For a closed subset K of a compact metric space A possessing an α-regular measure μ with μ(K) > 0, we prove that whenever s > α, any sequence of weighted minimal Riesz s-energy configurations ωN = {x i,N} N i=1 on K (for ‘nice’ weights) is quasi-uniform in the sense that the ratios of its mesh norm to separation distance remain bounded as N grows large. Furthermore, if K is an α-rectifiable com...

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

Evolutionary algorithms (EAs) excel in optimizing systems with a large number of variables. Previous mathematical and empirical studies have shown that opposition-based algorithms can improve EA performance. We review existing opposition-based algorithms and introduce a new one. The proposed algorithm is named fitness-based quasi-reflection and employs the relative fitness of solution candidate...

We study in the setting of probabilistic default reasoning under coherence the quasi conjunction, which is a basic notion for defining consistency of conditional knowledge bases, and the Goodman & Nguyen inclusion relation for conditional events. We deepen two results given in a previous paper: the first result concerns p-entailment from a finite family F of conditional events to the quasi conj...

Let α1, . . . , αk satisfy ∑ i αi = 1 and suppose a k-uniform hypergraph on n vertices satisfies the following property; in any partition of its vertices into k sets A1, . . . , Ak of sizes α1n, . . . , αkn, the number of edges intersecting A1, . . . , Ak is (asymptotically) the number one would expect to find in a random k-uniform hypergraph. Can we then infer that H is quasi-random? We show t...

Császár’s condition is a well-known property introduced about 50 years ago in the axiomatic theory of conditional probability. In recent years such condition has been reconsidered by some authors, who have studied its role in the coherence-based approach to conditional probability. In this paper we consider the probabilistic entailment of a conditional knowledge base by another one. We represen...

A probabilistic constrained stochastic programming problem is considered, where the underlying problem has linear constraints with random technology matrix. The rows of the matrix are assumed to be stochastically independent and normally distributed. For the convexity of the problem the quasi-concavity of the constraining function is needed that is ensured if the factors are uniformly quasiconc...

Probabilistic automata are a computational model introduced by Michael Rabin, extending nondeterministic finite automata with probabilistic transitions. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are undecidable. In this work we focus on the emptiness problem, which asks whether a given probabilistic automaton accepts some word with pr...

Quasi three-dimensional (3D) plasmonic nanostructures consisting of Au nanosquares on top of SU-8 nanopillars and Au nanoholes on the bottom were developed and fabricated using nanoimprint lithography with simultaneous thermal and UV exposure. These 3D plasmonic nanostructures were used to detect cell concentration of lung cancer A549 cells, retinal pigment epithelial (RPE) cells, and breast ca...