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SPIRES-BOOKS: FIND KEYWORD FUNCTIONS,SPECIAL *END*INIT* use /tmp/qspiwww.webspi1/11266.34 QRY 131.225.70.96 . find keyword functions,special ( in books using www Cover
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Call number:99972668917:ONLINE Show nearby items on shelf
Title:QUANTUM ALGORITHMS VIA LINEAR ALGEBRA: A PRIMER
Author(s): Richard J. Lipton
Kenneth W. Regan
Date:2015
Publisher:MIT Press
Size:207 p
Contents:Introduction -- Numbers and strings -- Basic linear algebra -- Boolean functions, quantum bits, and feasibility -- Special matrices -- Tricks -- Phil's algorithm -- Deutsch's algorithm -- the Deuthsch-Jozsa algorithm -- Simon's algorithm -- Shor's algorithm -- Factoring integers -- Grover's algorithm -- Quantum walks -- Quantum walk search algorithms -- Quantum computation and BQP -- Beyond
ISBN:9780262323567
Series:eBOOKS
Keywords: Quantum computers
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Call number:9781498777810:ONLINE Show nearby items on shelf
Title:CRC Standard Mathematical Tables and Formulas [electronic resource]
Author(s): Daniel Zwillinger
Date:2018
Edition:33rd edition
Publisher:CRC Press
Size:1 electronic resource (800 pages) p
Contents:Numbers and elementary mathematics -- Elementary algebra -- Discrete mathematics -- Geometry -- Analysis -- Special functions -- Probability and statistics -- Scientific computing -- Mathematical formulas from the sciences -- Miscellaneous
ISBN:9781498777810
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Call number:0471113131:ONLINE Show nearby items on shelf
Title:Special Functions: An Introduction to the Classical Mathematical Physics
Author(s): Temme
Date:1996
Publisher:Wiley-Interscience
Size:1 online resource (393 p.)
ISBN:9780471113133
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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Call number:TA330.J44::2002 Show nearby items on shelf
Title:Advanced engineering mathematics
Author(s): Alan Jeffrey
Date:2002
Publisher:Harcourt Academic Press
Note:Volume 2 is the solutions manual
Contents:Review of Prerequisites
Vectors and Matrices
Vectors and Vector Spaces
Matrices and Systems of Linear Equations
Eigenvalues, Eigenvectors and Diagonalization
Ordinary Differential Equations
First Order Differential Equations
Second and Higher Order Linear Differential Equations and Systems
The Laplace Transform
Series Solutions of Differential Equations, Special Functions, and Sturm-Liouville Equations
Fourier Series
Fourier Integrals and the Fourier Transform
Vector Calculus
Vector Differential Calculus
Vector Integral Calculus
Complex analysis
Analytic Functions
Complex Integration
Laurent Series, Residues, and Contour Integration
The Laplace Inversion Integral
Particla Differential Equations
Numerical Mathematics
ISBN:012382592X
Keywords: Engineering mathematics
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Call number:SPRINGER-2016-9783319312811:ONLINE Show nearby items on shelf
Title:Mathematical Analysis, Approximation Theory and Their Applications
Author(s):
Date:2016
Size:1 online resource (20 p.)
Note:10.1007/978-3-319-31281-1
Contents:A brief history of the Favard operator and its variants -- Bivariate extension of linear positive operators -- Positive Green’s Functions for Boundary Value Problems with Conformable Derivatives -- The retraction-displacement condition in the theo ry of fixed point equation with a convergent iterative algorithm -- An adaptive finite element method for solving a free boundary problem with periodic boundary conditions in lubrication theory -- Evolution solutions of equilibrium problems - a computatio nal approach -- Cantor, Banach and Baire theorems in generalized metric spaces -- A Survey of Perturbed Ostrowski Type Inequalities -- Hyers-Ulam-Rassias stability of the generalized Wilson’s functional equation -- Approximation under Exponential Growth Conditions by Szász and Baskakov Type Operators in the Complex Plane -- On the asymptotic behavior of sequences of positive linear approximation operators -- Approximation of functions by additive and by quadratic mappings -- Bernstein Type
Inequalities concerning Growth of Polynomials -- Approximation for generalization of Baskakov-Durrmeyer operators -- A Tour on p (x)-Laplacian Problems When p = ∞ -- An umbral calculus approach to Bernoulli-Padé polynomials -- Hadamard Matrices: Insights into their growth factor and determinant computations -- Localized summability kernels for Jacobi expansions -- Quadrature rules with multiple nodes -- A -summability of sequences of linear conservative operators -- Simultaneous Weighted Approxim ation with Multivariate Baskakov-Schurer Operators -- Approximation of Discontinuous Functions by q-Bernstein Polynomials -- Nests, and their Role in the Orderability Problem -- Resolvent Operators for Some Classes of Integro-Differential Equations -- Com ponent Matrices of a Square Matrix and their Properties -- Solutions of Some Types of Differential Equations and of Their Associated Physical Problems by Means of Inverse Differential Operators -- A modified pointwise estimate on simultaneous
approximation by Bernstein polynomials -- Structural Fixed Point Results in Metric Spaces -- Models of Fuzzy Linear Regression: An Application in Engineering -- Properties of Functions of generalized bounded variations
ISBN:9783319312811
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Optimization and Its Applications: 111
Keywords: Mathematics , Global analysis (Mathematics) , Manifolds (Mathematics) , Operator theory , Special functions , Computer mathematics , Calculus of variations , Mathematics , Calculus of Variations and Optimal Control Optimization , Operator Theory , Special Functions , Global Analysis and Analysis on Manifolds , Computational Mathematics and Numerical Analysis
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Call number:SPRINGER-2016-9783319290003:ONLINE Show nearby items on shelf
Title:Divergent Series, Summability and Resurgence III Resurgent Methods and the First Painlevé Equation
Author(s): Eric Delabaere
Date:2016
Size:1 online resource (14 p.)
Note:10.1007/978-3-319-29000-3
Contents:Avant-Propos -- Preface to the three volumes -- Preface to this volume -- Some elements about ordinary differential equations -- The first Painlevé equation -- Tritruncated solutions for the first Painlevé equation -- A step beyond Borel-Laplace summability -- Transseries and formal integral for the first Painlevé equation -- Truncated solutions for the first Painlevé equation -- Supplements to resurgence theory -- Resurgent structure for the first Painlevé equation -- Index
ISBN:9783319290003
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 2155
Keywords: Mathematics , Functions of complex variables , Differential equations , Sequences (Mathematics) , Special functions , Mathematics , Sequences, Series, Summability , Ordinary Differential Equations , Functions of a Complex Variable , Special Functions
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Call number:SPRINGER-2016-9783319284002:ONLINE Show nearby items on shelf
Title:Introduction to Calculus and Classical Analysis
Author(s): Omar Hijab
Date:2016
Edition:4th ed. 2016
Size:1 online resource (1 p.)
Note:10.1007/978-3-319-28400-2
Contents:Preface -- A Note to the Reader -- 1. The Set of Real Numbers -- 2. Continuity -- 3. Differentiation.-4. Integration -- 5. Applications -- 6. Generalizations -- A. Solutions -- References -- Index
ISBN:9783319284002
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Approximation theory , Sequences (Mathematics) , Special functions , Combinatorics , Mathematics , Approximations and Expansions , Sequences, Series, Summability , Special Functions , Combinatorics
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Call number:SPRINGER-2016-9783319252742:ONLINE Show nearby items on shelf
Title:The Special Theory of Relativity Foundations, Theory, Verification, Applications
Author(s): Costas Christodoulides
Date:2016
Edition:1st ed. 2016
Size:1 online resource (480 p.)
