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Regularity and Planarity of Token Graphs

100%
Carballosa W., Fabila-Monroy R., Leaños J., Rivera L. M.
Discussiones Mathematicae Graph Theory
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2017
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tom 37
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nr 3
573-586
EN
Let G = (V, E) be a graph of order n and let 1 ≤ k < n be an integer. The k-token graph of G is the graph whose vertices are all the k-subsets of V, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this paper we characterize precisely, for each value of k, which graphs have a regular k-token graph and which connected graphs have a planar k-token graph.
2
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On functional differential inclusions in Hilbert spaces

100%
Aitalioubrahim M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2012
|
tom 32
|
nr 1
63-85
EN
We prove the existence of monotone solutions, of the functional differential inclusion ẋ(t) ∈ f(t,T(t)x) +F(T(t)x) in a Hilbert space, where f is a Carathéodory single-valued mapping and F is an upper semicontinuous set-valued mapping with compact values contained in the Clarke subdifferential $∂_{c} V(x)$ of a uniformly regular function V.
3
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On the stochastic regularity of sequence transformations operating in a Banach space

100%
Lavastre H.
Applicationes Mathematicae
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1993-1995
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tom 22
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nr 4
477-484
4
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A family of regular vertex operator algebras with two generators

88%
Adamović D.
Open Mathematics
|
2007
|
tom 5
|
nr 1
1-18
EN
For every m ∈ ℂ ∖ {0, −2} and every nonnegative integer k we define the vertex operator (super)algebra D m,k having two generators and rank $$\frac{{3m}}{{m + 2}}$$ . If m is a positive integer then D m,k can be realized as a subalgebra of a lattice vertex algebra. In this case, we prove that D m,k is a regular vertex operator (super) algebra and find the number of inequivalent irreducible modules.
5
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Generalized Newton and NCP-methods: convergence, regularity, actions

75%
Kummer B.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2000
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tom 20
|
nr 2
209-244
EN
Solutions of several problems can be modelled as solutions of nonsmooth equations. Then, Newton-type methods for solving such equations induce particular iteration steps (actions) and regularity requirements in the original problems. We study these actions and requirements for nonlinear complementarity problems (NCP's) and Karush-Kuhn-Tucker systems (KKT) of optimization models. We demonstrate their dependence on the applied Newton techniques and the corresponding reformulations. In this way, connections to SQP-methods, to penalty-barrier methods and to general properties of so-called NCP-functions are shown. Moreover, direct comparisons of the hypotheses and actions in terms of the original problems become possible. Besides, we point out the possibilities and bounds of such methods in dependence of smoothness.
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