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

Fast Erasure-and error decoding of algebraic geometry codes up to the Feng-Rao bound

DEFF Research Database (Denmark)

Høholdt, Tom; Jensen, Helge Elbrønd; Sakata, Shojiro

1998-01-01

This correspondence gives an errata (that is erasure-and error-) decoding algorithm of one-point algebraic-geometry codes up to the Feng-Rao designed minimum distance using Sakata's multidimensional generalization of the Berlekamp-Massey algorithm and the voting procedure of Feng and Rao....

ASAP - A symbolic algebra package for accelerator design

International Nuclear Information System (INIS)

Bozoki, E.; Friedman, A.; Ben-Zvi, I.

1991-01-01

The design of a modern accelerator is a complicated task that involves the integration of many devices. As a consequence many parameters must be optimized in order to achieve a satisfactory result. Even the design of a simple subsystem, such as a bending system, requires that the designer will pick a successful choice from a wide range of alternatives. Usually, the task is too large to allow an analytical design, and the designer has to use a computer code (such as MAD or TRANSPORT) to simulate the system and numerically find the desired conditions. The disadvantages of this numerical method are, that (1) the solutions, i.e. the choice of the parameters may or may not be optimal and (2) each change in a parameter requires to recalculate the whole system, thus a detailed design is lengthy and costly. The authors report the conceptual design and primary implementation steps of a symbolic algebra program based on MACSYMA for the design of accelerators, storage rings and transport lines. The motivation for using symbolic algebra is discussed and a design case is presented that shows the advantage of this approach

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.

Algebraic coding theory over finite commutative rings

CERN Document Server

Dougherty, Steven T

2017-01-01

This book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings. It is the first to offer a comprehensive account on the subject. Coding theory has its origins in the engineering problem of effective electronic communication where the alphabet is generally the binary field. Since its inception, it has grown as a branch of mathematics, and has since been expanded to consider any finite field, and later also Frobenius rings, as its alphabet. This book presents a broad view of the subject as a branch of pure mathematics and relates major results to other fields, including combinatorics, number theory and ring theory. Suitable for graduate students, the book will be of interest to anyone working in the field of coding theory, as well as algebraists and number theorists looking to apply coding theory to their own work.

New features in the design code TLIE

International Nuclear Information System (INIS)

van Zeijts, J.

1993-01-01

We present features recently installed in the arbitrary-order accelerator design code TLIE. The code uses the MAD input language, and implements programmable extensions modeled after the C language that make it a powerful tool in a wide range of applications: from basic beamline design to high precision-high order design and even control room applications. The basic quantities important in accelerator design are easily accessible from inside the control language. Entities like parameters in elements (strength, current), transfer maps (either in Taylor series or in Lie algebraic form), lines, and beams (either as sets of particles or as distributions) are among the type of variables available. These variables can be set, used as arguments in subroutines, or just typed out. The code is easily extensible with new datatypes

LEGO: A modular accelerator design code

International Nuclear Information System (INIS)

Cai, Y.; Donald, M.; Irwin, J.; Yan, Y.

1997-08-01

An object-oriented accelerator design code has been designed and implemented in a simple and modular fashion. It contains all major features of its predecessors: TRACY and DESPOT. All physics of single-particle dynamics is implemented based on the Hamiltonian in the local frame of the component. Components can be moved arbitrarily in the three dimensional space. Several symplectic integrators are used to approximate the integration of the Hamiltonian. A differential algebra class is introduced to extract a Taylor map up to arbitrary order. Analysis of optics is done in the same way both for the linear and nonlinear case. Currently, the code is used to design and simulate the lattices of the PEP-II. It will also be used for the commissioning

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.

Performance analysis of a decoding algorithm for algebraic-geometry codes

DEFF Research Database (Denmark)

Høholdt, Tom; Jensen, Helge Elbrønd; Nielsen, Rasmus Refslund

1999-01-01

The fast decoding algorithm for one point algebraic-geometry codes of Sakata, Elbrond Jensen, and Hoholdt corrects all error patterns of weight less than half the Feng-Rao minimum distance. In this correspondence we analyze the performance of the algorithm for heavier error patterns. It turns out...

Designing Spreadsheet-Based Tasks for Purposeful Algebra

Science.gov (United States)

Ainley, Janet; Bills, Liz; Wilson, Kirsty

2005-01-01

We describe the design of a sequence of spreadsheet-based pedagogic tasks for the introduction of algebra in the early years of secondary schooling within the Purposeful Algebraic Activity project. This design combines two relatively novel features to bring a different perspective to research in the use of spreadsheets for the learning and…

Genetic hotels for the standard genetic code: evolutionary analysis based upon novel three-dimensional algebraic models.

Science.gov (United States)

José, Marco V; Morgado, Eberto R; Govezensky, Tzipe

2011-07-01

Herein, we rigorously develop novel 3-dimensional algebraic models called Genetic Hotels of the Standard Genetic Code (SGC). We start by considering the primeval RNA genetic code which consists of the 16 codons of type RNY (purine-any base-pyrimidine). Using simple algebraic operations, we show how the RNA code could have evolved toward the current SGC via two different intermediate evolutionary stages called Extended RNA code type I and II. By rotations or translations of the subset RNY, we arrive at the SGC via the former (type I) or via the latter (type II), respectively. Biologically, the Extended RNA code type I, consists of all codons of the type RNY plus codons obtained by considering the RNA code but in the second (NYR type) and third (YRN type) reading frames. The Extended RNA code type II, comprises all codons of the type RNY plus codons that arise from transversions of the RNA code in the first (YNY type) and third (RNR) nucleotide bases. Since the dimensions of remarkable subsets of the Genetic Hotels are not necessarily integer numbers, we also introduce the concept of algebraic fractal dimension. A general decoding function which maps each codon to its corresponding amino acid or the stop signals is also derived. The Phenotypic Hotel of amino acids is also illustrated. The proposed evolutionary paths are discussed in terms of the existing theories of the evolution of the SGC. The adoption of 3-dimensional models of the Genetic and Phenotypic Hotels will facilitate the understanding of the biological properties of the SGC.

Algebraic Algorithm Design and Local Search

National Research Council Canada - National Science Library

Graham, Robert

1996-01-01

.... Algebraic techniques have been applied successfully to algorithm synthesis by the use of algorithm theories and design tactics, an approach pioneered in the Kestrel Interactive Development System (KIDS...

FOURTH SEMINAR TO THE MEMORY OF D.N. KLYSHKO: Algebraic solution of the synthesis problem for coded sequences

Science.gov (United States)

Leukhin, Anatolii N.

2005-08-01

The algebraic solution of a 'complex' problem of synthesis of phase-coded (PC) sequences with the zero level of side lobes of the cyclic autocorrelation function (ACF) is proposed. It is shown that the solution of the synthesis problem is connected with the existence of difference sets for a given code dimension. The problem of estimating the number of possible code combinations for a given code dimension is solved. It is pointed out that the problem of synthesis of PC sequences is related to the fundamental problems of discrete mathematics and, first of all, to a number of combinatorial problems, which can be solved, as the number factorisation problem, by algebraic methods by using the theory of Galois fields and groups.

Design of deterministic interleaver for turbo codes

International Nuclear Information System (INIS)

Arif, M.A.; Sheikh, N.M.; Sheikh, A.U.H.

2008-01-01

The choice of suitable interleaver for turbo codes can improve the performance considerably. For long block lengths, random interleavers perform well, but for some applications it is desirable to keep the block length shorter to avoid latency. For such applications deterministic interleavers perform better. The performance and design of a deterministic interleaver for short frame turbo codes is considered in this paper. The main characteristic of this class of deterministic interleaver is that their algebraic design selects the best permutation generator such that the points in smaller subsets of the interleaved output are uniformly spread over the entire range of the information data frame. It is observed that the interleaver designed in this manner improves the minimum distance or reduces the multiplicity of first few spectral lines of minimum distance spectrum. Finally we introduce a circular shift in the permutation function to reduce the correlation between the parity bits corresponding to the original and interleaved data frames to improve the decoding capability of MAP (Maximum A Posteriori) probability decoder. Our solution to design a deterministic interleaver outperforms the semi-random interleavers and the deterministic interleavers reported in the literature. (author)

The genetic code as a periodic table: algebraic aspects.

Science.gov (United States)

Bashford, J D; Jarvis, P D

2000-01-01

The systematics of indices of physico-chemical properties of codons and amino acids across the genetic code are examined. Using a simple numerical labelling scheme for nucleic acid bases, A=(-1,0), C=(0,-1), G=(0,1), U=(1,0), data can be fitted as low order polynomials of the six coordinates in the 64-dimensional codon weight space. The work confirms and extends the recent studies by Siemion et al. (1995. BioSystems 36, 231-238) of the conformational parameters. Fundamental patterns in the data such as codon periodicities, and related harmonics and reflection symmetries, are here associated with the structure of the set of basis monomials chosen for fitting. Results are plotted using the Siemion one-step mutation ring scheme, and variants thereof. The connections between the present work, and recent studies of the genetic code structure using dynamical symmetry algebras, are pointed out.

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

Transoptr-a second order beam transport design code with automatic internal optimization and general constraints

International Nuclear Information System (INIS)

Heighway, E.A.

1980-07-01

A second order beam transport design code with parametric optimization is described. The code analyzes the transport of charged particle beams through a user defined magnet system. The magnet system parameters are varied (within user defined limits) until the properties of the transported beam and/or the system transport matrix match those properties requested by the user. The code uses matrix formalism to represent the transport elements and optimization is achieved using the variable metric method. Any constraints that can be expressed algebraically may be included by the user as part of his design. Instruction in the use of the program is given. (auth)

"ON ALGEBRAIC DECODING OF Q-ARY REED-MULLER AND PRODUCT REED-SOLOMON CODES"

Energy Technology Data Exchange (ETDEWEB)

SANTHI, NANDAKISHORE [Los Alamos National Laboratory

2007-01-22

We consider a list decoding algorithm recently proposed by Pellikaan-Wu for q-ary Reed-Muller codes RM{sub q}({ell}, m, n) of length n {le} q{sup m} when {ell} {le} q. A simple and easily accessible correctness proof is given which shows that this algorithm achieves a relative error-correction radius of {tau} {le} (1-{radical}{ell}q{sup m-1}/n). This is an improvement over the proof using one-point Algebraic-Geometric decoding method given in. The described algorithm can be adapted to decode product Reed-Solomon codes. We then propose a new low complexity recursive aJgebraic decoding algorithm for product Reed-Solomon codes and Reed-Muller codes. This algorithm achieves a relative error correction radius of {tau} {le} {Pi}{sub i=1}{sup m} (1 - {radical}k{sub i}/q). This algorithm is then proved to outperform the Pellikaan-Wu algorithm in both complexity and error correction radius over a wide range of code rates.

A Linear Algebra Framework for Static High Performance Fortran Code Distribution

Directory of Open Access Journals (Sweden)

Corinne Ancourt

1997-01-01

Full Text Available High Performance Fortran (HPF was developed to support data parallel programming for single-instruction multiple-data (SIMD and multiple-instruction multiple-data (MIMD machines with distributed memory. The programmer is provided a familiar uniform logical address space and specifies the data distribution by directives. The compiler then exploits these directives to allocate arrays in the local memories, to assign computations to elementary processors, and to migrate data between processors when required. We show here that linear algebra is a powerful framework to encode HPF directives and to synthesize distributed code with space-efficient array allocation, tight loop bounds, and vectorized communications for INDEPENDENT loops. The generated code includes traditional optimizations such as guard elimination, message vectorization and aggregation, and overlap analysis. The systematic use of an affine framework makes it possible to prove the compilation scheme correct.

Codes and curves

CERN Document Server

Walker, Judy L

2000-01-01

When information is transmitted, errors are likely to occur. Coding theory examines efficient ways of packaging data so that these errors can be detected, or even corrected. The traditional tools of coding theory have come from combinatorics and group theory. Lately, however, coding theorists have added techniques from algebraic geometry to their toolboxes. In particular, by re-interpreting the Reed-Solomon codes, one can see how to define new codes based on divisors on algebraic curves. For instance, using modular curves over finite fields, Tsfasman, Vladut, and Zink showed that one can define a sequence of codes with asymptotically better parameters than any previously known codes. This monograph is based on a series of lectures the author gave as part of the IAS/PCMI program on arithmetic algebraic geometry. Here, the reader is introduced to the exciting field of algebraic geometric coding theory. Presenting the material in the same conversational tone of the lectures, the author covers linear codes, inclu...

Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs

Directory of Open Access Journals (Sweden)

Gene Frantz

2007-01-01

Full Text Available Numerical linear algebra algorithms use the inherent elegance of matrix formulations and are usually implemented using C/C++ floating point representation. The system implementation is faced with practical constraints because these algorithms usually need to run in real time on fixed point digital signal processors (DSPs to reduce total hardware costs. Converting the simulation model to fixed point arithmetic and then porting it to a target DSP device is a difficult and time-consuming process. In this paper, we analyze the conversion process. We transformed selected linear algebra algorithms from floating point to fixed point arithmetic, and compared real-time requirements and performance between the fixed point DSP and floating point DSP algorithm implementations. We also introduce an advanced code optimization and an implementation by DSP-specific, fixed point C code generation. By using the techniques described in the paper, speed can be increased by a factor of up to 10 compared to floating point emulation on fixed point hardware.

Design of variable-weight quadratic congruence code for optical CDMA

Science.gov (United States)

Feng, Gang; Cheng, Wen-Qing; Chen, Fu-Jun

2015-09-01

A variable-weight code family referred to as variable-weight quadratic congruence code (VWQCC) is constructed by algebraic transformation for incoherent synchronous optical code division multiple access (OCDMA) systems. Compared with quadratic congruence code (QCC), VWQCC doubles the code cardinality and provides the multiple code-sets with variable code-weight. Moreover, the bit-error rate (BER) performance of VWQCC is superior to those of conventional variable-weight codes by removing or padding pulses under the same chip power assumption. The experiment results show that VWQCC can be well applied to the OCDMA with quality of service (QoS) requirements.

Designing Cognitively Diagnostic Assessment for Algebraic Content Knowledge and Thinking Skills

Science.gov (United States)

Zhang, Zhidong

2018-01-01

This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…

An introduction to central simple algebras and their applications to wireless communication

CERN Document Server

Berhuy, Gre�gory

2013-01-01

Central simple algebras arise naturally in many areas of mathematics. They are closely connected with ring theory, but are also important in representation theory, algebraic geometry and number theory. Recently, surprising applications of the theory of central simple algebras have arisen in the context of coding for wireless communication. The exposition in the book takes advantage of this serendipity, presenting an introduction to the theory of central simple algebras intertwined with its applications to coding theory. Many results or constructions from the standard theory are presented in classical form, but with a focus on explicit techniques and examples, often from coding theory. Topics covered include quaternion algebras, splitting fields, the Skolem-Noether Theorem, the Brauer group, crossed products, cyclic algebras and algebras with a unitary involution. Code constructions give the opportunity for many examples and explicit computations. This book provides an introduction to the theory of central alg...

Representations of Lie algebras and partial differential equations

CERN Document Server

Xu, Xiaoping

2017-01-01

This book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the author’s works and his joint works with his former students.  Further, it presents various oscillator generalizations of the classical representation theorem on harmonic polynomials, and highlights new functors from the representation category of a simple Lie algebra to that of another simple Lie algebra. Partial differential equations play a key role in solving certain representation problems. The weight matrices of the minimal and adjoint representations over the simple Lie algebras of types E and F are proved to generate ternary orthogonal linear codes with large minimal distances. New multi-variable hypergeometric functions related to the root systems of simple Lie algebras are introduced in connection with quantum many-body systems in one dimension. In addition, the book identifies certai...

Genetic coding and united-hypercomplex systems in the models of algebraic biology.

Science.gov (United States)

Petoukhov, Sergey V

2017-08-01

Structured alphabets of DNA and RNA in their matrix form of representations are connected with Walsh functions and a new type of systems of multidimensional numbers. This type generalizes systems of complex numbers and hypercomplex numbers, which serve as the basis of mathematical natural sciences and many technologies. The new systems of multi-dimensional numbers have interesting mathematical properties and are called in a general case as "systems of united-hypercomplex numbers" (or briefly "U-hypercomplex numbers"). They can be widely used in models of multi-parametrical systems in the field of algebraic biology, artificial life, devices of biological inspired artificial intelligence, etc. In particular, an application of U-hypercomplex numbers reveals hidden properties of genetic alphabets under cyclic permutations in their doublets and triplets. A special attention is devoted to the author's hypothesis about a multi-linguistic in DNA-sequences in a relation with an ensemble of U-numerical sub-alphabets. Genetic multi-linguistic is considered as an important factor to provide noise-immunity properties of the multi-channel genetic coding. Our results attest to the conformity of the algebraic properties of the U-numerical systems with phenomenological properties of the DNA-alphabets and with the complementary device of the double DNA-helix. It seems that in the modeling field of algebraic biology the genetic-informational organization of living bodies can be considered as a set of united-hypercomplex numbers in some association with the famous slogan of Pythagoras "the numbers rule the world". Copyright © 2017 Elsevier B.V. All rights reserved.

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

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.

