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Morse theory for C*-algebras: a geometric interpretation of some noncommutative manifolds
Applied General Topology, 2011 The approach we present is a modification of the Morse theory for unital C*-algebras. We provide tools for the geometric interpretation of noncommutative CW complexes. Some examples are given to illustrate these geometric information.
Vida Milani +2 more
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Research on P System with Chain Structure and Application and Simulation in Arithmetic Operation
Discrete Dynamics in Nature and Society, 2015 Considering the advantages of distribution and maximum parallelism of membrane computing and availability of discrete Morse theory to deal with discrete structure, in this paper, combining discrete Morse theory and membrane computing, a novel membrane ...
Jing Luan, Zhong Yao
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Multiple Solutions for Biharmonic Equations with Asymptotically Linear Nonlinearities
Boundary Value Problems, 2010 The existence of multiple solutions for a class of fourth elliptic equation with respect to the resonance and nonresonance conditions is established by using the minimax method and Morse theory.
Ruichang Pei
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Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems
Discrete Dynamics in Nature and Society, 2011 By using Morse theory, the critical point theory, and the character of 𝐾1/2, we consider the existence and multiplicity results of solutions to the following discrete nonlinear two-point boundary value problem −Δ2𝑥(𝑘−1)=𝑓(𝑘,𝑥(𝑘)),𝑘∈ℤ(1,𝑇) subject to 𝑥(0)=
Jianmin Guo, Caixia Guo
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International Journal of Mathematics and Mathematical Sciences, 1990 A simple proof of a theorem of H. Hopf [1], via Morse theory, is given.
Takis Sakkalis
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Periodic solutions of second order Hamiltonian systems with nonlinearity of general linear growth
Electronic Journal of Qualitative Theory of Differential Equations, 2021 In this paper we consider a class of second order Hamiltonian system with the nonlinearity of linear growth. Compared with the existing results, we do not assume an asymptotic of the nonlinearity at infinity to exist. Moreover, we allow the system to be
Guanggang Liu
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Existence of nontrivial solutions for semilinear problems with strictly differentiable nonlinearity
Abstract and Applied Analysis, 2006 The existence of a nontrivial solution for semilinear elliptic problems with strictly differentiable nonlinearity is proved. A result of homological linking under nonstandard geometrical assumption is also shown. Techniques of Morse theory are employed.
Sergio Lancelotti
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Higgs bundles for M-theory on G 2-manifolds
Journal of High Energy Physics, 2019 M-theory compactified on G 2-holonomy manifolds results in 4d N $$ \mathcal{N} $$ = 1 supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained from a ...
Andreas P. Braun +3 more
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Smoothing, scattering and a conjecture of Fukaya
Forum of Mathematics, PiIn 2002, Fukaya [19] proposed a remarkable explanation of mirror symmetry detailing the Strominger–Yau–Zaslow (SYZ) conjecture [47] by introducing two correspondences: one between the theory of pseudo-holomorphic curves on a Calabi–Yau manifold ...
Kwokwai Chan +2 more
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Axiomatic S1 Morse–Bott theory [PDF]
Algebraic & Geometric Topology, 2020 In various situations in Floer theory, one extracts homological invariants from "Morse-Bott" data in which the "critical set" is a union of manifolds, and the moduli spaces of "flow lines" have evaluation maps taking values in the critical set. This requires a mix of analytic arguments (establishing properties of the moduli spaces and evaluation maps ...
Hutchings, Michael, Nelson, Jo
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