Band 67, Heft 1

In this paper, we define the notions of a state ⊔-hoop and a state-morphism ⊔-hoop extending the language of hoop by adding a unary operator and investigate some properties of them. Also, we extend state ⊔-hoop to state hoop and study the relation between state hoops and state BL-algebras, MV-algebras and BCK-algebras.

In this paper, the notion of derivation on partially ordered sets is introduced and studied. Several characterization theorems on derivations are presented. The properties of the fixed points based on the derivations are investigated. Finally, the properties of ideals and operations related with derivations are studied.

Commutative basic algebras are non-associative generalizations of MV-algebras and form an algebraic semantics of a non-associative generalization of the propositional infinite-valued Łukasiewicz logic. In the paper we investigate additive closure and multiplicative interior operators on commutative basic algebras as a generalization of topological operators.

It is well known that Cayley graphs of groups are automatically vertex-transitive. A pioneer result of Kelarev and Praeger implies that Cayley graphs of semigroups can be regarded as a source of possibly new vertex-transitive graphs. In this note, we consider the following problem: Is every vertex-transitive Cayley graph of a semigroup isomorphic to a Cayley graph of a group? With the help of the results of Kelarev and Praeger, we show that the vertex-transitive, connected and undirected finite Cayley graphs of semigroups are isomorphic to Cayley graphs of groups, and all finite vertex-transitive Cayley graphs of inverse semigroups are isomorphic to Cayley graphs of groups. Furthermore, some related problems are proposed.

This paper deals with a criterion for sequences of Cantor type to have an expressible set with zero Lebesgue measure.

In this paper, with reference to the previous work [WITUŁA, R.—SŁOTA, D.: δ - Fibonacci numbers , Appl. Anal. Discrete Math. 3 (2009), 310–329] concerning the, so called, δ -Fibonacci numbers, the concepts of δ -Lucas numbers, δ -Fibonacci and δ -Lucas polynomials are introduced. There are discussed the basic properties of such objects, as well as their applications, especially for description of certain polynomials and identities of algebraic and trigonometric type. Many from among these identities describe the binomial transformations of the respective integer sequences and polynomials. Similarly as for δ -Fibonacci numbers, also for δ -Lucas numbers some attractive identities–bridges are obtained, connecting these numbers in practice with every sequence of integer numbers.

Let D ∈ ℤ and let C D be the set of all monic cubic polynomials x 3 + ax 2 + bx + c ∈ ℤ[ x ] with the discriminant equal to D . Along the line of our preceding papers, the following Theorem has been proved: If D is square-free and 3 ∤ h (−3 D ) where h (−3 D ) is the class number of Q(− 3D), $\mathbb Q(\sqrt {-3D}),$ then all polynomials in C D have the same type of factorization over the Galois field 𝔽 p where p is a prime, p > 3. In this paper, we prove the validity of the above implication also for primes 2 and 3.

The aim of this paper is to investigate closed hereditary coreflective subcategories in epireflective subcategories A of Top , mainly in the case that ZD ⊆ A ⊆ Tych . Particularly the closed hereditary coreflective hull of the one-point compactification of the discrete space on the set of all non-negative integers in such epireflective subcategories is studied. It is proved that under some set-theoretic assumptions it is the whole category A .

In this paper, by means of upper and lower solutions, we develop monotone iterative method for the existence of extremal solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments. We illustrate this technique with the help of an example.

The problem of a family functions representable as the difference of two lower semicontinuous strong Światkowski functions is discussed. Particularly, we suggest how to characterize such systems.

In this paper, we establish some Fejér-type inequalities for convex functions. They complement the results from the previous recent paper [Dragomir, S. S.—Milošević, D. S.——Sándor, J.: On some refinements of Hadamard’s inequalities and applications , Univ. Belgrad. Publ. Elek. Fak. Sci. Math. 4 (1993), 3–10].

Idempotent integration is an analogue of Lebesgue integration where σ -maxitive measures replace σ -additive measures. In addition to reviewing and unifying several Radon–Nikodym like theorems proven in the literature for the idempotent integral, we also prove new results of the same kind.

