The Brunn–Minkowski Inequality for the <Emphasis Type="Italic">n</Emphasis>-dimensional Logarithmic Capacity of Convex Bodies

We define the n-dimensional logarithmic capacity for convex bodies in Rⁿ, with n2; then, for this quantity, we prove a Brunn–Minkowski type inequality, and we characterize the corresponding equality case. Mathematics Subject Classifications (2000) 31C15, 31A35, 52A20, 39B62.     

Planning for optimal expansion of leased line communication networks

We report a new heuristic algorithm useful for developing least-cost expansion plans for leased telecommunications networks in which there is a hierarchy of possible transmission facilities. The problem combines network topology design and capacity expansion problems. Implemented on a PC, the algorithm has successfully developed topology growth plans for twenty periods on networks with up to 31 nodes.     

Affine lines on ℚ-homology planes with logarithmic Kodaira dimension -∞

In the present paper, we study a topologically contractible irreducible algebraic curve C on a ℚ-homology plane S with We determine such a pair (S,C) when and C is smooth. Moreover, we prove that if C is not smooth, then C has exactly one singular point and theMakar-Limanov invariant of S is trivial. An erratum to this article is available at .     

Heat escape

We study non-uniqueness of nonnegative solutions of the Cauchy or Dirichlet problem for parabolic equations on domains which are not relatively compact in Riemannian manifolds. By introducing the notion of heat escape, we give a general and sharp sufficient condition for the non-uniqueness: If there is a heat escape, then the Cauchy problem (or Dirichlet problem) has a positive solution with zero initial value (or zero initial-boundary value). We also show, under a general and sharp condition, uniqueness of nonnegative solutions to the Dirichlet problem for parabolic equations. Mathematics Subject Classification (1991):31C12, 35K20, 35J25, 35K15, 58G11, 58G03, 31C05     

Extremal Polynomials on Discrete Sets

We study asymptotics for orthogonal polynomials and other extremalpolynomials on infinite discrete sets, typical examples beingthe Meixner polynomials and the Charlier polynomials. Followingideas of Rakhmanov, Dragnev and Saff, weshow that the asymptoticbehaviour is governed by a constrained extremal energy problemfor logarithmic potentials, which can be solved explicitly.We give formulas for the contracted zero distributions, thenth root asymptotics and the asymptotics of the largest zeros.1991 Mathematics Subject Classification: 42C05, 33C25, 31A15.     

Topological Structures in Colombeau Algebras: Topological $\widetilde{\mathbb{C}}$ -modules and Duality Theory

We study modules over the ring of complex generalized numbers from a topological point of view, introducing the notions of -linear topology and locally convex -linear topology. In this context particular attention is given to completeness, continuity of -linear maps and elements of duality theory for topological -modules. As main examples we consider various Colombeau algebras of generalized functions.Mathematics Subject Classifications (2000) 46F30, 13J99, 46A20.Claudia Garetto: Current address: Institut für Technische Mathematik, Geometrie und Bauinformatik, Universität Innsbruck, 6020 Insbruck, Austria. e-mail: claudia@mat1.uibk.ac.at     

Potential-Theoretic Characterizations of Nonsmooth Domains

This paper describes–in terms of potential-theoretic properties–thenecessary and sufficient conditions required for a bounded domainsatisfying the capacity density condition to be, respectively:a John domain, a uniform domain and an inner uniform domain.2000 Mathematics Subject Classification 31B05, 31B25.     

On Singularity of Energy Measures on Self-Similar Sets II

We provide a criterion for the energy measures of regular Dirichletforms on post-critically finite self-similar sets to be singularwith respect to every self-similar measure. A probabilisticinterpretation of the singularity is also discussed. 2000 MathematicsSubject Classification 60G30 (primary), 28A80, 31C25, 60J60(secondary).     

Convexity Theorem for Subharmonic Functions with Respect to the Kolmogorov Operator

In this note, a version of the classical Riesz theorem for convexity of mean of subharmonic function on a annulus is given for the Kolmogorov's operator. Further, potential theoretical interpretations of a `mean value measure' are listed. Mathematics Subject Classifications (2000): 31B35, 31C05, 31C15.     

Capacitary Criteria for Poincaré-Type Inequalities

The Poincaré-type inequality is a unification of various inequalities including the F-Sobolev inequalities, Sobolev-type inequalities, logarithmic Sobolev inequalities, and so on. The aim of this paper is to deduce some unified upper and lower bounds of the optimal constants in Poincaré-type inequalities for a large class of normed linear (Banach, Orlicz) spaces in terms of capacity. The lower and upper bounds differ only by a multiplicative constant, and so the capacitary criteria for the inequalities are also established. Both the transient and the ergodic cases are treated. Besides, the explicit lower and upper estimates in dimension one are computed. Mathematics Subject Classifications (2000) 60J55, 31C25, 60J35, 47D07.Research supported in part NSFC (No. 10121101) and 973 Project.     

