Cerebellum, Language, and Cognition in Autism and Specific Language Impairment

    Science.gov (United States)

    Hodge, Steven M.; Makris, Nikos; Kennedy, David N.; Caviness, Verne S., Jr.; Howard, James; McGrath, Lauren; Steele, Shelly; Frazier, Jean A.; Tager-Flusberg, Helen; Harris, Gordon J.

    2010-01-01

    We performed cerebellum segmentation and parcellation on magnetic resonance images from right-handed boys, aged 6-13 years, including 22 boys with autism [16 with language impairment (ALI)], 9 boys with Specific Language Impairment (SLI), and 11 normal controls. Language-impaired groups had reversed asymmetry relative to unimpaired groups in…

  10. Vertex algebras and algebraic curves

    CERN Document Server

    Frenkel, Edward

    2004-01-01

    Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book co...

  11. Algebraic partial Boolean algebras

    International Nuclear Information System (INIS)

    Smith, Derek

    2003-01-01

    Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A 5 sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E 8

  12. Simplicity and Specificity in Language: Domain-General Biases Have Domain-Specific Effects

    Science.gov (United States)

    Culbertson, Jennifer; Kirby, Simon

    2016-01-01

    The extent to which the linguistic system—its architecture, the representations it operates on, the constraints it is subject to—is specific to language has broad implications for cognitive science and its relation to evolutionary biology. Importantly, a given property of the linguistic system can be “specific” to the domain of language in several ways. For example, if the property evolved by natural selection under the pressure of the linguistic function it serves then the property is domain-specific in the sense that its design is tailored for language. Equally though, if that property evolved to serve a different function or if that property is domain-general, it may nevertheless interact with the linguistic system in a way that is unique. This gives a second sense in which a property can be thought of as specific to language. An evolutionary approach to the language faculty might at first blush appear to favor domain-specificity in the first sense, with individual properties of the language faculty being specifically linguistic adaptations. However, we argue that interactions between learning, culture, and biological evolution mean any domain-specific adaptations that evolve will take the form of weak biases rather than hard constraints. Turning to the latter sense of domain-specificity, we highlight a very general bias, simplicity, which operates widely in cognition and yet interacts with linguistic representations in domain-specific ways. PMID:26793132

  13. Specific Language Impairment

    Science.gov (United States)

    ... Some of the tests use interactions between the child and puppets and other toys to focus on specific rules of grammar, especially ... is not treated early, it can affect a child’s performance in school. ... language development. This kind of classroom program might enlist normally ...

  14. Community-Specific Strategies of Intergenerational Language ...

    African Journals Online (AJOL)

    This study concerns minority language maintenance, specifically it explores local practices that make it possible for a community to sustain its traditional language. Two variables were the focus of the research; speakers' attitudes and language use patterns. These were examined to determine their influence in facilitating ...

  15. Application software, domain-specific languages, and language design assistants

    NARCIS (Netherlands)

    J. Heering (Jan)

    2000-01-01

    textabstractWhile application software does the real work, domain-specific languages (DSLs) are tools to help produce it efficiently, and language design assistants in turn are meta-tools to help produce DSLs quickly. DSLs are already in wide use (HTML for web pages, Excel macros for spreadsheet

  16. Multilingualism and Specific Language Impairment

    OpenAIRE

    Engel de Abreu, Pascale

    2014-01-01

    Is a multilingual education beneficial for children? What are the optimal conditions under which a child can become perfectly multilingual? When should we be concerned about a multilingual child's language skills? What are the signs of Specific Language Impairment in a child who speaks more than one language? Developmental psychologist and Associate Professor in multilingual cognitive development at the University of Luxembourg Pascale Engel de Abreu will address these questions based on what...

  17. How Language Is Embodied in Bilinguals and Children with Specific Language Impairment

    Science.gov (United States)

    Adams, Ashley M.

    2016-01-01

    This manuscript explores the role of embodied views of language comprehension and production in bilingualism and specific language impairment. Reconceptualizing popular models of bilingual language processing, the embodied theory is first extended to this area. Issues such as semantic grounding in a second language and potential differences between early and late acquisition of a second language are discussed. Predictions are made about how this theory informs novel ways of thinking about teaching a second language. Secondly, the comorbidity of speech, language, and motor impairments and how embodiment theory informs the discussion of the etiology of these impairments is examined. A hypothesis is presented suggesting that what is often referred to as specific language impairment may not be so specific due to widespread subclinical motor deficits in this population. Predictions are made about how weaknesses and instabilities in speech motor control, even at a subclinical level, may disrupt the neural network that connects acoustic input, articulatory motor plans, and semantics. Finally, I make predictions about how this information informs clinical practice for professionals such as speech language pathologists and occupational and physical therapists. These new hypotheses are placed within the larger framework of the body of work pertaining to semantic grounding, action-based language acquisition, and action-perception links that underlie language learning and conceptual grounding. PMID:27582716

  18. Methodes for identification of specific language impairment

    Directory of Open Access Journals (Sweden)

    Toktam Maleki Shahmahmood

    2014-06-01

    Full Text Available Background and Aim: Specific language impiarment (SLI is one of the most prevalent developmental language disorders its diagnosis is a problematic issue among researchers and clinicians because of the heterogeneity of language profiles in the affected population and overlapping with other developmental language disorders. The aim of this study was to review the suggested diagnostic criteria for this disorder, controversies about these criteria and identify the most accurate diagnostic methods.Methods: Published article from 1980 to 2012 in bibliographic and publisher databases including Pubmed, Google scholar, Cochran library, Web of Science, ProQuest, Springer, Oxford, Science direct, Ovid, Iran Medex and Magiran about the diagnostic methods for discriminating preschoool children with specific language impiarment from normal developing children were reviewd in this article. These keywords were used for research: “specific language impairment”, “SLI”, “diagnosis or identification”, “standardized tests”, and “tests for language development”.Conclusion: The results of this study show inspite of agreement of researchers and clinicians about exclusionary criteria as one basic part of the diagnosis of specific language impiarment , there is no consensus about the other part, inclusionary criteria. Different studies used different inclusionary criteria which can be divided to categories of clincal judgment, discrepancy-based criteria, standardized testing, clinical markers and markers from spontaneous speech samples. Advantages, disadvantages, and clinical applicability of each diagnostic method are discussed in this article.

  19. Application software, domain-specific languages, and language design assistants

    OpenAIRE

    Heering, Jan

    2000-01-01

    textabstractWhile application software does the real work, domain-specific languages (DSLs) are tools to help produce it efficiently, and language design assistants in turn are meta-tools to help produce DSLs quickly. DSLs are already in wide use (HTML for web pages, Excel macros for spreadsheet applications, VHDL for hardware design, ...), but many more will be needed for both new as well as existing application domains. Language design assistants to help develop them currently exist only in...

  20. Intertextuality and Sense Production in the Learning of Algebraic Methods

    Science.gov (United States)

    Rojano, Teresa; Filloy, Eugenio; Puig, Luis

    2014-01-01

    In studies carried out in the 1980s the algebraic symbols and expressions are revealed through prealgebraic readers as non-independent texts, as texts that relate to other texts that in some cases belong to the reader's native language or to the arithmetic sign system. Such outcomes suggest that the act of reading algebraic texts submerges…

  1. Clifford Algebras and magnetic monopoles

    International Nuclear Information System (INIS)

    Recami, E.

    1987-01-01

    It is known that the introduction of magnetic monopolies in electromagnetism does still present formal problems from the point of view of classical field theory. The author attempts to overcome at least some of them by making recourse to the Clifford Algebra formalism. In fact, while the events of a two-dimensional Minkowski space-time M(1,1) are sufficiently well represented by ordinary Complex Numbers, when dealing with the events of the four-dimensional Minkowski space M(1,3)identical to M/sub 4/ one has of course to look for hypercomplex numbers or, more generally, for the elements of a Clifford Algebra. The author uses the Clifford Algebras in terms of ''multivectors'', and in particular by Hestenes' language, which suits space-time quite well. He recalls that the Clifford product chiγ is the sum of the internal product chi . γ and of the wedge product chiΛγ

  2. Does simultaneous bilingualism aggravate children's specific language problems?

    Science.gov (United States)

    Korkman, Marit; Stenroos, Maria; Mickos, Annika; Westman, Martin; Ekholm, Pia; Byring, Roger

    2012-09-01

    There is little data on whether or not a bilingual upbringing may aggravate specific language problems in children. This study analysed whether there was an interaction of such problems and simultaneous bilingualism. Participants were 5- to 7-year-old children with specific language problems (LANG group, N = 56) or who were typically developing (CONTR group, N = 60). Seventy-three children were Swedish-Finnish bilingual and 43 were Swedish-speaking monolingual. Assessments (in Swedish) included tests of expressive language, comprehension, repetition and verbal memory. Per definition, the LANG group had lower scores than the CONTR group on all language tests. The bilingual group had lower scores than the monolingual group only on a test of body part naming. Importantly, the interaction of group (LANG or CONTR) and bilingualism was not significant on any of the language scores. Simultaneous bilingualism does not aggravate specific language problems but may result in a slower development of vocabulary both in children with and without specific language problems. Considering also advantages, a bilingual upbringing is an option also for children with specific language problems. In assessment, tests of vocabulary may be sensitive to bilingualism, instead tests assessing comprehension, syntax and nonword repetition may provide less biased methods. © 2012 The Author(s)/Acta Paediatrica © 2012 Foundation Acta Paediatrica.

  3. Linear Algebra and Smarandache Linear Algebra

    OpenAIRE

    Vasantha, Kandasamy

    2003-01-01

    The present book, on Smarandache linear algebra, not only studies the Smarandache analogues of linear algebra and its applications, it also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense. We have introduced Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra and their fuzzy equivalents. Moreover, in this book, we have brought out the study of linear algebra and vector spaces over finite p...

  4. Algebras and manifolds: Differential, difference, simplicial and quantum

    International Nuclear Information System (INIS)

    Finkelstein, D.; Rodriguez, E.

    1986-01-01

    Generalized manifolds and Clifford algebras depict the world at levels of resolution ranging from the classical macroscopic to the quantum microscopic. The coarsest picture is a differential manifold and algebra (dm), direct integral of familiar local Clifford algebras of spin operators in curved time-space. Next is a finite difference manifold (Δm) of Regge calculus. This is a subalgebra of the third, a Minkowskian simplicial manifold (Σm). The most detailed description is the quantum manifold (Qm), whose algebra is the free Clifford algebra S of quantum set theory. We surmise that each Σm is a classical 'condensation' of a Qm. Quantum simplices have both integer and half-integer spins in their spectrum. A quantum set theory of nature requires a series of reductions leading from the Qm and a world descriptor W up through the intermediate Σm and Δm to a dm and an action principle. What may be a new algebraic language for topology, classical or quantum, is a by-product of the work. (orig.)

  5. What Characterizes the Algebraic Competence of Norwegian Upper Secondary School Students? Evidence from TIMSS Advanced

    Science.gov (United States)

    Pedersen, Ida Friestad

    2015-01-01

    Algebra is the fundamental language of mathematics, and a profound understanding of school algebra is an important prerequisite for further studies in mathematical sciences. The aim of this study is to characterize the algebraic competence of the Norwegian upper secondary school students participating in Trends in International Mathematics and…

  6. Introduction to vertex algebras, Borcherds algebras and the Monster Lie algebras

    International Nuclear Information System (INIS)

    Gebert, R.W.

    1993-09-01

    The theory of vertex algebras constitutes a mathematically rigorous axiomatic formulation of the algebraic origins of conformal field theory. In this context Borcherds algebras arise as certain ''physical'' subspaces of vertex algebras. The aim of this review is to give a pedagogical introduction into this rapidly-developing area of mathematics. Based on the machinery of formal calculus we present the axiomatic definition of vertex algebras. We discuss the connection with conformal field theory by deriving important implications of these axioms. In particular, many explicit calculations are presented to stress the eminent role of the Jacobi identity axiom for vertex algebras. As a class of concrete examples the vertex algebras associated with even lattices are constructed and it is shown in detail how affine Lie algebras and the fake Monster Lie algebra naturally appear. This leads us to the abstract definition of Borcherds algebras as generalized Kac-Moody algebras and their basic properties. Finally, the results about the simplest generic Borcherds algebras are analysed from the point of view of symmetry in quantum theory and the construction of the Monster Lie algebra is sketched. (orig.)

  7. Comparison of Spontaneously Elicited Language Patterns in Specific Language Impairment and High-Functioning Autism.

    Science.gov (United States)

    Craig, Megan; Trauner, Doris

    2018-02-01

    We aimed to characterize differences in the use of language in children with specific language impairment and high-functioning autism by analyzing verbal responses on standardized tests. The overall goal was to provide clinicians with additional tools with which to aid in distinguishing the two neurodevelopmental disorders. This study included 16 children with specific language impairment, 28 children with high-functioning autism, and 52 typically developing participants between the ages of six and 14. Groups were matched for age, and specific language impairment and high-functioning autism groups were matched on verbal and performance IQ. Responses from standardized tests were examined for response length, grammatical errors, filler words, perseverations, revisions (repeated attempts to begin or continue a sentence), off-topic attention shifts (lapses in attention to the task), and rambling. Data were analyzed using parametric and nonparametric methods. Specific language impairment responses were longer and contained more filler words than did those of the other two groups, whereas high-functioning autism responses exhibited more grammatical errors, off-topic attention shifts, and rambling. Specific language impairment and high-functioning autism responses showed higher rates of perseveration compared with controls. There were no significant differences in revisions among the three groups. Differences in language patterns of participants with specific language impairment and high-functioning autism may be useful to the clinician in helping to differentiate isolated language impairment from high-functioning autism. The results also support the conclusion that the two conditions are separable, and each exhibits a different pattern of language dysfunction. Copyright © 2017 Elsevier Inc. All rights reserved.

  8. Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C

    OpenAIRE

    Blaha, Stephen

    2002-01-01

    We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.

  9. The Logic of the RAISE Specification Language

    DEFF Research Database (Denmark)

    George, Chris; Haxthausen, Anne Elisabeth

    2008-01-01

    This chapter describes the logic of the RAISE Specification Language, RSL. It explains the particular logic chosen for RAISE, and motivates this choice as suitable for a wide spectrum language to be used for designs as well as initial specifications, and supporting imperative and concurrent...

  10. The Logic of the RAISE Specification Language

    DEFF Research Database (Denmark)

    George, Chris; Haxthausen, Anne Elisabeth

    2003-01-01

    This paper describes the logic of the RAISE Specification Language, RSL. It explains the particular logic chosen for RAISE, and motivates this choice as suitable for a wide spectrum language to be used for designs as well as initial specifications, and supporting imperative and concurrent...

  11. Quantum W-algebras and elliptic algebras

    International Nuclear Information System (INIS)

    Feigin, B.; Kyoto Univ.; Frenkel, E.

    1996-01-01

    We define a quantum W-algebra associated to sl N as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary W-algebra of sl N , or the q-deformed classical W-algebra of sl N . We construct free field realizations of the quantum W-algebras and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in U q (n). (orig.)

  12. Recoupling Lie algebra and universal ω-algebra

    International Nuclear Information System (INIS)

    Joyce, William P.

    2004-01-01

    We formulate the algebraic version of recoupling theory suitable for commutation quantization over any gradation. This gives a generalization of graded Lie algebra. Underlying this is the new notion of an ω-algebra defined in this paper. ω-algebra is a generalization of algebra that goes beyond nonassociativity. We construct the universal enveloping ω-algebra of recoupling Lie algebras and prove a generalized Poincare-Birkhoff-Witt theorem. As an example we consider the algebras over an arbitrary recoupling of Z n graded Heisenberg Lie algebra. Finally we uncover the usual coalgebra structure of a universal envelope and substantiate its Hopf structure

  13. Critical analysis of algebraic collective models

    International Nuclear Information System (INIS)

    Moshinsky, M.

    1986-01-01

    The author shall understand by algebraic collective models all those based on specific Lie algebras, whether the latter are suggested through simple shell model considerations like in the case of the Interacting Boson Approximation (IBA), or have a detailed microscopic foundation like the symplectic model. To analyze these models critically, it is convenient to take a simple conceptual example of them in which all steps can be implemented analytically or through elementary numerical analysis. In this note he takes as an example the symplectic model in a two dimensional space i.e. based on a sp(4,R) Lie algebra, and show how through its complete discussion we can get a clearer understanding of the structure of algebraic collective models of nuclei. In particular he discusses the association of Hamiltonians, related to maximal subalgebras of our basic Lie algebra, with specific types of spectra, and the connections between spectra and shapes

  14. An Integrated Framework to Specify Domain-Specific Modeling Languages

    DEFF Research Database (Denmark)

    Zarrin, Bahram; Baumeister, Hubert

    2018-01-01

    , a logic-based specification language. The drawback of MS DSL Tools is it does not provide a formal and rigorous approach for semantics specifications. In this framework, we use Microsoft DSL Tools to define the metamodel and graphical notations of DSLs, and an extended version of ForSpec as a formal......In this paper, we propose an integrated framework that can be used by DSL designers to implement their desired graphical domain-specific languages. This framework relies on Microsoft DSL Tools, a meta-modeling framework to build graphical domain-specific languages, and an extension of ForSpec...... language to define their semantics. Integrating these technologies under the umbrella of Microsoft Visual Studio IDE allows DSL designers to utilize a single development environment for developing their desired domain-specific languages....

  15. Differential Hopf algebra structures on the universal enveloping algebra ofa Lie algebra

    NARCIS (Netherlands)

    N.W. van den Hijligenberg; R. Martini

    1995-01-01

    textabstractWe discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra

  16. Linear algebra

    CERN Document Server

    Stoll, R R

    1968-01-01

    Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand

  17. The Yoneda algebra of a K2 algebra need not be another K2 algebra

    OpenAIRE

    Cassidy, T.; Phan, C.; Shelton, B.

    2010-01-01

    The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. K2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a K2 algebra would be another K2 algebra. We show that this is not necessarily the case by constructing a monomial K2 algebra for which the corresponding Yoneda algebra is not K2.

  18. Cluster algebras in mathematical physics

    International Nuclear Information System (INIS)

    Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

    2014-01-01

    identities in conformal field theory and so forth. It is remarkable that the key ingredients in such a variety of theories and models are captured and described universally in the common language of cluster algebras. This special issue provides a bird's-eye view of the known and latest results in various topics in mathematical physics where cluster algebras have played an essential role. The contributed articles are themselves an eloquent illustration of the breadth and depth of the subject of cluster algebras. We are confident that the issue will stimulate both newcomers and experts, since the applications to physics still seem to be growing

  19. Unipotent and nilpotent classes in simple algebraic groups and lie algebras

    CERN Document Server

    Liebeck, Martin W

    2012-01-01

    This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of...

  20. Forum on specification and Design Languages

    CERN Document Server

    Maehne, Torsten

    2015-01-01

    This book brings together a selection of the best papers from the sixteenth edition of the Forum on specification and Design Languages Conference (FDL), which was held in September 2013 in Paris, France. FDL is a well-established international forum devoted to dissemination of research results, practical experiences and new ideas in the application of specification, design and verification languages to the design, modeling and verification of integrated circuits, complex hardware/software embedded systems, and mixed-technology systems. • Covers applications of formal methods for specification, verification and debug; • Includes embedded analog and mixed-signal system design; • Enables model-driven engineering for embedded systems design and development.

  1. Sentence Repetition in Deaf Children with Specific Language Impairment in British Sign Language

    Science.gov (United States)

    Marshall, Chloë; Mason, Kathryn; Rowley, Katherine; Herman, Rosalind; Atkinson, Joanna; Woll, Bencie; Morgan, Gary

    2015-01-01

    Children with specific language impairment (SLI) perform poorly on sentence repetition tasks across different spoken languages, but until now, this methodology has not been investigated in children who have SLI in a signed language. Users of a natural sign language encode different sentence meanings through their choice of signs and by altering…

  2. Componential Skills in Second Language Development of Bilingual Children with Specific Language Impairment

    Science.gov (United States)

    Verhoeven, Ludo; Steenge, Judit; van Leeuwe, Jan; van Balkom, Hans

    2017-01-01

    In this study, we investigated which componential skills can be distinguished in the second language (L2) development of 140 bilingual children with specific language impairment in the Netherlands, aged 6-11 years, divided into 3 age groups. L2 development was assessed by means of spoken language tasks representing different language skills…

  3. Language and executive functioning in the context of specific language impairment and bilingualism

    NARCIS (Netherlands)

    Laloi, A.

    2015-01-01

    The present thesis has investigated how French-speaking monolingual and bilingual children with SLI (specific language impairment) performed on various tasks examining language and executive functioning (EF) abilities, in comparison to monolingual and bilingual peers without SLI. Language was

  4. Algebra for Enterprise Ontology: towards analysis and synthesis of enterprise models

    Science.gov (United States)

    Suga, Tetsuya; Iijima, Junichi

    2018-03-01

    Enterprise modeling methodologies have made enterprises more likely to be the object of systems engineering rather than craftsmanship. However, the current state of research in enterprise modeling methodologies lacks investigations of the mathematical background embedded in these methodologies. Abstract algebra, a broad subfield of mathematics, and the study of algebraic structures may provide interesting implications in both theory and practice. Therefore, this research gives an empirical challenge to establish an algebraic structure for one aspect model proposed in Design & Engineering Methodology for Organizations (DEMO), which is a major enterprise modeling methodology in the spotlight as a modeling principle to capture the skeleton of enterprises for developing enterprise information systems. The results show that the aspect model behaves well in the sense of algebraic operations and indeed constructs a Boolean algebra. This article also discusses comparisons with other modeling languages and suggests future work.

  5. Algebraic Aspects of Families of Fuzzy Languages

    NARCIS (Netherlands)

    Asveld, P.R.J.; Heylen, Dirk K.J.; Nijholt, Antinus; Scollo, Giuseppe

    2000-01-01

    We study operations on fuzzy languages such as union, concatenation,Kleene $\\star$, intersection with regular fuzzy languages, and several kinds of (iterated) fuzzy substitution. Then we consider families of fuzzy languages, closed under a fixed collection of these operations, which results in the

  6. Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra

    NARCIS (Netherlands)

    van den Hijligenberg, N.W.; van den Hijligenberg, N.W.; Martini, Ruud

    1995-01-01

    We discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra structure of

  7. Domain Specific Language for Modeling Waste Management Systems

    DEFF Research Database (Denmark)

    Zarrin, Bahram

    environmental technologies i.e. solid waste management systems. Flow-based programming is used to support concurrent execution of the processes, and provides a model-integration language for composing processes from homogeneous or heterogeneous domains. And a domain-specific language is used to define atomic......In order to develop sustainable waste management systems with considering life cycle perspective, scientists and domain experts in environmental science require readily applicable tools for modeling and evaluating the life cycle impacts of the waste management systems. Practice has proved...... a domain specific language for modeling of waste-management systems on the basis of our framework. We evaluate the language by providing a set of case studies. The contributions of this thesis are; addressing separation of concerns in Flow-based programming and providing the formal specification of its...

  8. A Methodology For The Development Of Complex Domain Specific Languages

    CERN Document Server

    Risoldi, Matteo; Falquet, Gilles

    2010-01-01

    The term Domain-Specific Modeling Language is used in software development to indicate a modeling (and sometimes programming) language dedicated to a particular problem domain, a particular problem representation technique and/or a particular solution technique. The concept is not new -- special-purpose programming language and all kinds of modeling/specification languages have always existed, but the term DSML has become more popular due to the rise of domain-specific modeling. Domain-specific languages are considered 4GL programming languages. Domain-specific modeling techniques have been adopted for a number of years now. However, the techniques and frameworks used still suffer from problems of complexity of use and fragmentation. Although in recent times some integrated environments are seeing the light, it is not common to see many concrete use cases in which domain-specific modeling has been put to use. The main goal of this thesis is tackling the domain of interactive systems and applying a DSML-based...

  9. Introducing Algebra through the Graphical Representation of Functions: A Study among LD Students

    Science.gov (United States)

    Sauriol, Jennifer

    2013-01-01

    This longitudinal study evaluates the impact of a new Algebra 1 course at a High School for language-based learning-disabled (LD) students. The new course prioritized the teaching of relationship graphs and functions as an introduction to algebra. Across three studies, the dissertation documents and evaluates the progress made by LD high school…

  10. Fuzzy Graph Language Recognizability

    OpenAIRE

    Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros

    2012-01-01

    Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.

  11. Introduction to relation algebras relation algebras

    CERN Document Server

    Givant, Steven

    2017-01-01

    The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly ...

  12. Software engineering with application-specific languages

    Science.gov (United States)

    Campbell, David J.; Barker, Linda; Mitchell, Deborah; Pollack, Robert H.

    1993-01-01

    Application-Specific Languages (ASL's) are small, special-purpose languages that are targeted to solve a specific class of problems. Using ASL's on software development projects can provide considerable cost savings, reduce risk, and enhance quality and reliability. ASL's provide a platform for reuse within a project or across many projects and enable less-experienced programmers to tap into the expertise of application-area experts. ASL's have been used on several software development projects for the Space Shuttle Program. On these projects, the use of ASL's resulted in considerable cost savings over conventional development techniques. Two of these projects are described.

  13. From Rota-Baxter algebras to pre-Lie algebras

    International Nuclear Information System (INIS)

    An Huihui; Ba, Chengming

    2008-01-01

    Rota-Baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics. Rota-Baxter algebras provide a construction of pre-Lie algebras from associative algebras. In this paper, we give all Rota-Baxter operators of weight 1 on complex associative algebras in dimension ≤3 and their corresponding pre-Lie algebras

  14. Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras

    International Nuclear Information System (INIS)

    Marquette, Ian

    2013-01-01

    We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently

  15. Writing Motivation of Students with Specific Language Impairments

    Science.gov (United States)

    Brouwer, Kyle Lee

    2010-01-01

    This study was designed to compare the writing motivation of students with specific language impairments with their non-disabled peers. Due to the cognitive and linguistic demands of the writing process, students with language impairments face unique difficulties during the writing process. It was hypothesized that students with specific language…

  16. An algorithm for analysis of the structure of finitely presented Lie algebras

    Directory of Open Access Journals (Sweden)

    Vladimir P. Gerdt

    1997-12-01

    Full Text Available We consider the following problem: what is the most general Lie algebra satisfying a given set of Lie polynomial equations? The presentation of Lie algebras by a finite set of generators and defining relations is one of the most general mathematical and algorithmic schemes of their analysis. That problem is of great practical importance, covering applications ranging from mathematical physics to combinatorial algebra. Some particular applications are constructionof prolongation algebras in the Wahlquist-Estabrook method for integrability analysis of nonlinear partial differential equations and investigation of Lie algebras arising in different physical models. The finite presentations also indicate a way to q-quantize Lie algebras. To solve this problem, one should perform a large volume of algebraic transformations which is sharply increased with growth of the number of generators and relations. For this reason, in practice one needs to use a computer algebra tool. We describe here an algorithm for constructing the basis of a finitely presented Lie algebra and its commutator table, and its implementation in the C language. Some computer results illustrating our algorithmand its actual implementation are also presented.

  17. Yoneda algebras of almost Koszul algebras

    Indian Academy of Sciences (India)

    Abstract. Let k be an algebraically closed field, A a finite dimensional connected. (p,q)-Koszul self-injective algebra with p, q ≥ 2. In this paper, we prove that the. Yoneda algebra of A is isomorphic to a twisted polynomial algebra A![t; β] in one inde- terminate t of degree q +1 in which A! is the quadratic dual of A, β is an ...

  18. Abnormal Functional Lateralization and Activity of Language Brain Areas in Typical Specific Language Impairment (Developmental Dysphasia)

    Science.gov (United States)

    de Guibert, Clement; Maumet, Camille; Jannin, Pierre; Ferre, Jean-Christophe; Treguier, Catherine; Barillot, Christian; Le Rumeur, Elisabeth; Allaire, Catherine; Biraben, Arnaud

    2011-01-01

    Atypical functional lateralization and specialization for language have been proposed to account for developmental language disorders, yet results from functional neuroimaging studies are sparse and inconsistent. This functional magnetic resonance imaging study compared children with a specific subtype of specific language impairment affecting…

  19. Algebra: A Challenge at the Crossroads of Policy and Practice

    Science.gov (United States)

    Stein, Mary Kay; Kaufman, Julia Heath; Sherman, Milan; Hillen, Amy F.

    2011-01-01

    The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…

  20. Quantum cluster algebras and quantum nilpotent algebras

    Science.gov (United States)

    Goodearl, Kenneth R.; Yakimov, Milen T.

    2014-01-01

    A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

  1. Abnormal functional lateralization and activity of language brain areas in typical specific language impairment (developmental dysphasia)

    Science.gov (United States)

    De Guibert, Clément; Maumet, Camille; Jannin, Pierre; Ferré, Jean-Christophe; Tréguier, Catherine; Barillot, Christian; Le Rumeur, Elisabeth; Allaire, Catherine; Biraben, Arnaud

    2011-01-01

    Atypical functional lateralization and specialization for language have been proposed to account for developmental language disorders, yet results from functional neuroimaging studies are sparse and inconsistent. This functional magnetic resonance imaging study compared children with a specific subtype of specific language impairment affecting structural language (n=21), to a matched group of typically-developing children using a panel of four language tasks neither requiring reading nor metalinguistic skills, including two auditory lexico-semantic tasks (category fluency and responsive naming) and two visual phonological tasks based on picture naming. Data processing involved normalizing the data with respect to a matched pairs pediatric template, groups and between-groups analysis, and laterality indexes assessment within regions of interest using single and combined task analysis. Children with specific language impairment exhibited a significant lack of left lateralization in all core language regions (inferior frontal gyrus-opercularis, inferior frontal gyrus-triangularis, supramarginal gyrus, superior temporal gyrus), across single or combined task analysis, but no difference of lateralization for the rest of the brain. Between-group comparisons revealed a left hypoactivation of Wernicke’s area at the posterior superior temporal/supramarginal junction during the responsive naming task, and a right hyperactivation encompassing the anterior insula with adjacent inferior frontal gyrus and the head of the caudate nucleus during the first phonological task. This study thus provides evidence that this specific subtype of specific language impairment is associated with atypical lateralization and functioning of core language areas. PMID:21719430

  2. The Virasoro algebra in integrable hierarchies and the method of matrix models

    International Nuclear Information System (INIS)

    Semikhatov, A.M.

    1992-01-01

    The action of the Virasoro algebra on hierarchies of nonlinear integrable equations, and also the structure and consequences of Virasoro constraints on these hierarchies, are studied. It is proposed that a broad class of hierarchies, restricted by Virasoro constraints, can be defined in terms of dressing operators hidden in the structure of integrable systems. The Virasoro-algebra representation constructed on the dressing operators displays a number of analogies with structures in conformal field theory. The formulation of the Virasoro constraints that stems from this representation makes it possible to translate into the language of integrable systems a number of concepts from the method of the 'matrix models' that describe nonperturbative quantum gravity, and, in particular, to realize a 'hierarchical' version of the double scaling limit. From the Virasoro constraints written in terms of the dressing operators generalized loop equations are derived, and this makes it possible to do calculations on a reconstruction of the field-theoretical description. The reduction of the Kadomtsev-Petviashvili (KP) hierarchy, subject to Virasoro constraints, to generalized Korteweg-deVries (KdV) hierarchies is implemented, and the corresponding representation of the Virasoro algebra on these hierarchies is found both in the language of scalar differential operators and in the matrix formalism of Drinfel'd and Sokolov. The string equation in the matrix formalism does not replicate the structure of the scalar string equation. The symmetry algebras of the KP and N-KdV hierarchies restricted by Virasoro constraints are calculated: A relationship is established with algebras from the family W ∞ (J) of infinite W-algebras

  3. A conceptual model specification language (CMSL Version 2)

    NARCIS (Netherlands)

    Wieringa, Roelf J.

    1992-01-01

    Version 2 of a language (CMSL) to specify conceptual models is defined. CMSL consists of two parts, the value specification language VSL and the object spercification language OSL. There is a formal semantics and an inference system for CMSL but research on this still continues. A method for

  4. The structure of the super-W∞(λ) algebra

    International Nuclear Information System (INIS)

    Bergshoeff, E.; Wit, B. de; Vasiliev, M.

    1991-01-01

    We give a comprehensive treatment of the super-W ∞ (λ) algebra, an extension of the super-Virasoro algebra that contains generators of spin S ≥ 1/2. The parameter λ defines the embedding of the Virasoro subalgebra. We describe how to obtain the super-W ∞ (λ) algebra from the associative algebra of superspace differential operators. We discuss the structure of this associative algebra and its relation with the so-called wedge algebra, in which the generators for given spin are restricted to finite-dimensional representations of sl(2). From the super-W ∞ (λ) algebra one can obtain a variety of W ∞ algebras by consistent truncations for specific values of λ. Without truncation the algebras are formally isomorphic for different values of λ. We present a realization in terms of the currents of a supersymmetric bc system. (orig.)

  5. Students’ Algebraic Thinking Process in Context of Point and Line Properties

    Science.gov (United States)

    Nurrahmi, H.; Suryadi, D.; Fatimah, S.