In this paper we investigate the possible relation between two meromorphic functions f n f ( k ) and g n g ( k ) that share a nonzero polynomial and obtain two results which are related to a conjecture of X. Y. Cao and B. X. Zhang [ Uniqueness of meromorphic functions sharing two values , J. Ineq. Appl., 1(100) (2012)]

In this paper, we establish the Hyers-Ulam-Rassias stability of the quadratic functional equation of Pexiderized type f ( x + y )+ f ( x - y ) = 2 g ( x )+ 2 h ( y ) , x ⊥ y in which ⊥ is the orthogonality in the sense of Rätz in modular spaces.

Following the methods of G. Gát, in this work we prove the a.e convergence of the subsequence (σ mn2Mnf)n $\begin{array}{} (\sigma_{\frac{m_{n}}{2}M_{n}}f)_{n} \end{array}$ , for every integrable function f on unbounded Vilenkin groups, such that the sequence ( m n ) n contains infinitely many even terms satisfying the estimate ln⁡ mk− 1ln⁡ mkmk=O(1). $\begin{array}{} \frac{\ln m_{k-1}\ln m_{k}}{m_{k}}=O(1). \end{array} $

We study projectivity and injectivity for Banach modules over abstract Segal algebras. We then apply these results to abstract Segal algebras related to locally compact groups.

We study variable exponent Sobolev spaces on compact metric spaces. Without the assumption of log-Hölder continuity of the exponent, the compact Sobolev-type embeddings theorems for these spaces are shown.

We give a condition on commutativity of a pair of self-adjoint elements in a C * -algebra with respect to the continuous functional calculus. We also give an answer to the question raised by Jeang and Ko that if a non-constant continuous function totally spans the given C * -algebra.

Let 𝒜 and ℬ be two prime C * -algebras. In this paper, we investigate the additivity of map Φ from 𝒜 onto ℬ that are bijective unital and satisfies Φ (AP+λ PA∗ )=Φ (A)Φ (P)+λ Φ (P)Φ (A)∗ , $$\Phi(AP+\lambda PA^{*})=\Phi(A)\Phi(P)+\lambda \Phi(P)\Phi(A)^{*}, $$ for all A ∊ 𝒜 and P ∊ { P 1 , I 𝒜 − P 1 } where P 1 is a nontrivial projection in 𝒜 and λ ∊ {−1, +1}. Then, Φ is *-additive.

In this paper we construct examples of different types of connections starting from a semi-symmetric metric connection g , for example a connection which is a symmetric metric connection with respect to a conformally related metric, but symmetric non-metric with respect to the initial metric. We formulate an open problem: to find a parallel complex structure on a Kaehler manifold with respect to such a new connection.

We show that for every Lindelöf P -space a weaker version of the Sokolov property holds. Besides, if K is a scattered Eberlein compact space and X is obtained from K by declaring open all G δ -subsets of K , then X is monotonically Sokolov. The proof of this statement uses the fact that every Lindelöf subspace of a scattered Eberlein compact space must be σ -compact; this result seems to be interesting in itself. We also give an example of a Lindelöf P -space X such that C p ( X ) has uncountable extent. In particular, neither X nor C p ( X ) has the Sokolov property.

Let { X ni , i ≥ 1, n ≥1} be an array of rowwise negatively orthant dependent random variables which is stochastically dominated by a random variable X . Wang et al. [15. Complete convergence for arrays of rowwise negatively orthant dependent random variables , RACSAM, 106 (2012), 235–245] studied the complete convergence for arrays of rowwise negatively orthant dependent random variables under the condition that X has an exponential moment, which seems too strong. We will further study the complete convergence for arrays of rowwise negatively orthant dependent random variables under the condition that X has a moment, which is weaker than exponential moment. Our results improve the corresponding ones of Wang et al. [15].

In this paper, we consider the problem of the existence of a least absolute deviations estimator for the Michaelis-Menten model function. We give necessary and sufficient conditions under which the least absolute deviations problem has a solution. In order to illustrate the usefulness of such conditions we give several numerical examples.

In this paper, we first introduce the concept of congruence pairs on the class of principal p -algebras. Then, we show that every congruence relation θ on a principal p -algebra L can be uniquely determined by a congruence pair ( θ 1 , θ 2 ). Moreover, the strong extensions of principal p -algebras and the permutability of congruences will be investigated by congruence pairs.