Sub-Markovian resolvents under weak duality hypothesis

 We study the weak duality between two sub-Markovian resolvents of kernels on a Lusin topological space with respect to a given measure m. Our frame covers the probabilistic context of two Borel Markov processes in weak duality. The main results are related to: the coincidence of the m-semipolar and m-cosemipolar sets, the Revuz correspondence between the measures charging no cofinely open m-polar set and the potential kernels associated with the homogeneous random measures of the process, the equivalence between smoothness and cosmoothness (a smooth measure is the Revuz measure of a continuous additive functional). We extend and improve results of R.M. Blumenthal-R.K. Getoor, J. Azéma, D. Revuz, J.B. Walsh, R.K. Getoor-M.J. Sharpe. Received: 24 July 2001 / Revised version: 29 December 2002 / Published online: 12 May 2003 Supported by the CNCSIS grant no. 33518/2002 (code 431), the CERES program of the Romanian Ministry of Ed. and Research, contract no. 152/2001 and the EURROMMAT program ICA1-CT-2000-70022 of the European Commission. Mathematics Subject Classification (2000): 60J40, 60J45, 60J55, 60J35, 31C15, 31C25, 31D05     

Équations aux différences dans les vecteurs de Witt

We prove an approximation property for Frobenius difference equations in the Witt vectors, analog to a theorem of Greenberg [Publ. Math. IHES 31 (1966) 59–64]. To cite this article: L. Bélair, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Stratifying systems via relative simple modules

In this paper we continue the study of stratifying systems, which were introduced by K. Erdmann and C. Sáenz in [Comm. Algebra 31 (7) (2003) 3429–3446]. We show that this new concept provides a categorical generalization of the Δ-modules for a standardly stratified algebra.     

Symplectic capacity and the Weinstein conjecture in certain cotangent bundles and Stein manifolds

We use the method proposed by H. Hofer. and C. Viterbo in [18] to calculate the Hofer-Zehnder capacity and prove the Weinstein conjecture in certain cotangent bundles and Stein manifolds.Supported in parts by SFB237 and the Forschunginstitut für Mathematik, ETH-Zentrum, Switzerland.     

Hausdorff dimension of Cantor sets and polynomial hulls

We give examples of Cantor sets in of Hausdorff dimension 1 whose polynomial hulls have non-empty interior.

     

基于通径分析的装配式建筑发展关键影响因素研究

基于装配式建筑发展能力视角,选取2016-2018年31个省份的实际数据,运用通径分析方法,分析经济能力、基础能力、政策环境能力三个维度影响因素对装配式建筑发展速度和发展规模两个层面的影响.研究发现,目前政策环境对发展速度促进作用最直接和显著,构件厂产能为代表的基础设施能力对发展规模直接作用最显著,以GDP为代表的经济...     

Estimation of Weak Lensing Parameters by Stochastic Integration

Abstract

A procedure for computing distance–redshift statistics in inhomogeneous universes is described. We interpret the generalized Dyer–Roeder equation [Dyer, C. C.; Roeder, R. C. The distance-redshift relation for universes with no intergalactic medium. Astrophys. J. 1972, 174, L115–L117; Dyer, C. C.; Roeder, R. C. Distance-redshift relations for universes with some intergalactic medium. Astrophys. J. 1972, 180, L31–L34] as a stochastic differential equation which treats the shearing forces as Brownian movement and yields a Monte-Carlo procedure. Shear distributions taken from N-body simulations produce a redshift dependent diffusion coefficient.     

Urysohn’s lemma for g-functions and homotopy extension theorem

Summary We give here a generalization of the classical Urysohn’s lemma for g-functions and apply it to the proof of the homotopy extension theorem for g-functions. It was also necessary to generalize the concept of algebraic operation, what is interesting in itself. Entrata in Redazione il 31 agosto 1970. This work was done with partial support of the National Research Council of Canada during the Summer Institute for Mathematics in Vancouver, B. C. (1970).     

On singularity of energy measures on self-similar sets

We provide general criteria for energy measures of regular Dirichlet forms on self-similar sets to be singular to Bernoulli type measures. In particular, every energy measure is proved to be singular to the Hausdorff measure for canonical Dirichlet forms on 2-dimensional Sierpinski carpets.Partially supported by Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Encouragement of Young Scientists, 15740089.Mathematics Subject Classification (2000): 28A80 (60G30, 31C25, 60J60)