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31.
We investigate several versions of a cardinal characteristic defined by Frankiewicz. Vojtáš showed , and Blass showed . We show that all the versions coincide and that is greater than or equal to the splitting number. We prove the consistency of and of .
Received: 2 October 1996 / Revised version: 22 May 1997 相似文献
32.
Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic
inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results
on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number
of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient,
we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of
the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing
collisions between particles, which leads to a second-order limiting PDE.
Received: 5 August 1996 / In revised form: 17 October 1996 相似文献
33.
J. Schropp 《Numerische Mathematik》1997,78(1):87-101
Summary. We use the qualitative properties of the solution flow of the gradient equation to compute a local minimum of a real-valued function . Under the regularity assumption of all equilibria we show a convergence result for bounded trajectories of a consistent,
strictly stable linear multistep method applied to the gradient equation. Moreover, we compare the asymptotic features of
the numerical and the exact solutions as done by Humphries, Stuart (1994) and Schropp (1995) for one-step methods. In the
case of -stable formulae this leads to an efficient solver for stiff minimization problems.
Received July 10, 1995 / Revised version received June 27, 1996 相似文献
34.
35.
Genkai Zhang 《manuscripta mathematica》1998,97(3):371-388
Let X=G
* be a compact Hermitian symmetric space. We study the Berezin transform on L
2(X) and calculate its spectrum under the decomposition of L
2(X) into the irreducible representations of G
*. As applications we find the expansion of powers of the canonical polynomial (Bergman reproducing kernel for the canonical
line bundle) in terms of the spherical polynomials on X, and we find the irreducible decomposition of tensor products of Bergman spaces on X.
Received: 10 September 1996 / Revised version: 10 September 1997 相似文献
36.
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39.
Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for
the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration
phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper
bounds on spectral gaps.
Received: 10 June 1996 / In revised form: 9 August 1996 相似文献
40.
本文用试验测定和理论计算表明,在多剖面法中利用复合试样测定焊接接头断裂韧性时,可测到的HAZ小区与板厚、试样厚度、线能量、预热温度及坡口角度等因素有关,并非总能测出全部小区的δ_(is)值.对提高测试精度的有关技术问题进行了探讨. 相似文献