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 Call number: SPRINGER-2001-9783642567551:ONLINE Show nearby items on shelf Title: Finite Fields and Applications Proceedings of The Fifth International Conference on Finite Fields and Applications F q 5, held at the University of Augsburg, Germany, August 2–6, 1999 Author(s): Date: 2001 Size: 1 online resource (490 p.) Note: 10.1007/978-3-642-56755-1 Contents: Projective Generalized Reed-Muller Codes over p-adic Numbers and Finite Rings -- Towards a Basis for the Space of Regular Functions in a Tower of Function Fields Meeting the Drinfeld-Vladut Bound -- Self-Dual Normal Bases and Related Topics -- Permutations amongst the Dembowski-Ostrom Polynomials -- Associative Rational Functions in Two Variables -- A Note on the Minimal Polynomial of the Product of Linear Recurring Sequences -- Gelfond-Gramain’s Theorem for Function Fields -- On Generalized Bent and q-ary Perfect Nonlinear Functions -- Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group or a Unitary Group. -- A Permutation of a Small Infinite Field -- Almost Perfect Nonlinear Power Functions on GF(2n): A New Case for n Divisible by 5 -- On Non-Abelian Semi-Regular Relative Difference Sets -- Applications of Arithmetical Geometry to Cryptographic Constructions -- Gauß Periods in Finite Fields -- Constructions of Orthomorphisms of ?2n -- Period Polynomials for $${F_{{{p^{2}}}}}$$ of Fixed Small Degree -- Universal Generators for Primary Closures of Galois Fields -- Irreducible Polynomials Generated by Decimations -- Decoding Reed-Muller Codes beyond Half the Minimum Distance -- On Binary Cyclic Codes With Few Weights -- Mac Williams Identities for Linear Codes over Finite Frobenius Rings -- Cyclotomic Function Fields with Many Rational Places -- On the Siamese Twin Designs -- On the Brauer Monoid for Finite Fields -- Algorithms for Factoring Polynomials over Finite Fields -- Gauss Sums over Quasi-Frobenius Rings -- On the Early History of Galois Fields -- Linear Blocking Sets: a Survey -- Comparison of Techniques on Divisibility Properties of Exponential Sums and Applications -- On the Rank of Appearance and the Number of Zeros of the Lucas Sequences over Fq -- A Permutation Problem for Finite Fields -- The L-Function of Gold Exponential Sum -- On Permutation Polynomials and Derivable Translation Planes -- Pure L-Functions from Algebraic Geometry over Finite Fields -- Incomplete Additive Character Sums and Applications -- Applications of Algebraic Curves to Constructions of Codes and Almost Perfect Sequences -- Author Index ISBN: 9783642567551 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Mathematics , Data structures (Computer science) , Data encryption (Computer science) , Algebra , Computer mathematics , Discrete mathematics , Combinatorics , Mathematics , Discrete Mathematics , Combinatorics , Data Structures, Cryptology and Information Theory , Algebra , Computational Mathematics and Numerical Analysis , Data Encryption Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE

 Call number: SPRINGER-1994-9789401120029:ONLINE Show nearby items on shelf Title: Algorithmic and Combinatorial Algebra Author(s): L. A Bokut’ Date: 1994 Size: 1 online resource (384 p.) Note: 10.1007/978-94-011-2002-9 Contents: 1 Composition Method for Associative Algebras -- 1.1 Introduction -- 1.2 Free Semigroups and Free Groups -- 1.3 The Composition Lemma -- 1.4 The Composition Lemma for Semigroup Algebras -- 1.5 The Generalised Clifford Algebra and Some Other Examples -- 1.6 Finite-Dimensional Representation of a Generalised Clifford Algebra -- 1.7 More on Embeddings into Simple Algebras -- 2 Free Lie Algebras -- 2.1 Introduction -- 2.2 The Definition of Free Lie Algebras -- 2.3 Projective Algebras -- 2.4 Elementary Transformations and Automorphisms of Free Algebras -- 2.5 Lie Algebra Derivations -- 2.6 The Ideal of Codimension 1 -- 2.7 Constructing Generators for an Arbitrary Subalgebra in a