    2017-09-01

    Learning of schools algebra is limited to symbols and operating procedures, so students are able to work on problems that only require the ability to operate symbols but unable to generalize a pattern as one of part of algebraic thinking. The purpose of this study is to create a didactic design that facilitates students to do algebraic thinking process through the generalization of patterns, especially in the context of the property of point and line. This study used qualitative method and includes Didactical Design Research (DDR). The result is students are able to make factual, contextual, and symbolic generalization. This happen because the generalization arises based on facts on local terms, then the generalization produced an algebraic formula that was described in the context and perspective of each student. After that, the formula uses the algebraic letter symbol from the symbol t hat uses the students’ language. It can be concluded that the design has facilitated students to do algebraic thinking process through the generalization of patterns, especially in the context of property of the point and line. The impact of this study is this design can use as one of material teaching alternative in learning of school algebra.

  6. Domain Specific Language Support for Exascale

    Energy Technology Data Exchange (ETDEWEB)

    Mellor-Crummey, John [Rice Univ., Houston, TX (United States)

    2017-10-20

    A multi-institutional project known as D-TEC (short for “Domain- specific Technology for Exascale Computing”) set out to explore technologies to support the construction of Domain Specific Languages (DSLs) to map application programs to exascale architectures. DSLs employ automated code transformation to shift the burden of delivering portable performance from application programmers to compilers. Two chief properties contribute: DSLs permit expression at a high level of abstraction so that a programmer’s intent is clear to a compiler and DSL implementations encapsulate human domain-specific optimization knowledge so that a compiler can be smart enough to achieve good results on specific hardware. Domain specificity is what makes these properties possible in a programming language. If leveraging domain specificity is the key to keep exascale software tractable, a corollary is that many different DSLs will be needed to encompass the full range of exascale computing applications; moreover, a single application may well need to use several different DSLs in conjunction. As a result, developing a general toolkit for building domain-specific languages was a key goal for the D-TEC project. Different aspects of the D-TEC research portfolio were the focus of work at each of the partner institutions in the multi-institutional project. D-TEC research and development work at Rice University focused on on three principal topics: understanding how to automate the tuning of code for complex architectures, research and development of the Rosebud DSL engine, and compiler technology to support complex execution platforms. This report provides a summary of the research and development work on the D-TEC project at Rice University.

  7. Polynomials in algebraic analysis

    OpenAIRE

    Multarzyński, Piotr

    2012-01-01

    The concept of polynomials in the sense of algebraic analysis, for a single right invertible linear operator, was introduced and studied originally by D. Przeworska-Rolewicz \\cite{DPR}. One of the elegant results corresponding with that notion is a purely algebraic version of the Taylor formula, being a generalization of its usual counterpart, well known for functions of one variable. In quantum calculus there are some specific discrete derivations analyzed, which are right invertible linear ...

  8. Differential Hopf algebra structures on the Universal Enveloping Algebra of a Lie Algebra

    NARCIS (Netherlands)

    van den Hijligenberg, N.W.; van den Hijligenberg, N.; Martini, Ruud

    1995-01-01

    We discuss a method to construct a De Rham complex (differential algebra) of Poincaré–Birkhoff–Witt type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebrastructure of U(g).

  9. AN ADA LINEAR ALGEBRA PACKAGE MODELED AFTER HAL/S

    Science.gov (United States)

    Klumpp, A. R.

    1994-01-01

    This package extends the Ada programming language to include linear algebra capabilities similar to those of the HAL/S programming language. The package is designed for avionics applications such as Space Station flight software. In addition to the HAL/S built-in functions, the package incorporates the quaternion functions used in the Shuttle and Galileo projects, and routines from LINPAK that solve systems of equations involving general square matrices. Language conventions in this package follow those of HAL/S to the maximum extent practical and minimize the effort required for writing new avionics software and translating existent software into Ada. Valid numeric types in this package include scalar, vector, matrix, and quaternion declarations. (Quaternions are fourcomponent vectors used in representing motion between two coordinate frames). Single precision and double precision floating point arithmetic is available in addition to the standard double precision integer manipulation. Infix operators are used instead of function calls to define dot products, cross products, quaternion products, and mixed scalar-vector, scalar-matrix, and vector-matrix products. The package contains two generic programs: one for floating point, and one for integer. The actual component type is passed as a formal parameter to the generic linear algebra package. The procedures for solving systems of linear equations defined by general matrices include GEFA, GECO, GESL, and GIDI. The HAL/S functions include ABVAL, UNIT, TRACE, DET, INVERSE, TRANSPOSE, GET, PUT, FETCH, PLACE, and IDENTITY. This package is written in Ada (Version 1.2) for batch execution and is machine independent. The linear algebra software depends on nothing outside the Ada language except for a call to a square root function for floating point scalars (such as SQRT in the DEC VAX MATHLIB library). This program was developed in 1989, and is a copyrighted work with all copyright vested in NASA.

  10. Elements of algebraic coding systems

    CERN Document Server

    Cardoso da Rocha, Jr, Valdemar

    2014-01-01

    Elements of Algebraic Coding Systems is an introductory text to algebraic coding theory. In the first chapter, you'll gain inside knowledge of coding fundamentals, which is essential for a deeper understanding of state-of-the-art coding systems. This book is a quick reference for those who are unfamiliar with this topic, as well as for use with specific applications such as cryptography and communication. Linear error-correcting block codes through elementary principles span eleven chapters of the text. Cyclic codes, some finite field algebra, Goppa codes, algebraic decoding algorithms, and applications in public-key cryptography and secret-key cryptography are discussed, including problems and solutions at the end of each chapter. Three appendices cover the Gilbert bound and some related derivations, a derivation of the Mac- Williams' identities based on the probability of undetected error, and two important tools for algebraic decoding-namely, the finite field Fourier transform and the Euclidean algorithm f...

  11. The relation between quantum W algebras and Lie algebras

    International Nuclear Information System (INIS)

    Boer, J. de; Tjin, T.

    1994-01-01

    By quantizing the generalized Drinfeld-Sokolov reduction scheme for arbitrary sl 2 embeddings we show that a large set W of quantum W algebras can be viewed as (BRST) cohomologies of affine Lie algebras. The set W contains many known W algebras such as W N and W 3 (2) . Our formalism yields a completely algorithmic method for calculating the W algebra generators and their operator product expansions, replacing the cumbersome construction of W algebras as commutants of screening operators. By generalizing and quantizing the Miura transformation we show that any W algebra in W can be embedded into the universal enveloping algebra of a semisimple affine Lie algebra which is, up to shifts in level, isomorphic to a subalgebra of the original affine algebra. Therefore any realization of this semisimple affine Lie algebra leads to a realization of the W algebra. In particular, one obtains in this way a general and explicit method for constructing the free field realizations and Fock resolutions for all algebras in W. Some examples are explicitly worked out. (orig.)

  12. 2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras

    International Nuclear Information System (INIS)

    Ayupov, Shavkat; Kudaybergenov, Karimbergen

    2016-01-01

    The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra A with the inner derivation property we prove that any 2-local derivation on the algebra M 2 n (A), n ≥ 2, is a derivation. We apply this result to AW*-algebras and show that any 2-local derivation on an arbitrary AW*-algebra is a derivation. (paper)

  13. Computer-aided tool for the teaching of relational algebra in data base courses

    Directory of Open Access Journals (Sweden)

    Johnny Villalobos Murillo

    2016-03-01

    Full Text Available This article describes the design and implementation of computer-aided tool called Relational Algebra Translator (RAT in data base courses, for the teaching of relational algebra. There was a problem when introducing the relational algebra topic in the course EIF 211 Design and Implementation of Databases, which belongs to the career of Engineering in Information Systems of the National University of Costa Rica, because students attending this course were lacking profound mathematical knowledge, which led to a learning problem, being this an important subject to understand what the data bases search and request do RAT comes along to enhance the teaching-learning process. It introduces the architectural and design principles required for its implementation, such as: the language symbol table, the gramatical rules and the basic algorithms that RAT uses to translate from relational algebra to SQL language. This tool has been used for one periods and has demonstrated to be effective in the learning-teaching process.  This urged investigators to publish it in the web site: www.slinfo.una.ac.cr in order for this tool to be used in other university courses.

  14. The relationship between mathematics and language: academic implications for children with specific language impairment and English language learners.

    Science.gov (United States)

    Alt, Mary; Arizmendi, Genesis D; Beal, Carole R

    2014-07-01

    The present study examined the relationship between mathematics and language to better understand the nature of the deficit and the academic implications associated with specific language impairment (SLI) and academic implications for English language learners (ELLs). School-age children (N = 61; 20 SLI, 20 ELL, 21 native monolingual English [NE]) were assessed using a norm-referenced mathematics instrument and 3 experimental computer-based mathematics games that varied in language demands. Group means were compared with analyses of variance. The ELL group was less accurate than the NE group only when tasks were language heavy. In contrast, the group with SLI was less accurate than the groups with NE and ELLs on language-heavy tasks and some language-light tasks. Specifically, the group with SLI was less accurate on tasks that involved comparing numerical symbols and using visual working memory for patterns. However, there were no group differences between children with SLI and peers without SLI on language-light mathematics tasks that involved visual working memory for numerical symbols. Mathematical difficulties of children who are ELLs appear to be related to the language demands of mathematics tasks. In contrast, children with SLI appear to have difficulty with mathematics tasks because of linguistic as well as nonlinguistic processing constraints.

  15. Quantum cluster algebra structures on quantum nilpotent algebras

    CERN Document Server

    Goodearl, K R

    2017-01-01

    All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts.

  16. Working Memory Capacity and Language Processes in Children with Specific Language Impairment

    Science.gov (United States)

    Marton, Klara; Schwartz, Richard G.

    2003-01-01

    This study examined the interaction between working memory and language comprehension in children with specific language impairment (SLI), focusing on the function of the central executive component and its interaction with the phonological loop (A. D. Baddeley, 1986) in complex working memory tasks. Thirteen children with SLI and 13 age-matched…

  17. Quadratic algebras

    CERN Document Server

    Polishchuk, Alexander

    2005-01-01

    Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.

  18. Numerical linear algebra a concise introduction with Matlab and Julia

    CERN Document Server

    Bornemann, Folkmar

    2018-01-01

    This book offers an introduction to the algorithmic-numerical thinking using basic problems of linear algebra. By focusing on linear algebra, it ensures a stronger thematic coherence than is otherwise found in introductory lectures on numerics. The book highlights the usefulness of matrix partitioning compared to a component view, leading not only to a clearer notation and shorter algorithms, but also to significant runtime gains in modern computer architectures. The algorithms and accompanying numerical examples are given in the programming environment MATLAB, and additionally – in an appendix – in the future-oriented, freely accessible programming language Julia. This book is suitable for a two-hour lecture on numerical linear algebra from the second semester of a bachelor's degree in mathematics.

  19. Regularity of C*-algebras and central sequence algebras

    DEFF Research Database (Denmark)

    Christensen, Martin S.

    The main topic of this thesis is regularity properties of C*-algebras and how these regularity properties are re ected in their associated central sequence algebras. The thesis consists of an introduction followed by four papers [A], [B], [C], [D]. In [A], we show that for the class of simple...... Villadsen algebra of either the rst type with seed space a nite dimensional CW complex, or the second type, tensorial absorption of the Jiang-Su algebra is characterized by the absence of characters on the central sequence algebra. Additionally, in a joint appendix with Joan Bosa, we show that the Villadsen...... algebra of the second type with innite stable rank fails the corona factorization property. In [B], we consider the class of separable C*-algebras which do not admit characters on their central sequence algebra, and show that it has nice permanence properties. We also introduce a new divisibility property...

  20. Real division algebras and other algebras motivated by physics

    International Nuclear Information System (INIS)

    Benkart, G.; Osborn, J.M.

    1981-01-01

    In this survey we discuss several general techniques which have been productive in the study of real division algebras, flexible Lie-admissible algebras, and other nonassociative algebras, and we summarize results obtained using these methods. The principal method involved in this work is to view an algebra A as a module for a semisimple Lie algebra of derivations of A and to use representation theory to study products in A. In the case of real division algebras, we also discuss the use of isotopy and the use of a generalized Peirce decomposition. Most of the work summarized here has appeared in more detail in various other papers. The exceptions are results on a class of algebras of dimension 15, motivated by physics, which admit the Lie algebra sl(3) as an algebra of derivations

  1. Improving developer productivity with C++ embedded domain specific languages

    Science.gov (United States)

    Kozacik, Stephen; Chao, Evenie; Paolini, Aaron; Bonnett, James; Kelmelis, Eric

    2017-05-01

    Domain-specific languages are a useful tool for productivity allowing domain experts to program using familiar concepts and vocabulary while benefiting from performance choices made by computing experts. Embedding the domain specific language into an existing language allows easy interoperability with non-domain-specific code and use of standard compilers and build systems. In C++, this is enabled through the template and preprocessor features. C++ embedded domain specific languages (EDSLs) allow the user to write simple, safe, performant, domain specific code that has access to all the low-level functionality that C and C++ offer as well as the diverse set of libraries available in the C/C++ ecosystem. In this paper, we will discuss several tools available for building EDSLs in C++ and show examples of projects successfully leveraging EDSLs. Modern C++ has added many useful new features to the language which we have leveraged to further extend the capability of EDSLs. At EM Photonics, we have used EDSLs to allow developers to transparently benefit from using high performance computing (HPC) hardware. We will show ways EDSLs combine with existing technologies and EM Photonics high performance tools and libraries to produce clean, short, high performance code in ways that were not previously possible.

  2. Conflict resolution abilities in children with Specific Language Impairment.

    Science.gov (United States)

    Paula, Erica Macêdo de; Befi-Lopes, Debora Maria

    2013-01-01

    To investigate the conflict resolution abilities of children with Specific Language Impairment, and to verify whether the time of speech-language therapy correlates to the performance on the conflict resolution task. Participants included 20 children with Specific Language Impairment (Research Group) and 40 children with normal language development (Control Group), with ages ranging from 7 years to 8 years and 11 months. To assess the conflict resolution abilities, five hypothetical contexts of conflict were presented. The strategies used by the children were classified and scored by the following levels: level 0 (solutions that do not match the other levels), level 1 (physical solutions), level 2 (unilateral solutions), level 3 (cooperative solutions), and level 4 (mutual solutions). Statistical analysis showed group effect for the variable total score. There was a difference between the groups for modal development level, with higher level of modal development observed in the Control Group. There was no correlation between the period of speech-language therapy attendance and the total score. Children with Specific Language Impairment present difficulties in solving problems, in view of the fact that they mainly use physical and unilateral strategies. There was no correlation between the time of speech-language therapy and performance in the task.

  3. Hom-Novikov algebras

    International Nuclear Information System (INIS)

    Yau, Donald

    2011-01-01

    We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting along any algebra endomorphism. All algebra endomorphisms on complex Novikov algebras of dimensions 2 or 3 are computed, and their associated Hom-Novikov algebras are described explicitly. Another class of Hom-Novikov algebras is constructed from Hom-commutative algebras together with a derivation, generalizing a construction due to Dorfman and Gel'fand. Two other classes of Hom-Novikov algebras are constructed from Hom-Lie algebras together with a suitable linear endomorphism, generalizing a construction due to Bai and Meng.

  4. Language-specific dysgraphia in Korean stroke patients.

    Science.gov (United States)

    Yoon, Ji Hye; Suh, Mee Kyung; Kim, HyangHee

    2010-12-01

    We investigated how changes in the writing of 14 Korean stroke patients reflect the unique features of the Korean writing system. The Korean writing system, Han-geul, has both linguistic and visuospatial/constructive characteristics. In the visuospatial construction of a syllable, the component consonant(s) and vowel(s) must be arranged from top-to-bottom and/or left-to-right within the form of a square. This syllabic organization, unique to Korean writing, may distinguish dysgraphia in Korean patients from the disorder in other languages, and reveal the effects of stroke on visuospatial/constructive abilities. We compared 2 groups of patients affected by stroke, 1 group with left hemisphere (LH) lesions and the other with right hemisphere (RH) lesions. We instructed them to write from a dictation of 90 monosyllabic stimuli, each presented with a real word cue. Patients had to repeat a target syllable and a word cue, and then to write the target syllable only. Patients with LH and RH lesions produced qualitatively different error patterns. While the LH lesion group produced primarily linguistic errors, visuospatial/constructive errors predominated in the group with RH lesions. With regard to language-specific features, these Korean patients with RH lesions produced diverse visuospatial/constructive errors not commonly observed in dysgraphia of the English language. Language-specific writing errors by Korean stroke patients reflect the unique characteristics of Korean writing, which include the arrangement of strokes and graphemes within a square syllabic form by dimensional and spatial rules. These findings support the notion that the Korean writing system possesses a language-specific nature with both linguistic and visuospatial/constructive processes. Distinctive patterns of dysgraphia in the Korean language also suggest interactivity between linguistic and visuospatial/constructive levels of processing. This study is noteworthy for its systematic description of

  5. On one method of realization of commutation relation algebra

    International Nuclear Information System (INIS)

    Sveshnikov, K.A.

    1983-01-01

    Method for constructing the commulation relation representations based on the purely algebraic construction of joined algebraic representation with specially selected composition law has been suggested9 Purely combinatorial construction realizing commulation relations representation has been obtained proceeding from formal equivalence of operatopr action on vector and adding a simbol to a sequences of symbols. The above method practically has the structure of calculating algorithm, which assigns some rule of ''word'' formation of an initial set of ''letters''. In other words, a computer language with definite relations between words (an analogy between quantum mechanics and computer linguistics has been applied)

  6. Interval algebra - an effective means of scheduling surveillance radar networks

    CSIR Research Space (South Africa)

    Focke, RW

    2015-05-01

    Full Text Available Interval Algebra provides an effective means to schedule surveillance radar networks, as it is a temporal ordering constraint language. Thus it provides a solution to a part of resource management, which is included in the revised Data Fusion...

  7. Interval algebra: an effective means of scheduling surveillance radar networks

    CSIR Research Space (South Africa)

    Focke, RW

    2015-05-01

    Full Text Available Interval Algebra provides an effective means to schedule surveillance radar networks, as it is a temporal ordering constraint language. Thus it provides a solution to a part of resource management, which is included in the revised Data Fusion...

  8. Procedures for, and Experiences in, Introducing Algebra in New South Wales.

    Science.gov (United States)

    Pegg, John; Redden, Edward

    1990-01-01

    Discussed are the philosophy and procedures behind the introduction of algebra to students in grade 7 in Australia. Included are the importance of concrete experiences, language development, and the consequences involved in this procedure. (CW)

  9. Principles of algebraic geometry

    CERN Document Server

    Griffiths, Phillip A

    1994-01-01

    A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special top

  10. Predictors of second language acquisition in Latino children with specific language impairment.

    Science.gov (United States)

    Gutiérrez-Clellen, Vera; Simon-Cereijido, Gabriela; Sweet, Monica

    2012-02-01

    This study evaluated the extent to which the language of intervention, the child's development in Spanish, and the effects of English vocabulary, use, proficiency, and exposure predict differences in the rates of acquisition of English in Latino children with specific language impairment (SLI). In this randomized controlled trial, 188 Latino preschoolers with SLI participated in a small-group academic enrichment program for 12 weeks and were followed up 3 and 5 months later. Children were randomly assigned to either a bilingual or an English-only program. Predictors of English growth included measures of Spanish language skills and English vocabulary, use, proficiency, and exposure. Performance on English outcomes (i.e., picture description and narrative sample) was assessed over time. A series of longitudinal models were tested via multilevel modeling with baseline and posttreatment measures nested within child. Children demonstrated growth on the English outcomes over time. The language of intervention, Spanish skills, English vocabulary, and English use significantly predicted differences in rates of growth across children for specific measures of English development. This study underscores the role of the child's first language skills, the child's level of English vocabulary development, and level of English use for predicting differences in English acquisition in Latino preschoolers with SLI. These factors should be carefully considered in making clinical decisions.

  11. Current algebra and bosonization in three dimensions

    International Nuclear Information System (INIS)

    Le Guillou, J.C.; Schaposnik, F.A.

    1996-01-01

    We consider the fermion-boson mapping in three dimensional space-time, in the Abelian case, from the current algebra point of view. We show that in a path-integral framework one can derive a general bosonization recipe leading, in the bosonic language, to the correct equal-time current commutators of the original free fermionic theory. Copyright copyright 1996 Academic Press, Inc

  12. Toward robust scalable algebraic multigrid solvers

    International Nuclear Information System (INIS)

    Waisman, Haim; Schroder, Jacob; Olson, Luke; Hiriyur, Badri; Gaidamour, Jeremie; Siefert, Christopher; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

    2010-01-01

    This talk highlights some multigrid challenges that arise from several application areas including structural dynamics, fluid flow, and electromagnetics. A general framework is presented to help introduce and understand algebraic multigrid methods based on energy minimization concepts. Connections between algebraic multigrid prolongators and finite element basis functions are made to explored. It is shown how the general algebraic multigrid framework allows one to adapt multigrid ideas to a number of different situations. Examples are given corresponding to linear elasticity and specifically in the solution of linear systems associated with extended finite elements for fracture problems.

  13. Algebraic reasoning and bat-and-ball problem variants: Solving isomorphic algebra first facilitates problem solving later.

    Science.gov (United States)

    Hoover, Jerome D; Healy, Alice F

    2017-12-01

    The classic bat-and-ball problem is used widely to measure biased and correct reasoning in decision-making. University students overwhelmingly tend to provide the biased answer to this problem. To what extent might reasoners be led to modify their judgement, and, more specifically, is it possible to facilitate problem solution by prompting participants to consider the problem from an algebraic perspective? One hundred ninety-seven participants were recruited to investigate the effect of algebraic cueing as a debiasing strategy on variants of the bat-and-ball problem. Participants who were cued to consider the problem algebraically were significantly more likely to answer correctly relative to control participants. Most of this cueing effect was confined to a condition that required participants to solve isomorphic algebra equations corresponding to the structure of bat-and-ball question types. On a subsequent critical question with differing item and dollar amounts presented without a cue, participants were able to generalize the learned information to significantly reduce overall bias. Math anxiety was also found to be significantly related to bat-and-ball problem accuracy. These results suggest that, under specific conditions, algebraic reasoning is an effective debiasing strategy on bat-and-ball problem variants, and provide the first documented evidence for the influence of math anxiety on Cognitive Reflection Test performance.

  14. Modular Domain-Specific Language Components in Scala

    DEFF Research Database (Denmark)

    Hofer, Christian; Ostermann, Klaus

    2010-01-01

    Programs in domain-­specific embedded languages (DSELs) can be represented in the host language in different ways, for instance implicitly as libraries, or explicitly in the form of abstract syntax trees. Each of these representations has its own strengths and weaknesses. The implicit approach ha...... or transformation. We propose a new design for implementing DSELs in Scala which makes it easy to use different program representations at the same time. It enables the DSL implementor to define modular language components and to compose transformations and interpretations for them....

  15. Extended Virasoro algebra and algebra of area preserving diffeomorphisms

    International Nuclear Information System (INIS)

    Arakelyan, T.A.

    1990-01-01

    The algebra of area preserving diffeomorphism plays an important role in the theory of relativistic membranes. It is pointed out that the relation between this algebra and the extended Virasoro algebra associated with the generalized Kac-Moody algebras G(T 2 ). The highest weight representation of these infinite-dimensional algebras as well as of their subalgebras is studied. 5 refs

  16. An application of the division algebras, Jordan algebras and split composition algebras

    International Nuclear Information System (INIS)

    Foot, R.; Joshi, G.C.

    1992-01-01

    It has been established that the covering group of the Lorentz group in D = 3, 4, 6, 10 can be expressed in a unified way, based on the four composition division algebras R, C, Q and O. In this paper, the authors discuss, in this framework, the role of the complex numbers of quantum mechanics. A unified treatment of quantum-mechanical spinors is given. The authors provide an explicit demonstration that the vector and spinor transformations recently constructed from a subgroup of the reduced structure group of the Jordan algebras M n 3 are indeed the Lorentz transformations. The authors also show that if the division algebras in the construction of the covering groups of the Lorentz groups in D = 3, 4, 6, 10 are replaced by the split composition algebras, then the sequence of groups SO(2, 2), SO(3, 3) and SO(5, 5) result. The analysis is presumed to be self-contained as the relevant aspects of the division algebras and Jordan algebras are reviewed. Some applications to physical theory are indicated

  17. Interactions Between Representation Ttheory, Algebraic Topology and Commutative Algebra

    CERN Document Server

    Pitsch, Wolfgang; Zarzuela, Santiago

    2016-01-01

    This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest dev...

  18. Phonological deficits in specific language impairment and developmental dyslexia: towards a multidimensional model

    Science.gov (United States)

    Ramus, Franck; Marshall, Chloe R.; Rosen, Stuart

    2013-01-01

    An on-going debate surrounds the relationship between specific language impairment and developmental dyslexia, in particular with respect to their phonological abilities. Are these distinct disorders? To what extent do they overlap? Which cognitive and linguistic profiles correspond to specific language impairment, dyslexia and comorbid cases? At least three different models have been proposed: the severity model, the additional deficit model and the component model. We address this issue by comparing children with specific language impairment only, those with dyslexia-only, those with specific language impairment and dyslexia and those with no impairment, using a broad test battery of language skills. We find that specific language impairment and dyslexia do not always co-occur, and that some children with specific language impairment do not have a phonological deficit. Using factor analysis, we find that language abilities across the four groups of children have at least three independent sources of variance: one for non-phonological language skills and two for distinct sets of phonological abilities (which we term phonological skills versus phonological representations). Furthermore, children with specific language impairment and dyslexia show partly distinct profiles of phonological deficit along these two dimensions. We conclude that a multiple-component model of language abilities best explains the relationship between specific language impairment and dyslexia and the different profiles of impairment that are observed. PMID:23413264

  19. Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

    Science.gov (United States)

    Verburgt, Lukas M

    2016-01-01

    This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.

  20. Experimental analysis of specification language impact on NPP software diversity

    International Nuclear Information System (INIS)

    Yoo, Chang Sik; Seong, Poong Hyun

    1998-01-01

    When redundancy and diversity is applied in NPP digital computer system, diversification of system software may be a critical point for the entire system dependability. As the means of enhancing software diversity, specification language diversity is suggested in this study. We set up a simple hypothesis for the specification language impact on common errors, and an experiment based on NPP protection system application was performed. Experiment result showed that this hypothesis could be justified and specification language diversity is effective in overcoming software common mode failure problem

  1. Electrical brain responses in language-impaired children reveal grammar-specific deficits.

    Directory of Open Access Journals (Sweden)

    Elisabeth Fonteneau

    2008-03-01

    Full Text Available Scientific and public fascination with human language have included intensive scrutiny of language disorders as a new window onto the biological foundations of language and its evolutionary origins. Specific language impairment (SLI, which affects over 7% of children, is one such disorder. SLI has received robust scientific attention, in part because of its recent linkage to a specific gene and loci on chromosomes and in part because of the prevailing question regarding the scope of its language impairment: Does the disorder impact the general ability to segment and process language or a specific ability to compute grammar? Here we provide novel electrophysiological data showing a domain-specific deficit within the grammar of language that has been hitherto undetectable through behavioural data alone.We presented participants with Grammatical(G-SLI, age-matched controls, and younger child and adult controls, with questions containing syntactic violations and sentences containing semantic violations. Electrophysiological brain responses revealed a selective impairment to only neural circuitry that is specific to grammatical processing in G-SLI. Furthermore, the participants with G-SLI appeared to be partially compensating for their syntactic deficit by using neural circuitry associated with semantic processing and all non-grammar-specific and low-level auditory neural responses were normal.The findings indicate that grammatical neural circuitry underlying language is a developmentally unique system in the functional architecture of the brain, and this complex higher cognitive system can be selectively impaired. The findings advance fundamental understanding about how cognitive systems develop and all human language is represented and processed in the brain.

  2. Verifying Process Algebra Proofs in Type Theory

    NARCIS (Netherlands)

    Sellink, M.P.A.

    In this paper we study automatic verification of proofs in process algebra. Formulas of process algebra are represented by types in typed λ-calculus. Inhabitants (terms) of these types represent proofs. The specific typed λ-calculus we use is the Calculus of Inductive Constructions as implemented

  3. Monomial algebras

    CERN Document Server

    Villarreal, Rafael

    2015-01-01

    The book stresses the interplay between several areas of pure and applied mathematics, emphasizing the central role of monomial algebras. It unifies the classical results of commutative algebra with central results and notions from graph theory, combinatorics, linear algebra, integer programming, and combinatorial optimization. The book introduces various methods to study monomial algebras and their presentation ideals, including Stanley-Reisner rings, subrings and blowup algebra-emphasizing square free quadratics, hypergraph clutters, and effective computational methods.

  4. Algebra

    CERN Document Server

    Tabak, John

    2004-01-01

    Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries, and offers biographical data on the key figures. Concise and comprehensive text accompanied by many illustrations presents the ideas and historical development of algebra, showcasing the relevance and evolution of this branch of mathematics.

  5. [From Algebra as art to School Algebra : The textbooks written by Pierre de La Ramée, Bernard Salignac and Lazare Schöner].

    Science.gov (United States)

    Loget, François

    2011-01-01

    Bernard Salignac and Lazare Schöner both published a treatise based on La Ramée's Algebra. Why did they endeavour to republish a book that their master had abandoned ? What changes did they make in the original ? They turned algebra into apedagogical discipline at a time when Ramism was making its presence felt in some Northern European educational establishments. Salignac took La Ramée's thoughts concerning the language of mathematics further and offered an original and precocious contribution to what I call the "scriptural turn" of mathematics at the end of the 16(th) century.

  6. Iwahori-Hecke algebras and Schur algebras of the symmetric group

    CERN Document Server

    Mathas, Andrew

    1999-01-01

    This volume presents a fully self-contained introduction to the modular representation theory of the Iwahori-Hecke algebras of the symmetric groups and of the q-Schur algebras. The study of these algebras was pioneered by Dipper and James in a series of landmark papers. The primary goal of the book is to classify the blocks and the simple modules of both algebras. The final chapter contains a survey of recent advances and open problems. The main results are proved by showing that the Iwahori-Hecke algebras and q-Schur algebras are cellular algebras (in the sense of Graham and Lehrer). This is proved by exhibiting natural bases of both algebras which are indexed by pairs of standard and semistandard tableaux respectively. Using the machinery of cellular algebras, which is developed in Chapter 2, this results in a clean and elegant classification of the irreducible representations of both algebras. The block theory is approached by first proving an analogue of the Jantzen sum formula for the q-Schur algebras. T...

  7. Algebra of pseudo-differential operators over C*-algebra

    International Nuclear Information System (INIS)

    Mohammad, N.

    1982-08-01

    Algebras of pseudo-differential operators over C*-algebras are studied for the special case when in Hormander class Ssub(rho,delta)sup(m)(Ω) Ω = Rsup(n); rho = 1, delta = 0, m any real number, and the C*-algebra is infinite dimensional non-commutative. The space B, i.e. the set of A-valued C*-functions in Rsup(n) (or Rsup(n) x Rsup(n)) whose derivatives are all bounded, plays an important role. A denotes C*-algebra. First the operator class Ssub(phi,0)sup(m) is defined, and through it, the class Lsub(1,0)sup(m) of pseudo-differential operators. Then the basic asymptotic expansion theorems concerning adjoint and product of operators of class Ssub(1,0)sup(m) are stated. Finally, proofs are given of L 2 -continuity theorem and the main theorem, which states that algebra of all pseudo-differential operators over C*-algebras is itself C*-algebra

  8. Commutative algebra with a view toward algebraic geometry

    CERN Document Server

    Eisenbud, David

    1995-01-01

    Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algeb...

  9. Interoperable domain-specific languages families for code generation

    Czech Academy of Sciences Publication Activity Database

    Malohlava, M.; Plášil, F.; Bureš, Tomáš; Hnětynka, P.

    2013-01-01

    Roč. 43, č. 5 (2013), s. 479-499 ISSN 0038-0644 R&D Projects: GA ČR GD201/09/H057 EU Projects: European Commission(XE) ASCENS 257414 Grant - others:GA AV ČR(CZ) GAP103/11/1489 Program:FP7 Institutional research plan: CEZ:AV0Z10300504 Keywords : code generation * domain specific languages * models reuse * extensible languages * specification * program synthesis Subject RIV: JC - Computer Hardware ; Software Impact factor: 1.148, year: 2013

  10. Analogical Reasoning in Children with Specific Language Impairment

    Science.gov (United States)

    Leroy, Sandrine; Parisse, Christophe; Maillart, Christelle

    2012-01-01

    Usage-based theory considers analogical reasoning as a cognitive process required in language development. We hypothesized that difficulties with analogical reasoning could hinder the abstraction of construction schemas, thus slowing down morphosyntactic development for children with specific language impairment (SLI). We also hypothesized, in…

  11. Language Cultural Specificity of the Language Units “Cat” and “Dog” in English and Chinese Languages

    Directory of Open Access Journals (Sweden)

    Жером Багана

    2016-12-01

    Full Text Available The article deals with the national and cultural features of zoonyms “cat” and “dog” in English and Chinese languages. The authors point out zoonyms’ main characteristics and their national cultural originality. Zoonyms represent the special features of national linguistic world view and values in the comparative analysis’ aspect The article represents interpretation of the language units in the monolingual explanatory dictionaries. The dictionary definitions of the terms phraseology and zoonym are given. The research is devoted to phraseology in the English and Chinese languages. The historical notes about the attitude toward cats and dogs in Britain and China are shown. Also some peculiarities of zoonyms function in English and Chinese animal fairy-tales are observed. Based on the differences the authors notice differences of phraseology between zoonyms “cat” and “dog”. Some examples in the English and Chinese languages are observed. The analysis represents universal and national specific semantic features of the present units in the languages so far as phraseology contains the most vivid representation of the national-cultural specificity of world view, connotative features and values peoples in Europe and Asia.

