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- 要約等...aph theory combines the authorit...... with the engaging freshness of ......mark of active mathematics. It covers the......fs, while offering glimpses of m......vanced methods in each field via......tools for applying the regularity lemma, brings the tangle t......eory of graph minors up to the cutting edge of curre......hi-boundedness in perfect graph ......le text for an introductory graduate course and is also suitable f...
- 関連情報Graduate texts in mathematics
- 掲載誌Graduate texts in mathematics
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- 要約等"This self-contained text introduces Euclid......er Analysis to graduate students who h......pleted courses in Real Analysis ......ourse sequence in Fourier Analys......nalysis at the graduate level. In true pedagogic......with targeted hints that will as......ist the reader in the developmen......rich understanding and improve o......trations build intuition in the proofs. Appendices contain background mat......ach as it contains shorter sections, more refined proofs, and ......rcises. Topics include the Fouri...... Multipliers, Singular Integrals, Little......ly covered within two semesters."--
- 内容細目Introductory mate......te identities Singular integrals Vector-valued singular integrals and Lit......ory Fractional integrability or ......paces Weighted inequalities Hist......sposes and adjoints of linear operators A......sicovitch covering lemma
- 関連情報Graduate texts in mathematics
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- 要約等In addition to covering the essential......, the author's intention in writing this text is ......t" for a first graduate course in mathematical l......uld be covered in a traditional ......ter course, an instructor can co......eeks' worth of interesting advanced topi......that have been introduced. The t......used by people in various course......the many appealing aspects of th...... to be covered in a single course is p......or further reading. New definitions, formali......ve been streamlined to engage th......reader quickly into the heart of......eory, highlighting the model the......x numbers. The interplay between logic and othe...
- 内容細目Introduction I. T......eories 2 Embeddings and Substruc......Quantifier Elimination 8 Model T...... Universal Machines and Undecida......tic Sets 12 Turing Reducibility ......Arithmetic and Incompleteness.-13 Gödel's Incompleteness Th......Arithmetic and Independence Resu......ibliography. - Index
- 関連情報Graduate texts in mathematics
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- 要約等"This textbook offers an introduction to the theory of Drinfeld modules, m......eniently recalling prerequisites......sis, Chapter 3 introduces Drinfeld modules an...... and torsion points. Over the ne......ur chapters, Drinfeld modules are studied in settings of various f......mportance, culminating in the case of gl...... emphasized. Drinfeld Modules gu......esearch topics in function field......ithmetic, assuming only familiarity with graduate-level abstract......ercises of varying difficulty included in each section, ......textbook for a graduate course on the ......ce for courses in algebraic numb......e, researchers in algebra and number theory wil...
- 内容細目...lgebraic Preliminaries Chapter 2......roperties of Drinfeld Modules Chapter 4. Drinfeld Modules over Finite Fields Chap......ic Theory of Drinfeld Modules Chapter 6. Drinfeld Modules ov......s Chapter 7. Drinfeld Modules ov...... Appendix A. Drinfeld modules fo......eral function rings Appendix B. ......s Bibliography Index
- 件名Drinfeld modules--Textbooks Drinfeld modules--M......s Modules de Drinfeld--Modèles ......thématiques Drinfeld modules
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- 要約等"More Explorations in Complex Functions is something of a sequel t......, Explorations in Complex Functions. Both texts introduce a varie...... core material in the mainstream of compl......re widely used in other areas of mathematics and applicatio...... but there is minimal overlap be......two books. The intended readersh......e same, namely graduate students and researchers in complex analysis, independent readers, seminar attendees, or instructors for a second course in complex analysis. Instructors will ......s for constructing a second cour......d first course in complex analys...... more material in this present text than one co...
- 内容細目Basics Further preliminaries Complex d......iconformal mapping Introduction to T......imants and continued fractions Riemann-Hilbert ...
- 関連情報Graduate texts in mathematics
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- 要約等...andom walks on infinite, finitely generated......long with certain background material in measure-theore......ability. The main objective is t......extbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory......rt course covering the main results regarding transience/re......ly to students in probability th...... whose primary interests are in geometry, ergodic theory, or ...