Note:10.1007/978-3-319-25274-2
Contents:Historical Introduction -- The Main Landmarks in the Development of the Special Theory of Relativity -- The Principle of Relativity of Galileo. Galileo’s Invariance Hypothesis. The Law of Inertia. Inertial Frames of Reference
Relativity -- Rømer and the Speed of Light -- Newton’s Laws of Motion. Inertia and Inertial Frames of Reference -- The Aberration of Light -- Arago’s Measurements Concerning the Constancy of the Speed of Light from Stars --
Measurements of the Speed of Light in the Laboratory -- Attempts to Measure the Dragging of Aether by Moving Media -- Maxwell’s Equations and the Wave Equation -- The Experiment of Michelson and Morley -- The Lorentz-Fitzgerald
Contraction Hypothesis -- The Increase of the Mass of the Electron with Speed -- The Invariance of Maxwell’s Equations and the Lorentz Transformation -- The Formulation of the Special Theory of Relativity -- Prolegomena -- Inertial
Frames of Reference -- The Calibration of a Frame of Reference and the Synchronization of its Clocks -- The Relativity of Simultaneity -- The Relativity of Time and Length -- The Inevitability of the Special Theory of Relativity --
Relativistic Kinematics -- The Lorentz Transformation for the Coordinates of an Event -- The Transformation of Velocity -- The Transformation of Acceleration -- Applications of Relativistic Kinematics -- The ‘Meson’ Paradox -- The
apparent focusing of fast charged particle beams due to the dilation of time -- The Sagnac Effect -- Clocks Moving Around the Earth -- The Experiment of Hafele and Keating -- Einstein’s Train -- The Twin Paradox -- Motion with a
Constant Proper Acceleration. Hyperbolic Motion -- Two Successive Lorentz Transformations. The Wigner Rotation -- Optical Phenomena -- The Aberration of Light -- Fizeau’s Experiment. Fresnel’s Aether Dragging Theory -- The Doppler
Effect -- Relativistic Beaming or the Headlight Effect -- The Pressure Exerted by Light -- Relativistic Dynamics -- The Dfinition of Relativistic Momentum. Relativistic Mass -- Relativistic Energy -- The Relationship Between Momentum
and Energy -- Classical Approximations -- Particles with Zero Rest Mass -- The Conservation of Momentum and of Energy -- The Equivalence of Mass and Energy -- The Transformation of Momentum and Energy -- The Zero-Momentum Frame of
Reference -- The Transformation of the Total Momentum and the Total Energy of a System of Particles -- The Collision of two Identical Particles -- The Transformation of Force -- Motion Under the Influence of a Constant Force. The
Motion of a Charged Particle in a Constant Uniform Electric Field -- The Motion of a Charged Particle in a Constant Homogeneous Magnetic Field -- Applications of Relativistic Dynamics -- The Compton Effect -- The Inverse Compton Effect
-- The Consequences of the Special Theory of Relativity on the Design of Particle Accelerators -- Mass Defect and Binding Energy of the Atomic Nucleus -- Threshold Energy -- The General Equations for the Motion of a Relativistic Rocket
-- Minkowski’s Spacetime and Four-Vectors -- The ‘World’ of Minkowski -- Four-Vectors -- Electromagnetism -- Introduction -- The Invariance of Electric Charge -- The Transformations of the Electric Field and the Magnetic Field -- The
Fields of a Moving Electric Charge -- The Derivation of the Differential form of the Biot-Savart Law from Coulomb’s Law -- The Force Exerted on a Moving Charge by an Electric Current -- Experiments -- The Speed of Light -- The Aether
-- The Dilation of Time -- The Relativistic Doppler Effect -- The Contraction of Length -- The Test of the Predictions of Relativistic Kinematics -- The Sagnac Effect -- The Relativistic Mass -- The Equivalence of Mass and Energy --
The Test of the Predictions of Relativistic Dynamics -- The Invariance of Electric Charge -- Appendix 1. The Paradox of the Room and the Rod -- Appendix 2. The Appearance of Moving Bodies -- Appendix 3. The Derivation of the Expression
for the Relativistic Mass in General -- Appendix .4. The Invariance of the Equations of Maxwell and the Wave Equation Under the Lorentz Transformation -- Appendix 5. Tachyons -- Appendix 6. The Lorentz Transformation in Matrix Form --
Appendix 7. Table of Some Functions of the Speed -- Solutions of the Problem
ISBN:9783319252742
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Physics , Gravitation , Observations, Astronomical , Astronomy , Physics , Classical and Quantum Gravitation, Relativity Theory , Astronomy, Observations and Techniques
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Call number:SPRINGER-2016-9783319229669:ONLINE Show nearby items on shelf
Title:Concepts in Quantum Field Theory A Practitioner's Toolkit
Author(s): Victor Ilisie
Date:2016
Size:1 online resource (190 p.)
Note:10.1007/978-3-319-22966-9
Contents:1 Vectors, tensors, manifolds and Special Relativity -- 2 Lagrangians, Hamiltonians and Noether's Theorem -- 3 Relativistic kinematics and phase space -- 4 Angular Distributions -- 5 Dirac algebra -- 6 Dimensional regularization.
Ultraviolet and infrared divergences -- 7 QED renormalization -- 8 One-loop two and three-point functions -- 9 Massive spin one and renormalizable gauges -- 10 Symmetries and effective vertices -- 11 Effective field theory -- 12
Optical theorem -- A Master integral -- B Renormalization group equations -- C Feynman rules for derivative couplings
ISBN:9783319229669
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Physics , Quantum field theory , String theory , Elementary particles (Physics) , Physics , Elementary Particles, Quantum Field Theory , Quantum Field Theories, String Theory
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Call number:SPRINGER-2014-9784431549192:ONLINE Show nearby items on shelf
Title:Bernoulli Numbers and Zeta Functions [electronic resource]
Author(s): Tsuneo Arakawa
Tomoyoshi Ibukiyama
Masanobu Kaneko
Date:2014
Publisher:Tokyo : Springer Japan : Imprint: Springer
Size:1 online resource
Note:Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powersof consecutive integers . The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advancedtopics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers a formula for Bernoulli numbers by Stirling numbers the Clausenvon Staudttheorem on the denominators of Bernoulli numbers Kummer's congruence betw een Bernoulli numbers and a related theory of p-adic measures the EulerMaclaurin summation formula the functional equation of the Riemann zeta function andthe Dirichlet L functions, and their special values at suitable integers various formulas of exponen tial sums expressed by generalized Bernoulli numbers the relation between ideal classes of orders of quadratic fields and equivalenceclasses of binary quadratic forms class number formula for positive definite binary quadratic forms congruences between so me class numbers and Bernoulli numbers simple zeta functions of prehomogeneous vector spaces Hurwitz numbers
ISBN:9784431549192
Series:eBooks
Series:SpringerLink
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Global analysis (Mathematics) , Number theory
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Call number:SPRINGER-2014-9783662438312:ONLINE Show nearby items on shelf
Title:Conformal Field Theory, Automorphic Forms and Related Topics [electronic resource] : CFT, Heidelberg, September 19-23, 2011
Author(s): Winfried Kohnen
Rainer Weissauer
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:This book, part of the seriesContributions in Mathematical and Computational Sciences,reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics. Themathematical theory of VOAs orig inated from the famous monstrous moonshine conjectures of J.H. Conway and S.P. Norton, which predicted a deep relationship between the characters of the largest simple finite sporadic group, the Monster,and the theory of modular forms inspired by the obse rvations of J. MacKay and J. Thompson. The contributions are based on lectures delivered at the 2011 conference on Conformal Field Theory, Automorphic Forms and Related Topics,organized by the editors as part of a special program offered at Heidelberg Un iversity that summer under the sponsorship of the MAThematics Center Heidelberg (MATCH)
Contents:1. A. Milas: Characters of Modules of Irrational Vertex Algebras
2. G. Mason: Lattice subalgebras of strongly regular vertex operator algebras
3. C. Dong and C. Jiang: A Characterization of the vertex operator algebra V
4. H. Yamauchi: Extended Griess algebras and Matsuo
Norton trace formulae
5. M.R. Gaberdiel and R. Volpato: Mathieu Moonshine and Orbifold K3s
6. M.C.N. Cheng and J.F.R. Duncan: Rademacher Sums and Rademacher Series
7. G. Mason and M.P. Tuite: Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II
8. A. Zuevsky: Twisted correlation functions
ISBN:9783662438312
Series:eBooks
Series:SpringerLink
Series:Contributions in Mathematical and Computational Sciences, 2191-303X : v8
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Number theory , Mathematical physics
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Call number:SPRINGER-2014-9783319062488:ONLINE Show nearby items on shelf
Title:Geometric Methods in Physics [electronic resource] : XXXII Workshop, Biaowiea, Poland, June 30-July 6, 2013
Author(s): Piotr Kielanowski
Pierre Bieliavsky
Alexander Odesskii
Anatol Odzijewicz
Martin Schlichenmaier
Theodore Voronov
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Birkhuser
Size:1 online resource
Note:The Biaowiea Workshops on Geometric Methods in Physics, which are hosted in the unique setting of the Biaowiea natural forest in Poland, are among the most important meetings in the field. Every year some 80 to 100participants from both the mathemati cs and physics world join to discuss new developments and to exchange ideas. The current volume was produced on the occasion of the 32nd meeting in 2013. It is now becoming a tradition that theWorkshop is followed by a School on Geometry and Physics, whic h consists of advanced lectures for graduate students and young researchers. Selected speakers at the 2013 Workshop were asked to contribute to this book, and their work wassupplemented by additional review articles. The selection shows that, despite its now long tradition, the workshop remains at the cutting edge of research. The 2013 Workshop also celebrated the 75th birthday of Daniel Sternheimer, andon this occasion the discussion mainly focused on his contributions to mathematical physics such as def ormation quantization, Poisson geometry, symplectic geometry and non-commutative differential geometry
Contents:Preface
Part I: Deformation, Quantization: Scientific Landmarks of Daniel Sternheimer
Part II: Quantum Mechanics
Part III: Groups and Non
commutative Structures
Part IV: Differential Equations and Special Functions
Part V: General Methods
ISBN:9783319062488
Series:eBooks
Series:SpringerLink
Series:Trends in Mathematics, 2297-0215