Free Lie Algebra -- 2.8 The Shirshov Theorem on Free Lie Algebra Subalgebras -- 2.9 Automorphisms of Free Lie Algebras of Finite Rank -- 2.10 A Criterion for a Lie Algebra to be Free -- 2.11 Bases of a Free Lie Algebra -- 2.12 Construction of Free Lie Algebras -- 2.13 Universal Enveloping Associative Algebra -- 2.14 On Subrings of Free Rings with Operators -- 2.15 Embedding Lie Rings into Associative Rings with Operators -- 2.16 Restricted Lie Algebras -- 2.17 Relatively Free Lie Algebras -- 2.18 Embedding Countable-Dimensional Lie Algebras into Lie Algebras with Two Generators -- 2.19 The Residual Finiteness of Associative and Lie Algebras -- 2.20 Residual Finiteness of Free Rings and Algebras -- 3 The Composition Method in the Theory of Lie Algebras -- 3.1 Introduction -- 3.2 The Composition Lemma -- 3.3 Formulation of Decision Problems. One-Relator Lie Algebras -- 3.4 Embedding Lie Algebras into Simple Lie Algebras -- 3.5 The Main Algorithmic Problems for Lie Algebras are Unsolvable -- 3.6 Unrecognizable Markov Properties for Finitely Presented Lie Algebras -- 3.7 Defining Relations of a Subalgebra -- 3.8 Residual Finiteness and Decision Problems -- 3.9 On Residual Finiteness of One-Relator Lie Algebras -- 3.10 Constructing Free Resolutions -- 3.11 Cohomological Dimension of Almost Free Lie Algebras -- 4 Amalgamated Products of Lie Algebras -- 4.1 Introduction -- 4.2 Definition of Amalgamated Products -- 4.3 Constructing the Free Product of Associative Algebras without 1 -- 4.4 Constructing the Amalgamated Product of Lie Algebras -- 4.5 Subalgebras of the Free Product of Lie Algebras -- 4.6 Generators of a Subalgebra of the Free Product of Lie Algebras -- 4.7 Decomposition of a Free Product into the Sum of Two Subalgebras, One Free -- 4.8 Decomposition of a Subalgebra of a Free Product into the Sum of Two Subalgebras, One Free -- 4.9 The Theorem on Subalgebras of an Amalgamated Product of Lie Algebras -- 4.10 Free Subalgebras in a Free Product of Lie Algebras -- 4.11 The Case in Which the Kurosh Formula Almost Holds -- 4.12 Supplementary Facts on Free Products -- 4.13 Residual Finiteness of Free Products of Associative and Lie Algebras -- 4.14 Residual Finiteness of Free Soluble Lie Algebras with respect to Inclusion into Finitely Generated Subalgebras -- 4.15 On Residual Finiteness of Free Soluble Groups with respect to Inclusion into Finitely Generated Subgroups -- 4.16 On Residual Properties of Free Products of Lie Algebras. Central Systems in Free Products -- 5 The Problem of Endomorph Reducibility and Relatively Free Groups with the Word Problem Unsolvable -- 5.1 Introduction -- 5.2 When the Problem of Endomorph Reducibility for Relatively Free Rings is Unsolvable -- 5.3 When the Problem of Endomorph Reducibility is Solvable -- 5.4 The Problem of Endomorph Reducibility for Relatively Free Groups -- 5.5 The Variety R Included in NN -- 5.6 The Free Group T of the Variety $$(\mathcal{A}_2^2 \cap \mathcal{N}_2 )\mathcal{A}_2 \mathcal{R}$$ and its Quotient Group S -- 5.7 The Main Construction -- 5.8 Application to Constructing Non-Finitely-Based Varieties -- 5.9 An Interpretation of Polynomials -- 5.10 Unsolvability of Some Algorithmic Problems in the Theory of Group -- 6 The Constructive Method in the Theory of HNN-extensions. Groups with Standard Normal Form -- 6.1 Introduction -- 6.2 Novikov-Boone Groups -- 6.3 The Novikov Lemma and the Britton Lemma -- 6.4 The Definition of Groups with Standard Normal Form -- 6.5 The Novikov Group AP1P2 -- 6.6 The Boone Group -- 7 The Constructive Method for HNN-extensions and the Conjugacy Problem for Novikov-Boone Groups -- 7.1 Introduction -- 7.2 The Conjugacy Problem for the Group G1 -- 7.3 The Group G2 -- 7.4 Some Calculuses -- 7.5 The Conjugacy Problem for the Group AP1P2 -- 7.6 Auxiliary facts -- Appendix 1 Calculations in Free Groups -- Appendix 2 Algorithmic Properties of the Wreath Products of Groups -- Appendix 3 Survey of the Theory of Absolutely Free Algebras ISBN: 9789401120029 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Mathematics and Its Applications : 255 Keywords: Mathematics , Algebra , Algorithms , Mathematics , Algebra , Algorithms Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. 