- 内容細目...rne-Varopoulos Inequality 5 Isoperimetric Inequalities and ......ty 6 Markov Chains and Harmonic ......7 Dirichlets Principle and the R...... Theorem 8 Martingales 9 Bounded......endix A: A 57-Minute Course in MeasureTheoretic Probability
- 件名Random walks (Mathematics) Infinite groups Prob......iques) Groupes infinis Probabilités probability.
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- 要約等...for a one-year graduate course in real algebraic......res a thorough introduction to o......closed fields, including the Tarski-Se......and transfer principle. Classica......lts such as Artin's solution to ...... are presented in detail. Other features include careful introductions to ......vstellensätze in great detail and in various settings, together wi......ions to semidefinite programming and polynomia...... optimization, including recent research on semidefinite representat......itten by a leading expert and ba......can be covered in a one-semester......ifficulty, are included in the book
- 内容細目...B: Convex Sets in Real Infinite-Dimensional Vector Spaces
- 関連情報Graduate texts in mathematics
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- 要約等...textbook is to introduce and stu......ourse, for the independent study......en from the beginnings of the subje......reas of modern mathematics, with deep con......ated to developing the notion of......tations are defined locally, cus......ns and Eisenstein series are defined globally, and Rankin-Selberg L-functions are defined to give a link between the g...... and local settings. This prepar......eatment of distinguished representations in global and local settings. The link between distinguished represe......ometry is explained in a chapter on t......metric spaces (in particular, Sh...... powerful tool in the Langlands Program, is dis...
- 関連情報Graduate texts in mathematics
- 掲載誌Graduate texts in mathematics
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- 要約等This graduate text presents ...... theory of continuous parameter ......ocus on developing context and intuition before formalizing the theory of...... the reader is introduced to semigroup theory, including the HilleYosi...... construct continuous parameter ...... of Fellers seminal theory of th......usions studied in a later chapte......processes with independent increments, or Lv......ted to Its fascinating theory of sto...... of diffusions in all dimensions......tant examples. Intimate connecti......iffusions and linear second orde......s are laid out in two chapters, ......he other on an intriguing multi-phase homogeniz...
- 内容細目A Review of Martingales, Stopping Times, and th......mple Paths Continuous Parameter ......Processes with Independent Increments The Stochastic Integral Construc......ma Cameron-Martin-Girsanov Theor......Support of Nonsingular Diffusion......utions to Certain PDEs Probabili......Stability for Singular Diffusions Stochastic Integrals with L2-Martingales Local Tim......Topic: The Martingale Problem Sp...... for Transport in Periodic Media......iecewise Deterministic Markov Processes in Population Biology The Hille-...
- 関連情報Graduate texts in mathematics
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- 要約等"This textbook introduces reader......isite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, ......ok provides an introduction to the rich interplay between......ysis. Arranged into three parts, the book begins with a rigoro......to probability in mind. The second p......dom variables, independence, con......dom variables. In the third part, in which all chap......rs can be read independently, th......crete-time martingales, countabl......pace Markov chains, and Brownian......ection of illuminating exercises of varying difficulty. S......onal analysis, in particular on Hilbert and Ban...
- 内容細目...surable spaces Integration of me......ability theory Independence Conv......ables Conditioning Part III : St...... Theory of Martingales Markov chains Brownian motion A few facts ...
- 関連情報Graduate texts in mathematics
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- 要約等"This textbook introduces the st......al equations using both analytic......al methods. By intertwining the two compl...... study. Motivating examples from......l sciences, engineering, and economic...... complete this integrated approa......e of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vib......uid flow, and financial markets.......ant characterizing properties ar...... an accessible introduction to H......resented first in dimension one, before being extended to a......ds focuses on finite difference and finite element met...... Euclidean domains. The Black-Scholes equation ...
- 一般注記Translation of: Partielle Differenzialgleichungen. Berlin, Germany : Springer Spektrum, 2018
- 関連情報Graduate texts in mathematics
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- 要約等...plores two distinct stochastic p......rocesses. Building from simple e......ocus on developing context and intuition before formalizing the theory of......ch topic. This inviting approach illuminates the key id......d computations in the proofs, forming an ideal basi......y. After recapping the essential......s, the book begins with an introduction to t......rocess. Topics in ergodic theory follow, including Birkhoff's Er......Theorem and an introduction to d......ety of topics, including birth-death chains, hitting probabilities......to equilibrium includes a splitting condition tha......ucture of certain iterated maps in a novel way....
