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An Elementary Recursive Bound For Effective Positivstellensatz And Hilberts 17th Problem
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Book Synopsis An Elementary Recursive Bound for Effective Positivstellensatz and Hilbert’s 17th Problem by : Henri Lombardi
Download or read book An Elementary Recursive Bound for Effective Positivstellensatz and Hilbert’s 17th Problem written by Henri Lombardi and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely they express a nonnegative polynomial as a sum of squares of rational functions and obtain as degree estimates for the numerators and denominators the following tower of five exponentials 222d4k where d is the number of variables of the input polynomial. The authors' method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely the authors give an algebraic certificate of the emptyness of the realization of a system of sign conditions and obtain as degree bounds for this certificate a tower of five exponentials, namely 22(2max{2,d}4k+s2kmax{2,d}16kbit(d)) where d is a bound on the degrees, s is the number of polynomials and k is the number of variables of the input polynomials.
Book Synopsis An Introduction to Polynomial and Semi-Algebraic Optimization by : Jean Bernard Lasserre
Download or read book An Introduction to Polynomial and Semi-Algebraic Optimization written by Jean Bernard Lasserre and published by Cambridge University Press. This book was released on 2015-02-19 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic functions). In particular, the author explains how to use relatively recent results from real algebraic geometry to provide a systematic numerical scheme for computing the optimal value and global minimizers. Indeed, among other things, powerful positivity certificates from real algebraic geometry allow one to define an appropriate hierarchy of semidefinite (SOS) relaxations or LP relaxations whose optimal values converge to the global minimum. Several extensions to related optimization problems are also described. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided.
Book Synopsis Reachability Problems by : Mikolai Bojanczyk
Download or read book Reachability Problems written by Mikolai Bojanczyk and published by Springer. This book was released on 2015-10-12 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 9th International Workshop on Reachability Problems, RP 2015, held in Warsaw, Poland, in September 2015. The 14 papers presented together with 6 extended abstracts in this volume were carefully reviewed and selected from 23 submissions. The papers cover a range of topics in the field of reachability for infinite state systems; rewriting systems; reachability analysis in counter/timed/cellular/communicating automata; Petri nets; computational aspects of semigroups, groups, and rings; reachability in dynamical and hybrid systems; frontiers between decidable and undecidable reachability problems; complexity and decidability aspects; predictability in iterative maps and new computational paradigms.
Book Synopsis Global Smooth Solutions for the Inviscid SQG Equation by : Angel Castro
Download or read book Global Smooth Solutions for the Inviscid SQG Equation written by Angel Castro and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.
Book Synopsis Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators by : Jonathan Gantner
Download or read book Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators written by Jonathan Gantner and published by American Mathematical Society. This book was released on 2021-02-10 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Łojasiewicz-Simon Gradient Inequalities for Coupled Yang-Mills Energy Functionals by : Paul M Feehan
Download or read book Łojasiewicz-Simon Gradient Inequalities for Coupled Yang-Mills Energy Functionals written by Paul M Feehan and published by American Mathematical Society. This book was released on 2021-02-10 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Fundamental Bessel Functions of High Rank by : Zhi Qi
Download or read book Theory of Fundamental Bessel Functions of High Rank written by Zhi Qi and published by American Mathematical Society. This book was released on 2021-02-10 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case by : Jacob Bedrossian
Download or read book Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case written by Jacob Bedrossian and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $epsilon leq c_0mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t rightarrow infty $. For times $t gtrsim mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of ``2.5 dimensional'' streamwise-independent solutions referred to as streaks.
Book Synopsis Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms by : Kazuyuki Hatada
Download or read book Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms written by Kazuyuki Hatada and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence by : Camille Male
Download or read book Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence written by Camille Male and published by American Mathematical Society. This book was released on 2021-02-10 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by permutation matrices. This fact leads naturally to an extension of free probability, formalized under the notions of traffic probability. The author first establishes this construction for random matrices and then defines the traffic distribution of random matrices, which is richer than the $^*$-distribution of free probability. The knowledge of the individual traffic distributions of independent permutation invariant families of matrices is sufficient to compute the limiting distribution of the join family. Under a factorization assumption, the author calls traffic independence the asymptotic rule that plays the role of independence with respect to traffic distributions. Wigner matrices, Haar unitary matrices and uniform permutation matrices converge in traffic distributions, a fact which yields new results on the limiting $^*$-distributions of several matrices the author can construct from them. Then the author defines the abstract traffic spaces as non commutative probability spaces with more structure. She proves that at an algebraic level, traffic independence in some sense unifies the three canonical notions of tensor, free and Boolean independence. A central limiting theorem is stated in this context, interpolating between the tensor, free and Boolean central limit theorems.