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Global analysis
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Call number:SPRINGER-2014-9783319062099:ONLINE Show nearby items on shelf
Title:From Real to Complex Analysis [electronic resource]
Author(s): R. H Dyer
D. E Edmunds
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis andtopology. Beginning with the theory of the Riemann integral (and its improper extension) on the real line, the fundamentals of metric spaces are then developed, with special attention being paid to connectedness, simple connectednessand various forms of homotopy. The final chapter d evelops the theory of complex analysis, in which emphasis is placed on the argument, the winding number, and a general (homology) version of Cauchy's theorem which is proved using theapproach due to Dixon. Special features are the inclusion of proofs of M ontel's theorem, the Riemann mapping theorem and the Jordan curve theorem that arise naturally from the earlier development. Extensive exercises are included ineach of the chapters, detailed solutions of the majority of which are given at the end. From Re al to Complex Analysis is aimed at senior undergraduates and beginning graduate students in mathematics. It offers a sound grounding inanalysis in particular, it gives a solid base in complex analysis from which progress to more advanced topics may be mad e
Contents:The Riemann integral
Metric spaces
Complex Analysis
Sets and functions
ISBN:9783319062099
Series:eBooks
Series:SpringerLink
Series:Springer Undergraduate Mathematics Series, 1615-2085
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables
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Call number:SPRINGER-2014-9783319057231:ONLINE Show nearby items on shelf
Title:Invariant Probabilities of Transition Functions [electronic resource]
Author(s): Radu Zaharopol
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transitionfunctions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated usingtransition functions defined by flows, semiflows, a nd one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 areextended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structureof the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of the state space, where the invariant ergodic probability measures play a significant role. Other topics covered include: characterizationsof the supports of various types of invariant probability measures and the use of these to obtain criteria for un ique ergodicity, and the proofs of two mean ergodic theorems for a certain type of transition functions. The book will beof interest to mathematicians working in ergodic theory, dynamical systems, or the theory of Markov processes. Biologists, physicists and economists interested in interacting particle systems and rigorous mathematics will also findthis book a valuable resource. Parts of it are suitable for advanced graduate courses. Prerequisites are basic notions and results on functional analysis, gen eral topology, measure theory, the Bochner integral and some of itsapplications
Contents:Introduction
1.Transition Probabilities
2.Transition Functions
3.Vector Integrals and A.E. Convergence
4.Special Topics
5.The KBBY Ergodic Decomposition, Part I
6.The KBBY Ergodic Decomposition, Part II
7.Feller Transition Functions
Appendices: A.Semiflows and Flows: Introduction
B.Measures and Convolutions
Bibliography
Index
ISBN:9783319057231
Series:eBooks
Series:SpringerLink
Series:Probability and Its Applications, 1431-7028
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Operator theory , Potential theory (Mathematics) , Distribution (Probability theory)
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Call number:SPRINGER-2014-9783319053110:ONLINE Show nearby items on shelf
Title:Inequalities [electronic resource] : With Applications to Engineering
Author(s): Michael J Cloud
Byron C Drachman
Leonid P Lebedev
Date:2014
Edition:2nd ed. 2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This book offers a concise introduction to mathematical inequalities for graduate students and researchers in the fields of engineering and applied mathematics. It begins by reviewing essential facts from algebra andcalculusandproceeds with a present ation of the central inequalities of applied analysis, illustrating a wide variety of practical applications. The text provides a gentle introduction to abstract spaces, such as metric, normed, andinner product spaces. It also provides full coverage of th e central inequalities of applied analysis, such as Young's inequality, the inequality of the means, Hlder's inequality, Minkowski's inequality, the CauchySchwarzinequality, Chebyshev's inequality, Jensen's inequality, and the triangle inequality. The sec ond edition features extended coverage of applications, including continuum mechanics and interval analysis. It also includes many additionalexamples and exercises with hints and full solutions that may appeal to upper-level undergraduate and graduate stu dents, as well asresearchers in engineering, mathematics, physics, chemistry, or any other quantitative science
Contents:Preface
1. Basic Review and Elementary Facts
2. Methods from the Calculus
3. Some Standard Inequalities
4. Inequalities in Abstract Spaces
5. Some Applications
6. Inequalities for Differential Equations
7. Brief Introduction to Interval Analysis
Hints for Selected Problems
References
Appendix
ISBN:9783319053110
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions, special , Engineering mathematics
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Call number:SPRINGER-2014-9783319038568:ONLINE Show nearby items on shelf
Title:Proportional Representation [electronic resource] : Apportionment Methods and Their Applications
Author(s): Friedrich Pukelsheim
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The book offers a rigorous description of the procedures that proportional representation systems use to translate vote counts into seat numbers. Since the methodological analysis is guided by practical needs, plenty of empiricalinstances are provide d and reviewed to motivate the development, and to illustrate the results. Concrete examples, like the 2009 elections to the European Parliament in each of the 27 Member States and the 2013 election to the GermanBundestag, are analyzed in full detail. The level of mathematical exposition, as well as the relation to political sciences and constitutional jurisprudence makes this book suitable for special graduate courses and seminars
Contents:Exposing Methods: The 2009 European Parliament Elections
Imposing Constitutionality: The 2009 Bundestag Election
From Reals to Integers: Rounding Functions, Rounding Rules
Divisor Methods of Apportionment: Divide and Round
Quota Methods of Apportionment: Divide and Rank
Targeting the House Size: Discrepancy Distribution
Favoring Some at the Expense of Others: Seat Biases
Preferring Stronger Parties to Weaker Parties: Majorization
Securing System Consistency: Coherence and Paradoxes
Appraising Electoral Equality: Goodness
of
Fit Criteria
Tracing Peculiarities: Vote
ISBN:9783319038568
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Statistics
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Call number:SPRINGER-2014-9783319038476:ONLINE Show nearby items on shelf
Title:Computations with Modular Forms [electronic resource] : Proceedings of a Summer School and Conference, Heidelberg, August/September 2011
Author(s): Gebhard Bckle
Gabor Wiese
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of theConference and Summer School was the interplay between theory, algorithms and experiment. The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as originalresearch articles reporting on the latest develop ments in the field. The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms,including computing cohomology of arithmetic groups, algebraic automorph ic forms, and overconvergent modular symbols. The 11 Conference papers cover a wide range of themes related to computations with modular forms, including latticemethods for algebraic modular forms on classical groups, a generalization of the Maeda conject ure, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data ofBianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular form s, and more
Contents:Part I Summer School: Lectures on Computing Cohomology of Arithmetic Groups by P.E. Gunnells
Computing with Algebraic Automorphic Forms by D. Loeffler
Overconvergent Modular Symbols by R. Pollack
Part II Conference and Research Contributions: Congruence Subgroups, Cusps and Manin Symbols over Number Fields by J. E. Cremona and M. T. Arans
Computing Weight One Modular Forms over C and Fp by K. Buzzard
Lattice Methods for Algebraic Modular Forms on Classical Groups by M. Greenberg and J. Voight
Efficient Computation of Rankin p
Adic L
Functions by A.G.B. Lauder
Formes Modu
ISBN:9783319038476
Series:eBooks
Series:SpringerLink
Series:Contributions in Mathematical and Computational Sciences, 2191-303X : v6
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Algorithms , Number theory
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Call number:SPRINGER-2014-9783319020990:ONLINE Show nearby items on shelf
Title:Introduction to Partial Differential Equations [electronic resource]
Author(s): Peter J Olver
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, andelsewhere. The exposition car efully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, andinclude straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material thatmotivates the student to delve further into the subject. No previous experien ce with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- andmulti-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to formthe core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximu m Principle, financial models, dispersion and solitons, Huygens' Principle, quantum mechanical systems,and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes ar e an important component of any introductory course, and the text covers the twomost basic approaches: finite differences and finite elements. Peter J. Olver is professor of mathematics at the University of Minnesota. His wide-ranging research interests a re centered on the development of symmetry-based methodsfor differential equations and their manifold applications. He is the author of over 130 papers published in major scientific research
Contents:What are Partial Differential Equations?
Linear and Nonlinear Waves
Fourier Series
Separation of Variables
Finite Differences
Generalized Functions and Greens Functions
Complex Analysis and Conformal Mapping
Fourier Transforms
Linear and Nonlinear Evolution Equations
A General Framework forLinear Partial Differential Equations
FiniteElements and Weak Solutions
Dynamics of Planar Media
Partial Differential Equations in Space .
