Volume 47, Issue 1

In this article, we study the center of a generalized effect algebra (GEA), relate it to the exocenter, and in case the GEA is centrally orthocomplete (a COGEA), relate it to the exocentral cover system. Our main results are that the center of a COGEA is a complete boolean algebra and that a COGEA decomposes uniquely as the direct sum of an effect algebra (EA) that contains the center of the COGEA and a complementary direct summand in which no nonzero direct summand is an EA.

Let R be a prime ring with Utumi quotient ring U and with extended centroid C, I a non-zero right ideal of R ƒ (x1… xn) a multilinear polynomial over C which is not central valued on R and G, H two generalized derivations of R. Suppose that G(ƒ (r)) ƒ (r)- ƒ (r)H(ƒ (r)) ∈ C, for all r =(r 1 ,….,r n ) ∈ I n . Then one of the following holds: 1. there exist a; b; p ∈ U and α C such that G(x)= ax + [p, x] and H(x) = bx, for all x ∈ R, and (a-b)I=(0)=(a + p- α)I; 2. R satisfies s 4 , the standard identity of degree 4, and there exist a; a' ∈ U, α,β ∈ C such that G(x) =ax + xa' + αx and H(x) = a'x - xa +βx, for all x ∈ R; 3. R satisfies s 4 and there exist a; a' ∈ U, and d : R → R, a derivation of R, such that G(x) = ax + d(x) and H(x)= xa'- d(x), for all x ∈ R, with a + a' ∈ C; 4. R satisfies s 4 and there exist a; a' ∈ U, and d : R → R, a derivation of R, such that G(x) = xa + d(x) and H(x) = ax' - d(x), for all x ∈ R, with a - a' ∈ C; 5. there exists e 2 = e ∈ Soc(RC) such that I = eR and one of the following holds: (a) [ƒ (x 1 ,…., x n ); x n + 1 ] x n+2 is an identity for I; (b) char (R) = 2 and s 4 (x 1 ; x 2 ; x 3 ; x 4 )x 5 is an identity for I; (c) [ƒ (x 1 , …, x n ) 2 ; x n+1 ]x n+2 is an identity for I and there exist a, a', b, b' ∈ U,α ∈ C and d : R → R, a derivation of R, such that G(x) = ax + xa' + d(x), H(x)=bx + xb' - d(x), for all x ∈ R, with (a - b' - α) I=(0)=( b-a'-α )I

Some new inequalities of the Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are given

In this paper, we characterize the maximal additive and multiplicative classes for lower and upper semicontinuous strong Świątkowsk functions and lower and upper semicontinuous extra strong Świątkowski functions. Moreover, we characterize the maximal class with respect to maximums for lower semicontinuous strong Świątkowski functions and lower and upper semicontinuous extra strong Świątkowski functions.

We prove that if a superposition operator maps a subset of the space of all metric-vector-space-valued-functions of bounded n-dimensional Φ-variation into another such space, and is uniformly continuous, then the generating function of the operator is an affine function in the functional variable

In this short note, we construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some well chosen function spirals around the origin. The inversion mapping carries this example into an example of a gradient spiraling dynamics at infinity

In this paper, we obtain some sufficient criteria for the oscillation of the solutions of linear impulsive partial difference equations with continuous variables

This paper is devoted to the study of the following perturbed system of nonlinear functional equations x ∊Ω=[-b,b], i = 1,…., n; where ε is a small parameter, a ijk ; b ijk are the given real constants, R ijk , S ijk , X ijk : Ω → Ω ,g i → Ω →ℝ , Ψ: Ω x ℝ 2 → ℝ are the given continuous functions and ƒ i :Ω →ℝ are unknown functions. First, by using the Banach fixed point theorem, we find sufficient conditions for the unique existence and stability of a solution of (E). Next, in the case of Ψ ∊ C 2 (Ω x ℝ 2 ; ℝ); we investigate the quadratic convergence of (E). Finally, in the case of Ψ ∊ C N (Ω x ℝ 2 ; ℝ) and ε sufficiently small, we establish an asymptotic expansion of the solution of (E) up to order N + 1 in ε. In order to illustrate the results obtained, some examples are also given