Applied algebra codes, ciphers and discrete algorithms

CERN Document Server

Hardy, Darel W; Walker, Carol L

2009-01-01

This book attempts to show the power of algebra in a relatively simple setting.-Mathematical Reviews, 2010… The book supports learning by doing. In each section we can find many examples which clarify the mathematics introduced in the section and each section is followed by a series of exercises of which approximately half are solved in the end of the book. Additional the book comes with a CD-ROM containing an interactive version of the book powered by the computer algebra system Scientific Notebook. … the mathematics in the book are developed as needed and the focus of the book lies clearly o

The general theory of convolutional codes

Science.gov (United States)

Mceliece, R. J.; Stanley, R. P.

1993-01-01

This article presents a self-contained introduction to the algebraic theory of convolutional codes. This introduction is partly a tutorial, but at the same time contains a number of new results which will prove useful for designers of advanced telecommunication systems. Among the new concepts introduced here are the Hilbert series for a convolutional code and the class of compact codes.

Linear algebra and matrices topics for a second course

CERN Document Server

Shapiro, Helene

2015-01-01

Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first c...

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...

Some questions of using the algebraic coding theory for construction of special-purpose processors in high energy physics spectrometers

International Nuclear Information System (INIS)

Nikityuk, N.M.

1989-01-01

The results of investigations of using the algebraic coding theory for the creation of parallel encoders, majority coincidence schemes and coordinate processors for the first and second trigger levels are described. Concrete examples of calculation and structure of special-purpose processor using the table arithmetic method are given for multiplicity t ≤ 5. The question of using parallel and sequential syndrome coding methods for the registration of events with clusters is discussed. 30 refs.; 10 figs

Generic programming for deterministic neutron transport codes

International Nuclear Information System (INIS)

Plagne, L.; Poncot, A.

2005-01-01

This paper discusses the implementation of neutron transport codes via generic programming techniques. Two different Boltzmann equation approximations have been implemented, namely the Sn and SPn methods. This implementation experiment shows that generic programming allows us to improve maintainability and readability of source codes with no performance penalties compared to classical approaches. In the present implementation, matrices and vectors as well as linear algebra algorithms are treated separately from the rest of source code and gathered in a tool library called 'Generic Linear Algebra Solver System' (GLASS). Such a code architecture, based on a linear algebra library, allows us to separate the three different scientific fields involved in transport codes design: numerical analysis, reactor physics and computer science. Our library handles matrices with optional storage policies and thus applies both to Sn code, where the matrix elements are computed on the fly, and to SPn code where stored matrices are used. Thus, using GLASS allows us to share a large fraction of source code between Sn and SPn implementations. Moreover, the GLASS high level of abstraction allows the writing of numerical algorithms in a form which is very close to their textbook descriptions. Hence the GLASS algorithms collection, disconnected from computer science considerations (e.g. storage policy), is very easy to read, to maintain and to extend. (authors)

CTCN: Colloid transport code -- nuclear

International Nuclear Information System (INIS)

Jain, R.

1993-01-01

This report describes the CTCN computer code, designed to solve the equations of transient colloidal transport of radionuclides in porous and fractured media. This Fortran 77 package solves systems of coupled nonlinear differential-algebraic equations with a wide range of boundary conditions. The package uses the Method of Lines technique with a special section which forms finite-difference discretizations in up to four spatial dimensions to automatically convert the system into a set of ordinary differential equations. The CTCN code then solves these equations using a robust, efficient ODE solver. Thus CTCN can be used to solve population balance equations along with the usual transport equations to model colloid transport processes or as a general problem solver to treat up to four-dimensional differential-algebraic systems

Maiorana-McFarland class: Degree optimization and algebraic properties

DEFF Research Database (Denmark)

Pasalic, Enes

2006-01-01

degree of functions in the extended Maiorana-McFarland (MM) class (nonlinear resilient functions F : GF (2)(n) -> GF (2)(m) derived from linear codes). We also show that in the Boolean case, the same subclass seems not to have an optimized algebraic immunity, hence not providing a maximum resistance......In this paper, we consider a subclass of the Maiorana-McFarland class used in the design of resilient nonlinear Boolean functions. We show that these functions allow a simple modification so that resilient Boolean functions of maximum algebraic degree may be generated instead of suboptimized degree...... in the original class. Preserving a high-nonlinearity value immanent to the original construction method, together with the degree optimization gives in many cases functions with cryptographic properties superior to all previously known construction methods. This approach is then used to increase the algebraic...

On the Use of an Algebraic Signature Analyzer for Mixed-Signal Systems Testing

Directory of Open Access Journals (Sweden)

Vadim Geurkov

2014-01-01

Full Text Available We propose an approach to design of an algebraic signature analyzer that can be used for mixed-signal systems testing. The analyzer does not contain carry propagating circuitry, which improves its performance as well as fault tolerance. The common design technique of a signature analyzer for mixed-signal systems is based on the rules of an arithmetic finite field. The application of this technique to the systems with an arbitrary radix is a challenging task and the devices designed possess high hardware complexity. The proposed technique is simple and applicable to systems of any size and radix. The hardware complexity is low. The technique can also be used in arithmetic/algebraic coding and cryptography.

Order functions and evaluation codes

DEFF Research Database (Denmark)

Høholdt, Tom; Pellikaan, Ruud; van Lint, Jack

1997-01-01

Based on the notion of an order function we construct and determine the parameters of a class of error-correcting evaluation codes. This class includes the one-point algebraic geometry codes as wella s the generalized Reed-Muller codes and the parameters are detremined without using the heavy...... machinery of algebraic geometry....

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

International Nuclear Information System (INIS)

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

1994-01-01

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

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...

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.

An algebraic approach to graph codes

DEFF Research Database (Denmark)

Pinero, Fernando

This thesis consists of six chapters. The first chapter, contains a short introduction to coding theory in which we explain the coding theory concepts we use. In the second chapter, we present the required theory for evaluation codes and also give an example of some fundamental codes in coding...... theory as evaluation codes. Chapter three consists of the introduction to graph based codes, such as Tanner codes and graph codes. In Chapter four, we compute the dimension of some graph based codes with a result combining graph based codes and subfield subcodes. Moreover, some codes in chapter four...

Fast Bitwise Implementation of the Algebraic Normal Form Transform

OpenAIRE

Bakoev, Valentin

2017-01-01

The representation of Boolean functions by their algebraic normal forms (ANFs) is very important for cryptography, coding theory and other scientific areas. The ANFs are used in computing the algebraic degree of S-boxes, some other cryptographic criteria and parameters of errorcorrecting codes. Their applications require these criteria and parameters to be computed by fast algorithms. Hence the corresponding ANFs should also be obtained by fast algorithms. Here we continue o...

ZLIB++: Object Oriented Numerical Library for Differential Algebra

International Nuclear Information System (INIS)

Yan, Yiton T

2003-01-01

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

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

Gröbner Bases, Coding, and Cryptography

CERN Document Server

Sala, Massimiliano; Perret, Ludovic

2009-01-01

Coding theory and cryptography allow secure and reliable data transmission, which is at the heart of modern communication. This book offers a comprehensive overview on the application of commutative algebra to coding theory and cryptography. It analyzes important properties of algebraic/geometric coding systems individually.

Algebraic complexities and algebraic curves over finite fields.

Science.gov (United States)

Chudnovsky, D V; Chudnovsky, G V

1987-04-01

We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169-180]. We prove lower and upper bounds on minimal complexities over finite fields, both linear in the number of inputs, using the relationship with linear coding theory and algebraic curves over finite fields.

Elementary and advanced Lie algebraic methods with applications to accelerator design, electron microscopes, and light optics

International Nuclear Information System (INIS)

Dragt, A.J.

1987-01-01

A review is given of elementary Lie algebraic methods for treating Hamiltonian systems. This review is followed by a brief exposition of advanced Lie algebraic methods including resonance bases and conjugacy theorems. Finally, applications are made to the design of third-order achromats for use in accelerators, to the design of subangstroem resolution electron microscopes, and to the classification and study of high order aberrations in light optics. (orig.)

Comparison of design margin for core shroud in between design and construction code and fitness-for-service code

International Nuclear Information System (INIS)

Dozaki, Koji

2007-01-01

Structural design methods for core shroud of BWR are specified in JSME Design and Construction Code, like ASME Boiler and Pressure Vessel Code Sec. III, as a part of core support structure. Design margins are defined according to combination of the structural design method selected and service limit considered. Basically, those margins in JSME Code were determined after ASME Sec. III. Designers can select so-called twice-slope method for core shroud design among those design methods. On the other hand, flaw evaluation rules have been established for core shroud in JSME Fitness-for-Service Code. Twice-slope method is also adopted for fracture evaluation in that code even when the core shroud contains a flaw. Design margin was determined as structural factors separately from Design and Construction Code. As a natural consequence, there is a difference in those design margins between the two codes. In this paper, it is shown that the design margin in Fitness-for-Service Code is conservative by experimental evidences. Comparison of design margins between the two codes is discussed. (author)

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

Codes on the Klein quartic, ideals, and decoding

DEFF Research Database (Denmark)

Hansen, Johan P.

1987-01-01

descriptions as left ideals in the group-algebra GF(2^{3})[G]. This description allows for easy decoding. For instance, in the case of the single error correcting code of length21and dimension16with minimal distance3. decoding is obtained by multiplication with an idempotent in the group algebra.......A sequence of codes with particular symmetries and with large rates compared to their minimal distances is constructed over the field GF(2^{3}). In the sequence there is, for instance, a code of length 21 and dimension10with minimal distance9, and a code of length21and dimension16with minimal...... distance3. The codes are constructed from algebraic geometry using the dictionary between coding theory and algebraic curves over finite fields established by Goppa. The curve used in the present work is the Klein quartic. This curve has the maximal number of rational points over GF(2^{3})allowed by Serre...

Algorithmic Algebraic Combinatorics and Gröbner Bases

CERN Document Server

Klin, Mikhail; Jurisic, Aleksandar

2009-01-01

This collection of tutorial and research papers introduces readers to diverse areas of modern pure and applied algebraic combinatorics and finite geometries with a special emphasis on algorithmic aspects and the use of the theory of Grobner bases. Topics covered include coherent configurations, association schemes, permutation groups, Latin squares, the Jacobian conjecture, mathematical chemistry, extremal combinatorics, coding theory, designs, etc. Special attention is paid to the description of innovative practical algorithms and their implementation in software packages such as GAP and MAGM

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...

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.

An Optimal Linear Coding for Index Coding Problem

OpenAIRE

Pezeshkpour, Pouya

2015-01-01

An optimal linear coding solution for index coding problem is established. Instead of network coding approach by focus on graph theoric and algebraic methods a linear coding program for solving both unicast and groupcast index coding problem is presented. The coding is proved to be the optimal solution from the linear perspective and can be easily utilize for any number of messages. The importance of this work is lying mostly on the usage of the presented coding in the groupcast index coding ...

Secret Codes, Remainder Arithmetic, and Matrices.

Science.gov (United States)

Peck, Lyman C.

This pamphlet is designed for use as enrichment material for able junior and senior high school students who are interested in mathematics. No more than a clear understanding of basic arithmetic is expected. Students are introduced to ideas from number theory and modern algebra by learning mathematical ways of coding and decoding secret messages.…

New simple algebraic root locus method for design of feedback control systems

Directory of Open Access Journals (Sweden)

Cingara Aleksandar M.

2008-01-01

Full Text Available New concept of algebraic characteristic equation decomposition method is presented to simplify the design of closed-loop systems for practical applications. The method consists of two decompositions. The first one, decomposition of the characteristic equation into two lower order equations, was performed in order to simplify the analysis and design of closed loop systems. The second is the decomposition of Laplace variable, s, into two variables, damping coefficient, ζ, and natural frequency, ω n. Those two decompositions reduce the design of any order feedback systems to setting of two complex dominant poles in the desired position. In the paper, we derived explicit equations for six cases: first, second and third order system with P and PI. We got the analytical solutions for the case of fourth and fifth order characteristic equations with the P and PI controller; one may obtain a complete analytical solution of controller gain as a function of the desired damping coefficient. The complete derivation is given for the third order equation with P and PI controller. We can extend the number of specified poles to the highest order of the characteristic equation working in a similar way, so we can specify the position of each pole. The concept is similar to the root locus but root locus is implicit, which makes it more complicated and this is simpler explicit root locus. Standard procedures, root locus and Bode diagrams or Nichol Charts, are neither algebraic nor explicit. We basically change controller parameters and observe the change of some function until we get the desired specifications. The derived method has three important advantage over the standard procedures. It is general, algebraic and explicit. Those are the best poles design results possible; it is not possible to get better controller design results.

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...

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

The linear algebra survival guide illustrated with Mathematica

CERN Document Server

Szabo, Fred

2015-01-01

The Linear Algebra Survival Guide is a reference book with a free downloadable Mathematica notebook containing all of interactive code to make the content of the book playable in Mathematica and the Mathematica Player. It offers a concise introduction to the core topics of linear algebra which includes numerous exercises that will accompany a first or second course in linear algebra. This book will guide you through the powerful graphic displays and visualization of Mathematica that make the most abstract theories seem simple-- allowing you to tackle realistic problems using simple mathematic

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…

List Decoding of Algebraic Codes

DEFF Research Database (Denmark)

Nielsen, Johan Sebastian Rosenkilde

We investigate three paradigms for polynomial-time decoding of Reed–Solomon codes beyond half the minimum distance: the Guruswami–Sudan algorithm, Power decoding and the Wu algorithm. The main results concern shaping the computational core of all three methods to a problem solvable by module...... Hermitian codes using Guruswami–Sudan or Power decoding faster than previously known, and we show how to Wu list decode binary Goppa codes....... to solve such using module minimisation, or using our new Demand–Driven algorithm which is also based on module minimisation. The decoding paradigms are all derived and analysed in a self-contained manner, often in new ways or examined in greater depth than previously. Among a number of new results, we...

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)

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...

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.)

Computer code development plant for SMART design

International Nuclear Information System (INIS)

Bae, Kyoo Hwan; Choi, S.; Cho, B.H.; Kim, K.K.; Lee, J.C.; Kim, J.P.; Kim, J.H.; Chung, M.; Kang, D.J.; Chang, M.H.

1999-03-01

In accordance with the localization plan for the nuclear reactor design driven since the middle of 1980s, various computer codes have been transferred into the korea nuclear industry through the technical transfer program from the worldwide major pressurized water reactor supplier or through the international code development program. These computer codes have been successfully utilized in reactor and reload core design works. As the results, design- related technologies have been satisfactorily accumulated. However, the activities for the native code development activities to substitute the some important computer codes of which usages are limited by the original technique owners have been carried out rather poorly. Thus, it is most preferentially required to secure the native techniques on the computer code package and analysis methodology in order to establish the capability required for the independent design of our own model of reactor. Moreover, differently from the large capacity loop-type commercial reactors, SMART (SYSTEM-integrated Modular Advanced ReacTor) design adopts a single reactor pressure vessel containing the major primary components and has peculiar design characteristics such as self-controlled gas pressurizer, helical steam generator, passive residual heat removal system, etc. Considering those peculiar design characteristics for SMART, part of design can be performed with the computer codes used for the loop-type commercial reactor design. However, most of those computer codes are not directly applicable to the design of an integral reactor such as SMART. Thus, they should be modified to deal with the peculiar design characteristics of SMART. In addition to the modification efforts, various codes should be developed in several design area. Furthermore, modified or newly developed codes should be verified their reliability through the benchmarking or the test for the object design. Thus, it is necessary to proceed the design according to the

Computer code development plant for SMART design

Energy Technology Data Exchange (ETDEWEB)

Bae, Kyoo Hwan; Choi, S.; Cho, B.H.; Kim, K.K.; Lee, J.C.; Kim, J.P.; Kim, J.H.; Chung, M.; Kang, D.J.; Chang, M.H

1999-03-01

In accordance with the localization plan for the nuclear reactor design driven since the middle of 1980s, various computer codes have been transferred into the korea nuclear industry through the technical transfer program from the worldwide major pressurized water reactor supplier or through the international code development program. These computer codes have been successfully utilized in reactor and reload core design works. As the results, design- related technologies have been satisfactorily accumulated. However, the activities for the native code development activities to substitute the some important computer codes of which usages are limited by the original technique owners have been carried out rather poorly. Thus, it is most preferentially required to secure the native techniques on the computer code package and analysis methodology in order to establish the capability required for the independent design of our own model of reactor. Moreover, differently from the large capacity loop-type commercial reactors, SMART (SYSTEM-integrated Modular Advanced ReacTor) design adopts a single reactor pressure vessel containing the major primary components and has peculiar design characteristics such as self-controlled gas pressurizer, helical steam generator, passive residual heat removal system, etc. Considering those peculiar design characteristics for SMART, part of design can be performed with the computer codes used for the loop-type commercial reactor design. However, most of those computer codes are not directly applicable to the design of an integral reactor such as SMART. Thus, they should be modified to deal with the peculiar design characteristics of SMART. In addition to the modification efforts, various codes should be developed in several design area. Furthermore, modified or newly developed codes should be verified their reliability through the benchmarking or the test for the object design. Thus, it is necessary to proceed the design according to the

Error-correction coding for digital communications

Science.gov (United States)

Clark, G. C., Jr.; Cain, J. B.

This book is written for the design engineer who must build the coding and decoding equipment and for the communication system engineer who must incorporate this equipment into a system. It is also suitable as a senior-level or first-year graduate text for an introductory one-semester course in coding theory. Fundamental concepts of coding are discussed along with group codes, taking into account basic principles, practical constraints, performance computations, coding bounds, generalized parity check codes, polynomial codes, and important classes of group codes. Other topics explored are related to simple nonalgebraic decoding techniques for group codes, soft decision decoding of block codes, algebraic techniques for multiple error correction, the convolutional code structure and Viterbi decoding, syndrome decoding techniques, and sequential decoding techniques. System applications are also considered, giving attention to concatenated codes, coding for the white Gaussian noise channel, interleaver structures for coded systems, and coding for burst noise channels.