  12. Jordan algebras versus C*- algebras

    International Nuclear Information System (INIS)

    Stormer, E.

    1976-01-01

    The axiomatic formulation of quantum mechanics and the problem of whether the observables form self-adjoint operators on a Hilbert space, are discussed. The relation between C*- algebras and Jordan algebras is studied using spectral theory. (P.D.)

  13. Fundamentals of algebraic graph transformation

    CERN Document Server

    Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele

    2006-01-01

    Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...

  14. Australian Curriculum Linked Lessons: Reasoning in Number and Algebra

    Science.gov (United States)

    Day, Lorraine

    2014-01-01

    The Reasoning Proficiency in number and algebra is about children making sense of the mathematics by explaining their thinking, giving reasons for their decisions and describing mathematical situations and concepts. Lorraine Day notes, children need to be able to speak, read and write the language of mathematics while investigating pattern and…

  15. HAL/S language specification. Version IR-542

    Science.gov (United States)

    1980-01-01

    The formal HAL/S language specification is documented with particular referral to the essentials of HAL/S syntax and semantics. The language is intended to satisfy virtually all of the flight software requirements of NASA programs. To achieve this, HAL/S incorporates a wide range of features, including applications oriented data types and organizations, real time control mechanisms, and constructs for systems programming tasks.

  16. Interaction of Language Processing and Motor Skill in Children with Specific Language Impairment

    Science.gov (United States)

    DiDonato Brumbach, Andrea C.; Goffman, Lisa

    2014-01-01

    Purpose: To examine how language production interacts with speech motor and gross and fine motor skill in children with specific language impairment (SLI). Method: Eleven children with SLI and 12 age-matched peers (4-6 years) produced structurally primed sentences containing particles and prepositions. Utterances were analyzed for errors and for…

  17. Implicative Algebras

    African Journals Online (AJOL)

    Tadesse

    In this paper we introduce the concept of implicative algebras which is an equivalent definition of lattice implication algebra of Xu (1993) and further we prove that it is a regular Autometrized. Algebra. Further we remark that the binary operation → on lattice implicative algebra can never be associative. Key words: Implicative ...

  18. Lexical Specificity Training Effects in Second Language Learners

    Science.gov (United States)

    Janssen, Caressa; Segers, Eliane; McQueen, James M.; Verhoeven, Ludo

    2015-01-01

    Children who start formal education in a second language may experience slower vocabulary growth in that language and subsequently experience disadvantages in literacy acquisition. The current study asked whether lexical specificity training can stimulate bilingual children's phonological awareness, which is considered to be a precursor to…

  19. Language-specific memory for everyday arithmetic facts in Chinese-English bilinguals.

    Science.gov (United States)

    Chen, Yalin; Yanke, Jill; Campbell, Jamie I D

    2016-04-01

    The role of language in memory for arithmetic facts remains controversial. Here, we examined transfer of memory training for evidence that bilinguals may acquire language-specific memory stores for everyday arithmetic facts. Chinese-English bilingual adults (n = 32) were trained on different subsets of simple addition and multiplication problems. Each operation was trained in one language or the other. The subsequent test phase included all problems with addition and multiplication alternating across trials in two blocks, one in each language. Averaging over training language, the response time (RT) gains for trained problems relative to untrained problems were greater in the trained language than in the untrained language. Subsequent analysis showed that English training produced larger RT gains for trained problems relative to untrained problems in English at test relative to the untrained Chinese language. In contrast, there was no evidence with Chinese training that problem-specific RT gains differed between Chinese and the untrained English language. We propose that training in Chinese promoted a translation strategy for English arithmetic (particularly multiplication) that produced strong cross-language generalization of practice, whereas training in English strengthened relatively weak, English-language arithmetic memories and produced little generalization to Chinese (i.e., English training did not induce an English translation strategy for Chinese language trials). The results support the existence of language-specific strengthening of memory for everyday arithmetic facts.

  20. Open algebraic surfaces

    CERN Document Server

    Miyanishi, Masayoshi

    2000-01-01

    Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. There is a long history of research on projective algebraic surfaces, and there exists a beautiful Enriques-Kodaira classification of such surfaces. The research accumulated by Ramanujan, Abhyankar, Moh, and Nagata and others has established a classification theory of open algebraic surfaces comparable to the Enriques-Kodaira theory. This research provides powerful methods to study the geometry and topology of open algebraic surfaces. The theory of open algebraic surfaces is applicable not only to algebraic geometry, but also to other fields, such as commutative algebra, invariant theory, and singularities. This book contains a comprehensive account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine surfaces. Prerequisite to understanding the text is a basic b...

  1. Separable algebras

    CERN Document Server

    Ford, Timothy J

    2017-01-01

    This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.

  2. n-ary algebras: a review with applications

    International Nuclear Information System (INIS)

    De Azcarraga, J A; Izquierdo, J M

    2010-01-01

    This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. 3-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert-Gustavsson model. As a result, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations (it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A 4 model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization. (topical

  3. Phonological working memory and auditory processing speed in children with specific language impairment

    Directory of Open Access Journals (Sweden)

    Fatemeh Haresabadi

    2015-02-01

    Full Text Available Background and Aim: Specific language impairment (SLI, one variety of developmental language disorder, has attracted much interest in recent decades. Much research has been conducted to discover why some children have a specific language impairment. So far, research has failed to identify a reason for this linguistic deficiency. Some researchers believe language disorder causes defects in phonological working memory and affects auditory processing speed. Therefore, this study reviews the results of research investigating these two factors in children with specific language impairment.Recent Findings: Studies have shown that children with specific language impairment face constraints in phonological working memory capacity. Memory deficit is one possible cause of linguistic disorder in children with specific language impairment. However, in these children, disorder in information processing speed is observed, especially regarding the auditory aspect.Conclusion: Much more research is required to adequately explain the relationship between phonological working memory and auditory processing speed with language. However, given the role of phonological working memory and auditory processing speed in language acquisition, a focus should be placed on phonological working memory capacity and auditory processing speed in the assessment and treatment of children with a specific language impairment.

  4. Towards tool support for spreadsheet-based domain-specific languages

    DEFF Research Database (Denmark)

    Adam, Marian Sorin; Schultz, Ulrik Pagh

    2015-01-01

    Spreadsheets are commonly used by non-programmers to store data in a structured form, this data can in some cases be considered to be a program in a domain-specific language (DSL). Unlike ordinary text-based domain-specific languages, there is however currently no formalism for expressing...... the syntax of such spreadsheet-based DSLs (SDSLs), and there is no tool support for automatically generating language infrastructure such as parsers and IDE support. In this paper we define a simple notion of two-dimensional grammars for SDSLs, and show how such grammars can be used for automatically...

  5. Generalized EMV-Effect Algebras

    Science.gov (United States)

    Borzooei, R. A.; Dvurečenskij, A.; Sharafi, A. H.

    2018-04-01

    Recently in Dvurečenskij and Zahiri (2017), new algebraic structures, called EMV-algebras which generalize both MV-algebras and generalized Boolean algebras, were introduced. We present equivalent conditions for EMV-algebras. In addition, we define a partial algebraic structure, called a generalized EMV-effect algebra, which is close to generalized MV-effect algebras. Finally, we show that every generalized EMV-effect algebra is either an MV-effect algebra or can be embedded into an MV-effect algebra as a maximal ideal.

  6. Special set linear algebra and special set fuzzy linear algebra

    OpenAIRE

    Kandasamy, W. B. Vasantha; Smarandache, Florentin; Ilanthenral, K.

    2009-01-01

    The authors in this book introduce the notion of special set linear algebra and special set fuzzy Linear algebra, which is an extension of the notion set linear algebra and set fuzzy linear algebra. These concepts are best suited in the application of multi expert models and cryptology. This book has five chapters. In chapter one the basic concepts about set linear algebra is given in order to make this book a self contained one. The notion of special set linear algebra and their fuzzy analog...

  7. Math remediation for the college bound how teachers can close the gap, from the basics through algebra

    CERN Document Server

    Khatri, Daryao

    2011-01-01

    Algebra is the language that must be mastered for any course that uses math because it is the gateway for entry into any science, technology, engineering, and mathematics (STEM) discipline. This book fosters mastery of critical math and algebraic concepts and skills essential to all of the STEM disciplines and some of the social sciences.

  8. Banach Synaptic Algebras

    Science.gov (United States)

    Foulis, David J.; Pulmannov, Sylvia

    2018-04-01

    Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Størmer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C∗-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW∗-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.

  9. Hamiltonian reduction of Kac-Moody algebras

    International Nuclear Information System (INIS)

    Kimura, Kazuhiro

    1991-01-01

    Feigin-Fucks construction provides us methods to treat rational conformal theories in terms of free fields. This formulation enables us to describe partition functions and correlation functions in the Fock space of free fields. There are several attempt extending to supersymmetric theories. In this report authors present an explicit calculation of the Hamiltonian reduction based on the free field realization. In spite of the results being well-known, the relations can be clearly understood in the language of bosons. Authors perform the hamiltonian reduction by imposing a constraint with appropriate gauge transformations which preserve the constraint. This approaches enables us to gives the geometric interpretation of super Virasoro algebras and relations of the super gravity. In addition, author discuss the properties of quantum groups by using the explicit form of the group element. It is also interesting to extend to super Kac-Moody algebras. (M.N.)

  10. Grassmann algebras

    International Nuclear Information System (INIS)

    Garcia, R.L.

    1983-11-01

    The Grassmann algebra is presented briefly. Exponential and logarithm of matrices functions, whose elements belong to this algebra, are studied with the help of the SCHOONSCHIP and REDUCE 2 algebraic manipulators. (Author) [pt

  11. The perception and expression of verb morphology in bilinguals with specific language impairment

    Directory of Open Access Journals (Sweden)

    Hourieh Ahadi

    2014-04-01

    Full Text Available Background and Aim: Most of the researches are about bilingual children with specific language impairment and importance of it in recognition and treatment. This study aimed to assess verb morphology in bilinguals with specific language impairment (SLI and compare them with normal bilinguals.Methods: Six bilingual (Azeri and Persian children with specific language impairment at the age of 7-8 years were collected from clinics of Tehran, Iran. They were evaluated about verb morphology using narrative speech and specific language impairment test and then, compared with six age-matched and six other language-matched children as control group. Children with specific language impairment were diagnosed by exhibiting a significant delay (more than one year in language that can not be explained by intelligence deficits, hearing loss or visual impairment. We used Man-Whitney test for comparing the groups.Results: Bilingual children with specific language impairment had delay in comparison with their age-matched group in subject-verb agreement (p=0.020 and articulating tense morphemes (p=0.019. They also had meaningful delay in using proper tense of verbs (past, present, and future in comparison with language-matched control group (p=0.029.Conclusion: Comparison of typical development of bilingual children and bilinguals with specific language impairment shows that verb morphology is a good clinical marker for diagnosing and treatment of these children.

  12. Algebraic geometry

    CERN Document Server

    Lefschetz, Solomon

    2005-01-01

    An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

  13. Converting nested algebra expressions into flat algebra expressions

    NARCIS (Netherlands)

    Paredaens, J.; Van Gucht, D.

    1992-01-01

    Nested relations generalize ordinary flat relations by allowing tuple values to be either atomic or set valued. The nested algebra is a generalization of the flat relational algebra to manipulate nested relations. In this paper we study the expressive power of the nested algebra relative to its

  14. Fibered F-Algebra

    OpenAIRE

    Kleyn, Aleks

    2007-01-01

    The concept of F-algebra and its representation can be extended to an arbitrary bundle. We define operations of fibered F-algebra in fiber. The paper presents the representation theory of of fibered F-algebra as well as a comparison of representation of F-algebra and of representation of fibered F-algebra.

  15. Which Preschool Children with Specific Language Impairment Receive Language Intervention?

    Science.gov (United States)

    Wittke, Kacie; Spaulding, Tammie J.

    2018-01-01

    Purpose: Potential biases in service provision for preschool children with specific language impairment (SLI) were explored. Method: In Study 1, children with SLI receiving treatment (SLI-T) and those with SLI not receiving treatment (SLI-NT) were compared on demographic characteristics and developmental abilities. Study 2 recruited children with…

  16. The structure of the super-W sub infinity (. lambda. ) algebra

    Energy Technology Data Exchange (ETDEWEB)

    Bergshoeff, E [CERN, Geneva (Switzerland). Theory Div.; Wit, B de [Utrecht Univ. (Netherlands). Inst. for Theoretical Physics; Vasiliev, M [AN SSSR, Moscow (USSR). Theoretical Dept., P.N. Lebedev Inst.

    1991-12-02

    We give a comprehensive treatment of the super-W{sub {infinity}}({lambda}) algebra, an extension of the super-Virasoro algebra that contains generators of spin S {>=} 1/2. The parameter {lambda} defines the embedding of the Virasoro subalgebra. We describe how to obtain the super-W{sub {infinity}}({lambda}) algebra from the associative algebra of superspace differential operators. We discuss the structure of this associative algebra and its relation with the so-called wedge algebra, in which the generators for given spin are restricted to finite-dimensional representations of sl(2). From the super-W{sub {infinity}}({lambda}) algebra one can obtain a variety of W{sub {infinity}} algebras by consistent truncations for specific values of {lambda}. Without truncation the algebras are formally isomorphic for different values of {lambda}. We present a realization in terms of the currents of a supersymmetric bc system. (orig.).

  17. The bubble algebra: structure of a two-colour Temperley-Lieb Algebra

    International Nuclear Information System (INIS)

    Grimm, Uwe; Martin, Paul P

    2003-01-01

    We define new diagram algebras providing a sequence of multiparameter generalizations of the Temperley-Lieb algebra, suitable for the modelling of dilute lattice systems of two-dimensional statistical mechanics. These algebras give a rigorous foundation to the various 'multi-colour algebras' of Grimm, Pearce and others. We determine the generic representation theory of the simplest of these algebras, and locate the nongeneric cases (at roots of unity of the corresponding parameters). We show by this example how the method used (Martin's general procedure for diagram algebras) may be applied to a wide variety of such algebras occurring in statistical mechanics. We demonstrate how these algebras may be used to solve the Yang-Baxter equations

  18. Language Teachers' Target Language Project: Language for Specific Purposes of Language Teaching

    Science.gov (United States)

    Korenev, Alexey; Westbrook, Carolyn; Merry, Yvonne; Ershova, Tatiana

    2016-01-01

    The Language Teachers' Target Language project (LTTL) aims to describe language teachers' target language use domain (Bachman & Palmer 2010) and to develop a language test for future teachers of English. The team comprises four researchers from Moscow State University (MSU) and Southampton Solent University.

  19. Language specific bootstraps for UG categories

    NARCIS (Netherlands)

    van Kampen, N.J.

    2005-01-01

    This paper argues that the universal categories N/V are not applied to content words before the grammatical markings for reference D(eterminers) and predication I(nflection) have been acquired (van Kampen, 1997, contra Pinker, 1984). Child grammar starts as proto-grammar with language-specific

  20. Forum on Specifications and Design Languages 2012

    CERN Document Server

    2014-01-01

    This book brings together a selection of the best papers from the fifteenth edition of the Forum on specification and Design Languages Conference (FDL), which was held in September 2012 at Vienna University of Technology, Vienna, Austria.  FDL is a well-established international forum devoted to dissemination of research results, practical experiences and new ideas in the application of specification, design and verification languages to the design, modeling and verification of integrated circuits, complex hardware/software embedded systems, and mixed-technology systems.  ·         Covers Assertion Based Design, Verification & Debug; ·         Includes language-based modeling and design techniques for embedded systems; ·         Covers design, modeling and verification of mixed physical domain and mixed signal systems that include significant analog parts in electrical and non-electrical domains; ·         Includes formal and semi-formal system level design methods fo...

  1. Predictors of Growth or Attrition of the First Language in Latino Children with Specific Language Impairment

    Science.gov (United States)

    Simon-Cereijido, Gabriela; Gutierrez-Clellen, Vera F.; Sweet, Monica

    2013-01-01

    We investigated the factors that may help understand the differential rates of language development in the home language (i.e., Spanish) of Latino preschoolers with specific language impairment. Children were randomly assigned to either bilingual or English-only small group interventions and followed from preschool to kindergarten. Predictors of…

  2. The Continuing Evolution of Languages for Specific Purposes

    Science.gov (United States)

    Grosse, Christine Uber; Voght, Geoffrey M.

    2012-01-01

    This overview to "The Modern Language Journal"'s Focus Issue on Languages for Specific Purposes (LSP) takes a fresh look at issues examined in a 1991 article by Grosse and Voght. Reflecting on change drivers and growth in LSP, the authors comment on current challenges to the field and future research needs. Their remarks are based on new insights…

  3. Algebraic monoids, group embeddings, and algebraic combinatorics

    CERN Document Server

    Li, Zhenheng; Steinberg, Benjamin; Wang, Qiang

    2014-01-01

    This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids.   Topics presented include:   v  structure and representation theory of reductive algebraic monoids v  monoid schemes and applications of monoids v  monoids related to Lie theory v  equivariant embeddings of algebraic groups v  constructions and properties of monoids from algebraic combinatorics v  endomorphism monoids induced from vector bundles v  Hodge–Newton decompositions of reductive monoids   A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semigroups are strongly π-regular.   Graduate students as well a...

  4. Developing Bigraphical Languages

    DEFF Research Database (Denmark)

    Damgaard, Troels Christoffer

    In this dissertation, we study bigraphical languages—languages based on the theory for bigraphs and bigraphical reactive systems developed by Milner and coworkers. We begin by examining algebraic theory for binding bigraphs. We give a term language for binding bigraphs and develop a complete......, a prototype tool for experimenting with bigraphical reactive systems. In a second line of work, we study bigraphical reactive systems as a vehicle for developing a language to model biochemical reactions at the level of cells and proteins. We discuss and isolate B,R-calculi, a family of bigraphical reactive...

  5. Specifying the Behaviour of Python Programs: Language and Basic Examples

    Directory of Open Access Journals (Sweden)

    2010-04-01

    Full Text Available This manuscript describe BeSSY, a function-centric language for formal behavioural specification that requires no more than high-school mathematics on arithmetic, functions, Boolean algebra and sets theory. An object can be modelled as a union of data sets and functions whereas inherited object can be modelled as a union of supersets and a set of object-specific functions. Python list and dictionary operations will be specified in BeSSY for illustration.

  6. Autistic symptomatology and language ability in autism spectrum disorder and specific language impairment.

    Science.gov (United States)

    Loucas, Tom; Charman, Tony; Pickles, Andrew; Simonoff, Emily; Chandler, Susie; Meldrum, David; Baird, Gillian

    2008-11-01

    Autism spectrum disorders (ASD) and specific language impairment (SLI) are common developmental disorders characterised by deficits in language and communication. The nature of the relationship between them continues to be a matter of debate. This study investigates whether the co-occurrence of ASD and language impairment is associated with differences in severity or pattern of autistic symptomatology or language profile. Participants (N = 97) were drawn from a total population cohort of 56,946 screened as part of study to ascertain the prevalence of ASD, aged 9 to 14 years. All children received an ICD-10 clinical diagnosis of ASD or No ASD. Children with nonverbal IQ > or =80 were divided into those with a language impairment (language score of 77 or less) and those without, creating three groups: children with ASD and a language impairment (ALI; N = 41), those with ASD and but no language impairment (ANL; N = 31) and those with language impairment but no ASD (SLI; N = 25). Children with ALI did not show more current autistic symptoms than those with ANL. Children with SLI were well below the threshold for ASD. Their social adaptation was higher than the ASD groups, but still nearly 2 SD below average. In ALI the combination of ASD and language impairment was associated with weaker functional communication and more severe receptive language difficulties than those found in SLI. Receptive and expressive language were equally impaired in ALI, whereas in SLI receptive language was stronger than expressive. Co-occurrence of ASD and language impairment is not associated with increased current autistic symptomatology but appears to be associated with greater impairment in receptive language and functional communication.

  7. Leavitt path algebras

    CERN Document Server

    Abrams, Gene; Siles Molina, Mercedes

    2017-01-01

    This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and...

  8. Zeta functional equation on Jordan algebras of type II

    International Nuclear Information System (INIS)

    Kayoya, J.B.

    2003-10-01

    Using the Jordan algebras method, specially the properties of Peirce decomposition and the Frobenius transformation, we compute the coefficients of the zeta functional equation, in the case of Jordan algebras of Type II. As particular cases of our result, we can cite the case of V M (n, R) studied by Gelbart and Godement-Jacquet, and the case of V Herm(3, O s ) studied by Muro. Let us also mention, that recently, Bopp and Rubenthaler have obtained a more general result on the zeta functional equation by using methods based on the algebraic properties of regular graded algebras which are in one to one correspondence with simple Jordan algebras. The method used in this paper is a direct application of specific properties of Jordan algebras of Type H. (author)

  9. Influence of Phonology on Morpho-Syntax in Romance Languages in Children with Specific Language Impairment (SLI)

    Science.gov (United States)

    Aguilar-Mediavilla, Eva; Sanz-Torrent, Monica; Serra-Raventos, Miquel

    2007-01-01

    Background: The profiles of children with Specific Language Impairment (SLI) differ greatly according to the language they speak. The Surface Hypothesis attempts to explain these differences through the theory that children with SLI will incorrectly produce elements in their language with low phonological weights or that are produced in a…

  10. Algebraic Modeling of Topological and Computational Structures and Applications

    CERN Document Server

    Theodorou, Doros; Stefaneas, Petros; Kauffman, Louis

    2017-01-01

    This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging). The main mathematical focus throughout the book is on algebraic modeling with particular emphasis on braid groups. The research methods include algebraic modeling using topological structures, such as knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address the simulation of polymer chains and ionic liquids, as well as the modeling of natural phenomena via topological surgery. The treatment of computational structures, including finite fields and cryptography, focuses on the development of novel techniques. These techniques can be applied to the design of algebraic specifications for systems modeling and verification. This book is the outcome of a w...

  11. Experimental analysis of specification language diversity impact on NPP software diversity

    International Nuclear Information System (INIS)

    Yoo, Chang Sik

    1999-02-01

    In order to increase computer system reliability, software fault tolerance methods have been adopted to some safety critical systems including NPP. Prevention of software common mode failure is very crucial problem in software fault tolerance, but the effective method for this problem is not found yet. In our research, to find out an effective method for prevention of software common mode failure, the impact of specification language diversity on NPP software diversity was examined experimentally. Three specification languages were used to compose three requirements specifications, and programmers made twelve product codes from the specifications. From the product codes analysis, using fault diversity criteria, we concluded that diverse specification language method would enhance program diversity through diversification of requirements specification imperfections

  12. Approximation of complex algebraic numbers by algebraic numbers of bounded degree

    OpenAIRE

    Bugeaud, Yann; Evertse, Jan-Hendrik

    2007-01-01

    We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1. It follows from our investigations that for every positive integer n there are complex algebraic numbers of degree larger than n that are better approximable by algebraic numbers of degree at most n than almost all complex numbers. As it turns out, these numbers ar...

  13. Operadic formulation of topological vertex algebras and gerstenhaber or Batalin-Vilkovisky algebras

    International Nuclear Information System (INIS)

    Huang Yizhi

    1994-01-01

    We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak topological vertex algebra) by combining this operadic formulation with a theorem of Getzler (or of Cohen) which formulates Batalin-Vilkovisky algebras (or Gerstenhaber algebras) in terms of the homology of the framed little disk operad (or of the little disk operad). (orig.)

  14. Brain responses in 4-month-old infants are already language specific.

    Science.gov (United States)

    Friederici, Angela D; Friedrich, Manuela; Christophe, Anne

    2007-07-17

    Language is the most important faculty that distinguishes humans from other animals. Infants learn their native language fast and effortlessly during the first years of life, as a function of the linguistic input in their environment. Behavioral studies reported the discrimination of melodic contours [1] and stress patterns [2, 3] in 1-4-month-olds. Behavioral [4, 5] and brain measures [6-8] have shown language-independent discrimination of phonetic contrasts at that age. Language-specific discrimination, however, has been reported for phonetic contrasts only for 6-12-month-olds [9-12]. Here we demonstrate language-specific discrimination of stress patterns in 4-month-old German and French infants by using electrophysiological brain measures. We compare the processing of disyllabic words differing in their rhythmic structure, mimicking German words being stressed on the first syllable, e.g., pápa/daddy[13], and French ones being stressed on the second syllable, e.g., papá/daddy. Event-related brain potentials reveal that experience with German and French differentially affects the brain responses of 4-month-old infants, with each language group displaying a processing advantage for the rhythmic structure typical in its native language. These data indicate language-specific neural representations of word forms in the infant brain as early as 4 months of age.

  15. Quasi-superconformal algebras in two dimensions and hamiltonian reduction

    International Nuclear Information System (INIS)

    Romans, L.J.

    1991-01-01

    In the standard quantum hamiltonian reduction, constraining the SL(3, R) WZNW model leads to a model of Zamolodchikov's W 3 -symmetry. In recent work, Polyakov and Bershadsky have considered an alternative reduction which leads to a new algebra, W 3 2 , a nonlinear extension of the Virasoro algebra by a spin-1 current and two bosonic spin-3/2 currents. Motivated by this result, we display two new infinite series of nonlinear extended conformal algebras, containing 2N bosonic spin-3/2 currents and spin-1 Kac-Moody currents for either U(N) or Sp(2 N); the W 3 2 algebra appears as the N = 1 member of the U(N) series. We discuss the relationship between these algebras and the Knizhnik-Bershadsky superconformal algebras, and provide realisations in terms of free fields coupled to Kac-Moody currents. We propose a specific procedure for obtaining the algebras for general N through hamiltonian reduction. (orig.)

  16. Textese and use of texting by children with typical language development and Specific Language Impairment

    NARCIS (Netherlands)

    Blom, E.; van Dijk, C.; Vasić, N.; van Witteloostuijn, M.; Avrutin, S.

    The purpose of this study was to investigate texting and textese, which is the special register used for sending brief text messages, across children with typical development (TD) and children with Specific Language Impairment (SLI). Using elicitation techniques, texting and spoken language messages

  17. Textese and use of texting by children with typical language development and Specific Language Impairment

    NARCIS (Netherlands)

    Blom, W.B.T.; van Dijk, Chantal; Vasic, Nada; van Witteloostuijn, Merel; Avrutin, S.

    2017-01-01

    The purpose of this study was to investigate texting and textese, which is the special register used for sending brief text messages, across children with typical development (TD) and children with Specific Language Impairment (SLI). Using elicitation techniques, texting and spoken language messages

  18. Wn(2) algebras

    International Nuclear Information System (INIS)

    Feigin, B.L.; Semikhatov, A.M.

    2004-01-01

    We construct W-algebra generalizations of the sl-circumflex(2) algebra-W algebras W n (2) generated by two currents E and F with the highest pole of order n in their OPE. The n=3 term in this series is the Bershadsky-Polyakov W 3 (2) algebra. We define these algebras as a centralizer (commutant) of the Uqs-bar (n vertical bar 1) quantum supergroup and explicitly find the generators in a factored, 'Miura-like' form. Another construction of the W n (2) algebras is in terms of the coset sl-circumflex(n vertical bar 1)/sl-circumflex(n). The relation between the two constructions involves the 'duality' (k+n-1)(k'+n-1)=1 between levels k and k' of two sl-circumflex(n) algebras

  19. Developmental Associations between Working Memory and Language in Children with Specific Language Impairment: A Longitudinal Study

    Science.gov (United States)

    Vugs, Brigitte; Hendriks, Marc; Cuperus, Juliane; Knoors, Harry; Verhoeven, Ludo

    2017-01-01

    Purpose: This longitudinal study examined differences in the development of working memory (WM) between children with specific language impairment (SLI) and typically developing (TD) children. Further, it explored to what extent language at ages 7-8 years could be predicted by measures of language and/or WM at ages 4-5 years. Method: Thirty…

  20. The vacuum preserving Lie algebra of a classical W-algebra

    International Nuclear Information System (INIS)

    Feher, L.; Tsutsui, I.

    1993-07-01

    We simplify and generalize an argument due to Bowcock and Watts showing that one can associate a finite Lie algebra (the 'classical vacuum preserving algebra') containing the Moebius sl(2) subalgebra to any classical W-algebra. Our construction is based on a kinematical analysis of the Poisson brackets of quasi-fields. In the case of the W S G -subalgebra S of a simple Lie algebra G, we exhibit a natural isomorphism between this finite Lie algebra and G whereby the Moebius sl(2) is identified with S. (orig.)

  1. Nonflexible Lie-admissible algebras

    International Nuclear Information System (INIS)

    Myung, H.C.

    1978-01-01

    We discuss the structure of Lie-admissible algebras which are defined by nonflexible identities. These algebras largely arise from the antiflexible algebras, 2-varieties and associator dependent algebras. The nonflexible Lie-admissible algebras in our discussion are in essence byproducts of the study of nonassociative algebras defined by identities of degree 3. The main purpose is to discuss the classification of simple Lie-admissible algebras of nonflexible type

  2. On 2-Banach algebras

    International Nuclear Information System (INIS)

    Mohammad, N.; Siddiqui, A.H.

    1987-11-01

    The notion of a 2-Banach algebra is introduced and its structure is studied. After a short discussion of some fundamental properties of bivectors and tensor product, several classical results of Banach algebras are extended to the 2-Banach algebra case. A condition under which a 2-Banach algebra becomes a Banach algebra is obtained and the relation between algebra of bivectors and 2-normed algebra is discussed. 11 refs

  3. Phonological reduplication in sign language: rules rule

    Directory of Open Access Journals (Sweden)

    Iris eBerent

    2014-06-01

    Full Text Available Productivity—the hallmark of linguistic competence—is typically attributed to algebraic rules that support broad generalizations. Past research on spoken language has documented such generalizations in both adults and infants. But whether algebraic rules form part of the linguistic competence of signers remains unknown. To address this question, here we gauge the generalization afforded by American Sign Language (ASL. As a case study, we examine reduplication (X→XX—a rule that, inter alia, generates ASL nouns from verbs. If signers encode this rule, then they should freely extend it to novel syllables, including ones with features that are unattested in ASL. And since reduplicated disyllables are preferred in ASL, such rule should favor novel reduplicated signs. Novel reduplicated signs should thus be preferred to nonreduplicative controls (in rating, and consequently, such stimuli should also be harder to classify as nonsigns (in the lexical decision task. The results of four experiments support this prediction. These findings suggest that the phonological knowledge of signers includes powerful algebraic rules. The convergence between these conclusions and previous evidence for phonological rules in spoken language suggests that the architecture of the phonological mind is partly amodal.

  4. Algebra

    CERN Document Server

    Flanders, Harley

    1975-01-01

    Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered, together with exponentials and logarithms.Comprised of eight chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of a

  5. An Ada Linear-Algebra Software Package Modeled After HAL/S

    Science.gov (United States)

    Klumpp, Allan R.; Lawson, Charles L.

    1990-01-01

    New avionics software written more easily. Software package extends Ada programming language to include linear-algebra capabilities similar to those of HAL/S programming language. Designed for such avionics applications as Space Station flight software. In addition to built-in functions of HAL/S, package incorporates quaternion functions used in Space Shuttle and Galileo projects and routines from LINPAK solving systems of equations involving general square matrices. Contains two generic programs: one for floating-point computations and one for integer computations. Written on IBM/AT personal computer running under PC DOS, v.3.1.

  6. A Module Language for Typing by Contracts

    Science.gov (United States)

    Glouche, Yann; Talpin, Jean-Pierre; LeGuernic, Paul; Gautier, Thierry

    2009-01-01

    Assume-guarantee reasoning is a popular and expressive paradigm for modular and compositional specification of programs. It is becoming a fundamental concept in some computer-aided design tools for embedded system design. In this paper, we elaborate foundations for contract-based embedded system design by proposing a general-purpose module language based on a Boolean algebra allowing to define contracts. In this framework, contracts are used to negotiate the correctness of assumptions made on the definition of a component at the point where it is used and provides guarantees to its environment. We illustrate this presentation with the specification of a simplified 4-stroke engine model.

  7. Lukasiewicz-Moisil algebras

    CERN Document Server

    Boicescu, V; Georgescu, G; Rudeanu, S

    1991-01-01

    The Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory.This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and &THgr;-valued algebras are presented, as well as &THgr;-algebras with negation.Mathematicians interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research.

