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- Summary, etc....hree levels of mathematical frames in which a simple......and associated mathematical structures, pr......en carried out in the process of......ical) formulas in enumerative combinatorics, theory......eory, study of integrable system......and so on. Originating from the pape......anics models using the theta fun......e formulas obtained at the q-lev......elliptic level in many research fields in mathematics and theoretical physics. In the present mo......tic extensions in the study of s......chastic models in equilibrium an......ions are used, including Jacobi's thet......nograph is not intended to be a handbook of mathematical formulas of these elliptic fu...
- ContentsIntroduction Brow......Macdonald Denominators KMLGV Determinants and Noncolliding Brownian Bridges Determinantal Point Processes Ass......Periodic Determinantal Point Processes Future Problems
- Subject Heading...es Statistical physics Elliptic funct......s. Statistical physics. Stochastic processes.
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National Diet LibraryOther Libraries in Japan
- Summary, etc.... such as the Painlevé and Garni......t class of nonlinear differential equations in mathematics and mathematical physics. For discrete ......hese equations in particular, mu...... has been made in recent decades......e known: the Painlevé test/ Painlevé property, reduction of integrable hierar......é method explained in this book prov......hose equations in both continuous and discre...... approximation/interpolation sup...... consider the linear differentia...... and f(x)Q(x). In choosing the suitable ...... problem, the linear differentia......stematic study including discrete case......ltaneously obtain various results such as the n...
- Contents...mation for q-Painlevé/Garnier e......tions 4. Padé interpolation 5. Padé interpolation on q-quadratic gri...
- Subject HeadingPadé approximant Painlevé equations Padé approximant. Painlevé equations.
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- Related MaterialSpringer briefs in mathematical physics
- Periodical TitleSpringer briefs in mathematical physics
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National Diet Library
- Summary, etc....owledge of the inverse problems arising in various areas in mathematics, physics, engineering, and medical ......il down to the mathematical question in which one trie......ts) or the domain (manifolds) fr...... the operators in question are o......hose of Schrödinger operators. ...... observe the main features of inverse spectral ......is the Borg-Levinson theorem in the inverse Dirichlet problem in a bounded domain elucidating basic motivation of the inverse problem a......mension. The main theme is the inverse scattering, in which the spec......'s S-matrix defined through the ......ic behavior at infinity of solutions Significan...
- ContentsChapter 1: One-dimensional inverse problems ......ti-dimensional inverse boundary ......: Other topics Index
- Subject HeadingSpectral theory (Mathematics) Scattering (Mathematics) Inverse problems (Differential e...
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- Summary, etc.Rich information-theoretic structure in out-of-equilib......ynamics exists in both the class......m regimes, leading to the fruitful interplay among statistical physics, quantum information theory, and mathematical theories such ...... theory. The main purpose of thi......to clarify how information theory works behind thermodynamic......on both purely information-theor......ions. From the mathematical point of view, rigo...... are presented in a self-contained manner. From the physics perspective, m......hermodynamics. In particular, re......nch of quantum information theor......es" and has an intrinsic connection to various ...
- Contents1Introduction 2Cla......Hypothesis testing CClassical asymptotic equipa...
- Title HeadingSpringerBriefs in mathematical physics ; v. 16. 2197-1765
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National Diet Library
- Summary, etc....on the subject including a brief histo...... quantum group in the Drinfeld realizatio......ction of both finite and infinite-dimensional......x operators as intertwining operators of ......ortant objects in representation......uantum groups. In this book, the......hypergeometric integral solutions. In particular, th......nctions appear in such solutions......lopes for certain equivariant el......ach to quantum integrable system...... a rapidly growing topic in mathematical physics related to the......etween quantum integrable system......cohomology. To invite the reader to such topics...
- Contents...nts Chapter 1: Introduction Chapter 2: Elliptic...
- Title HeadingSpringerBriefs in mathematical physics ; v. 37
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National Diet Library
- Summary, etc.This book furnishes a brief introduction to c......ocess of computing Gromov-Witten invariants of a C......threefold by using the Picard-Fu......tion of period integrals of its ......example, the quintic hypersurface in 4-dimensional ......y and the striking result proposed in the celebrated......metry are explained. Then the to......e B-model, are introduced. The c......thesis is explained as the equiv......A-model of a quintic hyper-surfa......au threefold using toric geometr......s briefly explained. Also given ...... of the period integrals and on ......rocess of deriving the instanton expansi......el Yukawa coupling based on the mirror symmetry...