An introduction to abstract algebra

CERN Document Server

Robinson, Derek JS

2003-01-01

This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra. The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader''s skill and progress. The book should be suitable for students ...

Computer codes for designing proton linear accelerators

International Nuclear Information System (INIS)

Kato, Takao

1992-01-01

Computer codes for designing proton linear accelerators are discussed from the viewpoint of not only designing but also construction and operation of the linac. The codes are divided into three categories according to their purposes: 1) design code, 2) generation and simulation code, and 3) electric and magnetic fields calculation code. The role of each category is discussed on the basis of experience at KEK (the design of the 40-MeV proton linac and its construction and operation, and the design of the 1-GeV proton linac). We introduce our recent work relevant to three-dimensional calculation and supercomputer calculation: 1) tuning of MAFIA (three-dimensional electric and magnetic fields calculation code) for supercomputer, 2) examples of three-dimensional calculation of accelerating structures by MAFIA, 3) development of a beam transport code including space charge effects. (author)

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.)

Vector Network Coding

OpenAIRE

Ebrahimi, Javad; Fragouli, Christina

2010-01-01

We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L X L coding matrices that play a similar role as coding coefficients in scalar coding. Our algorithms for scalar network jointly optimize the employed field size while selecting the coding coefficients. Similarly, for vector co...

Joint design of QC-LDPC codes for coded cooperation system with joint iterative decoding

Science.gov (United States)

Zhang, Shunwai; Yang, Fengfan; Tang, Lei; Ejaz, Saqib; Luo, Lin; Maharaj, B. T.

2016-03-01

In this paper, we investigate joint design of quasi-cyclic low-density-parity-check (QC-LDPC) codes for coded cooperation system with joint iterative decoding in the destination. First, QC-LDPC codes based on the base matrix and exponent matrix are introduced, and then we describe two types of girth-4 cycles in QC-LDPC codes employed by the source and relay. In the equivalent parity-check matrix corresponding to the jointly designed QC-LDPC codes employed by the source and relay, all girth-4 cycles including both type I and type II are cancelled. Theoretical analysis and numerical simulations show that the jointly designed QC-LDPC coded cooperation well combines cooperation gain and channel coding gain, and outperforms the coded non-cooperation under the same conditions. Furthermore, the bit error rate performance of the coded cooperation employing jointly designed QC-LDPC codes is better than those of random LDPC codes and separately designed QC-LDPC codes over AWGN channels.

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

An Inquiry-Based Linear Algebra Class

Science.gov (United States)

Wang, Haohao; Posey, Lisa

2011-01-01

Linear algebra is a standard undergraduate mathematics course. This paper presents an overview of the design and implementation of an inquiry-based teaching material for the linear algebra course which emphasizes discovery learning, analytical thinking and individual creativity. The inquiry-based teaching material is designed to fit the needs of a…

LUCID - an optical design and raytrace code

International Nuclear Information System (INIS)

Nicholas, D.J.; Duffey, K.P.

1980-11-01

A 2D optical design and ray trace code is described. The code can operate either as a geometric optics propagation code or provide a scalar diffraction treatment. There are numerous non-standard options within the code including design and systems optimisation procedures. A number of illustrative problems relating to the design of optical components in the field of high power lasers is included. (author)

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

Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory

CERN Document Server

Molina, Mercedes

2016-01-01

Presenting the collaborations of over thirty international experts in the latest developments in pure and applied mathematics, this volume serves as an anthology of research with a common basis in algebra, functional analysis and their applications. Special attention is devoted to non-commutative algebras, non-associative algebras, operator theory and ring and module theory. These themes are relevant in research and development in coding theory, cryptography and quantum mechanics. The topics in this volume were presented at the Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory, held May 23—25, 2014 at Cheikh Anta Diop University in Dakar, Senegal in honor of Professor Amin Kaidi. The workshop was hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications, in cooperation with the University of Almería and the University of Málaga. Dr. Kaidi's work focuses on non-associative rings and algebras, operator theory and functional analysis, and he...

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.

Structural analysis and design of multivariable control systems: An algebraic approach

Science.gov (United States)

Tsay, Yih Tsong; Shieh, Leang-San; Barnett, Stephen

1988-01-01

The application of algebraic system theory to the design of controllers for multivariable (MV) systems is explored analytically using an approach based on state-space representations and matrix-fraction descriptions. Chapters are devoted to characteristic lambda matrices and canonical descriptions of MIMO systems; spectral analysis, divisors, and spectral factors of nonsingular lambda matrices; feedback control of MV systems; and structural decomposition theories and their application to MV control systems.

Basic matrix algebra and transistor circuits

CERN Document Server

Zelinger, G

1963-01-01

Basic Matrix Algebra and Transistor Circuits deals with mastering the techniques of matrix algebra for application in transistors. This book attempts to unify fundamental subjects, such as matrix algebra, four-terminal network theory, transistor equivalent circuits, and pertinent design matters. Part I of this book focuses on basic matrix algebra of four-terminal networks, with descriptions of the different systems of matrices. This part also discusses both simple and complex network configurations and their associated transmission. This discussion is followed by the alternative methods of de

UCSMP Algebra. What Works Clearinghouse Intervention Report

Science.gov (United States)

What Works Clearinghouse, 2007

2007-01-01

"University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…

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.

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

CONSTRUCTION OF REGULAR LDPC LIKE CODES BASED ON FULL RANK CODES AND THEIR ITERATIVE DECODING USING A PARITY CHECK TREE

Directory of Open Access Journals (Sweden)

H. Prashantha Kumar

2011-09-01

Full Text Available Low density parity check (LDPC codes are capacity-approaching codes, which means that practical constructions exist that allow the noise threshold to be set very close to the theoretical Shannon limit for a memory less channel. LDPC codes are finding increasing use in applications like LTE-Networks, digital television, high density data storage systems, deep space communication systems etc. Several algebraic and combinatorial methods are available for constructing LDPC codes. In this paper we discuss a novel low complexity algebraic method for constructing regular LDPC like codes derived from full rank codes. We demonstrate that by employing these codes over AWGN channels, coding gains in excess of 2dB over un-coded systems can be realized when soft iterative decoding using a parity check tree is employed.

Vector Network Coding Algorithms

OpenAIRE

Ebrahimi, Javad; Fragouli, Christina

2010-01-01

We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L x L coding matrices that play a similar role as coding c in scalar coding. Our algorithms for scalar network jointly optimize the employed field size while selecting the coding coefficients. Similarly, for vector coding, our algori...

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 ...

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

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

Status of reactor core design code system in COSINE code package

Energy Technology Data Exchange (ETDEWEB)

Chen, Y.; Yu, H.; Liu, Z., E-mail: yuhui@snptc.com.cn [State Nuclear Power Software Development Center, SNPTC, National Energy Key Laboratory of Nuclear Power Software (NEKLS), Beijiing (China)

2014-07-01

For self-reliance, COre and System INtegrated Engine for design and analysis (COSINE) code package is under development in China. In this paper, recent development status of the reactor core design code system (including the lattice physics code and the core simulator) is presented. The well-established theoretical models have been implemented. The preliminary verification results are illustrated. And some special efforts, such as updated theory models and direct data access application, are also made to achieve better software product. (author)

Status of reactor core design code system in COSINE code package

International Nuclear Information System (INIS)

Chen, Y.; Yu, H.; Liu, Z.

2014-01-01

For self-reliance, COre and System INtegrated Engine for design and analysis (COSINE) code package is under development in China. In this paper, recent development status of the reactor core design code system (including the lattice physics code and the core simulator) is presented. The well-established theoretical models have been implemented. The preliminary verification results are illustrated. And some special efforts, such as updated theory models and direct data access application, are also made to achieve better software product. (author)

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

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 ...

SYNTHESIS METHODS OF ALGEBRAIC NORMAL FORM OF MANY-VALUED LOGIC FUNCTIONS

Directory of Open Access Journals (Sweden)

A. V. Sokolov

2016-01-01

Full Text Available The rapid development of methods of error-correcting coding, cryptography, and signal synthesis theory based on the principles of many-valued logic determines the need for a more detailed study of the forms of representation of functions of many-valued logic. In particular the algebraic normal form of Boolean functions, also known as Zhegalkin polynomial, that well describe many of the cryptographic properties of Boolean functions is widely used. In this article, we formalized the notion of algebraic normal form for many-valued logic functions. We developed a fast method of synthesis of algebraic normal form of 3-functions and 5-functions that work similarly to the Reed-Muller transform for Boolean functions: on the basis of recurrently synthesized transform matrices. We propose the hypothesis, which determines the rules of the synthesis of these matrices for the transformation from the truth table to the coefficients of the algebraic normal form and the inverse transform for any given number of variables of 3-functions or 5-functions. The article also introduces the definition of algebraic degree of nonlinearity of the functions of many-valued logic and the S-box, based on the principles of many-valued logic. Thus, the methods of synthesis of algebraic normal form of 3-functions applied to the known construction of recurrent synthesis of S-boxes of length N = 3k, whereby their algebraic degrees of nonlinearity are computed. The results could be the basis for further theoretical research and practical applications such as: the development of new cryptographic primitives, error-correcting codes, algorithms of data compression, signal structures, and algorithms of block and stream encryption, all based on the perspective principles of many-valued logic. In addition, the fast method of synthesis of algebraic normal form of many-valued logic functions is the basis for their software and hardware implementation.

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

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

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…

Blahut-Arimoto algorithm and code design for action-dependent source coding problems

DEFF Research Database (Denmark)

Trillingsgaard, Kasper Fløe; Simeone, Osvaldo; Popovski, Petar

2013-01-01

The source coding problem with action-dependent side information at the decoder has recently been introduced to model data acquisition in resource-constrained systems. In this paper, an efficient Blahut-Arimoto-type algorithm for the numerical computation of the rate-distortion-cost function...... for this problem is proposed. Moreover, a simplified two-stage code structure based on multiplexing is put forth, whereby the first stage encodes the actions and the second stage is composed of an array of classical Wyner-Ziv codes, one for each action. Leveraging this structure, specific coding/decoding...... strategies are designed based on LDGM codes and message passing. Through numerical examples, the proposed code design is shown to achieve performance close to the rate-distortion-cost function....

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

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).

Design evaluation on sodium piping system and comparison of the design codes

International Nuclear Information System (INIS)

Lee, Dong Won; Jeong, Ji Young; Lee, Yong Bum; Lee, Hyeong Yeon

2015-01-01

A large-scale sodium test loop of STELLA-1 (Sodium integral effect test loop for safety simulation and assessment) with two main piping systems has been installed at KAERI. In this study, design evaluations on the main sodium piping systems in STELLA-1 have been conducted according to the DBR (design by rule) codes of the ASME B31.1 and RCC-MRx RB-3600. In addition, design evaluations according to the DBA (design by analysis) code of the ASME Section III Subsection NB-3200 have been conducted. The evaluation results for the present piping systems showed that results from the DBR codes were more conservative than those from the DBA code, and among the DBR codes, the non-nuclear code of the ASME B31.1 was more conservative than the French nuclear DBR code of the RCC-MRx RB-3600. The conservatism on the DBR codes of the ASME B31.1 and RCC-MRx RB-3600 was quantified based on the present sodium piping analyses.

Design evaluation on sodium piping system and comparison of the design codes

Energy Technology Data Exchange (ETDEWEB)

Lee, Dong Won; Jeong, Ji Young; Lee, Yong Bum; Lee, Hyeong Yeon [KAERI, Daejeon (Korea, Republic of)

2015-03-15

A large-scale sodium test loop of STELLA-1 (Sodium integral effect test loop for safety simulation and assessment) with two main piping systems has been installed at KAERI. In this study, design evaluations on the main sodium piping systems in STELLA-1 have been conducted according to the DBR (design by rule) codes of the ASME B31.1 and RCC-MRx RB-3600. In addition, design evaluations according to the DBA (design by analysis) code of the ASME Section III Subsection NB-3200 have been conducted. The evaluation results for the present piping systems showed that results from the DBR codes were more conservative than those from the DBA code, and among the DBR codes, the non-nuclear code of the ASME B31.1 was more conservative than the French nuclear DBR code of the RCC-MRx RB-3600. The conservatism on the DBR codes of the ASME B31.1 and RCC-MRx RB-3600 was quantified based on the present sodium piping analyses.

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.)

Interleaver Design for Turbo Coding

DEFF Research Database (Denmark)

Andersen, Jakob Dahl; Zyablov, Viktor

1997-01-01

By a combination of construction and random search based on a careful analysis of the low weight words and the distance properties of the component codes, it is possible to find interleavers for turbo coding with a high minimum distance. We have designed a block interleaver with permutations...

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)

76 FR 11432 - Coding of Design Marks in Registrations

Science.gov (United States)

2011-03-02

...] Coding of Design Marks in Registrations AGENCY: United States Patent and Trademark Office, Commerce... practice of coding newly registered trademarks that include a design element with design mark codes based... notice and request for comments at 75 FR 81587, proposing to discontinue a secondary system of coding...

75 FR 81587 - Coding of Design Marks in Registrations

Science.gov (United States)

2010-12-28

... DEPARTMENT OF COMMERCE Patent and Trademark Office [Docket No. PTO-T-2010-0090] Coding of Design... discontinue its secondary design coding, the practice of coding newly registered trademarks in its searchable... temporarily retain the paper collection of registrations with design coding, while improving the accuracy of...

Algebraic modeling and thermodynamic design of fan-supplied tube-fin evaporators running under frosting conditions

International Nuclear Information System (INIS)

Ribeiro, Rafael S.; Hermes, Christian J.L.

2014-01-01

In this study, the method of entropy generation minimization (i.e., design aimed at facilitating both heat, mass and fluid flows) is used to assess the evaporator design (aspect ratio and fin density) considering the thermodynamic losses due to heat and mass transfer, and viscous flow processes. A fully algebraic model was put forward to simulate the thermal-hydraulic behavior of tube-fin evaporator coils running under frosting conditions. The model predictions were validated against experimental data, showing a good agreement between calculated and measured counterparts. The optimization exercise has pointed out that high aspect ratio heat exchanger designs lead to lower entropy generation in cases of fixed cooling capacity and air flow rate constrained by the characteristic curve of the fan. - Highlights: • An algebraic model for frost accumulation on tube-fin heat exchangers was advanced. • Model predictions for cooling capacity and air flow rate were compared with experimental data, with errors within ±5% band. • Minimum entropy generation criterion was used to optimize the evaporator geometry. • Thermodynamic analysis led to slender designs for fixed cooling capacity and fan characteristics

Advanced thermionic reactor systems design code

International Nuclear Information System (INIS)

Lewis, B.R.; Pawlowski, R.A.; Greek, K.J.; Klein, A.C.

1991-01-01

An overall systems design code is under development to model an advanced in-core thermionic nuclear reactor system for space applications at power levels of 10 to 50 kWe. The design code is written in an object-oriented programming environment that allows the use of a series of design modules, each of which is responsible for the determination of specific system parameters. The code modules include a neutronics and core criticality module, a core thermal hydraulics module, a thermionic fuel element performance module, a radiation shielding module, a module for waste heat transfer and rejection, and modules for power conditioning and control. The neutronics and core criticality module determines critical core size, core lifetime, and shutdown margins using the criticality calculation capability of the Monte Carlo Neutron and Photon Transport Code System (MCNP). The remaining modules utilize results of the MCNP analysis along with FORTRAN programming to predict the overall system performance

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.

Advanced hardware design for error correcting codes

CERN Document Server

Coussy, Philippe

2015-01-01

This book provides thorough coverage of error correcting techniques. It includes essential basic concepts and the latest advances on key topics in design, implementation, and optimization of hardware/software systems for error correction. The book’s chapters are written by internationally recognized experts in this field. Topics include evolution of error correction techniques, industrial user needs, architectures, and design approaches for the most advanced error correcting codes (Polar Codes, Non-Binary LDPC, Product Codes, etc). This book provides access to recent results, and is suitable for graduate students and researchers of mathematics, computer science, and engineering. • Examines how to optimize the architecture of hardware design for error correcting codes; • Presents error correction codes from theory to optimized architecture for the current and the next generation standards; • Provides coverage of industrial user needs advanced error correcting techniques.

2nd EACA International School on Computer Algebra and its Applications

CERN Document Server

Gimenez, Philippe; Sáenz-de-Cabezón, Eduardo

2017-01-01

Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations. "Computations and combinatorics in commutative algebra" has been written by experts in both theoretical and computational aspects of these three subjects and is aimed at a broad audience, from experienced researchers who want to have an easy but deep review of the topics covered to postgraduate students who need a quick introduction to the techniques. The computational treatment of the material, including plenty of examples and code, will be useful for a wide range of professionals interested in the connections between commutative algebra and combinatorics.

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.

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...

Card Games and Algebra Tic Tacmatics on Achievement of Junior Secondary II Students in Algebraic Expressions

Science.gov (United States)

Okpube, Nnaemeka Michael; Anugwo, M. N.