ISBN:9783319020990
Series:eBooks
Series:SpringerLink
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Differential equations, partial
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Call number:SPRINGER-2014-9783034808439:ONLINE Show nearby items on shelf
Title:Condenser Capacities and Symmetrization in Geometric Function Theory [electronic resource]
Author(s): Vladimir N Dubinin
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:This is the first systematic presentation of the capacitory approach and symmetrization in the context of complex analysis. The content of the book is original the main part has not been covered by existing textbooks andmonographs. After an introduc tion to the theory of condenser capacities in the plane, the monotonicity of the capacity under various special transformations (polarization, Gonchar transformation, averaging transformations and others)is established, followed by various types of symmet rization which are one of the main objects of the book. By using symmetrization principles, some metric properties of compact sets are obtained and some extremal decomposition problemsare solved. Moreover, the classical and present facts for univalent and multivalent meromorphic functions are proven. This book will be a valuable source for current and future researchers in various branches of complex analysis andpotential theory
Contents:Preface
1.Conformal capacity
2. Asymptotics of the condenser capacity when one of the plate degenerates
Special transformations
4. Symmetrization
5. Metric properties of sets and condensers
6. Problems of extremal decomposition
7. Univalent functions
8. Multivalent functions
Appendices: A1. Dirichlet principle
A2. Uniqueness theorem for contracting mapping
A3. On separating transformation of sets and condensers
A4. On conservation of reduced moduli under geometric trans
formation of domains
A5. Quadratic differentials
A6. Unsolved problems
Reference
ISBN:9783034808439
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics
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Call number:SPRINGER-2014-9783034808408:ONLINE Show nearby items on shelf
Title:Variable Lebesgue Spaces and Hyperbolic Systems [electronic resource]
Author(s): David Cruz-Uribe
Alberto Fiorenza
Michael Ruzhansky
Jens Wirth
Sergey Tikhonov
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesguespaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integralswith non-standard growth conditions. They ha ve applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function spaceproperties of variable Lebesgue spaces proofs are modeled on the classic al theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such asconvolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolicequations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems withtime-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Ca uchy problems are constructed as oscillatory integrals by working in appropriatetime-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lo wer order terms can change asymptotic properties and thuscomplements the exposition
Contents:Part I: Introduction to the Variable Lebesgue Spaces
Introduction and motivation
Properties of variable Lebesgue spaces
The Hardy
Littlewood maximal operator
Extrapolation in variable Lebesgue spaces
Part II:Asymptotic Behaviour of Solutions to Hyperbolic Equations and Systems
Equations with constant coefficients
Some interesting model cases
Time
dependent hyperbolic systems
Effective lower order perturbations
Examples and counter
examples
Related topics
ISBN:9783034808408
Series:eBooks
Series:SpringerLink
Series:Advanced Courses in Mathematics - CRM Barcelona, 2297-0304 : v27
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Integral equations , Differential equations, partial , Functions, special
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Call number:SPRINGER-2014-9783034807302:ONLINE Show nearby items on shelf
Title:Cardinal Invariants on Boolean Algebras [electronic resource] : Second Revised Edition
Author(s): J. Donald Monk
Date:2014
Edition:2nd ed. 2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its freesubalgebras, and cellularity , which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour ofthese functions under algebraic operations such as p roducts, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinitecombinatorics and forcing, the book reviews current knowledge about these f unctions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based onCardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) b y the same author, the present work is much larger than either of these. It contains solutions to many of the open problems of theearlier volumes. Among the new topics are continuum cardinals on Boolean algebras, with a lengthy treatment of the reaping nu mber. Diagrams at the end of the book summarize the relationships between the functions for many importantclasses of Boolean algebras, including interval algebras, tree algebras and superatomic algebras
Contents:Introduction
1. Special Operations on Boolean Algebras
2. Special Classes of Boolean Algebras
3. Cellularity
4. Depth
5. Topological Density
6. Pi
Weight
7. Length
8. Irredundance
9. Cardinality
10. Independence
11. Pi
Character
12. Tightness
13. Spread
14. Character
15. Hereditary Lindelf Degree
16. Hereditary Density
17. Incomparability
18. Hereditary Cofinality
19. Number of Ultrafilters
20. Number of Automorphisms
21. Number of Endomorphisms
22. Number of Ideals
23. Number of Subalgebras
24. Other Cardinal Functions
ISBN:9783034807302
Series:eBooks
Series:SpringerLink
Series:Progress in Mathematics, 0743-1643 : v142
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Logic, Symbolic and mathematical
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Call number:SPRINGER-2014-9783034806220:ONLINE Show nearby items on shelf
Title:Real Quaternionic Calculus Handbook [electronic resource]
Author(s): Joo Pedro Morais
Svetlin Georgiev
Wolfgang Sprig
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, suchas complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysishas become a well established branch in ma thematics and has been greatly successful in many different directions. This book is based onconcrete examples and exercises rather than general theorems, thus making it suitable for anintroductory one- or two-semester undergraduate course on some of the major aspects of real quaternion analysis in exercises. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises atthe end of each chapter and its straightforward writing style the book addresses readers w ho have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as real and complex analysis,ordinary differential equations, partial differential equations, and theory of distributions
Contents:1 An introduction to quaternions
2 Quaternions and spatial rotation
3 Quaternion sequences
4 Quaternion series and infinite products
5 Exponents and logarithms
6 Trigonometric functions
7 Hyperbolic functions
8 Inverse hyperbolic and trigonometric functions
9 Quaternion matrices
10 Monomials, polynomials and binomials
11 Solutions
Bibliography
Index
ISBN:9783034806220
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Algebra , Functions of complex variables , Combinatorics , Geometry
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Call number:SPRINGER-2014-9781493902583:ONLINE Show nearby items on shelf
Title:Analytic Number Theory, Approximation Theory, and Special Functions [electronic resource] : In Honor of Hari M. Srivastava
Author(s): Gradimir V Milovanovi
Michael Th Rassias
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematicalcommunity, including bot h research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions andquadratures, orthogonality, and special and co mplex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results,methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fieldsof mathematics, physics, and other computational and applied sciences
Contents:Part I. Analytic Number Theory, Combinatorics, and Special Sequences of Numbers and Polynomials
The mean values of the Riemann Zeta function on the critical line (A. Ivi)
Explicit bounds concerning non
trivial zeros of the Riemann Zeta function (M. Hassani)
On the value
distribution of logarithmic derivatives of Dirichlet L
functions (Y. Ihara, K. Matsumoto)
Multiple Gamma functions and their applications (J. Choi)
On partition functions of hyperbolic three
geometry and associated Hilbert schemes (A.A. Bytsenko and E. Elizalde)
Families of twisted Bernoulli numbers, twisted
ISBN:9781493902583
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional equations , Functional analysis , Number theory
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Call number:SPRINGER-2014-9781461471325:ONLINE Show nearby items on shelf
Title:Walter Gautschi, Volume 3 [electronic resource] : Selected Works with Commentaries
Author(s): Claude Brezinski
Ahmed Sameh
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He isworld renowned for his pi oneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi:Selected Works with Commentaries, is a compilation of G autschis most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemoratingWalters prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical ConditioningSpecial Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and B iography Miscellanea Works of Werner Gautschi
Contents:Part I Commentaries
Linear recurrence relations
Ordinary differential equations
Computer algorithms and software packages
History and biography
Miscellanea
Part II Reprints
Linear difference equations
Ordinary differential equations
Computer algorithms and software packages
History and biography
Miscellanea
Part III Werner Gautschi
Publications
Obituaries
Recording
ISBN:9781461471325
Series:eBooks
Series:SpringerLink
Series:Contemporary Mathematicians
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Differential Equations , Numerical analysis
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Call number:SPRINGER-2014-9781461470496:ONLINE Show nearby items on shelf
Title:Walter Gautschi, Volume 2 [electronic resource] : Selected Works with Commentaries
Author(s): Claude Brezinski
Ahmed Sameh
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He isworld renowned for his pi oneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi:Selected Works with Commentaries, is a compilation of G autschis most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemoratingWalters prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical ConditioningSpecial Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and B iography Miscellanea Works of Werner Gautschi
Contents:Part I Commentaries
Orthogonal polynomials on the real line
Polynomials orthogonal on the semicircle
Chebyshev quadrature
Kronrod and other quadratures
Gauss type quadrature
Part II Reprints
Orthogonal polynomials on the real line
Polynomials orthogonal on the semicircle
Chebyshev quadrature
Kronrod and other quadratures
ISBN:9781461470496
Series:eBooks
Series:SpringerLink
Series:Contemporary Mathematicians
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Differential Equations , Numerical analysis
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Call number:SPRINGER-2014-9781461470342:ONLINE Show nearby items on shelf
Title:Walter Gautschi, Volume 1 [electronic resource] : Selected Works with Commentaries
Author(s): Claude Brezinski
Ahmed Sameh
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He isworld renowned for his pi oneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi:Selected Works with Commentaries, is a compilation of G autschis most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemoratingWalters prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical ConditioningSpecial Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and B iography Miscellanea Works of Werner Gautschi
Contents:Preface
Part I Walter Gautschi
Biography of Walter Gautschi
A brief summary of my scientific work and highlights of my career
Publications
Part II Commentaries
Numerical conditioning
Special functions
Interpolation and approximation
Part III Reprints
