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61.
Mohan Namasivayam 《Annali di Matematica Pura ed Applicata》1986,144(1):157-172
Summary
Integral representations of junctions in the anisotropic Sobolev spaces
on unbounded domains are used in the study of the embeddings of these spaces into Lebesgue spaces. Estimates of entropy numbers of the embedding
are obtained, where k, p and q satisfy certain conditions and where is a certain type of quasibounded domain, 相似文献
62.
The generalized linear complementarity problem revisited 总被引:5,自引:0,他引:5
Given a vertical block matrixA, we consider in this paper the generalized linear complementarity problem VLCP(q, A) introduced by Cottle and Dantzig. We formulate this problem as a linear complementarity problem with a square matrixM, a formulation which is different from a similar formulation given earlier by Lemke. Our formulation helps in extending many
well-known results in linear complementarity to the generalized linear complementarity problem. We also show that the class
of vertical block matrices which Cottle and Dantzig's algorithm can process is the same as the class of equivalent square
matrices which Lemke's algorithm can process. We also present some degree-theoretic results on a vertical block matrix. 相似文献
63.
Hari Bercovici Vittorino Pata 《Proceedings of the American Mathematical Society》2000,128(4):1011-1015
Hincin characterized the class of infinitely divisible distributions on the line as the class of all distributional limits of sums of infinitesimal independent random variables. We show that an analogue of this characterization is true in the addition theory of free random variables introduced by Voiculescu.
64.
Comparison of multigrid algorithms for high‐order continuous finite element discretizations 下载免费PDF全文
Hari Sundar Georg Stadler George Biros 《Numerical Linear Algebra with Applications》2015,22(4):664-680
We present a comparison of different multigrid approaches for the solution of systems arising from high‐order continuous finite element discretizations of elliptic partial differential equations on complex geometries. We consider the pointwise Jacobi, the Chebyshev‐accelerated Jacobi, and the symmetric successive over‐relaxation smoothers, as well as elementwise block Jacobi smoothing. Three approaches for the multigrid hierarchy are compared: (1) high‐order h‐multigrid, which uses high‐order interpolation and restriction between geometrically coarsened meshes; (2) p‐multigrid, in which the polynomial order is reduced while the mesh remains unchanged, and the interpolation and restriction incorporate the different‐order basis functions; and (3) a first‐order approximation multigrid preconditioner constructed using the nodes of the high‐order discretization. This latter approach is often combined with algebraic multigrid for the low‐order operator and is attractive for high‐order discretizations on unstructured meshes, where geometric coarsening is difficult. Based on a simple performance model, we compare the computational cost of the different approaches. Using scalar test problems in two and three dimensions with constant and varying coefficients, we compare the performance of the different multigrid approaches for polynomial orders up to 16. Overall, both h‐multigrid and p‐multigrid work well; the first‐order approximation is less efficient. For constant coefficients, all smoothers work well. For variable coefficients, Chebyshev and symmetric successive over‐relaxation smoothing outperform Jacobi smoothing. While all of the tested methods converge in a mesh‐independent number of iterations, none of them behaves completely independent of the polynomial order. When multigrid is used as a preconditioner in a Krylov method, the iteration number decreases significantly compared with using multigrid as a solver. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
65.
We introduce the notion of a complementary cone and a nondegenerate linear transformation and characterize the finiteness of the solution set of a linear complementarity problem over a closed convex cone in a finite dimensional real inner product space. In addition to the above, other geometrical properties of complementary cones have been explored. 相似文献
66.
Three-dimensional quantitative structure–activity relationship (3D-QSAR) models were developed based on comparative molecular
field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA), on a series of 43 hydroxyethylamine
derivatives, acting as potent inhibitors of β-site amyloid precursor protein (APP) cleavage enzyme (BACE-1). The crystal structure of the BACE-1 enzyme (PDB ID: 2HM1)
with one of the most active compound 28 was available, and we assumed it to be the bioactive conformation of the studied series, for 3D-QSAR analysis. Statistically
significant 3D-QSAR model was established on a training set of 34 compounds, which were validated by a test set of 9 compounds.
For the best CoMFA model, the statistics are, r
2 = 0.998, r2cv = 0.810{r^{2}_{\rm cv} = 0.810} , n = 34 for the training set and r2pred = 0.934{r^{2}_{\rm pred} = 0.934} , n = 9 for the test set. For the best CoMSIA model (combined steric, electrostatic, hydrophobic, and hydrogen bond donor fields),
the statistics are r
2 = 0.978, r2cv = 0.754{r^{2}_{\rm cv} = 0.754} , n = 34 for the training set and r2pred = 0.750{r^{2}_{\rm pred} = 0.750} , n = 9 for the test set. The resulting contour maps, produced by the best CoMFA and CoMSIA models, were used to identify the
structural features relevant to the biological activity in this series of analogs. The data generated from the present study
will further help to design novel, potent, and selective BACE-1 inhibitors. 相似文献
67.
Shy-Der Lin Shuoh-Jung Liu Han-Chun Lu Hari Mohan Srivastava 《Czechoslovak Mathematical Journal》2013,63(4):969-987
The main object of this paper is to investigate several general families of hyper-geometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials of the first and second kinds. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials. 相似文献
68.
In this paper global asymptotic stability and asymptotic behaviour of solutions of nonlinear delay difference equations has been studied and a few sets of sufficient conditions for global asymptotic stability are derived. 相似文献
69.
为了能在双模态超燃冲压发动机流道方案初步论证中提供一种较快速的发动机性能计算方法,在二维N-S方程基础上,引入一维完全燃烧计算方法,提出了预估超燃冲压发动机性能的准二维计算方法。该方法能够计入激波、边界层分离等对发动机性能的影响,可在较短时间计算出整机推力、比冲性能和沿程热力学参数。通过对自由射流发动机计算,验证了此方法。并在此基础上,初步分析了燃料喷注位置和流道构型对发动机性能的影响。 相似文献
70.
[(Ph3PCu(I))6{(CH2)4Sn(IV)S2}6Cu(I)4Sn(II)], a walnut-type, heterometallic, heterovalent cluster, as confirmed by density functional theory calculations, was obtained under reductive solvothermal conditions and features an unprecedented metalloid core within a metal sulfide shell and an organic surface. 相似文献