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Sample records for time process algebra

  1. Located actions in process algebra with timing

    NARCIS (Netherlands)

    Bergstra, J.A.; Middelburg, C.A.

    2004-01-01

    We propose a process algebra obtained by adapting the process algebra with continuous relative timing from Baeten and Middelburg [Process Algebra with Timing, Springer, 2002, Chap. 4] to spatially located actions. This process algebra makes it possible to deal with the behaviour of systems with a

  2. Discrete time process algebra and the semantics of SDL

    NARCIS (Netherlands)

    J.A. Bergstra; C.A. Middelburg; Y.S. Usenko (Yaroslav)

    1998-01-01

    htmlabstractWe present an extension of discrete time process algebra with relative timing where recursion, propositional signals and conditions, a counting process creation operator, and the state operator are combined. Except the counting process creation operator, which subsumes the original

  3. Process algebra with timing : real time and discrete time

    NARCIS (Netherlands)

    Baeten, J.C.M.; Middelburg, C.A.; Bergstra, J.A.; Ponse, A.J.; Smolka, S.A.

    2001-01-01

    We present real time and discrete time versions of ACP with absolute timing and relative timing. The starting-point is a new real time version with absolute timing, called ACPsat, featuring urgent actions and a delay operator. The discrete time versions are conservative extensions of the discrete

  4. Process algebra with timing: Real time and discrete time

    NARCIS (Netherlands)

    Baeten, J.C.M.; Middelburg, C.A.

    1999-01-01

    We present real time and discrete time versions of ACP with absolute timing and relative timing. The startingpoint is a new real time version with absolute timing, called ACPsat , featuring urgent actions and a delay operator. The discrete time versions are conservative extensions of the discrete

  5. Model Checking Process Algebra of Communicating Resources for Real-time Systems

    DEFF Research Database (Denmark)

    Boudjadar, Jalil; Kim, Jin Hyun; Larsen, Kim Guldstrand

    2014-01-01

    This paper presents a new process algebra, called PACOR, for real-time systems which deals with resource constrained timed behavior as an improved version of the ACSR algebra. We define PACOR as a Process Algebra of Communicating Resources which allows to express preemptiveness, urgent ness...

  6. Model checking process algebra of communicating resources for real-time systems

    DEFF Research Database (Denmark)

    Boudjadar, Jalil; Kim, Jin Hyun; Larsen, Kim Guldstrand

    2014-01-01

    This paper presents a new process algebra, called PACoR, for real-time systems which deals with resource- constrained timed behavior as an improved version of the ACSR algebra. We define PACoR as a Process Algebra of Communicating Resources which allows to explicitly express preemptiveness...

  7. Real time process algebra with time-dependent conditions

    NARCIS (Netherlands)

    Baeten, J.C.M.; Middelburg, C.A.

    We extend the main real time version of ACP presented in [6] with conditionals in which the condition depends on time. This extension facilitates flexible dependence of proccess behaviour on initialization time. We show that the conditions concerned generalize the conditions introduced earlier

  8. 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

  9. 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

  10. Real space process algebra

    NARCIS (Netherlands)

    Bergstra, J.A.; Baeten, J.C.M.

    1993-01-01

    The real time process algebra of Baeten and Bergstra [Formal Aspects of Computing, 3, 142-188 (1991)] is extended to real space by requiring the presence of spatial coordinates for each atomic action, in addition to the required temporal attribute. It is found that asynchronous communication

  11. A consistent causality-based view on a timed process algebra including urgent interactions

    NARCIS (Netherlands)

    Katoen, Joost P.; Latella, Diego; Langerak, Romanus; Brinksma, Hendrik; Bolognesi, Tommaso

    1998-01-01

    This paper discusses a timed variant of a process algebra akin to LOTOS, baptized UPA, in a causality-based setting. Two timed features are incorporated—a delay function which constrains the occurrence time of atomic actions and an urgency operator that forces (local or synchronized) actions to

  12. A polynomial time algorithm for checking regularity of totally normed process algebra

    NARCIS (Netherlands)

    Yang, F.; Huang, H.

    2015-01-01

    A polynomial algorithm for the regularity problem of weak and branching bisimilarity on totally normed process algebra (PA) processes is given. Its time complexity is O(n 3 +mn) O(n3+mn), where n is the number of transition rules and m is the maximal length of the rules. The algorithm works for

  13. Priority in Process Algebras

    Science.gov (United States)

    Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.

    1999-01-01

    This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.

  14. General distributions in process algebra

    NARCIS (Netherlands)

    Katoen, Joost P.; d' Argenio, P.R.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.

    2001-01-01

    This paper is an informal tutorial on stochastic process algebras, i.e., process calculi where action occurrences may be subject to a delay that is governed by a (mostly continuous) random variable. Whereas most stochastic process algebras consider delays determined by negative exponential

  15. 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,

  16. Linear Algebra and Image Processing

    Science.gov (United States)

    Allali, Mohamed

    2010-01-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)

  17. 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...

  18. Towards a Process Algebra for Shared Processors

    DEFF Research Database (Denmark)

    Buchholtz, Mikael; Andersen, Jacob; Løvengreen, Hans Henrik

    2002-01-01

    We present initial work on a timed process algebra that models sharing of processor resources allowing preemption at arbitrary points in time. This enables us to model both the functional and the timely behaviour of concurrent processes executed on a single processor. We give a refinement relation...

  19. A process algebra model of QED

    International Nuclear Information System (INIS)

    Sulis, William

    2016-01-01

    The process algebra approach to quantum mechanics posits a finite, discrete, determinate ontology of primitive events which are generated by processes (in the sense of Whitehead). In this ontology, primitive events serve as elements of an emergent space-time and of emergent fundamental particles and fields. Each process generates a set of primitive elements, using only local information, causally propagated as a discrete wave, forming a causal space termed a causal tapestry. Each causal tapestry forms a discrete and finite sampling of an emergent causal manifold (space-time) M and emergent wave function. Interactions between processes are described by a process algebra which possesses 8 commutative operations (sums and products) together with a non-commutative concatenation operator (transitions). The process algebra possesses a representation via nondeterministic combinatorial games. The process algebra connects to quantum mechanics through the set valued process and configuration space covering maps, which associate each causal tapestry with sets of wave functions over M. Probabilities emerge from interactions between processes. The process algebra model has been shown to reproduce many features of the theory of non-relativistic scalar particles to a high degree of accuracy, without paradox or divergences. This paper extends the approach to a semi-classical form of quantum electrodynamics. (paper)

  20. A brief history of process algebra

    NARCIS (Netherlands)

    Baeten, J.C.M.

    2005-01-01

    This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author

  1. A brief history of process algebra

    NARCIS (Netherlands)

    Baeten, J.C.M.

    2004-01-01

    Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The

  2. 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.

  3. An algebra of discrete event processes

    Science.gov (United States)

    Heymann, Michael; Meyer, George

    1991-01-01

    This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.

  4. 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...

  5. Data-Driven Process Discovery: A Discrete Time Algebra for Relational Signal Analysis

    National Research Council Canada - National Science Library

    Conrad, David

    1996-01-01

    .... Proposed is a time series transformation that encodes and compresses real-valued data into a well defined, discrete-space of 13 primitive elements where comparative evaluation between variables...

  6. A brief history of process algebra

    OpenAIRE

    Baeten, J.C.M.

    2005-01-01

    This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author gives his personal views on these matters. He also considers the present situation, and states some challenges for the future.

  7. A brief history of process algebra

    OpenAIRE

    Baeten, J.C.M.

    2004-01-01

    Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author gives his personal views on these matters. He also considers the present situation, and states some challenges for the future.

  8. 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

  9. 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

  10. Highly Undecidable Questions for Process Algebras

    DEFF Research Database (Denmark)

    Srba, Jiri; Jancar, Petr

    2004-01-01

    We show Sigma^1_1-completeness of weak bisimilarity for PA (process algebra), and of wek simulation preorder/equivalence for PDA (pushdown automata), PA and PN (Petri nets). We also show Pi^1_1-hardness of weak omega-trace equivalence for the sub(classes) of BPA (basic process algebra) and BPP...

  11. Strong Bisimilarity of Simple Process Algebras

    DEFF Research Database (Denmark)

    Srba, Jirí

    2003-01-01

    We study bisimilarity and regularity problems of simple process algebras. In particular, we show PSPACE-hardness of the following problems: (i) strong bisimilarity of Basic Parallel Processes (BPP), (ii) strong bisimilarity of Basic Process Algebra (BPA), (iii) strong regularity of BPP, and (iv......) strong regularity of BPA. We also demonstrate NL-hardness of strong regularity problems for the normed subclasses of BPP and BPA. Bisimilarity problems of simple process algebras are introduced in a general framework of process rewrite systems, and a uniform description of the new techniques used...

  12. 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.

  13. Towards Model Checking Stochastic Process Algebra

    NARCIS (Netherlands)

    Hermanns, H.; Grieskamp, W.; Santen, T.; Katoen, Joost P.; Stoddart, B.; Meyer-Kayser, J.; Siegle, M.

    2000-01-01

    Stochastic process algebras have been proven useful because they allow behaviour-oriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviour- oriented style supports composition and abstraction in a natural way. However, analysis of

  14. What is algebraic in process theory?

    NARCIS (Netherlands)

    Luttik, B.

    2006-01-01

    This is an extended version of an essay with the same title that I wrote for the workshop Algebraic process calculi : the first twenty five years and beyond, held in Bertinoro, Italy in the first week of August 2005.

  15. What is algebraic in process theory?

    NARCIS (Netherlands)

    Luttik, B.

    2006-01-01

    This is an extended version of an essay with the same title that I wrote for the workshop Algebraic Process Calculi: The First Twenty Five Years and Beyond, held in Bertinoro, Italy in the first week of August 2005.

  16. Algebraic relaxation of a time correlation function

    International Nuclear Information System (INIS)

    Srivastava, S.; Kumar, C.N.; Tankeshwar, K.

    2004-06-01

    A second order non-linear differential equation obtained from Mori's integro- differential equation is shown to transform to another form which provides algebraic decay to a time correlation function. Involved parameters in algebraic formula are related to exact properties of the corresponding correlation function. The model has been used to study a sol-gel system which is known, experimentally, to exhibit a power law decay to stress auto-correlation function. The expression obtained for the viscosity shows a logarithmic divergence at some critical value of the parameter. Some features of the model have also been tested using available information about Lennard-Jones fluids. (author)

  17. Asynchronous communication in real space process algebra

    NARCIS (Netherlands)

    Baeten, J.C.M.; Bergstra, J.A.

    1991-01-01

    A version of classical real space process algebra is given in which messages travel with constant speed through a three-dimensional medium. It follows that communication is asynchronous and has a broadcasting character. A state operator is used to describe asynchronous message transfer and a

  18. Asynchronous communication in real space process algebra

    NARCIS (Netherlands)

    Bergstra, J.A.; Baeten, J.C.M.

    1992-01-01

    A version of classical real space process algebra is given in which messages travel with constant speed through a three-dimensional medium. It follows that communication is asynchronous and has a broadcasting character. A state operator is used to describe asynchronous message transfer and a

  19. Space-time algebra for the generalization of gravitational field

    Indian Academy of Sciences (India)

    The Maxwell–Proca-like field equations of gravitolectromagnetism are formulated using space-time algebra (STA). The gravitational wave equation with massive gravitons and gravitomagnetic monopoles has been derived in terms of this algebra. Using space-time algebra, the most generalized form of ...

  20. Asynchronous communication in real space process algebra

    OpenAIRE

    Baeten, JCM Jos; Bergstra, JA Jan

    1990-01-01

    A version of classical real space process algebra is given in which messages travel with constant speed through a three-dimensional medium. It follows that communication is asynchronous and has a broadcasting character. A state operator is used to describe asynchronous message transfer and a priority mechanism allows to express the broadcasting mechanism. As an application, a protocol is specified in which the receiver moves with respect to the sender.

  1. 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.

  2. Performance assessment in algebra learning process

    Science.gov (United States)

    Lestariani, Ida; Sujadi, Imam; Pramudya, Ikrar

    2017-12-01

    The purpose of research to describe the implementation of performance assessment on algebra learning process. The subject in this research is math educator of SMAN 1 Ngawi class X. This research includes descriptive qualitative research type. Techniques of data collecting are done by observation method, interview, and documentation. Data analysis technique is done by data reduction, data presentation, and conclusion. The results showed any indication that the steps taken by the educator in applying the performance assessment are 1) preparing individual worksheets and group worksheets, 2) preparing rubric assessments for independent worksheets and groups and 3) making performance assessments rubric to learners’ performance results with individual or groups task.

  3. Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes

    NARCIS (Netherlands)

    Cloth, L.; de Alfaro, L.; Gilmore, S.; Bohnenkamp, H.C.; Haverkort, Boudewijn R.H.M.

    2001-01-01

    In this paper, the concept of complete finite prefixes for process algebra expressions is extended to stochastic models. Events are supposed to happen after a delay that is determined by random variables assigned to the preceding conditions. Max-plus algebra expressions are shown to provide an

  4. Contradiction-tolerant process algebra with propositional signals

    NARCIS (Netherlands)

    Bergstra, J.A.; Middelburg, C.A.

    2017-01-01

    In a previous paper, an ACP-style process algebra was proposed in which propositions are used as the visible part of the state of processes and as state conditions under which processes may proceed. This process algebra, called ACPps, is built on classical propositional logic. In this paper, we

  5. A Process Algebra for Supervisory Coordination

    Directory of Open Access Journals (Sweden)

    Jos Baeten

    2011-08-01

    Full Text Available A supervisory controller controls and coordinates the behavior of different components of a complex machine by observing their discrete behaviour. Supervisory control theory studies automated synthesis of controller models, known as supervisors, based on formal models of the machine components and a formalization of the requirements. Subsequently, code generation can be used to implement this supervisor in software, on a PLC, or embedded microprocessor. In this article, we take a closer look at the control loop that couples the supervisory controller and the machine. We model both event-based and state-based observations using process algebra and bisimulation-based semantics. The main application area of supervisory control that we consider is coordination, referred to as supervisory coordination, and we give an academic and an industrial example, discussing the process-theoretic concepts employed.

  6. On algebraic time-derivative estimation and deadbeat state reconstruction

    DEFF Research Database (Denmark)

    Reger, Johann; Jouffroy, Jerome

    2009-01-01

    This paper places into perspective the so-called algebraic time-derivative estimation method recently introduced by Fliess and co-authors with standard results from linear statespace theory for control systems. In particular, it is shown that the algebraic method can essentially be seen...

  7. Bochvar-McCarthy logic and process algebra

    NARCIS (Netherlands)

    Bergstra, J.A.; Ponse, A.

    1998-01-01

    We propose a combination of Bochvar's strict three-valued logic, McCarthy's sequential three-valued logic, and process algebra via the conditional guard construct. This combination entails the introduction of a new constant meaningless in process algebra. We present an operational semantics

  8. 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

  9. 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

  10. Reachability for Finite-State Process Algebras Using Static Analysis

    DEFF Research Database (Denmark)

    Skrypnyuk, Nataliya; Nielson, Flemming

    2011-01-01

    of the Data Flow Analysis are used in order to “cut off” some of the branches in the reachability analysis that are not important for determining, whether or not a state is reachable. In this way, it is possible for our reachability algorithm to avoid building large parts of the system altogether and still......In this work we present an algorithm for solving the reachability problem in finite systems that are modelled with process algebras. Our method uses Static Analysis, in particular, Data Flow Analysis, of the syntax of a process algebraic system with multi-way synchronisation. The results...... solve the reachability problem in a precise way....

  11. On the Cyclotomic Quantum Algebra of Time Perception

    OpenAIRE

    Planat, Michel

    2004-01-01

    I develop the idea that time perception is the quantum counterpart to time measurement. Phase-locking and prime number theory were proposed as the unifying concepts for understanding the optimal synchronization of clocks and their 1/f frequency noise. Time perception is shown to depend on the thermodynamics of a quantum algebra of number and phase operators already proposed for quantum computational tasks, and to evolve according to a Hamiltonian mimicking Fechner's law. The mathematics is Bo...

  12. 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.

  13. Process algebras for hybrid systems : comparison and development

    NARCIS (Netherlands)

    Khadim, U.

    2008-01-01

    Our research is about formal speci¯cation and analysis of hybrid systems. The formalism used is process algebra. Hybrid systems are systems that exhibit both discrete and continuous behaviour. An example of a hybrid system is a digital controller controlling a physical device such as present in

  14. Visualisation for Stochastic Process Algebras: The Graphic Truth

    DEFF Research Database (Denmark)

    Smith, Michael James Andrew; Gilmore, Stephen

    2011-01-01

    and stochastic activity networks provide an automaton-based view of the model, which may be easier to visualise, at the expense of portability. In this paper, we argue that we can achieve the benefits of both approaches by generating a graphical view of a stochastic process algebra model, which is synchronised...

  15. Symbolic Reachability for Process Algebras with Recursive Data Types

    NARCIS (Netherlands)

    Blom, Stefan; van de Pol, Jan Cornelis; Fitzgerald, J.S.; Haxthausen, A.E.; Yenigun, H.

    2008-01-01

    In this paper, we present a symbolic reachability algorithm for process algebras with recursive data types. Like the various saturation based algorithms of Ciardo et al, the algorithm is based on partitioning of the transition relation into events whose influence is local. As new features, our

  16. Algebraic time-dependent variational approach to dynamical calculations

    International Nuclear Information System (INIS)

    Shi, S.; Rabitz, H.

    1988-01-01

    A set of time-dependent basis states is obtained with a group of unitary transformations generated by a Lie algebra. Applying the time-dependent variational principle to the trial function subspace constructed from the linear combination of the time-dependent basis states gives rise to a set of ''classical'' equations of motion for the group parameters and the expansion coefficients from which the time evolution of the system state can be determined. The formulation is developed for a general Lie algebra as well as for the commonly encountered algebra containing homogeneous polynominal products of the coordinate Q and momentum P operators (or equivalently the boson creation a/sup dagger/ and annihilation a operators) of order 0, 1, and 2. Explicit expressions for the transition amplitudes are derived by virtue of the cannonical transformation properties of the unitary transformation. The applicability of the present formalism in a variety of problems is implied by two illustrative examples: (a) a parametric amplifier; (b) the collinear collision of an atom with a Morse oscillator

  17. A linear process-algebraic format for probabilistic systems with data (extended version)

    NARCIS (Netherlands)

    Katoen, Joost P.; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette; Timmer, Mark

    2010-01-01

    This paper presents a novel linear process-algebraic format for probabilistic automata. The key ingredient is a symbolic transformation of probabilistic process algebra terms that incorporate data into this linear format while preserving strong probabilistic bisimulation. This generalises similar

  18. A linear process-algebraic format for probabilistic systems with data

    NARCIS (Netherlands)

    Katoen, Joost P.; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette; Timmer, Mark; Gomes, L.; Khomenko, V.; Fernandes, J.M.

    This paper presents a novel linear process algebraic format for probabilistic automata. The key ingredient is a symbolic transformation of probabilistic process algebra terms that incorporate data into this linear format while preserving strong probabilistic bisimulation. This generalises similar

  19. Polarized process algebra with reactive composition

    NARCIS (Netherlands)

    Bergstra, J.A.; Bethke, I.

    2005-01-01

    Polarized processes are introduced to model the asymmetric interaction of systems. The asymmetry stems from the distinction between service and request. The scheduled concurrent composition of two polarized processes is called client–server composition or reactive composition, placing one process in

  20. A Process Algebraic Approach to Software Architecture Design

    Science.gov (United States)

    Aldini, Alessandro; Bernardo, Marco; Corradini, Flavio

    Process algebra is a formal tool for the specification and the verification of concurrent and distributed systems. It supports compositional modeling through a set of operators able to express concepts like sequential composition, alternative composition, and parallel composition of action-based descriptions. It also supports mathematical reasoning via a two-level semantics, which formalizes the behavior of a description by means of an abstract machine obtained from the application of structural operational rules and then introduces behavioral equivalences able to relate descriptions that are syntactically different. In this chapter, we present the typical behavioral operators and operational semantic rules for a process calculus in which no notion of time, probability, or priority is associated with actions. Then, we discuss the three most studied approaches to the definition of behavioral equivalences - bisimulation, testing, and trace - and we illustrate their congruence properties, sound and complete axiomatizations, modal logic characterizations, and verification algorithms. Finally, we show how these behavioral equivalences and some of their variants are related to each other on the basis of their discriminating power.

  1. Gauge fields in algebraically special space-times

    International Nuclear Information System (INIS)

    Torres del Castillo, G.F.

    1985-01-01

    It is shown that in an algebraically special space-time which admits a congruence of null strings, a source-free gauge field aligned with the congruence is determined by a matrix potential which has to satisfy a second-order differential equation with quadratic nonlinearities. The Einstein--Yang--Mills equations are then reduced to a scalar and two matrix equations. In the case of self-dual gauge fields in a self-dual space-time, the existence of an infinite set of conservation laws, of an associated linear system, and of infinitesimal Baecklund transformations is demonstrated. All the results apply for an arbitrary gauge group

  2. Relating Reasoning Methodologies in Linear Logic and Process Algebra

    Directory of Open Access Journals (Sweden)

    Yuxin Deng

    2012-11-01

    Full Text Available We show that the proof-theoretic notion of logical preorder coincides with the process-theoretic notion of contextual preorder for a CCS-like calculus obtained from the formula-as-process interpretation of a fragment of linear logic. The argument makes use of other standard notions in process algebra, namely a labeled transition system and a coinductively defined simulation relation. This result establishes a connection between an approach to reason about process specifications and a method to reason about logic specifications.

  3. Algebraic Meta-Theory of Processes with Data

    Directory of Open Access Journals (Sweden)

    Daniel Gebler

    2013-07-01

    Full Text Available There exists a rich literature of rule formats guaranteeing different algebraic properties for formalisms with a Structural Operational Semantics. Moreover, there exist a few approaches for automatically deriving axiomatizations characterizing strong bisimilarity of processes. To our knowledge, this literature has never been extended to the setting with data (e.g. to model storage and memory. We show how the rule formats for algebraic properties can be exploited in a generic manner in the setting with data. Moreover, we introduce a new approach for deriving sound and ground-complete axiom schemata for a notion of bisimilarity with data, called stateless bisimilarity, based on intuitive auxiliary function symbols for handling the store component. We do restrict, however, the axiomatization to the setting where the store component is only given in terms of constants.

  4. Algebraic approach to time-delay data analysis for LISA

    International Nuclear Information System (INIS)

    Dhurandhar, S.V.; Nayak, K. Rajesh; Vinet, J.-Y.