Numerical conditioning
Special functions
Interpolation and approximation
ISBN:9781461470342
Series:eBooks
Series:SpringerLink
Series:Contemporary Mathematicians
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Differential Equations , Numerical analysis
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Call number:SPRINGER-2014-9781447164647:ONLINE Show nearby items on shelf
Title:Hypergeometric Summation [electronic resource] : An Algorithmic Approach to Summation and Special Function Identities
Author(s): Wolfram Koepf
Date:2014
Edition:2nd ed. 2014
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system Maple. The algorithms of Fasenmyer, Gosper, Zeilberger,Petkovek and van Hoeij for hyp ergeometric summation and recurrence equations, efficient multivariate summation as well as q-analogues of the above algorithms are covered. Similar algorithms concerning differential equations areconsidered. An equivalent theory of hyperexponential integ ration due to Almkvist and Zeilberger completes the book. The combination of these results gives orthogonal polynomials and (hypergeometric and q-hypergeometric) specialfunctions a solid algorithmic foundation. Hence, many examples from this very active f ield are given. The materials covered are suitable for an introductory course on algorithmic summation and will appeal to students and researchersalike
Contents:Introduction
The Gamma Function
Hypergeometric Identities
Hypergeometric Database
Holonomic Recurrence Equations
Gospers Algorithm
The Wilf
Zeilberger Method
Zeilbergers Algorithm
Extensions of the Algorithms
Petkovseks and Van Hoeijs Algorithm
Differential Equations for Sums
Hyperexponential Antiderivatives
Holonomic Equations for Integrals
Rodrigues Formulas and Generating Functions
ISBN:9781447164647
Series:eBooks
Series:SpringerLink
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential Equations , Functions, special , Algorithms , Computer software , Combinatorics
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Call number:SPRINGER-2013-9783642385650:ONLINE Show nearby items on shelf
Title:Application of Integrable Systems to Phase Transitions [electronic resource]
Author(s): C.B Wang
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The eigenvalue densities in various matrix models in quantum chromodynamics (QCD) are ultimately unified in this book by a unified model derived from the integrable systems. Many new density models and free energy functions areconsequently solved and presented. The phase transition models including critical phenomena with fractional power-law for the discontinuities of the free energies in the matrix models are systematically classified by means of a clearand rigorous mathematical demonstration. The methods here will stimulate new research directions such as the important Seiberg-Witten differential in Seiberg-Witten theory for solving the mass gap problem in quantum Yang-Mills theory.The formulations and results will benefit researchers and students in the fields of phase transitions, integrable systems, matrix models and Seiberg-Witten theory
Note:Springer eBooks
Contents:Introduction
Densities in Hermitian Matrix Models
Bifurcation Transitions and Expansions
Large
N Transitions and Critical Phenomena
Densities in Unitary Matrix Models
Transitions in the Unitary Matrix Models
Marcenko
Pastur Distribution and McKays Law
ISBN:9783642385650
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions, special
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Call number:SPRINGER-2013-9783642383007:ONLINE Show nearby items on shelf
Title:Introduction to Probability and Statistics for Engineers [electronic resource]
Author(s): Milan Holick
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The theory of probability and mathematical statistics is becoming an indispensable discipline in many branches of science and engineering. This is caused by increasing significance of various uncertainties affecting performance ofcomplex technologica l systems. Fundamental concepts and procedures used in analysis of these systems are often based on the theory of probability and mathematical statistics. The book sets out fundamental principles of the probabilitytheory, supplemented by theoretical model s of random variables, evaluation of experimental data, sampling theory, distribution updating and tests of statistical hypotheses. Basic concepts of Bayesian approach to probability andtwo-dimensional random variables, are also covered. Examples of relia bility analysis and risk assessment of technological systems are used throughout the book to illustrate basic theoretical concepts and their applications. The primaryaudience for the book includes undergraduate and graduate students of science and enginee ring, scientific workers and engineers and specialists in the field of reliability analysis and risk assessment. Except basic knowledge ofundergraduate mathematics no special prerequisite is required
Note:Springer eBooks
Contents:Foreword
1 Introduction
2.Basic Concepts of Probability
3.Evaluation of Statistical Data
4.Distributions of Random Variables
5.Selected Models of Discrete Variables
6.Selected Models of Continuous Variables
7.Functions of Random Variables
8.Estimations of the Population Parameters
9.Fractiles of Random Variables
10.Testing of Statistical Hypotheses
11.Correlation and Regression
12.Random Functions
Appendixes.
ISBN:9783642383007
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Statistics , Distribution (Probability theory) , Engineering , Engineering design
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Call number:SPRINGER-2013-9783642382826:ONLINE Show nearby items on shelf
Title:Scattering Theory [electronic resource]
Author(s): Harald Friedrich
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
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Note:This book presents a concise and modern coverage of scattering theory. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used,e.g. tothe field of ultr acold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. In thepresent treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited todescribe near-threshold bound and continuum statesin realistic binary systems such as diatomic molecules or molecular ions. Th e level of abstraction is keptas low as at all possible,and deeper questions related tomathematical foundations of scattering theory are passed by. Thebookshould beunderstandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. It i s intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalistsalike
Note:Springer eBooks
Contents:Classical Scattering Theory
Elastic Scattering by aConservative Potential
Internal Excitation, Inelastic Scattering
Special Topics
Scaling
Special Functions
ISBN:9783642382826
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v872
Series:Physics and Astronomy (Springer-11651)
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Call number:SPRINGER-2013-9783642381898:ONLINE Show nearby items on shelf
Title:Facets of Combinatorial Optimization [electronic resource] : Festschrift for Martin Grtschel
Author(s): Michael Jnger
Gerhard Reinelt
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Martin Grtschel is one of the most influential mathematicians of our time. He has received numerous honors and holds a number of key positions in the international mathematical community. He celebrated his 65th birthday onSeptember 10, 2013. Martin G rtschels doctoral descendant tree 19832012, i.e., the first 30 years, features 39 children, 74 grandchildren, 24 great-grandchildren, and 2 great-great-grandchildren, a total of 139 doctoraldescendants. This book starts with a personal tribute to Martin G rtschel by the editors (Part I), a contribution by his very special predecessor Manfred Padberg on Facets and Rank of Integer Polyhedra (Part II), and thedoctoral descendant tree 19832012 (Part III). The core of this book (Part IV) contains 16 contributio ns, each of which is coauthored by at least one doctoral descendant. The sequence of the articles starts with contributions tothe theory of mathematical optimization, including polyhedral combinatorics, extended formulations, mixed-integer convex optimiza tion, superclasses of perfect graphs, efficient algorithms for subtree-telecenters, junctions in acyclicgraphs, and preemptive restricted strip covering, as well as efficient approximation of non-preemptive restricted strip covering. Combinations of new t heoretical insights with algorithms and experiments deal with network designproblems, combinatorial optimization problems with submodular objective functions, and more general mixed-integer nonlinear optimization problems. Applications include VLSI layout design, systems biology, wireless network design,mean-risk optimization, and gas network optimization. Computational studies include a semidefinite branch and cut approach for the max k-cut problem, mixed-integer nonlinear optimal control, and mixed-inte ger linear optimization forscheduling and routing of fly-in safari planes. The two closing articles are devoted to computational advances in general mixed-integer li
Note:Springer eBooks
Contents:Martin Grtschel
a tribute: M.Jnger and G.Reinelt
Facets and rank of integer polyhedra:M.Padberg
Constructing extended formulations from reflection relations:V.Kaibel and K.Pashkovich
Exact algorithms for combinatorial optimization problems with submodular objective functions: F.Baumann, S.Berckey, and C.Buchheim
Solving k
way graph partitioning problems to optimality: The impact of semidefinite relaxations and the bundle method: M.F. Anjos, B.Ghaddar, L.Hupp, F.Liers and A.Wiegele
Mirror
descent methods in mixed
integer convex optimization: M.Baes, T.Oertel, Ch.Wagner
ISBN:9783642381898
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computational complexity , Algorithms , Mathematical optimization
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Call number:SPRINGER-2013-9783642368745:ONLINE Show nearby items on shelf
Title:Algebraic Approaches to Partial Differential Equations [electronic resource]
Author(s): Xiaoping Xu
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
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Note:This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: theMaxwell equations, the Dir ac equations, the KdV equation, the KP equation, the nonlinear Schrodinger equation, the Davey and Stewartson equations, the Boussinesq equations in geophysics, the Navier-Stokes equations and theboundary layer problems. In order to solve them, I have emp loyed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, symmetry transformations,linearization techniques and special functions. The book is self-contained and requires only a min imal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, thesciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research
Note:Springer eBooks
Contents:Preface
Introduction
Ordinary Differential Equations
Partial Differential Equations
Bibliography
Index
ISBN:9783642368745
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial
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Call number:SPRINGER-2013-9783642334061:ONLINE Show nearby items on shelf
Title:Invariant Random Fields on Spaces with a Group Action [electronic resource]
Author(s): Anatoliy Malyarenko
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
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Note:The author describes the current state of the art in the theory of invariant random fields. This theory is based on several different areas of mathematics, including probability theory, differential geometry, harmonic analysis,and special functions. The present volume unifies many results scattered throughout the mathematical, physical, and engineering literature, as well as itintroduces new results from this area first proved by the author. The book alsopresents many practical applications, in parti cular in such highly interesting areas as approximation theory, cosmology and earthquake engineering. It is intended for researchers and specialists working in the fields of stochasticprocesses, statistics, functional analysis, astronomy, and engineering.