  8. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    Science.gov (United States)

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  9. Computing with impure numbers - Automatic consistency checking and units conversion using computer algebra

    Science.gov (United States)

    Stoutemyer, D. R.

    1977-01-01

    The computer algebra language MACSYMA enables the programmer to include symbolic physical units in computer calculations, and features automatic detection of dimensionally-inhomogeneous formulas and conversion of inconsistent units in a dimensionally homogeneous formula. Some examples illustrate these features.

  10. Working memory and sentence comprehension of Hong Kong Chinese children with specific language impairment.

    Science.gov (United States)

    Siu, Elaine; Man, David W K

    2006-09-01

    Children with Specific Language Impairment present with delayed language development, but do not have a history of hearing impairment, mental deficiency, or associated social or behavioral problems. Non-word repetition was suggested as an index to reflect the capacity of phonological working memory. There is a paucity of such studies among Hong Kong Chinese children. This preliminary study aimed to examine the relationship between phonological working memory and Specific Language Impairment, through the processes of non-word repetition and sentence comprehension, of children with Specific Language Impairment and pre-school children with normal language development. Both groups of children were screened by a standardized language test. A list of Cantonese (the commonest dialect used in Hong Kong) multisyllabic nonsense utterances and a set of 18 sentences were developed for this study. t-tests and Pearson correlation were used to study the relationship between non-word repetition, working memory and specific language impairment. Twenty-three pre-school children with Specific Language Impairment (mean age = 68.30 months; SD = 6.90) and another 23 pre-school children (mean age = 67.30 months; SD = 6.16) participated in the study. Significant difference performance was found between the Specific Language Impairment group and normal language group in the multisyllabic nonsense utterances repetition task and the sentence comprehension task. Length effect was noted in Specific Language Impairment group children, which is consistent with the findings of other literature. In addition, correlations were also observed between the number of nonsense utterances repeated and the number of elements comprehended. Cantonese multisyllabic nonsense utterances might be worth further developing as a screening tool for the early detection of children with Specific Language Impairment.

  11. Social Stress in Young People with Specific Language Impairment

    Science.gov (United States)

    Wadman, Ruth; Durkin, Kevin; Conti-Ramsden, Gina

    2011-01-01

    Social interactions can be a source of social stress for adolescents. Little is known about how adolescents with developmental difficulties, such as specific language impairment (SLI), feel when interacting socially. Participants included 28 adolescents with SLI and 28 adolescents with typical language abilities (TL). Self-report measures of…

  12. Galilean Duffin-Kemmer-Petiau algebra and symplectic structure

    CERN Document Server

    Fernandes, M C B; Vianna, J D M

    2003-01-01

    We develop the Duffin-Kemmer-Petiau (DKP) approach in the phase-space picture of quantum mechanics by considering DKP algebras in a Galilean covariant context. Specifically, we develop an algebraic calculus based on a tensor algebra defined on a five-dimensional space which plays the role of spacetime background of the non-relativistic DKP equation. The Liouville operator is determined and the Liouville-von Neumann equation is written in two situations: the free particle and a particle in an external electromagnetic field. A comparison between the non-relativistic and the relativistic cases is commented.

  13. UPC Language and Library Specifications, Version 1.3

    Energy Technology Data Exchange (ETDEWEB)

    UPC Consortium; Bonachea, Dan; Funck, Gary

    2013-11-16

    UPC is an explicitly parallel extension to the ISO C 99 Standard. UPC follows the partitioned global address space programming model. This document is the formal specification for the UPC language and library syntax and semantics, and supersedes prior specification version 1.2 (LBNL-59208).

  14. The Boolean algebra and central Galois algebras

    Directory of Open Access Journals (Sweden)

    George Szeto

    2001-01-01

    Full Text Available Let B be a Galois algebra with Galois group G, Jg={b∈B∣bx=g(xb   for all   x∈B} for g∈G, and BJg=Beg for a central idempotent eg. Then a relation is given between the set of elements in the Boolean algebra (Ba,≤ generated by {0,eg∣g∈G} and a set of subgroups of G, and a central Galois algebra Be with a Galois subgroup of G is characterized for an e∈Ba.

  15. Wavelets and quantum algebras

    International Nuclear Information System (INIS)

    Ludu, A.; Greiner, M.

    1995-09-01

    A non-linear associative algebra is realized in terms of translation and dilation operators, and a wavelet structure generating algebra is obtained. We show that this algebra is a q-deformation of the Fourier series generating algebra, and reduces to this for certain value of the deformation parameter. This algebra is also homeomorphic with the q-deformed su q (2) algebra and some of its extensions. Through this algebraic approach new methods for obtaining the wavelets are introduced. (author). 20 refs

  16. Novikov-Jordan algebras

    OpenAIRE

    Dzhumadil'daev, A. S.

    2002-01-01

    Algebras with identity $(a\\star b)\\star (c\\star d) -(a\\star d)\\star(c\\star b)$ $=(a,b,c)\\star d-(a,d,c)\\star b$ are studied. Novikov algebras under Jordan multiplication and Leibniz dual algebras satisfy this identity. If algebra with such identity has unit, then it is associative and commutative.

  17. Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

    Science.gov (United States)

    Gonzalez-Vega, Laureano

    1999-01-01

    Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

  18. The Epstein-Glaser approach to perturbative quantum field theory: graphs and Hopf algebras

    International Nuclear Information System (INIS)

    Lange, Alexander

    2005-01-01

    The paper aims at investigating perturbative quantum field theory in the approach of Epstein and Glaser (EG) and, in particular, its formulation in the language of graphs and Hopf algebras (HAs). Various HAs are encountered, each one associated with a special combination of physical concepts such as normalization, localization, pseudounitarity, causal regularization, and renormalization. The algebraic structures, representing the perturbative expansion of the S-matrix, are imposed on operator-valued distributions equipped with appropriate graph indices. Translation invariance ensures the algebras to be analytically well defined and graded total symmetry allows to formulate bialgebras. The algebraic results are given embedded in the corresponding physical framework, covering the two EG versions by Fredenhagen and Scharf that differ with respect to the concrete recursive implementation of causality. Besides, the ultraviolet divergences occurring in Feynman's representation are mathematically reasoned. As a final result, the change of the renormalization scheme in the context of EG is modeled via a HA and interpreted as the EG analog of Kreimer's HA

  19. (Quasi-)Poisson enveloping algebras

    OpenAIRE

    Yang, Yan-Hong; Yao, Yuan; Ye, Yu

    2010-01-01

    We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.

  20. Iterated Leavitt Path Algebras

    International Nuclear Information System (INIS)

    Hazrat, R.

    2009-11-01

    Leavitt path algebras associate to directed graphs a Z-graded algebra and in their simplest form recover the Leavitt algebras L(1,k). In this note, we introduce iterated Leavitt path algebras associated to directed weighted graphs which have natural ± Z grading and in their simplest form recover the Leavitt algebras L(n,k). We also characterize Leavitt path algebras which are strongly graded. (author)

  1. Algebraic topological entropy

    International Nuclear Information System (INIS)

    Hudetz, T.

    1989-01-01

    As a 'by-product' of the Connes-Narnhofer-Thirring theory of dynamical entropy for (originally non-Abelian) nuclear C * -algebras, the well-known variational principle for topological entropy is eqivalently reformulated in purly algebraically defined terms for (separable) Abelian C * -algebras. This 'algebraic variational principle' should not only nicely illustrate the 'feed-back' of methods developed for quantum dynamical systems to the classical theory, but it could also be proved directly by 'algebraic' methods and could thus further simplify the original proof of the variational principle (at least 'in principle'). 23 refs. (Author)

  2. Linearizing W-algebras

    International Nuclear Information System (INIS)

    Krivonos, S.O.; Sorin, A.S.

    1994-06-01

    We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras W 3 and W (2) 3 can be embedded as subalgebras into some linear algebras with finite set of currents. Using these linear algebras we find new field realizations of W (2) 3 and W 3 which could be a starting point for constructing new versions of W-string theories. We also reveal a number of hidden relationships between W 3 and W (2) 3 . We conjecture that similar linear algebras can exist for other W-algebra as well. (author). 10 refs

  3. Structural Alterations of the Language Connectome in Children with Specific Language Impairment

    Czech Academy of Sciences Publication Activity Database

    Vydrová, R.; Komárek, V.; Šanda, J.; Štěrbová, K.; Jahodová, A.; Maulisová, A.; Žáčková, J.; Reissigová, Jindra; Kršek, P.; Kyncl, M.

    2015-01-01

    Roč. 151, December (2015), s. 35-41 ISSN 0093-934X Institutional support: RVO:67985807 Keywords : Specific language disorder * DTI * Arcuate fascicle * IFOF * Ventral stream Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 3.038, year: 2015

  4. Quantum deformed su(mvertical stroke n) algebra and superconformal algebra on quantum superspace

    International Nuclear Information System (INIS)

    Kobayashi, Tatsuo

    1993-01-01

    We study a deformed su(mvertical stroke n) algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. From the deformed su(1vertical stroke 4) algebra, we derive deformed Lorentz, translation of Minkowski space, iso(2,2) and its supersymmetric algebras as closed subalgebras with consistent automorphisms. (orig.)

  5. Linear algebraic groups

    CERN Document Server

    Springer, T A

    1998-01-01

    "[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style… [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature…appear for the first time in a text." –Mathematical Reviews (Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of t...

  6. Extended conformal algebras

    International Nuclear Information System (INIS)

    Goddard, Peter

    1990-01-01

    The algebra of the group of conformal transformations in two dimensions consists of two commuting copies of the Virasoro algebra. In many mathematical and physical contexts, the representations of ν which are relevant satisfy two conditions: they are unitary and they have the ''positive energy'' property that L o is bounded below. In an irreducible unitary representation the central element c takes a fixed real value. In physical contexts, the value of c is a characteristic of a theory. If c < 1, it turns out that the conformal algebra is sufficient to ''solve'' the theory, in the sense of relating the calculation of the infinite set of physically interesting quantities to a finite subset which can be handled in principle. For c ≥ 1, this is no longer the case for the algebra alone and one needs some sort of extended conformal algebra, such as the superconformal algebra. It is these algebras that this paper aims at addressing. (author)

  7. Generalized symmetry algebras

    International Nuclear Information System (INIS)

    Dragon, N.

    1979-01-01

    The possible use of trilinear algebras as symmetry algebras for para-Fermi fields is investigated. The shortcomings of the examples are argued to be a general feature of such generalized algebras. (author)

  8. ZLIB++: Object-oriented numerical library for differential algebra

    International Nuclear Information System (INIS)

    Malitsky, N.; Reshetov, A.; Yan, Y.

    1994-01-01

    New software engineering tools and object-oriented design have a great impact on the software development process. But in high energy physics all major packages were implemented in FORTRAN and porting of these codes to another language is rather complicated, primarily because of their huge size and heavy use of FORTRAN mathematical libraries. But some intrinsic accelerator concepts, such as nested structure of modern accelerators, look very pretty when implemented with the object-oriented approach. In this paper we present the object-oriented version of ZLIB, numerical library for differential algebra and show how the modern approaches can simplify the development and support of accelerator codes, decrease code size, and allow description of complex mathematical transformations by simple language

  9. SD-CAS: Spin Dynamics by Computer Algebra System.

    Science.gov (United States)

    Filip, Xenia; Filip, Claudiu

    2010-11-01

    A computer algebra tool for describing the Liouville-space quantum evolution of nuclear 1/2-spins is introduced and implemented within a computational framework named Spin Dynamics by Computer Algebra System (SD-CAS). A distinctive feature compared with numerical and previous computer algebra approaches to solving spin dynamics problems results from the fact that no matrix representation for spin operators is used in SD-CAS, which determines a full symbolic character to the performed computations. Spin correlations are stored in SD-CAS as four-entry nested lists of which size increases linearly with the number of spins into the system and are easily mapped into analytical expressions in terms of spin operator products. For the so defined SD-CAS spin correlations a set of specialized functions and procedures is introduced that are essential for implementing basic spin algebra operations, such as the spin operator products, commutators, and scalar products. They provide results in an abstract algebraic form: specific procedures to quantitatively evaluate such symbolic expressions with respect to the involved spin interaction parameters and experimental conditions are also discussed. Although the main focus in the present work is on laying the foundation for spin dynamics symbolic computation in NMR based on a non-matrix formalism, practical aspects are also considered throughout the theoretical development process. In particular, specific SD-CAS routines have been implemented using the YACAS computer algebra package (http://yacas.sourceforge.net), and their functionality was demonstrated on a few illustrative examples. Copyright © 2010 Elsevier Inc. All rights reserved.

  10. Rota-Baxter algebras and the Hopf algebra of renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Ebrahimi-Fard, K.

    2006-06-15

    Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

  11. Rota-Baxter algebras and the Hopf algebra of renormalization

    International Nuclear Information System (INIS)

    Ebrahimi-Fard, K.

    2006-06-01

    Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

  12. Galilean contractions of W-algebras

    Directory of Open Access Journals (Sweden)

    Jørgen Rasmussen

    2017-09-01

    Full Text Available Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as W-algebras. Known examples include contractions of pairs of the Virasoro algebra, its N=1 superconformal extension, or the W3 algebra. Here, we introduce a contraction prescription of the corresponding operator-product algebras, or equivalently, a prescription for contracting tensor products of vertex algebras. With this, we work out the Galilean conformal algebras arising from contractions of N=2 and N=4 superconformal algebras as well as of the W-algebras W(2,4, W(2,6, W4, and W5. The latter results provide evidence for the existence of a whole new class of W-algebras which we call Galilean W-algebras. We also apply the contraction prescription to affine Lie algebras and find that the ensuing Galilean affine algebras admit a Sugawara construction. The corresponding central charge is level-independent and given by twice the dimension of the underlying finite-dimensional Lie algebra. Finally, applications of our results to the characterisation of structure constants in W-algebras are proposed.

  13. Quantum affine algebras and deformations of the virasoro and W-algebras

    International Nuclear Information System (INIS)

    Frenkel, E.; Reshetikhin, N.

    1996-01-01

    Using the Wakimoto realization of quantum affine algebras we define new Poisson algebras, which are q-deformations of the classical W-algebras. We also define their free field realizations, i.e. homomorphisms into some Heisenberg-Poisson algebras. The formulas for these homomorphisms coincide with formulas for spectra of transfer-matrices in the corresponding quantum integrable models derived by the Bethe-Ansatz method. (orig.)

  14. Algebraic entropy for algebraic maps

    International Nuclear Information System (INIS)

    Hone, A N W; Ragnisco, Orlando; Zullo, Federico

    2016-01-01

    We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Bäcklund transformations. (letter)

  15. On hyper BCC-algebras

    OpenAIRE

    Borzooei, R. A.; Dudek, W. A.; Koohestani, N.

    2006-01-01

    We study hyper BCC-algebras which are a common generalization of BCC-algebras and hyper BCK-algebras. In particular, we investigate different types of hyper BCC-ideals and describe the relationship among them. Next, we calculate all nonisomorphic 22 hyper BCC-algebras of order 3 of which only three are not hyper BCK-algebras.

  16. On hyper BCC-algebras

    Directory of Open Access Journals (Sweden)

    R. A. Borzooei

    2006-01-01

    Full Text Available We study hyper BCC-algebras which are a common generalization of BCC-algebras and hyper BCK-algebras. In particular, we investigate different types of hyper BCC-ideals and describe the relationship among them. Next, we calculate all nonisomorphic 22 hyper BCC-algebras of order 3 of which only three are not hyper BCK-algebras.

  17. Algebraic theory of numbers

    CERN Document Server

    Samuel, Pierre

    2008-01-01

    Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal

  18. Failure to meet language milestones at two years of age is predictive of specific language impairment

    NARCIS (Netherlands)

    Diepeveen, F.B.; Dusseldorp, E.; Bol, G.W.; Oudesluys-Murphy, A.M.; Verkerk, P.H.

    2016-01-01

    This study established predictive properties of single language milestones for specific language impairment (SLI) after the age of four, as these had not previously been reported in the literature. Methods In this nested case-control study, children attending special needs schools for severe speech

  19. RAPID NAMING IN CHILDREN WITH SPECIFIC LANGUAGE IMPAIRMENT AND IN CHILDREN WITH TYPICAL LANGUAGE DEVELOPMENT

    Directory of Open Access Journals (Sweden)

    Neda MILOSHEVIĆ

    2017-03-01

    Full Text Available Aimed at the detailed insight into the phonological ability of Serbian-speaking children of preschool age, with and without language impairment, the ability of rapid naming was examined. Method: Operationalization of the set goal was carried out by using the Test for evaluating reading and writing pre-skills. In describing and analyzing the obtained data, methods of descriptive and inferential statistics were used. The sample included 120 subjects of both gender, 40 children diagnosed with specific language impairment (SLI, age from 5,11 to 7 years, and 80 children with typical language development (TLD, age between 5,11 and 7 years, with no statistically significant differences in relation to age and gender of the participants. Results: Summing up the overall results and achievements of children with SLI and children with TLD, we concluded that there are statistically significant differences in the rapid naming between children with specific language impairment and children with typical language development. Conclusions: As it is a global trend to work on preventing disorders and obstructions, and phonological skills in this age are a timely indicator of the development of reading and writing skills, the examined children with SLI are at risk for the occurrence of obstructions and disorders in the area of reading and writing abilities.

  20. Using principles of learning to inform language therapy design for children with specific language impairment.

    Science.gov (United States)

    Alt, Mary; Meyers, Christina; Ancharski, Alexandra

    2012-01-01

    Language treatment for children with specific language impairment (SLI) often takes months to achieve moderate results. Interventions often do not incorporate the principles that are known to affect learning in unimpaired learners. To outline some key findings about learning in typical populations and to suggest a model of how they might be applied to language treatment design as a catalyst for further research and discussion. Three main principles of implicit learning are reviewed: variability, complexity and sleep-dependent consolidation. After explaining these principles, evidence is provided as to how they influence learning tasks in unimpaired learners. Information is reviewed on principles of learning as they apply to impaired populations, current treatment designs are also reviewed that conform to the principles, and ways in which principles of learning might be incorporated into language treatment design are demonstrated. This paper provides an outline for how theoretical knowledge might be applied to clinical practice in an effort to promote discussion. Although the authors look forward to more specific details on how the principles of learning relate to impaired populations, there is ample evidence to suggest that these principles should be considered during treatment design. © 2012 Royal College of Speech and Language Therapists.

  1. The conceptual basis of mathematics in cardiology: (I) algebra, functions and graphs.

    Science.gov (United States)

    Bates, Jason H T; Sobel, Burton E

    2003-02-01

    This is the first in a series of four articles developed for the readers of. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease, abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and

  2. The BRS algebra of a free differential algebra

    International Nuclear Information System (INIS)

    Boukraa, S.

    1987-04-01

    We construct in this work, the Weil and the universal BRS algebras of theories that can have as a gauge symmetry a free differential (Sullivan) algebra, the natural extension of Lie algebras allowing the definition of p-form gauge potentials (p>1). The finite gauge transformations of these potentials are deduced from the infinitesimal ones and the group structure is shown. The geometrical meaning of these p-form gauge potentials is given by the notion of a Quillen superconnection. (author). 19 refs

  3. Pseudo-Riemannian Novikov algebras

    Energy Technology Data Exchange (ETDEWEB)

    Chen Zhiqi; Zhu Fuhai [School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071 (China)], E-mail: chenzhiqi@nankai.edu.cn, E-mail: zhufuhai@nankai.edu.cn

    2008-08-08

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.

  4. Introduction to W-algebras

    International Nuclear Information System (INIS)

    Takao, Masaru

    1989-01-01

    We review W-algebras which are generated by stress tensor and primary fields. Associativity plays an important role in determining the extended algebra and further implies the algebras to exist for special values of central charges. Explicitly constructing the algebras including primary fields of spin less than 4, we investigate the closure structure of the Jacobi identity of the extended algebras. (author)

  5. 13th Forum for Specification and Design Languages (FDL) conference

    CERN Document Server

    Morawiec, Adam; System Specification and Design Languages : Selected Contributions from FDL 2010

    2012-01-01

    This book brings together a selection of the best papers from the thirteenth edition of the Forum on specification and Design Languages Conference (FDL), which was held in Southampton, UK in September 2010.  FDL is a well established international forum devoted to dissemination of research results, practical experiences and new ideas in the application of specification, design and verification languages to the design, modelling and verification of integrated circuits, complex hardware/software embedded systems, and mixed-technology systems. Covers design verification, automatic synthesis and mechanized debug aids; Includes language-based modeling and design techniques for embedded systems; Covers design, modeling and verification of mixed physical domain and mixed signal systems that include significant analog parts in electrical and non-electrical domains; Includes formal and semi-formal system level design methods for complex embedded systems based on the Unified Modelling Language (UML) and Model Driven E...

  6. (Modular Effect Algebras are Equivalent to (Frobenius Antispecial Algebras

    Directory of Open Access Journals (Sweden)

    Dusko Pavlovic

    2017-01-01

    Full Text Available Effect algebras are one of the generalizations of Boolean algebras proposed in the quest for a quantum logic. Frobenius algebras are a tool of categorical quantum mechanics, used to present various families of observables in abstract, often nonstandard frameworks. Both effect algebras and Frobenius algebras capture their respective fragments of quantum mechanics by elegant and succinct axioms; and both come with their conceptual mysteries. A particularly elegant and mysterious constraint, imposed on Frobenius algebras to characterize a class of tripartite entangled states, is the antispecial law. A particularly contentious issue on the quantum logic side is the modularity law, proposed by von Neumann to mitigate the failure of distributivity of quantum logical connectives. We show that, if quantum logic and categorical quantum mechanics are formalized in the same framework, then the antispecial law of categorical quantum mechanics corresponds to the natural requirement of effect algebras that the units are each other's unique complements; and that the modularity law corresponds to the Frobenius condition. These correspondences lead to the equivalence announced in the title. Aligning the two formalisms, at the very least, sheds new light on the concepts that are more clearly displayed on one side than on the other (such as e.g. the orthogonality. Beyond that, it may also open up new approaches to deep and important problems of quantum mechanics (such as the classification of complementary observables.

  7. An algorithm to construct the basic algebra of a skew group algebra

    NARCIS (Netherlands)

    Horobeţ, E.

    2016-01-01

    We give an algorithm for the computation of the basic algebra Morita equivalent to a skew group algebra of a path algebra by obtaining formulas for the number of vertices and arrows of the new quiver Qb. We apply this algorithm to compute the basic algebra corresponding to all simple quaternion

  8. Taming the unknown a history of algebra from antiquity to the early twentieth century

    CERN Document Server

    Katz, Victor J

    2014-01-01

    What is algebra? For some, it is an abstract language of x's and y's. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century. Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further dev...

  9. Interaction of language processing and motor skill in children with specific language impairment.

    Science.gov (United States)

    DiDonato Brumbach, Andrea C; Goffman, Lisa

    2014-02-01

    To examine how language production interacts with speech motor and gross and fine motor skill in children with specific language impairment (SLI). Eleven children with SLI and 12 age-matched peers (4-6 years) produced structurally primed sentences containing particles and prepositions. Utterances were analyzed for errors and for articulatory duration and variability. Standard measures of motor, language, and articulation skill were also obtained. Sentences containing particles, as compared with prepositions, were less likely to be produced in a priming task and were longer in duration, suggesting increased difficulty with this syntactic structure. Children with SLI demonstrated higher articulatory variability and poorer gross and fine motor skills compared with aged-matched controls. Articulatory variability was correlated with generalized gross and fine motor performance. Children with SLI show co-occurring speech motor and generalized motor deficits. Current theories do not fully account for the present findings, though the procedural deficit hypothesis provides a framework for interpreting overlap among language and motor domains.

  10. Compact quantum group C*-algebras as Hopf algebras with approximate unit

    International Nuclear Information System (INIS)

    Do Ngoc Diep; Phung Ho Hai; Kuku, A.O.

    1999-04-01

    In this paper, we construct and study the representation theory of a Hopf C*-algebra with approximate unit, which constitutes quantum analogue of a compact group C*-algebra. The construction is done by first introducing a convolution-product on an arbitrary Hopf algebra H with integral, and then constructing the L 2 and C*-envelopes of H (with the new convolution-product) when H is a compact Hopf *-algebra. (author)

  11. Intervals in Generalized Effect Algebras and their Sub-generalized Effect Algebras

    Directory of Open Access Journals (Sweden)

    Zdenka Riečanová

    2013-01-01

    Full Text Available We consider subsets G of a generalized effect algebra E with 0∈G and such that every interval [0, q]G = [0, q]E ∩ G of G (q ∈ G , q ≠ 0 is a sub-effect algebra of the effect algebra [0, q]E. We give a condition on E and G under which every such G is a sub-generalized effect algebra of E.

  12. Variants of bosonization in parabosonic algebra: the Hopf and super-Hopf structures in parabosonic algebra

    International Nuclear Information System (INIS)

    Kanakoglou, K; Daskaloyannis, C

    2008-01-01

    Parabosonic algebra in finite or infinite degrees of freedom is considered as a Z 2 -graded associative algebra, and is shown to be a Z 2 -graded (or super) Hopf algebra. The super-Hopf algebraic structure of the parabosonic algebra is established directly without appealing to its relation to the osp(1/2n) Lie superalgebraic structure. The notion of super-Hopf algebra is equivalently described as a Hopf algebra in the braided monoidal category CZ 2 M. The bosonization technique for switching a Hopf algebra in the braided monoidal category H M (where H is a quasitriangular Hopf algebra) into an ordinary Hopf algebra is reviewed. In this paper, we prove that for the parabosonic algebra P B , beyond the application of the bosonization technique to the original super-Hopf algebra, a bosonization-like construction is also achieved using two operators, related to the parabosonic total number operator. Both techniques switch the same super-Hopf algebra P B to an ordinary Hopf algebra, thus producing two different variants of P B , with an ordinary Hopf structure

  13. On the intersection of irreducible components of the space of finite-dimensional Lie algebras

    International Nuclear Information System (INIS)

    Gorbatsevich, Vladimir V

    2012-01-01

    The irreducible components of the space of n-dimensional Lie algebras are investigated. The properties of Lie algebras belonging to the intersection of all the irreducible components of this kind are studied (these Lie algebras are said to be basic or founding Lie algebras). It is proved that all Lie algebras of this kind are nilpotent and each of these Lie algebras has an Abelian ideal of codimension one. Specific examples of founding Lie algebras of arbitrary dimension are described and, to describe the Lie algebras in general, we state a conjecture. The concept of spectrum of a Lie algebra is considered and some of the most elementary properties of the spectrum are studied. Bibliography: 6 titles.

  14. The C*-algebra of a vector bundle and fields of Cuntz algebras

    OpenAIRE

    Vasselli, Ezio

    2004-01-01

    We study the Pimsner algebra associated with the module of continuous sections of a Hilbert bundle, and prove that it is a continuous bundle of Cuntz algebras. We discuss the role of such Pimsner algebras w.r.t. the notion of inner endomorphism. Furthermore, we study bundles of Cuntz algebras carrying a global circle action, and assign to them a class in the representable KK-group of the zero-grade bundle. We compute such class for the Pimsner algebra of a vector bundle.

  15. Specific language impairment is associated with maternal and family factors

    NARCIS (Netherlands)

    Diepeveen, F.B.; Dommelen, P. van; Oudesluys-Murphy, A.M.; Verkerk, P.H.

    2017-01-01

    Background: This study aimed to identify risk factors associated with specific language impairment (SLI). Methods: In a nested case–control design, 253 children attending special needs schools for severe speech and language difficulties in the Netherlands were matched for sex and date of birth with

  16. Bicovariant quantum algebras and quantum Lie algebras

    International Nuclear Information System (INIS)

    Schupp, P.; Watts, P.; Zumino, B.

    1993-01-01

    A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(G q ) to U q g, given by elements of the pure braid group. These operators - the 'reflection matrix' Y= triple bond L + SL - being a special case - generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N). (orig.)

  17. Simple relation algebras

    CERN Document Server

    Givant, Steven

    2017-01-01

    This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics. The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatme...

  18. Languages for Specific Academic Purposes or Languages for General Academic Purposes? A Critical Reappraisal of a Key Issue for Language Provision in Higher Education

    Science.gov (United States)

    Krekeler, Christian

    2013-01-01

    The debate about the subject specificity of university language tuition has been going on for decades; it has mostly been discussed in the context of English for Academic Purposes. This paper considers the case for disciplinary specificity with regard to languages other than English. Few, if any, developed curricula, syllabuses, suitable textbooks…

  19. A non-Lie algebraic framework and its possible merits for symmetry descriptions

    International Nuclear Information System (INIS)

    Ktorides, C.N.

    1975-01-01

    A nonassociative algebraic construction is introduced which bears a relation to a Lie algebra L paralleling the relation between an associative enveloping algebra and L. The key ingredient of this algebraic construction is the presence of two parameters which relate it to the enveloping algebra of L. The analog of the Poincare--Birkhoff--Witt theorem is proved for the new algebra. Possibilities of physical relevance are also considered. It is noted that, if fully developed, the mathematical framework suggested by this new algebra should be non-Lie. Subsequently, a certain scheme resulting from specific considerations connected with this (non-Lie) algebraic structure is found to bear striking resemblance to a recent phenomenological theory proposed for explaining CP violation by the K 0 system. Some relevant speculations are also made in view of certain recent trends of thought in elementary particle physics. Finally, in an appendix, a Gell-Mann--Okubo-like mass formula for the new algebra is derived for an SU (3) octet

  20. Boolean algebra

    CERN Document Server

    Goodstein, R L

    2007-01-01

    This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.

  1. Diagrammatic Representations in Domain-Specific Languages

    OpenAIRE

    Tourlas, Konstantinos

    2002-01-01

    One emerging approach to reducing the labour and costs of software development favours the specialisation of techniques to particular application domains. The rationale is that programs within a given domain often share enough common features and assumptions to enable the incorporation of substantial support mechanisms into domain-specific programming languages and associated tools. Instead of being machine-oriented, algorithmic implementations, programs in many domain-speci...

  2. On The Role Of Division, Jordan And Related Algebras In Particle Physics

    International Nuclear Information System (INIS)

    Gursey, F.; C-H Tze

    1996-11-01

    This monograph surveys the role of some associative and non-associative algebras, remarkable by their ubiquitous appearance in contemporary theoretical physics,particularly in particle physics. It concerns the interplay between division algebras, specifically quaternions and octonions, between Jordan and related algebras on the one hand, and unified theories of the basic interactions on the other. Selected applications of these algebraic structures are discussed: quaternion analyticity of Yang Mills instantons, octonionic aspects of exceptional broken gauge, supergravity theories, division algebras in anyonic phenomena and in theories of extended objects in critical dimensions. The topics presented deal primarily with original contributions by the authors

  3. Combinatorial commutative algebra

    CERN Document Server

    Miller, Ezra

    2005-01-01

    Offers an introduction to combinatorial commutative algebra, focusing on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determined rings. The chapters in this work cover topics ranging from homological invariants of monomial ideals and their polyhedral resolutions, to tools for studying algebraic varieties.

  4. Topological أ-algebras with Cأ-enveloping algebras II

    Indian Academy of Sciences (India)

    necessarily complete) pro-Cأ-topology which coincides with the relative uniform .... problems in Cأ-algebras, Phillips introduced more general weakly Cأ- .... Banach أ-algebra obtained by completing A=Np in the norm jjxpjjp ¼ pًxق where.

  5. The acquisition of nouns in children with Specific Language Impairment

    OpenAIRE

    Krzemien, Magali; Thibaut, Jean-Pierre; Zghonda, Hela; Maillart, Christelle

    2017-01-01

    Specific Language Impairment (SLI) is a neurodevelopmental disorder that affects the language development of children with a normal nonverbal intelligence and no history of neurological disorder nor auditory deficit (Leonard, 2014). A difficulty linked to SLI is the poor language productivity and the input dependency that children display compared with their peers: they tend to use a limited variety of verbal forms compared to younger siblings (Conti-Ramsden & Jones, 1997) and use a high prop...

  6. C*-algebras by example

    CERN Document Server

    Davidson, Kenneth R

    1996-01-01

    The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of K-theory to provide a useful classification of AF algebras. These results were the beginning of a marvelous new set of tools for analyzing concrete C*-algebras. This book is an introductory graduate level text which presents the basics of the subject through a detailed analysis of several important classes of C*-algebras. The development of operator algebras in the last twenty yea

  7. The algebra and geometry of SU(3) matrices

    International Nuclear Information System (INIS)

    Mallesh, K.S.; Mukunda, N.

    1997-01-01

    We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of multiplying two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level system is outlined. (author)

  8. Non-freely generated W-algebras and construction of N=2 super W-algebras

    International Nuclear Information System (INIS)

    Blumenhagen, R.

