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101.
Luc Miller 《Bulletin des Sciences Mathématiques》2005,129(2):175-185
We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting) which implies that one cannot go infinitely far away from the control region without tending to the boundary (if any), but also applies when the distance to the control region is bounded. The proof builds on heat kernel estimates. Secondly, we describe a class of null-controllable heat equations on unbounded product domains. Elementary examples include an infinite strip in the plane controlled from one boundary and an infinite rod controlled from an internal infinite rod. The proof combines earlier results on compact manifolds with a new lemma saying that the null-controllability of an abstract control system and its null-controllability cost are not changed by taking its tensor product with a system generated by a non-positive self-adjoint operator. 相似文献
102.
Kan Hachiya 《Journal of Non》2003,321(3):217-224
First-principles calculations of the electronic structures of the wrong bonds were performed for amorphous germanium sulphides in order to explain their compositional dependence. Model cluster calculations of the density of states using a set of geometry similar to the crystalline-GeS2 coordination can reproduce the peak structure of the experimental valence band photoemission spectra. The bonding and anti-bonding states of the covalent Ge-S bonds form valence and conduction band respectively, and the top of the valence band is occupied with S 3p lone-pair states. The bonding states are modified by S-S bonds and the anti-bonding states are modified by Ge-Ge bonds, mainly through their hybridization with the wrong-bond states between p-orbitals. The lone-pair states do not interact either of them to form a different band, and obscure the modification induced by the S-S wrong bonds. Therefore, we can conclude that the narrowing of the bandgap with increasing Ge content from GeS2 composition is due to that of the conduction-band bottom with increasing germanium wrong bonds, though the narrowing with increasing S content is moderate due to the presence of the lone-pair states at the valence-band top. 相似文献
103.
Huazhong Tang Tao Tang Kun Xu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(3):365-382
In this paper, the Kinetic Flux Vector Splitting (KFVS)
scheme is extended to solving the shallow water equations with
source terms. To develop a well-balanced scheme between the source
term and the flow convection, the source term effect is accounted
in the flux evaluation across cell interfaces. This leads to a
modified gas-kinetic scheme with particular application to the
shallow water equations with bottom topography. Numerical
experiments show better resolution of the unsteady solution than
conventional finite difference method and KFVS method with little
additional cost. Moreover, some positivity properties of the
gas-kinetic scheme is established. 相似文献
104.
R. Weidmann 《Archiv der Mathematik》2003,81(5):589-595
We describe a family of graph manifolds that have 2-generated
fundamental group but do not admit a Heegaard splitting of genus 2. They are
closely related to the examples provided by Boileau and Zieschang if these are
considered as (non-proper) graph manifolds.Received: 14 August 2002 相似文献
105.
106.
Rashmi 《Solid State Communications》2005,134(3):217-222
A detailed analysis of nonlinear effects-electron switching and rectification, in InAlAs/InGaAs based Y-branch junction (YBJ) devices is presented to investigate the potential of YBJ for high frequency applications at 300 K. Results based on semi-classical simulations yield good qualitative agreement with measurements and previously reported theoretical and experimental results. The nonlinear parabolic behaviour of our device is attributed to device geometry and space charge effects. RF analysis shows that the YBJ has tremendous intrinsic potential to function as a frequency doubler and microwave rectifier when operated in the parabolic regime. The present analysis serves as a tool to optimize the bias conditions for RF measurements and to estimate the effect of interconnects and parasitic elements on the RF performance of real devices. 相似文献
107.
Yasufumi Hashimoto 《Journal of Number Theory》2007,122(2):324-335
In [P. Sarnak, Class numbers of indefinite binary quadratic forms, J. Number Theory 15 (1982) 229-247], it was proved that the Selberg zeta function for SL2(Z) is expressed in terms of the fundamental units and the class numbers of the primitive indefinite binary quadratic forms. The aim of this paper is to obtain similar arithmetic expressions of the logarithmic derivatives of the Selberg zeta functions for congruence subgroups of SL2(Z). As applications, we study the Brun-Titchmarsh type prime geodesic theorem and the asymptotic formula of the sum of the class number. 相似文献
108.
Franc Forstnerič 《Mathematische Annalen》1992,292(1):163-180
109.
Summary.
This paper is concerned with a high order convergent
discretization for the semilinear reaction-diffusion problem:
,
for , subject to ,
where .
We assume that on
, which
guarantees uniqueness of a solution to
the problem. Asymptotic properties of
this solution are discussed. We consider a
polynomial-based three-point
difference scheme on a simple piecewise
equidistant mesh of Shishkin type.
Existence and local uniqueness of a solution
to the scheme are analysed. We
prove that the scheme is almost fourth order
accurate in the discrete maximum
norm, uniformly in the perturbation parameter
. We present numerical
results in support of this result.
Received February 25, 1994 相似文献
110.
A robust and efficient adaptive reweighted estimator of multivariate location and scatter 总被引:1,自引:0,他引:1
Daniel Gervini 《Journal of multivariate analysis》2003,84(1):116-144
This article proposes a reweighted estimator of multivariate location and scatter, with weights adaptively computed from the data. Its breakdown point and asymptotic behavior under elliptical distributions are established. This adaptive estimator is able to attain simultaneously the maximum possible breakdown point for affine equivariant estimators and full asymptotic efficiency at the multivariate normal distribution. For the special case of hard-rejection weights and the MCD as initial estimator, it is shown to be more efficient than its non-adaptive counterpart for a broad range of heavy-tailed elliptical distributions. A Monte Carlo study shows that the adaptive estimator is as robust as its non-adaptive relative for several types of bias-inducing contaminations, while it is remarkably more efficient under normality for sample sizes as small as 200. 相似文献