    2002-01-01

    Cancellation of laser frequency noise in interferometers is crucial for attaining the requisite sensitivity of the triangular three-spacecraft LISA configuration. Raw laser noise is several orders of magnitude above the other noises and thus it is essential to bring it down to the level of other noises such as shot, acceleration, etc. Since it is impossible to maintain equal distances between spacecrafts, laser noise cancellation must be achieved by appropriately combining the six beams with appropriate time delays. It has been shown in several recent papers that such combinations are possible. In this paper, we present a rigorous and systematic formalism based on algebraic geometrical methods involving computational commutative algebra, which generates in principle all the data combinations canceling the laser frequency noise. The relevant data combinations form the first module of syzygies, as it is called in the literature of algebraic geometry. The module is over a polynomial ring in three variables, the three variables corresponding to the three time delays around the LISA triangle. Specifically, we list several sets of generators for the module whose linear combinations with polynomial coefficients generate the entire module. We find that this formalism can also be extended in a straightforward way to cancel Doppler shifts due to optical bench motions. The two modules are in fact isomorphic. We use our formalism to obtain the transfer functions for the six beams and for the generators. We specifically investigate monochromatic gravitational wave sources in the LISA band and carry out the maximization over linear combinations of the generators of the signal-to-noise ratios with the frequency and source direction angles as parameters

  5. A Parallel Algebraic Multigrid Solver on Graphics Processing Units

    KAUST Repository

    Haase, Gundolf

    2010-01-01

    The paper presents a multi-GPU implementation of the preconditioned conjugate gradient algorithm with an algebraic multigrid preconditioner (PCG-AMG) for an elliptic model problem on a 3D unstructured grid. An efficient parallel sparse matrix-vector multiplication scheme underlying the PCG-AMG algorithm is presented for the many-core GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster and a multi-GPU configuration with eight GPUs is about 100 times faster than a typical server CPU core. © 2010 Springer-Verlag.

  6. Process Algebra Approach for Action Recognition in the Maritime Domain

    Science.gov (United States)

    Huntsberger, Terry

    2011-01-01

    The maritime environment poses a number of challenges for autonomous operation of surface boats. Among these challenges are the highly dynamic nature of the environment, the onboard sensing and reasoning requirements for obeying the navigational rules of the road, and the need for robust day/night hazard detection and avoidance. Development of full mission level autonomy entails addressing these challenges, coupled with inference of the tactical and strategic intent of possibly adversarial vehicles in the surrounding environment. This paper introduces PACIFIC (Process Algebra Capture of Intent From Information Content), an onboard system based on formal process algebras that is capable of extracting actions/activities from sensory inputs and reasoning within a mission context to ensure proper responses. PACIFIC is part of the Behavior Engine in CARACaS (Cognitive Architecture for Robotic Agent Command and Sensing), a system that is currently running on a number of U.S. Navy unmanned surface and underwater vehicles. Results from a series of experimental studies that demonstrate the effectiveness of the system are also presented.

  7. Infinite-parametric extension of the conformal algebra in D>2 space-time dimension

    International Nuclear Information System (INIS)

    Fradkin, E.S.; Linetsky, V.Ya.

    1990-09-01

    On the basis of the analytic continuations of semisimple Lie algebras discovered recently by us we construct manifestly quasiconformal infinite-dimensional algebras AC(so(4,1)) and PAC(so(3,2)) extending the conformal algebras in three-dimensional Euclidean and Minkowski space-time like the Virasoro algebra extends so(2,1). Their higher spin generalizations are also constructed. A counterpart of the central extension for D>2 and possible applications in exactly solvable conformal quantum field models in D>2 are discussed. (author). 31 refs, 2 figs

  8. An introduction to the history of algebra solving equations from Mesopotamian times to the Renaissance

    CERN Document Server

    Sesiano, Jacques

    2009-01-01

    This text should not be viewed as a comprehensive history of algebra before 1600, but as a basic introduction to the types of problems that illustrate the earliest forms of algebra. It would be particularly useful for an instructor who is looking for examples to help enliven a course on elementary algebra with problems drawn from actual historical texts. -Warren Van Egmond about the French edition for MathSciNet This book does not aim to give an exhaustive survey of the history of algebra up to early modern times but merely to present some significant steps in solving equations and, wherever

  9. Zero-rest-mass fields in an algebraically special curved space-time

    Energy Technology Data Exchange (ETDEWEB)

    Fordy, A P [King' s Coll., London (UK). Dept. of Mathematics

    1977-04-01

    Zero-rest-mass higher-spin fields in algebraically special vacuum back-ground space-times are considered. It is shown that the algebraic speciality of the background metric strongly restricts the form of the solutions of these fields. These results are used to study perturbations of the Schwarzschild black hole.

  10. Real-Time Algebraic Derivative Estimations Using a Novel Low-Cost Architecture Based on Reconfigurable Logic

    Science.gov (United States)

    Morales, Rafael; Rincón, Fernando; Gazzano, Julio Dondo; López, Juan Carlos

    2014-01-01

    Time derivative estimation of signals plays a very important role in several fields, such as signal processing and control engineering, just to name a few of them. For that purpose, a non-asymptotic algebraic procedure for the approximate estimation of the system states is used in this work. The method is based on results from differential algebra and furnishes some general formulae for the time derivatives of a measurable signal in which two algebraic derivative estimators run simultaneously, but in an overlapping fashion. The algebraic derivative algorithm presented in this paper is computed online and in real-time, offering high robustness properties with regard to corrupting noises, versatility and ease of implementation. Besides, in this work, we introduce a novel architecture to accelerate this algebraic derivative estimator using reconfigurable logic. The core of the algorithm is implemented in an FPGA, improving the speed of the system and achieving real-time performance. Finally, this work proposes a low-cost platform for the integration of hardware in the loop in MATLAB. PMID:24859033

  11. Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras

    Energy Technology Data Exchange (ETDEWEB)

    Dobay, M. P. D., E-mail: maria.pamela.david@physik.uni-muenchen.de; Alberola, A. Piera; Mendoza, E. R.; Raedler, J. O., E-mail: joachim.raedler@physik.uni-muenchen.de [Ludwig-Maximilians University, Faculty of Physics, Center for NanoScience (Germany)

    2012-03-15

    Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.

  12. Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras

    International Nuclear Information System (INIS)

    Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.

    2012-01-01

    Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.

  13. Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras

    Science.gov (United States)

    Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.

    2012-03-01

    Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.

  14. Principles of Stagewise Separation Process Calculations: A Simple Algebraic Approach Using Solvent Extraction.

    Science.gov (United States)

    Crittenden, Barry D.

    1991-01-01

    A simple liquid-liquid equilibrium (LLE) system involving a constant partition coefficient based on solute ratios is used to develop an algebraic understanding of multistage contacting in a first-year separation processes course. This algebraic approach to the LLE system is shown to be operable for the introduction of graphical techniques…

  15. 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.

  16. Rosen's (M,R) system in process algebra.

    Science.gov (United States)

    Gatherer, Derek; Galpin, Vashti

    2013-11-17

    Robert Rosen's Metabolism-Replacement, or (M,R), system can be represented as a compact network structure with a single source and three products derived from that source in three consecutive reactions. (M,R) has been claimed to be non-reducible to its components and algorithmically non-computable, in the sense of not being evaluable as a function by a Turing machine. If (M,R)-like structures are present in real biological networks, this suggests that many biological networks will be non-computable, with implications for those branches of systems biology that rely on in silico modelling for predictive purposes. We instantiate (M,R) using the process algebra Bio-PEPA, and discuss the extent to which our model represents a true realization of (M,R). We observe that under some starting conditions and parameter values, stable states can be achieved. Although formal demonstration of algorithmic computability remains elusive for (M,R), we discuss the extent to which our Bio-PEPA representation of (M,R) allows us to sidestep Rosen's fundamental objections to computational systems biology. We argue that the behaviour of (M,R) in Bio-PEPA shows life-like properties.

  17. Killing vectors in algebraically special space-times

    International Nuclear Information System (INIS)

    Torres del Castillo, G.F.

    1984-01-01

    The form of the isometric, homothetic, and conformal Killing vectors for algebraically special metrics which admit a shear-free congruence of null geodesics is obtained by considering their complexification, using the existence of a congruence of null strings. The Killing equations are partially integrated and the reasons which permit this reduction are exhibited. In the case where the congruence of null strings has a vanishing expansion, the Killing equations are reduced to a single master equation

  18. Analysis of DIRAC's behavior using model checking with process algebra

    International Nuclear Information System (INIS)

    Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof; Diaz, Ricardo Graciani

    2012-01-01

    DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.

  19. Analysis of DIRAC's behavior using model checking with process algebra

    Science.gov (United States)

    Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Graciani Diaz, Ricardo; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof

    2012-12-01

    DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.

  20. 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.

  1. Study on time of flight property of electron optical systems by differential algebraic method

    International Nuclear Information System (INIS)

    Cheng Min; Tang Tiantong; Yao Zhenhua

    2002-01-01

    Differential algebraic method is a powerful and promising technique in computer numerical analysis. When applied to nonlinear dynamics systems, the arbitrary high-order transfer properties of the systems can be computed directly with high precision. In this paper, the principle of differential algebra is applied to study on the time of flight (TOF) property of electron optical systems and their arbitrary order TOF transfer properties can be numerically calculated out. As an example, TOF transfer properties of a uniform magnetic sector field analyzer have been studied by differential algebraic method. Relative errors of the first-order and second-order TOF transfer coefficients of the magnetic sector field analyzer are of the order 10 -11 or smaller compared with the analytic solutions. It is proved that differential algebraic TOF method is of high accuracy and very helpful for high-order TOF transfer property analysis of electron optical systems. (author)

  2. On Yang's Noncommutative Space Time Algebra, Holography, Area Quantization and C-space Relativity

    CERN Document Server

    Castro, C

    2004-01-01

    An isomorphism between Yang's Noncommutative space-time algebra (involving two length scales) and the holographic-area-coordinates algebra of C-spaces (Clifford spaces) is constructed via an AdS_5 space-time which is instrumental in explaining the origins of an extra (infrared) scale R in conjunction to the (ultraviolet) Planck scale lambda characteristic of C-spaces. Yang's space-time algebra allowed Tanaka to explain the origins behind the discrete nature of the spectrum for the spatial coordinates and spatial momenta which yields a minimum length-scale lambda (ultraviolet cutoff) and a minimum momentum p = (\\hbar / R) (maximal length R, infrared cutoff). The double-scaling limit of Yang's algebra : lambda goes to 0, and R goes to infinity, in conjunction with the large n infinity limit, leads naturally to the area quantization condition : lambda R = L^2 = n lambda^2 (in Planck area units) given in terms of the discrete angular-momentum eigenvalues n . The generalized Weyl-Heisenberg algebra in C-spaces is ...

  3. Karlin–McGregor-like formula in a simple time-inhomogeneous birth–death process

    International Nuclear Information System (INIS)

    Ohkubo, Jun

    2014-01-01

    Algebraic discussions are developed to derive transition probabilities for a simple time-inhomogeneous birth–death process. Algebraic probability theory and Lie algebraic treatments make it easy to treat the time-inhomogeneous cases. As a result, an expression based on the Charlier polynomials is obtained, which can be considered as an extension of a famous Karlin–McGregor representation for a time-homogeneous birth–death process. (paper)

  4. Investigation of continuous-time quantum walk via modules of Bose-Mesner and Terwilliger algebras

    International Nuclear Information System (INIS)

    Jafarizadeh, M A; Salimi, S

    2006-01-01

    The continuous-time quantum walk on the underlying graphs of association schemes has been studied, via the algebraic combinatorics structures of association schemes, namely semi-simple modules of their Bose-Mesner and Terwilliger algebras. It is shown that the Terwilliger algebra stratifies the graph into a (d + 1) disjoint union of strata which is different from the stratification based on distance, except for distance regular graphs. In underlying graphs of association schemes, the probability amplitudes and average probabilities are given in terms of dual eigenvalues of association schemes, such that the amplitudes of observing the continuous-time quantum walk on all sites belonging to a given stratum are the same, therefore there are at most (d + 1) different observing probabilities. The importance of association scheme in continuous-time quantum walk is shown by some worked out examples such as arbitrary finite group association schemes followed by symmetric S n , Dihedral D 2m and cyclic groups. At the end it is shown that the highest irreducible representations of Terwilliger algebras pave the way to use the spectral distributions method of Jafarizadeh and Salimi (2005 Preprint quant-ph/0510174) in studying quantum walk on some rather important graphs called distance regular graphs

  5. Coproduct and star product in field theories on Lie-algebra noncommutative space-times

    International Nuclear Information System (INIS)

    Amelino-Camelia, Giovanni; Arzano, Michele

    2002-01-01

    We propose a new approach to field theory on κ-Minkowski noncommutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a star product, a technique which is proving to be very fruitful in analogous studies of canonical noncommutative space-times, such as the ones recently found to play a role in the description of certain string-theory backgrounds. We find to be incorrect the expectation, previously reported in the literature, that the lack of symmetry of the κ-Poincare coproduct should lead to interaction vertices that are not symmetric under exchanges of the momenta of identical particles entering the relevant processes. We show that in κ-Minkowski the coproduct and the star product must indeed treat momenta in a nonsymmetric way, but the overall structure of interaction vertices is symmetric under exchange of identical particles. We also show that in κ-Minkowski field theories it is convenient to introduce the concepts of 'planar' and 'nonplanar' Feynman loop diagrams, again in close analogy with the corresponding concepts previously introduced in the study of field theories in canonical noncommutative space-times

  6. 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

  7. The algebra of space-time as basis of a quantum field theory of all fermions and interactions

    International Nuclear Information System (INIS)

    Wolf, A.K.

    2005-01-01

    In this thesis a construction of a grand unified theory on the base of algebras of vector fields on a Riemannian space-time is described. Hereby from the vector and covector fields a Clifford-geometrical algebra is generated. (HSI)

  8. Some experience in applying the REDUCE algebraic system to the calculation of scattering processes in QED and QCD

    International Nuclear Information System (INIS)

    Mohring, H.J.; Schiller, A.

    1980-01-01

    The problems arising in the use of the REDUCE algebraic system for calculating traces of the Dirac matrix products describing scattering processes in quantum electrodynamics (QED) and quantum chromodynamics (QCD) are considered. Application of the REDUCE system for describing two-photon processes in e + e - reactions is discussed. An example of using the REDUCE system for calculating matrix elements of elementary processes of hard scattering is described. The calculations were performed by means of the REDUCE2 version on an EC1040 computer. The computations take almost 10 minutes of machine time and computer storage capacity of abo t 800 kiuobites

  9. Reachability analysis for timed automata using max-plus algebra

    DEFF Research Database (Denmark)

    Lu, Qi; Madsen, Michael; Milata, Martin

    2012-01-01

    We show that max-plus polyhedra are usable as a data structure in reachability analysis of timed automata. Drawing inspiration from the extensive work that has been done on difference bound matrices, as well as previous work on max-plus polyhedra in other areas, we develop the algorithms needed...

  10. The algebraic approach to space-time geometry

    International Nuclear Information System (INIS)

    Heller, M.; Multarzynski, P.; Sasin, W.

    1989-01-01

    A differential manifold can be defined in terms of smooth real functions carried by it. By rejecting the postulate, in such a definition, demanding the local diffeomorphism of a manifold to the Euclidean space, one obtains the so-called differential space concept. Every subset of R n turns out to be a differential space. Extensive parts of differential geometry on differential spaces, developed by Sikorski, are reviewed and adapted to relativistic purposes. Differential space as a new model of space-time is proposed. The Lorentz structure and Einstein's field equations on differential spaces are discussed. 20 refs. (author)

  11. Generation and evaluation of business continuity processes using algebraic graph transformation and the mCRL2 process algebra

    NARCIS (Netherlands)

    Brandt, C.; Hermann, F.; Groote, J.F.

    2011-01-01

    Critical business processes can fail. Therefore, continuity processes are needed as back-up solutions. Today, those continuity processes are set up and maintained manually. They are mostly based on best practices that focus on specific continuity scenarios, Nevertheless, failures can occur in new

  12. Cylindric process algebras with conditionals give substitutionless $ p $ CRL

    NARCIS (Netherlands)

    S.P. Luttik (Bas)

    1999-01-01

    textabstract Theories that are designed to reason about processes and the information they exchange usually also include a construction to quantify over this information. We mention the input prefix mechanism of, e.g., the $pi$-calculus and the operation $gsum{$ for alternative quantification over

  13. A general conservative extension theorem in process algebras with inequalities

    NARCIS (Netherlands)

    d' Argenio, P.R.; Verhoef, Chris

    1997-01-01

    We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to

  14. Discrete Fourier and wavelet transforms an introduction through linear algebra with applications to signal processing

    CERN Document Server

    Goodman, Roe W

    2016-01-01

    This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.

  15. Reachability for Finite-state Process Algebras Using Horn Clauses

    DEFF Research Database (Denmark)

    Skrypnyuk, Nataliya; Nielson, Flemming

    2013-01-01

    of the Data Flow Analysis are used in order to build a set of Horn clauses whose least model corresponds to an overapproximation of the reachable states. The computed model can be refined after each transition, and the algorithm runs until either a state whose reachability should be checked is encountered...... or it is not in the least model for all constructed states and thus is definitely unreachable. The advantages of the algorithm are that in many cases only a part of the Labelled Transition System will be built which leads to lower time and memory consumption. Also, it is not necessary to save all the encountered states...... which leads to further reduction of the memory requirements of the algorithm....

  16. Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory

    CERN Document Server

    Landau, Olav Arnfinn

    2011-01-01

    This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory o

  17. Some new classes of division algebras and potential applications to space-time block coding

    OpenAIRE

    Steele, Andrew

    2014-01-01

    In this thesis we study some new classes of nonassociative division algebras. First we introduce a generalisation of both associative cyclic algebras and of Waterhouse's nonassociative quaternions. An important aspect of these algebras is the simplicity of their construction, which is a modification of the classical definition of associative cyclic algebras. By taking the parameter used in the classical definition from a larger field, we lose the property of associativity but gain many new ex...

  18. "Real-Time Optical Laboratory Linear Algebra Solution Of Partial Differential Equations"

    Science.gov (United States)

    Casasent, David; Jackson, James

    1986-03-01

    A Space Integrating (SI) Optical Linear Algebra Processor (OLAP) employing space and frequency-multiplexing, new partitioning and data flow, and achieving high accuracy performance with a non base-2 number system is described. Laboratory data on the performance of this system and the solution of parabolic Partial Differential Equations (PDEs) is provided. A multi-processor OLAP system is also described for the first time. It use in the solution of multiple banded matrices that frequently arise is then discussed. The utility and flexibility of this processor compared to digital systolic architectures should be apparent.

  19. Modelling and performance analysis of clinical pathways using the stochastic process algebra PEPA.

    Science.gov (United States)

    Yang, Xian; Han, Rui; Guo, Yike; Bradley, Jeremy; Cox, Benita; Dickinson, Robert; Kitney, Richard

    2012-01-01

    Hospitals nowadays have to serve numerous patients with limited medical staff and equipment while maintaining healthcare quality. Clinical pathway informatics is regarded as an efficient way to solve a series of hospital challenges. To date, conventional research lacks a mathematical model to describe clinical pathways. Existing vague descriptions cannot fully capture the complexities accurately in clinical pathways and hinders the effective management and further optimization of clinical pathways. Given this motivation, this paper presents a clinical pathway management platform, the Imperial Clinical Pathway Analyzer (ICPA). By extending the stochastic model performance evaluation process algebra (PEPA), ICPA introduces a clinical-pathway-specific model: clinical pathway PEPA (CPP). ICPA can simulate stochastic behaviours of a clinical pathway by extracting information from public clinical databases and other related documents using CPP. Thus, the performance of this clinical pathway, including its throughput, resource utilisation and passage time can be quantitatively analysed. A typical clinical pathway on stroke extracted from a UK hospital is used to illustrate the effectiveness of ICPA. Three application scenarios are tested using ICPA: 1) redundant resources are identified and removed, thus the number of patients being served is maintained with less cost; 2) the patient passage time is estimated, providing the likelihood that patients can leave hospital within a specific period; 3) the maximum number of input patients are found, helping hospitals to decide whether they can serve more patients with the existing resource allocation. ICPA is an effective platform for clinical pathway management: 1) ICPA can describe a variety of components (state, activity, resource and constraints) in a clinical pathway, thus facilitating the proper understanding of complexities involved in it; 2) ICPA supports the performance analysis of clinical pathway, thereby assisting

  20. Finite-Time Stabilization for a Class of Nonlinear Differential-Algebraic Systems Subject to Disturbance

    Directory of Open Access Journals (Sweden)

    Xiaohui Mo

    2017-01-01

    Full Text Available In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach.

  1. Development process of in-service training intended for teachers to perform teaching of mathematics with computer algebra systems

    Science.gov (United States)

    Ardıç, Mehmet Alper; Işleyen, Tevfik

    2018-01-01

    In this study, we deal with the development process of in-service training activities designed in order for mathematics teachers of secondary education to realize teaching of mathematics, utilizing computer algebra systems. In addition, the results obtained from the researches carried out during and after the in-service training were summarized. Last section focuses on suggestions any teacher can use to carry out activities aimed at using computer algebra systems in teaching environments.

  2. 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

  3. On the algebraic approach to the time-dependent quadratic Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Urdaneta, Ines; Palma, Alejandro [Instituto de Fisica, Benemerita Universidad Autonoma de Puebla, Puebla (Mexico); Sandoval, Lourdes, E-mail: urdaneta@sirio.ifuap.buap.m [Facultad de Ciencias de la Computacion, Benemerita Universidad Autonoma de Puebla, Puebla (Mexico)

    2010-09-24

    The unitary operator V(t) that diagonalizes the time-dependent quadratic Hamiltonian (TDQH) into a time-dependent harmonic oscillator (TDHO) is obtained using a Lie algebra. The method involves a factorization of the TDQH into a TDHO through a unitary Bogoliubov transformation in terms of creation and annihilation operators with time-dependent coefficients. It is shown that this operator can be easily achieved by means of the factorization, together with the commonly known Wei-Norman theorem. We discuss the conditions under which this unitary operator converges to the evolution operator U(t) of the Schroedinger equation for the TDQH, giving then a straightforward calculation of the evolution operator with respect to the procedures published in the literature.

  4. 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)

  5. Using process algebra to develop predator-prey models of within-host parasite dynamics.

    Science.gov (United States)

    McCaig, Chris; Fenton, Andy; Graham, Andrea; Shankland, Carron; Norman, Rachel

    2013-07-21

    As a first approximation of immune-mediated within-host parasite dynamics we can consider the immune response as a predator, with the parasite as its prey. In the ecological literature of predator-prey interactions there are a number of different functional responses used to describe how a predator reproduces in response to consuming prey. Until recently most of the models of the immune system that have taken a predator-prey approach have used simple mass action dynamics to capture the interaction between the immune response and the parasite. More recently Fenton and Perkins (2010) employed three of the most commonly used prey-dependent functional response terms from the ecological literature. In this paper we make use of a technique from computing science, process algebra, to develop mathematical models. The novelty of the process algebra approach is to allow stochastic models of the population (parasite and immune cells) to be developed from rules of individual cell behaviour. By using this approach in which individual cellular behaviour is captured we have derived a ratio-dependent response similar to that seen in the previous models of immune-mediated parasite dynamics, confirming that, whilst this type of term is controversial in ecological predator-prey models, it is appropriate for models of the immune system. Copyright © 2013 Elsevier Ltd. All rights reserved.