    1994-07-01

    Firstly, we investigate the origin of the bosonic W-algebras W(2, 3, 4, 5), W(2, 4, 6) and W(2, 4, 6) found earlier by direct construction. We present a coset construction for all three examples leading to a new type of finitely, non-freely generated quantum W-algebras, which we call unifying W-algebras. Secondly, we develop a manifest covariant formalism to construct N = 2 super W-algebras explicitly on a computer. Applying this algorithm enables us to construct the first four examples of N = 2 super W-algebras with two generators and the N = 2 super W 4 algebra involving three generators. The representation theory of the former ones shows that all examples could be divided into four classes, the largest one containing the N = 2 special type of spectral flow algebras. Besides the W-algebra of the CP(3) Kazama-Suzuki coset model, the latter example with three generators discloses a second solution which could also be explained as a unifying W-algebra for the CP(n) models. (orig.)

  9. ZLIB++: Object Oriented Numerical Library for Differential Algebra

    International Nuclear Information System (INIS)

    Yan, Yiton T

    2003-01-01

    New software engineering tools and object-oriented design have a great impact on the software development process. but in high energy physics all major packages were implemented in FORTRAN and porting of these codes to another language is rather complicated, primarily because of their huge size and heavy use of FORTRAN mathematical libraries. But some intrinsic accelerator concepts, such as nested structure of modern accelerators, look very pretty when implemented with the object-oriented approach. In this paper the authors present the object-oriented version of ZLIB, numerical library for differential algebra, and show how the modern approaches can simplify the development and support of accelerator codes, decrease code size, and allow description of complex mathematical transformations by simple language

  10. Algebraic conformal field theory

    International Nuclear Information System (INIS)

    Fuchs, J.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica

    1991-11-01

    Many conformal field theory features are special versions of structures which are present in arbitrary 2-dimensional quantum field theories. So it makes sense to describe 2-dimensional conformal field theories in context of algebraic theory of superselection sectors. While most of the results of the algebraic theory are rather abstract, conformal field theories offer the possibility to work out many formulae explicitly. In particular, one can construct the full algebra A-bar of global observables and the endomorphisms of A-bar which represent the superselection sectors. Some explicit results are presented for the level 1 so(N) WZW theories; the algebra A-bar is found to be the enveloping algebra of a Lie algebra L-bar which is an extension of the chiral symmetry algebra of the WZW theory. (author). 21 refs., 6 figs

  11. (Dis)connections between Specific Language Impairment and Dyslexia in Chinese

    Science.gov (United States)

    Wong, Anita M.-Y.; Ho, Connie S.-H.; Au, Terry K.-F.; Kidd, Joanna C.; Ng, Ashley K.-H.; Yip, Lesley P.-W.; Lam, Catherine C.-C.

    2015-01-01

    Specific language impairment (SLI) and dyslexia are found to co-occur in school-aged children learning Chinese, a non-alphabetic language (Wong, Kidd, Ho, & Au in "Sci Stud Read" 14:30--57, 2010). This paper examined the "Distinct" hypothesis--that SLI and dyslexia have different cognitive deficits and behavioural…

  12. Discipline-Specific Language Instruction for International Students in Introductory Economics

    Science.gov (United States)

    Nguyen, Trien T.; Williams, Julia; Trimarchi, Angela

    2015-01-01

    This paper explores student perceptions of the effects of pairing discipline-specific language instruction with the traditional method of course delivery in economics. Our research involved teaching content-based English as an additional language (EAL) tutorials to a small group of ten international students taking first-year introductory…

  13. HAL/S language specification

    Science.gov (United States)

    Newbold, P. M.

    1974-01-01

    A programming language for the flight software of the NASA space shuttle program was developed and identified as HAL/S. The language is intended to satisfy virtually all of the flight software requirements of the space shuttle. The language incorporates a wide range of features, including applications-oriented data types and organizations, real time control mechanisms, and constructs for systems programming tasks.

  14. Representations of the Virasoro algebra from lattice models

    International Nuclear Information System (INIS)

    Koo, W.M.; Saleur, H.

    1994-01-01

    We investigate in detail how the Virasoro algebra appears in the scaling limit of the simplest lattice models of XXZ or RSOS type. Our approach is straightforward but to our knowledge had never been tried so far. We simply formulate a conjecture for the lattice stress-energy tensor motivated by the exact derivation of lattice global Ward identities. We then check that the proper algebraic relations are obeyed in the scaling limit. The latter is under reasonable control thanks to the Bethe-ansatz solution. The results, which are mostly numerical for technical reasons, are remarkably precise. They are also corroborated by exact pieces of information from various sources, in particular Temperley-Lieb algebra representation theory. Most features of the Virasoro algebra (like central term, null vectors, metric properties, etc.) can thus be observed using the lattice models. This seems of general interest for lattice field theory, and also more specifically for finding relations between conformal invariance and lattice integrability, since a basis for the irreducible representations of the Virasoro algebra should now follow (at least in principle) from Bethe-ansatz computations. ((orig.))

  15. Skill-specificity of language practice and transferability of language skills: The case of listening and speaking

    Directory of Open Access Journals (Sweden)

    Majid Farshid

    2014-08-01

    Full Text Available The study of skill acquisition is of great importance in cognitive psychology. One aspect of skill acquisition research is whether practice in SLA is skill-specific or not. To date, research done has not led to either unanimous rejection or acceptance of the theory. This article is an attempt to examine this question in an EFL context where L2 learners have limited or no access to target language data outside the classroom. More specifically, it tries to see whether listening and speaking in an EFL context necessitate their own specific practice or not. Based on a post-test only design, 16 male, beginner Iranian EFL learners received input-based instruction for three months. When the instruction was over, both listening and speaking performances of the subjects were assessed. The result showed that the subjects had significantly improved their listening ability while their speaking ability had little or no improvement, indicating that different language skills in EFL contexts need specific practice. The findings not only confirm the skill-specificity of language practice, but also rejects VanPatten’s seminal claim that comprehension practice is enough to bring about development, not only in comprehension but also in production.

  16. Discipline-Specific Language Instruction for International Students in Introductory Economics

    Directory of Open Access Journals (Sweden)

    Trien T. Nguyen

    2015-12-01

    Full Text Available This paper explores student perceptions of the effects of pairing discipline-specific language instruction with the traditional method of course delivery in economics. Our research involved teaching content-based English as an additional language (EAL tutorials to a small group of ten international students taking first-year introductory economics courses. These voluntary participants completed pre- and post-treatment assessments with exit interviews at the end of the project. Assessment results and interviews suggest that students perceive that discipline-specific language instruction such as our EAL tutorials assists in the development of increased content and language proficiency. They also believe that vocabulary development is one of the most critical activities to support these goals; reading skills are also important but require more time and commitment than students can afford to give. Despite the students’ interest in the project, their heavy class schedules prevented many from participating; our group was limited to ten students which precludes any assurance of statistical significance. In spite of the limitations, we believe that the project can still contribute valuable qualitative lessons to the literature of content-based language instruction in which the discipline of economics has not been well represented.

  17. Boolean algebra essentials

    CERN Document Server

    Solomon, Alan D

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Boolean Algebra includes set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean

  18. q-deformed Poincare algebra

    International Nuclear Information System (INIS)

    Ogievetsky, O.; Schmidke, W.B.; Wess, J.; Muenchen Univ.; Zumino, B.; Lawrence Berkeley Lab., CA

    1992-01-01

    The q-differential calculus for the q-Minkowski space is developed. The algebra of the q-derivatives with the q-Lorentz generators is found giving the q-deformation of the Poincare algebra. The reality structure of the q-Poincare algebra is given. The reality structure of the q-differentials is also found. The real Laplaacian is constructed. Finally the comultiplication, counit and antipode for the q-Poincare algebra are obtained making it a Hopf algebra. (orig.)

  19. Generalizing the bms3 and 2D-conformal algebras by expanding the Virasoro algebra

    Science.gov (United States)

    Caroca, Ricardo; Concha, Patrick; Rodríguez, Evelyn; Salgado-Rebolledo, Patricio

    2018-03-01

    By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the bms3 algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite-dimensional lifts of the so-called Bk, Ck and Dk algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Kač-Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.

  20. Predictors of growth or attrition of the first language in Latino children with specific language impairment

    Science.gov (United States)

    Simon-Cereijido, Gabriela; Gutiérrez-Clellen, Vera F.; Sweet, Monica

    2012-01-01

    We investigated the factors that may help understand the differential rates of language development in the home language (i.e., Spanish) of Latino preschoolers with specific language impairment (SLI). Children were randomly assigned to either bilingual or English-only small group interventions and followed from preschool to kindergarten. Predictors of Spanish growth included the language of intervention, the child’s level of language development or severity, the child’s socio-emotional skills, and the child’s level of English use. Spanish performance outcomes were assessed over time using a series of longitudinal models with baseline and post-treatment measures nested within child. Children demonstrated growth on Spanish outcomes over time. The language of instruction and the child’s level of vocabulary and socio-emotional development at baseline were significant predictors of differences in rates of growth in the home language. Clinicians may need to take into consideration these factors when making clinical recommendations. PMID:24489415

  1. Introduction to quantum algebras

    International Nuclear Information System (INIS)

    Kibler, M.R.

    1992-09-01

    The concept of a quantum algebra is made easy through the investigation of the prototype algebras u qp (2), su q (2) and u qp (1,1). The latter quantum algebras are introduced as deformations of the corresponding Lie algebras; this is achieved in a simple way by means of qp-bosons. The Hopf algebraic structure of u qp (2) is also discussed. The basic ingredients for the representation theory of u qp (2) are given. Finally, in connection with the quantum algebra u qp (2), the qp-analogues of the harmonic oscillator are discussed and of the (spherical and hyperbolical) angular momenta. (author) 50 refs

  2. Model Checking Processes Specified In Join-Calculus Algebra

    Directory of Open Access Journals (Sweden)

    Sławomir Piotr Maludziński

    2014-01-01

    Full Text Available This article presents a model checking tool used to verify concurrent systems specified in join-calculus algebra. The temporal properties of systems under verification are expressed in CTL logic. Join-calculus algebra with its operational semantics defined by the chemical abstract machine serves as the basic method for the specification of concurrent systems and their synchronization mechanisms, and allows the examination of more complex systems.

  3. Continuum analogues of contragredient Lie algebras

    International Nuclear Information System (INIS)

    Saveliev, M.V.; Vershik, A.M.

    1989-03-01

    We present an axiomatic formulation of a new class of infinite-dimensional Lie algebras - the generalizations of Z-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras ''continuum Lie algebras''. The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential Cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered. (author). 9 refs

  4. A Requirement Specification Language for AADL

    Science.gov (United States)

    2016-06-01

    models. The objective of ReqSpec is to support the elicitation , definition, and modeling of requirements for real-time embedded systems in an iterative...A Requirement Specification Language for AADL Peter H. Feiler Julien Delange Lutz Wrage June 2016 TECHNICAL REPORT CMU/SEI-2016-TR-008...is required for any other external and/or commercial use. Requests for permission should be directed to the Software En- gineering Institute at

  5. Theory of Mind Ability in Children with Specific Language Impairment

    Science.gov (United States)

    Gillott, A.; Furniss, F.; Walter, A.

    2004-01-01

    Whilst evidence of theory of mind impairments in children with autism is well established, possible impairments in children with language disorder have only recently been investigated. Children with specific language impairment aged between eight and 12 years were matched by age and gender to high functioning children with autism and normally…

  6. Basic linear algebra subprograms for FORTRAN usage

    Science.gov (United States)

    Lawson, C. L.; Hanson, R. J.; Kincaid, D. R.; Krogh, F. T.

    1977-01-01

    A package of 38 low level subprograms for many of the basic operations of numerical linear algebra is presented. The package is intended to be used with FORTRAN. The operations in the package are dot products, elementary vector operations, Givens transformations, vector copy and swap, vector norms, vector scaling, and the indices of components of largest magnitude. The subprograms and a test driver are available in portable FORTRAN. Versions of the subprograms are also provided in assembly language for the IBM 360/67, the CDC 6600 and CDC 7600, and the Univac 1108.

  7. Lectures on algebraic statistics

    CERN Document Server

    Drton, Mathias; Sullivant, Seth

    2009-01-01

    How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.

  8. Quiver W-algebras

    Science.gov (United States)

    Kimura, Taro; Pestun, Vasily

    2018-06-01

    For a quiver with weighted arrows, we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al. and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds-Kac-Moody Lie algebras, their quantum affinizations and associated W-algebras.

  9. An Algebraic Approach to Incomparable Families of Formal Languages

    NARCIS (Netherlands)

    Rozenberg, G.; Asveld, P.R.J.; Salomaa, A.

    1993-01-01

    We extend some results of Ginsburg and Spanier [S. Ginsburg & E.H. Spanier, On incomparable Abstract Families of Languages (AFL), J. Comput. Systems Sci. 9 (1974) 88-108] on incomparable full AFL's (full Abstract Families of Languages) to similar structures like full hyper-AFL's, full hyper(1)-AFL's

  10. An Algebraic Approach to Incomparable Families of Formal Languages

    NARCIS (Netherlands)

    Asveld, P.R.J.; Rozenberg, G.; Salomaa, A.

    1992-01-01

    We extend some results of Ginsburg and Spanier [S. Ginsburg & E.H. Spanier, On incomparable Abstract Families of Languages (AFL), J. Comput. Systems Sci. 9 (1974) 88-108] on incomparable full AFL's (full Abstract Families of Languages) to similar structures like full hyper-AFL's, full hyper(1)-AFL's

  11. Impact of specific language impairment and type of school on different language subsystems.

    Science.gov (United States)

    Puglisi, Marina Leite; Befi-Lopes, Debora Maria

    2016-01-01

    This study aimed to explore quantitative and qualitative effects of type of school and specific language impairment (SLI) on different language abilities. 204 Brazilian children aged from 4 to 6 years old participated in the study. Children were selected to form three groups: 1) 63 typically developing children studying in private schools (TDPri); 2) 102 typically developing children studying in state schools (TDSta); and 39 children with SLI studying in state schools (SLISta). All individuals were assessed regarding expressive vocabulary, number morphology and morphosyntactic comprehension. All language subsystems were vulnerable to both environmental (type of school) and biological (SLI) effects. The relationship between the three language measures was exactly the same to all groups: vocabulary growth correlated with age and with the development of morphological abilities and morphosyntactic comprehension. Children with SLI showed atypical errors in the comprehension test at the age of 4, but presented a pattern of errors that gradually resembled typical development. The effect of type of school was marked by quantitative differences, while the effect of SLI was characterised by both quantitative and qualitative differences.

  12. College algebra

    CERN Document Server

    Kolman, Bernard

    1985-01-01

    College Algebra, Second Edition is a comprehensive presentation of the fundamental concepts and techniques of algebra. The book incorporates some improvements from the previous edition to provide a better learning experience. It provides sufficient materials for use in the study of college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, exponential and logarithmic functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter c

  13. Social stress in young people with specific language impairment

    OpenAIRE

    Wadman, Ruth; Durkin, Kevin; Conti-Ramsden, Gina

    2010-01-01

    Social interactions can be a source of social stress for adolescents. Little is known about how adolescents with developmental difficulties, such as specific language impairment (SLI), feel when interacting socially. Participants included 28 adolescents with SLI and 28 adolescents with typical language abilities (TL). Self-report measures of social stress, social skills and social acceptance were obtained. Participants with SLI reported experiencing significantly more social stress than did p...

  14. Working, declarative and procedural memory in specific language impairment

    DEFF Research Database (Denmark)

    Lum, J. A. G.; Conti-Ramsden, G.; Page, D.

    2012-01-01

    at declarative memory for visual information, and at declarative memory in the verbal domain after controlling for working memory and language. Visuo-spatial short-term memory was intact, whereas verbal working memory was impaired, even when language deficits were held constant. Correlation analyses showed......According to the Procedural Deficit Hypothesis (PDH), abnormalities of brain structures underlying procedural memory largely explain the language deficits in children with specific language impairment (SLI). These abnormalities are posited to result in core deficits of procedural memory, which...... in turn explain the grammar problems in the disorder. The abnormalities are also likely to lead to problems with other, non-procedural functions, such as working memory, that rely at least partly on the affected brain structures. In contrast, declarative memory is expected to remain largely intact...

  15. Twisted classical Poincare algebras

    International Nuclear Information System (INIS)

    Lukierski, J.; Ruegg, H.; Tolstoy, V.N.; Nowicki, A.

    1993-11-01

    We consider the twisting of Hopf structure for classical enveloping algebra U(g), where g is the inhomogeneous rotations algebra, with explicite formulae given for D=4 Poincare algebra (g=P 4 ). The comultiplications of twisted U F (P 4 ) are obtained by conjugating primitive classical coproducts by F element of U(c)xU(c), where c denotes any Abelian subalgebra of P 4 , and the universal R-matrices for U F (P 4 ) are triangular. As an example we show that the quantum deformation of Poincare algebra recently proposed by Chaichian and Demiczev is a twisted classical Poincare algebra. The interpretation of twisted Poincare algebra as describing relativistic symmetries with clustered 2-particle states is proposed. (orig.)

  16. Domain Specific Language Support for Exascale

    Energy Technology Data Exchange (ETDEWEB)

    Sadayappan, Ponnuswamy [The Ohio State Univ., Columbus, OH (United States)

    2017-02-24

    Domain-Specific Languages (DSLs) offer an attractive path to Exascale software since they provide expressive power through appropriate abstractions and enable domain-specific optimizations. But the advantages of a DSL compete with the difficulties of implementing a DSL, even for a narrowly defined domain. The DTEC project addresses how a variety of DSLs can be easily implemented to leverage existing compiler analysis and transformation capabilities within the ROSE open source compiler as part of a research program focusing on Exascale challenges. The OSU contributions to the DTEC project are in the area of code generation from high-level DSL descriptions, as well as verification of the automatically-generated code.

  17. Pre-Algebra Essentials For Dummies

    CERN Document Server

    Zegarelli, Mark

    2010-01-01

    Many students worry about starting algebra. Pre-Algebra Essentials For Dummies provides an overview of critical pre-algebra concepts to help new algebra students (and their parents) take the next step without fear. Free of ramp-up material, Pre-Algebra Essentials For Dummies contains content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical pre-algebra course, from fractions, decimals, and percents to scientific notation and simple variable equations. This guide is also a perfect reference for parents who need to review critical pre-algebra

  18. Representations of quantum bicrossproduct algebras

    International Nuclear Information System (INIS)

    Arratia, Oscar; Olmo, Mariano A del

    2002-01-01

    We present a method to construct induced representations of quantum algebras which have a bicrossproduct structure. We apply this procedure to some quantum kinematical algebras in (1+1) dimensions with this kind of structure: null-plane quantum Poincare algebra, non-standard quantum Galilei algebra and quantum κ-Galilei algebra

  19. Algorithms in Algebraic Geometry

    CERN Document Server

    Dickenstein, Alicia; Sommese, Andrew J

    2008-01-01

    In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

  20. Computer algebra and operators

    Science.gov (United States)

    Fateman, Richard; Grossman, Robert

    1989-01-01

    The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

  1. Abstract Algebra to Secondary School Algebra: Building Bridges

    Science.gov (United States)

    Christy, Donna; Sparks, Rebecca

    2015-01-01

    The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

  2. Infinite dimension algebra and conformal symmetry

    International Nuclear Information System (INIS)

    Ragoucy-Aubezon, E.

    1991-04-01

    A generalisation of Kac-Moody algebras (current algebras defined on a circle) to algebras defined on a compact supermanifold of any dimension and with any number of supersymmetries is presented. For such a purpose, we compute all the central extensions of loop algebras defined on this supermanifold, i.e. all the cohomology classes of these loop algebras. Then, we try to extend the relation (i.e. semi-direct sum) that exists between the two dimensional conformal algebras (called Virasoro algebra) and the usual Kac-Moody algebras, by considering the derivation algebra of our extended Kac-Moody algebras. The case of superconformal algebras (used in superstrings theories) is treated, as well as the cases of area-preserving diffeomorphisms (used in membranes theories), and Krichever-Novikov algebras (used for interacting strings). Finally, we present some generalizations of the Sugawara construction to the cases of extended Kac-Moody algebras, and Kac-Moody of superalgebras. These constructions allow us to get new realizations of the Virasoro, and Ramond, Neveu-Schwarz algebras

  3. BPS algebras, genus zero and the heterotic Monster

    Science.gov (United States)

    Paquette, Natalie M.; Persson, Daniel; Volpato, Roberto

    2017-10-01

    In this note, we expand on some technical issues raised in (Paquette et al 2016 Commun. Number Theory Phys. 10 433-526) by the authors, as well as providing a friendly introduction to and summary of our previous work. We construct a set of heterotic string compactifications to 0  +  1 dimensions intimately related to the Monstrous moonshine module of Frenkel, Lepowsky, and Meurman (and orbifolds thereof). Using this model, we review our physical interpretation of the genus zero property of Monstrous moonshine. Furthermore, we show that the space of (second-quantized) BPS-states forms a module over the Monstrous Lie algebras mg —some of the first and most prominent examples of Generalized Kac-Moody algebras—constructed by Borcherds and Carnahan. In particular, we clarify the structure of the module present in the second-quantized string theory. We also sketch a proof of our methods in the language of vertex operator algebras, for the interested mathematician.

  4. Equivalency of two-dimensional algebras

    International Nuclear Information System (INIS)

    Santos, Gildemar Carneiro dos; Pomponet Filho, Balbino Jose S.

    2011-01-01

    Full text: Let us consider a vector z = xi + yj over the field of real numbers, whose basis (i,j) satisfy a given algebra. Any property of this algebra will be reflected in any function of z, so we can state that the knowledge of the properties of an algebra leads to more general conclusions than the knowledge of the properties of a function. However structural properties of an algebra do not change when this algebra suffers a linear transformation, though the structural constants defining this algebra do change. We say that two algebras are equivalent to each other whenever they are related by a linear transformation. In this case, we have found that some relations between the structural constants are sufficient to recognize whether or not an algebra is equivalent to another. In spite that the basis transform linearly, the structural constants change like a third order tensor, but some combinations of these tensors result in a linear transformation, allowing to write the entries of the transformation matrix as function of the structural constants. Eventually, a systematic way to find the transformation matrix between these equivalent algebras is obtained. In this sense, we have performed the thorough classification of associative commutative two-dimensional algebras, and find that even non-division algebra may be helpful in solving non-linear dynamic systems. The Mandelbrot set was used to have a pictorial view of each algebra, since equivalent algebras result in the same pattern. Presently we have succeeded in classifying some non-associative two-dimensional algebras, a task more difficult than for associative one. (author)

  5. From affine Hecke algebras to boundary symmetries

    International Nuclear Information System (INIS)

    Doikou, Anastasia

    2005-01-01

    Motivated by earlier works we employ appropriate realizations of the affine Hecke algebra and we recover previously known non-diagonal solutions of the reflection equation for the U q (gl n -bar ) case. The corresponding N site spin chain with open boundary conditions is then constructed and boundary non-local charges associated to the non-diagonal solutions of the reflection equation are derived, as coproduct realizations of the reflection algebra. With the help of linear intertwining relations involving the aforementioned solutions of the reflection equation, the symmetry of the open spin chain with the corresponding boundary conditions is exhibited, being essentially a remnant of the U q (gl n -bar ) algebra. More specifically, we show that representations of certain boundary non-local charges commute with the generators of the affine Hecke algebra and with the local Hamiltonian of the open spin chain for a particular choice of boundary conditions. Furthermore, we are able to show that the transfer matrix of the open spin chain commutes with a certain number of boundary non-local charges, depending on the choice of boundary conditions

  6. Working, declarative and procedural memory in specific language impairment

    OpenAIRE

    Lum, Jarrad A.G.; Conti-Ramsden, Gina; Page, Debra; Ullman, Michael T.

    2012-01-01

    According to the Procedural Deficit Hypothesis (PDH), abnormalities of brain structures underlying procedural memory largely explain the language deficits in children with specific language impairment (SLI). These abnormalities are posited to result in core deficits of procedural memory, which in turn explain the grammar problems in the disorder. The abnormalities are also likely to lead to problems with other, non-procedural functions, such as working memory, that rely at least partly on the...

  7. Valued Graphs and the Representation Theory of Lie Algebras

    Directory of Open Access Journals (Sweden)

    Joel Lemay

    2012-07-01

    Full Text Available Quivers (directed graphs, species (a generalization of quivers and their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their applications to the representation theory of associative algebras, Lie algebras, and quantum groups. In this paper, we discuss the most important results in the representation theory of species, such as Dlab and Ringel’s extension of Gabriel’s theorem, which classifies all species of finite and tame representation type. We also explain the link between species and K-species (where K is a field. Namely, we show that the category of K -species can be viewed as a subcategory of the category of species. Furthermore, we prove two results about the structure of the tensor ring of a species containing no oriented cycles. Specifically, we prove that two such species have isomorphic tensor rings if and only if they are isomorphic as “crushed” species, and we show that if K is a perfect field, then the tensor algebra of a K -species tensored with the algebraic closure of K is isomorphic to, or Morita equivalent to, the path algebra of a quiver.

  8. Specific language impairment as a maturational lag: evidence from longitudinal data on language and motor development.

    Science.gov (United States)

    Bishop, D V; Edmundson, A

    1987-08-01

    Longitudinal language-test data on 87 language-impaired children assessed at the ages of four, 4 1/2 and 5 1/2 years were converted to age-equivalent scores to compare the rates of development of children who recover from early language delay with those who have more persisting problems. On most measures, over the 18-month period all the children progressed by about 18 months. Thus although children with good and poor outcomes were distinguished in terms of initial level of performance, they did not differ in rate of progress. Speed on a peg-moving task was closely related to language performance. Children who had a good outcome after early language delay had significantly impaired scores at four years, but subsequently were indistinguishable from a control group. Quantitative but not qualitative differences in peg-moving performance were found for children with good and poor outcomes. No association was found between presumptive aetiological factors and language or pegboard performance. These findings are interpreted in terms of a theory which attributes specific language impairment to a maturational lag in neurological development.

  9. Axis Problem of Rough 3-Valued Algebras

    Institute of Scientific and Technical Information of China (English)

    Jianhua Dai; Weidong Chen; Yunhe Pan

    2006-01-01

    The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras and 3-valued Lukasiewicz algebras. A 3-valued Lukasiewicz algebra is a Stone algebra, a regular double Stone algebra, a semi-simple Nelson algebra, a pre-rough algebra. Thus, we call the algebra constructed by the collection of rough sets of an approximation space a rough 3-valued Lukasiewicz algebra. In this paper,the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras, are studied. Whether the rough 3-valued Lukasiewicz algebra is a axled 3-valued Lukasiewicz algebra is examined.

  10. Heritability of specific language impairment depends on diagnostic criteria.

    Science.gov (United States)

    Bishop, D V M; Hayiou-Thomas, M E

    2008-04-01

    Heritability estimates for specific language impairment (SLI) have been inconsistent. Four twin studies reported heritability of 0.5 or more, but a recent report from the Twins Early Development Study found negligible genetic influence in 4-year-olds. We considered whether the method of ascertainment influenced results and found substantially higher heritability if SLI was defined in terms of referral to speech and language pathology services than if defined by language test scores. Further analysis showed that presence of speech difficulties played a major role in determining whether a child had contact with services. Childhood language disorders that are identified by population screening are likely to have a different phenotype and different etiology from clinically referred cases. Genetic studies are more likely to find high heritability if they focus on cases who have speech difficulties and who have been referred for intervention.

  11. Memory Functioning and Mental Verbs Acquisition in Children with Specific Language Impairment

    Science.gov (United States)

    Spanoudis, George C.; Natsopoulos, Demetrios

    2011-01-01

    Memory and language operate in synergy. Recent literature stresses the importance of memory functioning in interpreting language deficits. Two groups of 50 children each, ages 8-12 were studied. The first group included children with specific language impairment, while the participants in the second group were typically developing children. The…

  12. Algebraic K- and L-theory and applications to the topology of manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Hambleton, I [Department of Mathematics and Statistics, McMaster University, Hamilton (Canada)

    2002-08-15

    The development of geometric topology has led to the identification of specific algebraic structures of great richness and usefulness. A common theme in this area is the study of algebraic invariants of discrete groups or rings by topological methods. The resulting subject is now called algebraic K-theory. The purpose of these lecture notes is to survey some of the main constructions and techniques in algebraic K-theory, together with an indication of the topological backnd and applications. More details about proofs can be found in the references. The material is organized into some introductory sections, concerning linear and unitary K-theory, followed by descriptions of four important geometric problems and their related algebraic methods.

  13. Enveloping σ-C C C-algebra of a smooth Frechet algebra crossed ...

    Indian Academy of Sciences (India)

    Home; Journals; Proceedings – Mathematical Sciences; Volume 116; Issue 2. Enveloping -*-Algebra of a Smooth Frechet Algebra Crossed Product by R R , K -Theory and Differential Structure in *-Algebras. Subhash J Bhatt. Regular Articles Volume 116 Issue 2 May 2006 pp 161-173 ...

  14. Hecke algebras with unequal parameters

    CERN Document Server

    Lusztig, G

    2003-01-01

    Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over p-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very interesting combinatorial properties. In the present book, the author extends the theory of the KL-basis to a more general class of Hecke algebras, the so-called algebras with unequal parameters. In particular, he formulates conjectures describing the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures in particular cases. Written in the author's precise style, the book gives rese...

  15. Analysis of Secondary School Students’ Algebraic Thinking and Math-Talk Learning Community to Help Students Learn

    Science.gov (United States)

    Nurhayati, D. M.; Herman, T.; Suhendra, S.

    2017-09-01

    This study aims to determine the difficulties of algebraic thinking ability of students in one of secondary school on quadrilateral subject and to describe Math-Talk Learning Community as the alternative way that can be done to overcome the difficulties of the students’ algebraic thinking ability. Research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and twenty three students as the sample that was chosen by purposive sampling technique. Data of algebraic thinking were collected through essay test. The results showed the percentage of achievement of students’ algebraic thinking’s indicators on three aspects: a) algebra as generalized arithmetic with the indicators (conceptually based computational strategies and estimation); b) algebra as the language of mathematics (meaning of variables, variable expressions and meaning of solution); c) algebra as a tool for functions and mathematical modelling (representing mathematical ideas using equations, tables, or words and generalizing patterns and rules in real-world contexts) is still low. It is predicted that because the secondary school students was not familiar with the abstract problem and they are still at a semi-concrete stage where the stage of cognitive development is between concrete and abstract. Based on the percentage achievement of each indicators, it can be concluded that the level of achievement of student’s mathematical communication using conventional learning is still low, so students’ algebraic thinking ability need to be improved.

  16. Categories and Commutative Algebra

    CERN Document Server

    Salmon, P

    2011-01-01

    L. Badescu: Sur certaines singularites des varietes algebriques.- D.A. Buchsbaum: Homological and commutative algebra.- S. Greco: Anelli Henseliani.- C. Lair: Morphismes et structures algebriques.- B.A. Mitchell: Introduction to category theory and homological algebra.- R. Rivet: Anneaux de series formelles et anneaux henseliens.- P. Salmon: Applicazioni della K-teoria all'algebra commutativa.- M. Tierney: Axiomatic sheaf theory: some constructions and applications.- C.B. Winters: An elementary lecture on algebraic spaces.

  17. Particle-like structure of Lie algebras

    Science.gov (United States)

    Vinogradov, A. M.

    2017-07-01

    If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i's, we say that 𝔤 is simply assembled from the 𝔤i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i's, one obtains a Lie algebra assembled in two steps from 𝔤i's, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions: which Lie algebras can be assembled from a given family of Lie algebras, and from which Lie algebras can a given Lie algebra be assembled. We develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of Lie algebras. The main result of our theory is that any finite-dimensional Lie algebra over an algebraically closed field of characteristic zero or over R can be assembled in a finite number of steps from two elementary constituents, which we call dyons and triadons. Up to an abelian summand, a dyon is a Lie algebra structure isomorphic to the non-abelian 2-dimensional Lie algebra, while a triadon is isomorphic to the 3-dimensional Heisenberg Lie algebra. As an example, we describe constructions of classical Lie algebras from triadons.

  18. Integrating Relational Databases and Constraint Languages

    DEFF Research Database (Denmark)

    Hansen, Michael Reichhardt; Hansen, Bo S.; Lucas, Peter

    1989-01-01

    A new structure of application programs is suggested, which separates the algorithmic parts from factual information (data and rules). The latter is to be stored in a repository that can be shared among multiple applications. It is argued that rules stating pure relations are better suited...... for sharing among different applications than procedural or functional rules because these latter rules always determine inputs and outputs.To support such a repository, an extended relational algebra is explored. This algebra serves as the semantic model for a proposed rules language and is the basis...

  19. Dynamical entropy of C* algebras and Von Neumann algebras

    International Nuclear Information System (INIS)

    Connes, A.; Narnhofer, H.; Thirring, W.

