Pointwise gradient estimates of solutions to onedimensional nonlinear parabolic equations

We present here an improved version of the method introduced by the first author to derive pointwise gradient estimates for the solutions of one-dimensional parabolic problems. After considering a general qualinear equation in divergence form we apply the method to the case of a nonlinear diffusion-convection equation. The conclusions are stated first for classical solutions and then for generalized and mild solutions. In the case of unbounded initial datum we obtain several regularizing effects for t > 0. Some unilateral pointwise gradient estimates are also obtained. The case of the Dirichlet problem is also considered. Finally, we collect, in the last section, several comments showing the connections among these estimates and the study of the free boundaries associated to the solutions of the diffusion-convection equation.     

The K–nucleus cross sections in relativistic non-linear models

The K⁺−nucleus cross sections have been calculated in relativistic non-linear models taking into account the in-medium modifications of nucleons and mesons properties. More precisely, we have taken into account both the dressing of the nucleon effective mass by the scalar nuclear field in the target and the coupling of the mesons exchanged between the K⁺ and the nucleons to the polarization of the medium. First, using the most recent relativistic non-linear models, the in-medium σ, ω and ρ meson masses have been obtained in the nuclear matter rest frame. The influence of the non-linear contributions on the K⁺−nucleus cross sections has then been studied. Finally, we have compared our results with the experimental data.     

Approximation of a laminated microstructure for a rotationally invariant,double well energy density

Summary. We give error estimates for the approximation of a laminated microstructure which minimizes the energy for a rotationally invariant, double well energy density . We present error estimates for the convergence of the deformation in the convergence of directional derivatives of the deformation in the “twin planes,” the weak convergence of the deformation gradient, the convergence of the microstructure (or Young measure) of the deformation gradients, and the convergence of nonlinear integrals of the deformation gradient. Received July 25, 1995 / Revised version received November 20, 1995     

Holomorphic Maps of Compact Generalized Hopf Manifolds

We investigate holomorphic maps between compact generalized Hopf manifolds (i.e., locally conformal Kähler manifolds with parallel Lee form). We show that they preserve the canonical foliations. Moreover, we study compact complex submanifolds of g.H. manifolds and holomorphic submersions from compact g.H. manifolds.     

Lower bounds for the discrepancy of triples of inversive congruential pseudorandom numbers with power of two modulus

This paper deals with the inversive congruential method with power of two modulusm for generating uniform pseudorandom numbers. Statistical independence properties of the generated sequences are studied based on the distribution of triples of successive pseudorandom numbers. It is shown that there exist parameters in the inversive congruential method such that the discrepancy of the corresponding point sets in the unit cube is of an order of magnitude at leastm ^–1/3. The method of proof relies on a detailed analysis of certain rational exponential sums.     

Défaut d'exactitude des modéles¶de Néron toriques sur un corps local

Let R be a complete discrete valuation ring with mixed characteristic. Denote by K its field of fractions and by k its residue field. Let 0 →A ^K →B ^K →C ^K → 0 be an exact sequence of abelian varieties over K and consider the corresponding complex of Nérons models 0 →A→B→C→ 0, over R. We assume that the identity component B _k ⁰ of the special fibre B _k of B is a torus and we study the defect of exactmess at B in this last sequence.

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Re?u: 4 décembre 1997/ Version revisée: 15 décembre 1997     

Total absolute curvature and tightness of noncompact manifolds

In the first part we prove an extension of the Chern-Lashof inequality for noncompact immersed manifolds with finitely many ends. For this we give a lower bound of the total absolute curvature in terms of topological invariants of the manifold. In the second part we discuss tightness properties for such immersions. Finally, we give an upper bound for the substantial codimension.

     

Existence for a degenerate diffusion problem with a nonlinear operator

We study a degenerate nonlinear variational inequality which can be reduced to a multivalued inclusion by an appropriate change of the unknown function. We establish existence, uniqueness and regularity results. An application arising in the theory of water diffusion in porous media is discussed as an example.      

Ab initio study of the electronic structures and conduction properties of some novel low band-gap donor-acceptor polymers

The results of the electronic structures and conduction properties of four novel donor-acceptor polymers based on polysilole, obtained on the basis of ab initio Hartree-Fock crystal orbital method using their optimized geometries, are reported. The repeat unit of these polymers consists of bicyclopentadisilole unit bridged by an electron-accepting group Y(Y=CCH₂ in PSICH, CO in PSICF, CCF₂ and CC(CN)₂ in PSICN). All the polymers on the basis of their geometries and π-bond order values are found to have benzenoid-type electronic structures. Comparison of the important electronic properties such as ionization potential, electron affinity and band-gap of these polymers indicates PSICN to be the best candidate for intrinsic conductivity and reductive (n-) doping while PSICH is predicted to be the best candidate for oxidative (p-) doping. All these polymers are estimated to have band-gap values ranging between 1 and 2 eV. The low band-gap values of these polymers are rationalised on the basis of the patterns of their frontier orbitals.