Studia Mathematica
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Simultaneous primality of the integers $n$ and $2n - d$
(2013)A necessary and sufficient condition for the simultaneous primality of integers $n$ and $2n-d$ is given by means of congruences ${mod n(2n - d)}$ that hold if and only if they form a prime pair. These are used to obtain ... -
On a sum form functional equation containing three unknown mappings
(2013)The general solutions of a sum form functional equation containing three unknown mappings have been obtained without imposing any regularity condition on any of three mappings. -
On Levinson's inequality
(2013)We give a very simple proof of the classical Levinson inequality and generalize the result by Mercer. -
The Littlewood-Paley g-function associated with the Riemann-Liouville operator
(2013)First, we study the Gauss and Poisson semigroups connected with the Riemann-Liouville operator. Next, we define and study the Littlewood- Paley $g$-function associated with the Riemann-Liouville operator for which we ... -
Approximation by some combinations of the Poisson integrals for Hermite and Laguerre expansions
(2013)The aim of this paper is the study of a rate of convergence of some combinations of the Poisson integrals for Hermite and Laguerre expansions. We are able to achieve faster convergence for our modified operators over ... -
Construction of an $A$-manifold on a principal torus bundle
(2013)We construct a new example of an $A$-manifold, i.e. a Riemannian manifold with cyclic-parallel Ricci tensor. This condition can be viewed as a generalization of the Einstein condition. The underlying manifold for ... -
Annales Universitatis Paedagogicae Cracoviensis. 128. Studia Mathematica 12
(Wydawnictwo Naukowe Uniwersytetu Pedagogicznego, Kraków, 2013) -
Classes of multivalent analytic functions with Montel's normalization
(2012)In this paper we define classes of functions with Montel's normalization. We investigate the coeffcients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and ... -
An analytic description of the class of rational associative functions
(2012)We dael with the following problem: which rational functions of two variables are associative? We provide a complete answer to that question. -
Rank function equations
(2012)The purpose of this paper is to introduce the notion of rank function equation, and to present some results on such equations. In particular, we find all sequences $(A_{1}, ..., A_{k}, B)$ of nonzero nilpotent $n \times ... -
Congruences characterizing twin primes
(2012)Inspired by P.A. Clement’s results in [2], we give new necessary and sufficient conditions for two prime numbers to be twin primes. -
On stability of some functional equations and topology of their target spaces
(2012)Some remarks about the coherence of the stability of several functional equations with topology of their target spaces are given. The equations in question are: homogeneity (first of all) and quadratic ones, as well as ... -
Multivalued second order differential problem
(2012)Let $K$ be a closed convex cone with nonempty interior in a real Banach space and let $F,G,H: K → cc(K)$ be three given continuous additive set-valued functions. We study the existence and uniqueness of a solution of the ... -
Ma's identity and its application
(2012)In the paper we distinguish the, so called, Ma's polynomials and we introduce connections of these polynomials with the classic Cauchy polynomials and the Ferrers-Jackson's polynomials. Presented connections enable to ... -
Blowup and specialization methods for the study of linear systems
(2012)The computation of the dimension of linear systems of curves with imposed base multiple points on surfaces is a difficult problem, with open conjectures that are being approached only with partial success. Among others, ... -
Annales Universitatis Paedagogicae Cracoviensis. 122. Studia Mathematica 11
(Wydawnictwo Naukowe Uniwersytetu Pedagogicznego, Kraków, 2012) -
On Minkowski decomposition of Okounkov bodies on a Del Pezzo surface
(2011)We show that on a blow up of $ℙ^2$ in 3 general points there exists a finite set of nef divisors $P_1 ,..., P_s$ such that the Okounkov body $∆(D)$ of an arbitrary effective $ℝ–divisor$ $D$ on $X$ is the Minkowski ... -
Über Extrema mit Nebenbedingungen
(2011)Zweck der vorliegenden Arbeit is es, eine gut handhabbare Methode zu zeigen, womit man die hinreichende Bedingung für die Existenz eines Extremums unter Nebenbedingungen behandeln kann. Das Resultat ist eigentlich nicht ...
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