  6. Contribution to the minimization of time for the solution of algebraic differential equations system

    International Nuclear Information System (INIS)

    Michael, Samir.

    1982-11-01

    This note deals with the solution of large algebraic-differential systems involved in physical sciences specially in electronics and nuclear physics. The theoretical aspects for the stability of multistep methods is presented in detail. The stability condition is developed and we present our own conditions of stability. These conditions give rise to many new formulae that have very small truncation error. However for a real time simulation, it is necessary to obtain a very high computation speed. For this purpose, we have considered a multiprocessor machine and we have investigated the parallelization of the algorithm of generalized GEAR method. For a linear system, the method of GAUSS-JORDAN is used with some modifications. A new algorithm is presented for parallel matrix multiplication. This research work has been applied to the resolution of a system of equations corresponding to an experiment of gamma thermometry in a nuclear reactor (four thermometers in this case) [fr

  7. Opening a Gateway to College Access: Algebra at the Right Time. Research Brief

    Science.gov (United States)

    Snipes, Jason; Finkelstein, Neal

    2015-01-01

    Four years of math in high school, with a strong foundation in algebra that builds from middle school, is key to higher education access. Therefore, ensuring that middle and high school students succeed in math--and in algebra in particular--is an important issue for policy and practice. This research brief examines three recent Regional…

  8. A rigorous approach to investigating common assumptions about disease transmission: Process algebra as an emerging modelling methodology for epidemiology.

    Science.gov (United States)

    McCaig, Chris; Begon, Mike; Norman, Rachel; Shankland, Carron

    2011-03-01

    Changing scale, for example, the ability to move seamlessly from an individual-based model to a population-based model, is an important problem in many fields. In this paper, we introduce process algebra as a novel solution to this problem in the context of models of infectious disease spread. Process algebra allows us to describe a system in terms of the stochastic behaviour of individuals, and is a technique from computer science. We review the use of process algebra in biological systems, and the variety of quantitative and qualitative analysis techniques available. The analysis illustrated here solves the changing scale problem: from the individual behaviour we can rigorously derive equations to describe the mean behaviour of the system at the level of the population. The biological problem investigated is the transmission of infection, and how this relates to individual interactions.

  9. Modeling Stochastic Complexity in Complex Adaptive Systems: Non-Kolmogorov Probability and the Process Algebra Approach.

    Science.gov (United States)

    Sulis, William H

    2017-10-01

    Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.

  10. 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.

  11. 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

  12. Processes of negotiation of meanings on algebraic thinking in a community of practice of pre-service mathematics teacher education

    Directory of Open Access Journals (Sweden)

    Márcia Cristina de Costa Trindade Cyrino

    2011-12-01

    Full Text Available We presented in this paper results of a research which aimed to investigate how the community of practice context of pre-service mathematics teacher education collaborates for learning on algebraic thinking by these future teachers. We analyzed, taking into account the Social Theory of Learning developed by Wenger (1998 as a theoretical frame, processes of negotiation of meanings present in participants' algebraic thinking in the development of tasks in one of the actions of the project "Mathematical Education of Teachers of Mathematics" inside the program "Universidade sem Fronteiras". This analysis allowed us to define some forms of member participation and explicit reification of algebraic thinking, due to some interactions in the processes of negotiation of meanings, which revealed changes in the identity of participants in become teachers of mathematics.

  13. Generalized space-time supersymmetries, division algebras and octonionic M-theory

    International Nuclear Information System (INIS)

    Lukierski, Jerzy; Toppan, Francesco

    2002-03-01

    We describe the set of generalized Poincare and conformal superalgebras in D= 4,5 and 7 dimensions as two sequences of superalgebraic structures, taking values in the division algebras R, C and H. The generalized conformal superalgebras are described for D = 4 by OSp(1;8|R), for D = 5 by SU(4,4;1) and for D = 7 by U α U (8;1|H). The relation with other schemes, in particular the framework of conformal spin (super) algebras and Jordan (super) algebras is discussed. By extending the division-algebra-valued super-algebras to octonions we get in D= 11 an octonionic generalized Poincare superalgebra, which we call octonionic M-algebra, describing the octonionic M-theory. It contains 32 real supercharges but, due to the octonionic structure only 52 real bosonic generators remain independent in place of the 528 bosonic charges of standard M-algebra. In octonionic M-theory there is a sort of equivalence between the octonionic M2 (supermembrane) and the octonionic M5 (super-5-brane) sectors. We also define the octonionic generalized conformal M-superalgebra with 239 bosonic generators. (author)

  14. Time processing in dyscalculia

    Directory of Open Access Journals (Sweden)

    marinella eCappelletti

    2011-12-01

    Full Text Available To test whether atypical number development may affect other types of quantity processing, we investigated temporal discrimination in adults with developmental dyscalculia (DD. This also allowed us to test whether (1 number and time may be sub-served by a common quantity system or decision mechanisms –in which case they may both be impaired, or (2 whether number and time are distinct –and therefore they may dissociate. Participants judged which of two successively presented horizontal lines was longer in duration, the first line being preceded by either a small or a large number prime (‘1’ or ‘9’ or by a neutral symbol (‘#’, or in third task decide which of two Arabic numbers (either ‘1’, ‘5’, ’9’ lasted longer. Results showed that (i DD’s temporal discriminability was normal as long as numbers were not part of the experimental design even as task-irrelevant stimuli; however (ii task-irrelevant numbers dramatically disrupted DD’s temporal discriminability, the more their salience increased, though the actual magnitude of the numbers had no effect; and in contrast (iii controls’ time perception was robust to the presence of numbers but modulated by numerical quantity such that small number primes or numerical stimuli made durations appear shorter than veridical and the opposite for larger numerical prime or numerical stimuli. This study is the first to investigate continuous quantity as time in a population with a congenital number impairment and to show that atypical development of numerical competence leaves continuous quantity processing spared. Our data support the idea of a partially shared quantity system across numerical and temporal dimensions, which allows dissociations and interactions among dimensions; furthermore, they suggest that impaired number in DD is unlikely to originate from systems initially dedicated to continuous quantity processing like time.

  15. Time processing in dyscalculia.

    Science.gov (United States)

    Cappelletti, Marinella; Freeman, Elliot D; Butterworth, Brian L

    2011-01-01

    To test whether atypical number development may affect other types of quantity processing, we investigated temporal discrimination in adults with developmental dyscalculia (DD). This also allowed us to test whether number and time may be sub-served by a common quantity system or decision mechanisms: if they do, both should be impaired in dyscalculia, but if number and time are distinct they should dissociate. Participants judged which of two successively presented horizontal lines was longer in duration, the first line being preceded by either a small or a large number prime ("1" or "9") or by a neutral symbol ("#"), or in a third task participants decided which of two Arabic numbers (either "1," "5," "9") lasted longer. Results showed that (i) DD's temporal discriminability was normal as long as numbers were not part of the experimental design, even as task-irrelevant stimuli; however (ii) task-irrelevant numbers dramatically disrupted DD's temporal discriminability the more their salience increased, though the actual magnitude of the numbers had no effect; in contrast (iii) controls' time perception was robust to the presence of numbers but modulated by numerical quantity: therefore small number primes or numerical stimuli seemed to make durations appear shorter than veridical, but longer for larger numerical prime or numerical stimuli. This study is the first to show spared temporal discrimination - a dimension of continuous quantity - in a population with a congenital number impairment. Our data reinforce the idea of a partially shared quantity system across numerical and temporal dimensions, which supports both dissociations and interactions among dimensions; however, they suggest that impaired number in DD is unlikely to originate from systems initially dedicated to continuous quantity processing like time.

  16. Discrete event systems in dioid algebra and conventional algebra

    CERN Document Server

    Declerck, Philippe

    2013-01-01

    This book concerns the use of dioid algebra as (max, +) algebra to treat the synchronization of tasks expressed by the maximum of the ends of the tasks conditioning the beginning of another task - a criterion of linear programming. A classical example is the departure time of a train which should wait for the arrival of other trains in order to allow for the changeover of passengers.The content focuses on the modeling of a class of dynamic systems usually called "discrete event systems" where the timing of the events is crucial. Events are viewed as sudden changes in a process which i

  17. 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…

  18. 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...

  19. 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 ...

  20. Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

    International Nuclear Information System (INIS)

    Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.; Kunold, A.

    2015-01-01

    We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a

  1. Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

    Energy Technology Data Exchange (ETDEWEB)

    Ibarra-Sierra, V.G.; Sandoval-Santana, J.C. [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F. (Mexico); Cardoso, J.L. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Kunold, A., E-mail: akb@correo.azc.uam.mx [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico)

    2015-11-15

    We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a

  2. 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.

  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. Current algebra

    International Nuclear Information System (INIS)

    Jacob, M.

    1967-01-01

    The first three chapters of these lecture notes are devoted to generalities concerning current algebra. The weak currents are defined, and their main properties given (V-A hypothesis, conserved vector current, selection rules, partially conserved axial current,...). The SU (3) x SU (3) algebra of Gell-Mann is introduced, and the general properties of the non-leptonic weak Hamiltonian are discussed. Chapters 4 to 9 are devoted to some important applications of the algebra. First one proves the Adler- Weisberger formula, in two different ways, by either the infinite momentum frame, or the near-by singularities method. In the others chapters, the latter method is the only one used. The following topics are successively dealt with: semi leptonic decays of K mesons and hyperons, Kroll- Ruderman theorem, non leptonic decays of K mesons and hyperons ( ΔI = 1/2 rule), low energy theorems concerning processes with emission (or absorption) of a pion or a photon, super-convergence sum rules, and finally, neutrino reactions. (author) [fr

  5. Contractions of quantum algebraic structures

    International Nuclear Information System (INIS)

    Doikou, A.; Sfetsos, K.

    2010-01-01

    A general framework for obtaining certain types of contracted and centrally extended algebras is reviewed. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models. (Abstract Copyright [2010], Wiley Periodicals, Inc.)

  6. A systematic investigation of the link between rational number processing and algebra ability.

    Science.gov (United States)

    Hurst, Michelle; Cordes, Sara

    2018-02-01

    Recent research suggests that fraction understanding is predictive of algebra ability; however, the relative contributions of various aspects of rational number knowledge are unclear. Furthermore, whether this relationship is notation-dependent or rather relies upon a general understanding of rational numbers (independent of notation) is an open question. In this study, college students completed a rational number magnitude task, procedural arithmetic tasks in fraction and decimal notation, and an algebra assessment. Using these tasks, we measured three different aspects of rational number ability in both fraction and decimal notation: (1) acuity of underlying magnitude representations, (2) fluency with which symbols are mapped to the underlying magnitudes, and (3) fluency with arithmetic procedures. Analyses reveal that when looking at the measures of magnitude understanding, the relationship between adults' rational number magnitude performance and algebra ability is dependent upon notation. However, once performance on arithmetic measures is included in the relationship, individual measures of magnitude understanding are no longer unique predictors of algebra performance. Furthermore, when including all measures simultaneously, results revealed that arithmetic fluency in both fraction and decimal notation each uniquely predicted algebra ability. Findings are the first to demonstrate a relationship between rational number understanding and algebra ability in adults while providing a clearer picture of the nature of this relationship. © 2017 The British Psychological Society.

  7. Virasoro algebra with central charge c=1 on the horizon of a two-dimensional-Rindler space-time

    International Nuclear Information System (INIS)

    Moretti, Valter; Pinamonti, Nicola

    2004-01-01

    Using the holographic machinery built up in a previous work, we show that the hidden SL(2,R) symmetry of a scalar quantum field propagating in a Rindler space-time admits an enlargement in terms of a unitary positive-energy representation of Virasoro algebra defined in the Fock representation. That representation has central charge c=1. The Virasoro algebra of operators gets a manifest geometrical meaning if referring to the holographically associated quantum field theory on the horizon: It is nothing but a representation of the algebra of vector fields defined on the horizon equipped with a point at infinity. All that happens provided the Virasoro ground energy hcoloneμ 2 /2 vanishes and, in that case, the Rindler Hamiltonian is associated with a certain Virasoro generator. If a suitable regularization procedure is employed, for h=1/2, the ground state of that generator seems to correspond to a thermal state when examined in the Rindler wedge, taking the expectation value with respect to Rindler time. Finally, under Wick rotation in Rindler time, the pair of quantum field theories which are built up on the future and past horizon defines a proper two-dimensional conformal quantum field theory on a cylinder

  8. Matrix-algebra-based calculations of the time evolution of the binary spin-bath model for magnetization transfer.

    Science.gov (United States)

    Müller, Dirk K; Pampel, André; Möller, Harald E

    2013-05-01

    Quantification of magnetization-transfer (MT) experiments are typically based on the assumption of the binary spin-bath model. This model allows for the extraction of up to six parameters (relative pool sizes, relaxation times, and exchange rate constants) for the characterization of macromolecules, which are coupled via exchange processes to the water in tissues. Here, an approach is presented for estimating MT parameters acquired with arbitrary saturation schemes and imaging pulse sequences. It uses matrix algebra to solve the Bloch-McConnell equations without unwarranted simplifications, such as assuming steady-state conditions for pulsed saturation schemes or neglecting imaging pulses. The algorithm achieves sufficient efficiency for voxel-by-voxel MT parameter estimations by using a polynomial interpolation technique. Simulations, as well as experiments in agar gels with continuous-wave and pulsed MT preparation, were performed for validation and for assessing approximations in previous modeling approaches. In vivo experiments in the normal human brain yielded results that were consistent with published data. Copyright © 2013 Elsevier Inc. All rights reserved.

  9. 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.

  10. Algebraic Description of Motion

    Science.gov (United States)

    Davidon, William C.

    1974-01-01

    An algebraic definition of time differentiation is presented and used to relate independent measurements of position and velocity. With this, students can grasp certain essential physical, geometric, and algebraic properties of motion and differentiation before undertaking the study of limits. (Author)

  11. 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.)

  12. Real Time Processing

    CERN Multimedia

    CERN. Geneva; ANDERSON, Dustin James; DOGLIONI, Caterina

    2015-01-01

    The LHC provides experiments with an unprecedented amount of data. Experimental collaborations need to meet storage and computing requirements for the analysis of this data: this is often a limiting factor in the physics program that would be achievable if the whole dataset could be analysed. In this talk, I will describe the strategies adopted by the LHCb, CMS and ATLAS collaborations to overcome these limitations and make the most of LHC data: data parking, data scouting, and real-time analysis.

  13. Geometric Algebra Computing

    CERN Document Server

    Corrochano, Eduardo Bayro

    2010-01-01

    This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int

  14. Concurrence of Quantum States: Algebraic Dynamical Method Study XXX Models in a Time-Depending Random External Field

    International Nuclear Information System (INIS)

    Fu Chuanji; Zhu Qinsheng; Wu Shaoyi

    2010-01-01

    Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending external held. For this system, the property of the concurrence that is only dependent on the coupling constant J and total values of the external field is proved. Furthermore, we found that the thermal concurrence of the system under a static random external field is a function of the coupling constant J, temperature T, and the magnitude of external held. (general)

  15. 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.

  16. 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...

  17. Certain algebraic structures and their applications to physics

    International Nuclear Information System (INIS)

    Salingaros, N.A.

    1978-01-01

    The aim of this thesis is to understand internal and external symmetries in Physics as arising from the same algebra by different processes, while the algebra itself arises out of the geometry of space-time. The result obtained is the Associative Generalized Algebra of Tensor Types. This algebra is constructed from the differential forms of spacetime, and is an algebra in the mathematical sense, describing all tensor types together. It is associative, and therefore very easy to use. A calculational formalism is developed that simplifies algebraic manipulations. The construction allows a classification of algebras that appear useful in Physics. The geometry excludes self-dual Minkowski bivector fields, but allows self-dual Euclidean bivector fields, a result, with important consequences in the theory of solutions of Yang-Mills gauge fields are demonstrated. There is only one bivector field, and every other bivector field, such as the electromagnetic field, is isomorphic to it. An exhaustive classification of the transformations of all fields in space-time yields the result that the only transformations of the electromagnetic field are the Lorentz transformations and the duality rotation. A fundamental asymmetry between the electric and magnetic fields are demonstrated. The derivative in the algebra is associative, and combines the Cartan exterior derivative with the coderivative of Hodge. The simplest derivative equations satisfied by a field in flat space-time are precisely the Maxwell equations

  18. 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...

  19. Intermediate algebra & analytic geometry

    CERN Document Server

    Gondin, William R

    1967-01-01

    Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system

  20. Equivalent construction of the infinitesimal time translation operator in algebraic dynamics algorithm for partial differential evolution equation

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.

  1. 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.

  2. 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

  3. 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

  4. Calculations of time-of-flight aberrations in practical electrostatic electron lenses using the differential algebraic method

    International Nuclear Information System (INIS)

    Kang, Yongfeng; Zhao, Jingyi; Tang, Tiantong

    2013-01-01

    The high order time-of-flight (TOF) aberrations in a practical electrostatic electron lens are calculated using the differential algebraic (DA) method. The electrostatic fields of the electrostatic lens, which are calculated by the FEM methods, are in the form of discrete arrays. Thus, the proposed DA method is applicable for engineering designs, and programs are written to compute up to fifth order TOF aberrations of practical electrostatic electron lenses. An example is given, and TOF aberrations up to the fifth order are calculated. It is proven that the numerical results for the electrostatic fields in the form of discrete arrays have a good accuracy compared with the theoretical solutions. The accuracy is limited only by the accuracy of the numerical computation of the fields and the numerical computation algorithms for interpolation and integration. Finally, a practical electrostatic electron lens is analysed and discussed as an example.

  5. 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)

  6. 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.

  7. 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

  8. 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.

  9. 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...

  10. 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

  11. 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

  12. Lie algebras

    CERN Document Server

    Jacobson, Nathan

    1979-01-01

    Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its

  13. Basic algebra

    CERN Document Server

    Jacobson, Nathan

    2009-01-01

    A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references.Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as L

  14. ALGEBRAIC TOPOLOGY

    Indian Academy of Sciences (India)

    tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).

  15. Algebraic stacks

    Indian Academy of Sciences (India)

    Deligne, Mumford and Artin [DM, Ar2]) and consider algebraic stacks, then we can cons- truct the 'moduli ... the moduli scheme and the moduli stack of vector bundles. First I will give ... 1–31. © Printed in India. 1 ...... Cultura, Spain. References.

  16. Solving Algebraic Riccati Equation Real Time for Integrated Vehicle Dynamics Control

    NARCIS (Netherlands)

    Kunnappillil Madhusudhanan, A; Corno, M.; Bonsen, B.; Holweg, E.

    2012-01-01

    In this paper we present a comparison study of different computational methods to implement State Dependent Riccati Equation (SDRE) based control in real time for a vehicle dynamics control application. Vehicles are mechatronic systems with nonlinear dynamics. One of the promising nonlinear control

  17. Elementary matrix algebra

    CERN Document Server

    Hohn, Franz E

    2012-01-01

    This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics. The work starts with the most basic laws of matrix algebra and progresses to the sweep-out process for obtaining the complete solution of any given system of linear equations - homogeneous or nonhomogeneous - and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology.Other subjects include the complete treatment of the structur

  18. Applied linear algebra

    CERN Document Server

    Olver, Peter J

    2018-01-01

    This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the un...

  19. 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.

  20. Algebraic characterizations of measure algebras

    Czech Academy of Sciences Publication Activity Database

    Jech, Thomas

    2008-01-01

    Roč. 136, č. 4 (2008), s. 1285-1294 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190509 Institutional research plan: CEZ:AV0Z10190503 Keywords : Von - Neumann * sequential topology * Boolean-algebras * Souslins problem * Submeasures Subject RIV: BA - General Mathematics Impact factor: 0.584, year: 2008

  1. Superalgebras with Grassmann algebra-valued structure constants from superfields

    International Nuclear Information System (INIS)

    Azcarraga, J.A. de; Lukierski, J.

    1987-05-01

    We introduce generalized Lie algebras and superalgebras with generators and structure constants taking values in a Grassmann algebra. Such algebraic structures describe the equal time algebras in the superfield formalism. As an example we consider the equal time commutators and anticommutators among bilinears made out of the D=1 quantum superfields describing the supersymmetric harmonic oscillator. (author). 10 refs

  2. 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.)

  3. 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

  4. Algebraic and structural automata theory

    CERN Document Server

    Mikolajczak, B

    1991-01-01

    Automata Theory is part of computability theory which covers problems in computer systems, software, activity of nervous systems (neural networks), and processes of live organisms development.The result of over ten years of research, this book presents work in the following areas of Automata Theory: automata morphisms, time-varying automata, automata realizations and relationships between automata and semigroups.Aimed at those working in discrete mathematics and computer science, parts of the book are suitable for use in graduate courses in computer science, electronics, telecommunications, and control engineering. It is assumed that the reader is familiar with the basic concepts of algebra and graph theory.

  5. Color Algebras

    Science.gov (United States)

    Mulligan, Jeffrey B.

    2017-01-01

    A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. The difficulty addressed here is the fact that, because of metamerism, we cannot know with certainty the spectrum that produced a particular color solely on the basis of sensory data. Knowledge of the spectrum is not required to compute additive mixture of colors, but is critical for subtractive (multiplicative) mixture. Therefore, we cannot predict with certainty the multiplicative interactions between colors based solely on sensory data. There are two potential applications of a color algebra: first, to aid modeling phenomena of human visual perception, such as color constancy and transparency; and, second, to provide better models of the interactions of lights and surfaces for computer graphics rendering.

  6. 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.

  7. The Role of Cognitive Processes, Foundational Math Skill, and Calculation Accuracy and Fluency in Word-Problem Solving versus Pre-Algebraic Knowledge

    Science.gov (United States)

    Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.

    2016-01-01

    The purpose of this study was to examine child-level pathways in development of pre-algebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of grade 2; calculation accuracy and calculation fluency at end of grade 2; and pre-algebraic knowledge and word-problem solving at end of grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than pre-algebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students’ foundational mathematics skills or cognitive processes. PMID:27786534

  8. An Arithmetic-Algebraic Work Space for the Promotion of Arithmetic and Algebraic Thinking: Triangular Numbers

    Science.gov (United States)

    Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos

    2016-01-01

    This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…

  9. 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.)

  10. 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.)

  11. 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)

  12. 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.

  13. Algebraic and stochastic coding theory

    CERN Document Server

    Kythe, Dave K

    2012-01-01

    Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes.

  14. Algebraic functions

    CERN Document Server

    Bliss, Gilbert Ames

    1933-01-01

    This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors.... A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on t

  15. 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)

  16. 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)

  17. Universal algebra

    CERN Document Server

    Grätzer, George

    1979-01-01

    Universal Algebra, heralded as ". . . the standard reference in a field notorious for the lack of standardization . . .," has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well-selected additional bibliography of over 1250 papers and books which makes this a fine work for students, instructors, and researchers in the field. "This book will certainly be, in the years to come, the basic reference to the subject." --- The American Mathematical Monthly (First Edition) "In this reviewer's opinion [the author] has more than succeeded in his aim. The problems at the end of each chapter are well-chosen; there are more than 650 of them. The book is especially sui...

