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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 ... -
The regular density on the plane
(2011)In the note [1] the notion of the regular density point of the measu- rable subset of the real line was introduced. Then it was shown that the new definition is equivalent to the definition of O’Malley points, which has ... -
A more colorful hat problem
(2011)The topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The ... -
The research on the strong Markov property
(2011)Let $X(t, ω) ≜ {x_t(ω); t ≥ 0}$ be a Markov process defined on a probability space $(Ω, F, P)$ and valued in a measurable space $(E, ε)$. In this paper, we give the definitions of $σ-algebras$ prior to $α$ and $post-α$ ... -
Nonlocal Robin problem in a plane domain with a boundary corner point
(2011)We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of the boundary corner point. We find an exponent of the solution decreasing ... -
Annales Universitatis Paedagogicae Cracoviensis. 102. Studia Mathematica 10
(Wydawnictwo Naukowe Uniwersytetu Pedagogicznego, Kraków, 2011) -
Some properties of analytic sets with proper projections
(2010)We give an affective criterion when an analytic set with proper projection is algebraic. We take an ideal of polynomials vanishing on the set then we construct a polydisc convenient for reduction. If this polydisc is ... -
On systems of equations with unknown multifunctions related to the plurality function
(2010)Let $T$ be a nonempty set. Inspired by a problem posed by Z. Moszner in [10] we investigate for which additional assumptions put on multifunctions $Z(t):T → 2^{ℝ(m)}$, which fulfil condition \[ ⋃_{t ∈ T} Z(t)=ℝ(m)\], and ... -
Boundary value problems with shift for generalized analytic vectors
(2010)This paper is a survey of the most important work of the well-known Georgian mathematician Professor Giorgi Manjavidze “Boundary value problems for analytic and generalized analytic functions”. Here we present his original ... -
Boundary value problems for a second-order elliptic equation in unbounded domains
(2010)We investigate the behaviour of weak solutions to the boundary value problems for the second order elliptic linear equation in a neighborhood of innity. The exponent of the decreasing rate of solutions at innity has been ... -
On asymptotic cyclic contractions
(2010)We introduce asymptotic cyclic contractions as a generalization of cyclic contractions and this new type of mappings is considered under the recently introduced property UC for pairs of subsets of metric spaces. We show ... -
On Schwarz-type boundary-value problems of polyanalytic equation on a triangle
(2010)We will consider the Schwarz-type boundary-value problems (BVPs) of the polyanalytic equation on an isosceles orthogonal triangle. In contrast to [1], the expression of its unique solution are explicitly obtained by the ... -
On the hat problem, its variations, and their applications
(2010)The topic of our paper is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other ... -
On a generalization of the Popoviciu equation on groups
(2010)We determine a general solution of the Popoviciu type functional equation on groups. -
Unstable (Stable) system of stable (unstable) functional equations
(2010)In this note the answer to a question by Z. Moszner from the paper [1] about connections of stability of separate equations and the system of them, is given. -
Global aspects of the geometry of surfaces
(2010)Several open problems related to the behavior of the monoid of effective divisors and the nef cone for smooth projective surfaces over an algebraically closed field are discussed, motivating and putting into historical ... -
Annales Universitatis Paedagogicae Cracoviensis. 84. Studia Mathematica 9
(Wydawnictwo Naukowe Uniwersytetu Pedagogicznego, Kraków, 2010)
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