The Study of Minimax Inequalities, Abstract Economics and Applications to Variational Inequalities and Nash Equilibria

In this survey, a new minimax inequality and one equivalent geometricform are proved. Next, a theorem concerning the existence of maximalelements for an LC-majorized correspondence is obtained.By the maximal element theorem, existence theorems of equilibrium point fora noncompact one-person game and for a noncompact qualitative game withLC-majorized correspondences are given. Using the lastresult and employing 'approximation approach', we prove theexistence of equilibria for abstract economies in which the constraintcorrespondence is lower (upper) semicontinuous instead of having lower(upper) open sections or open graphs in infinite-dimensional topologicalspaces. Then, as the applications, the existence theorems of solutions forthe quasi-variational inequalities and generalized quasi-variationalinequalities for noncompact cases are also proven. Finally, with theapplications of quasi-variational inequalities, the existence theorems ofNash equilibrium of constrained games with noncompact are given. Our resultsinclude many results in the literature as special cases.     

Characterization of limits of Bayes procedures

For the problem of estimating the natural parameter of a p-dimensional exponential family, a characterization of regular limits of Bayes procedures is obtained which generalizes results of Sacks [14], Brown [3], and Berger and Srinivasan [1]. The form is deduced under regularity conditions for the loss function which are more general than squared error. As a corollary it is then stated that the class of procedures with this form is a complete class. The parameter space may be open, and when it is closed, the limits of Bayes procedures are generalized Bayes.     

Immobilization of a primary amine-containing drug,adriamycin

Literature reports have described the covalent coupling of the primary amine-containing anticancer drug, adriamycin, to polymeric supports through the amine group on the drug. These reports also have described drug mechanism studies with the immobilized adriamycin, where the release of the drug would undermine the validity of the conclusions. In the present paper, detailed experimental conditions are given for preparation of nonwater-soluble particles of polyvinyl alcohol by crosslinking water-soluble polyvinyl alcohol with 1,4-benzenedicarboxaldehyde, and for activation with cyanuric chloride and covalent attachment of adriamycin. The expected stability of this drug-support linkage against hydrolytic cleavage is compared mechanistically to that expected for less stable coupling through a carbamate linkage or for less stable coupling via an azomethine link.     

Mass transfer effects in microencapsulated hybridoma cells producing monoclonal antibodies

Rat-mouse and mouse-mouse hybridoma cell lines were used for formation of monoclonal antibodies (MAbs) in microcapsules of different sizes. Microcapsules were made of poly L-lysine-alginate hydrogel membranes. The effects of extracapsule liquid film, intra-capsule and transmembrane transfer limitations of nutrients/products on system’s performance were investigated. An agitation speed of 45 rpm (4 cm/s tip speed) was found to be optimal in spinner flasks to overcome liquid film resistances around capsules. Capsule sizes need to be reduced to smaller than 350 ε in order to eliminate intracapsule transfer limitations with a typical initial viable cell concentration of 0.5x10⁵ viable cells/mL capsule. Double coating of capsules to improve strength of capsules resulted in higher transmembrane transfer resistances.     

Elliptic Problems with Singular Potential and Double-Power Nonlinearity

We prove the existence of positive symmetric solutions to the semilinear elliptic problem

A half-moment model for radiative transfer in a 3D gray medium and its reduction to a moment model for hot, opaque sources

We present in this paper a new 3D half-moment model for radiative transfer in a gray medium, called the model, which uses maximum entropy closure. This model is a generalization to 3D of the 1D version recently proposed in (J. Comp. Phys. 180 (2002) 584). The direction space Ω is divided into two pieces, Ω⁺ and Ω^-, in a dynamical way by the plane perpendicular to the total radiative flux, and the half moments are defined from these subspaces. The model closure and the integrations of the radiative transfer equation performed on the moving Ω^± spaces are detailed. 1D planar results, which have motivated the extension of the model of (J. Comp. Phys. 180 (2002) 584) to multi-dimensions, are shown. These results are very good. The model is thereafter derived for 3D spherically symmetric geometry, where the correctness of the non-trivial border terms can be checked. Two 3D spherically symmetric problems are numerically solved in order to show the accuracy of the closure and the role of the border terms. Once again, compared to the solution obtained with a ray tracing solver, results are very good. From the 3D half-moment model, a new moment model, called , is derived for the particular case of a 3D hot and opaque source radiating into a cold medium, for applications such as simulations of stellar atmospheres and fires. Two-dimensional numerical results are presented and compared to those obtained solving the RTE and with other moment models. They demonstrate the very good accuracy of the model, its good convergence properties, and better prediction compared to all other existing moment models in its domain of applicability.     

Lyapunov modular functions

We prove a Lyapunov type theorem for modular functions on complemented lattices.     

Riemannian manifolds carrying a pair of skew symmetric conformal vector fields

We deal with a Riemannian manifoldM carrying a pair of skew symmetric conformal vector fields (X, Y). The existence of such a pairing is determined by an exterior differential system in involution (in the sense of Cartan). In this case,M is foliated by 3-dimensional totally geodesic submanifolds. Additional geometric properties are proved. Supported by a JSPS postdoctoral fellowship.     

On splitting of totally singular quadratic forms

In this note we completely study the standard splitting of quasi-Pfister forms and their neighbors, and we include some general results on standard splitting towers of totally singular quadratic forms. The author was supported by the European research network HPRN-CT-2002-00287 “AlgebraicK-Theory, Linear Algebraic Groups and Related Structures”.