Joint probabilities of noncommuting operators and incompleteness of quantum mechanics

We use joint probabilities to analyze the EPR argument in the Bohm's example of spins.⁽¹⁾ The properties of distribution functions for two, three, or more noncommuting spin components are explicitly studied and their limitations are pointed out. Within the statistical ensemble interpretation of quantum theory (where only statements about repeated events can be made), the incompleteness of quantum theory does not follow, as the consistent use of joint probabilities shows. This does not exclude a completion of quantum mechanics, going beyond it, by a more general theory of single events, using hidden variables, for example.     

All Loop Topological String Amplitudes from Chern-Simons Theory

We demonstrate the equivalence of all loop closed topological string amplitudes on toric local Calabi-Yau threefolds with computations of certain knot invariants for Chern-Simons theory. We use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera. In particular we explicitly compute the topological string amplitudes for ² up to degree 12 and ¹× ¹ up to total degree 10 to all genera. This also leads to certain novel large N dualities in the context of ordinary superstrings, involving duals of type II superstrings on local Calabi-Yau three-folds without any fluxes.This research is supported in part by NSF grants PHY-9802709 and DMS-0074329     

On fractional powers of a pair of matrices and a plate-beam problem

In this paper we consider the transversal deflections of a dynamically-coupled Von Kármán system consisting of a plate which has a beam attached to its one edge. The problem is considered in the form of a non-linear evolution problem in a product space. We show the existence of a unique local solution by following a fractional powers approach to first construct a “weak” solution in a larger space. Regularity properties for this solution yield a unique local strong solution for the original boundary-value problem. This approach entails the introduction of fractional powers of a pair of matrices.     

A note on Robinson–Ursescu and Lyusternik–Graves theorem

The aim of this note is twofold. First, we prove an analogue of the well-known Robinson–Ursescu Theorem on the relative openness with a linear rate (restrictive metric regularity) of a multivalued mapping. Second, we prove a generalization of Graves Open Mapping Theorem for a class of mappings which can be approximated at a reference point by a bunch of linear mappings. The approximated non-linear mapping is restricted to a closed convex subset of a Banach space.     

Reproducing Subgroups of Sp(2,\mathbb{R}). Part I: Algebraic Classification

We classify the connected Lie subgroups of the symplectic group $Sp(2,{\mathbb{R}})$ whose elements are matrices in block lower triangular form. The classification is up to conjugation within $Sp(2,{\mathbb{R}})$ . Their study is motivated by the need of a unified approach to continuous 2D signal analyses, as those provided by wavelets and shearlets.     

Preparation of 3-(4-chlorophenyl)-2-(2-aminothiazol-4-yl)-5-methoxybenzo[b]furan derivatives and their leukotriene B(4) inhibitory activity

A series of 3-(4-chlorophenyl)-2-(2-aminothiazol-4-yl)benzo[b]furan derivatives 6-10 were prepared and their leukotriene B(4) inhibitory activity was evaluated. We found that several compounds showed strong inhibition of calcium mobilization in CHO cells overexpressing human BLT(1) and BLT(2) receptors. Among them, 3-(4-chlorophenyl)-2-[5-formyl-2-[(dimethylamino)methyleneamino]thiazol-4-yl]-5-methoxybenzo[b]furan 9b showed the most potent and selective inhibition for the human BLT(2) receptor, and its IC(50) value was smaller than that of the selected positive control compound, ZK-158252.     

Deformation and Flow Driven by Osmotic Processes in Porous Materials: Application to Bituminised Waste Materials

This paper presents a coupled Chemo-Hydro-Mechanical (CHM) analysis of the behaviour of leached Bituminized Waste materials (BW). Under geological disposal conditions the main factor that affects the long-term behaviour of this kind of materials is water uptake. First, the long-term behavior of BW in contact with water has been studied. A formulation has been proposed for the analysis of deformation induced by dissolution of salts in porous media in contact with water. The equations include the effect of coupled transport phenomena and the formulation has been included as an extension in the coupled THM program CODE_BRIGHT. The impact of osmotic forces on the swelling of the material has been investigated by simulating water uptake swelling tests under confined conditions. The numerical analysis has proven to be able to furnish a satisfactory representation of the main observed patterns of the behaviour. A sensitivity analysis has also been carried out to examine the effect of various key parameters.     

Keller-Osserman type conditions for differential inequalities with gradient terms on the Heisenberg group

We study the qualitative behavior of non-negative entire solutions of differential inequalities with gradient terms on the Heisenberg group. We focus on two classes of inequalities: Δφu?f(u)l(|∇u|) and Δφu?f(u)−h(u)g(|∇u|), where f, l, h, g are non-negative continuous functions satisfying certain monotonicity properties. The operator Δφ, called the φ-Laplacian, generalizes the p-Laplace operator considered by various authors in this setting. We prove some Liouville theorems introducing two new Keller-Osserman type conditions, both extending the classical one which appeared long ago in the study of the prototype differential inequality Δu?f(u) in Rm. We show sharpness of our conditions when we specialize to the p-Laplacian. While proving these results we obtain a strong maximum principle for Δφ which, to the best of our knowledge, seems to be new. Our results continue to hold, with the obvious minor modifications, also for Euclidean space.