    1986-01-01

    The definition of the dynamical entropy is extended for automorphism groups of C * algebras. As example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density. (Author)

  20. A Typed Text Retrieval Query Language for XML Documents.

    Science.gov (United States)

    Colazzo, Dario; Sartiani, Carlo; Albano, Antonio; Manghi, Paolo; Ghelli, Giorgio; Lini, Luca; Paoli, Michele

    2002-01-01

    Discussion of XML focuses on a description of Tequyla-TX, a typed text retrieval query language for XML documents that can search on both content and structures. Highlights include motivations; numerous examples; word-based and char-based searches; tag-dependent full-text searches; text normalization; query algebra; data models and term language;…

  1. Gradings on simple Lie algebras

    CERN Document Server

    Elduque, Alberto

    2013-01-01

    Gradings are ubiquitous in the theory of Lie algebras, from the root space decomposition of a complex semisimple Lie algebra relative to a Cartan subalgebra to the beautiful Dempwolff decomposition of E_8 as a direct sum of thirty-one Cartan subalgebras. This monograph is a self-contained exposition of the classification of gradings by arbitrary groups on classical simple Lie algebras over algebraically closed fields of characteristic not equal to 2 as well as on some nonclassical simple Lie algebras in positive characteristic. Other important algebras also enter the stage: matrix algebras, the octonions, and the Albert algebra. Most of the presented results are recent and have not yet appeared in book form. This work can be used as a textbook for graduate students or as a reference for researchers in Lie theory and neighboring areas.

  2. Elementary Algebra Connections to Precalculus

    Science.gov (United States)

    Lopez-Boada, Roberto; Daire, Sandra Arguelles

    2013-01-01

    This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

  3. Extension of specification language for soundness and completeness of service workflow

    Science.gov (United States)

    Viriyasitavat, Wattana; Xu, Li Da; Bi, Zhuming; Sapsomboon, Assadaporn

    2018-05-01

    A Service Workflow is an aggregation of distributed services to fulfill specific functionalities. With ever increasing available services, the methodologies for the selections of the services against the given requirements become main research subjects in multiple disciplines. A few of researchers have contributed to the formal specification languages and the methods for model checking; however, existing methods have the difficulties to tackle with the complexity of workflow compositions. In this paper, we propose to formalize the specification language to reduce the complexity of the workflow composition. To this end, we extend a specification language with the consideration of formal logic, so that some effective theorems can be derived for the verification of syntax, semantics, and inference rules in the workflow composition. The logic-based approach automates compliance checking effectively. The Service Workflow Specification (SWSpec) has been extended and formulated, and the soundness, completeness, and consistency of SWSpec applications have been verified; note that a logic-based SWSpec is mandatory for the development of model checking. The application of the proposed SWSpec has been demonstrated by the examples with the addressed soundness, completeness, and consistency.

  4. Interactions between working memory and language in young children with specific language impairment (SLI).

    Science.gov (United States)

    Vugs, Brigitte; Knoors, Harry; Cuperus, Juliane; Hendriks, Marc; Verhoeven, Ludo

    2016-01-01

    The underlying structure of working memory (WM) in young children with and without specific language impairment (SLI) was examined. The associations between the components of WM and the language abilities of young children with SLI were then analyzed. The Automated Working Memory Assessment and four linguistic tasks were administered to 58 children with SLI and 58 children without SLI, aged 4-5 years. The WM of the children was best represented by a model with four separate but interacting components of verbal storage, visuospatial storage, verbal central executive (CE), and visuospatial CE. The associations between the four components of WM did not differ significantly for the two groups of children. However, the individual components of WM showed varying associations with the language abilities of the children with SLI. The verbal CE component of WM was moderately to strongly associated with all the language abilities in children with SLI: receptive vocabulary, expressive vocabulary, verbal comprehension, and syntactic development. These results show verbal CE to be involved in a wide range of linguistic skills; the limited ability of young children with SLI to simultaneously store and process verbal information may constrain their acquisition of linguistic skills. Attention should thus be paid to the language problems of children with SLI, but also to the WM impairments that can contribute to their language problems.

  5. Topological conformal algebra and BRST algebra in non-critical string theories

    International Nuclear Information System (INIS)

    Fujikawa, Kazuo; Suzuki, Hiroshi.

    1991-03-01

    The operator algebra in non-critical string theories is studied by treating the cosmological term as a perturbation. The algebra of covariantly regularized BRST and related currents contains a twisted N = 2 superconformal algebra only at d = -2 in bosonic strings, and a twisted N = 3 superconformal algebra only at d = ±∞ in spinning strings. The bosonic string at d = -2 is examined by replacing the string coordinate by a fermionic matter with c = -2. The resulting bc-βγ system accommodates various forms of BRST cohomology, and the ghost number assignment and BRST cohomology are different in the c = -2 string theory and two-dimensional topological gravity. (author)

  6. Type Error Customization for Embedded Domain-Specific Languages

    NARCIS (Netherlands)

    Serrano Mena, Alejandro

    2018-01-01

    Domain-specific languages (DSLs) are a widely used technique in the programming world, since they make communication between experts and developers more fluid. Some well-known examples are SQL for databases and HTML for web page description. There are two different approaches to developing DSLs:

  7. Algebraic K-theory

    CERN Document Server

    Srinivas, V

    1996-01-01

    Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and graduate students in mathematics. The book is based on lectures given at the author's home institution, the Tata Institute in Bombay, and elsewhere. A detailed appendix on topology was provided in the first edition to make the treatment accessible to readers with a limited background in topology. The second edition also includes an appendix on algebraic geometry that contains the required definitions and results needed to understand the core of the book; this makes the book accessible to a wider audience. A central part of the book is a detailed exposition of the ideas of Quillen as contained in his classic papers "Higher Algebraic K-Theory, I, II." A more elementary proof of the theorem of Merkujev--Suslin is given in this edition; this makes the treatment of this topic self-contained. An application ...

  8. Head First Algebra A Learner's Guide to Algebra I

    CERN Document Server

    Pilone, Tracey

    2008-01-01

    Having trouble understanding algebra? Do algebraic concepts, equations, and logic just make your head spin? We have great news: Head First Algebra is designed for you. Full of engaging stories and practical, real-world explanations, this book will help you learn everything from natural numbers and exponents to solving systems of equations and graphing polynomials. Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive i

  9. Novikov algebras with associative bilinear forms

    Energy Technology Data Exchange (ETDEWEB)

    Zhu Fuhai; Chen Zhiqi [School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071 (China)

    2007-11-23

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.

  10. An algebraic approach to analysis of recursive and concurrent programs

    DEFF Research Database (Denmark)

    Terepeta, Michal Tomasz

    -approximation of (or induced from) another flow algebra. Furthermore, we show how flow algebras can be used in communicating or weighted pushdown systems. To achieve that, we show that it is possible to relax some of the requirements imposed by original formulation of those techniques without compromising...... such a language. We also introduce an abstract domain that symbolically represents the messages sent between the concurrently executing processes. It stores prefixes or suffixes of communication traces including various constraints imposed on the messages. Since the problem has exponential complexity, we also...... present a compact data structure as well as efficient algorithms for the semiring operations. Apart from that, we discuss an improvement to Pre* and Post* algorithms for pushdown systems, making it possible to directly use program representations such as program graphs. We present a modular library...

  11. Lie algebra in quantum physics by means of computer algebra

    OpenAIRE

    Kikuchi, Ichio; Kikuchi, Akihito

    2017-01-01

    This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold way model, and the usage of Weyl character formula (in order to construct w...

  12. Tensor spaces and exterior algebra

    CERN Document Server

    Yokonuma, Takeo

    1992-01-01

    This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

  13. Profinite algebras and affine boundedness

    OpenAIRE

    Schneider, Friedrich Martin; Zumbrägel, Jens

    2015-01-01

    We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a topological algebra, whereas for topological groups, rings, semigroups, and distributive lattices, profiniteness turns out to be a purely topological property as it is is equivalent to the underlying topological space being a Stone space. Condensing the core...

  14. The Systems Biology Markup Language (SBML): Language Specification for Level 3 Version 1 Core.

    Science.gov (United States)

    Hucka, Michael; Bergmann, Frank T; Hoops, Stefan; Keating, Sarah M; Sahle, Sven; Schaff, James C; Smith, Lucian P; Wilkinson, Darren J

    2015-09-04

    Computational models can help researchers to interpret data, understand biological function, and make quantitative predictions. The Systems Biology Markup Language (SBML) is a file format for representing computational models in a declarative form that can be exchanged between different software systems. SBML is oriented towards describing biological processes of the sort common in research on a number of topics, including metabolic pathways, cell signaling pathways, and many others. By supporting SBML as an input/output format, different tools can all operate on an identical representation of a model, removing opportunities for translation errors and assuring a common starting point for analyses and simulations. This document provides the specification for Version 1 of SBML Level 3 Core. The specification defines the data structures prescribed by SBML as well as their encoding in XML, the eXtensible Markup Language. This specification also defines validation rules that determine the validity of an SBML document, and provides many examples of models in SBML form. Other materials and software are available from the SBML project web site, http://sbml.org/.

  15. Double-partition Quantum Cluster Algebras

    DEFF Research Database (Denmark)

    Jakobsen, Hans Plesner; Zhang, Hechun

    2012-01-01

    A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but sub-classes have been studied previously by other authors. The algebras are indexed by double parti- tions or double flag varieties. Equivalently, they are indexed by broken lines L. By grouping...... together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of one broken line to another. Compatible pairs can be written down. The algebras are equal to their upper cluster algebras. The variables of the quantum seeds are given by elements of the dual canonical basis....

  16. Algebra II workbook for dummies

    CERN Document Server

    Sterling, Mary Jane

    2014-01-01

    To succeed in Algebra II, start practicing now Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for future success. Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebr

  17. Very true operators on MTL-algebras

    Directory of Open Access Journals (Sweden)

    Wang Jun Tao

    2016-01-01

    Full Text Available The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.

  18. A new algebraic white-noise modal combination rule - GAC(A)

    International Nuclear Information System (INIS)

    Mertens, P.G.

    1994-01-01

    It is a well known fact that above the rigid frequency the maximum dynamic modal responses even with different multiple supports can be combined algebraically. Below the rigid frequency, and more specifically in the white-noise (amplified) region of the response spectrum, algebraic modal combination is still a matter of controversy, demonstrated e.g. by the NRC R.G. 1.92 requirement to take the absolute values of the modal responses in heuristic modal combination rules; whereas algebraic support combination is only allowed in conjunction with the envelope support response spectrum (ERS). Such regulatory requirements can lead to unrealistically high calculated responses e.g. in the coupled analysis of light secondary systems attached to heavy primary structures and in the decoupled analysis of systems when the centres of mass and stiffness do not coincide, or when the ERS is used. A new Generalised Algebraic Combination (GAC) methodology has been theoretically developed which allows practical algebraic modal and support combination over the whole frequency range of multiple support spectra. The present paper deals with the GAC-(A) i.e. the modal combination version in the white noise region of a single response spectrum and more specifically its time history integration validation, which shows that this new modal combination rule can satisfy any realistic conservatism that may be required by regulatory institutions. (orig.)

  19. Specific "scientific" data structures, and their processing

    Directory of Open Access Journals (Sweden)

    Jerzy Karczmarczuk

    2011-09-01

    Full Text Available Programming physicists use, as all programmers, arrays, lists, tuples, records, etc., and this requires some change in their thought patterns while converting their formulae into some code, since the "data structures" operated upon, while elaborating some theory and its consequences, are rather: power series and Padé approximants, differential forms and other instances of differential algebras, functionals (for the variational calculus, trajectories (solutions of differential equations, Young diagrams and Feynman graphs, etc. Such data is often used in a [semi-]numerical setting, not necessarily "symbolic", appropriate for the computer algebra packages. Modules adapted to such data may be "just libraries", but often they become specific, embedded sub-languages, typically mapped into object-oriented frameworks, with overloaded mathematical operations. Here we present a functional approach to this philosophy. We show how the usage of Haskell datatypes and - fundamental for our tutorial - the application of lazy evaluation makes it possible to operate upon such data (in particular: the "infinite" sequences in a natural and comfortable manner.

  20. Declarative capacity does not trade-off with procedural capacity in children with specific language impairment

    Directory of Open Access Journals (Sweden)

    Sengottuvel Kuppuraj

    2016-10-01

    Full Text Available Background and aims The procedural deficit hypothesis attributes the language phenotype in children with specific language impairment to an impaired procedural and relatively intact declarative memory system. The declarative compensatory hypothesis is an extension of the procedural deficit hypothesis which claims that the declarative system in specific language impairment compensates for the procedural deficit. The present study’s aim was to examine the claims of the procedural deficit hypothesis and declarative compensatory hypothesis by examining these memory systems and relation between them in specific language impairment. Methods Participants were children aged 8–13 years, 30 with specific language impairment and 30 typically developing controls, who spoke Kannada (an agglutinating language of the Dravidian family. Procedural learning was assessed using a serial reaction time task. Declarative memory was assessed using two non-verbal tasks that differed at the level of encoding and retrieval: a recognition memory task after incidental encoding using real and novel object images and a recall task after intentional encoding using visual paired associates. Retrieval was examined after short (10 min and long (60 min delays after encoding on both declarative tasks. Results Findings confirmed that children with specific language impairment (SLI have impaired procedural memory on a non-verbal serial reaction time task. On recognition memory task after incidental encoding though children with specific language impairment encoded less well, they recognized items as well as typically developing controls. Both the groups retrieved more at short compared to long intervals and retrieved real (verbalizable objects better than novel objects. On visual paired associates (recall task with intentional encoding children with specific language impairment retrieved less than typically developing children (even after controlling for non-verbal ability

  1. Experimental and Theoretical Methods in Algebra, Geometry and Topology

    CERN Document Server

    Veys, Willem; Bridging Algebra, Geometry, and Topology

    2014-01-01

    Algebra, geometry and topology cover a variety of different, but intimately related research fields in modern mathematics. This book focuses on specific aspects of this interaction. The present volume contains refereed papers which were presented at the International Conference “Experimental and Theoretical Methods in Algebra, Geometry and Topology”, held in Eforie Nord (near Constanta), Romania, during 20-25 June 2013. The conference was devoted to the 60th anniversary of the distinguished Romanian mathematicians Alexandru Dimca and Ştefan Papadima. The selected papers consist of original research work and a survey paper. They are intended for a large audience, including researchers and graduate students interested in algebraic geometry, combinatorics, topology, hyperplane arrangements and commutative algebra. The papers are written by well-known experts from different fields of mathematics, affiliated to universities from all over the word, they cover a broad range of topics and explore the research f...

  2. Strategies for Solving Fraction Tasks and Their Link to Algebraic Thinking

    Science.gov (United States)

    Pearn, Catherine; Stephens, Max

    2015-01-01

    Many researchers argue that a deep understanding of fractions is important for a successful transition to algebra. Teaching, especially in the middle years, needs to focus specifically on those areas of fraction knowledge and operations that support subsequent solution processes for algebraic equations. This paper focuses on the results of Year 6…

  3. Hopf algebras in noncommutative geometry

    International Nuclear Information System (INIS)

    Varilly, Joseph C.

    2001-10-01

    We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)

  4. W-realization of Lie algebras. Application to so(4,2) and Poincare algebras

    International Nuclear Information System (INIS)

    Barbarin, F.; Ragoucy, E.; Sorba, P.

    1996-05-01

    The property of some finite W-algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra G is exploited for the obtention of new G-realizations from a 'canonical' differential one. The method is applied to the conformal algebra so(4,2) and therefore yields also results for its Poincare subalgebra. Unitary irreducible representations of these algebras are recognized in this approach, which is naturally compared -or associated to - the induced representation technique. (author)

  5. Extended Kac-Moody algebras and applications

    International Nuclear Information System (INIS)

    Ragoucy, E.; Sorba, P.

    1991-04-01

    The notion of a Kac-Moody algebra defined on the S 1 circle is extended to super Kac-Moody algebras defined on MxG N , M being a smooth closed compact manifold of dimension greater than one, and G N the Grassman algebra with N generators. All the central extensions of these algebras are computed. Then, for each such algebra the derivation algebra constructed from the MxG N diffeomorphism is determined. The twists of such super Kac-Moody algebras as well as the generalization to non-compact surfaces are partially studied. Finally, the general construction is applied to the study of conformal and superconformal algebras, as well as area-preserving diffeomorphisms algebra and its supersymmetric extension. (author) 65 refs

  6. Lie algebras and applications

    CERN Document Server

    Iachello, Francesco

    2015-01-01

    This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators...

  7. (Fuzzy) Ideals of BN-Algebras

    Science.gov (United States)

    Walendziak, Andrzej

    2015-01-01

    The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050

  8. Domain Specific Languages for Interactive Web Services

    DEFF Research Database (Denmark)

    Brabrand, Claus

    This dissertation shows how domain specific languages may be applied to the domain of interactive Web services to obtain flexible, safe, and efficient solutions. We show how each of four key aspects of interactive Web services involving sessions, dynamic creation of HTML/XML documents, form field......, , that supports virtually all aspects of the development of interactive Web services and provides flexible, safe, and efficient solutions....

  9. Non-relativistic Bondi-Metzner-Sachs algebra

    Science.gov (United States)

    Batlle, Carles; Delmastro, Diego; Gomis, Joaquim

    2017-09-01

    We construct two possible candidates for non-relativistic bms4 algebra in four space-time dimensions by contracting the original relativistic bms4 algebra. bms4 algebra is infinite-dimensional and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed nrbms4 algebras can be regarded as two infinite-dimensional extensions of the Bargmann algebra. We also study a canonical realization of one of these algebras in terms of the Fourier modes of a free Schrödinger field, mimicking the canonical realization of relativistic bms4 algebra using a free Klein-Gordon field.

  10. Is recursion language-specific? Evidence of recursive mechanisms in the structure of intentional action.

    Science.gov (United States)

    Vicari, Giuseppe; Adenzato, Mauro

    2014-05-01

    In their 2002 seminal paper Hauser, Chomsky and Fitch hypothesize that recursion is the only human-specific and language-specific mechanism of the faculty of language. While debate focused primarily on the meaning of recursion in the hypothesis and on the human-specific and syntax-specific character of recursion, the present work focuses on the claim that recursion is language-specific. We argue that there are recursive structures in the domain of motor intentionality by way of extending John R. Searle's analysis of intentional action. We then discuss evidence from cognitive science and neuroscience supporting the claim that motor-intentional recursion is language-independent and suggest some explanatory hypotheses: (1) linguistic recursion is embodied in sensory-motor processing; (2) linguistic and motor-intentional recursions are distinct and mutually independent mechanisms. Finally, we propose some reflections about the epistemic status of HCF as presenting an empirically falsifiable hypothesis, and on the possibility of testing recursion in different cognitive domains. Copyright © 2014 Elsevier Inc. All rights reserved.

  11. Safety properties test data selection from an algebraic model of Lustre programs; Selection de tests de proprietes de surete a partir d'une modelisation algebrique de programmes lustre

    Energy Technology Data Exchange (ETDEWEB)

    Hsiao, N.Ch

    1995-07-01

    In the context to validate an industrial software, which is a set of reactive programs, we are confronted with the safety properties verification problem. This thesis reports an experience in which our goal is to generate the test data satisfying a safety property. The software to be validated is designed with the SAGA tool, in which a view can be regarded as a program of a programming language called LUSTRE. We adapt a test data generation tool called LOFT to this kind of programs. In this way, we consider the functional testing method on which the LOFT tool is based. Given any LUSTRE program, we try to give it an algebraic model because LOFT treats algebraic specifications. So, our task consists In defining a formal framework in which any LUSTRE program can be translated into a LOFT module: based on an operational semantics of the LUSTRE language, the flow types 'T-flow' are specified with the constructive algebraic formalism, then implemented in a LOFT modules base. Next, in a test selection process assisted by LOFT, a safety property Is expressed by an equation to join other control hypotheses, and to guide the test data selection. Some concrete test data set are generated in this way on some significant examples. This experience confirm the feasibility of formal method on test data selection for the reactive programs. (author)

  12. The Unitality of Quantum B-algebras

    Science.gov (United States)

    Han, Shengwei; Xu, Xiaoting; Qin, Feng

    2018-02-01

    Quantum B-algebras as a generalization of quantales were introduced by Rump and Yang, which cover the majority of implicational algebras and provide a unified semantic for a wide class of substructural logics. Unital quantum B-algebras play an important role in the classification of implicational algebras. The main purpose of this paper is to construct unital quantum B-algebras from non-unital quantum B-algebras.

  13. On Weak-BCC-Algebras

    Science.gov (United States)

    Thomys, Janus; Zhang, Xiaohong

    2013-01-01

    We describe weak-BCC-algebras (also called BZ-algebras) in which the condition (x∗y)∗z = (x∗z)∗y is satisfied only in the case when elements x, y belong to the same branch. We also characterize ideals, nilradicals, and nilpotent elements of such algebras. PMID:24311983

  14. G-identities of non-associative algebras

    International Nuclear Information System (INIS)

    Bakhturin, Yu A; Zaitsev, M V; Sehgal, S K

    1999-01-01

    The main class of algebras considered in this paper is the class of algebras of Lie type. This class includes, in particular, associative algebras, Lie algebras and superalgebras, Leibniz algebras, quantum Lie algebras, and many others. We prove that if a finite group G acts on such an algebra A by automorphisms and anti-automorphisms and A satisfies an essential G-identity, then A satisfies an ordinary identity of degree bounded by a function that depends on the degree of the original identity and the order of G. We show in the case of ordinary Lie algebras that if L is a Lie algebra, a finite group G acts on L by automorphisms and anti-automorphisms, and the order of G is coprime to the characteristic of the field, then the existence of an identity on skew-symmetric elements implies the existence of an identity on the whole of L, with the same kind of dependence between the degrees of the identities. Finally, we generalize Amitsur's theorem on polynomial identities in associative algebras with involution to the case of alternative algebras with involution

  15. W-realization of Lie algebras. Application to so(4,2) and Poincare algebras

    Energy Technology Data Exchange (ETDEWEB)

    Barbarin, F.; Ragoucy, E.; Sorba, P.

    1996-05-01

    The property of some finite W-algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra G is exploited for the obtention of new G-realizations from a `canonical` differential one. The method is applied to the conformal algebra so(4,2) and therefore yields also results for its Poincare subalgebra. Unitary irreducible representations of these algebras are recognized in this approach, which is naturally compared -or associated to - the induced representation technique. (author). 12 refs.

  16. On Dunkl angular momenta algebra

    Energy Technology Data Exchange (ETDEWEB)

    Feigin, Misha [School of Mathematics and Statistics, University of Glasgow,15 University Gardens, Glasgow G12 8QW (United Kingdom); Hakobyan, Tigran [Yerevan State University,1 Alex Manoogian, 0025 Yerevan (Armenia); Tomsk Polytechnic University,Lenin Ave. 30, 634050 Tomsk (Russian Federation)

    2015-11-17

    We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl(N) version of the subalgebra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.

  17. Algebraic computing

    International Nuclear Information System (INIS)

    MacCallum, M.A.H.

    1990-01-01

    The implementation of a new computer algebra system is time consuming: designers of general purpose algebra systems usually say it takes about 50 man-years to create a mature and fully functional system. Hence the range of available systems and their capabilities changes little between one general relativity meeting and the next, despite which there have been significant changes in the period since the last report. The introductory remarks aim to give a brief survey of capabilities of the principal available systems and highlight one or two trends. The reference to the most recent full survey of computer algebra in relativity and brief descriptions of the Maple, REDUCE and SHEEP and other applications are given. (author)

  18. Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra

    CERN Document Server

    Cox, David A; O'Shea, Donal

    2015-01-01

    This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem, and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and, with some supplementation perhaps, for beginning graduate level courses in algebraic geom...

  19. Space-time algebra

    CERN Document Server

    Hestenes, David

    2015-01-01

    This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, a...

  20. Connections between algebra, combinatorics, and geometry

    CERN Document Server

    Sather-Wagstaff, Sean

    2014-01-01

    Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...

  1. Abstract algebra for physicists

    International Nuclear Information System (INIS)

    Zeman, J.

    1975-06-01

    Certain recent models of composite hadrons involve concepts and theorems from abstract algebra which are unfamiliar to most theoretical physicists. The algebraic apparatus needed for an understanding of these models is summarized here. Particular emphasis is given to algebraic structures which are not assumed to be associative. (2 figures) (auth)

  2. The Development of English as a Second Language With and Without Specific Language Impairment: Clinical Implications.

    Science.gov (United States)

    Paradis, Johanne

    2016-02-01

    The purpose of this research forum article is to provide an overview of typical and atypical development of English as a second language (L2) and to present strategies for clinical assessment with English language learners (ELLs). A review of studies examining the lexical, morphological, narrative, and verbal memory abilities of ELLs is organized around 3 topics: timeframe and characteristics of typical English L2 development, comparison of the English L2 development of children with and without specific language impairment (SLI), and strategies for more effective assessment with ELLs. ELLs take longer than 3 years to converge on monolingual norms and approach monolingual norms asynchronously across linguistic subdomains. Individual variation is predicted by age, first language, language learning aptitude, length of exposure to English in school, maternal education, and richness of the English environment outside school. ELLs with SLI acquire English more slowly than ELLs with typical development; their morphological and nonword repetition abilities differentiate them the most. Use of strategies such as parent questionnaires on first language development and ELL norm referencing can result in accurate discrimination of ELLs with SLI. Variability in the language abilities of ELLs presents challenges for clinical practice. Increased knowledge of English language learning development with and without SLI together with evidence-based alternative assessment strategies can assist in overcoming these challenges.

  3. Basic notions of algebra

    CERN Document Server

    Shafarevich, Igor Rostislavovich

    2005-01-01

    This book is wholeheartedly recommended to every student or user of mathematics. Although the author modestly describes his book as 'merely an attempt to talk about' algebra, he succeeds in writing an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields, commutative rings and groups studied in every university math course, through Lie groups and algebras to cohomology and category theory, the author shows how the origins of each algebraic concept can be related to attempts to model phenomena in physics or in other branches

  4. Characterizations of locally C*-algebras

    International Nuclear Information System (INIS)

    Mohammad, N.; Somasundaram, S.

    1991-08-01

    We seek the generalization of the Gelfand-Naimark theorems for locally C*-algebras. Precisely, if A is a unital commutative locally C*-algebra, then it is shown that A is *-isomorphic (topologically and algebraically) to C(Δ). Further, if A is any locally C*-algebra, then it is realized as a closed *-subalgebra of some L(H) up to a topological algebraic *-isomorphism. Also, a brief exposition of the Gelfand-Naimark-Segal construction is given and some of its consequences are discussed. (author). 16 refs

  5. Spoken Word Recognition in Adolescents with Autism Spectrum Disorders and Specific Language Impairment

    Science.gov (United States)

    Loucas, Tom; Riches, Nick; Baird, Gillian; Pickles, Andrew; Simonoff, Emily; Chandler, Susie; Charman, Tony

    2013-01-01

    Spoken word recognition, during gating, appears intact in specific language impairment (SLI). This study used gating to investigate the process in adolescents with autism spectrum disorders plus language impairment (ALI). Adolescents with ALI, SLI, and typical language development (TLD), matched on nonverbal IQ listened to gated words that varied…

  6. Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras

    NARCIS (Netherlands)

    Put, Marius van der

    1999-01-01

    The Galois theory of linear differential equations is presented, including full proofs. The connection with algebraic groups and their Lie algebras is given. As an application the inverse problem of differential Galois theory is discussed. There are many exercises in the text.

  7. Theory of mind and specific language impairment in school-age children.

    Science.gov (United States)

    Spanoudis, George

    2016-01-01

    Research on the relationship between aspects of language development and Theory of Mind (ToM) in children with language impairments suggests that children with language impairment show a delay in ToM development. This study aimed to examine the relationships of the syntactic, semantic, and pragmatic skills with ToM in school-age children. Twenty children with Specific Language Impairment (SLI) aged 9-12 years and two control groups, one matched for chronological age (CA) and one for language ability (LA) (aged 8-10 years) were compared on a set of language tasks tapping syntactic, semantic, and pragmatic skills and on an advanced test of ToM. Results showed that children with SLI performed poorly on the ToM task compared to the CA matches. Also, analysis showed that language skills and ToM are related and that syntactic and pragmatic abilities contributed significantly to the prediction of ToM performance in the SLI group. It is concluded that the syntax/pragmatic aspects of the language impact on ToM understanding in children with SLI. Copyright © 2016 Elsevier Inc. All rights reserved.

  8. Brauer algebras of type B

    NARCIS (Netherlands)

    Cohen, A.M.; Liu, S.

    2011-01-01

    For each n>0, we define an algebra having many properties that one might expect to hold for a Brauer algebra of type Bn. It is defined by means of a presentation by generators and relations. We show that this algebra is a subalgebra of the Brauer algebra of type Dn+1 and point out a cellular

  9. A course in BE-algebras

    CERN Document Server

    Mukkamala, Sambasiva Rao

    2018-01-01

    This book presents a unified course in BE-algebras with a comprehensive introduction, general theoretical basis and several examples. It introduces the general theoretical basis of BE-algebras, adopting a credible style to offer students a conceptual understanding of the subject. BE-algebras are important tools for certain investigations in algebraic logic, because they can be considered as fragments of any propositional logic containing a logical connective implication and the constant "1", which is considered as the logical value “true”.  Primarily aimed at graduate and postgraduate students of mathematics, it also helps researchers and mathematicians to build a strong foundation in applied abstract algebra. Presenting insights into some of the abstract thinking that constitutes modern abstract algebra, it provides a transition from elementary topics to advanced topics in BE-algebras. With abundant examples and exercises arranged after each section, it offers readers a comprehensive, easy-to-follow int...

  10. On Associative Conformal Algebras of Linear Growth

    OpenAIRE

    Retakh, Alexander

    2000-01-01

    Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We introduce the notions of conformal identity and unital associative conformal algebras and classify finitely generated simple unital associative conformal algebras of linear growth. These are precisely the complete algebras of conformal endomorphisms of finite ...

  11. An algebraic approach to modeling in software engineering

    International Nuclear Information System (INIS)

    Loegel, C.J.; Ravishankar, C.V.

    1993-09-01

    Our work couples the formalism of universal algebras with the engineering techniques of mathematical modeling to develop a new approach to the software engineering process. Our purpose in using this combination is twofold. First, abstract data types and their specification using universal algebras can be considered a common point between the practical requirements of software engineering and the formal specification of software systems. Second, mathematical modeling principles provide us with a means for effectively analyzing real-world systems. We first use modeling techniques to analyze a system and then represent the analysis using universal algebras. The rest of the software engineering process exploits properties of universal algebras that preserve the structure of our original model. This paper describes our software engineering process and our experience using it on both research and commercial systems. We need a new approach because current software engineering practices often deliver software that is difficult to develop and maintain. Formal software engineering approaches use universal algebras to describe ''computer science'' objects like abstract data types, but in practice software errors are often caused because ''real-world'' objects are improperly modeled. There is a large semantic gap between the customer's objects and abstract data types. In contrast, mathematical modeling uses engineering techniques to construct valid models for real-world systems, but these models are often implemented in an ad hoc manner. A combination of the best features of both approaches would enable software engineering to formally specify and develop software systems that better model real systems. Software engineering, like mathematical modeling, should concern itself first and foremost with understanding a real system and its behavior under given circumstances, and then with expressing this knowledge in an executable form

  12. The Linear Span of Projections in AH Algebras and for Inclusions of C*-Algebras

    Directory of Open Access Journals (Sweden)

    Dinh Trung Hoa

    2013-01-01

    Full Text Available In the first part of this paper, we show that an AH algebra A=lim→(Ai,ϕi has the LP property if and only if every element of the centre of Ai belongs to the closure of the linear span of projections in A. As a consequence, a diagonal AH-algebra has the LP property if it has small eigenvalue variation in the sense of Bratteli and Elliott. The second contribution of this paper is that for an inclusion of unital C*-algebras P⊂A with a finite Watatani index, if a faithful conditional expectation E:A→P has the Rokhlin property in the sense of Kodaka et al., then P has the LP property under the condition thatA has the LP property. As an application, let A be a simple unital C*-algebra with the LP property, α an action of a finite group G onto Aut(A. If α has the Rokhlin property in the sense of Izumi, then the fixed point algebra AG and the crossed product algebra A ⋊α G have the LP property. We also point out that there is a symmetry on the CAR algebra such that its fixed point algebra does not have the LP property.

  13. Negative Sentences in Children with Specific Language Impairment

    Science.gov (United States)

    Thornton, Rosalind; Rombough, Kelly; Martin, Jasmine; Orton, Linda

    2016-01-01

    This study used elicited production methodology to investigate the negative sentences that are produced by English-speaking children with specific language impairment (SLI). Negative sentences were elicited in contexts in which adults use the negative auxiliary verb doesn't (e.g., "It doesn't fit"). This form was targeted to see how…

  14. Non-commutative multiple-valued logic algebras

    CERN Document Server

    Ciungu, Lavinia Corina

    2014-01-01

    This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects.   A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing.   Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.

