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Author : Jeffrey Galkowski
Publisher :
ISBN 13 : 9781470452513
Total Pages : pages
Book Rating : 4.4/5 (525 download)
Download or read book Distribution of Resonances in Scattering by Thin Barriers written by Jeffrey Galkowski and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jeffrey Galkowski
Publisher : American Mathematical Soc.
ISBN 13 : 1470435721
Total Pages : 152 pages
Book Rating : 4.4/5 (74 download)
Download or read book Distribution of Resonances in Scattering by Thin Barriers written by Jeffrey Galkowski and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies high energy resonances for the operators where is strictly convex with smooth boundary, may depend on frequency, and is the surface measure on .
Author : Jeffrey Eric Galkowski
Publisher :
ISBN 13 :
Total Pages : 290 pages
Book Rating : 4.:/5 (919 download)
Download or read book Distribution of Resonances in Scattering by Thin Barriers written by Jeffrey Eric Galkowski and published by . This book was released on 2015 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis contains a detailed study of the rates of wave decay for scattering by thin barriers. Thin barriers are systems in which, except for a narrow region, waves do not interact. This type of behavior is observed in physical systems including concert halls and quantum corrals. A quantum corral is constructed by configuring individual atoms or molecules to form a barrier which partially confines electrons to its interior. Here, the atoms produce a potential which plays the role of the thin barrier. In the setting of concert halls, the walls play the role of the barrier and produce partial confinement of sound waves. Rather than studying systems with a finite width interaction region, we imagine that the interaction region is reduced to a single hypersurface in R^d by taking a limit of barriers whose width is decreasing and intensity is increasing. Specifically, we are interested in wave equations with delta and delta' potentials on a hypersurface. These operators are used as models for leaky quantum graphs and quantum corrals.
Author : Semyon Dyatlov
Publisher : American Mathematical Soc.
ISBN 13 : 147044366X
Total Pages : 634 pages
Book Rating : 4.4/5 (74 download)
Download or read book Mathematical Theory of Scattering Resonances written by Semyon Dyatlov and published by American Mathematical Soc.. This book was released on 2019-09-10 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
Author : Chen Wan
Publisher : American Mathematical Soc.
ISBN 13 : 1470436868
Total Pages : 90 pages
Book Rating : 4.4/5 (74 download)
Download or read book A Local Relative Trace Formula for the Ginzburg-Rallis Model: The Geometric Side written by Chen Wan and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, the author is able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, the author proves a multiplicity formula of the Ginzburg-Rallis model for the supercuspidal representations. Using that multiplicity formula, the author proves the multiplicity one theorem for the Ginzburg-Rallis model over Vogan packets in the supercuspidal case.
Author : Antonio Alarcón
Publisher : American Mathematical Soc.
ISBN 13 : 1470441616
Total Pages : 77 pages
Book Rating : 4.4/5 (74 download)
Download or read book New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Rn written by Antonio Alarcón and published by American Mathematical Soc.. This book was released on 2020-05-13 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: All the new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables the authors to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, they construct proper non-orientable conformal minimal surfaces in Rn with any given conformal structure, complete non-orientable minimal surfaces in Rn with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits n hyperplanes of CPn−1 in general position, complete non-orientable minimal surfaces bounded by Jordan curves, and complete proper non-orientable minimal surfaces normalized by bordered surfaces in p-convex domains of Rn.
Author : David Carchedi
Publisher : American Mathematical Soc.
ISBN 13 : 1470441446
Total Pages : 120 pages
Book Rating : 4.4/5 (74 download)
Download or read book Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity-Topoi written by David Carchedi and published by American Mathematical Soc.. This book was released on 2020 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of points of such objects. He chooses to model higher orbifolds and Deligne-Mumford stacks as infinity-topoi equipped with a structure sheaf, thus naturally generalizing the work of Lurie, but his approach applies not only to different settings of algebraic geometry such as classical algebraic geometry, derived algebraic geometry, and the algebraic geometry of commutative ring spectra but also to differential topology, complex geometry, the theory of supermanifolds, derived manifolds etc., where it produces a theory of higher generalized orbifolds appropriate for these settings. This universal framework yields new insights into the general theory of Deligne-Mumford stacks and orbifolds, including a representability criterion which gives a categorical characterization of such generalized Deligne-Mumford stacks. This specializes to a new categorical description of classical Deligne-Mumford stacks, which extends to derived and spectral Deligne-Mumford stacks as well.
Author : Luigi Ambrosio
Publisher : American Mathematical Soc.
ISBN 13 : 1470439131
Total Pages : 121 pages
Book Rating : 4.4/5 (74 download)
Download or read book Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces written by Luigi Ambrosio and published by American Mathematical Soc.. This book was released on 2020-02-13 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD∗(K,N) condition of Bacher-Sturm.
Author : Jaroslav Nešetřil
Publisher : American Mathematical Soc.