2016-01-01

This study investigated the Card Games and Algebra tic-Tacmatics on Junior Secondary II Students' Achievement in Algebraic Expressions. Three research questions and three null hypotheses guided the study. The study adopted the pre-test, post-test control group design. A total of two hundred and forty (240) Junior Secondary School II students were…

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

An Algebraic Programming Style for Numerical Software and Its Optimization

Directory of Open Access Journals (Sweden)

T.B. Dinesh

2000-01-01

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

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.

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.

Improved Design of Unequal Error Protection LDPC Codes

Directory of Open Access Journals (Sweden)

Sandberg Sara

2010-01-01

Full Text Available We propose an improved method for designing unequal error protection (UEP low-density parity-check (LDPC codes. The method is based on density evolution. The degree distribution with the best UEP properties is found, under the constraint that the threshold should not exceed the threshold of a non-UEP code plus some threshold offset. For different codeword lengths and different construction algorithms, we search for good threshold offsets for the UEP code design. The choice of the threshold offset is based on the average a posteriori variable node mutual information. Simulations reveal the counter intuitive result that the short-to-medium length codes designed with a suitable threshold offset all outperform the corresponding non-UEP codes in terms of average bit-error rate. The proposed codes are also compared to other UEP-LDPC codes found in the literature.

A note on the algebraic evaluation of correlators in local chiral conformal field theory

International Nuclear Information System (INIS)

Honecker, A.

1992-09-01

We comment on a program designed for the study of local chiral algebras and their representations in 2D conformal field theory. Based on the algebraic approach described by W. Nahm, this program efficiently calculates arbitrary n-point functions of these algebras. The program is designed such that calculations involving e.g. current algebras, W-algebras and N-Superconformal algebras can be performed. As a non-trivial application we construct an extension of the Virasoro algebra by two fields with spin four and six using the N=1-Super-Virasoro algebra. (orig.)

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.

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

Solving the Unknown with Algebra: Poster/Teaching Guide for Pre-Algebra Students. Expect the Unexpected with Math[R

Science.gov (United States)

Actuarial Foundation, 2013

2013-01-01

"Solving the Unknown with Algebra" is a new math program aligned with the National Council of Teachers of Mathematics (NCTM) standards and designed to help students practice pre-algebra skills including using formulas, solving for unknowns, and manipulating equations. Developed by The Actuarial Foundation with Scholastic, this program provides…

Third order TRANSPORT with MAD [Methodical Accelerator Design] input

International Nuclear Information System (INIS)

Carey, D.C.

1988-01-01

This paper describes computer-aided design codes for particle accelerators. Among the topics discussed are: input beam description; parameters and algebraic expressions; the physical elements; beam lines; operations; and third-order transfer matrix

Essential idempotents and simplex codes

Directory of Open Access Journals (Sweden)

Gladys Chalom

2017-01-01

Full Text Available We define essential idempotents in group algebras and use them to prove that every mininmal abelian non-cyclic code is a repetition code. Also we use them to prove that every minimal abelian code is equivalent to a minimal cyclic code of the same length. Finally, we show that a binary cyclic code is simplex if and only if is of length of the form $n=2^k-1$ and is generated by an essential idempotent.

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

International Nuclear Information System (INIS)

Foot, R.; Joshi, G.C.

1992-01-01

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

An Improved Algorithm for Generating Database Transactions from Relational Algebra Specifications

Directory of Open Access Journals (Sweden)

Daniel J. Dougherty

2010-03-01

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

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...

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.

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.

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.

Iwahori-Hecke algebras and Schur algebras of the symmetric group

CERN Document Server

Mathas, Andrew

1999-01-01

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

A class of Sudan-decodable codes

DEFF Research Database (Denmark)

Nielsen, Rasmus Refslund

2000-01-01

In this article, Sudan's algorithm is modified into an efficient method to list-decode a class of codes which can be seen as a generalization of Reed-Solomon codes. The algorithm is specialized into a very efficient method for unique decoding. The code construction can be generalized based...... on algebraic-geometry codes and the decoding algorithms are generalized accordingly. Comparisons with Reed-Solomon and Hermitian codes are made....

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

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...

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.)

System Design Description for the TMAD Code

International Nuclear Information System (INIS)

Finfrock, S.H.

1995-01-01

This document serves as the System Design Description (SDD) for the TMAD Code System, which includes the TMAD code and the LIBMAKR code. The SDD provides a detailed description of the theory behind the code, and the implementation of that theory. It is essential for anyone who is attempting to review or modify the code or who otherwise needs to understand the internal workings of the code. In addition, this document includes, in Appendix A, the System Requirements Specification for the TMAD System

Using Peephole Optimization on Intermediate Code

NARCIS (Netherlands)

Tanenbaum, A.S.; van Staveren, H.; Stevenson, J.W.

1982-01-01

Many portable compilers generate an intermediate code that is subsequently translated into the target machine's assembly language. In this paper a stack-machine-based intermediate code suitable for algebraic languages (e.g., PASCAL, C, FORTRAN) and most byte-addressed mini- and microcomputers is

Numerical linear algebra with applications using Matlab

CERN Document Server

Ford, William

2014-01-01

Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. It provides necessary mathematical background information for

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 ...

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...

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.

From tracking code to analysis generalised Courant-Snyder theory for any accelerator model

CERN Document Server

Forest, Etienne

2016-01-01

This book illustrates a theory well suited to tracking codes, which the author has developed over the years. Tracking codes now play a central role in the design and operation of particle accelerators. The theory is fully explained step by step with equations and actual codes that the reader can compile and run with freely available compilers. In this book, the author pursues a detailed approach based on finite “s”-maps, since this is more natural as long as tracking codes remain at the center of accelerator design. The hierarchical nature of software imposes a hierarchy that puts map-based perturbation theory above any other methods. This is not a personal choice: it follows logically from tracking codes overloaded with a truncated power series algebra package. After defining abstractly and briefly what a tracking code is, the author illustrates most of the accelerator perturbation theory using an actual code: PTC. This book may seem like a manual for PTC; however, the reader is encouraged to explore...

Fundamentals of information theory and coding design

CERN Document Server

Togneri, Roberto

2003-01-01

In a clear, concise, and modular format, this book introduces the fundamental concepts and mathematics of information and coding theory. The authors emphasize how a code is designed and discuss the main properties and characteristics of different coding algorithms along with strategies for selecting the appropriate codes to meet specific requirements. They provide comprehensive coverage of source and channel coding, address arithmetic, BCH, and Reed-Solomon codes and explore some more advanced topics such as PPM compression and turbo codes. Worked examples and sets of basic and advanced exercises in each chapter reinforce the text's clear explanations of all concepts and methodologies.

Space-Time Code Designs for Broadband Wireless Communications

National Research Council Canada - National Science Library

Xia, Xiang-Gen

2005-01-01

The goal of this research is to design new space AND time codes, such as complex orthogonal space AND time block codes with rate above 1/2 from complex orthogonal designs for QAM, PSK, and CPM signals...

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.

Thirty-three miniatures mathematical and algorithmic applications of linear algebra

CERN Document Server

Matousek, Jiří

2010-01-01

This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lov�sz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products. The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for s...

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...

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.

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

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.

Use of the algebraic coding theory in nuclear electronics

International Nuclear Information System (INIS)

Nikityuk, N.M.

1990-01-01

New results of studies of the development and use of the syndrome coding method in nuclear electronics are described. Two aspects of using the syndrome coding method are considered for sequential coding devices and for the creation of fast parallel data compression devices. Specific examples of the creation of time-to-digital converters based on circular counters are described. Several time intervals can be coded very fast and with a high resolution by means of these converters. The effective coding matrix which can be used for light signal coding. The rule of constructing such coding matrices for arbitrary number of channels and multiplicity n is given. The methods for solving ambiguities in silicon detectors and for creating the special-purpose processors for high-energy spectrometers are given. 21 refs.; 9 figs.; 3 tabs

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

Algebraic topology a first course

CERN Document Server

Fulton, William

1995-01-01

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re­ lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ­ ential topology, etc.), we concentrate our attention on concrete prob­ lems in low dimensions, introducing only as much algebraic machin­ ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol­ ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel­ opment of the subject. What would we like a student to know after a first course in to­ pology (assuming we reject the answer: ...

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.

The DIT nuclear fuel assembly physics design code

International Nuclear Information System (INIS)

Jonsson, A.

1988-01-01

The DIT code is the Combustion Engineering, Inc. (C-E) nuclear fuel assembly design code. It belongs to a class of codes, all similar in structure and strategy, that may be characterized by the spectrum and spatial calculations being performed in two dimensions and in a single job step for the entire assembly. The forerunner of this class of codes is the United Kingdom Atomic Energy Authority WIMS code, the first version of which was completed 25 yr ago. The structure and strategy of assembly spectrum codes have remained remarkably similar to the original concept thus proving its usefulness. As other organizations, including C-E, have developed their own versions of the concept, many important variations have been added that significantly influence the accuracy and performance of the resulting computational tool. Those features, which are unique to the DIT code and which might be of interest to the community of fuel assembly physics design code users and developers, are described and discussed

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

International Nuclear Information System (INIS)

Grimm, Uwe; Martin, Paul P

2003-01-01

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

A Semantic Analysis Method for Scientific and Engineering Code

Science.gov (United States)

Stewart, Mark E. M.

1998-01-01

This paper develops a procedure to statically analyze aspects of the meaning or semantics of scientific and engineering code. The analysis involves adding semantic declarations to a user's code and parsing this semantic knowledge with the original code using multiple expert parsers. These semantic parsers are designed to recognize formulae in different disciplines including physical and mathematical formulae and geometrical position in a numerical scheme. In practice, a user would submit code with semantic declarations of primitive variables to the analysis procedure, and its semantic parsers would automatically recognize and document some static, semantic concepts and locate some program semantic errors. A prototype implementation of this analysis procedure is demonstrated. Further, the relationship between the fundamental algebraic manipulations of equations and the parsing of expressions is explained. This ability to locate some semantic errors and document semantic concepts in scientific and engineering code should reduce the time, risk, and effort of developing and using these codes.

Ada Linear-Algebra Program

Science.gov (United States)

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

1988-01-01

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

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...

The Influence of Building Codes on Recreation Facility Design.

Science.gov (United States)

Morrison, Thomas A.

1989-01-01

Implications of building codes upon design and construction of recreation facilities are investigated (national building codes, recreation facility standards, and misperceptions of design requirements). Recreation professionals can influence architectural designers to correct past deficiencies, but they must understand architectural and…

Design of Packet-Based Block Codes with Shift Operators

Directory of Open Access Journals (Sweden)

Ilow Jacek

2010-01-01

Full Text Available This paper introduces packet-oriented block codes for the recovery of lost packets and the correction of an erroneous single packet. Specifically, a family of systematic codes is proposed, based on a Vandermonde matrix applied to a group of information packets to construct redundant packets, where the elements of the Vandermonde matrix are bit-level right arithmetic shift operators. The code design is applicable to packets of any size, provided that the packets within a block of information packets are of uniform length. In order to decrease the overhead associated with packet padding using shift operators, non-Vandermonde matrices are also proposed for designing packet-oriented block codes. An efficient matrix inversion procedure for the off-line design of the decoding algorithm is presented to recover lost packets. The error correction capability of the design is investigated as well. The decoding algorithm, based on syndrome decoding, to correct a single erroneous packet in a group of received packets is presented. The paper is equipped with examples of codes using different parameters. The code designs and their performance are tested using Monte Carlo simulations; the results obtained exhibit good agreement with the corresponding theoretical results.

Computer codes for RF cavity design

International Nuclear Information System (INIS)

Ko, K.

1992-08-01

In RF cavity design, numerical modeling is assuming an increasingly important role with the help of sophisticated computer codes and powerful yet affordable computers. A description of the cavity codes in use in the accelerator community has been given previously. The present paper will address the latest developments and discuss their applications to cavity toning and matching problems

Preliminary design studies for the DESCARTES and CIDER codes

International Nuclear Information System (INIS)

Eslinger, P.W.; Miley, T.B.; Ouderkirk, S.J.; Nichols, W.E.

1992-12-01

The Hanford Environmental Dose Reconstruction (HEDR) project is developing several computer codes to model the release and transport of radionuclides into the environment. This preliminary design addresses two of these codes: Dynamic Estimates of Concentrations and Radionuclides in Terrestrial Environments (DESCARTES) and Calculation of Individual Doses from Environmental Radionuclides (CIDER). The DESCARTES code will be used to estimate the concentration of radionuclides in environmental pathways, given the output of the air transport code HATCHET. The CIDER code will use information provided by DESCARTES to estimate the dose received by an individual. This document reports on preliminary design work performed by the code development team to determine if the requirements could be met for Descartes and CIDER. The document contains three major sections: (i) a data flow diagram and discussion for DESCARTES, (ii) a data flow diagram and discussion for CIDER, and (iii) a series of brief statements regarding the design approach required to address each code requirement

Approximation of complex algebraic numbers by algebraic numbers of bounded degree

OpenAIRE

Bugeaud, Yann; Evertse, Jan-Hendrik

2007-01-01

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

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...

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

International Nuclear Information System (INIS)

Huang Yizhi

1994-01-01

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

The Dit nuclear fuel assembly physics design code

International Nuclear Information System (INIS)

Jonsson, A.

1987-01-01

DIT is the Combustion Engineering, Inc. (C-E) nuclear fuel assembly design code. It belongs to a class of codes, all similar in structure and strategy, which may be characterized by the spectrum and spatial calculations being performed in 2D and in a single job step for the entire assembly. The forerunner of this class of codes is the U.K.A.E.A. WIMS code, the first version of which was completed 25 years ago. The structure and strategy of assembly spectrum codes have remained remarkably similar to the original concept thus proving its usefulness. As other organizations, including C-E, have developed their own versions of the concept, many important variations have been added which significantly influence the accuracy and performance of the resulting computational tool. This paper describes and discusses those features which are unique to the DIT code and which might be of interest to the community of fuel assembly physics design code users and developers

Structural reliability codes for probabilistic design

DEFF Research Database (Denmark)

Ditlevsen, Ove Dalager

1997-01-01

probabilistic code format has not only strong influence on the formal reliability measure, but also on the formal cost of failure to be associated if a design made to the target reliability level is considered to be optimal. In fact, the formal cost of failure can be different by several orders of size for two...... different, but by and large equally justifiable probabilistic code formats. Thus, the consequence is that a code format based on decision theoretical concepts and formulated as an extension of a probabilistic code format must specify formal values to be used as costs of failure. A principle of prudence...... is suggested for guiding the choice of the reference probabilistic code format for constant reliability. In the author's opinion there is an urgent need for establishing a standard probabilistic reliability code. This paper presents some considerations that may be debatable, but nevertheless point...

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...

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

Application of differential-and-Lie-algebraic techniques to the orbit dynamics of cyclotrons

International Nuclear Information System (INIS)

Davies, W.G.; Douglas, S.R.; Pusch, G.D.; Lee-Whiting, G.E.

1991-01-01

A new orbit-dynamics code, DACYC, is being developed for the TASCC superconducting cyclotron. DACYC makes use of differential algebra and Lie Algebra to calculate and analyze partial, one-and/or multi-turn maps to very high order. Accurate, three-dimensional, analytic models of the magnetic and RF fields are used, which satisfy Maxwell's equations exactly. The maps can be analyzed with normal-form methods or to produce linear or high-order phase-space plots

Computer codes for RF cavity design

International Nuclear Information System (INIS)

Ko, K.

1992-01-01

In RF cavity design, numerical modeling is assuming an increasingly important role with the help of sophisticated computer codes and powerful yet affordable computers. A description of the cavity codes in use in the accelerator community has been given previously. The present paper will address the latest developments and discuss their applications to cavity tuning and matching problems. (Author) 8 refs., 10 figs

The vacuum preserving Lie algebra of a classical W-algebra

International Nuclear Information System (INIS)

Feher, L.; Tsutsui, I.

1993-07-01

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

Evaluation of the DRAGON code for VHTR design analysis.

Energy Technology Data Exchange (ETDEWEB)

Taiwo, T. A.; Kim, T. K.; Nuclear Engineering Division

2006-01-12

This letter report summarizes three activities that were undertaken in FY 2005 to gather information on the DRAGON code and to perform limited evaluations of the code performance when used in the analysis of the Very High Temperature Reactor (VHTR) designs. These activities include: (1) Use of the code to model the fuel elements of the helium-cooled and liquid-salt-cooled VHTR designs. Results were compared to those from another deterministic lattice code (WIMS8) and a Monte Carlo code (MCNP). (2) The preliminary assessment of the nuclear data library currently used with the code and libraries that have been provided by the IAEA WIMS-D4 Library Update Project (WLUP). (3) DRAGON workshop held to discuss the code capabilities for modeling the VHTR.

