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11.
This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R0-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically. 相似文献
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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
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Anzalone PW Baru AR Danielson EM Hayes PD Nguyen MP Panico AF Smith RC Mohan RS 《The Journal of organic chemistry》2005,70(6):2091-2096
[reaction: see text] Three one-pot methods for the conversion of aldehydes to homoallyl ethers catalyzed by Bi(OTf)(3).xH(2)O (1 < x < 4) have been developed. The one-pot synthesis of homoallyl ethers can be achieved either by in situ generation of the acetal followed by its reaction with allyltrialkylsilane or by a three-component synthesis in which the aldehyde, trimethylorthoformate or an alkoxytrimethylsilane and allyltrimethylsilane are mixed together in the presence of bismuth triflate (0.1-1.0 mol %). In addition, a three-component synthesis of homoallyl acetates, which is achieved by reacting the aldehyde, acetic anhydride, and allyltrimethylsilane in the presence of bismuth triflate (3.0-5.0 mol %), has been developed. The use of a relatively nontoxic, easy to handle, and inexpensive catalyst adds to the versatility of these methods. 相似文献
18.
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
19.
A. Lakshmi Sailaja K. Kishore Kumar D. V. R. Ravi Kumar C. Mohan Kumar N. M. Yugandhar G. Srinubabu 《Chromatographia》2007,65(5-6):359-361
A simple, rapid, and sensitive high-performance liquid chromatographic method for estimation of efavirenz in human plasma
has been developed and validated. Chromatography was performed with C18 analytical column and 50:50 acetonitrile–phosphate buffer (pH 3.5) as mobile phase. Compounds were monitored by UV detection
at 247 nm. The retention time for efavirenz was 6.45 min and that for the internal standard, nelfinavir, was 2.042 min. Response
was a linear over the concentration range of 0.1 μg–10 μg mL−1 in human plasma. The method was simple, specific, precise and accurate and was useful for bioequivalence and pharmacokinetic
studies of efavirenz. 相似文献
20.
A total synthesis of d-(+)-biotin is described starting from d-(+)-glucosamine using acyliminium chemistry. 相似文献