ISBN 13 : 1470440652
Total Pages : 108 pages
Book Rating : 4.4/5 (74 download)
Download or read book A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth written by Jaroslav Nešetřil and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors introduce a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as “tractable cases” of a general theory. As an outcome of this, the authors provide extensions of known results. The authors believe that this puts these into a broader context. The second part of the paper is devoted to the study of sparse structures. First, the authors consider limits of structures with bounded diameter connected components and prove that in this case the convergence can be “almost” studied component-wise. They also propose the structure of limit objects for convergent sequences of sparse structures. Eventually, they consider the specific case of limits of colored rooted trees with bounded height and of graphs with bounded tree-depth, motivated by their role as “elementary bricks” these graphs play in decompositions of sparse graphs, and give an explicit construction of a limit object in this case. This limit object is a graph built on a standard probability space with the property that every first-order definable set of tuples is measurable. This is an example of the general concept of modeling the authors introduce here. Their example is also the first “intermediate class” with explicitly defined limit structures where the inverse problem has been solved.
Author : Ines Kath
Publisher : American Mathematical Soc.
ISBN 13 : 1470441039
Total Pages : 84 pages
Book Rating : 4.4/5 (74 download)
Download or read book Compact Quotients of Cahen-Wallach Spaces written by Ines Kath and published by American Mathematical Soc.. This book was released on 2020-02-13 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. The authors derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these parameters.
Author : Christopher L Douglas
Publisher : American Mathematical Soc.
ISBN 13 : 1470437716
Total Pages : 111 pages
Book Rating : 4.4/5 (74 download)
Download or read book Cornered Heegaard Floer Homology written by Christopher L Douglas and published by American Mathematical Soc.. This book was released on 2020-02-13 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. The authors construct cornered Floer homology invariants of 3-manifolds with codimension-2 corners and prove that the bordered Floer homology of a 3-manifold with boundary, split into two pieces with corners, can be recovered as a tensor product of the cornered invariants of the pieces.
Author : J. I. Hall
Publisher : American Mathematical Soc.
ISBN 13 : 1470436221
Total Pages : 186 pages
Book Rating : 4.4/5 (74 download)
Download or read book Moufang Loops and Groups with Triality are Essentially the Same Thing written by J. I. Hall and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1925 Élie Cartan introduced the principal of triality specifically for the Lie groups of type D4, and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title in 1978 was made by Stephen Doro, who was in turn motivated by the work of George Glauberman from 1968. Here the author makes the statement precise in a categorical context. In fact the most obvious categories of Moufang loops and groups with triality are not equivalent, hence the need for the word “essentially.”
Author : Victor Beresnevich
Publisher : American Mathematical Soc.
ISBN 13 : 1470440954
Total Pages : 77 pages
Book Rating : 4.4/5 (74 download)
Download or read book Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation written by Victor Beresnevich and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Oskari Ajanki
Publisher : American Mathematical Soc.
ISBN 13 : 1470436833
Total Pages : 133 pages
Book Rating : 4.4/5 (74 download)
Download or read book Quadratic Vector Equations on Complex Upper Half-Plane written by Oskari Ajanki and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the nonlinear equation −1m=z+Sm with a parameter z in the complex upper half plane H, where S is a positivity preserving symmetric linear operator acting on bounded functions. The solution with values in H is unique and its z-dependence is conveniently described as the Stieltjes transforms of a family of measures v on R. In a previous paper the authors qualitatively identified the possible singular behaviors of v: under suitable conditions on S we showed that in the density of v only algebraic singularities of degree two or three may occur. In this paper the authors give a comprehensive analysis of these singularities with uniform quantitative controls. They also find a universal shape describing the transition regime between the square root and cubic root singularities. Finally, motivated by random matrix applications in the authors' companion paper they present a complete stability analysis of the equation for any z∈H, including the vicinity of the singularities.
Author : Massimiliano Berti
Publisher : American Mathematical Soc.
ISBN 13 : 1470440695
Total Pages : 171 pages
Book Rating : 4.4/5 (74 download)
Download or read book Quasi-periodic Standing Wave Solutions of Gravity-Capillary Water Waves written by Massimiliano Berti and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
Author : Mircea Mustaţă
Publisher : American Mathematical Soc.
ISBN 13 : 1470437813
Total Pages : 78 pages
Book Rating : 4.4/5 (74 download)
Download or read book Hodge Ideals written by Mircea Mustaţă and published by American Mathematical Soc.. This book was released on 2020-02-13 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors use methods from birational geometry to study the Hodge filtration on the localization along a hypersurface. This filtration leads to a sequence of ideal sheaves, called Hodge ideals, the first of which is a multiplier ideal. They analyze their local and global properties, and use them for applications related to the singularities and Hodge theory of hypersurfaces and their complements.
Author : S. V. Ivanov
Publisher : American Mathematical Soc.
ISBN 13 : 1470441438
Total Pages : 106 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Bounded and Precise Word Problems for Presentations of Groups written by S. V. Ivanov and published by American Mathematical Soc.. This book was released on 2020-05-13 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, the author obtains polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. The author also obtains polynomial time bounds for these problems.
