We introduce a notion of ternary distributive algebraic structure, give examples, and relate it to the notion of a quandle. Classification is given for low order structures of this type. Constructions of such structures from 3-Lie algebras are provided. We also describe ternary distributive algebraic structures coming from groups and give examples from vector spaces whose bases are elements of a finite ternary distributive set. We introduce a cohomology theory that is analogous to Hochschild cohomology and relate it to a formal deformation theory of these structures.

In this paper, we consider the nonlinear hyperbolic equations with forcing term. Some suffcient conditions for the oscillation are derived by using integral averaging method and a generalized Riccati technique.

A graph G of order n has prime cordial labeling if its vertices can be assigned the distinct labels 1, , n such that if each edge xy in G is assigned the label 1 in case the labels of x and y are relatively prime and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper, we give a complete characterization of complete graphs which are prime cordial and we give a prime cordial labeling of the closed helm , and present a new way of prime cordial labeling of . Finally we make a correction of the proof of Theorem 2.5 in [12].

In this paper, we consider a discrete predator-prey system obtained from a continuous Beddington-DeAngelis type predator-prey system by using the method in [9]. In order to investigate dynamical behaviors of this discrete system, we find out all equilibrium points of the system and study their stability by using eigenvalues of a Jacobian matrix for each equilibrium points. In addition, we illustrate some numerical examples in order to substantiate theoretical results.

In this work, we shall give the degree of approximation for functions belonging to class by matrix summability method of multiple Fourier series in the metric.

For a positive integer k, a k-rainbow dominating function of a digraph D is a function f from the vertex set V (D) to the set of all subsets of the set such that for any vertex with $f(v)

Let M and N be modules over a ring R. The purpose of this paper is to study modules M, N for which the bi-module [M, N] is regular or pi. It is proved that the bi-module [M, N] is regular if and only if a module N is semi M-projective and for all , if and only if a module M is semi N-injective and for all . Also, it is proved that the bi-module [M, N] is pi if and only if a module N is direct M-projective and for any there exists such that , if and only if a module M is direct N-injective and for any there exists such that . The relationship between the Jacobson radical and the (co)singular ideal of [M, N] is described.

As a generalization of Q-algebra, the notion of pseudo Q-algebra is introduced, and some of their properties are investigated. The notions of pseudo subalgebra, pseudo ideal, and pseudo atom in a pseudo Q-algebra are introduced. Characterizations of their properties are provided.

Let R be a commutative semiring. The purpose of this note is to investigate the concept of 2-absorbing (resp., weakly 2-absorbing) primary ideals generalizing of 2-absorbing (resp., weakly 2-absorbing) ideals of semirings. A proper ideal I of R said to be a 2-absorbing (resp., weakly 2-absorbing) primary ideal if whenever such that (resp., ), then either or or . Moreover, when I is a Q-ideal and P is a k-ideal of R/I with , it is shown that if P is a 2-absorbing (resp., weakly 2-absorbing) primary ideal of R, then P/I is a 2-absorbing (resp., weakly 2-absorbing) primary ideal of R/I and it is also proved that if I and P/I are weakly 2-absorbing primary ideals, then P is a weakly 2-absorbing primary ideal of R.

In this paper, we compute the number of distinct centralizers and commutativity degree of a class of finite groups. These computations produce a further class of examples of groups answering one question raised by Belcastro and Sherman and another one raised by Lescot.

A finite rank difference of two composition operators is studied on a Hilbert Lebesgue space or a Hilbert Hardy space.

The main object of this paper is to present two general integral formulas whose integrands are the integrand given in the integral formula (3) and a finite product of the generalized Bessel function of the first kind.

In this paper we study the oscillation criteria for the second order nonlinear differential equation with delay and advanced arguments of the form ^{\alpha})^{{\prime}{\prime}}+q(t)x^{\beta}(t-{\tau}_1)+q(t)x^{\gamma}(t+{\tau}_2)

In this paper, we obtained some properties for subclasses of starlike functions defined by convolution such as partial sums, integral means, square root and integral transform for these classes.

In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some differantiable mappings that are connected with the celebrated Ostrowski type integral inequality.

Mock theta functions are the most interesting topic mentioned in Ramanujan`s Lost Notebook, due to its emerging application in the field of Number theory, Quantum invariants theory and etc. In the present research articles we have made an attempt to develop continued fractions representation of all the existing Mock theta functions.

We study the Gauss and Poisson semigroups connected with the Riemann-Liouville operator defined on the half plane. Next, we establish a principle of maximum for the singular partial differential operator $${\Delta}_{\alpha}

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

The purpose of this paper is to introduce sufficient conditions for (Gaussian) hypergeometric functions to be in various subclasses of analytic functions. Also, we investigate several mapping properties involving these subclasses.

There are many concepts around classical theta functions, theta vectors and quantum theta functions. Manin clarified the relation among these concepts with the symmetry of functional equations. We extend his results to the super torus.

In this paper, we compute the trace field of C(2, s), the complement of two component chain link with s left half twists in , for every s. As a result, for every , we can find such that the degree of the trace field of C(2, s) is n. We also prove that if for fixed p, the degree of the trace field of C(p, s) runs over , then p is contained in {1, 2, 4, 8}.

In this paper, we obtain that every biharmonic non-degenerate hypersurfaces in semi-Euclidean space with constant scalar curvature of diagonal shape operator has zero mean curvature.

For the complex torus, there is the Riemann condition on the polarization for it to be an abelian variety. We extend this condition on the super torus for super abelian variety.

In this paper, we introduce and study the concept of a new class of sets called paraopen sets and paraclosed sets in topological spaces. During this process some of their properties are obtained. Also we introduce and investigate a new class of maps called paracontinuous, *-paracontinuous, parairresolute, minimal paracontinuous and maximal paracontinuous maps and study their basic properties in topological spaces.