Aim of this paper is to consider a problem formulated in [6]. Namely, it has been proven that for any sequences , , for every interval [a, b] ⊂ [-∞,∞], there exist a nondecreasing sequence {kn} ∞ n=1 of positive integers and a sequence {ε n } ∞ n=1 of ±1 signs such that the set of limit points of the series ∑ε n x kn a n is equal to [a, b]

Let R be a 2-torsion free semiprime ring equipped with an involution *. An additive mapping T : R→R is called a left (resp. right) Jordan α-*centralizer associated with a function α: R→R if T(x2)=T(x)α(x*) (resp. T(x2)=α(x*)T(x)) holds for all x ∊ R. If T is both left and right Jordan α-* centralizer of R, then it is called Jordan α-* centralizer of R. In the present paper it is shown that if α is an automorphism of R, and T : R→ R is an additive mapping such that 2T(xyx)=T(x) α(y*x*) +α(x*y*)T(x) holds for all x, y ∊ R, then T is a Jordan α-*centralizer of R

In this note we study the connection between orthogonal polynomials on an ellipse and orthogonal Laurent polynomials on the unit circle relative to some multiplicative measures and then establish the recurrence relations for orthogonal polynomials on an ellipse. The matrix representation of the operator of multiplication by coordinate function is obtained

In this paper, we introduce the notion of an F-weak contraction and prove a fixed point theorem for F-weak contractions. Examples are given to show that our result is a proper extension of some results known in the literature

In this paper, we give the explicit determinations of dual plane curves, general dual helices and dual slant helices in terms of its dual curvature and dual torsion as a fundamental theory of dual curves in a dual 3-space

After brief introduction, we prove that a totally contact umbilical CR- lightlike submanifold is totally contact geodesic. We obtain a necessary and sufficient condition for a CR-lightlike submanifold to be an anti-invariant submanifold. Finally, we characterize a contact CR-lightlike submanifold of indefinite Sasakian manifold to be a contact CR-lightlike product

We prove a common fixed point theorem for a pair of self mappings satisfying a generalized contractive type condition in a complete G-metric space. We also deal with other fixed point results for a self mapping in the setting of generalized metric space. Our results generalize some recent results in the literature

We show that the space P/G of orbits of a proper action of a Lie group G on a locally compact differential space P is a locally compact differential space with quotient topology. Applying this result to reduction of symmetries of Hamiltonian systems, we prove the reduction by stages theorem

Positive definite norm dependent matrices are of interest in stochastic modeling of distance/norm dependent phenomena in nature. An example is the application of geostatistics in geographic information systems or mathematical analysis of varied spatial data. Because the positive definiteness is a necessary condition for a matrix to be a valid correlation matrix, it is desirable to give a characterization of the family of the distance/norm dependent functions that form a valid (positive definite) correlation matrix. Thus, the main reason for writing this paper is to give an overview of characterizations of norm dependent real functions and consequently norm dependent matrices, since this information is somehow hidden in the theory of geometry of Banach spaces

Let {X n̲ , n̲ ∊ V ⊆ℕ d } be a d-dimensional random field indexed by some subset V of lattice ℕ d , which are stochastically dominated by a random variable X. Let {a n̲, i̲ ; n̲, i̲ ∊ V } be a 2d-dimensional random field independent of {X n̲, n̲ ∊ V} and such that |a n̲, i̲ | M, n̲, i̲ ∊ V for some constant M. In this paper, we give conditions under which the following series is convergent for some real t, some fixed p > 0 and all ε > 0. Here |n̲| is used for Π d i=1 n i . The randomly indexed sums of field {X n̲ ;n̲ ∊ V } are considered too

The volume of a tetrahedron is represented in terms of the twelve face angles, inradii of the faces of tetrahedron, circumradii of the faces and the radius of the sphere circumscribing the tetrahedron

A problem of optimal dividend policy for a firm with a bank loan is considered. A regularity of a value function is established. A numerical example of calculating value function is given