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On Degree Spectra of Topological Spaces

Lobachevskii Journal of Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Selivanov V.L.
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Nanomechanical topological insulators with an auxiliary orbital degree of freedom

Nature Nanotechnology, 2021
Discrete degrees of freedom, such as spin and orbital, provide a tool to manipulate electrons, photons and phonons. Topological insulators have stimulated intense interests in condensed-matter physics, optics, acoustics and mechanics, usually with a ...
Xiang Xi, Xiankai Sun, Ma Jingwen
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The Calculation of the Topological Degree by Quadrature

SIAM Journal on Numerical Analysis, 1975
The topological degree of a function on $R^n $, a useful tool in applied mathematics, is computed by applying Gauss–Legendre quadrature to Kronecker’s integral definition. An error analysis is developed from the Sarma–Eberlein measure of goodness.
O'Neil, T., Thomas, J. W.
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The Topological Degree of A-Proper Maps

Canadian Journal of Mathematics, 1971
Recently several fixed-point theorems have been proved for new classes of non-compact maps between Banach spaces. First, Petryshyn [15] generalized the concept of compact and quasi-compact maps when he introduced the P-compact maps and proved a fixed-point theorem for this class of maps.
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Degrees of recursively enumerable topological spaces

Journal of Symbolic Logic, 1983
In [5], Metakides and Nerode introduced the study of recursively enumerable (r.e.) substructures of a recursively presented structure. The main line of study presented in [5] is to examine the effective content of certain algebraic structures. In [6], Metakides and Nerode studied the lattice of r.e.
Iraj Kalantari, Jeffrey B. Remmel
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The Topological Degree

2016
In this chapter we develop the theory of topological degree. We first deal with the case of a finite dimensional space, by constructing the Brouwer degree. We then extend such a construction to the infinite dimensional setting, introducing the Leray–Schauder degree.
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Topological Degree in Infinite Dimensions

1985
In this basic chapter we shall study some basic problems concerning equations of the form f (x) = y, where f is a continuous map from a subset Ω ⊂ ℝ n into ℝ n and y is a given point in ℝ n . First of all we want to know whether such an equation has at least one solution x ∈Ω.
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On Turing degrees of points in computable topology

Mathematical Logic Quarterly, 2008
AbstractThis paper continues our study of computable point‐free topological spaces and the metamathematical points in them. For us, a point is the intersection of a sequence of basic open sets with compact and nested closures. We call such a sequence a sharp filter.
Iraj Kalantari, Larry Welch
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A New Topology with Odd Degree for Multiprocessor Systems

Journal of Parallel and Distributed Computing, 1996
A new topology for interconnection networks has been proposed. The underlying network graph hasN= 4nnodes (n? 2) and isalmostregular with maximum degree 5 and diameter ? ?3/4 log2N? + 1. Algorithms for point-to-point routing and single node broadcast have also been developed.
Rajib K. Das, Bhabani P. Sinha
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Topological degree and periodic solutions of differential inclusions

Nonlinear Analysis: Theory, Methods & Applications, 1999
In this interesting paper, the authors study the existence of periodic solutions to differential inclusions of the form \[ x'(t)\in F(t,x(t)),\quad x(a)= x(0),\tag{Q\(_F\)} \] where \(F\) is a multivalued map. Under an assumption on the existence of some guiding potentials for \(F\) and other reasonable conditions, they prove that the problem \((Q_F)\)
DE BLASI, FRANCESCO SAVERIO, Gorniewicz, L, Pianigiani, G.   +2 more
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