Note:Springer eBooks
Contents:1.Introduction
2.Spectral Expansions
3.L2 Theory of Invariant Random Fields
4.Sample Path Properties of Gaussian Invariant Random Fields
5.Applications
A.Mathematical Background
References
Index
ISBN:9783642334061
Series:e-books
Series:SpringerLink (Online service)
Series:Probability and Its Applications, 1431-7028
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Distribution (Probability theory)
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Call number:SPRINGER-2013-9783642314070:ONLINE Show nearby items on shelf
Title:Lvy Matters II [electronic resource] : Recent Progress in Theory and Applications: Fractional Lvy Fields, and Scale Functions
Author(s): Serge Cohen
Alexey Kuznetsov
Andreas E Kyprianou
Victor Rivero
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
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Note:This is the second volume in a subseries of the Lecture Notes in Mathematics called Lvy Matters, whichis published at irregular intervals over the years. Each volume examines a number of key topics in the theory orapplications of Lvy processes and pa ys tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The expository articles in this second volume cover two important topics inthe area of Lvy processes. The first article by Serge Cohen re views the most important findings on fractional Lvy fields to date in a self-contained piece, offering a theoretical introduction as well as possible applications andsimulation techniques. The second article, by Alexey Kuznetsov, Andreas E. Kyprianou, and Victor Rivero, presents an up to date account of the theory and application of scale functions for spectrally negative Lvy processes, includingan extensive numerical overview
Note:Springer eBooks
ISBN:9783642314070
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2061
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Distribution (Probability theory)
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Call number:SPRINGER-2013-9783034805858:ONLINE Show nearby items on shelf
Title:Pseudo-Differential Operators, Generalized Functions and Asymptotics [electronic resource]
Author(s): Shahla Molahajloo
Stevan Pilipovi
Joachim Toft
M. W Wong
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
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Note:This volume consists of twenty peer-reviewed papers from the special sessions on pseudodifferential operators and on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples FriendshipUniversity of Russia in Moscow on August 2227, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifoldswith edges, heat kernels and Green functions of sub-Lapla cians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, L^p-boundedness of pseudo-differential operators on thetorus, and pseudo-differential operators related to time-frequency analysis. The s econd group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlineardifferential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differ ential equations. This second group of papers is related to the third collection of papers via the setting ofColombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volumecontains the synergi es of the three areas treatedand is a useful complement toitspredecessorspublished in the same series
Note:Springer eBooks
Contents:Preface
Elliptic Theory for Operators Associated with Diffeomorphisms of Smooth Manifolds
The Singular Functions of Branching Edge Asymptotics
The Heat Kernel and Green Function of the Sub
Laplacian on the Heisenberg Group
Metaplectic Equivalence of the Hierarchical Twisted Laplacian
The Heat Kernel and Green Function of a Sub
Laplacian on the Hierarchical Heisenberg Group
Lp
Bounds for Pseudo
Differential Operators on the Torus
Multiplication Properties in Gelfand
Shilov Pseudo
Differential Calculus
Operator Invariance
Initial Value Problems in the Time
Frequency Do
ISBN:9783034805858
Series:e-books
Series:SpringerLink (Online service)
Series:Operator Theory: Advances and Applications : v231
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global analysis , Operator theory , Differential equations, partial
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Call number:SPRINGER-2013-9783034805728:ONLINE Show nearby items on shelf
Title:Offbeat Integral Geometry on Symmetric Spaces [electronic resource]
Author(s): Valery V Volchkov
Vitaly V Volchkov
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
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Note:The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces ofarbitrary ranks as we ll as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for variousclasses of functions, far-reaching generalizatio ns of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful invarious fields of contemporary mathematics. The proofs given are mini mal in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historicalperspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and theHeisenberg group, integral equations, special functions, and transmutation operators theory
Note:Springer eBooks
Contents:Preface
Part 1. Analysis on Symmetric Spaces. 1 Preliminaries
2 The Euclidean case
3 Symmetric spaces of the non
compact type
4 Analogies for compact two
point homogeneous Spaces
5 The phase space associated to the Heisenberg group
Part 2. Offbeat Integral Geometry
1 Functions with zero ball means on Euclidean space
2 Two
radii theorems in symmetric spaces
3 The problem of finding a function from its ball means
4 Sets with the Pompeiu property
5 Functions with zero integrals over polytopes
6 Ellipsoidal means
7 The Pompeiu property on a sphere
8 The Pompeiu
ISBN:9783034805728
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Integral Transforms , Functions, special , Global differential geometry
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Call number:SPRINGER-2013-9783034805636:ONLINE Show nearby items on shelf
Title:Special Functions of Mathematical (Geo-)Physics [electronic resource]
Author(s): Willi Freeden
Martin Gutting
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
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Note:Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A goodunderstanding of special fun ctions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The specialfunctions to be discussed in this monograph vary great ly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective fieldcharacteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercisesthat reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields ofresearch, where special functions are essential to application. All in all, the book is an equally valuable resource for educa tion in geomathematics and the study of applied and harmonic analysis. Students who wish to continue withfurther studies should consult the literature given as supplements for each topic covered in the exercises
Note:Springer eBooks
Contents:1 Introduction: Geomathematical Motivation
Part I: Auxiliary Functions
2 The Gamma Function
3 Orthogonal Polynomials
Part II: Spherically Oriented Functions
4 Scalar Spherical Harmonics in R^3
5 Vectorial Spherical Harmonics in R^3
6 Spherical Harmonics in R^q
7 Classical Bessel Functions
8 Bessel Functions in R^q
Part III: Periodically Oriented Functions
9 Lattice Functions in R
10 Lattice Functions in R^q
11 Concluding Remarks
References
Index
ISBN:9783034805636
Series:e-books
Series:SpringerLink (Online service)
Series:Applied and Numerical Harmonic Analysis
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Physical geography , Meteorology , Harmonic analysis , Differential equations, partial , Functions, special
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Call number:SPRINGER-2013-9781461482598:ONLINE Show nearby items on shelf
Title:Prolate Spheroidal Wave Functions of Order Zero [electronic resource] : Mathematical Tools for Bandlimited Approximation
Author(s): Andrei Osipov
Vladimir Rokhlin
Hong Xiao
Date:2013
Publisher:Boston, MA : Springer US : Imprint: Springer
Size:1 online resource
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Note:Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. As such, they play an important role in signal processing, Fourier analysis, and approximation theory. Whilehistorically the numerical eval uation of PSWFs presented serious difficulties, the developments of the last fifteen years or so made them as computationally tractable as any other class of special functions. As a result, PSWFs havebeen becoming a popular computational tool. The present book serves as a complete, self-contained resource for both theory and computation. It will be of interest to a wide range of scientists and engineers, from mathematiciansinterested in PSWF as an analytical tool to electrical engineers designing filters and antennas
Note:Springer eBooks
Contents:Introduction
Mathematical and Numerical Preliminaries
Overview
Analysis of the Differential Operator
Analysis of the Integral Operator
Rational Approximations of PSWFs
Miscellaneous Properties of PSWFs
Asymptotic Analysis of PSWFs
Quadrature Rules and Interpolation via PSWFs
Numerical Algorithms
ISBN:9781461482598
Series:e-books
Series:SpringerLink (Online service)
Series:Applied Mathematical Sciences, 0066-5452 : v187
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Numerical analysis , Engineering mathematics
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Call number:SPRINGER-2013-9781461479727:ONLINE Show nearby items on shelf
Title:Harmonic Analysis on Symmetric SpacesEuclidean Space, the Sphere, and the Poincar Upper Half-Plane [electronic resource]
Author(s): Audrey Terras
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:Springer 2013 e-book collections
Note:This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincar upper half plane. This book is intended for beginning graduate students inmathematics or researchers in phy sics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, andengineering. Many corrections, new topics, and updates have be en incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T.Sunada, Marie-France Vignras, Carolyn Gordon, and others on Mark Kac's question Can y ou hear the shape of a drum?, Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maasswaveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summationformula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon tr ansform, non-Euclidean geometry on the Poincar upper half plane H or unit disc andapplications to microwave engineering, fundamental domains in H for discrete groups , tessellations of H from such discrete group actions, automorphic forms, the Selberg tra ce formula and its applications in spectral theory as wellas number theory
Note:Springer eBooks
Contents:Chapter1 Flat Space. Fourier Analysis on R^m
1.1 Distributions or Generalized Functions
1.2 Fourier Integrals
1.3 Fourier Series and the Poisson Summation Formula
1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions
1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyls Criterion for Uniform Distribution