  18. 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 ...

  19. 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...

  20. Typography in process algebra

    NARCIS (Netherlands)

    Baeten, J.C.M.; Klop, J.W.; Vonderen, van C.

    2011-01-01

    This note is dedicated in gratitude to Jan Karel Lenstra, who reputedly is able to distinguish an ordinary full stop symbol (".") from its italicized version ("."), and who has inspired us with his knowledge and passion for typography. For his amusement we offer him a sample of typographical matters

  1. Distribution theory of algebraic numbers

    CERN Document Server

    Yang, Chung-Chun

    2008-01-01

    The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions Algebraic numbers Algebraic geometry Height functions The abc-conjecture Roth''s theorem Subspace theorems Vojta''s conjectures L-functions.

  2. Grassmann, super-Kac-Moody and super-derivation algebras

    International Nuclear Information System (INIS)

    Frappat, L.; Ragoucy, E.; Sorba, P.

    1989-05-01

    We study the cyclic cocycles of degree one on the Grassmann algebra and on the super-circle with N supersymmetries (i.e. the tensor product of the algebra of functions on the circle times a Grassmann algebra with N generators). They are related to central extensions of graded loop algebras (i.e. super-Kac-Moody algebras). The corresponding algebras of super-derivations have to be compatible with the cocycle characterizing the extension; we give a general method for determining these algebras and examine in particular the cases N = 1,2,3. We also discuss their relations with the Ademollo et al. algebras, and examine the possibility of defining new kinds of super-conformal algebras, which, for N > 1, generalize the N = 1 Ramond-Neveu-Schwarz algebra

  3. Linear algebra

    CERN Document Server

    Said-Houari, Belkacem

    2017-01-01

    This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...

  4. 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.

  5. 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

  6. 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.

  7. 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.

  8. 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 ...

  9. 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

  10. 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.

  11. 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

  12. The algebras of large N matrix mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Halpern, M.B.; Schwartz, C.

    1999-09-16

    Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.

  13. Further linear algebra

    CERN Document Server

    Blyth, T S

    2002-01-01

    Most of the introductory courses on linear algebra develop the basic theory of finite­ dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num­ ber of illustrative and worked examples, as well as many exercises that are strategi­ cally placed throughout the text. Solutions to the ex...

  14. Solving Langevin equation with the stochastic algebraically correlated noise

    International Nuclear Information System (INIS)

    Ploszajczak, M.; Srokowski, T.

    1996-01-01

    Long time tail in the velocity and force autocorrelation function has been found recently in the molecular dynamics simulations of the peripheral collisions of ions. Simulation of those slowly decaying correlations in the stochastic transport theory requires the development of new methods of generating stochastic force of arbitrarily long correlation times. The Markovian process and the multidimensional Kangaroo process which permit describing various algebraic correlated stochastic processes are proposed. (author)

  15. A division algebra classification of generalized supersymmetries

    International Nuclear Information System (INIS)

    Toppan, Francesco

    2004-10-01

    Generalized supersymmetries admitting bosonic tensor central charges are classified in accordance with their division algebra properties. Division algebra consistent constraints lead (in the complex and quaternionic cases) to the classes of hermitian and holomorphic generalized supersymmetries. Applications to the analytic continuation of the M-algebra to the Euclidean and the systematic investigation of certain classes of models in generic space-times are briefly mentioned. (author)

  16. Time-dependent automorphism-inducing diffeomorphisms, open algebras and the generality of the Kantowski-Sachs vacuum geometry

    Science.gov (United States)

    Christodoulakis, T.; Papadopoulos, G. O.

    2002-10-01

    Following the spirit of a previous work of ours, we investigate the group of those general coordinate transformations (GCTs) which preserve manifest spatial homogeneity. In contrast to the case of Bianchi type models, here we permit an isometry group of motions G4 = SO(3) ⊗ Tr, where Tr is the translations group, along the radial direction, while SO(3) acts multiply transitively on each hypersurface of simultaneity Σt. The basis 1-forms cannot be invariant under the action of the entire isometry group and hence produce an open Lie algebra. In order for these GCTs to exist and have a nontrivial, well-defined action, certain integrability conditions have to be satisfied; their solutions, exhibiting the maximum expected 'gauge' freedom, can be used to simplify the generic, spatially homogeneous, line element. In this way an alternative proof of the generality of the Kantowski-Sachs (KS) vacuum is given, while its most general, manifestly homogeneous, form is explicitly presented.

  17. 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...

  18. Computers in nonassociative rings and algebras

    CERN Document Server

    Beck, Robert E

    1977-01-01

    Computers in Nonassociative Rings and Algebras provides information pertinent to the computational aspects of nonassociative rings and algebras. This book describes the algorithmic approaches for solving problems using a computer.Organized into 10 chapters, this book begins with an overview of the concept of a symmetrized power of a group representation. This text then presents data structures and other computational methods that may be useful in the field of computational algebra. Other chapters consider several mathematical ideas, including identity processing in nonassociative algebras, str

  19. Factors affecting medication-order processing time.

    Science.gov (United States)

    Beaman, M A; Kotzan, J A

    1982-11-01

    The factors affecting medication-order processing time at one hospital were studied. The order processing time was determined by directly observing the time to process randomly selected new drug orders on all three work shifts during two one-week periods. An order could list more than one drug for an individual patient. The observer recorded the nature, location, and cost of the drugs ordered, as well as the time to process the order. The time and type of interruptions also were noted. The time to process a drug order was classified as six dependent variables: (1) total time, (2) work time, (3) check time, (4) waiting time I--time from arrival on the dumbwaiter until work was initiated, (5) waiting time II--time between completion of the work and initiation of checking, and (6) waiting time III--time after the check was completed until the order left on the dumbwaiter. The significant predictors of each of the six dependent variables were determined using stepwise multiple regression. The total time to process a prescription order was 58.33 +/- 48.72 minutes; the urgency status of the order was the only significant determinant of total time. Urgency status also significantly predicted the three waiting-time variables. Interruptions and the number of drugs on the order were significant determinants of work time and check time. Each telephone interruption increased the work time by 1.72 minutes. While the results of this study cannot be generalized to other institutions, pharmacy managers can use the method of determining factors that affect medication-order processing time to identify problem areas in their institutions.

  20. Development of abstract mathematical reasoning: the case of algebra.

    Science.gov (United States)

    Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja

    2014-01-01

    Algebra typically represents the students' first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students' ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16-17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15-16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students' transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition.

  1. 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

  2. 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.

  3. 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

  4. Time delay of quantum scattering processes

    International Nuclear Information System (INIS)

    Martin, P.A.

    1981-01-01

    The author presents various aspects of the theory of the time delay of scattering processes. The author mainly studies non-relativistic two-body scattering processes, first summarizing briefly the theory of simple scattering systems. (Auth.)

  5. Training and evaluation of neural networks for multi-variate time series processing

    DEFF Research Database (Denmark)

    Fog, Torben L.; Larsen, Jan; Hansen, Lars Kai

    1995-01-01

    We study the training and generalization for multi-variate time series processing. It is suggested to used a quasi-maximum likelihood approach rather than the standard sum of squared errors, thus taking dependencies among the errors of the individual time series into account. This may lead...... to improved generalization performance. Further, we extend the optimal brain damage pruning technique to the multi-variate case. A key ingredient is an algebraic expression for the generalization ability of a multi-variate model. The variability of the suggested techniques are successfully demonstrated...

  6. 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.

  7. Families talen en algebra

    NARCIS (Netherlands)

    Asveld, P.R.J.

    1976-01-01

    Operaties op formele talen geven aanleiding tot bijbehorende operatoren op families talen. Bepaalde onderwerpen uit de algebra (universele algebra, tralies, partieel geordende monoiden) kunnen behulpzaam zijn in de studie van verzamelingen van dergelijke operatoren.

  8. Rudiments of algebraic geometry

    CERN Document Server

    Jenner, WE

    2017-01-01

    Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.

  9. 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.

  10. 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.

  11. Storm real-time processing cookbook

    CERN Document Server

    Anderson, Quinton

    2013-01-01

    A Cookbook with plenty of practical recipes for different uses of Storm.If you are a Java developer with basic knowledge of real-time processing and would like to learn Storm to process unbounded streams of data in real time, then this book is for you.

  12. Directed Abelian algebras and their application to stochastic models.

    Science.gov (United States)

    Alcaraz, F C; Rittenberg, V

    2008-10-01

    With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma_(tau)=32 ). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma_(tau)=1.780+/-0.005 .

  13. 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

  14. Just Say Yes to Early Algebra!

    Science.gov (United States)

    Stephens, Ana; Blanton, Maria; Knuth, Eric; Isler, Isil; Gardiner, Angela Murphy

    2015-01-01

    Mathematics educators have argued for some time that elementary school students are capable of engaging in algebraic thinking and should be provided with rich opportunities to do so. Recent initiatives like the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) have taken up this call by reiterating the place of early algebra in…

  15. Newtonian gravity and the Bargmann algebra

    NARCIS (Netherlands)

    Andringa, Roel; Bergshoeff, Eric; Panda, Sudhakar; de Roo, Mees

    2011-01-01

    We show how the Newton-Cartan formulation of Newtonian gravity can be obtained from gauging the Bargmann algebra, i.e. the centrally extended Galilean algebra. In this gauging procedure several curvature constraints are imposed. These convert the spatial (time) translational symmetries of the

  16. Timed Comparisons of Semi-Markov Processes

    DEFF Research Database (Denmark)

    Pedersen, Mathias Ruggaard; Larsen, Kim Guldstrand; Bacci, Giorgio

    2018-01-01

    -Markov processes, and investigate the question of how to compare two semi-Markov processes with respect to their time-dependent behaviour. To this end, we introduce the relation of being “faster than” between processes and study its algorithmic complexity. Through a connection to probabilistic automata we obtain...

  17. 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)

  18. 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.

  19. A linear algebraic approach to electron-molecule collisions

    International Nuclear Information System (INIS)

    Collins, L.A.; Schnieder, B.I.

    1982-01-01

    The linear algebraic approach to electron-molecule collisions is examined by firstly deriving the general set of coupled integrodifferential equations that describe electron collisional processes and then describing the linear algebraic approach for obtaining a solution to the coupled equations. Application of the linear algebraic method to static-exchange, separable exchange and effective optical potential, is examined. (U.K.)

  20. Meanings Given to Algebraic Symbolism in Problem-Posing

    Science.gov (United States)

    Cañadas, María C.; Molina, Marta; del Río, Aurora

    2018-01-01

    Some errors in the learning of algebra suggest that students might have difficulties giving meaning to algebraic symbolism. In this paper, we use problem posing to analyze the students' capacity to assign meaning to algebraic symbolism and the difficulties that students encounter in this process, depending on the characteristics of the algebraic…

  1. Space-time-modulated stochastic processes

    Science.gov (United States)

    Giona, Massimiliano

    2017-10-01

    Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

  2. Processing of visually presented clock times.

    Science.gov (United States)

    Goolkasian, P; Park, D C

    1980-11-01

    The encoding and representation of visually presented clock times was investigated in three experiments utilizing a comparative judgment task. Experiment 1 explored the effects of comparing times presented in different formats (clock face, digit, or word), and Experiment 2 examined angular distance effects created by varying positions of the hands on clock faces. In Experiment 3, encoding and processing differences between clock faces and digitally presented times were directly measured. Same/different reactions to digitally presented times were faster than to times presented on a clock face, and this format effect was found to be a result of differences in processing that occurred after encoding. Angular separation also had a limited effect on processing. The findings are interpreted within the framework of theories that refer to the importance of representational codes. The applicability to the data of Bank's semantic-coding theory, Paivio's dual-coding theory, and the levels-of-processing view of memory are discussed.

  3. Modeling nonhomogeneous Markov processes via time transformation.

    Science.gov (United States)

    Hubbard, R A; Inoue, L Y T; Fann, J R

    2008-09-01

    Longitudinal studies are a powerful tool for characterizing the course of chronic disease. These studies are usually carried out with subjects observed at periodic visits giving rise to panel data. Under this observation scheme the exact times of disease state transitions and sequence of disease states visited are unknown and Markov process models are often used to describe disease progression. Most applications of Markov process models rely on the assumption of time homogeneity, that is, that the transition rates are constant over time. This assumption is not satisfied when transition rates depend on time from the process origin. However, limited statistical tools are available for dealing with nonhomogeneity. We propose models in which the time scale of a nonhomogeneous Markov process is transformed to an operational time scale on which the process is homogeneous. We develop a method for jointly estimating the time transformation and the transition intensity matrix for the time transformed homogeneous process. We assess maximum likelihood estimation using the Fisher scoring algorithm via simulation studies and compare performance of our method to homogeneous and piecewise homogeneous models. We apply our methodology to a study of delirium progression in a cohort of stem cell transplantation recipients and show that our method identifies temporal trends in delirium incidence and recovery.

  4. 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

  5. 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)

  6. 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

  7. 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.

  8. Practical algebraic renormalization

    International Nuclear Information System (INIS)

    Grassi, Pietro Antonio; Hurth, Tobias; Steinhauser, Matthias

    2001-01-01

    A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the standard model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process B→X s γ

  9. Generating loop graphs via Hopf algebra in quantum field theory

    International Nuclear Information System (INIS)

    Mestre, Angela; Oeckl, Robert

    2006-01-01

    We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be evaluated directly as contributions to the connected n-point functions. The recursion proceeds by loop order and vertex number

  10. 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.

  11. 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)

  12. 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

  13. 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

  14. 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.)

  15. 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.

  16. 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

  17. Semicrossed products of operator algebras by semigroups

    CERN Document Server

    Davidson, Kenneth R; Kakariadis, Evgenios T A

    2017-01-01

    The authors examine the semicrossed products of a semigroup action by *-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.

  18. 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

  19. Hurwitz Algebras and the Octonion Algebra

    Science.gov (United States)

    Burdik, Čestmir; Catto, Sultan

    2018-02-01

    We explore some consequences of a theory of internal symmetries for elementary particles constructed on exceptional quantum mechanical spaces based on Jordan algebra formulation that admit exceptional groups as gauge groups.

  20. First Passage Time Intervals of Gaussian Processes

    Science.gov (United States)

    Perez, Hector; Kawabata, Tsutomu; Mimaki, Tadashi

    1987-08-01

    The first passage time problem of a stationary Guassian process is theretically and experimentally studied. Renewal functions are derived for a time-dependent boundary and numerically calculated for a Gaussian process having a seventh-order Butterworth spectrum. The results show a multipeak property not only for the constant boundary but also for a linearly increasing boundary. The first passage time distribution densities were experimentally determined for a constant boundary. The renewal functions were shown to be a fairly good approximation to the distribution density over a limited range.

  1. 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

  2. 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.

  3. PROCESS TIME OPTIMIZATION IN DEPOSITOR AND FILLER

    Directory of Open Access Journals (Sweden)

    Jesús Iván Ruíz-Ibarra

    2017-07-01

    Full Text Available As in any industry, in soft drink manufacturing demand, customer service and production is of great importance that forces this production to have their equipment and production machines in optimal conditions for the product to be in the hands of the consumer without delays, therefore it is important to have the established times of each process, since the syrup is elaborated, packaged, distributed, until it is purchased by the consumer. After a chronometer analysis, the most common faults were detected in each analyzed process. In the filler machine the most frequent faults are: accumulation of bottles in the subsequent and previous processes to filling process, which in general the cause of the collection of bottles is due to failures in the other equipment of the production line. In the process of unloading the most common faults are: boxes jammed in bump and pusher (pushing boxes; boxes fallen in rollers and platforms transporter. According to observations in each machine, the actions to be followed are presented to solve the problems that arise. Also described the methodology to obtain results, to data analyze and decisions. Firstly an analysis of operations is done to know each machine, supported by the manuals of the machines and the operators themselves a study of times is done by chronometer to determine the standard time of the process where also they present the most common faults, then observations are made on the machines according to the determined sample size, thus obtaining the information necessary to take measurements and to make the study of optimization of the production processes. An analysis of the predetermined process times is also performed by the MTM methods and the MOST time analysis. The results of operators with MTM: Fault Filler = 0.846 minutes, Faultless Filler = 0.61 minutes, Fault Breaker = 0.74 minutes and Fault Flasher = 0.45 minutes. The results of MOST operators are: Fault Filler = 2.58 minutes, Filler Fails

  4. Enhanced Time Out: An Improved Communication Process.

    Science.gov (United States)

    Nelson, Patricia E

    2017-06-01

    An enhanced time out is an improved communication process initiated to prevent such surgical errors as wrong-site, wrong-procedure, or wrong-patient surgery. The enhanced time out at my facility mandates participation from all members of the surgical team and requires designated members to respond to specified time out elements on the surgical safety checklist. The enhanced time out incorporated at my facility expands upon the safety measures from the World Health Organization's surgical safety checklist and ensures that all personnel involved in a surgical intervention perform a final check of relevant information. Initiating the enhanced time out at my facility was intended to improve communication and teamwork among surgical team members and provide a highly reliable safety process to prevent wrong-site, wrong-procedure, and wrong-patient surgery. Copyright © 2017 AORN, Inc. Published by Elsevier Inc. All rights reserved.

  5. Time-changed Ornstein–Uhlenbeck process

    International Nuclear Information System (INIS)

    Gajda, Janusz; Wyłomańska, Agnieszka

    2015-01-01

    The Ornstein–Uhlenbeck process is one of the most popular systems used for financial data description. However, this process has also been examined in the context of many other phenomena. In this paper we consider the so-called time-changed Ornstein–Uhlenbeck process, in which time is replaced by an inverse subordinator of general infinite divisible distribution. Time-changed processes nowadays play an important role in various fields of mathematical physics, chemistry, and biology as well as in finance. In this paper we examine the main characteristics of the time-changed Ornstein–Uhlenbeck process, such as the covariance function. Moreover, we also prove the formula for a generalized fractional Fokker–Planck equation that describes the one-dimensional probability density function of the analyzed system. For three cases of subordinators we show the special forms of obtained general formulas. Furthermore, we mention how to simulate the trajectory of the Ornstein–Uhlenbeck process delayed by a general inverse subordinator. (paper)

  6. 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)

  7. 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

  8. 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.

  9. 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.

  10. 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...

  11. 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...

  12. 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.)

  13. Expectation propagation for continuous time stochastic processes

    International Nuclear Information System (INIS)

    Cseke, Botond; Schnoerr, David; Sanguinetti, Guido; Opper, Manfred

    2016-01-01

    We consider the inverse problem of reconstructing the posterior measure over the trajectories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference, giving rise to an expectation propagation type algorithm. For non-linear diffusion processes, this is achieved by leveraging moment closure approximations. We then show how the approximation can be extended to a wide class of discrete-state Markov jump processes by making use of the chemical Langevin equation. Our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems. (paper)

  14. El desempeño del docente en el proceso de desarrollo de habilidades de trabajo con algoritmos en la disciplina Álgebra Lineal / Teachers' performance and the process of developing skills to work with algorithms in Linear Algebra

    Directory of Open Access Journals (Sweden)

    Ivonne Burguet Lago

    2018-05-01

    Full Text Available ABSTRACT The paper describes a proposal of professional pedagogical performance tests to assess teachers’ role in the process of developing the skill of working with algorithms in Linear Algebra. It aims at devising a testing tool to assess teachers’ performance in the skill-developing process. This tool is a finding of Cuba theory of Advanced Education, systematically used in recent years. The findings include the test design and the illustration of its use in a sample of 22 Linear Algebra teachers during the first term of the 2017-2018 academic year at Informatics Sciences Engineering major. Keywords: ABSTRACT The paper describes a proposal of professional pedagogical performance tests to assess teachers’ role in the process of developing the skill of working with algorithms in Linear Algebra. It aims at devising a testing tool to assess teachers’ performance in the skill-developing process. This tool is a finding of Cuba theory of Advanced Education, systematically used in recent years. The findings include the test design and the illustration of its use in a sample of 22 Linear Algebra teachers during the first term of the 2017-2018 academic year at Informatics Sciences Engineering major.

  15. 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.

  16. 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

  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. 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.

  19. 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

  20. 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

  1. 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

  2. Applied linear algebra and matrix analysis

    CERN Document Server

    Shores, Thomas S

    2018-01-01

    In its second edition, this textbook offers a fresh approach to matrix and linear algebra. Its blend of theory, computational exercises, and analytical writing projects is designed to highlight the interplay between these aspects of an application. This approach places special emphasis on linear algebra as an experimental science that provides tools for solving concrete problems. The second edition’s revised text discusses applications of linear algebra like graph theory and network modeling methods used in Google’s PageRank algorithm. Other new materials include modeling examples of diffusive processes, linear programming, image processing, digital signal processing, and Fourier analysis. These topics are woven into the core material of Gaussian elimination and other matrix operations; eigenvalues, eigenvectors, and discrete dynamical systems; and the geometrical aspects of vector spaces. Intended for a one-semester undergraduate course without a strict calculus prerequisite, Applied Linear Algebra and M...

  3. Applications of computer algebra

    CERN Document Server

    1985-01-01

    Today, certain computer software systems exist which surpass the computational ability of researchers when their mathematical techniques are applied to many areas of science and engineering. These computer systems can perform a large portion of the calculations seen in mathematical analysis. Despite this massive power, thousands of people use these systems as a routine resource for everyday calculations. These software programs are commonly called "Computer Algebra" systems. They have names such as MACSYMA, MAPLE, muMATH, REDUCE and SMP. They are receiving credit as a computational aid with in­ creasing regularity in articles in the scientific and engineering literature. When most people think about computers and scientific research these days, they imagine a machine grinding away, processing numbers arithmetically. It is not generally realized that, for a number of years, computers have been performing non-numeric computations. This means, for example, that one inputs an equa­ tion and obtains a closed for...

  4. Time Processing in Children with Tourette's Syndrome

    Science.gov (United States)

    Vicario, Carmelo Mario; Martino, Davide; Spata, Felice; Defazio, Giovanni; Giacche, Roberta; Martino, Vito; Rappo, Gaetano; Pepi, Anna Maria; Silvestri, Paola Rosaria; Cardona, Francesco

    2010-01-01

    Background: Tourette syndrome (TS) is characterized by dysfunctional connectivity between prefrontal cortex and sub-cortical structures, and altered meso-cortical and/or meso-striatal dopamine release. Since time processing is also regulated by fronto-striatal circuits and modulated by dopaminergic transmission, we hypothesized that time…

  5. Teachers' Understanding of Algebraic Generalization

    Science.gov (United States)

    Hawthorne, Casey Wayne

    Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby teachers respond to and build upon the ideas that arise from students' explorations of these activities. Although more and more teachers are engaging their students in such generalizing tasks, little is known about teachers' understanding of generalization and their understanding of students' mathematical thinking in this domain. In this work, I addressed this gap, exploring the understanding of algebraic generalization of 4 exemplary 8th-grade teachers from multiple perspectives. A significant feature of this investigation is an examination of teachers' understanding of the generalization process, including the use of algebraic symbols. The research consisted of two phases. Phase I was an examination of the teachers' understandings of the underlying quantities and quantitative relationships represented by algebraic notation. In Phase II, I observed the instruction of 2 of these teachers. Using the lens of professional noticing of students' mathematical thinking, I explored the teachers' enacted knowledge of algebraic generalization, characterizing how it supported them to effectively respond to the needs and queries of their students. Results indicated that teachers predominantly see these figural patterns as enrichment activities, disconnected from course content. Furthermore, in my analysis, I identified conceptual difficulties teachers experienced when solving generalization tasks, in particular, connecting multiple symbolic representations with the quantities in the figures. Moreover, while the teachers strived to overcome the challenges of connecting different representations, they invoked both productive and unproductive

  6. The Identity Process in Times of Ruptures

    DEFF Research Database (Denmark)

    Awad, Sarah H.

