Volume 67, Issue 5

It is well known that given a Steiner triple system (STS) one can define a binary operation * upon its base set by assigning x * x = x for all x and x * y = z , where z is the third point in the block containing the pair { x , y }. The same can be done for Mendelsohn triple systems (MTS), directed triple systems (DTS) as well as hybrid triple systems (HTS), where ( x , y ) is considered to be ordered. In the case of STSs and MTSs the operation yields a quasigroup, however this is not necessarily the case for DTSs and HTSs. A DTS or an HTS which induces a quasigroup is said to be Latin. In this paper we study Latin DTSs and Latin HTSs which admit a cyclic or a 1-rotational automorphism. We prove the existence spectra for these systems as well as the existence spectra for their pure variants. As a side result we also obtain the existence spectra of pure cyclic and pure 1-rotational MTSs.

In this paper we shall investigate the mildly distributive meet-semilattices by means of the study of their filters and Frink-ideals as well as applying the theory of annihilator. We recall some characterizations of the condition of mildly-distributivity and we give several new characterizations. We prove that the definition of strong free distributive extension, introduced by Hickman in 1984, can be simplified and we show a correspondence between (prime) Frink-ideals of a mildly distributive semilattice and (prime) ideals of its strong free distributive extension.

The notion of generalized completely distributivity is modified in order to obtain a tractable and consistent property of ordered sets.

Non-associative MV-algebras (NMV-algebras) ( A , ⊕, ¬, 0) were introduced in [CHAJDA, I.—KÜHR, J.: A non-associative generalization of MV-algebras , Math. Slovaca 57 (2007), 301–312]. In the present paper we prove some properties of these algebras, investigate when intervals of the form [ a , 1] can be made into NMV-algebras in some natural way and consider idempotent elements and derivations of NMV-algebras. Moreover, we study decompositions of NMV-algebras and characterize the congruences on NMV-algebras by means of so-called filters.

In the present paper we introduce the upper and lower exponential density functions of subsets A ⊆ ℕ*. We identify completely the form of the upper density and find many properties for the lower one. We provide examples and list some open problems.

We investigate the permutation behavior of a special class of Dembowski-Ostrom polynomials over a finite field of characteristic 2 of the form P ( X ) = L 1 ( X )( L 2 ( X )+ L 1 ( X ) L 3 ( X )) where L 1 , L 2 , L 3 are linearized polynomials. To our knowledge, the given class has not been studied previously in the literature. We identify several new types of permutation polynomials of this class. While most of the newly identified polynomials are linearly equivalent to permutation monomials, we show that there exist subclasses that are not affine equivalent to monomials, and we describe their forms. One of the newly identified classes contains a subclass of complete mappings. We use these complete mappings to define new sets of mutually orthogonal Latin squares, as well as new vectorial bent functions from the Maiorana-McFarland class. Moreover, the quasigroup polynomials obtained in the process are different and inequivalent to the previously known ones.

A finite group G is called an F -group ( G ∈ F ) if for every x , y ∈ G ∖ Z ( G ), C G ( x ) ≤ C G ( y ) implies that C G ( x ) = C G ( y ). An important subclass of F -groups are CA -groups, consisting of groups in which all centralizers of noncentral elements are abelian. In this paper, among other results, we find the number of element centralizers and the maximum cardinality of subsets of pairwise non-commuting elements in an F -group G with |GZ(G)$\frac{G}{Z(G)}$ | = p 4 for some prime p .

We consider the following families of real-valued functions: Darboux, quasi-continuous, Świątkowski functions and strong Świątkowski functions. The aim of this paper is to compare this sets in terms of topology.

Interest rates (or nominal yields) can be negative, this is an unavoidable fact which has already been visible during the Great Depression (1929–39). Nowadays we can find negative rates easily by e.g. auditing. Several theoretical and practical ideas how to model and eventually overcome empirical negative rates can be suggested, however, they are far beyond a simple practical realization. In this paper we discuss the dynamical reasons why negative interest rates can happen in the second order differential dynamics and how they can influence the variance and expectation of the interest rate process. Such issues are highly practical, involving e.g. the banking sector and pension securities.

In this paper, we present a method to generate homoclinic and heteroclinic motions in impulsive systems. We rigorously prove the presence of such motions in the case that the systems are under the influence of a discrete map that possesses homoclinic and heteroclinic orbits. Simulations that support the theoretical results are represented by means of a Duffing equation with impacts.

In this paper, we investigate the existence and uniqueness of a fixed point of certain contraction via auxiliary functions in the context of complete Branciari metric spaces endowed with a transitive binary relation. Our results unify and extend some existing fixed point results in the related literature.

In the present paper we give some results concerning the S-essential spectra of linear bounded operators on a Banach space using the notion of a measure of noncompactness.

The paper provides a generalization of a metric with values in a general structure. Quantales and special kinds of ordered monoids are shown to be suitable for this purpose. Topological and categorical properties of spaces with such generalized metrics are studied and a special emphasis is given on paths in these spaces.

The notion of porouscontinuous function introduced by Borsík and Holos is studied. Relations between porouscontinuous, continuous and ϱ -upper continuous are investigated. Moreover, we show that porouscontinuous functions may not belong to Baire class one.

The notion of rU-space is given and investigated. A space X is said to be a rU-space if X is a Hausdorff space and for every x ∈ X and every open neighbourhood V of x there exists an open neighbourhood U of x such that U ⊆ Cl( V ) and Bd( U ) ⊆ V . The class of rU-spaces is properly placed between the classes of regular and Urysohn spaces.

We present a complete functional formula expressing the i th ℤ 2 -Betti number of the oriented Grassmann manifold of oriented 3-dimensional vector subspaces in Euclidean n -space for i from the range determined by the characteristic rank of the canonical oriented 3-dimensional vector bundle over this manifold. The same formula explicitly exhibits the number of linearly independent semi-invariants of degree 3 of a binary form of degree n − 3. Using the approach and data presented in this note, analogous results can be obtained for the oriented Grassmann manifold of oriented 4-dimensional vector subspaces in Euclidean n -space and semi-invariants of degree 4 of a binary form of degree n − 4.

In this paper, we introduce a generalization of Baskakov operators based on a function ρ . We prove a weighted Korovkin type theorem and compute the rate of convergence via weighted modulus of continuity for these operators. Also we give a Voronovskaya type asymptotic formula.