Chapter2 A Compact Symmetric Space
The Sphere
2.1 Fourier Analysis on the Sphere
2.2 O(3) and R^3. The Radon Transform
Chapter 3 The Poincar Upper Half
Plane
3.1 Hyperbolic Geometry
3.2 Harmonic Analysis on H
3.3 Fundamental Domains for
ISBN:9781461479727
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Topological Groups , Harmonic analysis , Fourier analysis , Functions of complex variables , Functions, special
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Call number:SPRINGER-2013-9781461474883:ONLINE Show nearby items on shelf
Title:Quadratic and Higher Degree Forms [electronic resource]
Author(s): Krishnaswami Alladi
Manjul Bhargava
David Savitt
Pham Huu Tiep
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth ofthree seminal conferences on these topics held in 2009,two at the University of Florida andone at the Arizona Winter Sc hool. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms andautomorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduatestudents and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from thepresentations atconferences atthe University of Florida as well as survey lectures on quadratic forms b ased on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volumeprovide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expositorypapers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics
Note:Springer eBooks
Contents:Preface
Toy Models for D. H. Lehmer's Conjecture II (E. Bannai, T. Miezaki)
On the Representation of an Integer by X2+Y2+Z2 and the Modular Equations of Degree 3 and 5 (A. Berkovich)
Almost Universal Ternary Sums of Squares and Triangular Numbers (W. Chan, A. Haensch)
Weighted Generating Functions for Type II Lattices and Codes (N. Elkies, S. Kominers)
Quadratic and Automorphic Forms (J. Hanke)
Integral Positive Ternary Quadratic Forms (W. Jagy)
Some Aspects of the Algebraic Theory of Quadratic Forms (R. Parimala)
On the Length of Binary Forms (B. Reznick)
Representa
ISBN:9781461474883
Series:e-books
Series:SpringerLink (Online service)
Series:Developments in Mathematics, 1389-2177 : v31
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions, special , Combinatorics , Number theory
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Call number:SPRINGER-2013-9781461467625:ONLINE Show nearby items on shelf
Title:Limits, Series, and Fractional Part Integrals [electronic resource] : Problems in Mathematical Analysis
Author(s): Ovidiu Furdui
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis features original problems in classical analysis that invite the reader to explore a host of strategies and mathematical tools used for solving realanalysis problems. Th e book is designed to fascinate the novice, puzzle the expert, and trigger the imaginations of all. The text is geared toward graduate students in mathematics and engineering, researchers, and anyone who works ontopics at the frontier of pure and applied mathematics. Moreover, it is the first book in mathematical literature concerning the calculation of fractional part integrals and series of various types. Most problems are neither easy norstandard and deal with modern topics of classical analysis. Each chapter has a section of open problems that may be considered as research projects for students who are taking advanced calculus classes. The intention of having theseproblems collected in the book is to stimulate the creativity and the discovery of new a nd original methods for proving known results and establishing new ones. The book is divided into three parts, each of them containing a chapterdealing with a particular type of problems. The first chapter contains problems on limits of special sequences and Riemann integrals the second chapter deals with the calculation of special classes of integrals involving a fractionalpart term and the third chapter hosts a collection of problems on the calculation of series (single or multiple) involving either a n umerical or a functional term.
Note:Springer eBooks
Contents:Preface
Notations
1. Limits
2. Fractional Part Integrals
3. A Bouquet ofSeries
A. Elements of Classical Analysis
B. StolzCesro Lemma
References
Index
ISBN:9781461467625
Series:e-books
Series:SpringerLink (Online service)
Series:Problem Books in Mathematics, 0941-3502
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Sequences (Mathematics) , Functions, special
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Call number:SPRINGER-2013-9781461466604:ONLINE Show nearby items on shelf
Title:Approximation Theory and Harmonic Analysis on Spheres and Balls [electronic resource]
Author(s): Feng Dai
Yuan Xu
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book containsmainstream material on the s ubject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part ofthe book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate studentsin analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewiczmultiplier theorem, the Riesz transform, and doubling weights are all familiar tools to re searchers in this area
Note:Springer eBooks
Contents:1 Spherical Harmonics
2 Convolution and Spherical Harmonic Expansion
3 Littlewood
Paley Theory and Multiplier Theorem
4 Approximation on the Sphere
5 Weighted Polynomial Inequalities
6 Cubature Formulas on Spheres
7 Harmonic Analysis Associated to Reflection Groups
8 Boundedness of Projection Operator and Cesro Means
9 Projection Operators and Cesro Means in L^p Spaces
10 Weighted Best Approximation by Polynomials
11 Harmonic Analysis on the Unit Ball
12 Polynomial Approximation on the Unit Ball
13 Harmonic Analysis on the Simplex
14 Applications
ISBN:9781461466604
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Fourier analysis , Functions, special
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Call number:SPRINGER-2013-9781461466574:ONLINE Show nearby items on shelf
Title:Elliptic Curves and Arithmetic Invariants [electronic resource]
Author(s): Haruzo Hida
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including -invariant, L-invariant, and similar topics. This book can be regarded as anintroductory text to the author's pr evious book p-Adic Automorphic Forms on Shimura Varieties. Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that providemotivation for the reader. Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate studentsstudying number theory. Key topics include non-triviality of arithmetic invariants and special values of L-functions elliptic curves over complex and p-adic fields Hecke algebras scheme theory elliptic and modular curves overrings and Shimura curves
Note:Springer eBooks
Contents:1 Non
triviality of Arithmetic Invariants
2Elliptic Curves and Modular Forms
3Invariants, Shimura Variety and Hecke Algebra
4Review of Scheme Theory
5Geometry of Variety
6 Elliptic and Modular Curves over Rings
7Modular Curves as Shimura Variety
8Non
vanishing Modulo p of Hecke Lvalues
9p
Adic Hecke L
functions and their
invariants
10Toric Subschemes in a Split Formal Torus
11Hecke Stable Subvariety is a Shimura Subvariety
References
Symbol Index
Statement Index
Subject Index
ISBN:9781461466574
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Number theory
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Call number:SPRINGER-2013-9781461463931:ONLINE Show nearby items on shelf
Title:Advances in Applied Mathematics and Approximation Theory [electronic resource] : Contributions from AMAT 2012
Author(s): George A Anastassiou
Oktay Duman
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:Advances in Applied Mathematics and Approximation Theory: Contributions from AMAT 2012 is a collection of the bestarticlespresented at Applied Mathematics and Approximation Theory 2012, an international conference heldin Ankara, Turkey, May 17-20, 20 12. This volume brings together key work from authors in the field covering topics such as ODEs, PDEs, difference equations, applied analysis, computational analysis, signal theory, positive operators,statistical approximation, fuzzy approximation, fracti onal analysis, semigroups, inequalities, special functions and summability. The collection willbe a useful resource for researchers in applied mathematics, engineering andstatistics
Note:Springer eBooks
Contents:Approximation by Neural Networks Iterates. George A. Anastassiou
Univariate Hardy Type Fractional Inequalities. George A. Anastassiou
Statistical Convergence on Time Scales and its Characterizations. Ceylan Turan and Oktay Duman
On the g
Jacobi Matrix Functions Bayram C ekim and Esra Erkus
Duman
Linear Combinations of Genuine Szasz
Mirakjan
Durrmeyer Operators. Margareta Heilmann and Gancho Tachev
Extensions of Schurs Inequality for the Leading Coefficient of Bounded Polynomials with Two Prescribed Zeros. Heinz
Joachim Rack
An Example of Optimal Nodes for Interpolati
ISBN:9781461463931
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v41
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential Equations , Differential equations, partial
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Call number:SPRINGER-2013-9781461463634:ONLINE Show nearby items on shelf
Title:Design of Experiments in Nonlinear Models [electronic resource] : Asymptotic Normality, Optimality Criteria and Small-Sample Properties
Author(s): Luc Pronzato
Andrej Pzman
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Design of Experiments in Nonlinear Models: Asymptotic Normality, Optimality Criteria and Small-Sample Properties provides a comprehensivecoverage of the various aspects of experimental design for nonlinear models. The bookcontains original contributi ons to the theory of optimal experiments that will interest students and researchers in the field. Practitionners motivated by applications will find valuable tools to help them designing theirexperiments. The first three chapters expose theconnections be tween the asymptotic properties of estimators in parametric models and experimental design, with more emphasis than usual on some particular aspects like the estimationof a nonlinear function of the model parameters,models with heteroscedastic errors, etc . Classical optimality criteriabased on those asymptotic properties are then presented thoroughly in a special chapter. Three chapters arededicated to specificissues raised by nonlinear models. The construction of designcriteria derived from non-asymptoti c considerations (small-sample situation) is detailed. The connection between design andidentifiability/estimability issues is investigated. Several approaches are presented to face the problem caused by the dependence of an optimal design on the value of the parameters to be estimated. A survey of algorithmic methodsfor the construction of optimal designs is provided
Note:Springer eBooks
Contents:Introduction
Asymptotic designs and uniform convergence. Asymptotic properties of the LS estimator
Asymptotic properties of M, ML and maximum a posteriori estimators
Local optimality criteria based on asymptotic normality
Criteria based on the small
sample precision of the LS estimator