    2016-01-01

    revolution, at which time Egypt has witnessed major social and political changes. The aim is to understand the identity process of individuals as they develop and adapt through changing social contexts and how they create alternative social relations as they engage in prefigurative politics. The findings...... of agency in individuals’ ability to create new meanings of their world in spite of the socio-cultural and political constraints. This study presents narratives as an informing methodological resource that connects identity process with social representations and emphasizes the value of storytelling......This is a longitudinal study of the identity process through times of dramatic social change. Using a narrative psychological approach this research follows the life stories of five Egyptian bloggers as they write their stories on online blogs over the course of the three years following the 2011...

  7. 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...

  8. Quantum measurement and algebraic quantum field theories

    International Nuclear Information System (INIS)

    DeFacio, B.

    1976-01-01

    It is shown that the physics and semantics of quantum measurement provide a natural interpretation of the weak neighborhoods of the states on observable algebras without invoking any ideas of ''a reading error'' or ''a measured range.'' Then the state preparation process in quantum measurement theory is shown to give the normal (or locally normal) states on the observable algebra. Some remarks are made concerning the physical implications of normal state for systems with an infinite number of degrees of freedom, including questions on open and closed algebraic theories

  9. Current algebra for parafields

    International Nuclear Information System (INIS)

    Palev, Ch.D.

    1976-01-01

    Within the framework of the Lagrangean QFT a generalization of canonical commutation and anticommutation relations in terms of three-linear commutation relations, corresponding to the parastatistics, s discussed. A detailed derivation of these three-linear relations for a set of parafermi fields is presented. Then for a Lagrangean, depending of a family of parabose fields and a family of paraferm fields, is shown that the fundamental hypothesis of current algebra is valid. In other words, the currents corresponding to the linear gauge transformations are found to meet the commutation relation: [Jsub(f)sup(0)(x), Jsub(g)sup(0)]sub(x 0 =y 0 ) = -idelta(x vector - y vector)Jsub([f,g])sup(0) (x), where Jsub(f)sup(0) is a time component of the current, corresponding to transformation f. (S.P.)

  10. (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.

  11. Time Optimal Run-time Evaluation of Distributed Timing Constraints in Process Control Software

    DEFF Research Database (Denmark)

    Drejer, N.; Kristensen, C.H.

    1993-01-01

    This paper considers run-time evaluation of an important class of constraints; Timing constraints. These appear extensively in process control systems. Timing constraints are considered in distributed systems, i.e. systems consisting of multiple autonomous nodes......

  12. Ready, Set, Algebra?

    Science.gov (United States)

    Levy, Alissa Beth

    2012-01-01

    The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this dissertation,…

  13. Learning Activity Package, Algebra.

    Science.gov (United States)

    Evans, Diane

    A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…

  14. Who Takes College Algebra?

    Science.gov (United States)

    Herriott, Scott R.; Dunbar, Steven R.

    2009-01-01

    The common understanding within the mathematics community is that the role of the college algebra course is to prepare students for calculus. Though exceptions are emerging, the curriculum of most college algebra courses and the content of most textbooks on the market both reflect that assumption. This article calls that assumption into question…

  15. 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.

  16. Pre-Algebra Lexicon.

    Science.gov (United States)

    Hayden, Dunstan; Cuevas, Gilberto

    The pre-algebra lexicon is a set of classroom exercises designed to teach the technical words and phrases of pre-algebra mathematics, and includes the terms most commonly found in related mathematics courses. The lexicon has three parts, each with its own introduction. The first introduces vocabulary items in three groups forming a learning…

  17. Computer algebra applications

    International Nuclear Information System (INIS)

    Calmet, J.

    1982-01-01

    A survey of applications based either on fundamental algorithms in computer algebra or on the use of a computer algebra system is presented. Recent work in biology, chemistry, physics, mathematics and computer science is discussed. In particular, applications in high energy physics (quantum electrodynamics), celestial mechanics and general relativity are reviewed. (Auth.)

  18. Linear-Algebra Programs

    Science.gov (United States)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  19. Geometric approach to the (BRS-) differential algebras of supersymmetric YM-theories

    International Nuclear Information System (INIS)

    Gieres, F.

    1987-01-01

    The (BRS-) differential algebra of susy YM-theories is defined in terms of superfields and forms on rigid U(N)-superspace. For d = 4 and N = 1.2 we show that it projects to the ''BRS-component field algebra in the WZ-gauge'' without any supergauge fixing. In this process the supergeometry is destroyed with the result that the final algebra becomes a prototype for a differential algebra which cannot be associated with an ordinary Lie algebra

  20. 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...

  1. Characteristic time scales for diffusion processes through layers and across interfaces

    Science.gov (United States)

    Carr, Elliot J.

    2018-04-01

    This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

  2. Image reconstruction of computed tomograms using functional algebra

    International Nuclear Information System (INIS)

    Bradaczek, M.; Bradaczek, H.

    1997-01-01

    A detailed presentation of the process for calculating computed tomograms from the measured data by means of functional algebra is given and an attempt is made to demonstrate the relationships to those inexperienced in mathematics. Suggestions are also made to the manufacturers for improving tomography software although the authors cannot exclude the possibility that some of the recommendations may have already been realized. An interpolation in Fourier space to right-angled coordinates was not employed so that additional computer time and errors resulting from the interpolation are avoided. The savings in calculation time can only be estimated but should amount to about 25%. The error-correction calculation is merely a suggestion since it depends considerably on the apparatus used. Functional algebra is introduced here because it is not so well known but does provide appreciable simplifications in comparison to an explicit presentation. Didactic reasons as well as the possibility for reducing calculation time provided the foundation for this work. (orig.) [de

  3. Processing implicit control: evidence from reading times

    Directory of Open Access Journals (Sweden)

    Michael eMcCourt

    2015-10-01

    Full Text Available Sentences such as The ship was sunk to collect the insurance exhibit an unusual form of anaphora, implicit control, where neither anaphor nor antecedent is audible. The nonfinite reason clause has an understood subject, PRO, that is anaphoric; here it may be understood as naming the agent of the event of the host clause. Yet since the host is a short passive, this agent is realized by no audible dependent. The putative antecedent to PRO is therefore implicit, which it normally cannot be. What sorts of representations subserve the comprehension of this dependency? Here we present four self-paced reading time studies directed at this question. Previous work showed no processing cost for implicit versus explicit control, and took this to support the view that PRO is linked syntactically to a silent argument in the passive. We challenge this conclusion by reporting that we also find no processing cost for remote implicit control, as in: The ship was sunk. The reason was to collect the insurance. Here the dependency crosses two independent sentences, and so cannot, we argue, be mediated by syntax. Our Experiments 1-4 examined the processing of both implicit (short passive and explicit (active or long passive control in both local and remote configurations. Experiments 3 and 4 added either three days ago or just in order to the local conditions, to control for the distance between the passive and infinitival verbs, and for the predictability of the reason clause, respectively. We replicate the finding that implicit control does not impose an additional processing cost. But critically we show that remote control does not impose a processing cost either. Reading times at the reason clause were never slower when control was remote. In fact they were always faster. Thus efficient processing of local implicit control cannot show that implicit control is mediated by syntax; nor, in turn, that there is a silent but grammatically active argument in passives.

  4. Computing algebraic transfer entropy and coupling directions via transcripts

    Science.gov (United States)

    Amigó, José M.; Monetti, Roberto; Graff, Beata; Graff, Grzegorz

    2016-11-01

    Most random processes studied in nonlinear time series analysis take values on sets endowed with a group structure, e.g., the real and rational numbers, and the integers. This fact allows to associate with each pair of group elements a third element, called their transcript, which is defined as the product of the second element in the pair times the first one. The transfer entropy of two such processes is called algebraic transfer entropy. It measures the information transferred between two coupled processes whose values belong to a group. In this paper, we show that, subject to one constraint, the algebraic transfer entropy matches the (in general, conditional) mutual information of certain transcripts with one variable less. This property has interesting practical applications, especially to the analysis of short time series. We also derive weak conditions for the 3-dimensional algebraic transfer entropy to yield the same coupling direction as the corresponding mutual information of transcripts. A related issue concerns the use of mutual information of transcripts to determine coupling directions in cases where the conditions just mentioned are not fulfilled. We checked the latter possibility in the lowest dimensional case with numerical simulations and cardiovascular data, and obtained positive results.

  5. Synchronization of integral and fractional order chaotic systems a differential algebraic and differential geometric approach with selected applications in real-time

    CERN Document Server

    Martínez-Guerra, Rafael; Gómez-Cortés, Gian Carlo

    2015-01-01

    This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design procedures for a wide variety of chaotic systems. The basic differential algebraic and geometric concepts are presented in the first few chapters in a novel way as design tools, together with selected experimental studies demonstrating their importance. The subsequent chapters treat recent applications. Written for graduate students in applied physical sciences, systems engineers, and applied mathematicians interested in synchronization of chaotic systems and in secure communications, this self-contained text requires only...

  6. Cluster algebras bases on vertex operator algebras

    Czech Academy of Sciences Publication Activity Database

    Zuevsky, Alexander

    2016-01-01

    Roč. 30, 28-29 (2016), č. článku 1640030. ISSN 0217-9792 Institutional support: RVO:67985840 Keywords : cluster alegbras * vertex operator algebras * Riemann surfaces Subject RIV: BA - General Mathematics Impact factor: 0.736, year: 2016 http://www.worldscientific.com/doi/abs/10.1142/S0217979216400300

  7. Algebraic K-theory and algebraic topology

    Energy Technology Data Exchange (ETDEWEB)

    Berrick, A J [Department of Mathematics, National University of Singapore (Singapore)

    2003-09-15

    This contribution treats the various topological constructions of Algebraic K-theory together with the underlying homotopy theory. Topics covered include the plus construction together with its various ramifications and applications, Topological Hochschild and Cyclic Homology as well as K-theory of the ring of integers.

  8. On Algebraic Approach for MSD Parametric Estimation

    OpenAIRE

    Oueslati , Marouene; Thiery , Stéphane; Gibaru , Olivier; Béarée , Richard; Moraru , George

    2011-01-01

    This article address the identification problem of the natural frequency and the damping ratio of a second order continuous system where the input is a sinusoidal signal. An algebra based approach for identifying parameters of a Mass Spring Damper (MSD) system is proposed and compared to the Kalman-Bucy filter. The proposed estimator uses the algebraic parametric method in the frequency domain yielding exact formula, when placed in the time domain to identify the unknown parameters. We focus ...

  9. 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

  10. Matrices and linear algebra

    CERN Document Server

    Schneider, Hans

    1989-01-01

    Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t

  11. 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...

  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. Adaptive algebraic reconstruction technique

    International Nuclear Information System (INIS)

    Lu Wenkai; Yin Fangfang

    2004-01-01

    Algebraic reconstruction techniques (ART) are iterative procedures for reconstructing objects from their projections. It is proven that ART can be computationally efficient by carefully arranging the order in which the collected data are accessed during the reconstruction procedure and adaptively adjusting the relaxation parameters. In this paper, an adaptive algebraic reconstruction technique (AART), which adopts the same projection access scheme in multilevel scheme algebraic reconstruction technique (MLS-ART), is proposed. By introducing adaptive adjustment of the relaxation parameters during the reconstruction procedure, one-iteration AART can produce reconstructions with better quality, in comparison with one-iteration MLS-ART. Furthermore, AART outperforms MLS-ART with improved computational efficiency

  14. 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

  15. Traditional vectors as an introduction to geometric algebra

    International Nuclear Information System (INIS)

    Carroll, J E

    2003-01-01

    The 2002 Oersted Medal Lecture by David Hestenes concerns the many advantages for education in physics if geometric algebra were to replace standard vector algebra. However, such a change has difficulties for those who have been taught traditionally. A new way of introducing geometric algebra is presented here using a four-element array composed of traditional vector and scalar products. This leads to an explicit 4 x 4 matrix representation which contains key requirements for three-dimensional geometric algebra. The work can be extended to include Maxwell's equations where it is found that curl and divergence appear naturally together. However, to obtain an explicit representation of space-time algebra with the correct behaviour under Lorentz transformations, an 8 x 8 matrix representation has to be formed. This leads to a Dirac representation of Maxwell's equations showing that space-time algebra has hidden within its formalism the symmetry of 'parity, charge conjugation and time reversal'

  16. Residence time and physical processes in lakes

    Directory of Open Access Journals (Sweden)

    Nicoletta SALA

    2003-09-01

    Full Text Available The residence time of a lake is highly dependent on internal physical processes in the water mass conditioning its hydrodynamics; early attempts to evaluate this physical parameter emphasize the complexity of the problem, which depends on very different natural phenomena with widespread synergies. The aim of this study is to analyse the agents involved in these processes and arrive at a more realistic definition of water residence time which takes account of these agents, and how they influence internal hydrodynamics. With particular reference to temperate lakes, the following characteristics are analysed: 1 the set of the lake's caloric components which, along with summer heating, determine the stabilizing effect of the surface layers, and the consequent thermal stratification, as well as the winter destabilizing effect; 2 the wind force, which transfers part of its momentum to the water mass, generating a complex of movements (turbulence, waves, currents with the production of active kinetic energy; 3 the water flowing into the lake from the tributaries, and flowing out through the outflow, from the standpoint of hydrology and of the kinetic effect generated by the introduction of these water masses into the lake. These factors were studied in the context of the general geographical properties of the lake basin and the watershed (latitude, longitude, morphology, also taking account of the local and regional climatic situation. Also analysed is the impact of ongoing climatic change on the renewal of the lake water, which is currently changing the equilibrium between lake and atmosphere, river and lake, and relationships

  17. 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...

  18. 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.

  19. 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

  20. The Raptor Real-Time Processing Architecture

    Science.gov (United States)

    Galassi, M.; Starr, D.; Wozniak, P.; Brozdin, K.

    The primary goal of Raptor is ambitious: to identify interesting optical transients from very wide field of view telescopes in real time, and then to quickly point the higher resolution Raptor ``fovea'' cameras and spectrometer to the location of the optical transient. The most interesting of Raptor's many applications is the real-time search for orphan optical counterparts of Gamma Ray Bursts. The sequence of steps (data acquisition, basic calibration, source extraction, astrometry, relative photometry, the smarts of transient identification and elimination of false positives, telescope pointing feedback, etc.) is implemented with a ``component'' approach. All basic elements of the pipeline functionality have been written from scratch or adapted (as in the case of SExtractor for source extraction) to form a consistent modern API operating on memory resident images and source lists. The result is a pipeline which meets our real-time requirements and which can easily operate as a monolithic or distributed processing system. Finally, the Raptor architecture is entirely based on free software (sometimes referred to as ``open source'' software). In this paper we also discuss the interplay between various free software technologies in this type of astronomical problem.

  1. Algebraic geometry in India

    Indian Academy of Sciences (India)

    algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.

  2. Linear algebra done right

    CERN Document Server

    Axler, Sheldon

    2015-01-01

    This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the ...

  3. Algebraic Semantics for Narrative

    Science.gov (United States)

    Kahn, E.

    1974-01-01

    This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)

  4. Groebner Finite Path Algebras

    OpenAIRE

    Leamer, Micah J.

    2004-01-01

    Let K be a field and Q a finite directed multi-graph. In this paper I classify all path algebras KQ and admissible orders with the property that all of their finitely generated ideals have finite Groebner bases. MS

  5. 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).

  6. Algebra for All: California’s Eighth-Grade Algebra Initiative as Constrained Curricula

    Science.gov (United States)

    Domina, Thurston; Penner, Andrew M.; Penner, Emily K.; Conley, Annemarie

    2015-01-01

    Background/Context Across the United States, secondary school curricula are intensifying as a growing proportion of students enroll in high-level academic math courses. In many districts, this intensification process occurs as early as eighth grade, where schools are effectively constraining their mathematics curricula by restricting course offerings and placing more students into Algebra I. This paper provides a quantitative single-case research study of policy-driven curricular intensification in one California school district. Research Questions (1a) What effect did 8th eighth grade curricular intensification have on mathematics course enrollment patterns in Towering Pines Unified schools? (2b) How did the distribution of prior achievement in Towering Pines math classrooms change as the district constrained the curriculum by universalizing 8th eighth grade Algebra? (3c) Did 8th eighth grade curricular intensification improve students’ mathematics achievement? Setting Towering Pines is an immigrant enclave in the inner-ring suburbs of a major metropolitan area. The district’s 10 middle schools together enroll approximately 4,000 eighth graders each year. The districts’ students are ethnically diverse and largely economically disadvantaged. The study draws upon administrative data describing 8th eighth graders in the district in the 2004–20-05 through 2007–20-08 school years. Intervention/Program/Practice During the study period, Towering Pines dramatically intensified middle school students’ math curricula: In the 2004–20-05 school year 32% of the district’s 8th eighth graders enrolled in Algebra or a higher- level mathematics course; by the 2007–20-08 school year that proportion had increased to 84%. Research Design We use an interrupted time-series design, comparing students’ 8th eighth grade math course enrollments, 10th grade math course enrollments, and 10th grade math test scores across the four cohorts, controlling for demographics and

  7. Algebra for All: California's Eighth-Grade Algebra Initiative as Constrained Curricula.

    Science.gov (United States)

    Domina, Thurston; Penner, Andrew M; Penner, Emily K; Conley, Annemarie

    2014-08-01

    Across the United States, secondary school curricula are intensifying as a growing proportion of students enroll in high-level academic math courses. In many districts, this intensification process occurs as early as eighth grade, where schools are effectively constraining their mathematics curricula by restricting course offerings and placing more students into Algebra I. This paper provides a quantitative single-case research study of policy-driven curricular intensification in one California school district. (1a) What effect did 8th eighth grade curricular intensification have on mathematics course enrollment patterns in Towering Pines Unified schools? (2b) How did the distribution of prior achievement in Towering Pines math classrooms change as the district constrained the curriculum by universalizing 8th eighth grade Algebra? (3c) Did 8th eighth grade curricular intensification improve students' mathematics achievement? Towering Pines is an immigrant enclave in the inner-ring suburbs of a major metropolitan area. The district's 10 middle schools together enroll approximately 4,000 eighth graders each year. The districts' students are ethnically diverse and largely economically disadvantaged. The study draws upon administrative data describing 8th eighth graders in the district in the 2004-20-05 through 2007-20-08 school years. During the study period, Towering Pines dramatically intensified middle school students' math curricula: In the 2004-20-05 school year 32% of the district's 8th eighth graders enrolled in Algebra or a higher- level mathematics course; by the 2007-20-08 school year that proportion had increased to 84%. We use an interrupted time-series design, comparing students' 8th eighth grade math course enrollments, 10th grade math course enrollments, and 10th grade math test scores across the four cohorts, controlling for demographics and prior achievement. We find that students' odds of taking higher level mathematics courses increased as this

  8. Gauging the octonion algebra

    International Nuclear Information System (INIS)

    Waldron, A.K.; Joshi, G.C.

    1992-01-01

    By considering representation theory for non-associative algebras the fundamental adjoint representations of the octonion algebra is constructed. It is then shown how these representations by associative matrices allow a consistent octonionic gauge theory to be realized. It was found that non-associativity implies the existence of new terms in the transformation laws of fields and the kinetic term of an octonionic Lagrangian. 13 refs

  9. Summing Boolean Algebras

    Institute of Scientific and Technical Information of China (English)

    Antonio AIZPURU; Antonio GUTI(E)RREZ-D(A)VILA

    2004-01-01

    In this paper we will study some families and subalgebras ( ) of ( )(N) that let us characterize the unconditional convergence of series through the weak convergence of subseries ∑i∈A xi, A ∈ ( ).As a consequence, we obtain a new version of the Orlicz-Pettis theorem, for Banach spaces. We also study some relationships between algebraic properties of Boolean algebras and topological properties of the corresponding Stone spaces.

  10. 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 ...

  11. Currents on Grassmann algebras

    International Nuclear Information System (INIS)

    Coquereaux, R.; Ragoucy, E.

    1993-09-01

    Currents are defined on a Grassmann algebra Gr(N) with N generators as distributions on its exterior algebra (using the symmetric wedge product). The currents are interpreted in terms of Z 2 -graded Hochschild cohomology and closed currents in terms of cyclic cocycles (they are particular multilinear forms on Gr(N)). An explicit construction of the vector space of closed currents of degree p on Gr(N) is given by using Berezin integration. (authors). 10 refs

  12. Introduction to abstract algebra

    CERN Document Server

    Nicholson, W Keith

    2012-01-01

    Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."-Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately be

  13. Timing matters: the processing of pitch relations

    Science.gov (United States)

    Weise, Annekathrin; Grimm, Sabine; Trujillo-Barreto, Nelson J.; Schröger, Erich

    2014-01-01

    The human central auditory system can automatically extract abstract regularities from a variant auditory input. To this end, temporarily separated events need to be related. This study tested whether the timing between events, falling either within or outside the temporal window of integration (~350 ms), impacts the extraction of abstract feature relations. We utilized tone pairs for which tones within but not across pairs revealed a constant pitch relation (e.g., pitch of second tone of a pair higher than pitch of first tone, while absolute pitch values varied across pairs). We measured the mismatch negativity (MMN; the brain’s error signal to auditory regularity violations) to second tones that rarely violated the pitch relation (e.g., pitch of second tone lower). A Short condition in which tone duration (90 ms) and stimulus onset asynchrony between the tones of a pair were short (110 ms) was compared to two conditions, where this onset asynchrony was long (510 ms). In the Long Gap condition, the tone durations were identical to Short (90 ms), but the silent interval was prolonged by 400 ms. In Long Tone, the duration of the first tone was prolonged by 400 ms, while the silent interval was comparable to Short (20 ms). Results show a frontocentral MMN of comparable amplitude in all conditions. Thus, abstract pitch relations can be extracted even when the within-pair timing exceeds the integration period. Source analyses indicate MMN generators in the supratemporal cortex. Interestingly, they were located more anterior in Long Gap than in Short and Long Tone. Moreover, frontal generator activity was found for Long Gap and Long Tone. Thus, the way in which the system automatically registers irregular abstract pitch relations depends on the timing of the events to be linked. Pending that the current MMN data mirror established abstract rule representations coding the regular pitch relation, neural processes building these templates vary with timing. PMID:24966823

  14. Timing matters: The processing of pitch relations

    Directory of Open Access Journals (Sweden)

    Annekathrin eWeise

    2014-06-01

    Full Text Available The human central auditory system can automatically extract abstract regularities from a variant auditory input. To this end, temporarily separated events need to be related. This study tested whether the timing between events, falling either within or outside the temporal window of integration (~350 ms, impacts the extraction of abstract feature relations. We utilized tone pairs for which tones within but not across pairs revealed a constant pitch relation (e.g. pitch of 2nd tone of a pair higher than pitch of 1st tone, while absolute pitch values varied across pairs. We measured the Mismatch Negativity (MMN; the brain’s error signal to auditory regularity violations to 2nd tones that rarely violated the pitch relation (e.g. pitch of 2nd tone lower. A Short condition in which tone duration (90 ms and stimulus onset asynchrony between the tones of a pair were short (110 ms was compared to two conditions, where this onset asynchrony was long (510 ms. In the Long Gap condition the tone durations were identical to Short (90 ms, but the silent interval was prolonged by 400 ms. In Long Tone the duration of the first tone was prolonged by 400 ms, while the silent interval was comparable to Short (20 ms. Results show a frontocentral MMN of comparable amplitude in all conditions. Thus, abstract pitch relations can be extracted even when the within-pair timing exceeds the integration period. Source analyses indicate MMN generators in the supratemporal cortex. Interestingly, they were located more anterior in Long Gap than in Short and Long Tone. Moreover, frontal generator activity was found for Long Gap and Long Tone. Thus, the way in which the system automatically registers irregular abstract pitch relations depends on the timing of the events to be linked. Pending that the current MMN data mirror established abstract rule representations coding the regular pitch relation, neural processes building these templates vary with timing.

