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21.
We study the stationary measure for the two-dimensional Boussinesq equation with random forcing. We prove the ergodicity for the two-dimensional stochastically forced Boussinesq equation. We also study the Galerkin truncations of the three-dimensional Boussinesq equations under degenerate stochastic forcing. We follow closely the previous results on the stochastically forced Navier–Stokes equations. 相似文献
22.
用A的不变子空间作参数,给出了算子方程AX=XAX的全部解。当A是单射或稠值域时,或者当A是正规算子时,给出了算子方程AX=XA=XAX的全部解。我们还给出正规算子X是算子方程AX=XZ=XAX的解的充分必要条件。 相似文献
23.
Gerhard Starke 《Numerische Mathematik》1997,78(1):103-117
Summary. The convergence rate of Krylov subspace methods for the solution of nonsymmetric systems of linear equations, such as GMRES
or FOM, is studied. Bounds on the convergence rate are presented which are based on the smallest real part of the field of
values of the coefficient matrix and of its inverse. Estimates for these quantities are available during the iteration from
the underlying Arnoldi process. It is shown how these bounds can be used to study the convergence properties, in particular,
the dependence on the mesh-size and on the size of the skew-symmetric part, for preconditioners for finite element discretizations
of nonsymmetric elliptic boundary value problems. This is illustrated for the hierarchical basis and multilevel preconditioners
which constitute popular preconditioning strategies for such problems.
Received May 3, 1996 相似文献
24.
Aït Hmaïdouch L. Mançour Billah S. El Hadek M. 《Journal of Thermal Analysis and Calorimetry》2002,69(2):659-667
The solid—liquid equilibria of the ternary system H2O—Al(NO3)3—Mg(NO3)2 were studied at –30, –20, –10 and 0°C by using a synthetic method which allows to detemine all the characteristic points of isothermal sections. The stable solid phases which appear are respectively: ice, Al(NO3)3·9H2O, Mg(NO3)2·9H2O and Mg(NO3)2·6H2O. Neither double salts nor mixed crystals are observed in the temperature and composition field studied. Polytherm diagram layout show two invariant transformations correspond with an eutectic point and a peritectic point.This revised version was published online in November 2005 with corrections to the Cover Date. 相似文献
25.
G. A. Watson 《Advances in Computational Mathematics》1994,2(4):393-405
The orthogonal Procrustes problem involves finding an orthogonal matrix which transforms one given matrix into another in
the least-squares sense, and thus it requires the minimization of the Frobenius matrix norm. We consider, the solution of
this problem for a family of orthogonally invariant norms which includes the Frobenius norm as a special case. 相似文献
26.
S.V. Astashkin F.A. Sukochev 《Journal of Mathematical Analysis and Applications》2007,336(2):1231-1258
We catalogue all Marcinkiewicz function and sequence spaces with the Banach-Saks property and present necessary and sufficient conditions for a wide subclass of spaces to possess the p-Banach-Saks property, 1<p<∞. We apply our results to several open problems. 相似文献
27.
A ring R has right SIP (SSP) if the intersection (sum) of two direct summands of R is also a direct summand. We show that the right SIP (SSP) is the Morita invariant property. We also prove that the trivial extension of R by M has SIP if and only if R has SIP and (1 – e)Me = 0 for every idempotent e in R. Moreover, we give necessary and sufficient conditions for the generalized upper triangular matrix rings to have SIP. 相似文献
28.
设x:M→S^n+1(n≥23)是n+1-维单位球中的无脐点超曲面,Moebius不变量G,Ф,A和B分别表示x的Moebius度量,Moebius形式,Blaschke形式和Moebius第二基本形式.本文证明了如果x的Moebius形式圣平行,并且A+λG+μB=0,其中λ,μ分别是定义在M上的光滑函数,那么Ф=0,由此及李海中、王长平(2003年)文献中的分类定理给出了眇州中具有平行的Moebius形式及满足A+λG+μB=0的超曲面的分类.此结果推广了他们及张廷枋(2003年)文献中的结果. 相似文献
29.
A generalized linear differential equation in a Banach space is studied. The construction of a phase space and solutions with the help of the spectral theory of linear operators, ergodic theorems, and degenerate semigroups of linear operators is carried out. 相似文献
30.
How can the basic compatibility of theory and observations be investigated for nonlinear processes without requiring stochastic characterizations for residual error terms? The present paper proposes a flexible least-cost approach. For each possible estimatex for the sequence of process states, letc D (x) andx M(x) denote the costs incurred for deviations away from the prior dynamic specifications and prior measurement specifications, respectively. Define the cost-efficiency frontier to be the greatest lower bound for the set of all possible cost pairs [c D (x),c M(x)], conditional on the given observations. State sequence estimatesx that attain the cost-efficiency frontier indicate the possible ways that the actual process could have developed over time in a manner minimally incompatible with the prior dynamic and measurement specifications. An algorithm is developed for the exact sequential updating of the cost-efficient state sequence estimates as the duration of the process increases and additional observations are obtained. 相似文献