Evaluation of the DRAGON code for VHTR design analysis

International Nuclear Information System (INIS)

Taiwo, T. A.; Kim, T. K.; Nuclear Engineering Division

2006-01-01

This letter report summarizes three activities that were undertaken in FY 2005 to gather information on the DRAGON code and to perform limited evaluations of the code performance when used in the analysis of the Very High Temperature Reactor (VHTR) designs. These activities include: (1) Use of the code to model the fuel elements of the helium-cooled and liquid-salt-cooled VHTR designs. Results were compared to those from another deterministic lattice code (WIMS8) and a Monte Carlo code (MCNP). (2) The preliminary assessment of the nuclear data library currently used with the code and libraries that have been provided by the IAEA WIMS-D4 Library Update Project (WLUP). (3) DRAGON workshop held to discuss the code capabilities for modeling the VHTR

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

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

The arbitrary order design code Tlie 1.0

International Nuclear Information System (INIS)

Zeijts, J. van; Neri, Filippo

1993-01-01

We describe the arbitrary order charged particle transfer map code TLIE. This code is a general 6D relativistic design code with a MAD compatible input language and among others implements user defined functions and subroutines and nested fitting and optimization. First we describe the mathematics and physics in the code. Aside from generating maps for all the standard accelerator elements we describe an efficient method for generating nonlinear transfer maps for realistic magnet models. We have implemented the method to arbitrary order in our accelerator design code for cylindrical current sheet magnets. We also have implemented a self-consistent space-charge approach as in CHARLIE. Subsequently we give a description of the input language and finally, we give several examples from productions run, such as cases with stacked multipoles with overlapping fringe fields. (Author)

Design of Packet-Based Block Codes with Shift Operators

Directory of Open Access Journals (Sweden)

Jacek Ilow

2010-01-01

Full Text Available This paper introduces packet-oriented block codes for the recovery of lost packets and the correction of an erroneous single packet. Specifically, a family of systematic codes is proposed, based on a Vandermonde matrix applied to a group of k information packets to construct r redundant packets, where the elements of the Vandermonde matrix are bit-level right arithmetic shift operators. The code design is applicable to packets of any size, provided that the packets within a block of k information packets are of uniform length. In order to decrease the overhead associated with packet padding using shift operators, non-Vandermonde matrices are also proposed for designing packet-oriented block codes. An efficient matrix inversion procedure for the off-line design of the decoding algorithm is presented to recover lost packets. The error correction capability of the design is investigated as well. The decoding algorithm, based on syndrome decoding, to correct a single erroneous packet in a group of n=k+r received packets is presented. The paper is equipped with examples of codes using different parameters. The code designs and their performance are tested using Monte Carlo simulations; the results obtained exhibit good agreement with the corresponding theoretical results.

Adventure Code Camp: Library Mobile Design in the Backcountry

OpenAIRE

Ward, David; Hahn, James; Mestre, Lori

2014-01-01

This article presents a case study exploring the use of a student Coding Camp as a bottom-up mobile design process to generate library mobile apps. A code camp sources student programmer talent and ideas for designing software services and features.  This case study reviews process, outcomes, and next steps in mobile web app coding camps. It concludes by offering implications for services design beyond the local camp presented in this study. By understanding how patrons expect to integrate li...

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

Adventure Code Camp: Library Mobile Design in the Backcountry

Directory of Open Access Journals (Sweden)

David Ward

2014-09-01

Full Text Available This article presents a case study exploring the use of a student Coding Camp as a bottom-up mobile design process to generate library mobile apps. A code camp sources student programmer talent and ideas for designing software services and features.  This case study reviews process, outcomes, and next steps in mobile web app coding camps. It concludes by offering implications for services design beyond the local camp presented in this study. By understanding how patrons expect to integrate library services and resources into their use of mobile devices, librarians can better design the user experience for this environment.

Multilevel LDPC Codes Design for Multimedia Communication CDMA System

Directory of Open Access Journals (Sweden)

Hou Jia

2004-01-01

Full Text Available We design multilevel coding (MLC with a semi-bit interleaved coded modulation (BICM scheme based on low density parity check (LDPC codes. Different from the traditional designs, we joined the MLC and BICM together by using the Gray mapping, which is suitable to transmit the data over several equivalent channels with different code rates. To perform well at signal-to-noise ratio (SNR to be very close to the capacity of the additive white Gaussian noise (AWGN channel, random regular LDPC code and a simple semialgebra LDPC (SA-LDPC code are discussed in MLC with parallel independent decoding (PID. The numerical results demonstrate that the proposed scheme could achieve both power and bandwidth efficiency.

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.

Explicit MDS Codes with Complementary Duals

DEFF Research Database (Denmark)

Beelen, Duals Peter; Jin, Lingfei

2018-01-01

In 1964, Massey introduced a class of codes with complementary duals which are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD codes have applications in communication system, side-channel attack (SCA) and so on. LCD codes have been extensively studied in literature....... On the other hand, MDS codes form an optimal family of classical codes which have wide applications in both theory and practice. The main purpose of this paper is to give an explicit construction of several classes of LCD MDS codes, using tools from algebraic function fields. We exemplify this construction...

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…

Linear codes associated to determinantal varieties

DEFF Research Database (Denmark)

Beelen, Peter; Ghorpade, Sudhir R.; Hasan, Sartaj Ul

2015-01-01

We consider a class of linear codes associated to projective algebraic varieties defined by the vanishing of minors of a fixed size of a generic matrix. It is seen that the resulting code has only a small number of distinct weights. The case of varieties defined by the vanishing of 2×2 minors is ...

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.

Design Research on Personalized Problem Posing in Algebra

Science.gov (United States)

Walkington, Candace

2017-01-01

Algebra is an area of pressing national concern around issues of equity and access in education. Recent theories and research suggest that personalization of instruction can allow students to activate their funds of knowledge and can elicit interest in the content to be learned. This paper examines the results of a large-scale teaching experiment…

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

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.

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)

Monomial codes seen as invariant subspaces

Directory of Open Access Journals (Sweden)

García-Planas María Isabel

2017-08-01

Full Text Available It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known. In this paper a generalization of this relationship is presented between monomial codes over a finite field and hyperinvariant subspaces of n under an appropriate linear transformation. Using techniques of Linear Algebra it is possible to deduce certain properties for this particular type of codes, generalizing known results on cyclic codes.

(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.

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)

Recent trends in coding theory and its applications

CERN Document Server

Li, Wen-Ching Winnie

2007-01-01

Coding theory draws on a remarkable selection of mathematical topics, both pure and applied. The various contributions in this volume introduce coding theory and its most recent developments and applications, emphasizing both mathematical and engineering perspectives on the subject. This volume covers four important areas in coding theory: algebraic geometry codes, graph-based codes, space-time codes, and quantum codes. Both students and seasoned researchers will benefit from the extensive and self-contained discussions of the development and recent progress in these areas.

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)

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

GPU Linear Algebra Libraries and GPGPU Programming for Accelerating MOPAC Semiempirical Quantum Chemistry Calculations.

Science.gov (United States)

Maia, Julio Daniel Carvalho; Urquiza Carvalho, Gabriel Aires; Mangueira, Carlos Peixoto; Santana, Sidney Ramos; Cabral, Lucidio Anjos Formiga; Rocha, Gerd B

2012-09-11

In this study, we present some modifications in the semiempirical quantum chemistry MOPAC2009 code that accelerate single-point energy calculations (1SCF) of medium-size (up to 2500 atoms) molecular systems using GPU coprocessors and multithreaded shared-memory CPUs. Our modifications consisted of using a combination of highly optimized linear algebra libraries for both CPU (LAPACK and BLAS from Intel MKL) and GPU (MAGMA and CUBLAS) to hasten time-consuming parts of MOPAC such as the pseudodiagonalization, full diagonalization, and density matrix assembling. We have shown that it is possible to obtain large speedups just by using CPU serial linear algebra libraries in the MOPAC code. As a special case, we show a speedup of up to 14 times for a methanol simulation box containing 2400 atoms and 4800 basis functions, with even greater gains in performance when using multithreaded CPUs (2.1 times in relation to the single-threaded CPU code using linear algebra libraries) and GPUs (3.8 times). This degree of acceleration opens new perspectives for modeling larger structures which appear in inorganic chemistry (such as zeolites and MOFs), biochemistry (such as polysaccharides, small proteins, and DNA fragments), and materials science (such as nanotubes and fullerenes). In addition, we believe that this parallel (GPU-GPU) MOPAC code will make it feasible to use semiempirical methods in lengthy molecular simulations using both hybrid QM/MM and QM/QM potentials.

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

International Nuclear Information System (INIS)

Kobayashi, Tatsuo

1993-01-01

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

COSY 5.0 - the fifth order code for corpuscular optical systems

International Nuclear Information System (INIS)

Berz, M.; Hoffmann, H.C.; Wollnik, H.

1987-01-01

COSY 5.0 is a new computer code for the design of corpuscular optical systems based on the principle of transfer matrices. The particle optical calculations include all image aberrations through fifth order. COSY 5.0 uses canonical coordinates and exploits the symplectic condition to increase the speed of computation. COSY 5.0 contains a library for the computation of matrix elements of all commonly used corpuscular optical elements such as electric and magnetic multipoles and sector fields. The corresponding formulas were generated algebraically by the computer code HAMILTON. Care was taken that the optimization of optical elements is achieved with minimal numerical effort. Finally COSY 5.0 has a very general mnemonic input code resembling a higher programming language. (orig.)

Lie Algebraic Treatment of Linear and Nonlinear Beam Dynamics

Energy Technology Data Exchange (ETDEWEB)

Alex J. Dragt; Filippo Neri; Govindan Rangarajan; David Douglas; Liam M. Healy; Robert D. Ryne

1988-12-01

The purpose of this paper is to present a summary of new methods, employing Lie algebraic tools, for characterizing beam dynamics in charged-particle optical systems. These methods are applicable to accelerator design, charged-particle beam transport, electron microscopes, and also light optics. The new methods represent the action of each separate element of a compound optical system, including all departures from paraxial optics, by a certain operator. The operators for the various elements can then be concatenated, following well-defined rules, to obtain a resultant operator that characterizes the entire system. This paper deals mostly with accelerator design and charged-particle beam transport. The application of Lie algebraic methods to light optics and electron microscopes is described elsewhere (1, see also 44). To keep its scope within reasonable bounds, they restrict their treatment of accelerator design and charged-particle beam transport primarily to the use of Lie algebraic methods for the description of particle orbits in terms of transfer maps. There are other Lie algebraic or related approaches to accelerator problems that the reader may find of interest (2). For a general discussion of linear and nonlinear problems in accelerator physics see (3).

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...

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)

Topics in quaternion linear algebra

CERN Document Server

Rodman, Leiba

2014-01-01

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses...

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)

On the Organizational Dynamics of the Genetic Code

KAUST Repository

Zhang, Zhang

2011-06-07

The organization of the canonical genetic code needs to be thoroughly illuminated. Here we reorder the four nucleotides—adenine, thymine, guanine and cytosine—according to their emergence in evolution, and apply the organizational rules to devising an algebraic representation for the canonical genetic code. Under a framework of the devised code, we quantify codon and amino acid usages from a large collection of 917 prokaryotic genome sequences, and associate the usages with its intrinsic structure and classification schemes as well as amino acid physicochemical properties. Our results show that the algebraic representation of the code is structurally equivalent to a content-centric organization of the code and that codon and amino acid usages under different classification schemes were correlated closely with GC content, implying a set of rules governing composition dynamics across a wide variety of prokaryotic genome sequences. These results also indicate that codons and amino acids are not randomly allocated in the code, where the six-fold degenerate codons and their amino acids have important balancing roles for error minimization. Therefore, the content-centric code is of great usefulness in deciphering its hitherto unknown regularities as well as the dynamics of nucleotide, codon, and amino acid compositions.

On the Organizational Dynamics of the Genetic Code

KAUST Repository

Zhang, Zhang; Yu, Jun

2011-01-01

The organization of the canonical genetic code needs to be thoroughly illuminated. Here we reorder the four nucleotides—adenine, thymine, guanine and cytosine—according to their emergence in evolution, and apply the organizational rules to devising an algebraic representation for the canonical genetic code. Under a framework of the devised code, we quantify codon and amino acid usages from a large collection of 917 prokaryotic genome sequences, and associate the usages with its intrinsic structure and classification schemes as well as amino acid physicochemical properties. Our results show that the algebraic representation of the code is structurally equivalent to a content-centric organization of the code and that codon and amino acid usages under different classification schemes were correlated closely with GC content, implying a set of rules governing composition dynamics across a wide variety of prokaryotic genome sequences. These results also indicate that codons and amino acids are not randomly allocated in the code, where the six-fold degenerate codons and their amino acids have important balancing roles for error minimization. Therefore, the content-centric code is of great usefulness in deciphering its hitherto unknown regularities as well as the dynamics of nucleotide, codon, and amino acid compositions.

SUPPORTING STUDENTS’ UNDERSTANDING OF LINEAR EQUATIONS WITH ONE VARIABLE USING ALGEBRA TILES

Directory of Open Access Journals (Sweden)

Sari Saraswati

2016-01-01

Full Text Available This research aimed to describe how algebra tiles can support students’ understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students use the algebra tiles to find a method to solve linear equations with one variable. Design research was used as an approach in this study. It consists of three phases, namely preliminary design, teaching experiment and retrospective analysis. Video registrations, students’ written works, pre-test, post-test, field notes, and interview are technic to collect data. The data were analyzed by comparing the hypothetical learning trajectory (HLT and the actual learning process. The result shows that algebra tiles could supports students’ understanding to find the formal solution of linear equation with one variable.Keywords: linear equation with one variable, algebra tiles, design research, balancing method, HLT DOI: http://dx.doi.org/10.22342/jme.7.1.2814.19-30

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.)

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.)

Galilean contractions of W-algebras

Directory of Open Access Journals (Sweden)

Jørgen Rasmussen

2017-09-01

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

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

International Nuclear Information System (INIS)

Frenkel, E.; Reshetikhin, N.

1996-01-01

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

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)

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.

Application of Computer Graphics to Graphing in Algebra and Trigonometry. Final Report.

Science.gov (United States)

Morris, J. Richard

This project was designed to improve the graphing competency of students in elementary algebra, intermediate algebra, and trigonometry courses at Virginia Commonwealth University. Computer graphics programs were designed using an Apple II Plus computer and implemented using Pascal. The software package is interactive and gives students control…

Computer codes used in particle accelerator design: First edition

International Nuclear Information System (INIS)

1987-01-01

This paper contains a listing of more than 150 programs that have been used in the design and analysis of accelerators. Given on each citation are person to contact, classification of the computer code, publications describing the code, computer and language runned on, and a short description of the code. Codes are indexed by subject, person to contact, and code acronym

Diagonal Eigenvalue Unity (DEU) code for spectral amplitude coding-optical code division multiple access

Science.gov (United States)

Ahmed, Hassan Yousif; Nisar, K. S.

2013-08-01

Code with ideal in-phase cross correlation (CC) and practical code length to support high number of users are required in spectral amplitude coding-optical code division multiple access (SAC-OCDMA) systems. SAC systems are getting more attractive in the field of OCDMA because of its ability to eliminate the influence of multiple access interference (MAI) and also suppress the effect of phase induced intensity noise (PIIN). In this paper, we have proposed new Diagonal Eigenvalue Unity (DEU) code families with ideal in-phase CC based on Jordan block matrix with simple algebraic ways. Four sets of DEU code families based on the code weight W and number of users N for the combination (even, even), (even, odd), (odd, odd) and (odd, even) are constructed. This combination gives DEU code more flexibility in selection of code weight and number of users. These features made this code a compelling candidate for future optical communication systems. Numerical results show that the proposed DEU system outperforms reported codes. In addition, simulation results taken from a commercial optical systems simulator, Virtual Photonic Instrument (VPI™) shown that, using point to multipoint transmission in passive optical network (PON), DEU has better performance and could support long span with high data rate.

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.

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

ASME Code requirements for multi-canister overpack design and fabrication

International Nuclear Information System (INIS)

SMITH, K.E.

1998-01-01

The baseline requirements for the design and fabrication of the MCO include the application of the technical requirements of the ASME Code, Section III, Subsection NB for containment and Section III, Subsection NG for criticality control. ASME Code administrative requirements, which have not historically been applied at the Hanford site and which have not been required by the US Nuclear Regulatory Commission (NRC) for licensed spent fuel casks/canisters, were not invoked for the MCO. As a result of recommendations made from an ASME Code consultant in response to DNFSB staff concerns regarding ASME Code application, the SNF Project will be making the following modifications: issue an ASME Code Design Specification and Design Report, certified by a Registered Professional Engineer; Require the MCO fabricator to hold ASME Section III or Section VIII, Division 2 accreditation; and Use ASME Authorized Inspectors for MCO fabrication. Incorporation of these modifications will ensure that the MCO is designed and fabricated in accordance with the ASME Code. Code Stamping has not been a requirement at the Hanford site, nor for NRC licensed spent fuel casks/canisters, but will be considered if determined to be economically justified

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

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.

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

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)

New way on designing majorant coincidence circuits

International Nuclear Information System (INIS)

Gajdamaka, R.I.; Kalinnikov, V.A.; Nikityuk, N.M.; Shirikov, V.P.

1982-01-01

A new way of designing fast devices of combinatorial selection by the number of particles passing through a multichannel charged particle detector is decribed. The algorithm of their operation is based on modern algebraic coding theory. By application of analytical computational methods Boolean expressions can be obtianed for designing basic circuits for a large number of inputs. An example of computation of 15 inputs majorant coincidence circuit is considered

(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.

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

NARCIS (Netherlands)

Horobeţ, E.

2016-01-01

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

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

International Nuclear Information System (INIS)

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

1999-04-01

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

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

Directory of Open Access Journals (Sweden)

Zdenka Riečanová

2013-01-01

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

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

International Nuclear Information System (INIS)

Kanakoglou, K; Daskaloyannis, C

2008-01-01

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

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

OpenAIRE

Vasselli, Ezio

2004-01-01

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

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.)

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...