  15. Forward error correction based on algebraic-geometric theory

    CERN Document Server

    A Alzubi, Jafar; M Chen, Thomas

    2014-01-01

    This book covers the design, construction, and implementation of algebraic-geometric codes from Hermitian curves. Matlab simulations of algebraic-geometric codes and Reed-Solomon codes compare their bit error rate using different modulation schemes over additive white Gaussian noise channel model. Simulation results of Algebraic-geometric codes bit error rate performance using quadrature amplitude modulation (16QAM and 64QAM) are presented for the first time and shown to outperform Reed-Solomon codes at various code rates and channel models. The book proposes algebraic-geometric block turbo codes. It also presents simulation results that show an improved bit error rate performance at the cost of high system complexity due to using algebraic-geometric codes and Chase-Pyndiah’s algorithm simultaneously. The book proposes algebraic-geometric irregular block turbo codes (AG-IBTC) to reduce system complexity. Simulation results for AG-IBTCs are presented for the first time.

  16. 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.

  17. 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

  18. Division algebra, generalized supersymmetries and octonionic M-theory

    International Nuclear Information System (INIS)

    Toppan, Francesco

    2004-11-01

    This is the report of the talk given at the conference 'Number, Time and Relativity', held at the Bauman University, Moscow, August 2004, concerning the recent research activity of the author and his collaborators about the inter-relation of the concepts of division algebras, representations of Clifford algebras, generalized supersymmetries with the introduction of an alternative description of the M-algebra in terms of the non-associative structure of the octonions. (author)

  19. Poincare invariant algebra from instant to light-front quantization

    International Nuclear Information System (INIS)

    Ji, Chueng-Ryong; Mitchell, Chad

    2001-01-01

    We present the Poincare algebra interpolating between instant and light-front time quantizations. The angular momentum operators satisfying SU(2) algebra are constructed in an arbitrary interpolation angle and shown to be identical to the ordinary angular momentum and Leutwyler-Stern angular momentum in the instant and light-front quantization limits, respectively. The exchange of the dynamical role between the transverse angular mometum and the boost operators is manifest in our newly constructed algebra

  20. BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS

    Science.gov (United States)

    Krogh, F. T.

    1994-01-01

    The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.

  1. 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...

  2. 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...

  3. 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.

  4. Algebraically special perturbations of the Schwarzschild solution in higher dimensions

    International Nuclear Information System (INIS)

    Dias, Óscar J C; Reall, Harvey S

    2013-01-01

    We study algebraically special perturbations of a generalized Schwarzschild solution in any number of dimensions. There are two motivations. First, to learn whether there exist interesting higher-dimensional algebraically special solutions beyond the known ones. Second, algebraically special perturbations present an obstruction to the unique reconstruction of general metric perturbations from gauge-invariant variables analogous to the Teukolsky scalars and it is desirable to know the extent of this non-uniqueness. In four dimensions, our results generalize those of Couch and Newman, who found infinite families of time-dependent algebraically special perturbations. In higher dimensions, we find that the only regular algebraically special perturbations are those corresponding to deformations within the Myers–Perry family. Our results are relevant for several inequivalent definitions of ‘algebraically special’. (paper)

  5. Non-unique factorizations algebraic, combinatorial and analytic theory

    CERN Document Server

    Geroldinger, Alfred

    2006-01-01

    From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory offers a look at the present state of the theory in a single, unified resource.Taking a broad look at the algebraic, combinatorial, and analytic fundamentals, this book derives factorization results and applies them in concrete arithmetical situations using appropriate transfer principles. It begins with a basic introduction that can be understood with knowledge of standard basic algebra. The authors then move to the algebraic theory of monoids, arithmetic theory of monoids, the structure of sets of lengths, additive group theory, arithmetical invariants, and the arithmetic of Krull monoids. They also provide a s...

  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. 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

  8. 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 ...

  9. 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...

  10. 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...

  11. 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.

  12. Noise limitations in optical linear algebra processors.

    Science.gov (United States)

    Batsell, S G; Jong, T L; Walkup, J F; Krile, T F

    1990-05-10

    A general statistical noise model is presented for optical linear algebra processors. A statistical analysis which includes device noise, the multiplication process, and the addition operation is undertaken. We focus on those processes which are architecturally independent. Finally, experimental results which verify the analytical predictions are also presented.

  13. 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)

  14. Computer algebra simulation - what can it do?; Was leistet Computer-Algebra-Simulation?

    Energy Technology Data Exchange (ETDEWEB)

    Braun, S. [Visual Analysis AG, Muenchen (Germany)

    2001-07-01

    Shortened development times require new and improved calculation methods. Numeric methods have long become state of the art. However, although numeric simulations provide a better understanding of process parameters, they do not give a feast overview of the interdependences between parameters. Numeric simulations are effective only if all physical parameters are sufficiently known; otherwise, the efficiency will decrease due to the large number of variant calculations required. Computer algebra simulation closes this gap and provides a deeper understanding of the physical fundamentals of technical processes. [German] Neue und verbesserte Berechnungsmethoden sind notwendig, um die staendige Verkuerzung der Entwicklungszyklen zu ermoeglichen. Herkoemmliche Methoden, die auf einem rein numerischen Ansatz basieren, haben sich in vielen Anwendungsbereichen laengst zum Standard entwickelt. Aber nicht nur die staendig kuerzer werdenden Entwicklungszyklen, sondern auch die weiterwachsende Komplexitaet machen es notwendig, ein besseres Verstaendnis der beteiligten Prozessparameter zu gewinnen. Die numerische Simulation besticht zwar durch Detailloesungen, selbst bei komplexen Strukturen und Prozessen, allerdings liefert sie keine schnelle Abschaetzung ueber die Zusammenhaenge zwischen den einzelnen Parametern. Die numerische Simulation ist nur dann effektiv, wenn alle physikalischen Parameter hinreichend bekannt sind; andernfalls sinkt die Effizienz durch die notwendige Anzahl von notwendigen Variantenrechnungen sehr stark. Die Computer-Algebra-Simulation schliesst diese Luecke in dem sie es erlaubt, sich einen tieferen Einblick in die physikalische Funktionsweise technischer Prozesse zu verschaffen. (orig.)

  15. Algebraic quantum field theory

    International Nuclear Information System (INIS)

    Foroutan, A.

    1996-12-01

    The basic assumption that the complete information relevant for a relativistic, local quantum theory is contained in the net structure of the local observables of this theory results first of all in a concise formulation of the algebraic structure of the superselection theory and an intrinsic formulation of charge composition, charge conjugation and the statistics of an algebraic quantum field theory. In a next step, the locality of massive particles together with their spectral properties are wed for the formulation of a selection criterion which opens the access to the massive, non-abelian quantum gauge theories. The role of the electric charge as a superselection rule results in the introduction of charge classes which in term lead to a set of quantum states with optimum localization properties. Finally, the asymptotic observables of quantum electrodynamics are investigated within the framework of algebraic quantum field theory. (author)

  16. Complex algebraic geometry

    CERN Document Server

    Kollár, János

    1997-01-01

    This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

  17. Algebraic design theory

    CERN Document Server

    Launey, Warwick De

    2011-01-01

    Combinatorial design theory is a source of simply stated, concrete, yet difficult discrete problems, with the Hadamard conjecture being a prime example. It has become clear that many of these problems are essentially algebraic in nature. This book provides a unified vision of the algebraic themes which have developed so far in design theory. These include the applications in design theory of matrix algebra, the automorphism group and its regular subgroups, the composition of smaller designs to make larger designs, and the connection between designs with regular group actions and solutions to group ring equations. Everything is explained at an elementary level in terms of orthogonality sets and pairwise combinatorial designs--new and simple combinatorial notions which cover many of the commonly studied designs. Particular attention is paid to how the main themes apply in the important new context of cocyclic development. Indeed, this book contains a comprehensive account of cocyclic Hadamard matrices. The book...

  18. Complex Algebraic Varieties

    CERN Document Server

    Peternell, Thomas; Schneider, Michael; Schreyer, Frank-Olaf

    1992-01-01

    The Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to talks given at the conference: all are original, fully refereed research articles. CONTENTS: A. Beauville: Annulation du H(1) pour les fibres en droites plats.- M. Beltrametti, A.J. Sommese, J.A. Wisniewski: Results on varieties with many lines and their applications to adjunction theory.- G. Bohnhorst, H. Spindler: The stability of certain vector bundles on P(n) .- F. Catanese, F. Tovena: Vector bundles, linear systems and extensions of (1).- O. Debarre: Vers uns stratification de l'espace des modules des varietes abeliennes principalement polarisees.- J.P. Demailly: Singular hermitian metrics on positive line bundles.- T. Fujita: On adjoint bundles of ample vector bundles.- Y. Kawamata: Moderate degenerations of algebraic surfaces.- U. Persson: Genus two fibra...

  19. Problems in abstract algebra

    CERN Document Server

    Wadsworth, A R

    2017-01-01

    This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.

  20. Higher regulators, algebraic

    CERN Document Server

    Bloch, Spencer J

    2000-01-01

    This book is the long-awaited publication of the famous Irvine lectures. Delivered in 1978 at the University of California at Irvine, these lectures turned out to be an entry point to several intimately-connected new branches of arithmetic algebraic geometry, such as regulators and special values of L-functions of algebraic varieties, explicit formulas for them in terms of polylogarithms, the theory of algebraic cycles, and eventually the general theory of mixed motives which unifies and underlies all of the above (and much more). In the 20 years since, the importance of Bloch's lectures has not diminished. A lucky group of people working in the above areas had the good fortune to possess a copy of old typewritten notes of these lectures. Now everyone can have their own copy of this classic work.

  1. Basic linear algebra

    CERN Document Server

    Blyth, T S

    2002-01-01

    Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers:...

  2. Algebraic topology a primer

    CERN Document Server

    Deo, Satya

    2018-01-01

    This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail. Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology. Targeted to undergraduate and graduate students of mathematics, the prerequisite for this book is minimal knowledge of linear algebra, group theory and topological spaces. The book discusses about the relevant concepts and ideas in a very lucid manner, providing suitable motivations and illustrations. All relevant topics are covered, including the classical theorems like the Brouwer’s fixed point theorem, Lefschetz fixed point theorem, Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of the domain. Most of the exercises are elementary, but sometimes chal...

  3. 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.)

  4. 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…

  5. 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

  6. Teaching Linear Algebra: Must the Fog Always Roll In?

    Science.gov (United States)

    Carlson, David

    1993-01-01

    Proposes methods to teach the more difficult concepts of linear algebra. Examines features of the Linear Algebra Curriculum Study Group Core Syllabus, and presents problems from the core syllabus that utilize the mathematical process skills of making conjectures, proving the results, and communicating the results to colleagues. Presents five…

  7. 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 ...

  8. Computer Program For Linear Algebra

    Science.gov (United States)

    Krogh, F. T.; Hanson, R. J.

    1987-01-01

    Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.

  9. Algebra for Gifted Third Graders.

    Science.gov (United States)

    Borenson, Henry

    1987-01-01

    Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)

  10. 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.

  11. 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.

  12. Dynamical systems and linear algebra

    OpenAIRE

    Colonius, Fritz (Prof.)

    2007-01-01

    Dynamical systems and linear algebra / F. Colonius, W. Kliemann. - In: Handbook of linear algebra / ed. by Leslie Hogben. - Boca Raton : Chapman & Hall/CRC, 2007. - S. 56,1-56,22. - (Discrete mathematics and its applications)

  13. Projector bases and algebraic spinors

    International Nuclear Information System (INIS)

    Bergdolt, G.

    1988-01-01

    In the case of complex Clifford algebras a basis is constructed whose elements satisfy projector relations. The relations are sufficient conditions for the elements to span minimal ideals and hence to define algebraic spinors

  14. Matrix algebra for linear models

    CERN Document Server

    Gruber, Marvin H J

    2013-01-01

    Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. This evolution has made matrix methods a vital part of statistical education. Traditionally, matrix methods are taught in courses on everything from regression analysis to stochastic processes, thus creating a fractured view of the topic. Matrix Algebra for Linear Models offers readers a unique, unified view of matrix analysis theory (where and when necessary), methods, and their applications. Written f

  15. Polynomial Heisenberg algebras

    International Nuclear Information System (INIS)

    Carballo, Juan M; C, David J Fernandez; Negro, Javier; Nieto, Luis M

    2004-01-01

    Polynomial deformations of the Heisenberg algebra are studied in detail. Some of their natural realizations are given by the higher order susy partners (and not only by those of first order, as is already known) of the harmonic oscillator for even-order polynomials. Here, it is shown that the susy partners of the radial oscillator play a similar role when the order of the polynomial is odd. Moreover, it will be proved that the general systems ruled by such kinds of algebras, in the quadratic and cubic cases, involve Painleve transcendents of types IV and V, respectively

  16. 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

  17. Algebraic number theory

    CERN Document Server

    Weiss, Edwin

    1998-01-01

    Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te

  18. Partially ordered algebraic systems

    CERN Document Server

    Fuchs, Laszlo

    2011-01-01

    Originally published in an important series of books on pure and applied mathematics, this monograph by a distinguished mathematician explores a high-level area in algebra. It constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The self-contained treatment features numerous problems, complete proofs, a detailed bibliography, and indexes. It presumes some knowledge of abstract algebra, providing necessary background and references where appropriate. This inexpensive edition of a hard-to-find systematic survey will fill a gap i

  19. 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

  20. Helmholtz algebraic solitons

    Energy Technology Data Exchange (ETDEWEB)

    Christian, J M; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Materials and Physics Research Centre, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P, E-mail: j.christian@salford.ac.u [Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)

    2010-02-26

    We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.

  1. Endomorphisms of graph algebras

    DEFF Research Database (Denmark)

    Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech

    2012-01-01

    We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D...... that the restriction to the diagonal MASA of an automorphism which globally preserves both D_E and the core AF-subalgebra eventually commutes with the corresponding one-sided shift. Secondly, we exhibit several properties of proper endomorphisms, investigate invertibility of localized endomorphisms both on C...

  2. Algebraic curves and cryptography

    CERN Document Server

    Murty, V Kumar

    2010-01-01

    It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a supply of such groups through Abelian varieties over finite fields. Of special interest are the Abelian varieties that are Jacobians of algebraic curves. All of the articles in this volume are centered on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields. The topics covered include Schoof's \\ell-adic point counting algorithm, the p-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on

  3. Elementary algebraic geometry

    CERN Document Server

    Kendig, Keith

    2015-01-01

    Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th

  4. Helmholtz algebraic solitons

    International Nuclear Information System (INIS)

    Christian, J M; McDonald, G S; Chamorro-Posada, P

    2010-01-01

    We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.

  5. Handbook of linear algebra

    CERN Document Server

    Hogben, Leslie

    2013-01-01

    With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.New to the Second EditionSeparate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of

  6. Algebra & trigonometry I essentials

    CERN Document Server

    REA, Editors of

    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. Algebra & Trigonometry I includes sets and set operations, number systems and fundamental algebraic laws and operations, exponents and radicals, polynomials and rational expressions, eq

  7. Algebra & trigonometry super review

    CERN Document Server

    2012-01-01

    Get all you need to know with Super Reviews! Each Super Review is packed with in-depth, student-friendly topic reviews that fully explain everything about the subject. The Algebra and Trigonometry Super Review includes sets and set operations, number systems and fundamental algebraic laws and operations, exponents and radicals, polynomials and rational expressions, equations, linear equations and systems of linear equations, inequalities, relations and functions, quadratic equations, equations of higher order, ratios, proportions, and variations. Take the Super Review quizzes to see how much y

  8. Linear Algebra Thoroughly Explained

    CERN Document Server

    Vujičić, Milan

    2008-01-01

    Linear Algebra Thoroughly Explained provides a comprehensive introduction to the subject suitable for adoption as a self-contained text for courses at undergraduate and postgraduate level. The clear and comprehensive presentation of the basic theory is illustrated throughout with an abundance of worked examples. The book is written for teachers and students of linear algebra at all levels and across mathematics and the applied sciences, particularly physics and engineering. It will also be an invaluable addition to research libraries as a comprehensive resource book for the subject.

  9. Pole-placement Predictive Functional Control for under-damped systems with real numbers algebra.

    Science.gov (United States)

    Zabet, K; Rossiter, J A; Haber, R; Abdullah, M

    2017-11-01

    This paper presents the new algorithm of PP-PFC (Pole-placement Predictive Functional Control) for stable, linear under-damped higher-order processes. It is shown that while conventional PFC aims to get first-order exponential behavior, this is not always straightforward with significant under-damped modes and hence a pole-placement PFC algorithm is proposed which can be tuned more precisely to achieve the desired dynamics, but exploits complex number algebra and linear combinations in order to deliver guarantees of stability and performance. Nevertheless, practical implementation is easier by avoiding complex number algebra and hence a modified formulation of the PP-PFC algorithm is also presented which utilises just real numbers while retaining the key attributes of simple algebra, coding and tuning. The potential advantages are demonstrated with numerical examples and real-time control of a laboratory plant. Copyright © 2017 ISA. All rights reserved.

  10. Computer Aided Continuous Time Stochastic Process Modelling

    DEFF Research Database (Denmark)

    Kristensen, N.R.; Madsen, Henrik; Jørgensen, Sten Bay

    2001-01-01

    A grey-box approach to process modelling that combines deterministic and stochastic modelling is advocated for identification of models for model-based control of batch and semi-batch processes. A computer-aided tool designed for supporting decision-making within the corresponding modelling cycle...

  11. 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.)

  12. 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.

  13. Meromorphic functions and linear algebra

    CERN Document Server

    Nevanlinna, Olavi

    2003-01-01

    This volume describes for the first time in monograph form important applications in numerical methods of linear algebra. The author presents new material and extended results from recent papers in a very readable style. The main goal of the book is to study the behavior of the resolvent of a matrix under the perturbation by low rank matrices. Whereas the eigenvalues (the poles of the resolvent) and the pseudospectra (the sets where the resolvent takes large values) can move dramatically under such perturbations, the growth of the resolvent as a matrix-valued meromorphic function remains essen

  14. Student and Instructor Perceptions of a Flipped College Algebra Classroom

    Science.gov (United States)

    Jaster, Robert W.

    2017-01-01

    Each year about half a million students fail to make planned academic progress due to college algebra, hence the need for researchers to find ways of improving the quality of instruction in the course. Recent research suggests that flipping college algebra to allow time for active learning in the classroom may improve student performance. Also,…

  15. Applications of Lie algebras in the solution of dynamic problems

    International Nuclear Information System (INIS)

    Fellay, G.

    1983-01-01

    The purpose of this paper is to give some insight into the Lie-algebras and their applications. The first part introduces the elementary properties of such algebras, e.g. nilpotency, solvability, etc. The second part shows how to use the demonstrated theory for solving differential equations with time-dependent coefficients. (Auth.)

  16. 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.)

  17. 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

  18. Assessing Elementary Algebra with STACK

    Science.gov (United States)

    Sangwin, Christopher J.

    2007-01-01

    This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

  19. Algebraic Methods to Design Signals

    Science.gov (United States)

    2015-08-27

    to date on designing signals using algebraic and combinatorial methods. Mathematical tools from algebraic number theory, representation theory and... combinatorial objects in designing signals for communication purposes. Sequences and arrays with desirable autocorrelation properties have many...multiple access methods in mobile radio communication systems. We continue our mathematical framework based on group algebras, character theory

  20. Time-Frequency Domain Memory and Processing

    National Research Council Canada - National Science Library

    Huestis, David

    2002-01-01

    This report summarizes the results of a 3-year program of research on the physics and technology needed to develop high-performance optical memory and optical processing systems based on the concept...

  1. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

  2. vector bilinear autoregressive time series model and its superiority

    African Journals Online (AJOL)

    KEYWORDS: Linear time series, Autoregressive process, Autocorrelation function, Partial autocorrelation function,. Vector time .... important result on matrix algebra with respect to the spectral ..... application to covariance analysis of super-.

  3. Probabilistic thread algebra

    NARCIS (Netherlands)

    Bergstra, J.A.; Middelburg, C.A.

    2015-01-01

    We add probabilistic features to basic thread algebra and its extensions with thread-service interaction and strategic interleaving. Here, threads represent the behaviours produced by instruction sequences under execution and services represent the behaviours exhibited by the components of execution

  4. Discourses on Algebra

    Indian Academy of Sciences (India)

    BOOK REVIEW ... To the Indian reader, the word discourse, evokes a respected ... I dug a bit deeper with Google trans- late, and ... published in a journal of mathematics educa- tion. ... The article on Shafarevich's work elsewhere ... goal then, is to develop the basics of algebra in ... ometric Greeks, and works like a magician.

  5. Thinking Visually about Algebra

    Science.gov (United States)

    Baroudi, Ziad

    2015-01-01

    Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…

  6. The algebraic collective model

    International Nuclear Information System (INIS)

    Rowe, D.J.; Turner, P.S.