- 内容細目...c Theory 6. An Introduction to D......s 7. Markov Chains 8. Markov Pro...... Space 9. Stopping Times and the......e of Markov Chains 11. BirthDeath Chains 12. Hitting Probabilities......ge Numbers and Invariant Probabi...... for Markov Chains by Renewal De...... for Markov Chains by Renewal De......sition 15. Martingale Central Li......LN & FCLT 17. Linear Markov Proc......ps 19. A Splitting Condition and......ependence, FKG Inequalities 24. ......: More on Coupling Methods and A......cial Topic: An Introduction to K......mpact Self-Adjoint Operators and......unded Self-Adjoint Operators C. ......ation Theorems in Functional Analysis
- 関連情報Graduate texts in mathematics
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- 要約等"This textbook provides an introduction to the combinatorial and sta......n emphasis on binomial ideals. In addition to th......plications of binomial ideals to......other areas of mathematics. The book begins with a brief, self-contained overview of ......tive algebra. Binomials and binomial ideals ar......hen considered in detail, along with a short introduction to c......opes. Chapters in the remainder of the text can be read independently and......the theory of binomial ideals, including edge rings and edge polytopes, join-meet ideals of finite lattices, binomial edge idea......enerated by 2-minors, and binomial ideals arisi...
- 内容細目...s: Polynomial rings and Gröbner......ebra Part II. Binomial ideals an......vex polytopes: Introduction to binomial ideals Co....... Applications in combinatorics and sta......opes and edge rings Join-meet ideals of finite lattices Binomial edge idea......enerated by 2-minors Statistics.
- 件名Binomial theorem--Textbooks. Commutative algebra--Textbooks. Binomial theorem. Commutative alg...
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- 要約等This book is a self-contained advanced tex......tems, which begins with a pedago......ary background information before moving on to subject......tive research, including topological p...... book explores in detail selected topics in quantum spin systems and la...... symmetry breaking in the antiferrom......isenberg model in two or higher ......ane phenomenon in antiferromagnetic quantum spin chains and related topics in topological ph......), and the origin of magnetism in various versio......epresents certain nontrivial phe......tures that are invariably encountered in a variety of q......-body systems, including quantum field theory, ...
- 内容細目Introduction Basi......s of quantum spin systems.-Long-...... symmetry breaking in the classical and quantum Ising models Long-r...... symmetry breaking in the antiferrom...... symmetry breaking" in Bose-Einstein condensates.-A......phase.-The origin of ferromagnet......ices Solutions Index.
- 関連情報Graduate texts in physics
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- 要約等This book is a systematic introduction to a......book is unique in various aspect......tial mechanics in a single and unified......tivistic viewpoints. Third, it explains both the orbi...... to the latest International Ast......s. The book is intended for undergraduate students of ph......s Japanese original manuscript w...... of artificial intelligence. A subsequent human...
- タイトル標目Graduate texts in physics, 1868-4513
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- 要約等This graduate textbook provi......iew of quantum information theor....... Clearly explaining the necessary......pics from both information-theor......chanical viewpoints and provides......dvanced topics in quantum commun...... superdense coding, quantum stat......m encryption. Since the publicat......n of the preceding book Quantum Information: An Introduction, the......endous strides in the field of quantum information. In particular, the following topics - all ......m state discrimination, quantum ......rem and uncertainty relation. Wi......tion of leaked information and i...... transmission. In addition, various types of th...
- 内容細目...uantum systems Information quant......ter estimation in classical syst......hypothesis testing and discrimination of quantu......tum channel coding (message tran......d trace-preserving completely po......e maps Quantum information geome......cols Source coding in quantum systems.
- 件名Quantum computing--Mathematics.
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- タイトル標目Graduate texts in mathematics ; 129. Graduate texts in mathematics. Readings in mathematics.
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- 一般注記... author's book in Japanese published in 3 volumes by Iwanami, Tokyo in 1977."
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- 一般注記Includes indexes.
- 著者標目竹内, 外史, 1926-2017 Zaring, Wilson M.
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- 件名Linear topological spaces. Topolo...
- 一般注記Reprint of the ed. pu......an Nostrand, Princeton, N.J., in series: The Un......versity series in higher mathematics. Includes index.
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