986 research outputs found
Parametric representation of univalent functions with boundary regular fixed points
Given a set of conformal maps of the unit disk into
itself that is closed under composition, we address the question whether
can be represented as the reachable set of a Loewner - Kufarev -
type ODE , , where the control functions form a convex cone . For the set of all conformal
with , , an affirmative answer to this question is
the essence of Loewner's well-known Parametric Representation of univalent
functions [Math. Ann. 89 (1923), 103-121]. In this paper, we study classes of
conformal self-maps defined by their boundary regular fixed points and, in part
of the cases, establish their Loewner-type representability.Comment: Version 3: Introduction has been modified; Example 3.1 added + other
minor correction
Angular and unrestricted limits of one-parameter semigroups in the unit disk
We study local boundary behaviour of one-parameter semigroups of holomorphic
functions in the unit disk. Earlier under some addition condition (the position
of the Denjoy - Wolff point) it was shown in [M.D.Contreras, S.Diaz-Madrigal
and Ch.Pommerenke, Ann. Acad. Sci. Fenn. Math. 29(2004), No.2, 471-488] that
elements of one-parameter semigroups have angular limits everywhere on the unit
circle and unrestricted limits at all boundary fixed points. We prove stronger
versions of these statements with no assumption on the position of the Denjoy -
Wolff point. In contrast to many other problems, in the question of existence
for unrestricted limits it appears to be more complicated to deal with the
boundary Denjoy - Wolff point (the case not covered in [M.D.Contreras,
S.Diaz-Madrigal and Ch.Pommerenke, Ann. Acad. Sci. Fenn. Math. 29(2004), No.2,
471-488]) than with all the other boundary fixed points of the semigroup.Comment: Some changes are made in this version: misprints and minor errors are
corrected, the information on the grant support is adde
Ірраціональні вірування людини як когнітивні утворення. (Irrational beliefs of personality as cognitive formation)
В статті досліджено психологічні особливості такого конструкту, як «ірраціональні вірування людини», охарактеризовано розуміння життєвих труднощів з точки зору когнітивної парадигми, подано ключові ірраціональні вірування сучасної вітчизняної вибірки, обґрунтовано доцільність вживання терміну «вірування» в контексті різних форм дисфункціональних когніцій людини.(An article researches psychological peculiarities of “human irrational beliefs” construct, describes cognitive approach to understanding of life difficulties, gives core irrational beliefs of contemporary national sample, explains necessity of using a construct of ‘beliefs’ in the context of different forms of human dysfunctional cognitions.
Valiron and Abel equations for holomorphic self-maps of the polydisc
We introduce a notion of hyperbolicity and parabolicity for a holomorphic
self-map of the polydisc which does not admit fixed
points in . We generalize to the polydisc two classical one-variable
results: we solve the Valiron equation for a hyperbolic and the Abel
equation for a parabolic nonzero-step . This is done by studying the
canonical Kobayashi hyperbolic semi-model of and by obtaining a normal form
for the automorphisms of the polydisc. In the case of the Valiron equation we
also describe the space of all solutions.Comment: A few references are adde
Matching univalent functions and conformal welding
Given a conformal mapping of the unit disk onto a simply
connected domain in the complex plane bounded by a closed Jordan curve, we
consider the problem of constructing a matching conformal mapping, i.e., the
mapping of the exterior of the unit disk onto the exterior domain
regarding to . The answer is expressed in terms of a linear
differential equation with a driving term given as the kernel of an operator
dependent on the original mapping . Examples are provided. This study is
related to the problem of conformal welding and to representation of the
Virasoro algebra in the space of univalent functions.Comment: 17 page
Transport connectivity as a factor in overcoming challenges of the periphery: the case of rural areas in the Kaliningrad region
Quality of life in rural areas is increasingly dependent on transport links to nearest towns and regional centres. In this article, we examine transport connectivity between villages and towns in the Kaliningrad region. We use the travel time access parameter to investigate the influence of transport connectivity on the population size and the prospects of socio-economic development in rural areas with different transport and geographical situations. Although the overall transport connectivity is high in the region, up to 10 per cent of villages score low on this parameter. We conclude that the demographic saturation of the Kaliningrad agglomeration has not been completed. Moreover, the smallness of the local consumer market impedes the formation of subregional centres in the eastern part of the region. The most alarming trend is the incipient concentration of population in peripheral border areas
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