48,106 research outputs found
Karhunen-Lo\`eve expansion for a generalization of Wiener bridge
We derive a Karhunen-Lo\`eve expansion of the Gauss process , , where is a
standard Wiener process and is a twice continuously
differentiable function with and . This
process is an important limit process in the theory of goodness-of-fit tests.
We formulate two special cases with the function
, , and , ,
respectively. The latter one corresponds to the Wiener bridge over from
to .Comment: 25 pages, 1 figure. The appendix is extende
Helicity Observation of Weak and Strong Fields
We report in this letter our analysis of a large sample of photospheric
vector magnetic field measurements. Our sample consists of 17200 vector
magnetograms obtained from January 1997 to August 2004 by Huairou Solar
Observing Station of the Chinese National Astronomical Observatory. Two
physical quantities, and current helicity, are calculated and their
signs and amplitudes are studied in a search for solar cycle variations.
Different from other studies of the same type, we calculate these quantities
for weak () fields separately. For
weak fields, we find that the signs of both and current helicity are
consistent with the established hemispheric rule during most years of the solar
cycle and their magnitudes show a rough tendency of decreasing with the
development of solar cycle. Analysis of strong fields gives an interesting
result: Both and current helicity present a sign opposite to that of
weak fields. Implications of these observations on dynamo theory and helicity
production are also briefly discussed.Comment: accepted for publication in ApJ Lette
Disability in Kazakhstan : an evaluation of official data
In order to answer the questions of (a) what is the true pattern of disability in Kazakhstan; (b) whether the incidence of disability is decreasing; and (c) what is the life expectancy of Kazakhstan's disabled, this paper attempts first to create an historical picture of disability in Kazakhstan by analyzing government population statistics and studying the evolution of disability determination procedure in the former Soviet Union and independent Kazakhstan. Doing so is not a trivial task, as there has been almost no systematic research, either in Russian or English. The paper concludes that the optimistic official picture of disability patterns in Kazakhstan is almost certainly inaccurate. The paper details that the quality of official disability data is high, and much can be learned from the patterns. However, changing definitions and strictness of enforcement make time series comparisons problematic, and the improvements in adult disability recorded are inconsistent both with trends for children, and with mortality trends. Rather, the authors note that barriers for applying disability benefits have increased and incentives to report disabilities have decreased markedly in the past 15 years, so that it is virtually certain that there is substantial hidden disability.Population Policies,Disease Control&Prevention,Disability,,Social Protections&Assistance
Kazakhstan's Pension System: Pressures for Change and Dramatic Reforms
Five years ago, Kazakhstan embarked on a dramatic reform of its pension and social security system in order to move from an unsustainable public defined benefit ("solidarity") system to one of defined mandatory contributions (accumulative system). While assessment of long-run success is premature, early results have exceeded expectations. This paper considers the reform's rationale and initial impact: Why did the Government of Kazakhstan decide to introduce a new pension system? What advantages did the state perceive? Was the Government's decision appropriate, and what alternatives existed? The paper also analyzes pension reform issues that have yet to be fully resolved.
Fertility and Marriage in Kazakhstan's Transition Period: Implications for Social Security Policy
Seven years ago, Kazakhstan embarked on a dramatic reform of its pension and social security system in order to move from an unsustainable public defined benefit ("solidarity") system to one of defined mandatory contributions (accumulative system). While much has been written on the financial implications for individual contributors, and on macro budgetary impacts, there has been no examination of how changing demographic structure is likely to affect the size of vulnerable pools. This paper explores the impact of these changes, and links demographic structure to economic performance. Focusing on changes in nuptiality (marriage) and fertility, we conclude that demographic structural shifts will increase overall system risk, but that current trends are favorable.
Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization
In this article, we study an analog of the Bj\"orling problem for isothermic
surfaces (that are more general than minimal surfaces): given a real analytic
curve in , and two analytic non-vanishing orthogonal
vector fields and along , find an isothermic surface that is
tangent to and that has and as principal directions of
curvature. We prove that solutions to that problem can be obtained by
constructing a family of discrete isothermic surfaces (in the sense of Bobenko
and Pinkall) from data that is sampled along , and passing to the limit
of vanishing mesh size. The proof relies on a rephrasing of the
Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its
discretization which is induced from the geometry of discrete isothermic
surfaces. The discrete-to-continuous limit is carried out for the Christoffel
and the Darboux transformations as well.Comment: 29 pages, some figure
Pension Reform in Central Asia: An Overview
Seven years ago, Kazakhstan embarked on a dramatic reform of its pension and social security system in order to move from a public defined benefit ("solidarity") system to one of defined mandatory contributions (accumulative system). At the same time, Kyrgyzstan embarked on a move to a notional defined contribution (NDC) system that has made little progress. Today, major reforms are being planned in both Uzbekistan and Tajikistan as well. This paper surveys the reforms that have taken place, discusses the planned reforms, and places them in the underlying fiscal and demographic contexts of the various countries in the region.
Approximation of conformal mappings using conformally equivalent triangular lattices
Consider discrete conformal maps defined on the basis of two conformally
equivalent triangle meshes, that is edge lengths are related by scale factors
associated to the vertices. Given a smooth conformal map , we show that it
can be approximated by such discrete conformal maps . In
particular, let be an infinite regular triangulation of the plane with
congruent triangles and only acute angles (i.e.\ ). We scale this
tiling by and approximate a compact subset of the domain of
with a portion of it. For small enough we prove that there exists a
conformally equivalent triangle mesh whose scale factors are given by
on the boundary. Furthermore we show that the corresponding discrete
conformal maps converge to uniformly in with error of
order .Comment: 14 pages, 3 figures; v2 typos corrected, revised introduction, some
proofs extende
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