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51.
Sparse approximate inverse (SAI) techniques have recently emerged as a new class of parallel preconditioning techniques for
solving large sparse linear systems on high performance computers. The choice of the sparsity pattern of the SAI matrix is
probably the most important step in constructing an SAI preconditioner. Both dynamic and static sparsity pattern selection
approaches have been proposed by researchers. Through a few numerical experiments, we conduct a comparable study on the properties
and performance of the SAI preconditioners using the different sparsity patterns for solving some sparse linear systems.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
52.
Three-dimensional (3-D) ZnO random-wall nanostructures and one-dimensional (1-D) ZnO nanorods were prepared on silicon substrates by a simple solid-vapour phase thermal sublimation technique. Optical pumped random lasing has been observed in the ZnO random-wall arrays with a threshold intensity of 0.38 MW/cm2 in the emission wavelength from 380 to 395 nm. The optical gain was attributed to the closed-loop scattering and light amplification of the ZnO random-wall. The experimental result suggests that the morphology of nanostructure is the key factor to effect random lasing. 相似文献
53.
Mursaleen 《Journal of Mathematical Analysis and Applications》2004,293(2):523-531
The idea of almost convergence for double sequences was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283-294] and they also characterized the four dimensional strong regular matrices. In this paper we define and characterize the almost strongly regular matrices for double sequences and apply these matrices to establish a core theorem. 相似文献
54.
Some non-singlet quasi-instabilities (QIs) cases that arise in the calculation of NMR-J parameters are analyzed within response theory. The relationship between ‘very close to zero’ eigenvalues of the principal propagator and the rate of convergency for specific coupling pathways is shown by a power series implemented to calculate the principal propagator matrix. A natural criterion for the analysis of the stability problem emerges from that series. This is more general and accurate compared with previous proposals. Its relationship with π-type molecular orbitals is given. We present an alternative scheme to minimize the effects of non-singlet QIs in such a way that the NMR-J parameters become close to the best theoretical calculations for H2CX (X=CH2, NH and O). 相似文献
55.
56.
B.E. Rhoades 《Journal of Mathematical Analysis and Applications》2003,277(1):375-378
We modify some of the conditions of the theorem to make it more applicable. 相似文献
57.
Frank N. Proske Madan L. Puri 《Proceedings of the American Mathematical Society》2003,131(9):2937-2944
In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.
58.
A q × n array with entries from 0, 1,…,q − 1 is said to form a difference matrix if the vector difference (modulo q) of each pair of columns consists of a permutation of [0, 1,… q − 1]; this definition is inverted from the more standard one to be found, e.g., in Colbourn and de Launey (1996). The following idea generalizes this notion: Given an appropriate δ (-[−1, 1]t, a λq × n array will be said to form a (t, q, λ, Δ) sign-balanced matrix if for each choice C1, C2,…, Ct of t columns and for each choice = (1,…,t) Δ of signs, the linear combination ∑j=1t jCj contains (mod q) each entry of [0, 1,…, q − 1] exactly λ times. We consider the following extremal problem in this paper: How large does the number k = k(n, t, q, λ, δ) of rows have to be so that for each choice of t columns and for each choice (1, …, t) of signs in δ, the linear combination ∑j=1t jCj contains each entry of [0, 1,…, q t- 1] at least λ times? We use probabilistic methods, in particular the Lovász local lemma and the Stein-Chen method of Poisson approximation to obtain general (logarithmic) upper bounds on the numbers k(n, t, q, λ, δ), and to provide Poisson approximations for the probability distribution of the number W of deficient sets of t columns, given a random array. It is proved, in addition, that arithmetic modulo q yields the smallest array - in a sense to be described. 相似文献
59.
Henrik Flyvbjerg 《Physica A》2004,340(4):552-558
The nature of self-organized criticality (SOC) is pin-pointed with a simple mechanical model: a pinball machine. Its phase space is fully parameterized by two integer variables, one describing the state of an on-going game, the other describing the state of the machine. This is the simplest possible SOC system, having only two degrees of freedom and no spatial correlations, yet is not solvable by analytical means. 相似文献
60.
In this paper we describe the general forms of all (nonlinear) continuous functionals on the sets of positive definite, positive semi-definite and Hermitian matrices which are multiplicative on the commuting elements. As a consequence, we obtain some new characterizations of the determinant on those classes of matrices.