2004, Studia Mathematica 4
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Oriented angles in affine space
(2004)The concept of a smooth oriented angle in an arbitrary affine space is introduced. This concept is based on a kinematics concept of a run. Also, a concept of an oriented angle in such a space is considered. Next, it is ... -
Seshadri fibrations on algebraic surfaces
(2004)We show that small Seshadri constants in a general point of a surface have strong geometrical implications, the surface is fibered by curves computing the Seshadri constant. We give a sharp bound in terms of the ... -
Seshadri constants of unisecant line bundles on ruled surfaces
(2004)The aim of this paper is to show that for any ruled surface $X$ with a unisecant polarization $L ≡ C_0 + μ_0f$ the Seshadri constant of $L$ at every point of $X$ is equal $1$. -
Local analytic solutions of a functional equation
(2004)All analytic solutions of the functional equation \[|f(r exp(iθ))|^2 + |f(1)|^2 = |f(r)|^2 + |f(exp(iθ))|^2\] in the annulus \[P := {z ∈ C : 1 − ε < |z| < 1 + ε}\] and in the domain \[D := {z = re^{iθ} ∈ C : ... -
On a class Riemannian manifolds with harmonic Weyl conformal curvature tensor
(2004)The paper deals with the local structure of those n-dimensional $(n ≥ 5)$ Riemannian manifolds of harmonic conformal curvature $(M, g)$ which are not conformally at and admit a non-homothetic conformal change of metric $g ... -
Abstract Lie groups and locally compact topological groups
(2004)We introduce a notion of abstract Lie group by means of the mapping which plays the role of the evolution operator. We show some basic properties of such groups very similar to the fundamentals of the infinite dimensional ... -
Higher order jet prolongations type gauge natural bundles over vector bundles
(2004)Let $r ≥ 3$ and $m ≥ 2$ be natural numbers and $E$ be a vector bundle with $m$-dimensional basis. We find all gauge natural bundles "similar" to the $r$-jet prolongation bundle $J^r$ $E$ of $E$. We also find all gauge ... -
On the rate of convergence theorem for the alternate Poisson integrals for Hermite and Laguerre expansions
(2004)The aim of this paper is the study of a rate of convergence of alternate Poisson integrals for Hermite and Laguerre expansions. We state some estimates of the rate of convergence of these integrals using the classical ... -
Locally conformal symplectic structures and their generalizations from the point of view of Lie algebroids
(2004)We study locally conformal symplectic structures and their generalizations from the point of view of transitive Lie algebroids. To consider l.c.s. structures and their generalizations we use Lie algebroids with trivial ... -
On conformally symmetric warped products
(2004)We prove the necessary and sufficient conditions for a warped product manifold to be conformally symmetric. Basing on these results we give two examples of such warped products. -
On the differential first-order invariants for the non-splitting subgroups of the generalized Poincare group P(1,4)
(2004)The functional bases of the differential first-order invariants for all non-splitting subgroups of the generalized Poincaré group P(1, 4) are constructed. Some applications of the results obtained are considered. -
Underlying functors on fibered manifolds
(2004)For a product preserving bundle functor on the category of fibered manifolds we describe subordinated functors and we introduce the concept of the underlying functor. We also show that there is an affine bundle structure ... -
Curvature properties of some submanifolds in space forms
(2004)Curvature properties of pseudosymmetry type of some submanifolds of codimension greater then 1 immersed isometrically in semi-Riemannian spaces of constant curvature are given. -
On some functional equations related to Steffensen's inequality
(2004)We consider the problem, proposed by the second author (cf. [1]) of solving functional equations stemming from the Steffensen integral inequality (S), which is applicable in actuarial problems, cf. [4]. Imposing some ... -
Functorial prolongations of some functional bundles
(2004)We discuss two kinds of functorial prolongations of the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. We study the prolongation of vector ... -
Strong maximum principles for implicit parabolic functional-differential problems together with initial inequalities
(2004)The aim of the paper is to give strong maximum principles for implicit non-linear parabolic functional-differential problems together with initial inequalities in relatively arbitrary (n+1)-dimensional time - space sets ...
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