  15. Automorphic Lie algebras with dihedral symmetry

    International Nuclear Information System (INIS)

    Knibbeler, V; Lombardo, S; A Sanders, J

    2014-01-01

    The concept of automorphic Lie algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. automorphic Lie algebras are obtained by imposing a discrete group symmetry on a current algebra of Krichever–Novikov type. Past work shows remarkable uniformity between algebras associated to different reduction groups. For example, if the base Lie algebra is sl 2 (C) and the poles of the automorphic Lie algebra are restricted to an exceptional orbit of the symmetry group, changing the reduction group does not affect the Lie algebra structure. In this research we fix the reduction group to be the dihedral group and vary the orbit of poles as well as the group action on the base Lie algebra. We find a uniform description of automorphic Lie algebras with dihedral symmetry, valid for poles at exceptional and generic orbits. (paper)

  16. Certain number-theoretic episodes in algebra

    CERN Document Server

    Sivaramakrishnan, R

    2006-01-01

    Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutative algebra arising from number theory. Self-contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available. Coverage is divided into four parts, beginning with elements of number theory and algebra such as theorems of Euler, Fermat, and Lagrange, Euclidean domains, and finite groups. In the second part, the book details ordered fields, fields with valuation, and other algebraic structures. This is followed by a review of fundamentals of algebraic number theory in the third part. The final part explores links with ring theory, finite dimensional algebras, and the Goldbach problem.

  17. A Case of Specific Language Impairment in a Deaf Signer of American Sign Language.

    Science.gov (United States)

    Quinto-Pozos, David; Singleton, Jenny L; Hauser, Peter C

    2017-04-01

    This article describes the case of a deaf native signer of American Sign Language (ASL) with a specific language impairment (SLI). School records documented normal cognitive development but atypical language development. Data include school records; interviews with the child, his mother, and school professionals; ASL and English evaluations; and a comprehensive neuropsychological and psychoeducational evaluation, and they span an approximate period of 7.5 years (11;10-19;6) including scores from school records (11;10-16;5) and a 3.5-year period (15;10-19;6) during which we collected linguistic and neuropsychological data. Results revealed that this student has average intelligence, intact visual perceptual skills, visuospatial skills, and motor skills but demonstrates challenges with some memory and sequential processing tasks. Scores from ASL testing signaled language impairment and marked difficulty with fingerspelling. The student also had significant deficits in English vocabulary, spelling, reading comprehension, reading fluency, and writing. Accepted SLI diagnostic criteria exclude deaf individuals from an SLI diagnosis, but the authors propose modified criteria in this work. The results of this study have practical implications for professionals including school psychologists, speech language pathologists, and ASL specialists. The results also support the theoretical argument that SLI can be evident regardless of the modality in which it is communicated. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

  18. Fusion rules of chiral algebras

    International Nuclear Information System (INIS)

    Gaberdiel, M.

    1994-01-01

    Recently we showed that for the case of the WZW and the minimal models fusion can be understood as a certain ring-like tensor product of the symmetry algebra. In this paper we generalize this analysis to arbitrary chiral algebras. We define the tensor product of conformal field theory in the general case and prove that it is associative and symmetric up to equivalence. We also determine explicitly the action of the chiral algebra on this tensor product. In the second part of the paper we demonstrate that this framework provides a powerful tool for calculating restrictions for the fusion rules of chiral algebras. We exhibit this for the case of the W 3 algebra and the N=1 and N=2 NS superconformal algebras. (orig.)

  19. Computations in finite-dimensional Lie algebras

    Directory of Open Access Journals (Sweden)

    A. M. Cohen

    1997-12-01

    Full Text Available This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System, within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]. This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n×n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra.

  20. Coset realization of unifying W-algebras

    International Nuclear Information System (INIS)

    Blumenhagen, R.; Huebel, R.

    1994-06-01

    We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and sl(2,R)+sl(2,R)/sl(2,R), and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying W-algebras of Casimir W-algebras. We show that it is possible to give coset realizations of various types of unifying W-algebras, e.g. the diagonal cosets based on the symplectic Lie algebras sp(2n) realize the unifying W-algebras which have previously been introduced as 'WD -n '. In addition, minimal models of WD -n are studied. The coset realizations provide a generalization of level-rank-duality of dual coset pairs. As further examples of finitely nonfreely generated quantum W-algebras we discuss orbifolding of W-algebras which on the quantum level has different properties than in the classical case. We demonstrate in some examples that the classical limit according to Bowcock and Watts of these nonfreely finitely generated quantum W-algebras probably yields infinitely nonfreely generated classical W-algebras. (orig.)

  1. Algebra

    CERN Document Server

    Sepanski, Mark R

    2010-01-01

    Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarizes the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems

  2. 18th edition of the Forum on specification and Design Languages Conference

    CERN Document Server

    Wille, Robert

    2016-01-01

    This book brings together a selection of the best papers from the eighteenth edition of the Forum on specification and Design Languages Conference (FDL), which took place on September 14-16, 2015, in Barcelona, Spain. FDL is a well-established international forum devoted to dissemination of research results, practical experiences and new ideas in the application of specification, design and verification languages to the design, modeling and verification of integrated circuits, complex hardware/software embedded systems, and mixed-technology systems. Covers Assertion Based Design, Verification & Debug; Includes language-based modeling and design techniques for embedded systems; Covers design, modeling and verification of mixed physical domain and mixed signal systems that include significant analog parts in electrical and non-electrical domains; Includes formal and semi-formal system level design methods for complex embedded systems based on the Unified Modelling Language (UML) and Model Driven Engineering...

  3. 17th edition of the Forum on specification and Design Languages Conference

    CERN Document Server

    Pasaje, Julio

    2016-01-01

    This book brings together a selection of the best papers from the seventeenth edition of the Forum on specification and Design Languages Conference (FDL), which took place on October 14-16, 2014, in Munich, Germany.  FDL is a well-established international forum devoted to dissemination of research results, practical experiences and new ideas in the application of specification, design and verification languages to the design, modeling and verification of integrated circuits, complex hardware/software embedded systems, and mixed-technology systems.   •Covers Assertion Based Design, Verification & Debug; •Includes language-based modeling and design techniques for embedded systems; •Covers design, modeling and verification of mixed physical domain and mixed signal systems; •Includes formal and semi-formal system level design methods for complex embedded systems based on the Unified Modelling Language (UML) and Model Driven Engineering (MDE); •Covers parallel architectures – both as platforms f...

  4. Assessment of short-term memory in Arabic speaking children with specific language impairment.

    Science.gov (United States)

    Kaddah, F A; Shoeib, R M; Mahmoud, H E

    2010-12-15

    Children with Specific Language Impairment (SLI) may have some kind of memory disorder that could increase their linguistic impairment. This study assessed the short-term memory skills in Arabic speaking children with either Expressive Language Impairment (ELI) or Receptive/Expressive Language Impairment (R/ELI) in comparison to controls in order to estimate the nature and extent of any specific deficits in these children that could explain the different prognostic results of language intervention. Eighteen children were included in each group. Receptive, expressive and total language quotients were calculated using the Arabic language test. Assessment of auditory and visual short-term memory was done using the Arabic version of the Illinois Test of Psycholinguistic Abilities. Both groups of SLI performed significantly lower linguistic abilities and poorer auditory and visual short-term memory in comparison to normal children. The R/ELI group presented an inferior performance than the ELI group in all measured parameters. Strong association was found between most tasks of auditory and visual short-term memory and linguistic abilities. The results of this study highlighted a specific degree of deficit of auditory and visual short-term memories in both groups of SLI. These deficits were more prominent in R/ELI group. Moreover, the strong association between the different auditory and visual short-term memories and language abilities in children with SLI must be taken into account when planning an intervention program for these children.

  5. Analysis of higher order optical aberrations in the SLC final focus using Lie Algebra techniques

    International Nuclear Information System (INIS)

    Walker, N.J.; Irwin, J.; Woodley, M.

    1993-04-01

    The SLC final focus system is designed to have an overall demagnification of 30:1, with a β at the interaction point (β*) of 5 mm, and an energy band pass of ∼0.4%. Strong sextupole pairs are used to cancel the large chromaticity which accrues primarily from the final triplet. Third-order aberrations limit the performance of the system, the dominating terms being U 1266 and U 3466 terms (in the notation of K. Brown). Using Lie Algebra techniques, it is possible to analytically calculate the soave of these terms in addition to understanding their origin. Analytical calculations (using Lie Algebra packages developed in the Mathematica language) are presented of the bandwidth and minimum spot size as a function of divergence at the interaction point (IP). Comparisons of the analytical results from the Lie Algebra maps and results from particle tracking (TURTLE) are also presented

  6. Identities and derivations for Jacobian algebras

    International Nuclear Information System (INIS)

    Dzhumadil'daev, A.S.

    2001-09-01

    Constructions of n-Lie algebras by strong n-Lie-Poisson algebras are given. First cohomology groups of adjoint module of Jacobian algebras are calculated. Minimal identities of 3-Jacobian algebra are found. (author)

  7. Situating the Debate on "Geometrical Algebra" within the Framework of Premodern Algebra.

    Science.gov (United States)

    Sialaros, Michalis; Christianidis, Jean

    2016-06-01

    Argument The aim of this paper is to employ the newly contextualized historiographical category of "premodern algebra" in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on "geometrical algebra." Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related to Elem. II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called "semi-algebraic" alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing "premodern algebra," and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.

  8. Cohomology of Effect Algebras

    Directory of Open Access Journals (Sweden)

    Frank Roumen

    2017-01-01

    Full Text Available We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space of the effect algebra, and can be computed using variations on the Kunneth and Mayer-Vietoris sequences. The second way involves a chain complex of ordered abelian groups, and gives rise to a cohomological characterization of state extensions on effect algebras. This has applications to no-go theorems in quantum foundations, such as Bell's theorem.

  9. Influence of Language Load on Speech Motor Skill in Children with Specific Language Impairment

    Science.gov (United States)

    Saletta, Meredith; Goffman, Lisa; Ward, Caitlin; Oleson, Jacob

    2018-01-01

    Purpose: Children with specific language impairment (SLI) show particular deficits in the generation of sequenced action--the quintessential procedural task. Practiced imitation of a sequence may become rote and require reduced procedural memory. This study explored whether speech motor deficits in children with SLI occur generally or only in…

  10. Graph-based specification and verification for aspect-oriented languages

    NARCIS (Netherlands)

    Staijen, T.

    2010-01-01

    Aspect-oriented software development aims at improving separation of concerns at all levels in the software development life-cycle, from architecture to code implementation. In this thesis we strive to develop verification methods specifically for aspect-oriented programming languages. For this

  11. Algebraic geometry and Bethe ansatz. Part I. The quotient ring for BAE

    Science.gov (United States)

    Jiang, Yunfeng; Zhang, Yang

    2018-03-01

    In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and powerful tools for understanding the structure of solution space of Bethe ansatz equations. In particular, we find novel efficient methods to count the number of solutions of Bethe ansatz equations based on Gröbner basis and quotient ring. We also develop analytical approach based on companion matrix to perform the sum of on-shell quantities over all physical solutions without solving Bethe ansatz equations explicitly. To demonstrate the power of our method, we revisit the completeness problem of Bethe ansatz of Heisenberg spin chain, and calculate the sum rules of OPE coefficients in planar N=4 super-Yang-Mills theory.

  12. Topology general & algebraic

    CERN Document Server

    Chatterjee, D

    2007-01-01

    About the Book: This book provides exposition of the subject both in its general and algebraic aspects. It deals with the notions of topological spaces, compactness, connectedness, completeness including metrizability and compactification, algebraic aspects of topological spaces through homotopy groups and homology groups. It begins with the basic notions of topological spaces but soon going beyond them reaches the domain of algebra through the notions of homotopy, homology and cohomology. How these approaches work in harmony is the subject matter of this book. The book finally arrives at the

  13. Graded associative conformal algebras of finite type

    OpenAIRE

    Kolesnikov, Pavel

    2011-01-01

    In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative conformal algebra which is graded by a finite group $\\Gamma $ is a pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group $G$ such that the identity component $G^0$ is the affine line and $G/G^0\\simeq \\Gamma $. A classification of simple...

  14. Principles of linear algebra with Mathematica

    CERN Document Server

    Shiskowski, Kenneth M

    2013-01-01

    A hands-on introduction to the theoretical and computational aspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationally intensive, and computer algebra systems such as Mathematica® are essential not only for learning to apply the concepts to computationally challenging problems, but also for visualizing many of the geometric aspects within this field of study. Principles of Linear Algebra with Mathematica uniquely bridges the gap between beginning linear algebra and computational linear algebra that is often encountered in applied settings,

  15. A survey of functional programming language principles

    Science.gov (United States)

    Holloway, C. M.

    1986-01-01

    Research in the area of functional programming languages has intensified in the 8 years since John Backus' Turing Award Lecture on the topic was published. The purpose of this paper is to present a survey of the ideas of functional programming languages. The paper assumes the reader is comfortable with mathematics and has knowledge of the basic principles of traditional programming languages, but does not assume any prior knowledge of the ideas of functional languages. A simple functional language is defined and used to illustrate the basic ideas. Topics discussed include the reasons for developing functional languages, methods of expressing concurrency, the algebra of functional programming languages, program transformation techniques, and implementations of functional languages. Existing functional languages are also mentioned. The paper concludes with the author's opinions as to the future of functional languages. An annotated bibliography on the subject is also included.

  16. Einstein algebras and general relativity

    International Nuclear Information System (INIS)

    Heller, M.

    1992-01-01

    A purely algebraic structure called an Einstein algebra is defined in such a way that every spacetime satisfying Einstein's equations is an Einstein algebra but not vice versa. The Gelfand representation of Einstein algebras is defined, and two of its subrepresentations are discussed. One of them is equivalent to the global formulation of the standard theory of general relativity; the other one leads to a more general theory of gravitation which, in particular, includes so-called regular singularities. In order to include other types of singularities one must change to sheaves of Einstein algebras. They are defined and briefly discussed. As a test of the proposed method, the sheaf of Einstein algebras corresponding to the space-time of a straight cosmic string with quasiregular singularity is constructed. 22 refs

  17. Analytic real algebras.

    Science.gov (United States)

    Seo, Young Joo; Kim, Young Hee

    2016-01-01

    In this paper we construct some real algebras by using elementary functions, and discuss some relations between several axioms and its related conditions for such functions. We obtain some conditions for real-valued functions to be a (edge) d -algebra.

  18. A Process Algebra Approach to Quantum Electrodynamics

    Science.gov (United States)

    Sulis, William

    2017-12-01

    The process algebra program is directed towards developing a realist model of quantum mechanics free of paradoxes, divergences and conceptual confusions. From this perspective, fundamental phenomena are viewed as emerging from primitive informational elements generated by processes. The process algebra has been shown to successfully reproduce scalar non-relativistic quantum mechanics (NRQM) without the usual paradoxes and dualities. NRQM appears as an effective theory which emerges under specific asymptotic limits. Space-time, scalar particle wave functions and the Born rule are all emergent in this framework. In this paper, the process algebra model is reviewed, extended to the relativistic setting, and then applied to the problem of electrodynamics. A semiclassical version is presented in which a Minkowski-like space-time emerges as well as a vector potential that is discrete and photon-like at small scales and near-continuous and wave-like at large scales. QED is viewed as an effective theory at small scales while Maxwell theory becomes an effective theory at large scales. The process algebra version of quantum electrodynamics is intuitive and realist, free from divergences and eliminates the distinction between particle, field and wave. Computations are carried out using the configuration space process covering map, although the connection to second quantization has not been fully explored.

  19. Biderivations of W-algebra $W(2,2)$ and Virasoro algebra without skewsymmetric condition and their applications

    OpenAIRE

    Tang, Xiaomin

    2016-01-01

    In this paper, we characterize the biderivations of W-algebra $W(2,2)$ and Virasoro algebra $Vir$ without skewsymmetric condition. We get two classes of non-inner biderivations. As applications, we also get the forms of linear commuting maps on W-algebra $W(2,2)$ and Virasoro algebra $Vir$.

  20. Differential algebras without differentials: An easy C++ implementation

    International Nuclear Information System (INIS)

    Michelotti, L.

    1989-03-01

    Automated differentiation can be motivated and explained rather plainly without any reference to infinitesimals or differentials whatsoever. We shall describe one possible approach in this paper. The method which we shall use will suggest its own implementation. However, FORTRAN is not the most natural language in which to carry it out. In the second section we shall describe an almost trivial implementation using C++. (Indeed, one of the motivations for writing this paper is to persuade militant FORTRAN extremists to invest the four or five days necessary to learn this powerful and easy language.) Take heed, however, that what we describe below is only a stripped-down implementation, written in three days, of differential algebra's most essential features; it is not as robust as and does not contain the battery of tools available in Berz's DA package, the product of a significant amount of work. 10 refs

  1. Differential algebras without differentials: An easy C++ implementation

    Energy Technology Data Exchange (ETDEWEB)

    Michelotti, L.

    1989-03-01

    Automated differentiation can be motivated and explained rather plainly without any reference to infinitesimals or differentials whatsoever. We shall describe one possible approach in this paper. The method which we shall use will suggest its own implementation. However, FORTRAN is not the most natural language in which to carry it out. In the second section we shall describe an almost trivial implementation using C++. (Indeed, one of the motivations for writing this paper is to persuade militant FORTRAN extremists to invest the four or five days necessary to learn this powerful and easy language.) Take heed, however, that what we describe below is only a stripped-down implementation, written in three days, of differential algebra's most essential features; it is not as robust as and does not contain the battery of tools available in Berz's DA package, the product of a significant amount of work. 10 refs.

  2. Evolution algebras generated by Gibbs measures

    International Nuclear Information System (INIS)

    Rozikov, Utkir A.; Tian, Jianjun Paul

    2009-03-01

    In this article we study algebraic structures of function spaces defined by graphs and state spaces equipped with Gibbs measures by associating evolution algebras. We give a constructive description of associating evolution algebras to the function spaces (cell spaces) defined by graphs and state spaces and Gibbs measure μ. For finite graphs we find some evolution subalgebras and other useful properties of the algebras. We obtain a structure theorem for evolution algebras when graphs are finite and connected. We prove that for a fixed finite graph, the function spaces have a unique algebraic structure since all evolution algebras are isomorphic to each other for whichever Gibbs measures are assigned. When graphs are infinite graphs then our construction allows a natural introduction of thermodynamics in studying of several systems of biology, physics and mathematics by theory of evolution algebras. (author)

  3. THE CONTRIBUTION OF COMPLEXITY, ACCURACY AND FLUENCY TO LANGUAGE FOR SPECIFIC PURPOSES

    Directory of Open Access Journals (Sweden)

    Anthony Rausch

    2016-03-01

    Full Text Available This paper will outline an instructional approach that proposes a Complexity, Accuracy, Fluency (CAF paradigm as a means of providing learners with the CAF-based communication consciousness and CAF-oriented manipulative skills that are increasingly important in language use in Language for Specific Purposes. Given the complex combinations of communicative tasks, communicative formats and communicative circumstances that accompany the wide-ranging and various contexts of contemporary professional communication, communicative competence demands a combinative consciousness and informed application of Complexity, Accuracy and Fluency as a communication paradigm. Viewed as a combination of its three components, a CAF paradigm constitutes a fundamental ‘information, language and communication’ triad that can guide professional language use in any communicative circumstance. Viewed as a communicative skill set, the CAF triad implies the capability to adjust specific elements and aspects of information, language and communication as needed for a communicative task, whether in oral or print communication and regardless of task category. Adjusting complexity in this context refers to both content and language complexity. Adjusting accuracy refers to the conventions that dictate appropriate or acceptable language in a given context. Finally, adjusting fluency refers to a sense of communicative fluency, that which yields either smooth and persuasive language as in a native-speaker normative view or explicit and clearly explanatory language as necessary in some communicative encounters. The need to manipulate these three components depends on circumstance variables such as objective, available time, audience characteristics and the degree of detail desired. This paper will outline this combinative CAF notion as background to a materials development project being undertaken in a Japanese university, introducing the specifics of an Extended Reading Aloud

  4. Analogical reasoning in children with specific language impairment: Evidence from a scene analogy task.

    Science.gov (United States)

    Krzemien, Magali; Jemel, Boutheina; Maillart, Christelle

    2017-01-01

    Analogical reasoning is a human ability that maps systems of relations. It develops along with relational knowledge, working memory and executive functions such as inhibition. It also maintains a mutual influence on language development. Some authors have taken a greater interest in the analogical reasoning ability of children with language disorders, specifically those with specific language impairment (SLI). These children apparently have weaker analogical reasoning abilities than their aged-matched peers without language disorders. Following cognitive theories of language acquisition, this deficit could be one of the causes of language disorders in SLI, especially those concerning productivity. To confirm this deficit and its link to language disorders, we use a scene analogy task to evaluate the analogical performance of SLI children and compare them to controls of the same age and linguistic abilities. Results show that children with SLI perform worse than age-matched peers, but similar to language-matched peers. They are more influenced by increased task difficulty. The association between language disorders and analogical reasoning in SLI can be confirmed. The hypothesis of limited processing capacity in SLI is also being considered.

  5. Specification of the GummyModule Language

    NARCIS (Netherlands)

    Malakuti Khah Olun Abadi, Somayeh

    2012-01-01

    The GummyModule language is an extension to the Java language and is the successor of the EventReactor language The GummyModule language adopts the linguistic constructs of offered by EventReactor to define event types, events and to publish events. As for EventReactor, GummyModule facilitates

  6. Classical algebraic chromodynamics

    International Nuclear Information System (INIS)

    Adler, S.L.

    1978-01-01

    I develop an extension of the usual equations of SU(n) chromodynamics which permits the consistent introduction of classical, noncommuting quark source charges. The extension involves adding a singlet gluon, giving a U(n) -based theory with outer product P/sup a/(u,v) = (1/2)(d/sup a/bc + if/sup a/bc)(u/sup b/v/sup c/ - v/sup b/u/sup c/) which obeys the Jacobi identity, inner product S (u,v) = (1/2)(u/sup a/v/sup a/ + v/sup a/u/sup a/), and with the n 2 gluon fields elevated to algebraic fields over the quark color charge C* algebra. I show that provided the color charge algebra satisfies the condition S (P (u,v),w) = S (u,P (v,w)) for all elements u,v,w of the algebra, all the standard derivations of Lagrangian chromodynamics continue to hold in the algebraic chromodynamics case. I analyze in detail the color charge algebra in the two-particle (qq, qq-bar, q-barq-bar) case and show that the above consistency condition is satisfied for the following unique (and, interestingly, asymmetric) choice of quark and antiquark charges: Q/sup a//sub q/ = xi/sup a/, Q/sup a//sub q/ = xi-bar/sup a/ + delta/sup a/0(n/2)/sup 3/2/1, with xi/sup a/xi/sup b/ = (1/2)(d/sup a/bc + if/sup a/bc) xi/sup c/, xi-bar/sup a/xi-bar/sup b/ = -(1/2)(d/sup a/bc - if/sup a/bc) xi-bar/sup c/. The algebraic structure of the two-particle U(n) force problem, when expressed on an appropriately diagonalized basis, leads for all n to a classical dynamics problem involving an ordinary SU(2) Yang-Mills field with uniquely specified classical source charges which are nonparallel in the color-singlet state. An explicit calculation shows that local algebraic U(n) gauge transformations lead only to a rigid global rotation of axes in the overlying classical SU(2) problem, which implies that the relative orientations of the classical source charges have physical significance

  7. Imitation of Body Postures and Hand Movements in Children with Specific Language Impairment

    Science.gov (United States)

    Marton, Klara

    2009-01-01

    Within the domain-general theory of language impairment, this study examined body posture and hand movement imitation in children with specific language impairment (SLI) and in their age-matched peers. Participants included 40 children with SLI (5 years 3 months to 6 years 10 months of age) and 40 children with typical language development (5…

  8. Working memory and language: skill-specific or domain-general relations to mathematics?

    Science.gov (United States)

    Purpura, David J; Ganley, Colleen M

    2014-06-01

    Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the specific relations of these two non-mathematical factors to individual aspects of early mathematics. Thus, the focus of this study was to determine whether working memory and language were related to only individual aspects of early mathematics or related to many components of early mathematics skills. A total of 199 4- to 6-year-old preschool and kindergarten children were assessed on a battery of early mathematics tasks as well as measures of working memory and language. Results indicated that working memory has a specific relation to only a few-but critically important-early mathematics skills and language has a broad relation to nearly all early mathematics skills. Copyright © 2014 Elsevier Inc. All rights reserved.

  9. On the classification of quantum W-algebras

    International Nuclear Information System (INIS)

    Bowcock, P.; Watts, G.T.M.

    1992-01-01

    In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each reductive W-algebra. The finite Lie algebra is also endowed with a preferred sl(2) subalgebra, which gives the conformal weights of the W-algebra. We extend this to cover W-algebras containing both bosonic and fermionic fields, and illustrate our ideas with the Poisson bracket algebras of generalised Drinfeld-Sokolov hamiltonian systems. We then discuss the possibilities of classifying deformable W-algebras which fall outside this class in the context of automorphisms of Lie algebras. In conclusion we list the cases in which the W-algebra has no weight-one fields, and further, those in which it has only one weight-two field. (orig.)

  10. Lie-Algebras. Pt. 1

    International Nuclear Information System (INIS)

    Baeuerle, G.G.A.; Kerf, E.A. de

    1990-01-01

    The structure of the laws in physics is largely based on symmetries. This book is on Lie algebras, the mathematics of symmetry. It gives a thorough mathematical treatment of finite dimensional Lie algebras and Kac-Moody algebras. Concepts such as Cartan matrix, root system, Serre's construction are carefully introduced. Although the book can be read by an undergraduate with only an elementary knowledge of linear algebra, the book will also be of use to the experienced researcher. Experience has shown that students who followed the lectures are well-prepared to take on research in the realms of string-theory, conformal field-theory and integrable systems. 48 refs.; 66 figs.; 3 tabs

  11. Semiprojectivity of universal -algebras generated by algebraic elements

    DEFF Research Database (Denmark)

    Shulman, Tatiana

    2012-01-01

    Let be a polynomial in one variable whose roots all have multiplicity more than 1. It is shown that the universal -algebra of a relation , , is semiprojective and residually finite-dimensional. Applications to polynomially compact operators are given.......Let be a polynomial in one variable whose roots all have multiplicity more than 1. It is shown that the universal -algebra of a relation , , is semiprojective and residually finite-dimensional. Applications to polynomially compact operators are given....

  12. Refined algebraic quantisation in a system with nonconstant gauge invariant structure functions

    International Nuclear Information System (INIS)

    Martínez-Pascual, Eric

    2013-01-01

    In a previous work [J. Louko and E. Martínez-Pascual, “Constraint rescaling in refined algebraic quantisation: Momentum constraint,” J. Math. Phys. 52, 123504 (2011)], refined algebraic quantisation (RAQ) within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling one momentum-type constraint was investigated. In the present work, the first steps to generalise this analysis to cases where more constraints occur are developed. The system under consideration contains two momentum-type constraints, originally abelian, where rescalings of these constraints by a non-vanishing function of the coordinates are allowed. These rescalings induce structure functions at the level of the gauge algebra. Providing a specific parametrised family of real-valued scaling functions, the implementation of the corresponding rescaled quantum momentum-type constraints is performed using RAQ when the gauge algebra: (i) remains abelian and (ii) undergoes into an algebra of a nonunimodular group with nonconstant gauge invariant structure functions. Case (ii) becomes the first example known to the author where an open algebra is handled in refined algebraic quantisation. Challenging issues that arise in the presence of non-gauge invariant structure functions are also addressed

  13. The formal theory of Hopf algebras part II: the case of Hopf algebras ...

    African Journals Online (AJOL)

    The category HopfR of Hopf algebras over a commutative unital ring R is analyzed with respect to its categorical properties. The main results are: (1) For every ring R the category HopfR is locally presentable, it is coreflective in the category of bialgebras over R, over every R-algebra there exists a cofree Hopf algebra. (2) If ...

  14. Children's understanding of fraction and decimal symbols and the notation-specific relation to pre-algebra ability.

    Science.gov (United States)

    Hurst, Michelle A; Cordes, Sara

    2018-04-01

    Fraction and decimal concepts are notoriously difficult for children to learn yet are a major component of elementary and middle school math curriculum and an important prerequisite for higher order mathematics (i.e., algebra). Thus, recently there has been a push to understand how children think about rational number magnitudes in order to understand how to promote rational number understanding. However, prior work investigating these questions has focused almost exclusively on fraction notation, overlooking the open questions of how children integrate rational number magnitudes presented in distinct notations (i.e., fractions, decimals, and whole numbers) and whether understanding of these distinct notations may independently contribute to pre-algebra ability. In the current study, we investigated rational number magnitude and arithmetic performance in both fraction and decimal notation in fourth- to seventh-grade children. We then explored how these measures of rational number ability predicted pre-algebra ability. Results reveal that children do represent the magnitudes of fractions and decimals as falling within a single numerical continuum and that, despite greater experience with fraction notation, children are more accurate when processing decimal notation than when processing fraction notation. Regression analyses revealed that both magnitude and arithmetic performance predicted pre-algebra ability, but magnitude understanding may be particularly unique and depend on notation. The educational implications of differences between children in the current study and previous work with adults are discussed. Copyright © 2017 Elsevier Inc. All rights reserved.

  15. Macdonald index and chiral algebra

    Science.gov (United States)

    Song, Jaewon

    2017-08-01

    For any 4d N = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type ( A 1 , A 2 n ) and ( A 1 , D 2 n+1) where the chiral algebras are given by Virasoro and \\widehat{su}(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.

  16. Specification of real-time automation systems with HybridUML; Spezifikation von Echtzeit-Automatisierungssystemen mit HybridUML

    Energy Technology Data Exchange (ETDEWEB)

    Berkenkoetter, K.; Bisanz, S.; Hannemann, U.; Peleska, J. [Univ. Bremen (Germany)

    2004-07-01

    Complex automation systems require specification formalisms supporting the description of real-time requirements with respect to both discrete and time-continuous observables. For this purpose, the authors have designed the HybridUML specification language. Discrete events, communication, and variable assignments are specified by state machines, timers, and invariant conditions. The time-continuous aspects of system behaviour are described by associating differential equations or time-dependent algebraic conditions with system states. The complexity of large systems is controlled by decomposing the specification into parallel components and hierarchical state machines. Instead of inventing a new language syntax, HybridUML is represented as a profile of the Unified Modeling Language UML 2.0. This allows to re-use the syntactic framework of well-accepted graphical UML constructs and development support provided by various UML case tools. The profile is associated with a precise language semantics linking unambiguous meaning to all HybridUML specifications. As a consequence, HybridUML specifications can be compiled into executable code which is suitable for execution in hard realtime on multi-processor computers. This serves both for the development of automation systems and for specification-based testing in real-time. This paper contains an introduction to HybridUML which is illustrated by an example from the field of automated train control. (orig.)

  17. Advanced modern algebra part 2

    CERN Document Server

    Rotman, Joseph J

    2017-01-01

    This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

  18. A q-deformed Lorentz algebra

    International Nuclear Information System (INIS)

    Schmidke, W.B.; Wess, J.; Muenchen Univ.; Zumino, B.; Lawrence Berkeley Lab., CA

    1991-01-01

    We derive a q-deformed version of the Lorentz algebra by deformating the algebra SL(2, C). The method is based on linear representations of the algebra on the complex quantum spinor space. We find that the generators usually identified with SL q (2, C) generate SU q (2) only. Four additional generators are added which generate Lorentz boosts. The full algebra of all seven generators and their coproduct is presented. We show that in the limit q→1 the generators are those of the classical Lorentz algebra plus an additional U(1). Thus we have a deformation of SL(2, C)xU(1). (orig.)

  19. Introduction to algebraic quantum field theory

    International Nuclear Information System (INIS)

    Horuzhy, S.S.

    1990-01-01

    This volume presents a systematic introduction to the algebraic approach to quantum field theory. The structure of the contents corresponds to the way the subject has advanced. It is shown how the algebraic approach has developed from the purely axiomatic theory of observables via superselection rules into the dynamical formalism of fields and observables. Chapter one discusses axioms and their consequences -many of which are now classical theorems- and deals, in general, with the axiomatic theory of local observable algebras. The absence of field concepts makes this theory incomplete and, in chapter two, superselection rules are shown to be the key to the reconstruction of fields from observables. Chapter three deals with the algebras of Wightman fields, first unbounded operator algebras, then Von Neumann field algebras (with a special section on wedge region algebras) and finally local algebras of free and generalised free fields. (author). 447 refs.; 4 figs

  20. Comments on N=4 superconformal algebras

    International Nuclear Information System (INIS)

    Rasmussen, J.

    2001-01-01

    We present a new and asymmetric N=4 superconformal algebra for arbitrary central charge, thus completing our recent work on its classical analogue with vanishing central charge. Besides the Virasoro generator and 4 supercurrents, the algebra consists of an internal SU(2)xU(1) Kac-Moody algebra in addition to two spin 1/2 fermions and a bosonic scalar. The algebra is shown to be invariant under a linear twist of the generators, except for a unique value of the continuous twist parameter. At this value, the invariance is broken and the algebra collapses to the small N=4 superconformal algebra. The asymmetric N=4 superconformal algebra may be seen as induced by an affine SL(2 vertical bar 2) current superalgebra. Replacing SL(2 vertical bar 2) with the coset SL(2 vertical bar 2)/U(1), results directly in the small N=4 superconformal algebra

  1. The theory of algebraic numbers

    CERN Document Server

    Pollard, Harry

    1998-01-01

    An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.