Evaluation of the analysis models in the ASTRA nuclear design code system

Energy Technology Data Exchange (ETDEWEB)

Cho, Nam Jin; Park, Chang Jea; Kim, Do Sam; Lee, Kyeong Taek; Kim, Jong Woon [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

2000-11-15

In the field of nuclear reactor design, main practice was the application of the improved design code systems. During the process, a lot of basis and knowledge were accumulated in processing input data, nuclear fuel reload design, production and analysis of design data, et al. However less efforts were done in the analysis of the methodology and in the development or improvement of those code systems. Recently, KEPO Nuclear Fuel Company (KNFC) developed the ASTRA (Advanced Static and Transient Reactor Analyzer) code system for the purpose of nuclear reactor design and analysis. In the code system, two group constants were generated from the CASMO-3 code system. The objective of this research is to analyze the analysis models used in the ASTRA/CASMO-3 code system. This evaluation requires indepth comprehension of the models, which is important so much as the development of the code system itself. Currently, most of the code systems used in domestic Nuclear Power Plant were imported, so it is very difficult to maintain and treat the change of the situation in the system. Therefore, the evaluation of analysis models in the ASTRA nuclear reactor design code system in very important.

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.

SUPPORTING STUDENTS’ UNDERSTANDING OF LINEAR EQUATIONS WITH ONE VARIABLE USING ALGEBRA TILES

Directory of Open Access Journals (Sweden)

Sari Saraswati

2016-01-01

Full Text Available This research aimed to describe how algebra tiles can support students’ understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students use the algebra tiles to find a method to solve linear equations with one variable. Design research was used as an approach in this study. It consists of three phases, namely preliminary design, teaching experiment and retrospective analysis. Video registrations, students’ written works, pre-test, post-test, field notes, and interview are technic to collect data. The data were analyzed by comparing the hypothetical learning trajectory (HLT and the actual learning process. The result shows that algebra tiles could supports students’ understanding to find the formal solution of linear equation with one variable.

Linear network error correction coding

CERN Document Server

Guang, Xuan

2014-01-01

There are two main approaches in the theory of network error correction coding. In this SpringerBrief, the authors summarize some of the most important contributions following the classic approach, which represents messages by sequences?similar to algebraic coding,?and also briefly discuss the main results following the?other approach,?that uses the theory of rank metric codes for network error correction of representing messages by subspaces. This book starts by establishing the basic linear network error correction (LNEC) model and then characterizes two equivalent descriptions. Distances an

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.

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.

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

SAFETY IN THE DESIGN OF SCIENCE LABORATORIES AND BUILDING CODES.

Science.gov (United States)

HOROWITZ, HAROLD

THE DESIGN OF COLLEGE AND UNIVERSITY BUILDINGS USED FOR SCIENTIFIC RESEARCH AND EDUCATION IS DISCUSSED IN TERMS OF LABORATORY SAFETY AND BUILDING CODES AND REGULATIONS. MAJOR TOPIC AREAS ARE--(1) SAFETY RELATED DESIGN FEATURES OF SCIENCE LABORATORIES, (2) LABORATORY SAFETY AND BUILDING CODES, AND (3) EVIDENCE OF UNSAFE DESIGN. EXAMPLES EMPHASIZE…

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

International Nuclear Information System (INIS)

Blumenhagen, R.

1994-07-01

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

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

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

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.)

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

Science.gov (United States)

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

2018-03-01

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

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

SWAAM code development, verification and application to steam generator design

International Nuclear Information System (INIS)

Shin, Y.W.; Valentin, R.A.

1990-01-01

This paper describes the family of SWAAM codes developed by Argonne National Laboratory to analyze the effects of sodium/water reactions on LMR steam generators. The SWAAM codes were developed as design tools for analyzing various phenomena related to steam generator leaks and to predict the resulting thermal and hydraulic effects on the steam generator and the intermediate heat transport system (IHTS). The theoretical foundations and numerical treatments on which the codes are based are discussed, followed by a description of code capabilities and limitations, verification of the codes by comparison with experiment, and applications to steam generator and IHTS design. (author). 25 refs, 14 figs

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

Establishment of computer code system for nuclear reactor design - analysis

International Nuclear Information System (INIS)

Subki, I.R.; Santoso, B.; Syaukat, A.; Lee, S.M.

1996-01-01

Establishment of computer code system for nuclear reactor design analysis is given in this paper. This establishment is an effort to provide the capability in running various codes from nuclear data to reactor design and promote the capability for nuclear reactor design analysis particularly from neutronics and safety points. This establishment is also an effort to enhance the coordination of nuclear codes application and development existing in various research centre in Indonesia. Very prospective results have been obtained with the help of IAEA technical assistance. (author). 6 refs, 1 fig., 1 tab

Squares of Random Linear Codes

DEFF Research Database (Denmark)

Cascudo Pueyo, Ignacio; Cramer, Ronald; Mirandola, Diego

2015-01-01

a positive answer, for codes of dimension $k$ and length roughly $\\frac{1}{2}k^2$ or smaller. Moreover, the convergence speed is exponential if the difference $k(k+1)/2-n$ is at least linear in $k$. The proof uses random coding and combinatorial arguments, together with algebraic tools involving the precise......Given a linear code $C$, one can define the $d$-th power of $C$ as the span of all componentwise products of $d$ elements of $C$. A power of $C$ may quickly fill the whole space. Our purpose is to answer the following question: does the square of a code ``typically'' fill the whole space? We give...

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.

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.

FLP: a field line plotting code for bundle divertor design

International Nuclear Information System (INIS)

Ruchti, C.

1981-01-01

A computer code was developed to aid in the design of bundle divertors. The code can handle discrete toroidal field coils and various divertor coil configurations. All coils must be composed of straight line segments. The code runs on the PDP-10 and displays plots of the configuration, field lines, and field ripple. It automatically chooses the coil currents to connect the separatrix produced by the divertor to the outer edge of the plasma and calculates the required coil cross sections. Several divertor designs are illustrated to show how the code works

A finite element code for electric motor design

Science.gov (United States)

Campbell, C. Warren

1994-01-01

FEMOT is a finite element program for solving the nonlinear magnetostatic problem. This version uses nonlinear, Newton first order elements. The code can be used for electric motor design and analysis. FEMOT can be embedded within an optimization code that will vary nodal coordinates to optimize the motor design. The output from FEMOT can be used to determine motor back EMF, torque, cogging, and magnet saturation. It will run on a PC and will be available to anyone who wants to use it.

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

CASL, the Common Algebraic Specification Language

DEFF Research Database (Denmark)

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

2008-01-01

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

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.)

College Algebra in Context: A Project Incorporating Social Issues

Directory of Open Access Journals (Sweden)

Michael T. Catalano

2010-01-01

Full Text Available This paper discusses the development of an innovative college algebra text designed for use in a data-driven, activity-oriented college algebra course, incorporating realistic problem situations emphasizing social and economic issues, including hunger and poverty, energy, and the environment. The course incorporates quantitative literacy themes, is informed by existing college algebra texts within the college algebra reform movement, and implements a collaborative pedagogical approach intended to provide future K-12 teachers an alternative model for the teaching of mathematics. The paper contains a short history of the project development phase, supported by an NSF grant (DUE #0442979, as well as the perceived role of the project in the college algebra reform and quantitative literacy movements. We make a short case for redefining the content of a college algebra course and acknowledging that for many students, it has become a terminal mathematics course. A description of the contents of the text, its relation to more traditional college algebra content, and four example student activities are included (on the topics of homelessness, the effects of airline deregulation, real estate versus savings as investment instruments, and the 2008 election. A summary of evaluation and assessment data from five years of pilot-testing, done primarily in conjuction with our NSF grant evaluation plan, is provided.

Pre-Algebra Essentials For Dummies

CERN Document Server

Zegarelli, Mark

2010-01-01

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

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

Symmetries in Genetic Systems and the Concept of Geno-Logical Coding

Directory of Open Access Journals (Sweden)

Sergey V. Petoukhov

2016-12-01

Full Text Available The genetic code of amino acid sequences in proteins does not allow understanding and modeling of inherited processes such as inborn coordinated motions of living bodies, innate principles of sensory information processing, quasi-holographic properties, etc. To be able to model these phenomena, the concept of geno-logical coding, which is connected with logical functions and Boolean algebra, is put forward. The article describes basic pieces of evidence in favor of the existence of the geno-logical code, which exists in p­arallel with the known genetic code of amino acid sequences but which serves for transferring inherited processes along chains of generations. These pieces of evidence have been received due to the analysis of symmetries in structures of molecular-genetic systems. The analysis has revealed a close connection of the genetic system with dyadic groups of binary numbers and with other mathematical objects, which are related with dyadic groups: Walsh functions (which are algebraic characters of dyadic groups, bit-reversal permutations, logical holography, etc. These results provide a new approach for mathematical modeling of genetic structures, which uses known mathematical formalisms from technological fields of noise-immunity coding of information, binary analysis, logical holography, and digital devices of artificial intellect. Some opportunities for a development of algebraic-logical biology are opened.

ACE - an algebraic compiler and encoder for the Chalk River datatron computer

International Nuclear Information System (INIS)

Kennedy, J.M.; Okazaki, E.A.; Millican, M.

1960-03-01

ACE is a program written for the Chalk River Datatron (Burroughs 205) Computer to enable the machine to compile a program for solving a problem from instructions supplied by the user in a notation related much more closely to algebra than to the machine's own code. (author)

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.

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…

Infinite dimension algebra and conformal symmetry

International Nuclear Information System (INIS)

Ragoucy-Aubezon, E.

1991-04-01

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

Equivalency of two-dimensional algebras

International Nuclear Information System (INIS)

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

2011-01-01

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

Optimal patch code design via device characterization

Science.gov (United States)

Wu, Wencheng; Dalal, Edul N.

2012-01-01

In many color measurement applications, such as those for color calibration and profiling, "patch code" has been used successfully for job identification and automation to reduce operator errors. A patch code is similar to a barcode, but is intended primarily for use in measurement devices that cannot read barcodes due to limited spatial resolution, such as spectrophotometers. There is an inherent tradeoff between decoding robustness and the number of code levels available for encoding. Previous methods have attempted to address this tradeoff, but those solutions have been sub-optimal. In this paper, we propose a method to design optimal patch codes via device characterization. The tradeoff between decoding robustness and the number of available code levels is optimized in terms of printing and measurement efforts, and decoding robustness against noises from the printing and measurement devices. Effort is drastically reduced relative to previous methods because print-and-measure is minimized through modeling and the use of existing printer profiles. Decoding robustness is improved by distributing the code levels in CIE Lab space rather than in CMYK space.

Mathematical modelling in engineering: A proposal to introduce linear algebra concepts

Directory of Open Access Journals (Sweden)

Andrea Dorila Cárcamo

2016-03-01

Full Text Available The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasize the development of mathematical abilities primarily associated with modelling and interpreting, which aren´t limited only to calculus abilities. Considering this, an instructional design was elaborated based on mathematic modelling and emerging heuristic models for the construction of specific linear algebra concepts:  span and spanning set. This was applied to first year engineering students. Results suggest that this type of instructional design contributes to the construction of these mathematical concepts and can also favour first year engineering students understanding of key linear algebra concepts and potentiate the development of higher order skills.

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.

Applications of American design codes for elevated temperature environment

International Nuclear Information System (INIS)

Severud, L.K.

1980-03-01

A brief summary of the ASME Code rules of Case N-47 is presented. An overview of the typical procedure used to demonstrate Code compliance is provided. Application experience and some examples of detailed inelastic analysis and simplified-approximate methods are given. Recent developments and future trends in design criteria and ASME Code rules are also presented

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

CALIOP: a multichannel design code for gas-cooled fast reactors. Code description and user's guide

International Nuclear Information System (INIS)

Thompson, W.I.

1980-10-01

CALIOP is a design code for fluid-cooled reactors composed of parallel fuel tubes in hexagonal or cylindrical ducts. It may be used with gaseous or liquid coolants. It has been used chiefly for design of a helium-cooled fast breeder reactor and has built-in cross section information to permit calculations of fuel loading, breeding ratio, and doubling time. Optional cross-section input allows the code to be used with moderated cores and with other fuels

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

Indian Academy of Sciences (India)

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

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...

Polynomial weights and code constructions

DEFF Research Database (Denmark)

Massey, J; Costello, D; Justesen, Jørn

1973-01-01

polynomial included. This fundamental property is then used as the key to a variety of code constructions including 1) a simplified derivation of the binary Reed-Muller codes and, for any primepgreater than 2, a new extensive class ofp-ary "Reed-Muller codes," 2) a new class of "repeated-root" cyclic codes...... of long constraint length binary convolutional codes derived from2^r-ary Reed-Solomon codes, and 6) a new class ofq-ary "repeated-root" constacyclic codes with an algebraic decoding algorithm.......For any nonzero elementcof a general finite fieldGF(q), it is shown that the polynomials(x - c)^i, i = 0,1,2,cdots, have the "weight-retaining" property that any linear combination of these polynomials with coefficients inGF(q)has Hamming weight at least as great as that of the minimum degree...

Groups, matrices, and vector spaces a group theoretic approach to linear algebra

CERN Document Server

Carrell, James B

2017-01-01

This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory ...

Design and Analysis of LT Codes with Decreasing Ripple Size

DEFF Research Database (Denmark)

Sørensen, Jesper Hemming; Popovski, Petar; Østergaard, Jan

2012-01-01

In this paper we propose a new design of LT codes, which decreases the amount of necessary overhead in comparison to existing designs. The design focuses on a parameter of the LT decoding process called the ripple size. This parameter was also a key element in the design proposed in the original...... work by Luby. Specifically, Luby argued that an LT code should provide a constant ripple size during decoding. In this work we show that the ripple size should decrease during decoding, in order to reduce the necessary overhead. Initially we motivate this claim by analytical results related...... to the redundancy within an LT code. We then propose a new design procedure, which can provide any desired achievable decreasing ripple size. The new design procedure is evaluated and compared to the current state of the art through simulations. This reveals a significant increase in performance with respect...

Automated Angular Momentum Recoupling Algebra

Science.gov (United States)

Williams, H. T.; Silbar, Richard R.

1992-04-01

We present a set of heuristic rules for algebraic solution of angular momentum recoupling problems. The general problem reduces to that of finding an optimal path from one binary tree (representing the angular momentum coupling scheme for the reduced matrix element) to another (representing the sub-integrals and spin sums to be done). The method lends itself to implementation on a microcomputer, and we have developed such an implementation using a dialect of LISP. We describe both how our code, called RACAH, works and how it appears to the user. We illustrate the use of RACAH for several transition and scattering amplitude matrix elements occurring in atomic, nuclear, and particle physics.

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.

Computational algebraic geometry of epidemic models

Science.gov (United States)

Rodríguez Vega, Martín.

2014-06-01

Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

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.

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)

GPU Linear algebra extensions for GNU/Octave

International Nuclear Information System (INIS)

Bosi, L B; Mariotti, M; Santocchia, A

2012-01-01

Octave is one of the most widely used open source tools for numerical analysis and liner algebra. Our project aims to improve Octave by introducing support for GPU computing in order to speed up some linear algebra operations. The core of our work is a C library that executes some BLAS operations concerning vector- vector, vector matrix and matrix-matrix functions on the GPU. OpenCL functions are used to program GPU kernels, which are bound within the GNU/octave framework. We report the project implementation design and some preliminary results about performance.

Using CAMAL for algebraic computations in general relativity

International Nuclear Information System (INIS)

Fitch, J.P.

1979-01-01

CAMAL is a collection of computer algebra systems developed in Cambridge, England for use mainly in theoretical physics. One of these was designed originally for general relativity calculations, although it is often used in other fields. In a recent paper Cohen, Leringe, and Sundblad compared six systems for algebraic computations applied to general relativity available in Stockholm. Here similar information for CAMAL is given and by using the same tests CAMAL is added to the comparison. (author)

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....

Design Aspects of the Rayleigh Convection Code

Science.gov (United States)

Featherstone, N. A.

2017-12-01

Understanding the long-term generation of planetary or stellar magnetic field requires complementary knowledge of the large-scale fluid dynamics pervading large fractions of the object's interior. Such large-scale motions are sensitive to the system's geometry which, in planets and stars, is spherical to a good approximation. As a result, computational models designed to study such systems often solve the MHD equations in spherical geometry, frequently employing a spectral approach involving spherical harmonics. We present computational and user-interface design aspects of one such modeling tool, the Rayleigh convection code, which is suitable for deployment on desktop and petascale-hpc architectures alike. In this poster, we will present an overview of this code's parallel design and its built-in diagnostics-output package. Rayleigh has been developed with NSF support through the Computational Infrastructure for Geodynamics and is expected to be released as open-source software in winter 2017/2018.

Algebraic Modeling of Topological and Computational Structures and Applications

CERN Document Server

Theodorou, Doros; Stefaneas, Petros; Kauffman, Louis

2017-01-01

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

SAGA advances in ShApes, Geometry, and Algebra : results from the Marie Curie initial training network

CERN Document Server

Muntingh, Georg

2014-01-01

This book summarizes research carried out in workshops of the SAGA project, an Initial Training Network exploring the interplay of Shapes, Algebra, Geometry and Algorithms. Written by a combination of young and experienced researchers, the book introduces new ideas in an established context. Among the central topics are approximate and sparse implicitization and surface parametrization; algebraic tools for geometric computing; algebraic geometry for computer aided design applications and problems with industrial applications. Readers will encounter new methods for the (approximate) transition between the implicit and parametric representation; new algebraic tools for geometric computing; new applications of isogeometric analysis, and will gain insight into the emerging research field situated between algebraic geometry and computer aided geometric design.

