n this paper, we consider continuity properties(especially, regularity, also viewed as an approximation property) for $%mathcal{p}_{0}(x)$-valued set multifunctions ($x$ being a linear,topological space), in order to obtain egoroff and lusin type theorems forset multifunctions in the vietoris hypertopology. some mathematicalapplications are established and several physical implications of thema...

We study the asymptotic behavior of stochastic hyperbolic–parabolic equations with slow–fast time scales. Both strong and weak convergence in averaging principle are established. Then we fluctuations original system around its averaged equation. show that normalized difference converges weakly to solution a linear wave An extra diffusion term appears limit which is given explicitly terms Poisso...

In this paper we study multipartite Ramsey numbers for odd cycles. Our main result is the proof of a conjecture of Gyárfás, Sárközy and Schelp [12]. Precisely, let n ≥ 5 be an arbitrary positive odd integer; then in any two-coloring of the edges of the complete 5-partite graph K(n−1)/2,(n−1)/2,(n−1)/2,(n−1)/2,1 there is a monochromatic cycle of length n. keywords: cycles, Ramsey number, Regular...

Let nand m be integers with n = m 2 + m + 1. Then the projective plane of order m has n points and" lines with each line containing m + 1 ""n 1/2 points. In this paper, we consider the analogous problem for the Euclidean plane and show that there cannot be a comparably large collection of lines each of which contains approximately n 1/ 2 points from a given set of n points. More precisely, we s...

A triple system is cancellative if no three of its distinct edges satisfy A ∪ B = A ∪ C. It is tripartite if it has a vertex partition into three parts such that every edge has exactly one point in each part. It is easy to see that every tripartite triple system is cancellative. We prove that almost all cancellative triple systems with vertex set [n] are tripartite. This sharpens a theorem of N...

familiarity with the normal and abnormal anatomy of the root canal system is essential for successful root canal treatment. the possibility of concomitant three-rooted and three- canalled maxillary and mandibular premolars are extremely rare. the purpose of this paper was to report a case with a three-rooted maxillary first premolar and two three-rooted mandibular premolars.

In this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. This leads to the characterization of a matrix for which the regularity index and the index are identical. Further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.

We give a simple and natural construction of hypergraph regularization. It yields a short proof of a hypergraph regularity lemma. Consequently, as an example of its applications, we have a short self-contained proof of Szemerédi’s classic theorem on arithmetic progressions (1975) as well as its multidimensional extension by Furstenberg-Katznelson (1978).

The main results of this paper are regularity and counting lemmas for 3uniform hypergraphs. A combination of these two results gives a new proof of a theorem of Frankl and Rödl, of which Szemerédi’s theorem for arithmetic progressions of length 4 is a notable consequence. Frankl and Rödl also prove regularity and counting lemmas, but the proofs here, and even the statements, are significantly d...

The central concept in Szemerédi’s powerful regularity lemma is the so-called ε-regular pair. A useful statement of Alon et al. essentially equates the notion of an ε-regular pair with degree uniformity of vertices and pairs of vertices. The known proof of this characterization uses a clever matrix argument. This paper gives a simple proof of the characterization without appealing to the matrix...