Results 71 to 80 of about 519,259 (281)

Algebraically constructible functions: real algebra and topology [PDF]

Panoramas & Syntheses 23, Soc. Math. France 2007, 68-85, 2002
Algebraically constructible functions connect real algebra with the topology of algebraic sets. In this survey we present some history, definitions, properties, and algebraic characterizations of algebraically constructible functions, and a description of local obstructions for a topological space to be homeomorphic to a real algebraic set.
arxiv  

Analysis of density matrix embedding theory around the non‐interacting limit

Communications on Pure and Applied Mathematics, EarlyView.
Abstract This article provides the first mathematical analysis of the Density Matrix Embedding Theory (DMET) method. We prove that, under certain assumptions, (i) the exact ground‐state density matrix is a fixed‐point of the DMET map for non‐interacting systems, (ii) there exists a unique physical solution in the weakly‐interacting regime, and (iii ...
Eric Cancès, Fabian M. Faulstich, Alfred Kirsch, Eloïse Letournel, Antoine Levitt   +4 more
wiley   +1 more source

Extensions of Rokhlin congruence for curves on surfaces [PDF]

arXiv, 1992
The subject of this paper is the problem of arrangement of a real nonsingular algebraic curve on a real non-singular algebraic surface. This paper contains new restrictions on this arrangement extending Rokhlin and Kharlamov-Gudkov-Krakhnov congruences for curves on surfaces.
arxiv  

First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet

Communications on Pure and Applied Mathematics, EarlyView.
Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
wiley   +1 more source

Integral Closures In Real Algebraic Geometry [PDF]

arXiv, 2018
We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety : the regular functions and the continuous rational functions.
arxiv  

On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
wiley   +1 more source

ON THE COMPLEXITY OF SEMIDEFINITE PROGRAMS ARISING IN POLYNOMIAL OPTIMIZATION

Croatian Operational Research Review, 2012
In this paper we investigate matrix inequalities which hold irrespective of the size of the matrices involved, and explain how the search for such inequalities can be implemented as a semidefinite program (SDP).
Igor Klep, Janez Povh, Angelika Wiegele
doaj  

An analytical solution of direction evolution of crack growth during progressive failure in brittle rocks

Deep Underground Science and Engineering, EarlyView.
A novel analytical method is proposed to evaluate the shear stress effect on the progressive compressive failure and microcrack growth direction in brittle rocks. The shear stress effect on the wing crack growth direction during the progressive compressive failure is determined. The initial crack angle effect on the y‐direction peak stress and the wing
Xiaozhao Li, Lianjie Li, Fayuan Yan, Chengzhi Qi, Mikhail A. Guzev, Evgenii V. Kozhevnikov, Artem A. Kunitskikh   +6 more
wiley   +1 more source

Varieties of four-dimensional gauge theories

Journal of High Energy Physics
We use algebraic geometry to study the anomaly-free representations of an arbitrary gauge Lie algebra for 4-dimensional spacetime fermions. For irreducible representations, the problem reduces to studying the Lie algebras 𝔰𝔲 n for n ≥ 3.
Ben Gripaios, Khoi Le Nguyen Nguyen
doaj   +1 more source

The Comparison of Diffeomorphic Images Based on the Construction of Persistent Homology

Моделирование и анализ информационных систем, 2019
An object shape analysis is a problem that is related to such areas as geometry, topology, image processing and machine learning. For analyzing the form, the deformation between the source and terminal form of the object is estimated.
Sergey N. Chukanov
doaj   +1 more source