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In the paper, we study eight properties of partial algebras most of which are related to diagonality. For each of the properties, we give sufficient conditions under which this property is preserved by powers of partial algebras.

In this paper, we provide some properties of homomorphism of BF-algebras. We also prove the Second and Third Isomorphism Theorems for BF2-algebras.

We explain how one can use the explicit formulas for the mean square values of L-functions which we established elsewhere to obtain explcit upper bounds on relative class numbers of cyclotomic number fields. As an example, we show that the relative class numbers of the cyclotomic fields of conductor 4p, p ≥ 3 a prime, are less than or equal to 8√p(p/16)(p−1)/2.

For 0 ≤ α < 1, the sharp radii of starlikeness and convexity of order α for functions of the form f(z) = z + a 2 z 2 + a 3 z 3 + ... whose Taylor coefficients a n satisfy the conditions |a 2| = 2b, 0 ≤ b ≤ 1, and |a n| ≤ n, M or M/n (M > 0) for n ≥ 3 are obtained. Also a class of functions related to Carathéodory functions is considered.

In the present paper, we introduce a new subclass S p,q,s,λm,l(γ, θ) of θ-spiral functions of order γ defined by a class of generalized multiplier transformations. Majorization properties for functions belonging to the class S p,q,s,λm,l(γ, θ) are considered. Moreover, we point out some new or known consequences of our main result.

This paper is devoted to proving some uniqueness results for meromorphic functions f(z) share sets with f(qz). We give a partial answer to a question of Gross concerning a zero-order meromorphic function f(z) and its q-difference f(qz).

Using some potential theory tools and the Schauder fixed point theorem, we prove the existence of positive bounded continuous solutions with a precise global behavior for the semilinear elliptic system Δu = p(x)u α ν r in domains D of ℝn, n ≥ 3, with compact boundary (bounded or unbounded) subject to some Dirichlet conditions, where α ≥ 1, β ≥ 1, r ≥ 0, s ≥ 0 and the potentials p, q are nonnegative and belong to the Kato class K(D).

In this paper we consider a family of 3-index generalizations of the classical Mittag-Leffler functions. We study the convergence of series in such functions in the complex plane. First we find the domains of convergence of such series and then study their behaviour on the boundaries of these domains. More precisely, Cauchy-Hadamard, Abel, Tauber and Littlewood type theorems are proved as analogues of the classical theorems for the power series.

In this paper, new oscillation criteria for the third-order quasilinear neutral differential equation $$\left( {a\left( t \right)\left( {z''\left( t \right)} \right)^\gamma } \right)^\prime + q\left( t \right)x^\gamma \left( {\tau \left( t \right)} \right) = 0, t \geqslant t_0 ,$$ are established, where z(t) = x(t) + p(t)x(δ(t)), and γ is a ratio of odd positive integers. Those results extend the oscillation criteria due to Sun [SUN, Y. G.: New Kamenev-type oscillation criteria for second-order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 (2004) 341–351] to the equation, and complement the existing results in literature. Two examples are provided to illustrate the relevance of our main theorems.

This paper is devoted to the study of persistence of forced periodic solutions for impact systems from single periodic solutions of unperturbed impact equations. An example of planar discontinuous ordinary differential equations is given to illustrate the theory.

By applying the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg neural networks on time scales. Moreover an example is given to illustrate our results.

In this paper we consider the equation ∇2 φ + A(r 2)X · ∇φ + C(r 2)φ = 0 for X ∈ ℝN whose coefficients are entire functions of the variable r = |X|. Corresponding to a specified axially symmetric solution φ and set C n of (n + 1) circles, an axially symmetric solution Λn*(x, η;C n) and Λn(x, η;C n) are found that interpolates to φ(x, η) on the C n and converges uniformly to φ(x, η) on certain axially symmetric domains. The main results are the characterization of growth parameters order and type in terms of axially symmetric harmonic polynomial approximation errors and Lagrange polynomial interpolation errors using the method developed in [MARDEN, M.: Axisymmetric harmonic interpolation polynomials in ℝN, Trans. Amer. Math. Soc. 196 (1974), 385–402] and [MARDEN, M.: Value distribution of harmonic polynomials in several real variables, Trans. Amer. math. Soc. 159 (1971), 137–154].

In this manuscript, we introduce and study the existence of solutions for a coupled system of differential equations under abstract boundary conditions of Rotenberg’s model type, this last arises in growing cell populations. The entries of block operator matrix associated to this system are nonlinear and act on the Banach space X p:= L p([0, 1] × [a, b]; dµ dv), where 0 ≤ a < b < ∞; 1 < p < ∞.

The purpose of this article is to modify the Halpern-type iteration algorithm for quasi-ϕ-asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results of Qin et al. [Convergence of a modified Halpern-type iterative algorithm for quasi-ϕ-nonexpansive mappings, Appl. Math. Lett. 22 (2009), 1051–1055], Wang et al. [A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011), 2364–2371], Su et al. [Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010), 3890–3906], Nartinez-Yanes et al}. [Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006), 2400–2411], and others.

Let ℝ+ = [0,∞) and let A ⊆ ℝ+n. We have found the necessary and sufficient conditions under which a function Φ: A → ℝ+ has an isotone subadditive continuation on ℝ+n. It allows us to describe the metrics, defined on the Cartesian product X 1×...×X n of given metric spaces $$\left( {X_1 ,d_{X_1 } } \right), \ldots ,\left( {X_n ,d_{X_n } } \right)$$, generated by the isotone metric preserving functions on ℝ+n. It is also shown that the isotone metric preserving functions Φ: ℝ+n → ℝ+ coincide with the first moduli of continuity of the nonconstant bornologous functions g: ℝ+n → ℝ+.

Recently, the authors [MIHEŢ, D.—SAADATI, R.—VAEZPOUR, S. M.: The stability of an additive functional equation in Menger probabilistic φ-normed spaces, Math. Slovaca 61 (2011), 817–826] considered the stability of an additive functional in Menger φ-normed spaces. In this paper, we establish some stability results concerning the cubic, quadratic and quartic functional equations in complete Menger φ-normed spaces via fixed point theory.

After a survey on some recent results of Riley and others on Ackermann functions and Hydra groups, we make an analogy between DNA sequences, whose growth is the same of that of Hydra groups, and a musical piece, written with the same algorithmic criterion. This is mainly an aesthetic observation, which emphasizes the importance of the combinatorics of words in two different contexts. A result of specific mathematical interest is placed at the end, where we sharpen some previous bounds on deterministic finite automata in which there are languages with hairpins.

Let P 0 and P 1 be projections in a Hilbert space H. We shall construct a class of optimal measurements for the problem of discrimination between quantum states $$\rho _i = \tfrac{1} {{\dim P_i }}P_i$$, with prior probabilities π 0 and π 1. The probabilities of failure for such measurements will also be derived.

For a ring A, an extension ring B, and a fixed right A-module M, we prove that M is costar module, r-costar module if and only if the induced module Hom A(B,M) is costar module, r-costar module respectively.