Volume 57, Issue 3

The notion of internal subdirect decomposition can be defined in each variety of algebras. In the present note we prove the validity of a cancellation rule concerning such decompositions for lattice ordered groups and for GMV-algebras. For the case of groups, this cancellation rule fails to be valid.

We investigate classes of algebras which can be obtained by a direct limit construction from an algebra. We generalize some results from monounary algebras.

A finite group G whose irreducible characters are rational valued is called a ℚ-group. In this paper we will be concerned with the structure of a finite ℚ-group that contains a strongly embedded subgroup and the structure of a finite ℚ-group satisfying the property that none of its sections is isomorphic to $$\mathbb{S}_4 $$ .

In this paper, we establish sufficient conditions to guarantee the existence of at least three or 2n − 1 positive solutions of nonlocal boundary value problems consisting of the second-order differential equation with p-Laplacian (1) $$[\phi _p (x'(t))]' + f(t,x(t)) = 0, t \in (0,1),$$ and one of following boundary conditions (2) $$x(0) = \int\limits_0^1 {x(s) dh(s),} \phi _p (x'(1)) = \int\limits_0^1 {\phi _p (x'(s)) dg(s)} ,$$ and (3) $$\phi _p (x'(0)) = \int\limits_0^1 {\phi _p (x'(s)) dh(s),} x(1) = \int\limits_0^1 {x(s) dg(s)} .$$ Examples are presented to illustrate the main results.

In this paper, we consider the discrete nonlinear delay population model exhibiting the Allee effect (*) $$x_{n + 1} = x_n \exp \left( {a + bx_{n - \tau }^p - cx_{n - \tau }^q } \right),$$ where a, b and c are constants and p, q and τ are positive integers. First, we study the local stability of the equilibrium points. Next, we establish some oscillation results of nonlinear delay difference equations with positive and negative coefficients and apply them to investigate the oscillatory character of all positive solutions of equation (*) about the positive steady state x * and prove that every nonoscillatory solution tends to x *.

In this paper we consider an enlargement of the notion of the probabilistic normed space. For this new class of probabilistic normed spaces we give some topological properties. By using properties of the probabilistic norm we prove some differential and integral properties of functions with values into probabilistic normed spaces. As special cases, results for deterministic and random functions can be obtained.

The aim of the paper is to present explicit formulae for parameter estimators and confidence regions in multivariate regression model with different kind of constraints and to give some comments to it. The covariance matrix of observation is either totally known, or some unknown parameters of it must be estimated, or the covariance matrix is totally unknown.

If f(z) is an entire function with ρ 1 > 0 as its exponent of convergence of zeros and if 0 ≤ α < ρ 1, then we prove the existence of entire functions each having α as its exponent of convergence of zeros.