A proximal method with separable Bregman distances for quasiconvex minimization over the nonnegative orthant

We present an interior proximal method with Bregman distance, for solving the minimization problem with quasiconvex objective function under nonnegative constraints. The Bregman function is considered separable and zone coercive, and the zone is the interior of the positive orthant. Under the assumption that the solution set is nonempty and the objective function is continuously differentiable, we establish the well definedness of the sequence generated by our algorithm and obtain two important convergence results, and show in the main one that the sequence converges to a solution point of the problem when the regularization parameters go to zero.     

Topological sensitivity analysis of a multi‐scale constitutive model considering a cracked microstructure

This paper deals with the sensitivity analysis of the macroscopic elasticity tensor to topological microstructural changes of the underlying material. In particular, the microstucture is topologicaly perturbed by the nucleation of a small circular inclusion. The derivation of the proposed sensitivity relies on the concept of topological derivative, applied within a variational multi‐scale constitutive framework where the macroscopic strain and stress at each point of the macroscopic continuum are defined as volume averages of their microscopic counterparts over a representative volume element (RVE) of material associated with that point. We consider that the RVE can contain a number of voids, inclusions and/or cracks. It is assumed that non‐penetration conditions are imposed at the crack faces, which do not allow the opposite crack faces to penetrate each other. The derived sensitivity leads to a symmetric fourth‐order tensor field over the unperturbed RVE domain, which measures how the macroscopic elasticity parameters estimated within the multi‐scale framework changes when a small circular inclusion is introduced at the micro‐scale level. Copyright © 2009 John Wiley & Sons, Ltd.     

Holomorphic rank of hypersurfaces with an isolated singularity

LetV be a germ at 0 C ²,n3, of hypersurface with an isolated singularity at 0. In this paper we prove that the maximal number of germs of vector fields inV ^*=V–0, which are linearly independent in all points ofV ^* is two. In the casesn=3,4 and of quasi homogeneous hypersurfaces (n3), we prove that this number is one.Dedicated to the memory of R. MañéThis research was partially supported by Pronex.     

The Borsuk�CUlam theorem for homotopy spherical space forms

In this work, we show for which odd-dimensional homotopy spherical space forms the Borsuk–Ulam theorem holds. These spaces are the quotient of a homotopy odd-dimensional sphere by a free action of a finite group. Also, the types of these spaces which admit a free involution are characterized. The case of even-dimensional homotopy spherical space forms is basically known.     

A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires

In this paper, we introduce a new proximal algorithm for equilibrium problems on a genuine Hadamard manifold, using a new regularization term. We first extend recent existence results by considering pseudomonotone bifunctions and a weaker sufficient condition than the coercivity assumption. Then, we consider the convergence of this proximal-like algorithm which can be applied to genuinely Hadamard manifolds and not only to specific ones, as in the recent literature. A striking point is that our new regularization term have a clear interpretation in a recent “variational rationality” approach of human behavior. It represents the resistance to change aspects of such human dynamics driven by motivation to change aspects. This allows us to give an application to the theories of desires, showing how an agent must escape to a succession of temporary traps to be able to reach, at the end, his desires.

     

Control of Crystallization Kinetics and Study of the Thermal, Structural and Morphological Properties of an Li2O–B2O3–Al2O3 Vitreous System

A glass matrix with nominal composition 50Li₂O·45B₂O₃·5Al₂O₃ (mol%) was synthesized, and its physical properties were investigated by differential thermal analysis (DTA), X-ray diffraction (XRD), and atomic force microscopy (AFM). The glass transition temperature T _g, the crystallization-onset temperature T _x,, the crystallization peak temperatures T _c1 and T _c2, and the fusion peak temperatures T _m1 and T _m2 were determined from at least two glass matrix phases to be approximately 382, 457, 486, 574, 761, and 787?°C, respectively, at 5?°C/min heating rate. Heat treatments at 450?°C for an increasing sequence of time intervals allowed control over the amount of crystallization. Additional information on the crystallization kinetics for the LBA glass matrix was gathered from AFM images, DTA thermograms, and XRD diffractograms. The latter technique showed that LiBO₂ (ICDD-16568) and Li₃AlB₂O₆ (ICDD-51754) phases are formed in the glass?Cceramic system. Debye?CScherrer analysis of the XRD peaks revealed a competition between the evolutions of crystal phases during heat treatment. Activation energies for crystallization, obtained from theoretical models applied to the DTA data showed that the crystallization is heterogeneous. The AFM images demonstrated that this heterogeneous crystallization starts at the surface of the LBA glass matrix and identified crystal sizes in agreement with the results of the Debye?CScherrer analysis. Our study shows that thermal and structural characterization techniques can be combined with theoretical results drawn from well-tested models to offer a unified view of crystallization in a glass?Cceramics system.     

Spectral editing of 13C cp/MAS NMR spectra of complex systems: application to the structural characterisation of cork cell walls

A mathematical method of obtaining 13C CP/MAS subspectra of single components of a complex system is presented and applied to three- and four-component systems. The method is based on previously reported work that exploits different proton relaxation properties for different domains of an heterogeneous system. However, unlike the original method that obtained subspectra through a trial-and-error approach, the method here presented solves the problem mathematically, thus avoiding the time-consuming and non-rigorous trial-and-error step. The method is applied to mixtures of three and four polymers and to a more complex system: cork cell walls. As expected, as the number of components increases, the sharing of relaxation properties between different components is increasingly probable, either due to incidental coincidence of relaxation times or to specific interactions and intimate mixing of compounds. While this hinders the calculation of the subspectra of single chemical components, it may provide useful information about inter-component interactions. This possibility was demonstrated by the application of this method to cork cell walls. Both three-component and four-component approaches showed that three domains exist in cork cell walls: carbohydrate/lignin matrix, mobile suberin close to (probably bonded to) lignin groups (about 42% w/w) and hindered suberin close to (probably bonded to) carbohydrate-OCH2O groups (about 4% w/w).     

Alternative Entropy Measures and Generalized Khinchin–Shannon Inequalities

The Khinchin–Shannon generalized inequalities for entropy measures in Information Theory, are a paradigm which can be used to test the Synergy of the distributions of probabilities of occurrence in physical systems. The rich algebraic structure associated with the introduction of escort probabilities seems to be essential for deriving these inequalities for the two-parameter Sharma–Mittal set of entropy measures. We also emphasize the derivation of these inequalities for the special cases of one-parameter Havrda–Charvat’s, Rényi’s and Landsberg–Vedral’s entropy measures.     

Symmetries and induced effects in bilayer and multilayer antiferroelectric and ferrielectric liquid crystal phases

The stable antiferroelectric and ferrielectric smectic phases which may arise below a chiral SmA* phase are investigated theoretically. The symmetry and physical properties of the bilayer and multilayer configurations are worked out. Antiferroelectric and ferrielectric bilayer and multilayer configurations, possessing an induced spontaneous ferroelectric polarization component perpendicular to the smectic layers, are shown to take place, as the result of a nonlinear piezoelectric effect. These states of low polar symmetries occur when the angle between the inlayer projections of the dipoles and the director of the molecules is different from 90 degrees.