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This study examines the problem of uniform convergence for the functions from the Nikolskii class. The uniform convergences for the Riesz means of the Fourier-Laplace series in the Nikolskii class Hpa(SN) proved under certain conditions. [ABSTRACT FROM AUTHOR]

Series defined by means of the Mittag-Leffer functions are considered in this paper and the behaviour of these series on the boundaries of their convergence domains is investigated. Necessary and sufficient conditions for their overconvergence are proposed. [ABSTRACT FROM AUTHOR]

In this paper, new subclasses of analytic functions in the open unit disk which are defined using generalized integral operator are introduced. Several interesting properties of these classes are obtained, such as inclusion relationships and integral preserving properties are derived. [ABSTRACT FROM AUTHOR]

Let G = (V,E) be a simple, connected, and finite graph. A function c from E to {1, 2, ..., k} is said rainbow kcoloring of G, if for any pair of vertices u and v in V, there exists au - vpath whose edges have different colors. The rainbow connection number of G, denoted by rc(G), is the smallest positive integer k such that Ghas a rainbow kcoloring. Furthermore, such the function c is said strong rainbow k-coloring, if for any pair of vertices u and v in V, there exists a rainbow u-v path with its length is equal to distance betweenu and v. The smallest positive integer k such that G has a strong rainbow k-coloring is defined as the strong rainbow connection number, denoted by src(G).In this paper, we introduce a new class of graphs, namely stellar graphs. A stellar graph on 2mn+1 vertices, denoted by Stm,n, is the corona product of a trivial graph and mcopies ladder graph on 2n vertices (K1⊙m.Ln). We determine the (strong) rainbow connection number of stellar graphs. [ABSTRACT FROM AUTHOR]

In this paper we review the properties of the difference-sign randomness test. First we analyse the exact and asymptotic distribution of the test statistic and provide a table with values for the exact distribution function, for samples of size n ≤ 32. Then, we also present several moments of the statistic test, under the null hypothesis of randomness and under the hypothesis of the existence of a linear trend. Finally, we present an illustration of the test difference-sign to a real data set. [ABSTRACT FROM AUTHOR]

The present paper, introduces a complex vague relation (CVR) as a generalization of avague relation by extending the range of truth-membership and false-membership functions from the closed unit interval [0, 1] to the unit circle in the complex plane. Then we introduce the basic operations on CVRs, namely complement, union and intersection. Some examples are given. [ABSTRACT FROM AUTHOR]

Let us recall that the bicomplex plane is a complex ring of complex dimension 2. It consists of couples of the kind (z, w) = z + jw, where z and w are complex numbers and j is a symbol with the property j² = -1. We note that the bicomplex plane admits singular points. The set of these singular points coincides with the cross-choped set of complex bisectrices (z, ±z), z is a complex. The main problem in the function theory on the bicomplex plane is to describe the interconnection between the same theory of the cross-choped subset and whole bicomplex plane. The first theory is of one complex variable and the second one is of two complex variables. Another problems are related with the comformal mappings and the movement of a partíais of this subset on the whole one. Presented paper is a start studies in this direction. [ABSTRACT FROM AUTHOR]

In this article, Dziok-Srivastava operator is used to define new subclasses of p-valent analytic functions. Some inclusion relationships are given and convolution results of Hadamard product involving the functions are introduced. Further, some applications of differential subordinations are also studied. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate some properties of functions of new class, radii of closeto-convexity, starlikeness, and convexity. [ABSTRACT FROM AUTHOR]

Exact order estimates are obtained for the best orthogonal trigonometric approximations of the Nikol'skii-Besov classes of periodic functions of many variables in the Lorentz space with the mixed norm. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate the concept of Abel ward continuity. A real function ƒ is Abel ward continuous if it preserves Abel quasi Cauchy sequences, where a sequence (pk) of point in R is called Abel quasi-Cauchy if the series Σk=0∞△pk·xk is convergent for 0 ≤ x < 1 and limx→1-(1-x)Σk=0∞△pk·xk=0, where → pk = pk+1 - pk for every non negative integer k. Some other types of continuities are also studied and interesting results are obtained. It turns out that uniform limit of a sequence of Abel ward continuous functions is Abel ward continuous and the set of Abel ward continuous functions is a closed subset of the set of continuous functions. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the inverse problem for diffusion operators on the finite interval [0,π] For a fixed n(n=0,1,2,...), we show that the potential function q(x) can be uniquely determined by the setsP{λn(q,Hk)}k=1. [ABSTRACT FROM AUTHOR]

This paper examines the problem of assigning a prior pdf for N positive parameters Z = {Z1, Z2,..., ZN} that are dependent in such a way that their sum is bounded by a known constant. It also derives a set of functions that map N independent and uniformly distributed parameters to the parameters z with the known dependance. [ABSTRACT FROM AUTHOR]

The aim of this paper is to use the notion of Ψ-operations in double fuzzy topological spaces to study the concept of (r,s)-fuzzy generalized ΨΡ-closed sets and (r,s)-fuzzy generalized ΨΡ-open sets, some characterizations and properties of these concepts are given. Moreover, we discussed the relationship between these sets in double fuzzy topological spaces. [ABSTRACT FROM AUTHOR]

Let f = h(z) + g(z) be a univalent sense-preserving harmonic mapping of the open unit disc D = {z||zs|<1}. If f satisfies the condition ... then f is called k-quasiconformal harmonic mapping in D. In the present paper we will give some properties of the class of k-quasiconformal mappings related to Janowski alpha-spirallike functions. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new class of generalizations of continuous functions via ωβ-open sets called weakly ωβ-continuous functions. Moreover, we study some of its fundamental properties and characterizations. The concept of weak ωβ-continuous is weaker than ωβ-continuous, weakly ω-continuous and weakly β-continuous functions, are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the classes Tnp(λ,A,B) and Knp(λ,μ,m,A,B) and we apply to the (n,δ)-neighborhoods of functions in the class Knp(λ,μ,m,A,B). [ABSTRACT FROM AUTHOR]

We study the class of pulsating strings in AdS5×Yp,q and AdS5×Lp,q,r. Using a generalized ansatz for pulsating string configurations, we find new solutions for this class in terms of Heun functions, and derive the particular case of AdS5×T1,1, which was analyzed in arXiv:1006.1539 [hep-th]. Unfortunately, Heun functions are still little studied, and we are not able to quantize the theory quasi-classically and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual N = 1 superconformal field theory. [ABSTRACT FROM AUTHOR]

The recursive relations for the 4-point superconformal blocks in N = 1 SCFT are discussed. The case of the blocks corresponding to correlation functions of four Ramond fields factorized on NS states is presented in detail. [ABSTRACT FROM AUTHOR]

We show that if one can find a coordinate system in which a moving wave front shape can be described via a linear combination of known geometrical functions, then it is possible to calculate a priori the optimal positions of time markers that measure the wave front speed. [ABSTRACT FROM AUTHOR]

For a function f, meromorphic in the unit disc D, and parameter values 0 < p < ∞, ... let New characterizations for the classes U B C and M1# in terms of fMp# are obtained. [ABSTRACT FROM AUTHOR]