Band 65, Heft 3

The fuzzification of pseudo subalgebras/ideals in d-algebras and pseudo BCK-ideals is discussed. Several properties are investigated. Relations between fuzzy pseudo BCK-ideals and fuzzy pseudo d-ideals are established. Conditions for a fuzzy set to be a fuzzy pseudo BCK-ideal are considered. Using the notion of fuzzy points, a general form of fuzzy pseudo d-subalgebras is introduced, and several properties including their characterizations are investigated.

Let p ≥ 3 be a prime, and let q p (2) := (2 P 1 - 1)/p be the Fermat quotient of p to base 2. In this note, we prove that . As an application, using two combinatorial identities due to T. B. Staver in 1947 and G. Galperin and H. Gauchman in 2004, we obtain four curious combinatorial congruences modulo p 2 . As an auxiliary result, here we present an elementary proof of a congruence established by E. Lehmer in 1938. Notice that this con­gruence together with some other congruences given in our lemmas leads to the elementary proof of a beautiful Morley’s congruence due to F. Morley in 1895.

The main purpose of this paper is using the analytic methods and the estimation of Dirichlet character of polynomials to study the asymptotic properties of one kind hybrid mean value involving the Dedekind sums and Kloosterman sums, and give two interesting asymptotic formulae.

Let π be a group. The main purpose of this paper is to provide further examples of crossed π-categories in the sense of Turaev. For this, we first introduce the notion of weak Hopf π-algebra as the dual notion of weak Hopf π-coalgebra and investigate the properties of weak Hopf π-algebra keeping close to weak Hopf algebra in sense of Böhm et al. It is shown that the category of the copresentations of weak Hopf π-algebra is braided crossed π-category. Finally, we shall consider the notion of weak Doi-Hopf group module in the weak Hopf π-algebra setting, and discuss the separability of a class of functors for the category of weak Doi-Hopf π-modules to the category of comodule over a suitable coalgebras. Also, the applications of our theories are presented.

In this paper, by introducing some parameters and estimating the weight coefficients, some new inequalities are established. All results of Hilbert, Hardy and Yang are considered as special cases of the new given inequalities.

The object of the present paper is to investigate some inclusion relationships and a number of other properties of several subclasses of multivalent analytic functions, which are defined here by using the hypergeometric function. Relevant connections of the results presented here with those obtained in earlier works are pointed out.

In the present paper, we obtain the estimates on initial coefficients of normalized analytic function f in the open unit disk with f and its inverse g = f −1 satisfying the conditions that zf′(z)/f(z) and zg′(z)/g(z) are both quasi-subordinate to a univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are established.

In this paper, we consider the existence of entire solutions of certain type of non-linear difference equation of the form: f(z) n + p(z)f(z + c) m = q(z). We also consider value distribution problems of difference polynomials of entire functions such as f(z) n (f(z)−1)f(z +c) for n = 1, which is a supplement of previous results.

The paper provides (necessary and) sufficient conditions for Ψ-strong stability of the trivial solution of a linear Lyapunov matrix differential equations. Further, sufficient condition are obtained for Ψ-strong stability of the trivial solution of a nonlinear Lyapunov matrix differential equation.

In this paper we prove an existence theorem for ordinary differential equations in Banach spaces. The main assumptions in our results, formulated in terms of the Kuratowski measure of noncompactness, are motivated by the paper [CONSTANTIN, A.: On Nagumo’s theorem, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), 41-44].

In this paper, we consider a delayed n + m-species competition predator-prey system on time scales with Holling III functional response and multiple exploited (or harvesting) terms. By using the continuation theorem based on Gaines and Mawhin’s coincidence degree theory, easily verifiable criteria are established for global existence of multiple positive periodic solutions for the above system.

Nonlinear Drinfeld-Sokolov system is studied analytically by using four different methods ((G′/G)-expansion, direct algebraic, different form of the (G′/G)-expansion methods, and direct integration) and the results are found numerically. New exact and numeric solutions are given and the comparison of the results obtained from these different methods, methods themselves and numerical results are discussed in detail. It is found that the (G′/G)-expansion and different form of the (G′/G)-expansion methods are really coincide and effective methods in the view of finding different solutions that cannot be obtained by using the direct integration for Drinfel-Sokolov system.

This paper continues the investigation of Esslamzadeh and the first author which was begun in [ESSLAMZADEH, G. H.-SHOJAEE, B.: Approximate weak amenability of Banach algebras, Bull. Belg. Math. Soc. Simon Stevin 18 (2011), 415-429]. It is shown that homomorphic image of an approximately cyclic amenable Banach algebra is again approximately cyclic amenable. Equivalence of approximate cyclic amenability of a Banach algebra A and approximate cyclic amenability of M n (A) is proved. It is shown that under certain conditions the approximate cyclic amenability of second dual A∗∗ implies the approximate cyclic amenability of A.

Let A, B be Banach A-modules with compatible actions and M be a left Banach A- A-module and a right Banach B- A-module. In the current paper, we study module amenability, n-weak module amenability and module Arens regularity of the triangular Banach algebra -. We employ these results to prove that for an inverse semigroup S with subsemigroup E of idempotents, the triangular Banach algebra is permanently weakly module amenable (as an . As an example, we show that T0 is T0-module Arens regular if and only if the maximal group homomorphic image GS of S is finite.

In this paper, the conditions of correct solvability are found for a class of the third order operator-differential equations whose principal part has multiple characteristics in the Sobolev type space with exponential weight. The estimations of the norms of intermediate derivative operators closely connected with the solvability conditions are carried out. Moreover, the connection between the weight exponent and the lower bound of the spectrum of the main operator involved in the principal part of the equation is determined in the results of the paper.

The purpose of this paper is to establish necessary and sufficient conditions for a point to be solution of a vector equilibrium problem with setvalued mappings and cone constraints. Using a separation theorem which involves the quasi-relative interior of a convex set, we obtain optimality conditions for solutions of the considered vector equilibrium problem. The main theorem recovers an earlier established result. Then, the results are applied to vector optimization problems and to Stampacchia vector variational inequalities with cone constraints.

In this paper, we study regular immersed hypersurfaces in Lorentzian space forms with a conformal metric, a conformal second fundamental form, the conformal Blaschke tensor and a conformal form, which are invariants under the conformal transformation group. We classify all the immersed hypersurfaces in Lorentzian space forms with two distinct constant Blaschke eigenvalues and vanishing conformal form.

A new proof of the following well-known theorem due to Fan is given: Let G be a 2-connected graph of order n, and 3 ≤ c ≤ n. Ifmax{d(u), d(v)} ≥ c/2 for any two vertices u, v at distance 2, then G contains a cycle of length at least c.