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.

SWAAM-code development and verification and application to steam generator designs

International Nuclear Information System (INIS)

Shin, Y.W.; Valentin, R.A.

1990-01-01

This paper describes the family of SWAAM codes which were developed by Argonne National Laboratory to analyze the effects of sodium-water reactions on LMR steam generators. The SWAAM codes were developed as design tools for analyzing various phenomena related to steam generator leaks and the resulting thermal and hydraulic effects on the steam generator and the intermediate heat transport system (IHTS). The paper discusses the theoretical foundations and numerical treatments on which the codes are based, followed by a description of code capabilities and limitations, verification of the codes and applications to steam generator and IHTS designs. 25 refs., 14 figs

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

International Nuclear Information System (INIS)

Fujikawa, Kazuo; Suzuki, Hiroshi.

1991-03-01

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

Elementary Algebra Connections to Precalculus

Science.gov (United States)

Lopez-Boada, Roberto; Daire, Sandra Arguelles

2013-01-01

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

A computer code to design liquid containers for vehicles

International Nuclear Information System (INIS)

Parizi, H.B.; Fard, M.P.; Dolatabadi, A.

2003-01-01

We are presenting the development of a modular code for the simulation of the fluid sloshing that occurs in the liquid containers in vehicles. Sloshing occurs when a partially filled container of liquid goes through transient or steady external forces. Under such conditions, the free surface of the liquid may move and the liquid may impact on the walls of the container, exchanging forces. These forces may cause numerous harmful and undesirable consequences in the operation of the vehicle, such as vehicle turn over. The fluid mechanic equations that describe the fluid sloshing in the container and the dynamic equations that describe the movement of the container are solved separately in two different codes. The codes are coupled weekly, such that the output of one code will be used as the input to the other code in the same time step. The outputs of the fluid code are the forces and torques that are applied to the body of the container due to sloshing, whereas the output of the dynamic code are the translational and rotational velocities and accelerations of the container. The proposed software can be used to test the performance of the designed container under various operating condition and allow effective improvements to the container design. The proposed code is different than the presently available codes, in that it will provide a true simulation of the coupled fluid and structure interaction. (author)

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 ...

Novikov algebras with associative bilinear forms

Energy Technology Data Exchange (ETDEWEB)

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

2007-11-23

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

A Quantitative Reasoning Approach to Algebra Using Inquiry-Based Learning

Directory of Open Access Journals (Sweden)

Victor I. Piercey

2017-07-01

Full Text Available In this paper, I share a hybrid quantitative reasoning/algebra two-course sequence that challenges the common assumption that quantitative literacy and reasoning are less rigorous mathematics alternatives to algebra and illustrates that a quantitative reasoning framework can be used to teach traditional algebra. The presentation is made in two parts. In the first part, which is somewhat philosophical and theoretical, I explain my personal perspective of what I mean by “algebra” and “doing algebra.” I contend that algebra is a form of communication whose value is precision, which allows us to perform algebraic manipulations in the form of simplification and solving moves. A quantitative reasoning approach to traditional algebraic manipulations rests on intentional and purposeful use of simplification and solving moves within contextual situations. In part 2, I describe a 6-week instructional module intended for undergraduate business students that was delivered to students who had placed into beginning algebra. The perspective described in part 1 heavily informed the design of this module. The course materials, which involve the use of Excel in multiple authentic contexts, are built around the use of inquiry-based learning. Upon completion of this module, the percentage of students who successfully complete model problems in an assessment is in the same range as surveyed students in precalculus and calculus, approximately two “grade levels” ahead of their placement.

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...

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.

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...

Double-partition Quantum Cluster Algebras

DEFF Research Database (Denmark)

Jakobsen, Hans Plesner; Zhang, Hechun

2012-01-01

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

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

Very true operators on MTL-algebras

Directory of Open Access Journals (Sweden)

Wang Jun Tao

2016-01-01

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

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

Science.gov (United States)

Suga, Tetsuya; Iijima, Junichi

2018-03-01

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

The effects of an integrated Algebra 1/physical science curriculum on student achievement in Algebra 1, proportional reasoning and graphing abilities

Science.gov (United States)

Lawrence, Lettie Carol

1997-08-01

The purpose of this investigation was to determine if an integrated curriculum in algebra 1/physical science facilitates acquisition of proportional reasoning and graphing abilities better than a non-integrated, traditional, algebra 1 curriculum. Also, this study was to ascertain if the integrated algebra 1/physical science curriculum resulted in greater student achievement in algebra 1. The curriculum used in the experimental class was SAM 9 (Science and Mathematics 9), an investigation-based curriculum that was written to integrate physical science and basic algebra content. The experiment was conducted over one school year. The subjects in the study were 61 ninth grade students. The experimental group consisted of one class taught concurrently by a mathematics teacher and a physical science teacher. The control group consisted of three classes of algebra 1 students taught by one mathematics teacher and taking physical science with other teachers in the school who were not participating in the SAM 9 program. This study utilized a quasi-experimental non-randomized control group pretest-posttest design. The investigator obtained end-of-algebra 1 scores from student records. The written open-ended graphing instruments and the proportional reasoning instrument were administered to both groups as pretests and posttests. The graphing instruments were also administered as a midtest. A two sample t-test for independent means was used to determine significant differences in achievement on the end-of-course algebra 1 test. Quantitative data from the proportional reasoning and graphing instruments were analyzed using a repeated measures analysis of variance to determine differences in scores over time for the experimental and control groups. The findings indicate no significant difference between the experimental and control groups on the end-of-course algebra 1 test. Results also indicate no significant differences in proportional reasoning and graphing abilities between

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)

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

International Nuclear Information System (INIS)

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

1996-05-01

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

Extended Kac-Moody algebras and applications

International Nuclear Information System (INIS)

Ragoucy, E.; Sorba, P.

1991-04-01

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

What ''Counts'' as Algebra in the Eyes of Preservice Elementary Teachers?

Science.gov (United States)

Stephens, Ana C.

2008-01-01

This study examined conceptions of algebra held by 30 preservice elementary teachers. In addition to exploring participants' general ''definitions'' of algebra, this study examined, in particular, their analyses of tasks designed to engage students in relational thinking or a deep understanding of the equal sign as well as student work on these…

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...

ALGEBRA: ALgorithm for the heterogeneous dosimetry based on GEANT4 for BRAchytherapy.

Science.gov (United States)

Afsharpour, H; Landry, G; D'Amours, M; Enger, S; Reniers, B; Poon, E; Carrier, J-F; Verhaegen, F; Beaulieu, L

2012-06-07

Task group 43 (TG43)-based dosimetry algorithms are efficient for brachytherapy dose calculation in water. However, human tissues have chemical compositions and densities different than water. Moreover, the mutual shielding effect of seeds on each other (interseed attenuation) is neglected in the TG43-based dosimetry platforms. The scientific community has expressed the need for an accurate dosimetry platform in brachytherapy. The purpose of this paper is to present ALGEBRA, a Monte Carlo platform for dosimetry in brachytherapy which is sufficiently fast and accurate for clinical and research purposes. ALGEBRA is based on the GEANT4 Monte Carlo code and is capable of handling the DICOM RT standard to recreate a virtual model of the treated site. Here, the performance of ALGEBRA is presented for the special case of LDR brachytherapy in permanent prostate and breast seed implants. However, the algorithm is also capable of handling other treatments such as HDR brachytherapy.

(Fuzzy) Ideals of BN-Algebras

Science.gov (United States)

Walendziak, Andrzej

2015-01-01

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

Non-Binary Protograph-Based LDPC Codes: Analysis,Enumerators and Designs

OpenAIRE

Sun, Yizeng

2013-01-01

Non-binary LDPC codes can outperform binary LDPC codes using sum-product algorithm with higher computation complexity. Non-binary LDPC codes based on protographs have the advantage of simple hardware architecture. In the first part of this thesis, we will use EXIT chart analysis to compute the thresholds of different protographs over GF(q). Based on threshold computation, some non-binary protograph-based LDPC codes are designed and their frame error rates are compared with binary LDPC codes. ...

Effects of feedback in an online algebra intervention

NARCIS (Netherlands)

Bokhove, C.; Drijvers, P.H.M.

2012-01-01

The design and arrangement of appropriate automatic feedback in digital learning environment is a widely recognized issue. In this article, we investigate the effect of feedback on the design and the results of a digital intervention for algebra. Three feedback principles guided the intervention:

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.

Using geometric algebra to understand pattern rotations in multiple mirror optical systems

International Nuclear Information System (INIS)

Hanlon, J.; Ziock, H.

1997-01-01

Geometric Algebra (GA) is a new formulation of Clifford Algebra that includes vector analysis without notation changes. Most applications of Ga have been in theoretical physics, but GA is also a very good analysis tool for engineering. As an example, the authors use GA to study pattern rotation in optical systems with multiple mirror reflections. The common ways to analyze pattern rotations are to use rotation matrices or optical ray trace codes, but these are often inconvenient. The authors use GA to develop a simple expression for pattern rotation that is useful for designing or tolerancing pattern rotations in a multiple mirror optical system by inspection. Pattern rotation is used in many optical engineering systems, but it is not normally covered in optical system engineering texts. Pattern rotation is important in optical systems such as: (1) the 192 beam National ignition Facility (NIF), which uses square laser beams in close packed arrays to cut costs; (2) visual optical systems, which use pattern rotation to present the image to the observer in the appropriate orientation, and (3) the UR90 unstable ring resonator, which uses pattern rotation to fill a rectangular laser gain region and provide a filled-in laser output beam

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.

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

How to be Brilliant at Algebra

CERN Document Server

Webber, Beryl

2010-01-01

How to be Brilliant at Algebra is contains 40 photocopiable worksheets designed to improve students' understanding of number relationships and patterns. They will learn about: odds and evens; patterns; inverse operations; variables; calendars; equations; pyramid numbers; digital root patterns; prime numbers; Fibonacci numbers; Pascal's triangle.

LDPC Code Design for Nonuniform Power-Line Channels

Directory of Open Access Journals (Sweden)

Sanaei Ali

2007-01-01

Full Text Available We investigate low-density parity-check code design for discrete multitone channels over power lines. Discrete multitone channels are well modeled as nonuniform channels, that is, different bits experience various channel parameters. We propose a coding system for discrete multitone channels that allows for using a single code over a nonuniform channel. The number of code parameters for the proposed system is much greater than the number of code parameters in conventional channel. Therefore, search-based optimization methods are impractical. We first formulate the problem of optimizing the rate of an irregular low-density parity-check code, with guaranteed convergence over a general nonuniform channel, as an iterative linear programming which is significantly more efficient than search-based methods. Then we use this technique for a typical power-line channel. The methodology of this paper is directly applicable to all decoding algorithms for which a density evolution analysis is possible.

G-identities of non-associative algebras

International Nuclear Information System (INIS)

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

1999-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1996-05-01

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

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.

Nuclear-thermal-coupled optimization code for the fusion breeding blanket conceptual design

International Nuclear Information System (INIS)

Li, Jia; Jiang, Kecheng; Zhang, Xiaokang; Nie, Xingchen; Zhu, Qinjun; Liu, Songlin

2016-01-01

Highlights: • A nuclear-thermal-coupled predesign code has been developed for optimizing the radial build arrangement of fusion breeding blanket. • Coupling module aims at speeding up the efficiency of design progress by coupling the neutronics calculation code with the thermal-hydraulic analysis code. • Radial build optimization algorithm aims at optimal arrangement of breeding blanket considering one or multiple specified objectives subject to the design criteria such as material temperature limit and available TBR. - Abstract: Fusion breeding blanket as one of the key in-vessel components performs the functions of breeding the tritium, removing the nuclear heat and heat flux from plasma chamber as well as acting as part of shielding system. The radial build design which determines the arrangement of function zones and material properties on the radial direction is the basis of the detailed design of fusion breeding blanket. For facilitating the radial build design, this study aims for developing a pre-design code to optimize the radial build of blanket with considering the performance of nuclear and thermal-hydraulic simultaneously. Two main features of this code are: (1) Coupling of the neutronics analysis with the thermal-hydraulic analysis to speed up the analysis progress; (2) preliminary optimization algorithm using one or multiple specified objectives subject to the design criteria in the form of constrains imposed on design variables and performance parameters within the possible engineering ranges. This pre-design code has been applied to the conceptual design of water-cooled ceramic breeding blanket in project of China fusion engineering testing reactor (CFETR).

Nuclear-thermal-coupled optimization code for the fusion breeding blanket conceptual design

Energy Technology Data Exchange (ETDEWEB)

Li, Jia, E-mail: lijia@ustc.edu.cn [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230027, Anhui (China); Jiang, Kecheng; Zhang, Xiaokang [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, Anhui (China); Nie, Xingchen [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230027, Anhui (China); Zhu, Qinjun; Liu, Songlin [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, Anhui (China)

2016-12-15

Highlights: • A nuclear-thermal-coupled predesign code has been developed for optimizing the radial build arrangement of fusion breeding blanket. • Coupling module aims at speeding up the efficiency of design progress by coupling the neutronics calculation code with the thermal-hydraulic analysis code. • Radial build optimization algorithm aims at optimal arrangement of breeding blanket considering one or multiple specified objectives subject to the design criteria such as material temperature limit and available TBR. - Abstract: Fusion breeding blanket as one of the key in-vessel components performs the functions of breeding the tritium, removing the nuclear heat and heat flux from plasma chamber as well as acting as part of shielding system. The radial build design which determines the arrangement of function zones and material properties on the radial direction is the basis of the detailed design of fusion breeding blanket. For facilitating the radial build design, this study aims for developing a pre-design code to optimize the radial build of blanket with considering the performance of nuclear and thermal-hydraulic simultaneously. Two main features of this code are: (1) Coupling of the neutronics analysis with the thermal-hydraulic analysis to speed up the analysis progress; (2) preliminary optimization algorithm using one or multiple specified objectives subject to the design criteria in the form of constrains imposed on design variables and performance parameters within the possible engineering ranges. This pre-design code has been applied to the conceptual design of water-cooled ceramic breeding blanket in project of China fusion engineering testing reactor (CFETR).

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

CERN Document Server

Cox, David A; O'Shea, Donal

2015-01-01

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

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.

Connections between algebra, combinatorics, and geometry

CERN Document Server

Sather-Wagstaff, Sean

2014-01-01

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

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)

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

Characterizations of locally C*-algebras

International Nuclear Information System (INIS)

Mohammad, N.; Somasundaram, S.

1991-08-01

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

The computer code system for reactor radiation shielding in design of nuclear power plant

International Nuclear Information System (INIS)

Li Chunhuai; Fu Shouxin; Liu Guilian

1995-01-01

The computer code system used in reactor radiation shielding design of nuclear power plant includes the source term codes, discrete ordinate transport codes, Monte Carlo and Albedo Monte Carlo codes, kernel integration codes, optimization code, temperature field code, skyshine code, coupling calculation codes and some processing codes for data libraries. This computer code system has more satisfactory variety of codes and complete sets of data library. It is widely used in reactor radiation shielding design and safety analysis of nuclear power plant and other nuclear facilities

Storage Tanks - Selection Of Type, Design Code And Tank Sizing

International Nuclear Information System (INIS)

Shatla, M.N; El Hady, M.

2004-01-01

The present work gives an insight into the proper selection of type, design code and sizing of storage tanks used in the Petroleum and Process industries. In this work, storage tanks are classified based on their design conditions. Suitable design codes and their limitations are discussed for each tank type. The option of storage under high pressure and ambient temperature, in spherical and cigar tanks, is compared to the option of storage under low temperature and slight pressure (close to ambient) in low temperature and cryogenic tanks. The discussion is extended to the types of low temperature and cryogenic tanks and recommendations are given to select their types. A study of pressurized tanks designed according to ASME code, conducted in the present work, reveals that tanks designed according to ASME Section VIII DIV 2 provides cost savings over tanks designed according to ASME Section VIII DlV 1. The present work is extended to discuss the parameters that affect sizing of flat bottom cylindrical tanks. The analysis shows the effect of height-to-diameter ratio on tank instability and foundation loads

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.

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

Developing a Coding Scheme to Analyse Creativity in Highly-constrained Design Activities

DEFF Research Database (Denmark)

Dekoninck, Elies; Yue, Huang; Howard, Thomas J.

2010-01-01

This work is part of a larger project which aims to investigate the nature of creativity and the effectiveness of creativity tools in highly-constrained design tasks. This paper presents the research where a coding scheme was developed and tested with a designer-researcher who conducted two rounds...... of design and analysis on a highly constrained design task. This paper shows how design changes can be coded using a scheme based on creative ‘modes of change’. The coding scheme can show the way a designer moves around the design space, and particularly the strategies that are used by a creative designer...... larger study with more designers working on different types of highly-constrained design task is needed, in order to draw conclusions on the modes of change and their relationship to creativity....

A course in BE-algebras

CERN Document Server

Mukkamala, Sambasiva Rao

2018-01-01

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

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

Design criteria and pressure vessel codes - an American view

International Nuclear Information System (INIS)

Tuppeny, W.H.

1975-01-01

To the pressure vessel designer, codes and criteria represent the common ground where the stress analyst and the metallurgist must interact and evolve rules and procedures which will ensure safety and open-ended responsiveness to technological, economic, and environmental change. The paper briefly discusses the evolution and rationale behind the current ASME code sections -emphasizing those portions applicable to designs operating in the creep range. The author then proposes a plan of action so that the analysts and materials people can make optimum use of time and resources, and evolve data and design criteria which will be responsive to changing technology and the economic and safety requirements of the future. (author)

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 ...

