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The existence of topological order is frequently associated with strongly coupled quantum matter. Here,we demonstrate the existence of topological phases in classical systems of densely packed, hard, anisotropic polyhedrally shape...
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The existence of topological order is frequently associated with strongly coupled quantum matter. Here,we demonstrate the existence of topological phases in classical systems of densely packed, hard, anisotropic polyhedrally shaped colloidal particles. We show that previously reported transitions in dense packings lead to the existence of topologically ordered thermodynamic phases, which we show are stable away from the dense packing limit. Our work expands the library of known topological phases, whose experimental realization could provide new means for constructing plasmonic materials that are robust in the presence of fluctuations.
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In is considered that asymmetrical material layout design solutions are caused by numerical roundoff and the convexity characteristics of alternative topology design formulations. Emphasis is placed here not on analyzing potential...
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In is considered that asymmetrical material layout design solutions are caused by numerical roundoff and the convexity characteristics of alternative topology design formulations. Emphasis is placed here not on analyzing potential instabilities that lead to asymmetrical designs, but on a method to stabilize topology design formulations. A novel symmetry reduction method is proposed, implemented and studied. While enforcing symmetry and significantly reducing the size of the optimization problem, the symmetry reduction method is shown to have the added benefit of greatly simplified design sensitivity analysis of non-simple repeated vibrational eigenvalues which occur in many symmetrical structures.
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This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, includ...
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This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respective categories of topological structures are topological over their ground categories. The theory also extends the notion of topological system of S.~Vickers (and its numerous many-valued modifications of J.~T.~Denniston, A.~Melton and S.~E.~Rodabaugh), and shows that the categories of catalg topological structures are isomorphic to coreflective subcategories of the categories of catalg topological systems. This extension initiates a new approach to soft topology, induced by the concept of soft set of D.~Molodtsov, and currently pursued by various researchers.
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There exists two different definitions for soft topological groups, the first due to Hida and the other due to Tariq Shah. In this paper, we give a generalization for both of them, and also, we study the topological properties for...
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There exists two different definitions for soft topological groups, the first due to Hida and the other due to Tariq Shah. In this paper, we give a generalization for both of them, and also, we study the topological properties for the construction of finer soft topology made by Nazmul and use the same technique to construct a soft topological group via Hida concept starting from a parametrized family of topological groups. Then, we introduce the concept of soft rough and rough soft topological group to generalize the concept of rough and soft topological group.
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Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all teir self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if ther...
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Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all teir self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major axiom in quantum physics than those formulated for example in Dirac's 'quantum mechanics', then a quantum physicist would not be able to tell a torus from a hole in the ground.
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Left Bol loops with the At-property or gyrogroups are generalization of groups which do not explicitly have associativity. In this work, we define topological gyrogroups and study some properties of them. In spite of having a weak...
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Left Bol loops with the At-property or gyrogroups are generalization of groups which do not explicitly have associativity. In this work, we define topological gyrogroups and study some properties of them. In spite of having a weaker algebraic form, topological gyrogroups carry almost the same basic properties owned by topological groups. In particular, we prove that being T-0 and T-3 are equivalent in topological gyrogroups. Furthermore, a topological gyrogroup is first countable if and only if it is premetrizable. Finally, a direct product of topological gyrogroups is a topological gyrogroup. (C) 2017 Elsevier B.V. All rights reserved.
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With this volume of contributions from colleagues and coauthors, we remember our colleague Hans-Peter Kunzi, who served both UCT (the University of Cape Town, South Africa), for more than a quarter of century, as well as the broad...
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With this volume of contributions from colleagues and coauthors, we remember our colleague Hans-Peter Kunzi, who served both UCT (the University of Cape Town, South Africa), for more than a quarter of century, as well as the broader community of topologists around the world, in the areas of General Topology, Category Theory, Topological Group Theory and Logic. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
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We evaluate the rich-club property of the Internet topology at the autonomous system (AS) level by comparing the Internet AS graphs of traceroute and BGP, and the synthetic graphs of PFP model. The results indicate that, for rich-...
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We evaluate the rich-club property of the Internet topology at the autonomous system (AS) level by comparing the Internet AS graphs of traceroute and BGP, and the synthetic graphs of PFP model. The results indicate that, for rich-club coefficient, PFP model can exactly match traceroute AS graphs in the early years around 2002, but it has significantly deviated from the grown AS graphs since about 2010.
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Let G be a locally compact group, A a subalgebra of the measure algebra M (G), and u a family of Borel subsets of G that is closed under finite unions. In this paper, among other results, we find sufficient conditions on beta u, t...
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Let G be a locally compact group, A a subalgebra of the measure algebra M (G), and u a family of Borel subsets of G that is closed under finite unions. In this paper, among other results, we find sufficient conditions on beta u, that imply A is a semi-topological algebra with respect to the strict topology flat. We also find necessary and sufficient conditions on G, that imply A is a topological algebra with respect to the strict topology beta u, where u is a family of Borel subsets of G with finite Haar measure. (C) 2017 Elsevier B.V. All rights reserved.
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A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, ...
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A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin and Pires, who classified toric origami manifolds by combinatorial origami templates. In this paper, we examine the topology of toric origami manifolds that have acyclic origami template and co?rientable folding hypersurface. We prove that the cohomology is concentrated in even degrees, and that the equivariant cohomology satisfies the Goresky, Kottwitz and MacPherson description. Finally, we show that toric origami manifolds with co?rientable folding hypersurface provide a class of examples of Masuda and Panov's torus manifolds.
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