Some geometrical aspects of semidefinite linear complementarity problems

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.     

Uniform convergence of Galerkin‐multigrid methods for nonconforming finite elements for second‐order problems with less than full elliptic regularity

In this article we prove uniform convergence estimates for the recently developed Galerkin‐multigrid methods for nonconforming finite elements for second‐order problems with less than full elliptic regularity. These multigrid methods are defined in terms of the “Galerkin approach,” where quadratic forms over coarse grids are constructed using the quadratic form on the finest grid and iterated coarse‐to‐fine intergrid transfer operators. Previously, uniform estimates were obtained for problems with full elliptic regularity, whereas these estimates are derived with less than full elliptic regularity here. Applications to the nonconforming P₁, rotated Q₁, and Wilson finite elements are analyzed. The result applies to the mixed method based on finite elements that are equivalent to these nonconforming elements. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 203–217, 2002; DOI 10.1002/num.10004     

Different acute effects of oral and intratracheal administration of disodium arsenate and gallium arsenide on heme synthesis in rats

The acute influences of arsenic compounds on the metabolism of porphyrins and heme in various organs of rats after oral or intratracheal administration of disodium arsenate (Na₂HAsO₄) and gallium arsenide (GaAs) were examined and compared. For the oral administration experiments, 21 or 84 mg of Na₂HAsO₄, or 2 or 4 g of GaAs, per cm³ saline per kg body weight of each animal was administered to Jcl: Wistar male rats and the organs were removed after exsanguination from the vein of the right axilla under anesthesia with ether, 16 h after administration. In the case of intratracheal administration, rats given 8.2 or 16.4 mg of Na₂HAsO₄, or 0.2 or 0.4 g GaAs per cm³ saline per kg body weight were examined under the same experimental conditions as for the administration route. Increase in the body weight of rats was suppressed after intratracheal administration of the two arsenic compounds. In these rats the hematocrit value increased significantly. These changes were not shown by the orally administered rats. Elevation in δ-aminolevulinate synthase (ALA-S, EC 2.3.1.37) activity in erythroblasts by Na₂HAsO₄ was much higher after intratracheal administration than after oral administration. Suppression in the activities of δ-aminolevulinate dehydratase (ALA-D, EC 4.2.1.24) and porphobilinogen deaminase (PBG-D, EC 4.3.1.8) in peripheral erythrocytes by Na₂HAsO₄ and GaAs were stronger by intratracheal administration than by the oral route. Influences of GaAs on the activity of PBG-D in rat liver were shown to be more effective by oral administration than by the intratracheal route. Oral administration of Na₂HAsO₄ and GaAs had a stronger suppression effect on the activities of ALA-D and PBG-D in rat kidney. It seems from these results that the different extents of the influence of arsenic compounds might depend on the routes of intake.     

Synthesis of functional polymers—Vinylidene fluoride based fluorinated copolymers and terpolymers bearing bromoaromatic side‐group

The radical co‐ and terpolymerization of 4‐[(α,β,β‐trifluorovinyl)oxy]bromo benzene (TFVOBB) with 1,1‐difluoroethylene (or vinylidene fluoride, VDF, or VF₂), hexafluoropropene (HFP), perfluoromethyl vinyl ether (PMVE), and chlorotrifluroroethylene (CTFE) is presented. Although TFVOBB could be thermocyclodimerized, it could not homopolymerize under radical initiation. TFVOBB could be copolymerized in solution under a radical initiator with VDF or CTFE comonomers, while its copolymerization with HFP or PMVE were unsuccessful. The terpolymerization of TFVOBB with VDF and HFP, or VDF and PMVE, or VDF and CTFE also led to original fluorinated terpolymers bearing bromoaromatic side‐groups. The conditions of co‐ and terpolymerization were optimized in terms of the nature of the radical initiators, and of the nature of solvents (fluorinated or nonhalogenated). Various monomer concentrations in the co‐ and terpolymers were assessed by ¹⁹F and ¹H‐NMR spectroscopy. The thermal and physico chemical properties were also studied. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5077–5097, 2004     

Influence of concentration on the activation energy for diffusion in polymer-solvent systems

The self-diffusion of benzene, toluene, and ethylbenzene in polystyrene have been analyzed using the Vrentas/Duda free-volume diffusion model. Diffusion coefficient predictions suggest an exponential concentration dependence of the activation energy required to overcome attractive forces, E. Without the use of any diffusion data approximating E as zero over the entire concentration range yields self-diffusion coefficient predictions which are in good agreement with experimental data. © 1992 John Wiley & Sons, Inc.     

Dialdehyde starch‐crosslinked chitosan films and their antimicrobial effects

For improved mechanical and water‐swelling properties of chitosan films, a series of transparent films were prepared with dialdehyde starch as a crosslinking agent. Fourier transform infrared and X‐ray analysis results demonstrated that the formation of Schiff's base disturbed the crystallization of chitosan. The mechanical properties and water‐swelling properties of the films were significantly improved. The best values of the tensile strength and breaking elongation were 113.1 MPa and 27.0%, respectively, when the dialdehyde starch content was 5%. All the crosslinked films still retained obvious antimicrobial effects toward S. aureus and E. coli, and they showed potential for biomedical applications. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 993–997, 2003     

Linearized and rational approximation method for solving non‐linear Burgers' equation

A new numerical method called linearized and rational approximation method is presented to solve non‐linear evolution equations. The utility of the method is demonstrated for the case of differentiation of functions involving steep gradients. The solution of Burgers' equation is presented to illustrate the effectiveness of the technique for the solution of non‐linear evolution equations exhibiting nearly discontinuous solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Some remarks on indiscernible sequences

We prove a property of generic homogeneity of tuples starting an infinite indiscernible sequence in a simple theory and we use it to give a shorter proof of the Independence Theorem for Lascar strong types. We also characterize the relation of starting an infinite indiscernible sequence in terms of coheirs.