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201.
Let
be a compact set with interior G. Let L
1
(G,dx), >0 dx-a.e. on G, and m:=dx. Let A=(a
ij
) be symmetric, and globally uniformly strictly elliptic on G. Let be such that
; f,
, is closable in L
2
(G,m) with closure (
r
,D(
r
)). The latter is fulfilled if satisfies the Hamza type condition, or
i
L
1
loc
(G,dx), 1id. Conservative, non-symmetric diffusion processes X
t
related to the extension of a generalized Dirichlet form
where
satisfies
are constructed and analyzed. If G is a bounded Lipschitz domain, H
1,1
(G), and a
ij
D(
r
), a Skorokhod decomposition for X
t
is given. This happens through a local time that is uniquely associated to the smooth measure 1{
Tr
()>0}
d, where Tr denotes the trace and the surface measure on G.This research has been financially supported by TMR grant HPMF-CT-2000-00942 of the European Union.
Mathematics Subject Classification (2000): 60J60, 60J55, 31C15, 31C25, 35J25 相似文献
202.
Hasan B.?Uzun Kenneth S.?AlexanderEmail author 《Probability Theory and Related Fields》2003,127(1):62-88
We consider boundary roughness for the ``droplet' created when supercritical two-dimensional Bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least l2, for large l. The maximum local roughness is the maximum inward deviation of the droplet boundary from the boundary of its own convex hull; we show that for large l this maximum is at least of order l1/3(logl)–2/3. This complements the upper bound of order l1/3(logl)–2/3 proved in [Al3] for the average local roughness. The exponent 1/3 on l here is in keeping with predictions from the physics literature for interfaces in two dimensions.
The research of the first author was supported by NSF grant DMS-9802368. The research of the second author was supported by NSF grants DMS-9802368 and DMS-0103790.Mathematics Subject Classification (2000): Primary 60K35; Secondary 82B20, 82B43 相似文献
203.
Gancho Tachev 《Journal of Computational Analysis and Applications》2001,3(4):361-381
A direct theorem for approximation by algebraic polynomials in two variables with different degrees in each variable in Lp-metric (1 p ) on rectangles is proved, and the dependence of the constants on various parameters is studied. 相似文献
204.
In this paper we present a new limit relation for the equidistant Lagrange interpolation polynomials to |x|, (0, 1] on the internal [–1, 1]. The result extends a well-known result of D. L. Berman and S. M. Losinskii. Furthermore, we briefly discuss on a possible connection of the limit relation to another prominent constant in best uniform polynomial approximation for |x| - the so-called Bernstein constant. 相似文献
205.
In this paper, we study orthogonal polynomials with respect to the bilinear form (f, g)
S
= V(f) A
V(g)
T
+ <u, f
(N)
g
(N)V(f) =(f(c
0), f "(c
0), ..., f
(n – 1)
0(c
0), ..., f(c
p
), f "(c
p
), ..., f
(n – 1)
p(c
p
))
u is a regular linear functional on the linear space P of real polynomials, c
0, c
1, ..., c
p
are distinct real numbers, n
0, n
1, ..., n
p
are positive integer numbers, N=n
0+n
1+...+n
p
, and A is a N × N real matrix with all its principal submatrices nonsingular. We establish relations with the theory of interpolation and approximation. 相似文献
206.
Zernike多项式是光机热集成分析中实现光、机、热各分析软件之间数据传递的重要工具。许多光学元件表面形状并不满足Zernike多项式的正交性条件,使有限元分析不能精确拟合光学元件表面变形及变形产生的各项像差。讨论影响Zernike正交性的几个因素,详细介绍将有限元分析得到的光学表面变形数据导入光学分析软件的一种新方法——干涉图插值法。该方法避开Zernike多项式拟合,在去除镜面刚体位移后将镜面畸变精确地表示成干涉图数据,直接生成数据接口。 相似文献
207.
This paper discusses the use of plasmonic nanostructured systems as nanoantennas for photodetection. Even though semiconductors and their heterostructures have many useful properties and widely used in photodetection, their electron density is very small compared to that of metals and, therefore, they have low absorption cross sections. The idea of using metal nanostructured antennas is to combine the high optical responses of metals with the functional electric properties of semiconductors. 相似文献
208.
When the stagnation temperature of a perfect gas increases, the specific heats and their ratio do not remain constant any
more and start to vary with this temperature. The gas remains perfect and its state equation always remains valid, except
it will be called a calorically imperfect gas. The aim of this research is to develop the relations of the necessary thermodynamics
and geometrical ratios and to study the supersonic flow at high temperature (lower than the threshold of dissociation). The
results are found by the resolution of nonlinear algebraic equations and integration of complex analytical functions where
the exact calculation is impossible. The dichotomy method is used to solve the nonlinear equation, and the Simpson algorithm
is used for the numerical integration of the found integrals. A condensation of the nodes is used, since the functions to
be integrated have a high gradient at the extremity of the interval of integration. A comparison is made with a calorifcally
perfect gas to determine the error of this. An application is made for air in a supersonic nozzle.
The text was submitted by the authors in English. 相似文献
209.
We study the technology of local anodic oxidation (LAO) by the AFM tip applied to semiconductor heterostructures with two-dimensional electron gas. The aim is to design mesoscopic rings with persistent current and one subband occupied. For this purpose the need is to oxidize narrow lines that represent energy barriers high enough. Using the electrostatic model, we explain the electric field distribution in the system tip-sample just before LAO starts. We study the influence of the conductivity of the cap layer on LAO and explain the origin of the saddle-like profile lines, observed in the experiment. Using Monte Carlo simulation we show that the carrier redistribution in the system with LAO energy barriers effectively lowers the barrier height. In the experimental part we have grown InGaP/AlGaAs/GaAs heterostructures by organometalic vapor phase epitaxy with an active layer only 31 nm below the surface. We have prepared oxide lines on the heterostructures by LAO and characterized them by the temperature-dependent transport measurement. 相似文献
210.
SUN Jin-Feng HU Qiu-Bo ZHU Zun-Lue WANG Xiao-Fei ZHANG Ji-Cai 《理论物理通讯》2007,47(6):1121-1124
Elastic scattering properties of the ultracold interaction for the triplet state of ^133Cs and ^85Rb atoms are studied using two kinds of potentials by the same phase Ф. One is the interpolation potential, and another is Lennard-Jones potential (LJl2,6 ). The radial Schrodtinger equation is also solved using two computational methods, the semiclassical method (WKB), and the Numerov method. Our results are found to be in an excellent agreement with the more recent theoretical values. It shows that the two potentials and methods are applicable for studying ultracold collisions between the mixing alkali atoms. 相似文献