Global Robust Exponential Stability Analysis for Interval Neural Networks with Mixed Delays by Yanke Du, Rui Xu

“…By employing H-matrix and M-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point to the neural networks are established and some previously published results are improved and generalized. …”
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The Embedding Theorem of an L0-Prebarreled Module into Its Random Biconjugate Space by Xia Zhang, Ming Liu

“…Then, we establish the embedding theorem of an L0-prebarreled random locally convex module, which says that if (S,P) is an L0-prebarreled random locally convex module such that S has the countable concatenation property, then the canonical embedding mapping J of S onto J(S)⊂(Ss⁎)s⁎ is an L0-linear homeomorphism, where (Ss⁎)s⁎ is the strong random biconjugate space of S under the locally L0-convex topology.…”
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Subobjects and Compactness in Point-Free Convergence by Emilio Angulo, Frédéric Mynard

“…We also give a point-free analog of the classical fact that a continuous bijection from a compact pseudotopology to a Hausdorff pseudotopology is a homeomorphism.…”
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Finite-part singular integral approximations in Hilbert spaces by E. G. Ladopoulos, G. Tsamasphyros, V. A. Zisis

“…Some new approximation methods are proposed for the numerical evaluation of the finite-part singular integral equations defined on Hilbert spaces when their singularity consists of a homeomorphism of the integration interval, which is a unit circle, on itself. …”
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Robust Asymptotical Stability and Stabilization of Fractional-Order Complex-Valued Neural Networks with Delay by Jingjing Zeng, Xujun Yang, Lu Wang, Xiaofeng Chen

“…Using the theorem of homeomorphism, the sufficient condition of the existence and uniqueness of the equilibrium point for the system is obtained. …”
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Noncommutative tensor triangulated categories and coherent frames by Mallick, Vivek Mohan, Ray, Samarpita

“…We further show that there is a homeomorphism between the spectral space of radical thick tensor ideals of a noncommutative tensor triangulated category and the collection of open subsets of its spectrum in the Hochster dual topology.…”
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Global Robust Exponential Stability and Periodic Solutions for Interval Cohen-Grossberg Neural Networks with Mixed Delays by Yanke Du, Rui Xu

“…By employing H-matrix and M-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions are established for the existence, uniqueness, and global robust exponential stability of the equilibrium point and the periodic solution to the neural networks. …”
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Mappings and Connectedness on Hesitant Fuzzy Soft Multispaces by A. Kandil, S. A. El-Sheikh, M. Hosny, M. Raafat

“…The concept of hesitant fuzzy soft multitopology is defined, and certain types of hesitant fuzzy soft multimapping such as continuity, open, closed, and homeomorphism are presented in detail. Also, their properties and results are studied. …”
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The Structure of Disjoint Groups of Continuous Functions by Hojjat Farzadfard, B. Khani Robati

“…We will show that (1) each group of the second type is conjugate, via a specific homeomorphism, to a piecewise linear group of the same type; (2) each group of the third type is a subgroup of a continuous disjoint iteration group. …”
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Global μ-Stability of Impulsive Complex-Valued Neural Networks with Leakage Delay and Mixed Delays by Xiaofeng Chen, Qiankun Song, Yurong Liu, Zhenjiang Zhao

“…The impulsive complex-valued neural networks with three kinds of time delays including leakage delay, discrete delay, and distributed delay are considered. Based on the homeomorphism mapping principle of complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural networks is proposed in terms of linear matrix inequality (LMI). …”
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Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales by Jian Liu, Fuyi Xu

“…We study the following third-order m-point boundary value problems on time scales (φ(uΔ∇))∇+a(t)f(u(t))=0, t∈[0,T]T, u(0)=∑i=1m−2biu(ξi), uΔ(T)=0, φ(uΔ∇(0))=∑i=1m−2ciφ(uΔ∇(ξi)), where φ:R→R is an increasing homeomorphism and homomorphism and φ(0)=0, 0<ξ1<⋯<ξm−2<ρ(T). …”
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Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems by Yusen Wu, Cui Zhang, Luju Liu

“…Firstly, we transform degenerate singular point into the origin via a homeomorphism. Moreover, we establish a new recursive algorithm to compute the so-called generalized period constants for the origin of the transformed system. …”
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Polynomials in Control Theory Parametrized by Their Roots by Baltazar Aguirre-Hernández, José Luis Cisneros-Molina, Martín-Eduardo Frías-Armenta

“…Viète's map gives a homeomorphism between the space of roots and the space of coefficients and it gives an explicit formula to relate both spaces. …”
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Decomposition of a Pythagorean fuzzy topological space and its application in determining topological relations between indeterminate spatial objects by Subhankar Jana, Anjali Patel, Juthika Mahanta

“…This paper contributes to the expanding study of Pythagorean fuzzy topological spaces by introducing core, fringe, outer, regular open set, regular closed set, double connectedness and homeomorphism in Pythagorean fuzzy environment. Using these definitions, the paper proposes an algebraic model, namely the pythagorean fuzzy 9-intersection matrix, to find topological relations between any two Pythagorean fuzzy sets in a Pythagorean topological space. …”
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A topological property of β(N) by Anastase Nakassis

“…In this paper we prove that the Stone-Cech-compactification of the natural numbers does not admit a countable infinite decomposition into subsets homeomorphic to each other and to the said compactification.…”
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On Absolute Continuity of Conjugations between Circle Maps with Break Points by Habibulla Akhadkulov, Mohd Salmi Md Noorani

“…Let T1 and T2 be piecewise smooth circle homeomorphisms with break points and identical irrational rotation numbers. …”
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The regular open-open topology for function spaces by Kathryn F. Porter

“…It is then shown that Troo on H(X), the collection of all self-homeomorphisms on a topological space, (X,T), is equivalent to the topology induced on H(X) by a specific quasi-uniformity on X, when X is a semi-regular space.…”
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Differentiable semigroups are Lie groups by John P. Holmes, Mitch Anderson

“…If S is a local semigroup with neighborhood of 1 homeomorphic to a Banach space and with multiplication strongly differentiable at 1, then S is a local Lie Group. …”
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Semi separation axioms and hyperspaces by Charles Dorsett

“…Also, it is shown that for each space (X,T), (S(X),E(X)), (S(X0),E(X0)), and (S(XS0),E(XS0)) are homeomorphic, where (X0,Q(X0)) is the T0-identification space of (X,T) and (XS0,Q(XS0)) is the semi-T0-identification space of (X,T), and that if (X,T) is s-regular and R0, then (S(X),E(X)) is semi-T2.…”
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A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems by Anna Pascoletti, Fabio Zanolin

“…., 2008, and Pascoletti and Zanolin, 2010, we have widely exposed the crossing lemma for planar regions homeomorphic to a square, and we have also presented some possible applications to the theory of topological horseshoes and to the study of chaotic-like dynamics for planar maps. …”
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