小周期复合材料热传导问题的双尺度渐近展开及收敛性分析

利用双尺度渐近展开和均匀化思想讨论了小周期复合材料的热传导问题,得到了具有高阶震荡系数的抛物型方程的渐近展开式,并证明了当Ω为R~2中的光滑的区域时渐近展开式在空间L~2(0,T;H~1(Ω))中具有较好的收敛性.     

Relating the second and fourth order terms in the asymptotic expansion of the heat equation

Leta _n be the coefficients in the asymptotic expansion of the heat equation. In this paper, we study the relationship betweena ₂ ² anda ₄ in the context of both Riemannian and affine geometry.Research partially supported by the DFG project on Affine differential geometryResearch partially supported by the NSF (USA) and MSRI (USA)     

On the asymptotic expansion of the solution of the plane Stokes problem in a perforated domain

This article deals with the asymptotic behavior as ε → 0 of the solution {u _ɛ, p _ɛ} of the plane Stokes problem in a perforated domain. The limit problem is constructed and estimates for the speed of convergence are obtained. It is shown that the speed of convergence is of order O(ε ^3/2). __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 3–20, 2005.     

Application of the two-dimensional differential transform method to heat conduction problem for heat transfer in longitudinal rectangular and convex parabolic fins

In this article, approximate analytical (series) solutions for the temperature distribution in a longitudinal rectangular and convex parabolic fins with temperature dependent thermal conductivity and heat transfer coefficient are derived. The transient heat conduction problem is solved for the first time using the two-dimensional differential transform method (2D DTM). The effects of some physical parameters such as the thermo-geometric parameter, exponent and thermal conductivity gradient on temperature distribution are studied. Furthermore, we study the temperature profile at the fin tip.     

The asymptotic expansion of the Feynman integral

We obtain an expansion of in powers of a small parameter, wherex _t is a random process satisfying the stochastic differential equation .Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 28–37, 1986.     

On the asymptotic expansion of Bergman kernel

We study the asymptotics of the Bergman kernel and the heat kernel of the ${\mathrm{spin}}^c$ Dirac operator on high tensor powers of a line bundle. To cite this article: X. Dai et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

The asymptotic expansion of the solution to the Cauchy problem for a parabolic equation in a perforated space

We consider the Cauchy problem for a second-order parabolic equation with rapidly oscillating coefficients of the forma(ɛ ⁻ x,ɛ ^−2k t) in a perforated space ℝ _ɛ ⁿ . We construct a complete asymptotic expansion for the solution of the said problem and obtain an estimate for the remainder term in this expansion. Bibliography: 8 titles. To my dear Teacher, Olga Arsenievna Oleinik This research was supported in part by Grant MIE000 from the International Science Foundation. Translated from Trudy Seminara imeni I. G. Petrovskogo. No. 19, pp. 000-000. 0000.     

The problem of differentiating an asymptotic expansion in real powers. Part II: Factorizational theory

In Part II of our work we approach the problem discussed in Part I from the new viewpoint of canonical factorizations of a certain nth order differential operator L. The main results include:

1. characterizations of the set of relations $$ f^{(k)} (x) = P^{(k)} (x) + o^{(k)} (x^{\alpha _n - k} ),x \to + \infty ,0 \leqslant k \leqslant n - 1, $$ where $$ P(x) = a_1 x^{\alpha _1 } + \cdots + a_n x^{\alpha _n } and \alpha _1 > \alpha _2 > \cdots > \alpha _n , $$ by means of suitable integral conditions
2. formal differentiation of a real-power asymptotic expansion under a Tauberian condition involving the order of growth of L
3. remarkable properties of asymptotic expansions of generalized convex functions.

     

The asymptotic expansion of the solution of a boundary-value problem with rapidly alternating type of boundary conditions

We consider a boundary-value problem for the Poisson equation with rapidly alternating type of boundary conditions in a domain between two parallel hyperplanes. The solution of the problem is assumed to be 1-periodic with respect to all the coordinates but one. We construct the asymptotic expansion for the solution in powers of a small parameter characterizing the alteration frequency of the boundary conditon. We obtain an estimate for the remainder term. Bibliography: 16 titles. Dedicated to Olga Arsenievna Oleinik This research has been supported in part by the foundation “Cultural Initiative”, by the International Science Foundation (Grant MIEOOO), and by the Russian Foundation for Basic Research. Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 19, pp. 000-000, 0000.     

Counterexamples to the asymptotic expansion of interpolation in finite elements

We present counterexamples to the asymptotic expansion of interpolation in finite element methods for solving differential equations, which was expected to hold in the finite element community.      

An asymptotic expansion for the distribution of asymptotic maximum likelihood estimators of vector parameters

It is shown that the probability that a suitably standardized asymptotic maximum likelihood estimator of a vector parameter (i.e., an estimator which approximates the solution of the likelihood equation in a reasonably good way) lies in a measurable convex set can be approximated by an integral involving a multidimensional normal density function and a series in $\text{n}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ with certain polynomials as coefficients.     

Full asymptotic expansion of the heat trace for non–self–adjoint elliptic cone operators

The operator e^–tA and its trace Tr e^–tA, for t > 0, are investigated in the case when A is an elliptic differential operator on a manifold with conical singularities. Under a certain spectral condition (parameter–ellipticity) we obtain a full asymptotic expansion in t of the heat trace as t → 0⁺. As in the smooth compact case, the problem is reduced to the investigation of the resolvent (A–λ)^–1. The main step consists in approximating this family by a parametrix of A – λ constructed within a suitable parameter–dependent calculus.     

Computation and asymptotic analysis in the impact problem

Non-linear numerical method is applied to solve the viscous-elastic-plastic material impact problem. The finite element simulation agrees with the celebrated European crash safety analysis. The complex material stress distribution in the large deformation has been obtained, when the impact happens. Also the posteriorestimate solver and asymptotic analysis have been used for the sensitive pre-stage deformation before the impact happening. This part of simulation is very interesting for the passive safety in automotive protection devices. It is an important part of the mathematical modelling. Supported by the National Natural Science Foundation of China (No. 10871225), Partly supported by EInstitutes of Shanghai Municipal Education Commission, N.E03004; Partly supported by Shanghai Pu Jiang Telent project [2006]118.     

A globally uniform asymptotic expansion of the hermite polynomials

In this article,the author extends the validity of a uniform asymptotic expansion of the Hermite polynomials Hn（√2n＋1α）to include all positive values of α. His method makes use of the rational functions introduced by Olde Daalhuis and Temme （SIAM J.Math.Anal.,（1994）,25：304-321）.A new estimate for the remainder is given.     

Chaos expansion and asymptotic behavior of the Pareto distribution

We give the chaos expansion of a random variable with Pareto distribution and we analyze, by using the Malliavin calculus, the convergence in the distribution of a sequence of random variable with Pareto distribution toward the standard exponential law.