Identifiability, estimability and extended optimality criteria
Nonlocal optimum design
Algorithmsa survey
Subdifferentials and subgradients
Computation of derivatives through sensitivity functions
Proofs
Symbols and notation
List of labeled assumptions
References
ISBN:9781461463634
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Statistics, 0930-0325 : v212
Series:Mathematics and Statistics (Springer-11649)
Keywords: Statistics
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Call number:SPRINGER-2013-9781461459699:ONLINE Show nearby items on shelf
Title:On the Higher-Order Sheffer Orthogonal Polynomial Sequences [electronic resource]
Author(s): Daniel J Galiffa
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:On the Higher-Order Sheffer Orthogonal Polynomial Sequences sheds light on the existence/non-existence of B-Type 1 orthogonal polynomials. This book presents a template for analyzing potential orthogonal polynomial sequencesincluding additional highe r-order Sheffer classes. This text not only shows that there are no OPS for the special case the B-Type 1 class, but that there are no orthogonal polynomial sequences for the general B-Type 1 class as well.Moreover, it is quite provocative how the seeming ly subtle transition from the B-Type 0 class to the B-Type 1 class leads to a drastically more difficult characterization problem. Despite this issue, a procedure is established thatyields a definite answer to our current characterization problem, which c an also be extended to various other characterization problems as well. Accessible to undergraduate students in the mathematical sciences and related fields, Thisbook functions as an important reference work regarding the Sheffer sequences. The author tak es advantage of Mathematica 7 to display unique detailed code and increase the reader's understanding of the implementation of Mathematica 7and facilitate further experimentation. In addition, this book provides an excellent example of how packages like M athematica 7 can be used to derive rigorous mathematical results
Note:Springer eBooks
Contents:1. The Sheffer A
Type 0 Orthogonal Polynomial Sequences and Related Results
2. Some Applications of the Sheffer A
Type 0 Orthogonal Polynomial Sequences
3. A Method for Analyzing a Special Case of the Sheffer B
Type 1 Polynomial Sequences
ISBN:9781461459699
Series:e-books
Series:SpringerLink (Online service)
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Computer science
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Call number:SPRINGER-2013-9781461453178:ONLINE Show nearby items on shelf
Title:Introduction to Queueing Systems with Telecommunication Applications [electronic resource]
Author(s): Laszlo Lakatos
Laszlo Szeidl
Miklos Telek
Date:2013
Publisher:Boston, MA : Springer US : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The book is composed of two main parts: mathematical background and queueing systems with applications. The mathematical background is a self containing introduction to the stochastic processes of the later studies queueingsystems. It starts with a q uick introduction to probability theory and stochastic processes and continues with chapters on Markov chains and regenerative processes. More recent advances of queueing systems are based on phase typedistributions, Markov arrival processes and quasy bir th death processes, which are introduced in the last chapter of the first part. The second part is devoted to queueing models and their applications. After the introduction of thebasic Markovian (from M/M/1 to M/M/1//N) and non-Markovian (M/G/1, G/M/1) qu eueing systems, a chapter presents the analysis of queues with phase type distributions, Markov arrival processes (from PH/M/1 to MAP/PH/1/K). The nextchapter presents the classical queueing network results and the rest of this part is devoted to the appl ication examples. There are queueing models for bandwidth charing with different traffic classes, slotted multiplexers, ATMswitches, media access protocols like Aloha and IEEE 802.11b, priority systems and retrial systems. An appendix supplements the tech nical content with Laplace and z transformation rules, Bessel functions and a list of notations. Thebook contains examples and exercises throughout and could be used for graduate students in engineering, mathematics and sciences
Note:Springer eBooks
Contents:Preface
Introduction to probability theory
Introduction to stochastic processes
Markov chains
Renewal and regenerative processes
Markov chains with special structures
Introduction to queueing systems
Markovian queueing systems
Non
Markovian queueing systems
Queueing systems with structured Markov chains
Queueing networks
Applied queueing systems
Functions and transforms
Exercises
References
ISBN:9781461453178
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer system performance , Distribution (Probability theory) , Telecommunication
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Call number:SPRINGER-2013-9781461445654:ONLINE Show nearby items on shelf
Title:Recent Advances in Harmonic Analysis and Applications [electronic resource] : In Honor of Konstantin Oskolkov
Author(s): Dmitriy Bilyk
Laura De Carli
Alexander Petukhov
Alexander M Stokolos
Brett D Wick
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Recent Advances in Harmonic Analysis and Applications is dedicated to the 65th birthday ofKonstantin Oskolkov and features contributions from analysts around the world. The volume contains expository articles by leadingexperts in their fields, as we ll asselected high quality research papers that explorenew results and trends in classical and computational harmonic analysis, approximation theory, combinatorics, convex analysis, differentialequations, functional analysis, Fourier analysis, graph theor y, orthogonal polynomials, special functions, and trigonometric series. Numerous articles in the volume emphasize remarkable connections between harmonic analysis andother seemingly unrelated areas of mathematics, such as the interaction between abstract problems in additive number theory, Fourier analysis, and experimentally discovered optical phenomena in physics. Survey and research articlesprovide an up-to-date account of various vital directions of modern analysis and will in particularbeof interest to young researchers who are just starting their career. This book will also be useful to experts in analysis,discrete mathematics, physics, signal processing, and other areas of science
Note:Springer eBooks
ISBN:9781461445654
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v25
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Harmonic analysis , Differential equations, partial , Algorithms , Number theory
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Call number:SPRINGER-2013-9781461440819:ONLINE Show nearby items on shelf
Title:Ramanujan's Lost Notebook [electronic resource] : Part IV
Author(s): George E Andrews
Bruce C Berndt
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pagesin the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, Ramanujan's lost notebook. Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This volume isthefourthof fivevolumes thatthe authors plan to write on Ramanujans lost notebook. In contrast to thefirst three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series. Most of the entriesexamined in this volume fall under the purviews of number theory and classical analysis. Se veral incomplete manuscripts of Ramanujan published by Narosa with the lost notebook are discussed. Three of the partial manuscripts are ondiophantine approximation, and others are in classical Fourier analysis and prime number theory. Most of the entries in number theory fall under the umbrella of classical analytic number theory. Perhaps the most intriguingentries are connected with the classical, unsolved circle and divisor problems. Reviewfrom the second volume: Fans of Ramanujan's mathematics are sur e to be delighted by this book. While some of the content is taken directly frompublished papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubte dly be inspiring research for decades to come. The nextinstallment in this series is eagerly awaited. - MathSciNet Review from the first volume: Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to a n understanding of the work ofthe genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complet
Note:Springer eBooks
Contents:Preface
1 Introduction
2 Double Series of Bessel Functions and the Circle and Divisor Problems
3 Koshliakov's Formula and Guinand's Formula
4 Theorems Featuring the Gamma Function
5 Hypergeometric Series
6 Euler's Constant
7 Problems in Diophantine Approximation
8 Number Theory
9 Divisor Sums
10 Identities Related to the Riemann Zeta Function and Periodic Zeta Functions
11 Two Partial Unpublished Manuscripts on Sums Involving Primes
12 Infinite Series
13 A Partial Manuscript on Fourier and Laplace Transforms
14 Integral Analogues of Theta Functions adn
ISBN:9781461440819
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Fourier analysis , Functions, special , Number theory
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Call number:SPRINGER-2013-9781461440451:ONLINE Show nearby items on shelf
Title:Quantum Plasmadynamics [electronic resource] : Magnetized Plasmas
Author(s): Donald Melrose
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:The covariant (4-tensor) theory for relativistic quantum plasmas presented in the first volume is generalized to magnetized plasma in this second volume. The firstfour chapters areconcerned with classical theory, includingcovariant forms of cold-plas ma, MHD and kinetic theory and the theory of gyromagnetic emission. The response 4-tensor for an arbitrary distribution is evaluated, using both the forward-scattering and Vlasov methods, applied to arelativistic thermal distribution and used to discuss w ave dispersion in relativistic magnetized plasmas. In the second half of the book, solutions of Dirac's equation for a magnetized electron are used to develop a magnetizedversion of QED. This form of QED is applied to gyromagnetic processes, the response of the magnetized vacuum and the response of a magnetized electron gas. The theory has a potentially wide range of applications, such as super-strongmagnetic fields in pulsars, high-powered lasers and spin-dependence in a laboratory electron gas
Note:Springer eBooks
Contents:Preface
Chapter 1: Covariant Fluid Models for Magnetized Plasmas
Chapter 2: Response Tensors for Magnetized Plasmas
Chapter 3: Waves in Magnetized Plasmas
Chapter 4: Gyromagnetic Processes
Chapter 5: Magnetized Dirac Electron
Chapter 6: Quantum Theory of Gyromagnetic Processes
Chapter 7: Second Order Gyromagnetic Processes
Chapter 8: Magnetized Vacuum
Chapter 9: Response of Magnetized Electron Gas
Appendix A: Special Functions
Index
ISBN:9781461440451
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v854
Series:Physics and Astronomy (Springer-11651)
Keywords: Quantum theory
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