  2. Methods for Identifying Specific Language Impairment in Bilingual Populations in Germany

    Directory of Open Access Journals (Sweden)

    Cornelia Hamann

    2017-10-01

    Full Text Available This study investigates the performance of 22 monolingual and 54 bilingual children with and without specific language impairment (SLI, in a non-word repetition task (NWRT and a sentence repetition task (SRT. Both tasks were constructed according to the principles for LITMUS tools (Language Impairment Testing in Multilingual Settings developed within COST Action IS0804 and incorporated phonological or syntactic structures that are linguistically complex and have been shown to be difficult for children with SLI across languages. For phonology these are in particular (nonwords containing consonant clusters. In morphosyntax, complexity has been attributed to factors such as embedding and/or syntactic movement. Tasks focusing on such structures are expected to identify SLI in bilinguals across language combinations. This is notoriously difficult because structures that are problematic for typically developing bilinguals (BiTDs and monolingual children with SLI (MoSLI often overlap. We show that the NWRT and the SRT are reliable tools for identification of SLI in bilingual contexts. However, interpretation of the performance of bilingual children depends on background information as provided by parental questionnaires. To evaluate the accuracy of our tasks, we recruited children in ordinary kindergartens or schools and in speech language therapy centers and verified their status with a battery of standardized language tests, assessing bilingual children in both their languages. We consider a bilingual child language impaired if she shows impairments in two language domains in both her languages. For assessment, we used tests normed for monolinguals (with one exception and adjusted the norms for bilingualism and for language dominance. This procedure established the following groups: 10 typical monolinguals (MoTD, 12 MoSLI, 46 BiTD, and 8 bilingual children with SLI (BiSLI. Our results show that both tasks target relevant structures: monolingual

  3. Quantum Heisenberg groups and Sklyanin algebras

    International Nuclear Information System (INIS)

    Andruskiewitsch, N.; Devoto, J.; Tiraboschi, A.

    1993-05-01

    We define new quantizations of the Heisenberg group by introducing new quantizations in the universal enveloping algebra of its Lie algebra. Matrix coefficients of the Stone-von Neumann representation are preserved by these new multiplications on the algebra of functions on the Heisenberg group. Some of the new quantizations provide also a new multiplication in the algebra of theta functions; we obtain in this way Sklyanin algebras. (author). 23 refs

  4. Declarative and Procedural Memory in Danish Speaking Children with Specific Language Impairment

    Science.gov (United States)

    Lum, Jarrad A. G.; Bleses, Dorthe

    2012-01-01

    It has been proposed that the language problems in specific language impairment (SLI) arise from basal ganglia abnormalities that lead to impairments with procedural and working memory but not declarative memory. In SLI, this profile of memory functioning has been hypothesized to underlie grammatical impairment but leave lexical knowledge…

  5. Methods and Techniques for the Design and Implementation of Domain-Specific Languages

    NARCIS (Netherlands)

    Hemel, Z.

    2012-01-01

    Domain-Specific Languages (DSLs) are programming language aimed at a particular problem domain, e.g. banking, database querying or website page lay-outs. Through the use of high-level concepts, a DSL raises the level of abstraction and expressive power of the programmer, and reduces the size of

  6. Optlang: An algebraic modeling language for mathematical optimization

    DEFF Research Database (Denmark)

    Jensen, Kristian; Cardoso, Joao; Sonnenschein, Nikolaus

    2016-01-01

    Optlang is a Python package implementing a modeling language for solving mathematical optimization problems, i.e., maximizing or minimizing an objective function over a set of variables subject to a number of constraints. It provides a common native Python interface to a series of optimization...

  7. Classification of simple flexible Lie-admissible algebras

    International Nuclear Information System (INIS)

    Okubo, S.; Myung, H.C.

    1979-01-01

    Let A be a finite-dimensional flexible Lie-admissible algebra over the complex field such that A - is a simple Lie algebra. It is shown that either A is itself a Lie algebra isomorphic to A - or A - is a Lie algebra of type A/sub n/ (n greater than or equal to 2). In the latter case, A is isomorphic to the algebra defined on the space of (n + 1) x (n + 1) traceless matrices with multiplication given by x * y = μxy + (1 - μ)yx - (1/(n + 100 Tr (xy) E where μ is a fixed scalar, xy denotes the matrix operators in Lie algebras which has been studied in theoretical physics. We also discuss a broader class of Lie algebras over arbitrary field of characteristic not equal to 2, called quasi-classical, which includes semisimple as well as reductive Lie algebras. For this class of Lie algebras, we can introduce a multiplication which makes the adjoint operator space into an associative algebra. When L is a Lie algebra with nondegenerate killing form, it is shown that the adjoint operator algebra of L in the adjoint representation becomes a commutative associative algebra with unit element and its dimension is 1 or 2 if L is simple over the complex field. This is related to the known result that a Lie algebra of type A/sub n/ (n greater than or equal to 2) alone has a nonzero completely symmetric adjoint operator in the adjoint representation while all other algebras have none. Finally, Lie-admissible algebras associated with bilinear form are investigated

  8. Quantitative Algebraic Reasoning

    DEFF Research Database (Denmark)

    Mardare, Radu Iulian; Panangaden, Prakash; Plotkin, Gordon

    2016-01-01

    We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We define an equality relation indexed by rationals: a =ε b which we think of as saying that “a is approximately equal to b up to an error of ε”. We have 4 interesting examples where we have a quantitative...... equational theory whose free algebras correspond to well known structures. In each case we have finitary and continuous versions. The four cases are: Hausdorff metrics from quantitive semilattices; pWasserstein metrics (hence also the Kantorovich metric) from barycentric algebras and also from pointed...

  9. Anyons, deformed oscillator algebras and projectors

    International Nuclear Information System (INIS)

    Engquist, Johan

    2009-01-01

    We initiate an algebraic approach to the many-anyon problem based on deformed oscillator algebras. The formalism utilizes a generalization of the deformed Heisenberg algebras underlying the operator solution of the Calogero problem. We define a many-body Hamiltonian and an angular momentum operator which are relevant for a linearized analysis in the statistical parameter ν. There exists a unique ground state and, in spite of the presence of defect lines, the anyonic weight lattices are completely connected by the application of the oscillators of the algebra. This is achieved by supplementing the oscillator algebra with a certain projector algebra.

  10. Alternative algebraic approaches in quantum chemistry

    International Nuclear Information System (INIS)

    Mezey, Paul G.

    2015-01-01

    Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed

  11. Alternative algebraic approaches in quantum chemistry

    Energy Technology Data Exchange (ETDEWEB)

    Mezey, Paul G., E-mail: paul.mezey@gmail.com [Canada Research Chair in Scientific Modeling and Simulation, Department of Chemistry and Department of Physics and Physical Oceanography, Memorial University of Newfoundland, 283 Prince Philip Drive, St. John' s, NL A1B 3X7 (Canada)

    2015-01-22

    Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.

  12. On graded algebras of global dimension 3

    International Nuclear Information System (INIS)

    Piontkovskii, D I

    2001-01-01

    Assume that a graded associative algebra A over a field k is minimally presented as the quotient algebra of a free algebra F by the ideal I generated by a set f of homogeneous elements. We study the following two extensions of A: the algebra F-bar=F/I oplus I/I 2 oplus ... associated with F with respect to the I-adic filtration, and the homology algebra H of the Shafarevich complex Sh(f,F) (which is a non-commutative version of the Koszul complex). We obtain several characterizations of algebras of global dimension 3. In particular, the A-algebra H in this case is free, and the algebra F-bar is isomorphic to the quotient algebra of a free A-algebra by the ideal generated by a so-called strongly free (or inert) set

  13. Elements of mathematics algebra

    CERN Document Server

    Bourbaki, Nicolas

    2003-01-01

    This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's, Algèbre, Chapters 4 to 7 (1981). This completes Algebra, 1 to 3, by establishing the theories of commutative fields and modules over a principal ideal domain. Chapter 4 deals with polynomials, rational fractions and power series. A section on symmetric tensors and polynomial mappings between modules, and a final one on symmetric functions, have been added. Chapter 5 was entirely rewritten. After the basic theory of extensions (prime fields, algebraic, algebraically closed, radical extension), separable algebraic extensions are investigated, giving way to a section on Galois theory. Galois theory is in turn applied to finite fields and abelian extensions. The chapter then proceeds to the study of general non-algebraic extensions which cannot usually be found in textbooks: p-bases, transcendental extensions, separability criterions, regular extensions. Chapter 6 treats ordered groups and fields and...

  14. Brauer algebra of type F4

    NARCIS (Netherlands)

    Liu, S.

    2012-01-01

    We present an algebra related to the Coxeter group of type F4 which can be viewed as the Brauer algebra of type F4 and is obtained as a subalgebra of the Brauer algebra of type E6. We also describe some properties of this algebra.

  15. Brauer algebras of type F4

    NARCIS (Netherlands)

    Liu, S.

    2013-01-01

    We present an algebra related to the Coxeter group of type F4 which can be viewed as the Brauer algebra of type F4 and is obtained as a subalgebra of the Brauer algebra of type E6. We also describe some properties of this algebra.

  16. New examples of continuum graded Lie algebras

    International Nuclear Information System (INIS)

    Savel'ev, M.V.

    1989-01-01

    Several new examples of continuum graded Lie algebras which provide an additional elucidation of these algebras are given. Here, in particular, the Kac-Moody algebras, the algebra S 0 Diff T 2 of infinitesimal area-preserving diffeomorphisms of the torus T 2 , the Fairlie, Fletcher and Zachos sine-algebras, etc., are described as special cases of the cross product Lie algebras. 8 refs

  17. Generalized Galilean algebras and Newtonian gravity

    Science.gov (United States)

    González, N.; Rubio, G.; Salgado, P.; Salgado, S.

    2016-04-01

    The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.

  18. Circle Maps and C*-algebras

    DEFF Research Database (Denmark)

    Schmidt, Thomas Lundsgaard

    such a map, generalising the transformation groupoid of a local homeomorphism first introduced by Renault in \\cite{re}. We conduct a detailed study of the relationship between the dynamics of $\\phi$, the properties of these groupoids, the structure of their corresponding reduced groupoid $C^*$-algebras, and......, for certain classes of maps, the K-theory of these algebras. When the map $\\phi$ is transitive, we show that the algebras $C^*_r(\\Gamma_\\phi)$ and $C^*_r(\\Gamma_\\phi^+)$ are purely infinite and satisfy the Universal Coefficient Theorem. Furthermore, we find necessary and sufficient conditions for simplicity...... of these algebras in terms of dynamical properties of $\\phi$. We proceed to consider the situation when the algebras are non-simple, and describe the primitive ideal spectrum in this case. We prove that any irreducible representation factors through the $C^*$-algebra of the reduction of the groupoid to the orbit...

  19. Spherical Hecke algebra in the Nekrasov-Shatashvili limit

    Energy Technology Data Exchange (ETDEWEB)

    Bourgine, Jean-Emile [Asia Pacific Center for Theoretical Physics (APCTP),Pohang, Gyeongbuk 790-784 (Korea, Republic of)

    2015-01-21

    The Spherical Hecke central (SHc) algebra has been shown to act on the Nekrasov instanton partition functions of N=2 gauge theories. Its presence accounts for both integrability and AGT correspondence. On the other hand, a specific limit of the Omega background, introduced by Nekrasov and Shatashvili (NS), leads to the appearance of TBA and Bethe like equations. To unify these two points of view, we study the NS limit of the SHc algebra. We provide an expression of the instanton partition function in terms of Bethe roots, and define a set of operators that generates infinitesimal variations of the roots. These operators obey the commutation relations defining the SHc algebra at first order in the equivariant parameter ϵ{sub 2}. Furthermore, their action on the bifundamental contributions reproduces the Kanno-Matsuo-Zhang transformation. We also discuss the connections with the Mayer cluster expansion approach that leads to TBA-like equations.

  20. Co-Localisation of Abnormal Brain Structure and Function in Specific Language Impairment

    Science.gov (United States)

    Badcock, Nicholas A.; Bishop, Dorothy V. M.; Hardiman, Mervyn J.; Barry, Johanna G.; Watkins, Kate E.

    2012-01-01

    We assessed the relationship between brain structure and function in 10 individuals with specific language impairment (SLI), compared to six unaffected siblings, and 16 unrelated control participants with typical language. Voxel-based morphometry indicated that grey matter in the SLI group, relative to controls, was increased in the left inferior…

  1. The Boolean algebra of Galois algebras

    Directory of Open Access Journals (Sweden)

    Lianyong Xue

    2003-02-01

    Full Text Available Let B be a Galois algebra with Galois group G, Jg={b∈B|bx=g(xb for all x∈B} for each g∈G, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|g∈G}, e a nonzero element in Ba, and He={g∈G|eeg=e}. Then, a monomial e is characterized, and the Galois extension Be, generated by e with Galois group He, is investigated.

  2. From General Game Descriptions to a Market Specification Language for General Trading Agents

    Science.gov (United States)

    Thielscher, Michael; Zhang, Dongmo

    The idea behind General Game Playing is to build systems that, instead of being programmed for one specific task, are intelligent and flexible enough to negotiate an unknown environment solely on the basis of the rules which govern it. In this paper, we argue that this principle has the great potential to bring to a new level artificially intelligent systems in other application areas as well. Our specific interest lies in General Trading Agents, which are able to understand the rules of unknown markets and then to actively participate in them without human intervention. To this end, we extend the general Game Description Language into a language that allows to formally describe arbitrary markets in such a way that these specifications can be automatically processed by a computer. We present both syntax and a transition-based semantics for this Market Specification Language and illustrate its expressive power by presenting axiomatizations of several well-known auction types.

  3. Geometry of Spin: Clifford Algebraic Approach

    Indian Academy of Sciences (India)

    Then the various algebraic properties of Pauli matricesare studied as properties of matrix algebra. What has beenshown in this article is that Pauli matrices are a representationof Clifford algebra of spin and hence all the propertiesof Pauli matrices follow from the underlying algebra. Cliffordalgebraic approach provides a ...

  4. Differential operators and W-algebra

    International Nuclear Information System (INIS)

    Vaysburd, I.; Radul, A.

    1992-01-01

    The connection between W-algebras and the algebra of differential operators is conjectured. The bosonized representation of the differential operator algebra with c=-2n and all the subalgebras are examined. The degenerate representations and null-state classifications for c=-2 are presented. (orig.)

  5. Donaldson invariants in algebraic geometry

    International Nuclear Information System (INIS)

    Goettsche, L.

    2000-01-01

    In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)

  6. Fractional supersymmetry and infinite dimensional lie algebras

    International Nuclear Information System (INIS)

    Rausch de Traubenberg, M.

    2001-01-01

    In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation D of any Lie algebra g. Here it is shown how infinite dimensional Lie algebras appear naturally within the framework of fractional supersymmetry. Using a differential realization of g this infinite dimensional Lie algebra, containing the Lie algebra g as a sub-algebra, is explicitly constructed

  7. Zero-One Law for Regular Languages and Semigroups with Zero

    OpenAIRE

    Sin'ya, Ryoma

    2015-01-01

    A regular language has the zero-one law if its asymptotic density converges to either zero or one. We prove that the class of all zero-one languages is closed under Boolean operations and quotients. Moreover, we prove that a regular language has the zero-one law if and only if its syntactic monoid has a zero element. Our proof gives both algebraic and automata characterisation of the zero-one law for regular languages, and it leads the following two corollaries: (i) There is an O(n log n) alg...

  8. Quantum algebra of N superspace

    International Nuclear Information System (INIS)

    Hatcher, Nicolas; Restuccia, A.; Stephany, J.

    2007-01-01

    We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the κ-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra

  9. Effective intervention for expressive grammar in children with specific language impairment.

    Science.gov (United States)

    Smith-Lock, Karen M; Leitao, Suze; Lambert, Lara; Nickels, Lyndsey

    2013-01-01

    Children with specific language impairment are known to struggle with expressive grammar. While some studies have shown successful intervention under laboratory conditions, there is a paucity of evidence for the effectiveness of grammar treatment in young children in community settings. To evaluate the effectiveness of a school-based intervention programme for expressive grammar in 5-year-olds with specific language impairment. Thirty-four 5-year-old children attending a specialized school for children with language impairment participated in the study. Nineteen children received treatment for expressive grammar (experimental group) and 15 children received a control treatment. Treatment consisted of weekly 1-h sessions of small group activities in a classroom setting for 8 weeks. Techniques included direct instruction, focused stimulation, recasting and imitation. Results were analysed at the group level and as a case series with each child as their own control in a single-subject design. There was a significant difference in grammatical performance pre- and post-treatment for children who received grammar treatment (Cohen's d = 1.24), but not for a group of children who received a control treatment. Further, no difference in performance was found in the equivalent time period prior to treatment, nor for an untreated target. Treatment success was more pronounced in children without articulation difficulties which interfered with their ability to produce the grammatical targets (Cohen's d = 1.66). Individual analyses indicated the treatment effect was significant for the majority of children. Individually targeted intervention delivered in small groups in a classroom setting was effective in improving production of expressive grammatical targets in 5-year-old children with specific language impairment. © 2013 Royal College of Speech and Language Therapists.

  10. On criteria for algebraic independence of collections of functions satisfying algebraic difference relations

    Directory of Open Access Journals (Sweden)

    Hiroshi Ogawara

    2017-01-01

    Full Text Available This paper gives conditions for algebraic independence of a collection of functions satisfying a certain kind of algebraic difference relations. As applications, we show algebraic independence of two collections of special functions: (1 Vignéras' multiple gamma functions and derivatives of the gamma function, (2 the logarithmic function, \\(q\\-exponential functions and \\(q\\-polylogarithm functions. In a similar way, we give a generalization of Ostrowski's theorem.

  11. An algebra of reversible computation.

    Science.gov (United States)

    Wang, Yong

    2016-01-01

    We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.

  12. On an extension of the Weil algebra

    International Nuclear Information System (INIS)

    Palev, Ch.

    An extension of the Weil algebra Wsub(n), generated by an appropriate topology is considered. The topology is introduced in such a way that algebraic operations in Wsub(n) to be continuous. The algebraic operations in Wsub(n) are extended by a natural way to a complement, which is noted as an extended Weil algebra. It turns out that the last algebra contains isomorphically the Heisenberg group. By the same way an arbitrary enveloping algebra of a Lie group may be extended. The extended algebra will contain the initial Lie group. (S.P.)

  13. Exponentiation and deformations of Lie-admissible algebras

    International Nuclear Information System (INIS)

    Myung, H.C.

    1982-01-01

    The exponential function is defined for a finite-dimensional real power-associative algebra with unit element. The application of the exponential function is focused on the power-associative (p,q)-mutation of a real or complex associative algebra. Explicit formulas are computed for the (p,q)-mutation of the real envelope of the spin 1 algebra and the Lie algebra so(3) of the rotation group, in light of earlier investigations of the spin 1/2. A slight variant of the mutated exponential is interpreted as a continuous function of the Lie algebra into some isotope of the corresponding linear Lie group. The second part of this paper is concerned with the representation and deformation of a Lie-admissible algebra. The second cohomology group of a Lie-admissible algebra is introduced as a generalization of those of associative and Lie algebras in the Hochschild and Chevalley-Eilenberg theory. Some elementary theory of algebraic deformation of Lie-admissible algebras is discussed in view of generalization of that of associative and Lie algebras. Lie-admissible deformations are also suggested by the representation of Lie-admissible algebras. Some explicit examples of Lie-admissible deformation are given in terms of the (p,q)-mutation of associative deformation of an associative algebra. Finally, we discuss Lie-admissible deformations of order one

  14. Clifford algebras and the minimal representations of the 1D N-extended supersymmetry algebra

    International Nuclear Information System (INIS)

    Toppan, Francesco

    2008-01-01

    The Atiyah-Bott-Shapiro classification of the irreducible Clifford algebra is used to derive general properties of the minimal representations of the 1D N-Extended Supersymmetry algebra (the Z 2 -graded symmetry algebra of the Supersymmetric Quantum Mechanics) linearly realized on a finite number of fields depending on a real parameter t, the time. (author)

  15. Contraction of graded su(2) algebra

    International Nuclear Information System (INIS)

    Patra, M.K.; Tripathy, K.C.

    1989-01-01

    The Inoenu-Wigner contraction scheme is extended to Lie superalgebras. The structure and representations of extended BRS algebra are obtained from contraction of the graded su(2) algebra. From cohomological consideration, we demonstrate that the graded su(2) algebra is the only superalgebra which, on contraction, yields the full BRS algebra. (orig.)

  16. Imitative Production of Regular Past Tense -Ed by English-Speaking Children with Specific Language Impairment

    Science.gov (United States)

    Dalal, Rinky Harish; Loeb, Diane Frome

    2005-01-01

    Background: Language intervention procedures often involve the speech-language pathologist highlighting or making more salient forms that are problematic for the child with a language impairment. According to limited processing accounts of specific language impairment (SLI), one way to increase the saliency of a form is to manipulate its sentence…

  17. Atomic effect algebras with compression bases

    International Nuclear Information System (INIS)

    Caragheorgheopol, Dan; Tkadlec, Josef

    2011-01-01

    Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.

  18. Operator theory, operator algebras and applications

    CERN Document Server

    Lebre, Amarino; Samko, Stefan; Spitkovsky, Ilya

    2014-01-01

    This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geo...

  19. A twisted generalization of Novikov-Poisson algebras

    OpenAIRE

    Yau, Donald

    2010-01-01

    Hom-Novikov-Poisson algebras, which are twisted generalizations of Novikov-Poisson algebras, are studied. Hom-Novikov-Poisson algebras are shown to be closed under tensor products and several kinds of twistings. Necessary and sufficient conditions are given under which Hom-Novikov-Poisson algebras give rise to Hom-Poisson algebras.

  20. Conceptual model of the globalization for domain-specific languages

    NARCIS (Netherlands)

    Clark, T.; van den Brand, M.; Combemale, B.; Rumpe, B.; Combemale, B.

    2015-01-01

    Domain Specific Languages (DSL) have received some prominence recently. Designing a DSL and all their tools is still cumbersome and lots of work. Engineering of DSLs is still at infancy, not even the terms have been coined and agreed on. In particular globalization and all its consequences need to

  1. From rational numbers to algebra: separable contributions of decimal magnitude and relational understanding of fractions.

    Science.gov (United States)

    DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J

    2015-05-01

    To understand the development of mathematical cognition and to improve instructional practices, it is critical to identify early predictors of difficulty in learning complex mathematical topics such as algebra. Recent work has shown that performance with fractions on a number line estimation task predicts algebra performance, whereas performance with whole numbers on similar estimation tasks does not. We sought to distinguish more specific precursors to algebra by measuring multiple aspects of knowledge about rational numbers. Because fractions are the first numbers that are relational expressions to which students are exposed, we investigated how understanding the relational bipartite format (a/b) of fractions might connect to later algebra performance. We presented middle school students with a battery of tests designed to measure relational understanding of fractions, procedural knowledge of fractions, and placement of fractions, decimals, and whole numbers onto number lines as well as algebra performance. Multiple regression analyses revealed that the best predictors of algebra performance were measures of relational fraction knowledge and ability to place decimals (not fractions or whole numbers) onto number lines. These findings suggest that at least two specific components of knowledge about rational numbers--relational understanding (best captured by fractions) and grasp of unidimensional magnitude (best captured by decimals)--can be linked to early success with algebraic expressions. Copyright © 2015 Elsevier Inc. All rights reserved.

  2. Process Algebra and Markov Chains

    NARCIS (Netherlands)

    Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.

    This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study

  3. Process algebra and Markov chains

    NARCIS (Netherlands)

    Brinksma, E.; Hermanns, H.; Brinksma, E.; Hermanns, H.; Katoen, J.P.

    2001-01-01

    This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study

  4. Language for Specific Purposes: A Course Design for PROGEST/CEFET-MG

    Directory of Open Access Journals (Sweden)

    Kellen S. Batista Marques

    2011-07-01

    Full Text Available This paper reports a course design based upon the language for specific purpose approach in CEFET-MG, for the Programa de Capacitação em Gestão de Obras - PROGEST (Program of Study in Engineering, Society and Technology. It is related to the subject matter Language for Professional Purposes, which provides space for discussion about the use and the importance of language and its variations. Its objective is to demonstrate the interaction between the diverse uses of the language, prioritizing the working environment of the professional pupils enrolled in the course. So, the target public profile, its work market - the Civil Construction, the demanded qualification as well as the influence of reading abilities and literacy on the social-communicational contract expected in such environment are discussed.

  5. Vertex ring-indexed Lie algebras

    International Nuclear Information System (INIS)

    Fairlie, David; Zachos, Cosmas

    2005-01-01

    Infinite-dimensional Lie algebras are introduced, which are only partially graded, and are specified by indices lying on cyclotomic rings. They may be thought of as generalizations of the Onsager algebra, but unlike it, or its sl(n) generalizations, they are not subalgebras of the loop algebras associated with sl(n). In a particular interesting case associated with sl(3), their indices lie on the Eisenstein integer triangular lattice, and these algebras are expected to underlie vertex operator combinations in CFT, brane physics, and graphite monolayers

  6. Invariants of triangular Lie algebras

    International Nuclear Information System (INIS)

    Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman

    2007-01-01

    Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated

  7. Waterloo Workshop on Computer Algebra

    CERN Document Server

    Zima, Eugene; WWCA-2016; Advances in computer algebra : in honour of Sergei Abramov's' 70th birthday

    2018-01-01

    This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC’2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23–24, 2016.   This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.

  8. Optimization Specifications for CUDA Code Restructuring Tool

    KAUST Repository

    Khan, Ayaz

    2017-03-13

    In this work we have developed a restructuring software tool (RT-CUDA) following the proposed optimization specifications to bridge the gap between high-level languages and the machine dependent CUDA environment. RT-CUDA takes a C program and convert it into an optimized CUDA kernel with user directives in a configuration file for guiding the compiler. RTCUDA also allows transparent invocation of the most optimized external math libraries like cuSparse and cuBLAS enabling efficient design of linear algebra solvers. We expect RT-CUDA to be needed by many KSA industries dealing with science and engineering simulation on massively parallel computers like NVIDIA GPUs.

  9. The Cuntz algebra Q_N and C*-algebras of product systems

    DEFF Research Database (Denmark)

    Hong, Jeong Hee; Larsen, Nadia S.; Szymanski, Wojciech

    2011-01-01

    We consider a product system over the multiplicative group semigroup N^x of Hilbert bimodules which is implicit in work of S. Yamashita and of the second named author. We prove directly, using universal properties, that the associated Nica-Toeplitz algebra is an extension of the C*-algebra Q...

  10. Lectures on algebraic quantum field theory and operator algebras

    International Nuclear Information System (INIS)

    Schroer, Bert

    2001-04-01

    In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as why mathematicians are/should be interested in algebraic quantum field theory would be equally fitting. besides a presentation of the framework and the main results of local quantum physics these notes may serve as a guide to frontier research problems in mathematical. (author)

  11. q-deformations of noncompact Lie (super-) algebras: The examples of q-deformed Lorentz, Weyl, Poincare' and (super-) conformal algebras

    International Nuclear Information System (INIS)

    Dobrev, V.K.

    1992-01-01

    We review and explain a canonical procedure for the q-deformation of the real forms G of complex Lie (super-) algebras associated with (generalized) Cartan matrices. Our procedure gives different q-deformations for the non-conjugate Cartan subalgebras of G. We give several in detail the q-deformed Lorentz and conformal (super-) algebras. The q-deformed conformal algebra contains as a subalgebra a q-deformed Poincare algebra and as Hopf subalgebras two conjugate 11-generator q-deformed Weyl algebras. The q-deformed Lorentz algebra in Hopf subalgebra of both Weyl algebras. (author). 24 refs

  12. Assessing Algebraic Solving Ability: A Theoretical Framework

    Science.gov (United States)

    Lian, Lim Hooi; Yew, Wun Thiam

    2012-01-01

    Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

  13. Associative and Lie deformations of Poisson algebras

    OpenAIRE

    Remm, Elisabeth

    2011-01-01

    Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations which preserves the underlying associative structure and we study deformations which preserve the underlying Lie algebra.

  14. Psychomotor profile of a child with specific language impairment and Dyslexia

    Directory of Open Access Journals (Sweden)

    Dias Tânia

    2013-01-01

    Full Text Available Projecting beyond the ideia of the organic and expressive body and cementing a close relationship between motor skills, cognition and language, the current practices Psychomotricity reach a new conceptual field. In this paper of qualitative nature, it was intended to draw the psychomotor profile of a 8 years old child with Specific Language Impairment (SLI and Dyslexia, by using the Vitor da Fonseca ‘s Observation Psychomotor Battery (OPB and correlate it with the linguistic and cognitive profiles. Through the triangulation of the results obtained in psychomotor, cognitive and language tests, the data in literature was corroborated, which clearly point to the existence of co-morbidity between PEL, Dyslexia and disturbances in the psychomotor’s profile, thereby demonstrating a strong correlation between psychomotricity, cognition and language. Therefore, it’s urgent, and possible, to sensitize the family, the health and education professionals for the need to a multidisciplinary approach in the areas of psychomotricity and language, both at a prophylactic or rehabilitative level.

  15. Paragrassmann analysis and covariant quantum algebras

    International Nuclear Information System (INIS)

    Filippov, A.T.; Isaev, A.P.; Kurdikov, A.B.; Pyatov, P.N.

    1993-01-01

    This report is devoted to the consideration from the algebraic point of view the paragrassmann algebras with one and many paragrassmann generators Θ i , Θ p+1 i = 0. We construct the paragrassmann versions of the Heisenberg algebra. For the special case, this algebra is nothing but the algebra for coordinates and derivatives considered in the context of covariant differential calculus on quantum hyperplane. The parameter of deformation q in our case is (p+1)-root of unity. Our construction is nondegenerate only for even p. Taking bilinear combinations of paragrassmann derivatives and coordinates we realize generators for the covariant quantum algebras as tensor products of (p+1) x (p+1) matrices. (orig./HSI)

  16. CLASSIFICATION OF 4-DIMENSIONAL GRADED ALGEBRAS

    OpenAIRE

    Armour, Aaron; Chen, Hui-Xiang; ZHANG, Yinhuo

    2009-01-01

    Let k be an algebraically closed field. The algebraic and geometric classification of finite dimensional algebras over k with ch(k) not equal 2 was initiated by Gabriel in [6], where a complete list of nonisomorphic 4-dimensional k-algebras was given and the number of irreducible components of the variety Alg(4) was discovered to be 5. The classification of 5-dimensional k-algebras was done by Mazzola in [10]. The number of irreducible components of the variety Alg(5) is 10. With the dimensio...

  17. Linear algebra

    CERN Document Server

    Liesen, Jörg

    2015-01-01

    This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

  18. JB*-Algebras of Topological Stable Rank 1

    Directory of Open Access Journals (Sweden)

    Akhlaq A. Siddiqui

    2007-01-01

    Full Text Available In 1976, Kaplansky introduced the class JB*-algebras which includes all C*-algebras as a proper subclass. The notion of topological stable rank 1 for C*-algebras was originally introduced by M. A. Rieffel and was extensively studied by various authors. In this paper, we extend this notion to general JB*-algebras. We show that the complex spin factors are of tsr 1 providing an example of special JBW*-algebras for which the enveloping von Neumann algebras may not be of tsr 1. In the sequel, we prove that every invertible element of a JB*-algebra is positive in certain isotope of ; if the algebra is finite-dimensional, then it is of tsr 1 and every element of is positive in some unitary isotope of . Further, it is established that extreme points of the unit ball sufficiently close to invertible elements in a JB*-algebra must be unitaries and that in any JB*-algebras of tsr 1, all extreme points of the unit ball are unitaries. In the end, we prove the coincidence between the λ-function and λu-function on invertibles in a JB*-algebra.

  19. (Super)conformal algebra on the (super)torus

    International Nuclear Information System (INIS)

    Mezincescu, L.; Nepomechie, R.I.; Zachos, C.K.

    1989-01-01

    A generalization of the Virasoro algebra has recently been introduced by Krichever and Novikov (KN). The KN algebra describes the algebra of general conformal transformations in a basis appropriate to a genus-g Riemann surface. We examine in detail the genus-one KN algebra, and find explicit expressions for the central extension. We, further, construct explicitly the superconformal algebra of the supertorus, which yields supersymmetric generalizations of the genus-one KN algebra. A novel feature of the odd-spin-structure case is that the algebra includes a central element which is anticommuting. We comment on possible applications to string theory. (orig.)

  20. Spin-4 extended conformal algebras

    International Nuclear Information System (INIS)

    Kakas, A.C.

    1988-01-01

    We construct spin-4 extended conformal algebras using the second hamiltonian structure of the KdV hierarchy. In the presence of a U(1) current a family of spin-4 algebras exists but the additional requirement that the spin-1 and spin-4 currents commute fixes the algebra uniquely. (orig.)