The application of Lie algebra techniques to beam transport design

International Nuclear Information System (INIS)

Irwin, J.

1990-01-01

Using a final focus system for high-energy linear colliders as an example of a beam transport system, we illustrate for each element, and for the interplay of elements, the connection of Lie algebra techniques with usual optical analysis methods. Our analysis describes, through fourth order, the calculation and compensation of all important aberrations. (orig.)

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

Directory of Open Access Journals (Sweden)

Dinh Trung Hoa

2013-01-01

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

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.

Non-commutative multiple-valued logic algebras

CERN Document Server

Ciungu, Lavinia Corina

2014-01-01

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

Automorphic Lie algebras with dihedral symmetry

International Nuclear Information System (INIS)

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

2014-01-01

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

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.

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.)

Computations in finite-dimensional Lie algebras

Directory of Open Access Journals (Sweden)

A. M. Cohen

1997-12-01

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

Coset realization of unifying W-algebras

International Nuclear Information System (INIS)

Blumenhagen, R.; Huebel, R.

1994-06-01

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

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

Algebraic collapsing acceleration of the characteristics method with anisotropic scattering

International Nuclear Information System (INIS)

Le Tellier, R.; Hebert, A.; Roy, R.

2004-01-01

In this paper, the characteristics solvers implemented in the lattice code Dragon are extended to allow a complete anisotropic treatment of the collision operator. An efficient synthetic acceleration method, called Algebraic Collapsing Acceleration (ACA), is presented. Tests show that this method can substantially speed up the convergence of scattering source iterations. The effect of boundary conditions, either specular or white reflections, on anisotropic scattering lattice-cell problems is also considered. (author)

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)

High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices

Science.gov (United States)

Dunham, Benjamin Z.

This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions--most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series--without changing data-type or modifying code line by line; this allows differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed "stencils," each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error. Although this use of the method in the "forward mode" is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with N inputs and an adjoint solver whose cost is independent of N--i.e., O(1)--the N x N Hessian can be found in O(N) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive--e.g., a N x N x N rank-three tensor can be found in O(N2). Alternatively, a Hessian-vector product can be found in O(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step differentiation (CD) technique is also shown to be capable of

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

Science.gov (United States)

Sialaros, Michalis; Christianidis, Jean

2016-06-01

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

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.

Ripple design of LT codes for AWGN channel

DEFF Research Database (Denmark)

Sørensen, Jesper Hemming; Koike-Akino, Toshiaki; Orlik, Philip

2012-01-01

In this paper, we present an analytical framework for designing LT codes in additive white Gaussian noise (AWGN) channels. We show that some of analytical results from binary erasure channels (BEC) also hold in AWGN channels with slight modifications. This enables us to apply a ripple-based design...

Sub-quadratic decoding of one-point hermitian codes

DEFF Research Database (Denmark)

Nielsen, Johan Sebastian Rosenkilde; Beelen, Peter

2015-01-01

We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power...... decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the matrix minimization algorithms from computer algebra, yielding similar asymptotic complexities....

Comparison of elevated temperature design codes of ASME Subsection NH and RCC-MRx

Energy Technology Data Exchange (ETDEWEB)

Lee, Hyeong-Yeon, E-mail: hylee@kaeri.re.kr

2016-11-15

Highlights: • Comparison of elevated temperature design (ETD) codes was made. • Material properties and evaluation procedures were compared. • Two heat-resistant materials of Grade 91 steel and austenitic stainless steel 316 are the target materials in the present study. • Application of the ETD codes to Generation IV reactor components and a comparison of the conservatism was conducted. - Abstract: The elevated temperature design (ETD) codes are used for the design evaluation of Generation IV (Gen IV) reactor systems such as sodium-cooled fast reactor (SFR), lead-cooled fast reactor (LFR), and very high temperature reactor (VHTR). In the present study, ETD code comparisons were made in terms of the material properties and design evaluation procedures for the recent versions of the two major ETD codes, ASME Section III Subsection NH and RCC-MRx. Conservatism in the design evaluation procedures was quantified and compared based on the evaluation results for SFR components as per the two ETD codes. The target materials are austenitic stainless steel 316 and Mod.9Cr-1Mo steel, which are the major two materials in a Gen IV SFR. The differences in the design evaluation procedures as well as the material properties in the two ETD codes are highlighted.

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

Lower bounds for the minimum distance of algebraic geometry codes

DEFF Research Database (Denmark)

Beelen, Peter

, such as the Goppa bound, the Feng-Rao bound and the Kirfel-Pellikaan bound. I will finish my talk by giving several examples. Especially for two-point codes, the generalized order bound is fairly easy to compute. As an illustration, I will indicate how a lower bound can be obtained for the minimum distance of some...... description of these codes in terms of order domains has been found. In my talk I will indicate how one can use the ideas behind the order bound to obtain a lower bound for the minimum distance of any AG-code. After this I will compare this generalized order bound with other known lower bounds...

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...

Principles of linear algebra with Mathematica

CERN Document Server

Shiskowski, Kenneth M

2013-01-01

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

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

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.

Evaluation of three coding schemes designed for improved data communication

Science.gov (United States)

Snelsire, R. W.

1974-01-01

Three coding schemes designed for improved data communication are evaluated. Four block codes are evaluated relative to a quality function, which is a function of both the amount of data rejected and the error rate. The Viterbi maximum likelihood decoding algorithm as a decoding procedure is reviewed. This evaluation is obtained by simulating the system on a digital computer. Short constraint length rate 1/2 quick-look codes are studied, and their performance is compared to general nonsystematic codes.

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

OpenAIRE

Tang, Xiaomin

2016-01-01

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

Evolution algebras generated by Gibbs measures

International Nuclear Information System (INIS)

Rozikov, Utkir A.; Tian, Jianjun Paul

2009-03-01

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

Many-core graph analytics using accelerated sparse linear algebra routines

Science.gov (United States)

Kozacik, Stephen; Paolini, Aaron L.; Fox, Paul; Kelmelis, Eric

2016-05-01

Graph analytics is a key component in identifying emerging trends and threats in many real-world applications. Largescale graph analytics frameworks provide a convenient and highly-scalable platform for developing algorithms to analyze large datasets. Although conceptually scalable, these techniques exhibit poor performance on modern computational hardware. Another model of graph computation has emerged that promises improved performance and scalability by using abstract linear algebra operations as the basis for graph analysis as laid out by the GraphBLAS standard. By using sparse linear algebra as the basis, existing highly efficient algorithms can be adapted to perform computations on the graph. This approach, however, is often less intuitive to graph analytics experts, who are accustomed to vertex-centric APIs such as Giraph, GraphX, and Tinkerpop. We are developing an implementation of the high-level operations supported by these APIs in terms of linear algebra operations. This implementation is be backed by many-core implementations of the fundamental GraphBLAS operations required, and offers the advantages of both the intuitive programming model of a vertex-centric API and the performance of a sparse linear algebra implementation. This technology can reduce the number of nodes required, as well as the run-time for a graph analysis problem, enabling customers to perform more complex analysis with less hardware at lower cost. All of this can be accomplished without the requirement for the customer to make any changes to their analytics code, thanks to the compatibility with existing graph APIs.

Implementing Computer Algebra Enabled Questions for the Assessment and Learning of Mathematics

Science.gov (United States)

Sangwin, Christopher J.; Naismith, Laura

2008-01-01

We present principles for the design of an online system to support computer algebra enabled questions for use within the teaching and learning of mathematics in higher education. The introduction of a computer algebra system (CAS) into a computer aided assessment (CAA) system affords sophisticated response processing of student provided answers.…

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

Algebraic computing in general relativity

International Nuclear Information System (INIS)

D'Inverno, R.A.

1975-01-01

The purpose of this paper is to bring to the attention of potential users the existence of algebraic computing systems, and to illustrate their use by reviewing a number of problems for which such a system has been successfully used in General Relativity. In addition, some remarks are included which may be of help in the future design of these systems. (author)

On the classification of quantum W-algebras

International Nuclear Information System (INIS)

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

1992-01-01

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

Lie-Algebras. Pt. 1

International Nuclear Information System (INIS)

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

1990-01-01

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

Semiprojectivity of universal -algebras generated by algebraic elements

DEFF Research Database (Denmark)

Shulman, Tatiana

2012-01-01

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

Design validation of the ITER EC upper launcher according to codes and standards

Energy Technology Data Exchange (ETDEWEB)

Spaeh, Peter, E-mail: peter.spaeh@kit.edu [Karlsruhe Institute of Technology, Institute for Applied Materials, Association KIT-EURATOM, P.O. Box 3640, D-76021 Karlsruhe (Germany); Aiello, Gaetano [Karlsruhe Institute of Technology, Institute for Applied Materials, Association KIT-EURATOM, P.O. Box 3640, D-76021 Karlsruhe (Germany); Gagliardi, Mario [Karlsruhe Institute of Technology, Association KIT-EURATOM, P.O. Box 3640, D-76021 Karlsruhe (Germany); F4E, Fusion for Energy, Joint Undertaking, Barcelona (Spain); Grossetti, Giovanni; Meier, Andreas; Scherer, Theo; Schreck, Sabine; Strauss, Dirk; Vaccaro, Alessandro [Karlsruhe Institute of Technology, Institute for Applied Materials, Association KIT-EURATOM, P.O. Box 3640, D-76021 Karlsruhe (Germany); Weinhorst, Bastian [Karlsruhe Institute of Technology, Institute for Neutron Physics and Reactor Technology, Association KIT-EURATOM, P.O. Box 3640, D-76021 Karlsruhe (Germany)

2015-10-15

Highlights: • A set of applicable codes and standards has been chosen for the ITER EC upper launcher. • For a particular component load combinations, failure modes and stress categorizations have been determined. • The design validation was performed in accordance with the “design by analysis”-approach of the ASME boiler and pressure vessel code section III. - Abstract: The ITER electron cyclotron (EC) upper launcher has passed the CDR (conceptual design review) in 2005 and the PDR (preliminary design review) in 2009 and is in its final design phase now. The final design will be elaborated by the European consortium ECHUL-CA with contributions from several research institutes in Germany, Italy, the Netherlands and Switzerland. Within this consortium KIT is responsible for the design of the structural components (the upper port plug, UPP) and also the design integration of the launcher. As the selection of applicable codes and standards was under discussion for the past decade, the conceptual and the preliminary design of the launcher structure were not elaborated in straight accordance with a particular code but with a variety of well-acknowledged engineering practices. For the final design it is compulsory to validate the design with respect to a typical engineering code in order to be compliant with the ITER quality and nuclear requirements and to get acceptance from the French regulator. This paper presents typical design validation of the closure plate, which is the vacuum and Tritium barrier and thus a safety relevant component of the upper port plug (UPP), performed with the ASME boiler and pressure vessel code. Rationales for choosing this code are given as well as a comparison between different design methods, like the “design by rule” and the “design by analysis” approach. Also the selections of proper load specifications and the identification of potential failure modes are covered. In addition to that stress categorizations, analyses

Design validation of the ITER EC upper launcher according to codes and standards

International Nuclear Information System (INIS)

Spaeh, Peter; Aiello, Gaetano; Gagliardi, Mario; Grossetti, Giovanni; Meier, Andreas; Scherer, Theo; Schreck, Sabine; Strauss, Dirk; Vaccaro, Alessandro; Weinhorst, Bastian

2015-01-01

Highlights: • A set of applicable codes and standards has been chosen for the ITER EC upper launcher. • For a particular component load combinations, failure modes and stress categorizations have been determined. • The design validation was performed in accordance with the “design by analysis”-approach of the ASME boiler and pressure vessel code section III. - Abstract: The ITER electron cyclotron (EC) upper launcher has passed the CDR (conceptual design review) in 2005 and the PDR (preliminary design review) in 2009 and is in its final design phase now. The final design will be elaborated by the European consortium ECHUL-CA with contributions from several research institutes in Germany, Italy, the Netherlands and Switzerland. Within this consortium KIT is responsible for the design of the structural components (the upper port plug, UPP) and also the design integration of the launcher. As the selection of applicable codes and standards was under discussion for the past decade, the conceptual and the preliminary design of the launcher structure were not elaborated in straight accordance with a particular code but with a variety of well-acknowledged engineering practices. For the final design it is compulsory to validate the design with respect to a typical engineering code in order to be compliant with the ITER quality and nuclear requirements and to get acceptance from the French regulator. This paper presents typical design validation of the closure plate, which is the vacuum and Tritium barrier and thus a safety relevant component of the upper port plug (UPP), performed with the ASME boiler and pressure vessel code. Rationales for choosing this code are given as well as a comparison between different design methods, like the “design by rule” and the “design by analysis” approach. Also the selections of proper load specifications and the identification of potential failure modes are covered. In addition to that stress categorizations, analyses

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

African Journals Online (AJOL)

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

Macdonald index and chiral algebra

Science.gov (United States)

Song, Jaewon

2017-08-01

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

Vertex algebras and mirror symmetry

International Nuclear Information System (INIS)

Borisov, L.A.

2001-01-01

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

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.

A q-deformed Lorentz algebra

International Nuclear Information System (INIS)

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

1991-01-01

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

Introduction to algebraic quantum field theory

International Nuclear Information System (INIS)

Horuzhy, S.S.

1990-01-01

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

Comments on N=4 superconformal algebras

International Nuclear Information System (INIS)

Rasmussen, J.

2001-01-01

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

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.

Quantum Heisenberg groups and Sklyanin algebras

International Nuclear Information System (INIS)

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

1993-05-01

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

EPIC: an Error Propagation/Inquiry Code

International Nuclear Information System (INIS)

Baker, A.L.

1985-01-01

The use of a computer program EPIC (Error Propagation/Inquiry Code) will be discussed. EPIC calculates the variance of a materials balance closed about a materials balance area (MBA) in a processing plant operated under steady-state conditions. It was designed for use in evaluating the significance of inventory differences in the Department of Energy (DOE) nuclear plants. EPIC rapidly estimates the variance of a materials balance using average plant operating data. The intent is to learn as much as possible about problem areas in a process with simple straightforward calculations assuming a process is running in a steady-state mode. EPIC is designed to be used by plant personnel or others with little computer background. However, the user should be knowledgeable about measurement errors in the system being evaluated and have a limited knowledge of how error terms are combined in error propagation analyses. EPIC contains six variance equations; the appropriate equation is used to calculate the variance at each measurement point. After all of these variances are calculated, the total variance for the MBA is calculated using a simple algebraic sum of variances. The EPIC code runs on any computer that accepts a standard form of the BASIC language. 2 refs., 1 fig., 6 tabs

Design of a VLSI Decoder for Partially Structured LDPC Codes

Directory of Open Access Journals (Sweden)

Fabrizio Vacca

2008-01-01

of their parity matrix can be partitioned into two disjoint sets, namely, the structured and the random ones. For the proposed class of codes a constructive design method is provided. To assess the value of this method the constructed codes performance are presented. From these results, a novel decoding method called split decoding is introduced. Finally, to prove the effectiveness of the proposed approach a whole VLSI decoder is designed and characterized.

Classification of simple flexible Lie-admissible algebras

International Nuclear Information System (INIS)

Okubo, S.; Myung, H.C.

1979-01-01

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

Partially Flipped Linear Algebra: A Team-Based Approach

Science.gov (United States)

Carney, Debra; Ormes, Nicholas; Swanson, Rebecca

2015-01-01

In this article we describe a partially flipped Introductory Linear Algebra course developed by three faculty members at two different universities. We give motivation for our partially flipped design and describe our implementation in detail. Two main features of our course design are team-developed preview videos and related in-class activities.…

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...

Supporting Students' Understanding of Linear Equations with One Variable Using Algebra Tiles

Science.gov (United States)

Saraswati, Sari; Putri, Ratu Ilma Indra; Somakim

2016-01-01

This research aimed to describe how algebra tiles can support students' understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students…

Diagnosing students' misconceptions in algebra: results from an experimental pilot study.

Science.gov (United States)

Russell, Michael; O'Dwyer, Laura M; Miranda, Helena

2009-05-01

Computer-based diagnostic assessment systems hold potential to help teachers identify sources of poor performance and to connect teachers and students to learning activities designed to help advance students' conceptual understandings. The present article presents findings from a study that examined how students' performance in algebra and their overcoming of common algebraic misconceptions were affected by the use of a diagnostic assessment system that focused on important algebra concepts. This study used a four-group randomized cluster trial design in which teachers were assigned randomly to one of four groups: a "business as usual" control group, a partial intervention group that was provided with access to diagnostic tests results, a partial intervention group that was provided with access to the learning activities, and a full intervention group that was given access to the test results and learning activities. Data were collected from 905 students (6th-12th grade) nested within 44 teachers. We used hierarchical linear modeling techniques to compare the effects of full, partial, and no (control) intervention on students' algebraic ability and misconceptions. The analyses indicate that full intervention had a net positive effect on ability and misconception measures.

Anyons, deformed oscillator algebras and projectors

International Nuclear Information System (INIS)

Engquist, Johan

2009-01-01

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

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

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.

On graded algebras of global dimension 3

International Nuclear Information System (INIS)

Piontkovskii, D I

2001-01-01

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

Unipotent and nilpotent classes in simple algebraic groups and lie algebras

CERN Document Server

Liebeck, Martin W

2012-01-01

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

Elements of mathematics algebra