Author: Rod G. DowneyPublisher:
ISBN: 9781470461379
Category : Computable functions
Languages : en
Pages : 90
Book Description
Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees
Author: Rod G. DowneyPublisher:
ISBN: 9781470461379
Category : Computable functions
Languages : en
Pages : 90
Book Description
Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees
Author: Rodney G. DowneyPublisher: American Mathematical Soc.
ISBN: 1470441624
Category : Mathematics
Languages : en
Pages : 90
Book Description
First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no $Delta^0_2$ set which Turing bounds a promptly simple set can have minimal weak truth table degree.
Art And Practice Of Mathematics, The: Interviews At The Institute For Mathematical Sciences, National University Of Singapore, 2010-2020
Author: Yu Kiang LeongPublisher: World Scientific
ISBN: 9811219605
Category : Mathematics
Languages : en
Pages : 442
Book Description
This book constitutes the second volume of interviews with prominent mathematicians and mathematical scientists who visited the Institute for Mathematical Sciences, National University of Singapore. First published in the Institute's newsletter Imprints during the period 2010-2020, they offer glimpses of an esoteric universe as viewed and experienced by some of the leading and creative practitioners of the craft of mathematics.The topics covered in this volume are wide-ranging, running from pure mathematics (logic, number theory, algebraic geometry) to applied mathematics (mathematical modeling, fluid dynamics) through probability and statistics, mathematical physics, theoretical computer science and financial mathematics. This eclectic mix of the abstract and the concrete should interest those who are enthralled by the mystique and power of mathematics, whether they are students, researchers or the non-specialists.By briefly tracing the paths traveled by the pioneers of different national backgrounds, the interviews attempt to put a cultural face to an intellectual endeavor that is often perceived as dry and austere by the uninitiated. They should also interest those who are intrigued by the influence of the environment on the creative spirit, and, in particular, those who are interested in the psychology and history of ideas.
Algorithmic Randomness and Complexity
Author: Rodney G. DowneyPublisher: Springer Science & Business Media
ISBN: 0387684417
Category : Computers
Languages : en
Pages : 855
Book Description
Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.
Differential Function Spectra, the Differential Becker-Gottlieb Transfer, and Applications to Differential Algebraic K-Theory
Author: Ulrich BunkePublisher: American Mathematical Soc.
ISBN: 1470446855
Category : Education
Languages : en
Pages : 177
Book Description
We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.
Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators
Author: Jonathan GantnerPublisher: American Mathematical Society
ISBN: 1470442388
Category : Mathematics
Languages : en
Pages : 114
Book Description
Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space $V$. This has technical reasons, as the space of bounded operators on $V$ is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.
Łojasiewicz-Simon Gradient Inequalities for Coupled Yang-Mills Energy Functionals
Author: Paul M FeehanPublisher: American Mathematical Society
ISBN: 1470443023
Category : Mathematics
Languages : en
Pages : 138
Book Description
The authors' primary goal in this monograph is to prove Łojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces that impose minimal regularity requirements on pairs of connections and sections.
Theory of Fundamental Bessel Functions of High Rank
Author: Zhi QiPublisher: American Mathematical Society
ISBN: 1470443252
Category : Mathematics
Languages : en
Pages : 123
Book Description
In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.
Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties
Author: Hiroshi IritaniPublisher: American Mathematical Soc.
ISBN: 1470443635
Category : Education
Languages : en
Pages : 92
Book Description
Gromov-Witten theory started as an attempt to provide a rigorous mathematical foundation for the so-called A-model topological string theory of Calabi-Yau varieties. Even though it can be defined for all the Kähler/symplectic manifolds, the theory on Calabi-Yau varieties remains the most difficult one. In fact, a great deal of techniques were developed for non-Calabi-Yau varieties during the last twenty years. These techniques have only limited bearing on the Calabi-Yau cases. In a certain sense, Calabi-Yau cases are very special too. There are two outstanding problems for the Gromov-Witten theory of Calabi-Yau varieties and they are the focus of our investigation.
Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms
Author: Kazuyuki HatadaPublisher: American Mathematical Soc.
ISBN: 1470443341
Category : Education
Languages : en
Pages : 165
Book Description
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