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61.
B. Dacorogna I. Fonseca J. Malý K. Trivisa 《Calculus of Variations and Partial Differential Equations》1999,9(3):185-206
The integral representation for the relaxation of a class of energy functionals where the admissible fields are constrained
to remain on a
-dimensional manifold is obtained. If is a continuous function satisfying for and for all then where is open, bounded, and is the tangential quasiconvexification of f at
belong to the tangent space to at
Received October 10, 1998 / Accepted December 1, 1998 相似文献
62.
Sandra Di Rocco 《Mathematische Zeitschrift》1999,231(1):169-188
The notion of a k-convex -support function for a toric variety is introduced. A criterion for a line bundle L to generate k-jets on X is given in terms of the k-convexity of the -support function . Equivalently L is proved to be k-jet ample if and only if the restriction to each invariant curve has degree at least k.
Received October 22, 1997; in final form January 12, 1998 相似文献
63.
Pao-Liu Chow Ildar A. Ibragimov Rafail Z. Khasminskii 《Probability Theory and Related Fields》1999,113(3):421-441
For linear partial differential equations, some inverse source problems are treated statistically based on nonparametric
estimation ideas. By observing the solution in a small Gaussian white noise, the kernel type of estimators is used to estimate
the unknown source function and its partial derivatives.. It is proved that such estimators are consistent as the noise intensity
tends to zero. Depending on the principal part of the differential operator, the optimal asymptotic rate of convergence is
ascertained within a wide class of risk functions in a minimax sense.
Received: 5 May 1997 / Revised version: 18 June 1998 相似文献
64.
Hermann Thorisson 《Probability Theory and Related Fields》1994,99(4):477-483
Summary The result linking shift-coupling to time-average total variation convergence and to the invariant -field is extended to continuous time and an analogous result established linking -couplings to smooth total variation convergence and to a smooth tail -field. Shift- and -coupling inequalities are presented. 相似文献
65.
66.
An algebra A over a field k is FCR if every finite dimensional representation of A is completely reducible and the intersection of the kernels of these representations is zero. We give a useful characterization of FCR-algebras and apply this to C *-algebras and to localizations. Moreover, we show that “small” products and sums of FCR-algebras are again FCR. Received: 25 October 2000 相似文献
67.
We consider d-dimensional Brownian motion in a scaled Poissonian potential and the principal Dirichlet eigenvalue (ground state energy)
of the corresponding Schr?dinger operator. The scaling is chosen to be of critical order, i.e. it is determined by the typical
size of large holes in the Poissonian cloud. We prove existence of a phase transition in dimensions d≥ 4: There exists a critical scaling constant for the potential. Below this constant the scaled infinite volume limit of the
corresponding principal Dirichlet eigenvalue is linear in the scale. On the other hand, for large values of the scaling constant
this limit is strictly smaller than the linear bound. For d > 4 we prove that this phase transition does not take place on that scale. Further we show that the analogous picture holds
true for the partition sum of the underlying motion process.
Received: 10 December 1999 / Revised version: 14 July 2000/?Published online: 15 February 2001 相似文献
68.
69.
In this work a class of nondissipative curves in Hilbert spaces whose correlation functions have a limit ast± is presented. These curves correspond to a class
of nondissipative basic operators that are a coupling of a dissipative operator and an antidissipative one. The wave operators and the scattering operator for the couple (A
*, A) (
) are obtained. The present work is a continuation and a generalization of the investigations of K.Kirchev and V.Zolotarev [1, 2, 3] on the model representations of curves in Hilbert spaces where the respective semigroup generator is a dissipative operator. This article includes four parts. A new form of the triangular model of M.S. Livic ([4, 5]) for the considered operators is introduced in the first part by the help of a suitable representation of the selfadjoint operatorL. This allows us to describe the studied class of nondissipative curves. The second part studies some results concerning the application of the analogue for multiplicative integrals of the well-known Privalov's theorem ([6]) about the limit values in the scalar case. This analogue is a reconstruction of measure by limit values in Stieltjes-Perron's style and it is obtained by L.A. Sakhnovich ([7]). Another problem, considered in the second part is the analogue inC
m
of the classical gamma-function and several properties for further consideration. In the third part the asymptotics of the studied curves corresponding to the nondissipative operators-couplings of a dissipative and an antidissipative operator with absolutely continuous real spectra and the limits of their correlation functions are obtained In the fourth part a scattering theory of a couple (A
*, A) with a nondissipative operatorA from
is constructed as in the selfadjoint case ([8, 9, 10]) and in the dissipative case ([7]). These results show an interesting new effect: the studied nondissipative case is near to the dissipative one.Partially supported by Grant MM-810/98 of MESC 相似文献
70.
The iterates of expanding maps of the unit interval into itself have many of the properties of a more conventional stochastic
process, when the expanding map satisfies some regularity conditions and when the starting point is suitably chosen at random.
In this paper, we show that the sequence of iterates can be closely tied to an m-dependent process. This enables us to prove good bounds on the accuracy of Gaussian approximations. Our main tools are coupling
and Stein's method.
Received: 27 June 1997 / Revised version: 21 September 1998 相似文献