    2005-01-01

    A recently proposed computationally tractable version of the Bohr collective model is developed to the extent that we are now justified in describing it as an algebraic collective model. The model has an SU(1,1)xSO(5) algebraic structure and a continuous set of exactly solvable limits. Moreover, it provides bases for mixed symmetry collective model calculations. However, unlike the standard realization of SU(1,1), used for computing beta wave functions and their matrix elements in a spherical basis, the algebraic collective model makes use of an SU(1,1) algebra that generates wave functions appropriate for deformed nuclei with intrinsic quadrupole moments ranging from zero to any large value. A previous paper focused on the SO(5) wave functions, as SO(5) (hyper-)spherical harmonics, and computation of their matrix elements. This paper gives analytical expressions for the beta matrix elements needed in applications of the model and illustrative results to show the remarkable gain in efficiency that is achieved by using such a basis in collective model calculations for deformed nuclei

  7. College Algebra I.

    Science.gov (United States)

    Benjamin, Carl; And Others

    Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in College Algebra I. Topics covered include: sets; vocabulary; linear equations; inequalities; real numbers; operations; factoring; fractions; formulas; ratio, proportion, and…

  8. Algebraic K-theory

    CERN Document Server

    Swan, R G

    1968-01-01

    From the Introduction: "These notes are taken from a course on algebraic K-theory [given] at the University of Chicago in 1967. They also include some material from an earlier course on abelian categories, elaborating certain parts of Gabriel's thesis. The results on K-theory are mostly of a very general nature."

  9. 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...

  10. Methods of algebraic geometry in control theory

    CERN Document Server

    Falb, Peter

    1999-01-01

    "Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is qui...

  11. Operator algebras and topology

    International Nuclear Information System (INIS)

    Schick, T.

    2002-01-01

    These notes, based on three lectures on operator algebras and topology at the 'School on High Dimensional Manifold Theory' at the ICTP in Trieste, introduce a new set of tools to high dimensional manifold theory, namely techniques coming from the theory of operator algebras, in particular C*-algebras. These are extensively studied in their own right. We will focus on the basic definitions and properties, and on their relevance to the geometry and topology of manifolds. A central pillar of work in the theory of C*-algebras is the Baum-Connes conjecture. This is an isomorphism conjecture, as discussed in the talks of Luck, but with a certain special flavor. Nevertheless, it has important direct applications to the topology of manifolds, it implies e.g. the Novikov conjecture. In the first chapter, the Baum-Connes conjecture will be explained and put into our context. Another application of the Baum-Connes conjecture is to the positive scalar curvature question. This will be discussed by Stephan Stolz. It implies the so-called 'stable Gromov-Lawson-Rosenberg conjecture'. The unstable version of this conjecture said that, given a closed spin manifold M, a certain obstruction, living in a certain (topological) K-theory group, vanishes if and only M admits a Riemannian metric with positive scalar curvature. It turns out that this is wrong, and counterexamples will be presented in the second chapter. The third chapter introduces another set of invariants, also using operator algebra techniques, namely L 2 -cohomology, L 2 -Betti numbers and other L 2 -invariants. These invariants, their basic properties, and the central questions about them, are introduced in the third chapter. (author)

  12. 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.

  13. 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.)

  14. Quantum algebraic representation of localization and motion of a Dirac electron

    International Nuclear Information System (INIS)

    Jaekel, Marc-Thierry; Reynaud, Serge

    2001-01-01

    Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since transformations to uniformly accelerated frames are naturally included in this conformally invariant description, the quantum algebra is also able to deal with uniformly accelerated motion

  15. Space-time description of hard processes

    International Nuclear Information System (INIS)

    Ioffe, B.L.; Khoze, V.A.; Lipatov, L.N.

    1984-01-01

    The authors show that the interaction in deep inelastic scattering processes occurs mainly in a region near the light cone. It is concluded that in all cases studied, the scaling behaviour of the structure functions corresponds to the same light cone singularities of the coordinate functions as in the case of scattering on a free spin-1/2 fermion (or, perhaps, on a spinless boson). (Auth.)

  16. Specification and Analysis of Soft Real-Time Systems: Quantity and Quality

    NARCIS (Netherlands)

    d' Argenio, P.R.; Katoen, Joost P.; Brinksma, Hendrik

    This paper presents a process algebra for specifying soft real-time constraints in a compositional way. For these soft constraints we take a stochastic point of view and allow arbitrary probability distributions to express delays of activities. The semantics of this process algebra is given in terms

  17. 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)

  18. 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.

  19. Linear algebra a first course with applications

    CERN Document Server

    Knop, Larry E

    2008-01-01

    Linear Algebra: A First Course with Applications explores the fundamental ideas of linear algebra, including vector spaces, subspaces, basis, span, linear independence, linear transformation, eigenvalues, and eigenvectors, as well as a variety of applications, from inventories to graphics to Google's PageRank. Unlike other texts on the subject, this classroom-tested book gives students enough time to absorb the material by focusing on vector spaces early on and using computational sections as numerical interludes. It offers introductions to Maple™, MATLAB®, and TI-83 Plus for calculating matri

  20. Classical impurities associated to high rank algebras

    Energy Technology Data Exchange (ETDEWEB)

    Doikou, Anastasia, E-mail: A.Doikou@hw.ac.uk [Department of Mathematics, Heriot–Watt University, EH14 4AS, Edinburgh (United Kingdom); Department of Computer Engineering and Informatics, University of Patras, Patras GR-26500 (Greece)

    2014-07-15

    Classical integrable impurities associated with high rank (gl{sub N}) algebras are investigated. A particular prototype, i.e. the vector non-linear Schrödinger (NLS) model, is chosen as an example. A systematic construction of local integrals of motion as well as the time components of the corresponding Lax pairs is presented based on the underlying classical algebra. Suitable gluing conditions compatible with integrability are also extracted. The defect contribution is also examined in the case where non-trivial integrable conditions are implemented. It turns out that the integrable boundaries may drastically alter the bulk behavior, and in particular the defect contribution.

  1. Fock representations of exchange algebras with involution

    International Nuclear Information System (INIS)

    Liguori, A.; Mintchev, M.; Rossi, M.

    1997-01-01

    An associative algebra scr(A) R with exchange properties generalizing the canonical (anti)commutation relations is considered. We introduce a family of involutions in scr(A) R and construct the relative Fock representations, examining the positivity of the metric. As an application of the general results, we rigorously prove unitarity of the scattering operator of integrable models in 1+1 space-time dimensions. In this context the possibility of adopting various involutions in the Zamolodchikov endash Faddeev algebra is also explored. copyright 1997 American Institute of Physics

  2. Classical impurities associated to high rank algebras

    International Nuclear Information System (INIS)

    Doikou, Anastasia

    2014-01-01

    Classical integrable impurities associated with high rank (gl N ) algebras are investigated. A particular prototype, i.e. the vector non-linear Schrödinger (NLS) model, is chosen as an example. A systematic construction of local integrals of motion as well as the time components of the corresponding Lax pairs is presented based on the underlying classical algebra. Suitable gluing conditions compatible with integrability are also extracted. The defect contribution is also examined in the case where non-trivial integrable conditions are implemented. It turns out that the integrable boundaries may drastically alter the bulk behavior, and in particular the defect contribution

  3. Current algebra and η → 3π

    International Nuclear Information System (INIS)

    Bell, J.S.; Sutherland, D.G.

    1995-01-01

    A critical review is given of developments in the theory subsequent to the demonstration that in first approximation η → 3π is forbidden. It remains difficult to understand the process with conventional ideas without reducing to an accident the success of current algebra, and a simple linear matrix element, in K → 3π. (author)

  4. Journal Writing: Enlivening Elementary Linear Algebra.

    Science.gov (United States)

    Meel, David E.

    1999-01-01

    Examines the various issues surrounding the implementation of journal writing in an undergraduate linear algebra course. Identifies the benefits of incorporating journal writing into an undergraduate mathematics course, which are supported with students' comments from their journals and their reflections on the process. Contains 14 references.…

  5. Applications of Maple To Algebraic Cryptography.

    Science.gov (United States)

    Sigmon, Neil P.

    1997-01-01

    Demonstrates the use of technology to enhance the appreciation of applications involving abstract algebra. The symbolic manipulator Maple can perform computations required for a linear cryptosystem. One major benefit of this process is that students can encipher and decipher messages using a linear cryptosystem without becoming confused and…

  6. 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

  7. Relaxation Processes and Time Scale Transformation.

    Science.gov (United States)

    1982-03-01

    the response function may be immediately recognized as being 14 of the Kubo - Green type in the classical regime. Given this general framework, it is now...b as a function of temperature is 24 equivalent to the Vogel-Beuche-Fulcher empirical law for viscosity or the Williams-Landel-Ferry empirical law...relaxation times. With the weighted sum in the form of an integral , one can write exp(-(t/T)b ] = f dT’g(r’) exp[-(t/T’)], O

  8. Construction Example for Algebra System Using Harmony Search Algorithm

    Directory of Open Access Journals (Sweden)

    FangAn Deng

    2015-01-01

    Full Text Available The construction example of algebra system is to verify the existence of a complex algebra system, and it is a NP-hard problem. In this paper, to solve this kind of problems, firstly, a mathematical optimization model for construction example of algebra system is established. Secondly, an improved harmony search algorithm based on NGHS algorithm (INGHS is proposed to find as more solutions as possible for the optimization model; in the proposed INGHS algorithm, to achieve the balance between exploration power and exploitation power in the search process, a global best strategy and parameters dynamic adjustment method are present. Finally, nine construction examples of algebra system are used to evaluate the optimization model and performance of INGHS. The experimental results show that the proposed algorithm has strong performance for solving complex construction example problems of algebra system.

  9. 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

  10. Real algebraic geometry

    CERN Document Server

    Bochnak, Jacek; Roy, Marie-Françoise

    1998-01-01

    This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.

  11. Algebra de Clifford

    Directory of Open Access Journals (Sweden)

    María Carolina Spinel G.

    1990-01-01

    Con esta base, en posteriores artículos de divulgación, presentaremos algunas aplicaciones que muestren la ventaja de su empleo en la descripción de sistema físico. Dado el amplio conocimiento que se tiene de los espacios vectoriales. La estructura y propiedades del algebra de Clifford suele presentarse con base en los elementos de un espacio vectorial. En esta dirección, en la sección 2 se define la notación y se describe la estructura de un algebra de Clifford Gn, introduciendo con detalle las operaciones básicas entre los elementos del álgebra. La sección 3 se dedica a describir una base tensorial de Gn.

  12. Split Malcev algebras

    Indian Academy of Sciences (India)

    project of the Spanish Ministerio de Educación y Ciencia MTM2007-60333. References. [1] Calderón A J, On split Lie algebras with symmetric root systems, Proc. Indian. Acad. Sci (Math. Sci.) 118(2008) 351–356. [2] Calderón A J, On split Lie triple systems, Proc. Indian. Acad. Sci (Math. Sci.) 119(2009). 165–177.

  13. Algebra of Majorana doubling.

    Science.gov (United States)

    Lee, Jaehoon; Wilczek, Frank

    2013-11-27

    Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.

  14. The Algebra Artist

    Science.gov (United States)

    Beigie, Darin

    2014-01-01

    Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…

  15. Fundamentals of linear algebra

    CERN Document Server

    Dash, Rajani Ballav

    2008-01-01

    FUNDAMENTALS OF LINEAR ALGEBRA is a comprehensive Text Book, which can be used by students and teachers of All Indian Universities. The Text has easy, understandable form and covers all topics of UGC Curriculum. There are lots of worked out examples which helps the students in solving the problems without anybody's help. The Problem sets have been designed keeping in view of the questions asked in different examinations.

  16. Algebras of Information States

    Czech Academy of Sciences Publication Activity Database

    Punčochář, Vít

    2017-01-01

    Roč. 27, č. 5 (2017), s. 1643-1675 ISSN 0955-792X R&D Projects: GA ČR(CZ) GC16-07954J Institutional support: RVO:67985955 Keywords : information states * relational semantics * algebraic semantics * intuitionistic logic * inquisitive disjunction Subject RIV: AA - Philosophy ; Religion OBOR OECD: Philosophy, History and Philosophy of science and technology Impact factor: 0.909, year: 2016

  17. Clifford Algebras and Spinors

    International Nuclear Information System (INIS)

    Todorov, Ivan

    2010-12-01

    Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses. It has a more mathematical flavour than the over twenty-six-year-old Introduction to Majorana masses [M84] and includes historical notes and biographical data on past participants in the story. (author)

  18. Algebra & trigonometry II essentials

    CERN Document Server

    REA, Editors of

    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. Algebra & Trigonometry II includes logarithms, sequences and series, permutations, combinations and probability, vectors, matrices, determinants and systems of equations, mathematica

  19. Modern algebra essentials

    CERN Document Server

    Lutfiyya, Lutfi A

    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. Modern Algebra includes set theory, operations, relations, basic properties of the integers, group theory, and ring theory.

  20. Irrational "Coefficients" in Renaissance Algebra.

    Science.gov (United States)

    Oaks, Jeffrey A

    2017-06-01

    Argument From the time of al-Khwārizmī in the ninth century to the beginning of the sixteenth century algebraists did not allow irrational numbers to serve as coefficients. To multiply by x, for instance, the result was expressed as the rhetorical equivalent of . The reason for this practice has to do with the premodern concept of a monomial. The coefficient, or "number," of a term was thought of as how many of that term are present, and not as the scalar multiple that we work with today. Then, in sixteenth-century Europe, a few algebraists began to allow for irrational coefficients in their notation. Christoff Rudolff (1525) was the first to admit them in special cases, and subsequently they appear more liberally in Cardano (1539), Scheubel (1550), Bombelli (1572), and others, though most algebraists continued to ban them. We survey this development by examining the texts that show irrational coefficients and those that argue against them. We show that the debate took place entirely in the conceptual context of premodern, "cossic" algebra, and persisted in the sixteenth century independent of the development of the new algebra of Viète, Decartes, and Fermat. This was a formal innovation violating prevailing concepts that we propose could only be introduced because of the growing autonomy of notation from rhetorical text.

  1. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations

    Institute of Scientific and Technical Information of China (English)

    WANG; Shunjin; ZHANG; Hua

    2006-01-01

    The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system.The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,and a new algorithm-algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method.In the new algorithm,the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator.The exact analytical piece-like solution of the ordinary differential equations is expressd in terms of Taylor series with a local convergent radius,and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.

  2. 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.

  3. 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.)

  4. Categorical Algebra and its Applications

    CERN Document Server

    1988-01-01

    Categorical algebra and its applications contain several fundamental papers on general category theory, by the top specialists in the field, and many interesting papers on the applications of category theory in functional analysis, algebraic topology, algebraic geometry, general topology, ring theory, cohomology, differential geometry, group theory, mathematical logic and computer sciences. The volume contains 28 carefully selected and refereed papers, out of 96 talks delivered, and illustrates the usefulness of category theory today as a powerful tool of investigation in many other areas.

  5. 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.

  6. Applications of Computer Algebra Conference

    CERN Document Server

    Martínez-Moro, Edgar

    2017-01-01

    The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.

  7. Chiral algebras for trinion theories

    International Nuclear Information System (INIS)

    Lemos, Madalena; Peelaers, Wolfger

    2015-01-01

    It was recently understood that one can identify a chiral algebra in any four-dimensional N=2 superconformal theory. In this note, we conjecture the full set of generators of the chiral algebras associated with the T n theories. The conjecture is motivated by making manifest the critical affine module structure in the graded partition function of the chiral algebras, which is computed by the Schur limit of the superconformal index for T n theories. We also explicitly construct the chiral algebra arising from the T 4 theory. Its null relations give rise to new T 4 Higgs branch chiral ring relations.

  8. Computational aspects of algebraic curves

    CERN Document Server

    Shaska, Tanush

    2005-01-01

    The development of new computational techniques and better computing power has made it possible to attack some classical problems of algebraic geometry. The main goal of this book is to highlight such computational techniques related to algebraic curves. The area of research in algebraic curves is receiving more interest not only from the mathematics community, but also from engineers and computer scientists, because of the importance of algebraic curves in applications including cryptography, coding theory, error-correcting codes, digital imaging, computer vision, and many more.This book cove

  9. Students’ Algebraic Reasonsing In Solving Mathematical Problems With Adversity Quotient

    Science.gov (United States)

    Aryani, F.; Amin, S. M.; Sulaiman, R.

    2018-01-01

    Algebraic reasoning is a process in which students generalize mathematical ideas from a set of particular instances and express them in increasingly formal and age-appropriate ways. Using problem solving approach to develop algebraic reasoning of mathematics may enhace the long-term learning trajectory of the majority students. The purpose of this research was to describe the algebraic reasoning of quitter, camper, and climber junior high school students in solving mathematical problems. This research used qualitative descriptive method. Subjects were determined by purposive sampling. The technique of collecting data was done by task-based interviews.The results showed that the algebraic reasoning of three students in the process of pattern seeking by identifying the things that are known and asked in a similar way. But three students found the elements of pattern recognition in different ways or method. So, they are generalize the problem of pattern formation with different ways. The study of algebraic reasoning and problem solving can be a learning paradigm in the improve students’ knowledge and skills in algebra work. The goal is to help students’ improve academic competence, develop algebraic reasoning in problem solving.

  10. 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)

  11. Inequalities, assessment and computer algebra

    Science.gov (United States)

    Sangwin, Christopher J.

    2015-01-01

    The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary curricula. We consider the formal mathematical processes by which such inequalities are solved, and we consider the notation and syntax through which solutions are expressed. We review the extent to which current CAS can accurately solve these inequalities, and the form given to the solutions by the designers of this software. Finally, we discuss the functionality needed to deal with students' answers, i.e. to establish equivalence (or otherwise) of expressions representing unions of intervals. We find that while contemporary CAS accurately solve inequalities there is a wide variety of notation used.

  12. Algebraic Varieties and System Design

    DEFF Research Database (Denmark)

    Aabrandt, Andreas

    of cover ideals of hypergraphs, the topological ranking demonstrates the non-trivial decisions that needs to be considered in system design. All the methods developed here have an underlying common structure, namely that they all appear at solution sets for systems of polynomials. These solution sets......Design and analysis of networks have many applications in the engineering sciences. This dissertation seeks to contribute to the methods used in the analysis of networks with a view towards assisting decision making processes. Networks are initially considered as objects in the category of graphs...... and later as objects in the category of hypergraphs. The connection with the category of simplicial pairs become apparent when the topology is analyzed using homological algebra. A topological ranking is developed that measures the ability of the network to stay path-connected. Combined with the analysis...

  13. 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)

  14. 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…

  15. 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.

  16. 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.

  17. A modal characterization of Peirce algebras

    NARCIS (Netherlands)

    M. de Rijke (Maarten)

    1995-01-01

    textabstractPeirce algebras combine sets, relations and various operations linking the two in a unifying setting.This note offers a modal perspective on Peirce algebras.It uses modal logic to characterize the full Peirce algebras.

  18. Quantum deformation of the affine transformation algebra

    International Nuclear Information System (INIS)

    Aizawa, N.; Sato, Haru-Tada

    1994-01-01

    We discuss a quantum deformation of the affine transformation algebra in one-dimensional space. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators. (orig.)

  19. Use of regularized algebraic methods in tomographic reconstruction

    International Nuclear Information System (INIS)

    Koulibaly, P.M.; Darcourt, J.; Blanc-Ferraud, L.; Migneco, O.; Barlaud, M.

    1997-01-01

    The algebraic methods are used in emission tomography to facilitate the compensation of attenuation and of Compton scattering. We have tested on a phantom the use of a regularization (a priori introduction of information), as well as the taking into account of spatial resolution variation with the depth (SRVD). Hence, we have compared the performances of the two methods by back-projection filtering (BPF) and of the two algebraic methods (AM) in terms of FWHM (by means of a point source), of the reduction of background noise (σ/m) on the homogeneous part of Jaszczak's phantom and of reconstruction speed (time unit = BPF). The BPF methods make use of a grade filter (maximal resolution, no noise treatment), single or associated with a Hann's low-pass (f c = 0.4), as well as of an attenuation correction. The AM which embody attenuation and scattering corrections are, on one side, the OS EM (Ordered Subsets, partitioning and rearranging of the projection matrix; Expectation Maximization) without regularization or SRVD correction, and, on the other side, the OS MAP EM (Maximum a posteriori), regularized and embodying the SRVD correction. A table is given containing for each used method (grade, Hann, OS EM and OS MAP EM) the values of FWHM, σ/m and time, respectively. One can observe that the OS MAP EM algebraic method allows ameliorating both the resolution, by taking into account the SRVD in the reconstruction process and noise treatment by regularization. In addition, due to the OS technique the reconstruction times are acceptable

  20. Algebra in Cuneiform

    DEFF Research Database (Denmark)

    Høyrup, Jens

    with basic Assyriology but otherwise philological details are avoided. All of these texts are from the second half of the Old Babylonian period, that is, 1800–1600 BCE. It is indeed during this period that the “algebraic” discipline, and Babylonian mathematics in general, culminates. Even though a few texts...... particular culture. Finally, it describes the origin of the discipline and its impact in later mathematics, not least Euclid’s geometry and genuine algebra as created in medieval Islam and taken over in European medieval and Renaissance mathematics....

  1. Algebraic topology and concurrency

    DEFF Research Database (Denmark)

    Fajstrup, Lisbeth; Raussen, Martin; Goubault, Eric

    2006-01-01

    We show in this article that some concepts from homotopy theory, in algebraic topology,are relevant for studying concurrent programs. We exhibit a natural semantics of semaphore programs, based on partially ordered topological spaces, which are studied up to “elastic deformation” or homotopy...... differences between ordinary and directed homotopy through examples. We also relate the topological view to a combinatorial view of concurrent programs closer to transition systems, through the notion of a cubical set. Finally we apply some of these concepts to the proof of the safeness of a two...

  2. Elements of abstract algebra

    CERN Document Server

    Clark, Allan

    1984-01-01

    This concise, readable, college-level text treats basic abstract algebra in remarkable depth and detail. An antidote to the usual surveys of structure, the book presents group theory, Galois theory, and classical ideal theory in a framework emphasizing proof of important theorems.Chapter I (Set Theory) covers the basics of sets. Chapter II (Group Theory) is a rigorous introduction to groups. It contains all the results needed for Galois theory as well as the Sylow theorems, the Jordan-Holder theorem, and a complete treatment of the simplicity of alternating groups. Chapter III (Field Theory)

  3. 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

  4. Handbook of algebra

    CERN Document Server

    Hazewinkel, M

    2008-01-01

    Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it i

  5. Flow time prediction for a single-server order picking workstation using aggregate process times

    NARCIS (Netherlands)

    Andriansyah, R.; Etman, L.F.P.; Rooda, J.E.

    2010-01-01

    In this paper we propose a simulation modeling approach based on aggregate process times for the performance analysis of order picking workstations in automated warehouses. The aggregate process time distribution is calculated from tote arrival and departure times. We refer to the aggregate process

  6. Real time loss detection for SNM in process

    International Nuclear Information System (INIS)

    Candy, J.V.; Dunn, D.R.; Gavel, D.T.

    1980-01-01

    This paper discusses the basis of a design for real time special nuclear material (SNM) loss detectors. The design utilizes process measurements and signal processing techniques to produce a timely estimate of material loss. A state estimator is employed as the primary signal processing algorithm. Material loss is indicated by changes in the states or process innovations (residuals). The design philosophy is discussed in the context of these changes

  7. 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.