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 Call number: SPRINGER-1993-9789401120067:ONLINE Show nearby items on shelf Title: Clifford Algebras and their Applications in Mathematical Physics Proceedings of the Third Conference held at Deinze, Belgium, 1993 Author(s): Date: 1993 Size: 1 online resource (411 p.) Note: 10.1007/978-94-011-2006-7 Contents: CLIFFORD ALGEBRAS and APPLICATIONS -- Quantum Clifford algebras -- Relations between Witt rings and Brauer groups -- Clifford algebra tables -- Finite geometry and the table of real Clifford algebras -- Jordan form in Clifford algebra -- CLIFFORD ANALYSIS: Local and global theory for Dirac—type operators -- Elliptic boundary value problems in unbounded domains -- Dirac operators and manifolds with boundary -- Spin structures and harmonic spinors on Riemann surfaces -- Spherical geometry and Möbius transformations -- Cauchy transforms and bi—axial monogenic power functions -- Note on the use of spherical vectorfields in Clifford analysis -- Quaternionic analysis and transmission problems -- C*—algebras of nonlocal quaternionic convolution type operators -- On the solutions of $${D^N}{\text{ }}{\hat D^M}{\text{ }}F = 0$$ -- Biregular quaternionic functions -- Monogenic and holomorphic functions -- Hypercomplex differentiability and its applications -- Clifford algebras and boundary estimates for harmonic functions -- Regularity of functions with values in Clifford algebra based on a generalized axially symmetric potential theory operator -- On the analogue of the $$\bar \partial$$ —problem in quaternionic analysis -- Hurwitz pairs and Clifford algebra representations -- On the Bergmann kernel function in the Clifford analysis -- SO(M)—invariant operators on Clifford tensors -- Invariant differential operators on polynomial—valued functions -- A distributional approach to vector manifolds -- Clifford analysis for higher spins -- Quaternionic operator calculus and domain perturbation problems -- Classical Mechanics -- A hamiltonian model of dissipation with Clifford algebraic generalizations -- A formulation of hamiltonian mechanics using geometric calculus -- Mathematical Physics -- Local automorphism invariance: a generalization of general relativity -- Differential forms in geometric calculus -- Clifford valued convolution operator algebras on the Heisenberg group -- Classical solutions of the Dirac equation: bound Coulomb states in Aharonov-Bohm and Zeeman fields -- Geometric algebra versus numerical cartesianism -- Classification of multivector theories and the modification of the postulates of physics -- The “ideal” approach to spinors reconsidered -- Geometric aspects of spinors -- A basis for double solution theory -- Spatial inversion and spinors -- Physical Models -- Non abelian gauge fields in the real Clifford algebra of space time -- Spin gauge theories: principles and predictions -- Gravity as a gauge theory in the spacetime algebra -- Cosmological consequences of a flat—space theory of gravity -- Zitterbewegung and electron structure -- Separation of the Dirac equation and positive definiteness of quantum numbers ISBN: 9789401120067 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Fundamental Theories of Physics, An International Book Series on The Fundametal Theories of Physics:Their Clarification,Development and Application : 55 Keywords: Physics , Associative rings , Rings (Algebra) , Mathematical analysis , Analysis (Mathematics) , Applied mathematics , Engineering mathematics , Physics , Theoretical, Mathematical and Computational Physics , Associative Rings and Algebras , Analysis , Applications of Mathematics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE