Displaying similar documents to “Digital shapes, digital boundaries and rigid transformations: A topological discussion”

Distributivity of strong implications over conjunctive and disjunctive uninorms

Daniel Ruiz-Aguilera, Joan Torrens (2006)

Kybernetika

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This paper deals with implications defined from disjunctive uninorms U by the expression I ( x , y ) = U ( N ( x ) , y ) where N is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a t -norm or a t -conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works...

Dimers and cluster integrable systems

Alexander B. Goncharov, Richard Kenyon (2013)

Annales scientifiques de l'École Normale Supérieure

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We show that the dimer model on a bipartite graph Γ on a torus gives rise to a quantum integrable system of special type, which we call a. The phase space of the classical system contains, as an open dense subset, the moduli space Ł Γ of line bundles with connections on the graph Γ . The sum of Hamiltonians is essentially the partition function of the dimer model. We say that two such graphs Γ 1 and Γ 2 areif the Newton polygons of the corresponding partition functions coincide up to translation....

Some results on spaces with ℵ 1 -calibre

Wei-Feng Xuan, Wei-Xue Shi (2016)

Commentationes Mathematicae Universitatis Carolinae

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We prove that, assuming , if X is a space with ℵ 1 -calibre and a zeroset diagonal, then X is submetrizable. This gives a consistent positive answer to the question of Buzyakova in Observations on spaces with zeroset or regular G δ -diagonals, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469–473. We also make some observations on spaces with ℵ 1 -calibre.

Piecewise linear approximation of smooth functions of two variables

Joseph H.G. Fu (2013)

Actes des rencontres du CIRM

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The normal cycle of a singular subset X of a smooth manifold is a basic tool for understanding and computing the curvature of X . If X is replaced by a singular function on ℝ n then there is a natural companion notion called the of f , which has been introduced by the author and by R. Jerrard. We discuss a few fundamental facts and open problems about functions f that admit gradient cycles, with particular attention to the first nontrivial dimension n = 2 .

On multiset colorings of generalized corona graphs

Yun Feng, Wensong Lin (2016)

Mathematica Bohemica

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A vertex k -coloring of a graph G is a if M ( u ) ≠ M ( v ) for every edge u v ∈ E ( G ) , where M ( u ) and M ( v ) denote the multisets of colors of the neighbors of u and v , respectively. The minimum k for which G has a multiset k -coloring is the χ m ( G ) of G . For an integer ℓ ≥ 0 , the ℓ - of a graph G , cor ℓ ( G ) , is the graph obtained from G by adding, for each vertex v in G , ℓ new neighbors which are end-vertices. In this paper, the multiset chromatic numbers are determined for ℓ - of all complete graphs, the regular complete...

Optimality conditions for maximizers of the information divergence from an exponential family

František Matúš (2007)

Kybernetika

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The information divergence of a probability measure P from an exponential family ℰ over a finite set is defined as infimum of the divergences of P from Q subject to Q ∈ ℰ . All directional derivatives of the divergence from ℰ are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for P to be a maximizer of the divergence from ℰ are presented, including new ones when P  is not projectable...