  8. 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

  9. 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

  10. Residence time modeling of hot melt extrusion processes.

    Science.gov (United States)

    Reitz, Elena; Podhaisky, Helmut; Ely, David; Thommes, Markus

    2013-11-01

    The hot melt extrusion process is a widespread technique to mix viscous melts. The residence time of material in the process frequently determines the product properties. An experimental setup and a corresponding mathematical model were developed to evaluate residence time and residence time distribution in twin screw extrusion processes. The extrusion process was modeled as the convolution of a mass transport process described by a Gaussian probability function, and a mixing process represented by an exponential function. The residence time of the extrusion process was determined by introducing a tracer at the extruder inlet and measuring the tracer concentration at the die. These concentrations were fitted to the residence time model, and an adequate correlation was found. Different parameters were derived to characterize the extrusion process including the dead time, the apparent mixing volume, and a transport related axial mixing. A 2(3) design of experiments was performed to evaluate the effect of powder feed rate, screw speed, and melt viscosity of the material on the residence time. All three parameters affect the residence time of material in the extruder. In conclusion, a residence time model was developed to interpret experimental data and to get insights into the hot melt extrusion process. Copyright © 2013 Elsevier B.V. All rights reserved.

  11. Disability Reconsideration Average Processing Time (in Days) (Excludes technical denials)

    Data.gov (United States)

    Social Security Administration — A presentation of the overall cumulative number of elapsed days (including processing time for transit, medical determinations, and SSA quality review) from the date...

  12. 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

  13. Current algebra; Algebre des courants

    Energy Technology Data Exchange (ETDEWEB)

    Jacob, M [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1967-07-01

    The first three chapters of these lecture notes are devoted to generalities concerning current algebra. The weak currents are defined, and their main properties given (V-A hypothesis, conserved vector current, selection rules, partially conserved axial current,...). The SU (3) x SU (3) algebra of Gell-Mann is introduced, and the general properties of the non-leptonic weak Hamiltonian are discussed. Chapters 4 to 9 are devoted to some important applications of the algebra. First one proves the Adler- Weisberger formula, in two different ways, by either the infinite momentum frame, or the near-by singularities method. In the others chapters, the latter method is the only one used. The following topics are successively dealt with: semi leptonic decays of K mesons and hyperons, Kroll- Ruderman theorem, non leptonic decays of K mesons and hyperons ( {delta}I = 1/2 rule), low energy theorems concerning processes with emission (or absorption) of a pion or a photon, super-convergence sum rules, and finally, neutrino reactions. (author) [French] La premiere partie de ce cours (trois premiers chapitres), traite des generalites concernant l'algebre de courants. Apres une definition rapide des courants faibles et un rappel de leurs proprietes (hypothese V-A, conservation du courant vecteur, regles de selection, courant axial partiellement conserve,...), l'on introduit l'algebre de Gell-Mann SU (3) x SU (3), et discute les proprietes generales de l'Hamiltonien faible non leptonique. Les chapitres IV a IX sont consacres a des applications importantes de l'algebre des courants. En premier lieu l'on demontre la formule de Adler et Weisberger, par deux methodes differentes, celle dite du repere de moment infini et celle des singularites proches. Cette derniere est seule utilisee dans la suite. Puis, l'on traite successivement les problemes suivants: desintegrations semi-leptoniques des mesons K et des hyperons, theoreme de Kroll-Ruderman, desintegrations non leptoniques des mesons

  14. 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

  15. Analysis and solution of algebraic-differential equations of the steam generation processes; Analisis y resolucion de ecuaciones algebraico-diferenciales de los procesos de generacion de vapor

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez Herrera, Juan Anibal

    1996-10-01

    This work presents the construction, analysis and solution of an equipment`s network in steady and dynamic state from: a) The mathematical models of individual equipment and of their geometry. b) The topology let interconnections between equipment. c) The selection of a numerical method to solve simultaneously the mathematical models. The selected mathematical models represent the cycle boiler-superheater. These models were taken from the MICROTERM-300 modular simulator, which contains the simplified models of the process (feedwater, boiler, turbines, etc.) of the thermoelectric plant Francisco Perez Rios from Tula Hidalgo, Mexico. This work was developed in the following stages: 1.- The selection of an appropiate numerical integration method to solve simultaneously the algebraic and differential equations of the equipment conforming the cycle boiler-superheater. 2.- The adaptation of individual mathematical models to allow changes in their geometry, operating conditions and different forms of connection. Also, this models were modified to have a representation of the equations to allow their analysis and an efficient organization to get their solution. 3.- The application of two computer-aided tools to trace possible coding errors in the mathematical models: a) A syntax analyzer which detect assignation and reference errors of variables. b) A structural analyzer to obtain the structural matrix, which relate the variables and the equations in a model. During this stage some improvements to these computer-aided tools were suggested. 4.- The individual testing of each mathematical model in steady and dynamic state in order to: a) Validate the mathematical models. b) Analyze the behavior of the variables of the mathematical models with different parameters, different operating conditions and different initial conditions. 5.- Lastly, the coupling between equipment analyzed to form an equipment`s network what represent the cycle boiler-superheater and the testing in

  16. High-speed optical signal processing using time lenses

    DEFF Research Database (Denmark)

    Galili, Michael; Hu, Hao; Guan, Pengyu

    2015-01-01

    This paper will discuss time lenses and their broad range of applications. A number of recent demonstrations of complex high-speed optical signal processing using time lenses will be outlined with focus on the operating principle.......This paper will discuss time lenses and their broad range of applications. A number of recent demonstrations of complex high-speed optical signal processing using time lenses will be outlined with focus on the operating principle....

  17. 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...

  18. Templates for Linear Algebra Problems

    NARCIS (Netherlands)

    Bai, Z.; Day, D.; Demmel, J.; Dongarra, J.; Gu, M.; Ruhe, A.; Vorst, H.A. van der

    1995-01-01

    The increasing availability of advanced-architecture computers is having a very signicant eect on all spheres of scientic computation, including algorithm research and software development in numerical linear algebra. Linear algebra {in particular, the solution of linear systems of equations and

  19. Differential Equation over Banach Algebra

    OpenAIRE

    Kleyn, Aleks

    2018-01-01

    In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.

  20. Smarandache hyper BCC-algebra

    OpenAIRE

    Ahadpanah, A.; Borumand Saeid, A.

    2011-01-01

    In this paper, we define the Smarandache hyper BCC-algebra, and Smarandache hyper BCC-ideals of type 1, 2, 3 and 4. We state and prove some theorems in Smarandache hyper BCC -algebras, and then we determine the relationships between these hyper ideals.

  1. Tilting-connected symmetric algebras

    OpenAIRE

    Aihara, Takuma

    2010-01-01

    The notion of silting mutation was introduced by Iyama and the author. In this paper we mainly study silting mutation for self-injective algebras and prove that any representation-finite symmetric algebra is tilting-connected. Moreover we give some sufficient conditions for a Bongartz-type Lemma to hold for silting objects.

  2. Algebraic study of chiral anomalies

    Indian Academy of Sciences (India)

    2012-06-14

    Jun 14, 2012 ... They form a group G which acts on the (affine) space of ... The curvature F of A is defined by (notice that in this paper the bracket is defined ... This purely algebraic formulation easily extends to the consideration of the Lie algebra of vector .... namely the case of perturbatively renormalizable theories in four ...

  3. Logarithmic residues in Banach algebras

    NARCIS (Netherlands)

    H. Bart (Harm); T. Ehrhardt; B. Silbermann

    1994-01-01

    textabstractLet f be an analytic Banach algebra valued function and suppose that the contour integral of the logarithmic derivative f′f-1 around a Cauchy domain D vanishes. Does it follow that f takes invertible values on all of D? For important classes of Banach algebras, the answer is positive. In

  4. Galois Connections for Flow Algebras

    DEFF Research Database (Denmark)

    Filipiuk, Piotr; Terepeta, Michal Tomasz; Nielson, Hanne Riis

    2011-01-01

    to the approach taken by Monotone Frameworks and other classical analyses. We present a generic framework for static analysis based on flow algebras and program graphs. Program graphs are often used in Model Checking to model concurrent and distributed systems. The framework allows to induce new flow algebras...

  5. The Algebra of Complex Numbers.

    Science.gov (United States)

    LePage, Wilbur R.

    This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

  6. 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)

  7. Learning Algebra from Worked Examples

    Science.gov (United States)

    Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.

    2014-01-01

    For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

  8. Covariant representations of nuclear *-algebras

    International Nuclear Information System (INIS)

    Moore, S.M.

    1978-01-01

    Extensions of the Csup(*)-algebra theory for covariant representations to nuclear *-algebra are considered. Irreducible covariant representations are essentially unique, an invariant state produces a covariant representation with stable vacuum, and the usual relation between ergodic states and covariant representations holds. There exist construction and decomposition theorems and a possible relation between derivations and covariant representations

  9. Robust algebraic image enhancement for intelligent control systems

    Science.gov (United States)

    Lerner, Bao-Ting; Morrelli, Michael

    1993-01-01

    Robust vision capability for intelligent control systems has been an elusive goal in image processing. The computationally intensive techniques a necessary for conventional image processing make real-time applications, such as object tracking and collision avoidance difficult. In order to endow an intelligent control system with the needed vision robustness, an adequate image enhancement subsystem capable of compensating for the wide variety of real-world degradations, must exist between the image capturing and the object recognition subsystems. This enhancement stage must be adaptive and must operate with consistency in the presence of both statistical and shape-based noise. To deal with this problem, we have developed an innovative algebraic approach which provides a sound mathematical framework for image representation and manipulation. Our image model provides a natural platform from which to pursue dynamic scene analysis, and its incorporation into a vision system would serve as the front-end to an intelligent control system. We have developed a unique polynomial representation of gray level imagery and applied this representation to develop polynomial operators on complex gray level scenes. This approach is highly advantageous since polynomials can be manipulated very easily, and are readily understood, thus providing a very convenient environment for image processing. Our model presents a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets.

  10. K-theory for group C*-algebras and semigroup C*-algebras

    CERN Document Server

    Cuntz, Joachim; Li, Xin; Yu, Guoliang

    2017-01-01

    This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions.

  11. A Process For Performance Evaluation Of Real-Time Systems

    Directory of Open Access Journals (Sweden)

    Andrew J. Kornecki

    2003-12-01

    Full Text Available Real-time developers and engineers must not only meet the system functional requirements, but also the stringent timing requirements. One of the critical decisions leading to meeting these timing requirements is the selection of an operating system under which the software will be developed and run. Although there is ample documentation on real-time systems performance and evaluation, little can be found that combines such information into an efficient process for use by developers. As the software industry moves towards clearly defined processes, creation of appropriate guidelines describing a process for performance evaluation of real-time system would greatly benefit real-time developers. This technology transition research focuses on developing such a process. PROPERT (PROcess for Performance Evaluation of Real Time systems - the process described in this paper - is based upon established techniques for evaluating real-time systems. It organizes already existing real-time performance criteria and assessment techniques in a manner consistent with a well-formed process, based on the Personal Software Process concepts.

  12. Method of parallel processing in SANPO real time system

    International Nuclear Information System (INIS)

    Ostrovnoj, A.I.; Salamatin, I.M.

    1981-01-01

    A method of parellel processing in SANPO real time system is described. Algorithms of data accumulation and preliminary processing in this system as a parallel processes using a specialized high level programming language are described. Hierarchy of elementary processes are also described. It provides the synchronization of concurrent processes without semaphors. The developed means are applied to the systems of experiment automation using SM-3 minicomputers [ru

  13. An efficient solution of real-time data processing for multi-GNSS network

    Science.gov (United States)

    Gong, Xiaopeng; Gu, Shengfeng; Lou, Yidong; Zheng, Fu; Ge, Maorong; Liu, Jingnan

    2017-12-01

    Global navigation satellite systems (GNSS) are acting as an indispensable tool for geodetic research and global monitoring of the Earth, and they have been rapidly developed over the past few years with abundant GNSS networks, modern constellations, and significant improvement in mathematic models of data processing. However, due to the increasing number of satellites and stations, the computational efficiency becomes a key issue and it could hamper the further development of GNSS applications. In this contribution, this problem is overcome from the aspects of both dense linear algebra algorithms and GNSS processing strategy. First, in order to fully explore the power of modern microprocessors, the square root information filter solution based on the blocked QR factorization employing as many matrix-matrix operations as possible is introduced. In addition, the algorithm complexity of GNSS data processing is further decreased by centralizing the carrier-phase observations and ambiguity parameters, as well as performing the real-time ambiguity resolution and elimination. Based on the QR factorization of the simulated matrix, we can conclude that compared to unblocked QR factorization, the blocked QR factorization can greatly improve processing efficiency with a magnitude of nearly two orders on a personal computer with four 3.30 GHz cores. Then, with 82 globally distributed stations, the processing efficiency is further validated in multi-GNSS (GPS/BDS/Galileo) satellite clock estimation. The results suggest that it will take about 31.38 s per epoch for the unblocked method. While, without any loss of accuracy, it only takes 0.50 and 0.31 s for our new algorithm per epoch for float and fixed clock solutions, respectively.

  14. Basic algebraic geometry, v.2

    CERN Document Server

    Shafarevich, Igor Rostislavovich

    1994-01-01

    Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...

  15. 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

  16. 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.

  17. 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...

  18. Representations of affine Hecke algebras

    CERN Document Server

    Xi, Nanhua

    1994-01-01

    Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest

  19. A Continuous Formulation for Logical Decisions in Differential Algebraic Systems using Mathematical Programs with Complementarity Constraints

    Directory of Open Access Journals (Sweden)

    Kody M. Powell

    2016-03-01

    Full Text Available This work presents a methodology to represent logical decisions in differential algebraic equation simulation and constrained optimization problems using a set of continuous algebraic equations. The formulations may be used when state variables trigger a change in process dynamics, and introduces a pseudo-binary decision variable, which is continuous, but should only have valid solutions at values of either zero or one within a finite time horizon. This formulation enables dynamic optimization problems with logical disjunctions to be solved by simultaneous solution methods without using methods such as mixed integer programming. Several case studies are given to illustrate the value of this methodology including nonlinear model predictive control of a chemical reactor using a surge tank with overflow to buffer disturbances in feed flow rate. Although this work contains novel methodologies for solving dynamic algebraic equation (DAE constrained problems where the system may experience an abrupt change in dynamics that may otherwise require a conditional statement, there remain substantial limitations to this methodology, including a limited domain where problems may converge and the possibility for ill-conditioning. Although the problems presented use only continuous algebraic equations, the formulation has inherent non-smoothness. Hence, these problems must be solved with care and only in select circumstances, such as in simulation or situations when the solution is expected to be near the solver’s initial point.

  20. 12 CFR 404.5 - Time for processing.

    Science.gov (United States)

    2010-01-01

    ... 12 Banks and Banking 4 2010-01-01 2010-01-01 false Time for processing. 404.5 Section 404.5 Banks and Banking EXPORT-IMPORT BANK OF THE UNITED STATES INFORMATION DISCLOSURE Procedures for Disclosure of Records Under the Freedom of Information Act. § 404.5 Time for processing. (a) General. Ex-Im Bank...

  1. Simulation of Simple Controlled Processes with Dead-Time.

    Science.gov (United States)

    Watson, Keith R.; And Others

    1985-01-01

    The determination of closed-loop response of processes containing dead-time is typically not covered in undergraduate process control, possibly because the solution by Laplace transforms requires the use of Pade approximation for dead-time, which makes the procedure lengthy and tedious. A computer-aided method is described which simplifies the…

  2. The time course of attentional modulation on emotional conflict processing.

    Science.gov (United States)

    Zhou, Pingyan; Yang, Guochun; Nan, Weizhi; Liu, Xun

    2016-01-01

    Cognitive conflict resolution is critical to human survival in a rapidly changing environment. However, emotional conflict processing seems to be particularly important for human interactions. This study examined whether the time course of attentional modulation on emotional conflict processing was different from cognitive conflict processing during a flanker task. Results showed that emotional N200 and P300 effects, similar to colour conflict processing, appeared only during the relevant task. However, the emotional N200 effect preceded the colour N200 effect, indicating that emotional conflict can be identified earlier than cognitive conflict. Additionally, a significant emotional N100 effect revealed that emotional valence differences could be perceived during early processing based on rough aspects of input. The present data suggest that emotional conflict processing is modulated by top-down attention, similar to cognitive conflict processing (reflected by N200 and P300 effects). However, emotional conflict processing seems to have more time advantages during two different processing stages.

  3. (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.

  4. 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

  5. Option Pricing with Time-changed Lévy Processes

    DEFF Research Database (Denmark)

    Klingler, Sven; Kim, Young Shin; Rachev, Svetlozar T.

    2013-01-01

    In this article, we introduce two new six-parameter processes based on time-changing tempered stable distributions and develop an option pricing model based on these processes. This model provides a good fit to observed option prices. To demonstrate the advantages of the new processes, we conduct...

  6. Efficient Processing of Multiple DTW Queries in Time Series Databases

    DEFF Research Database (Denmark)

    Kremer, Hardy; Günnemann, Stephan; Ivanescu, Anca-Maria

    2011-01-01

    . In many of today’s applications, however, large numbers of queries arise at any given time. Existing DTW techniques do not process multiple DTW queries simultaneously, a serious limitation which slows down overall processing. In this paper, we propose an efficient processing approach for multiple DTW...... for multiple DTW queries....

  7. Data-aware remaining time prediction of business process instances

    NARCIS (Netherlands)

    Polato, M.; Sperduti, A.; Burattin, A.; Leoni, de M.

    2014-01-01

    Accurate prediction of the completion time of a business process instance would constitute a valuable tool when managing processes under service level agreement constraints. Such prediction, however, is a very challenging task. A wide variety of factors could influence the trend of a process

  8. Real-time multiparameter pulse processing with decision tables

    International Nuclear Information System (INIS)

    Hull, K.; Griffin, H.

    1986-01-01

    Decision tables offer several advantages over other real-time multiparameter, data processing techniques. These include very high collection rates, minimum number of computer instructions, rates independent of the number of conditions applied per parameter, ease of adding or removing conditions during a session, and simplicity of implementation. Decisions table processing is important in multiparameter nuclear spectroscopy, coincidence experiments, multiparameter pulse processing (HgI 2 resolution enhancement, pulse discrimination, timing spectroscopy), and other applications can be easily implemented. (orig.)

  9. Higher-spin extended conformal algebras and W-gravities

    International Nuclear Information System (INIS)

    Hull, C.M.

    1991-01-01

    The construction of classical W 3 gravity is reviewed. It is suggested that the hidden symmetry for quantum W 3 gravity in the chiral gauge is not SL(3, R) but a group contraction of this, ISL(2, R). This is extended to W N gravity, and the case of W 4 gravity is presented in detail. The gauge transformations are realized on D free bosons, with the spin-n conserved current (2 ≤ n ≤ N) taking the form d sub(i i ...i n ) δ + Φ sup(i 1 ) δ + Φ sup(i n ) for some constant tensor d sub(i i ...i n ). The d-tensors must satisfy N-2 non-linear algebraic constraints and these constraints are shown to be satisfied if the d-tensors are taken to be the structure-tensors of an Nth degree Jordan algebra. The relation with Jordan algebras is used to give solutions of the d-tensor constraints for any value of D, N. The free-boson construction of the W N algebras is generalized to give a Sugaware-type construction of a large class of classical extended conformal algebras. The chiral gauging of any classical extended conformal algebra is shown to require only a linear Noether coupling to world-sheet gauge-fields, while gauging a non-chiral algebra in general leads to a non-polynomial action. A number of examples are examined, including W ∞ W-supergravity, Knizhnik-Berschadsky supergravity and 'W N/M ' algebras. Theories of higher-spin W-gravity of the type described are only possible in one and two space-time dimensions, and the one-dimensional cases is briefly discussed. The covariant formulation of W-gravity is briefly discussed and the relation between classical and quantum extended conformal algebras is analyzed. (orig.)

  10. 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

  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. 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

  13. An algebraic perspective to single-transponder underwater navigation

    DEFF Research Database (Denmark)

    Jouffroy, Jerome; Reger, Johann

    This paper studies the position estimation of an underwater vehicle using a single acoustic transponder. The chosen estimation approach is based on nonlinear differential algebraic methods which allow to express very simply conditions for observability. These are then used in combination with an ...... with an integrator-based time-derivative estimation technique to design an algebraic estimator, which, contrary to asymptotic observers, does not require sometimes tedious convergence verification. Simple simulation results are presented to illustrate the approach....

  14. 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)

  15. Sampling and Timing: A Task for the Environmetal Process

    NARCIS (Netherlands)

    Hilderink, G.H.; Broenink, Johannes F.

    2003-01-01

    Sampling and timing is considered a responsibility of the environment of controller software. In this paper we will illustrate a concept whereby an environmental process and multi-way events play an important role in applying timing for untimed CSP software architectures. We use this timing concept

  16. Finite-Time Approach to Microeconomic and Information Exchange Processes

    Directory of Open Access Journals (Sweden)

    Serghey A. Amelkin

    2009-07-01

    Full Text Available Finite-time approach allows one to optimize regimes of processes in macrosystems when duration of the processes is restricted. Driving force of the processes is difference of intensive variables: temperatures in thermodynamics, values in economics, etc. In microeconomic systems two counterflow fluxes appear due to the only driving force. They are goods and money fluxes. Another possible case is two fluxes with the same direction. The processes of information exchange can be described by this formalism.

  17. Algebra for cryptologists

    CERN Document Server

    Meijer, Alko R

    2016-01-01

    This textbook provides an introduction to the mathematics on which modern cryptology is based. It covers not only public key cryptography, the glamorous component of modern cryptology, but also pays considerable attention to secret key cryptography, its workhorse in practice. Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major disciplines: computer science, electronic engineering and mathematics. Within mathematics, group theory, the theory of finite fields, and elementary number theory as well as some topics not normally covered in courses in algebra, such as the theory of Boolean functions and Shannon theory, are involved. Although essentially self-contained, a degree of mathematical maturity on the part of the reader is assumed, corresponding to his o...

  18. 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 ...

  19. Reducing Design Cycle Time and Cost Through Process Resequencing

    Science.gov (United States)

    Rogers, James L.

    2004-01-01

    In today's competitive environment, companies are under enormous pressure to reduce the time and cost of their design cycle. One method for reducing both time and cost is to develop an understanding of the flow of the design processes and the effects of the iterative subcycles that are found in complex design projects. Once these aspects are understood, the design manager can make decisions that take advantage of decomposition, concurrent engineering, and parallel processing techniques to reduce the total time and the total cost of the design cycle. One software tool that can aid in this decision-making process is the Design Manager's Aid for Intelligent Decomposition (DeMAID). The DeMAID software minimizes the feedback couplings that create iterative subcycles, groups processes into iterative subcycles, and decomposes the subcycles into a hierarchical structure. The real benefits of producing the best design in the least time and at a minimum cost are obtained from sequencing the processes in the subcycles.

  20. 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