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Quadratic Vector Equations on Complex Upper Half-plane

2019 Electronic books
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Release : 2019
Genre : Electronic books
Kind : eBook
Book Rating : 142/5 ( reviews)

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Book Synopsis Quadratic Vector Equations on Complex Upper Half-plane by : Oskari Heikki Ajanki

Download or read book Quadratic Vector Equations on Complex Upper Half-plane written by Oskari Heikki Ajanki. This book was released on 2019. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the nonlinear equation -\frac 1m=z+Sm with a parameter z in the complex upper half plane \mathbb H , where S is a positivity preserving symmetric linear operator acting on bounded functions. The solution with values in \mathbb H is unique and its z-dependence is conveniently described as the Stieltjes transforms of a family of measures v on \mathbb 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.

Quadratic Vector Equations on Complex Upper Half-Plane

2019-12-02 Education
Download Quadratic Vector Equations on Complex Upper Half-Plane PDF Online Free

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Release : 2019-12-02
Genre : Education
Kind : eBook
Book Rating : 833/5 ( reviews)

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Book Synopsis Quadratic Vector Equations on Complex Upper Half-Plane by : Oskari Ajanki

Download or read book Quadratic Vector Equations on Complex Upper Half-Plane written by Oskari Ajanki. This book was released on 2019-12-02. 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.

Random Matrices

2019-10-30 Education
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Release : 2019-10-30
Genre : Education
Kind : eBook
Book Rating : 804/5 ( reviews)

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Book Synopsis Random Matrices by : Alexei Borodin

Download or read book Random Matrices written by Alexei Borodin. This book was released on 2019-10-30. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory has many roots and many branches in mathematics, statistics, physics, computer science, data science, numerical analysis, biology, ecology, engineering, and operations research. This book provides a snippet of this vast domain of study, with a particular focus on the notations of universality and integrability. Universality shows that many systems behave the same way in their large scale limit, while integrability provides a route to describe the nature of those universal limits. Many of the ten contributed chapters address these themes, while others touch on applications of tools and results from random matrix theory. This book is appropriate for graduate students and researchers interested in learning techniques and results in random matrix theory from different perspectives and viewpoints. It also captures a moment in the evolution of the theory, when the previous decade brought major break-throughs, prompting exciting new directions of research.

New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Rn

2020-05-13 Education
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Release : 2020-05-13
Genre : Education
Kind : eBook
Book Rating : 616/5 ( reviews)

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Book Synopsis New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Rn by : Antonio Alarcón

Download or read book New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Rn written by Antonio Alarcón. This book was released on 2020-05-13. 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.

Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity-Topoi

2020 Education
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Release : 2020
Genre : Education
Kind : eBook
Book Rating : 446/5 ( reviews)

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Book Synopsis Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity-Topoi by : David Carchedi

Download or read book Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity-Topoi written by David Carchedi. This book was released on 2020. 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.

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