Book Synopsis C-Projective Geometry by : David M Calderbank
Download or read book C-Projective Geometry written by David M Calderbank and published by American Mathematical Society. This book was released on 2021-02-10 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. The authors realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kähler manifold gives rise to a c-projective structure and this is one of the primary motivations for its study. The existence of two or more Kähler metrics underlying a given c-projective structure has many ramifications, which the authors explore in depth. As a consequence of this analysis, they prove the Yano–Obata Conjecture for complete Kähler manifolds: if such a manifold admits a one parameter group of c-projective transformations that are not affine, then it is complex projective space, equipped with a multiple of the Fubini-Study metric.
Book Synopsis The Riesz Transform of Codimension Smaller Than One and the Wolff Energy by : Benjamin Jaye
Download or read book The Riesz Transform of Codimension Smaller Than One and the Wolff Energy written by Benjamin Jaye and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fix $dgeq 2$, and $sin (d-1,d)$. The authors characterize the non-negative locally finite non-atomic Borel measures $mu $ in $mathbb R^d$ for which the associated $s$-Riesz transform is bounded in $L^2(mu )$ in terms of the Wolff energy. This extends the range of $s$ in which the Mateu-Prat-Verdera characterization of measures with bounded $s$-Riesz transform is known. As an application, the authors give a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator $(-Delta )^alpha /2$, $alpha in (1,2)$, in terms of a well-known capacity from non-linear potential theory. This result contrasts sharply with removability results for Lipschitz harmonic functions.
Book Synopsis The Irreducible Subgroups of Exceptional Algebraic Groups by : Adam R. Thomas
Download or read book The Irreducible Subgroups of Exceptional Algebraic Groups written by Adam R. Thomas and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is a contribution to the study of the subgroup structure of excep-tional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of G. In this paper we com-plete the classification of irreducible connected subgroups of exceptional algebraic groups, providing an explicit set of representatives for the conjugacy classes of such subgroups. Many consequences of this classification are also given. These include results concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible connected subgroups are determined by their composition factors on the adjoint module of G, with one exception. A result of Liebeck and Testerman shows that each irreducible connected sub-group X of G has only finitely many overgroups and hence the overgroups of X form a lattice. We provide tables that give representatives of each conjugacy class of connected overgroups within this lattice structure. We use this to prove results concerning the subgroup structure of G: for example, when the characteristic is 2, there exists a maximal connected subgroup of G containing a conjugate of every irreducible subgroup A1 of G.
Book Synopsis Conformal Graph Directed Markov Systems on Carnot Groups by : Vasileios Chousionis
Download or read book Conformal Graph Directed Markov Systems on Carnot Groups written by Vasileios Chousionis and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. They illustrate their results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.
Book Synopsis Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields by : Lisa Berger
Download or read book Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields written by Lisa Berger and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $mathbb F_p(t)$, when $p$ is prime and $rge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $mathbb F_q(t^1/d)$.
Book Synopsis Double Affine Hecke Algebras and Congruence Groups by : Bogdan Ion
Download or read book Double Affine Hecke Algebras and Congruence Groups written by Bogdan Ion and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group data. We show that DAAG/DAHA always admit a faithful action by auto-morphisms of a finite index subgroup of the Artin group of type A2, which descends to a faithful outer action of a congruence subgroup of SL(2, Z)or PSL(2, Z). This was previously known only in some special cases and, to the best of our knowledge, not even conjectured to hold in full generality. It turns out that the structural intricacies of DAAG/DAHA are captured by the underlying semisimple data and, to a large extent, even by adjoint data; we prove our main result by reduction to the adjoint case. Adjoint DAAG/DAHA correspond in a natural way to affine Lie algebras, or more precisely to their affinized Weyl groups, which are the semi-direct products W Q∨ of the Weyl group W with the coroot lattice Q∨. They were defined topologically by van der Lek, and independently, algebraically, by Cherednik. We now describe our results for the adjoint case in greater detail. We first give a new Coxeter-type presentation for adjoint DAAG as quotients of the Coxeter braid groups associated to certain crystallographic diagrams that we call double affine Coxeter diagrams. As a consequence we show that the rank two Artin groups of type A2,B2,G2 act by automorphisms on the adjoint DAAG/DAHA associated to affine Lie algebras of twist number r =1, 2, 3, respec-tively. This extends a fundamental result of Cherednik for r =1. We show further that the above rank two Artin group action descends to an outer action of the congruence subgroup Γ1(r). In particular, Γ1(r) acts naturally on the set of isomorphism classes of representations of an adjoint DAAG/DAHA of twist number r, giving rise to a projective representation of Γ1(r)on the spaceof aΓ1(r)-stable representation. We also provide a classification of the involutions of Kazhdan-Lusztig type that appear in the context of these actions.
Book Synopsis Filtrations and Buildings by : Christophe Cornut
Download or read book Filtrations and Buildings written by Christophe Cornut and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author constructs and studies a scheme theoretical version of the Tits vectorial building, relates it to filtrations on fiber functors, and uses them to clarify various constructions pertaining to affine Bruhat-Tits buildings, for which he also provides a Tannakian description.