- Contents1. Brief Introduction of M......n 7. Brief Outline of Direct Proof of Mirror Th...
- Title HeadingSpringerBriefs in mathematical physics ; v. 29.
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National Diet Library
- Title HeadingSpringerBriefs in mathematical physics ; v. 30.
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National Diet Library
- Summary, etc....theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coh......ut that the DT invariants have many interesting properties and appear in several contex...... on curve-counting theories, wall-crossing in derived catego......BPS state counting in string theory, and o......ich lead to refined versions of DT invariants such a......homological DT invariants. The i......homological DT invariants led to a mathematical definition of the GopakumarVafa invariant, which ...... GopakumarVafa in 1998, but its precise mathematical definition has not b......progress on DT invariants and related topics, w...
- ContentsDonaldson-Thomas Invariants on Cal......naldson-Thomas Invariants Donaldson-Thomas Invariants for Qu......naldson-Thomas Invariants for Br......ects Wall-Crossing Formulas of D......naldson-Thomas Invariants Cohomo......naldson-Thomas Invariants Gopakumar-Vafa Invariants Some Future Direction...
- Subject HeadingDonaldson-Thomas invariants Invariants de Donaldson-Thomas Donaldson-Thomas invariants.
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- Summary, etc.This book explains the mathematical structures of ......from the viewpoints of functional and infinite-dimensional......nalysis. The main mathematical objects are infinite-dimensional......rchers who are interested in mathematical analysis of quantum fields, including supersymmetric ones, and infinite-dimensional......ion of general mathematical structures that some models in the SQFT have in common, and the mathematically rigorous ana......bject are that in physics literature, su...... may be ill-defined mathematically. From a mathematical point of view, howe......cts related to infinite-dimensional......nt to show the mathematical existence of such models firs...
- ContentsIntro Preface Con......chanics 1.1 Definition and Basic...... of a Self-adjoint Supercharge 1......rsymmetry Breaking and an Index Formula 2 E...... Operators 2.7 Infinite Determinants 2.8 Boson ......ators 4.3.1 Definitions and Basi......s 4.3.2 A Cochain Complex 4.4 Operators in the Q-space Re......mplex 4.5.1 Definitions and Basi...... Operators of Finite Order and d......S(F) 4.12 Path Integral Representation of the Index of QS,+(F) 4.12.1 Path Integral Represen......ns of Pure Imaginary Time Correl...... Fields 4.12.2 Index Formula 5 Models in Supersymmetric......eory 5.1 Preliminaries 5.1.1 Mom......antum Particle in Tell 5.1.2 The Free Quantum K...
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- Summary, etc....en algorithmic information theor......s. Algorithmic information theor......for characterizing the notion of......domness for an individual object and for studying it closely an......mprehensively. In this book, a s......cal mechanical interpretation of AIT is introduced while explaining the basic not......ho has an acquaintance with an e......ion of the setting of AIT is the......less source coding in information theory. First, in the book, a st......cal mechanical interpretation of......less source coding scheme is introduced. It ca......at the notions in statistical me......are translated into the context of noiseless so...
- ContentsIntro; Preface; C......cal Mechanical Interpretation of......less Source Coding; 1.1 Introduction; 1.2 Instantaneous Cod......cal Mechanical Interpretation; 1......um Between Two Instantaneous Cod......cal Mechanical Interpretation of...... 2 Algorithmic Information Theor......otation and Definitions; 2.2 Com......refix-Free Machines and Program-......ure5.2 Fixed Point Theorems by T......of the Fixed Point Theorems; 5.3......refix-Free Machine; 6 Statistica......Mechanical Meaning of the Thermo......cal Mechanical Interpretation of......etic Treatment in Computability Theory8.2 Turing Machine Computing a Prefix-Free Machine; 8.3 R...
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- Summary, etc.In mathematical physics, one of the fascinating issues is the study of integrable systems. In particular, no......ed significant insight for real physics. There are bas......two notions of integrability: classical integrability and quantum integrability. In this book, the......mer, classical integrability. Wh...... system has a finite number of d...... of freedom is infinite, as in classical fiel...... theories, the integrable struct......ed profoundly. In fact, the stud......of classically integrable field ......y and various kinds of techniques, including the classical inverse scattering method, which......eloped so far. In previously published books, t...
- ContentsIntegrable Non-linear Sigma Models in (1+1)-dimensions Yang-Baxter ...
- Subject HeadingYang-Baxter equation Mathematical physics Mathematical physics. Yang-Baxter equation.
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National Diet LibraryOther Libraries in Japan
- Summary, etc.This book provides self-contained proofs of th......tes of several interaction models in quantum field theory. Interaction model......discussed here include the spin-boson model, t...... approximation in non-relativist......odels describe interactions betw......nd state is defined as the eigen...... of a self-adjoint operator describing the Hamiltoni......wever embedded in the continuum and then it...... ground states in non-perturbati......del, and the spin-boson model, and several kinds of proofs of...... provided. Key ingredients are c......pact operators in Hilbert spaces......also enhanced binding. The enhanced binding mea...
- Contents...t Cutoffs; 5 Spin-Boson Model; 5.1 Spin-Boson Hamilton......e; 6 Enhanced Bindings; 6.1 Enhanced Binding for the Pauli......sition From Unbinding to Binding; 6.1.5 Enhanced Binding by Cutoff Fun...... 6.2 Enhanced Binding for the Nelso......on Hamiltonian Intro; Preface; C......; Notations; 1 Introduction; 1.1......n Model; 1.4 Spin-Boson Model; 1.5 Infrared Problem; 1.6 Enhanced Binding; 1.6.1 Enhanced Binding for the Pauli.......6.2 Enhanced Binding for the Nelso......tness; 2 Preliminaries; 2.1 Comp...... Compact Embeddings; 2.2.1 Strong Compactness in Lp Spaces; 2.2.2 Sobolev Inequalities 6.2.......eReferences; ; Index
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- Title HeadingSpringerBriefs in mathematical physics ; v. 31.
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National Diet Library
- Contents...y Universality Intersection numbers of curves Intersection numbers of p-spin curves Open intersection numb...... Gromov-Witten invariants, P¹ model.
- Title HeadingSpringerBriefs in mathematical physics ; v.19.
- Author HeadingBrézin, E. 氷上, 忍, 1948-
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National Diet Library
- Summary, etc....d as a concise introduction to t......rks from the point of view of qu...... theory. The main topics are spe......y matrices of finite or infinite graphs and ......utions for growing graphs. The main vehicle is qua......matrices revealing their non-com......ns by means of interacting Fock spaces o......us concepts of independence in quantum probab...... and corresponding central limit......, and students interested in graph spectra,......ul for a quick introduction to quantum probabil...
- Contents...2. Spectra of Finite Graphs 3. S......ics References Index.
- Subject Heading.... MATHEMATICS--Mathematical Analysis. Mathematics. Mathematical Physics. Probability Theory and Stoch...
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- Contents1 Introduction to K......nal solitons 4 Introduction to the real Grassma...
- Subject Heading...eral SCIENCE / Physics / General Mathematics. Mathematical Physics. Difference and Functional Eq...
- Title HeadingSpringerBriefs in mathematical physics ; v. 22.
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- Subject HeadingQuantum computing. Fault-tolerant computing.
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- Summary, etc.C* tensor categories are a point of contact wh......are the underlying unifying concept for h......s of (properly infinite) von Neuman......s. The present introductory text......ross-relations in different cont......ve as complete invariants, both ......f which are defined only in the presence of a braiding. The last cha......levance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Co...
- ContentsIntroduction Homo......domorphisms of infinite factors Hom......s of Q-systems Induced Q-systems......n of Q-systems Intermediate Q-sy......tems Q-systems in braided tensor categories a-induction Mirror ......s Applications in QFT Basics of algebraic quant...
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- Contents...nces Solutions Index.
- Subject HeadingMathematical physics. Probabilities......eral SCIENCE / Physics / General
- Note (General)"Extras online"--Cover.