Numerical resolution of an exact heat conduction model with a delay term

In this paper we analyze, from the numerical point of view, a dynamic thermoelastic problem. Here, the so-called exact heat conduction model with a delay term is used to obtain the heat evolution. Thus, the thermomechanical problem is written as a coupled system of partial differential equations, and its variational formulation leads to a system written in terms of the velocity and the temperature fields. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, from which the linear convergence of the algorithm could be derived under suitable additional regularity conditions. Finally, a two-dimensional numerical example is solved to show the accuracy of the approximation and the decay of the discrete energy.     

Optimal strategies with option compensation under mean reverting returns or volatilities

Computational Management Science - We study the problem of a fund manager whose contractual incentive is given by the sum of a constant and a variable term. The manager has a power utility function...     

Sobolev spaces on Lie groups: Embedding theorems and algebra properties

Let G be a noncompact connected Lie group, denote with ρ a right Haar measure and choose a family of linearly independent left-invariant vector fields X on G satisfying Hörmander's condition. Let χ be a positive character of G and consider the measure ${\mu }_{\chi }$ whose density with respect to ρ is χ. In this paper, we introduce Sobolev spaces $L_{\alpha }^p({\mu }_{\chi })$ adapted to X and ${\mu }_{\chi }$ ($1<p<\infty$, $\alpha \ge 0$) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and regularity results of solutions of some nonlinear heat and Schrödinger equations on the group.     

On the convergence toward nonequilibrium stationary states in thermostatted kinetic models

A differential equation‐based framework is suitable for the modeling of nonequilibrium complex systems if its solution is able to reach, as time goes to infinity, the related nonequilibrium steady states. The thermostatted kinetic theory framework has been recently proposed for the modeling of complex systems subjected to an external force field. The present paper is devoted to the mathematical proof of the convergence of the solutions of the thermostatted kinetic framework towards the related nonequilibrium stationary states. The proof of the main result is gained by employing the Fourier transform and distribution theory arguments.     

ATRP synthesis and association properties of thermoresponsive anionic block copolymers

Thermosensitive anionic block copolymers of sodium 2‐acrylamido‐2‐methylpropanesulfonate (AMPS) and N‐isopropylacrylamide (NIPAAM) with different block lengths were prepared by atom transfer radical polymerization (ATRP). Controlled polymerization was achieved by using ethyl 2‐chloropropionate (ECP) as initiator and CuCl/CuCl₂/tris(2‐dimethylaminoethyl)amine (Me₆TREN) catalytic system in DMF:water 50:50 (v/v) mixtures at 20 °C. Blocks lengths ranging from 36 to 98 repeating units were obtained. The association properties in aqueous solutions at different NaCl ionic strengths were studied as a function of temperature and polymer concentration by dynamic light scattering, fluorescence spectroscopy, and energy‐filtered transmission electron microscopy. The block copolymers with a higher pNIPAAM/pAMPS ratio formed spherical core‐shell type micelles independently of the ionic strength. The block copolymers with lower pNIPAAM/pAMPS ratio formed core‐shell type micelles at high ionic strength. Larger particles were observed at low ionic strength, which could be due to the formation of vesicles or compound micelles/micellar clusters. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4830–4842, 2008     

Electrochemical Kinetic Characterization of Redox Mediated Glucose Oxidase Reactions: A Simplified Approach

One of the main drawbacks affecting first‐generation electrochemical biosensors in the analysis of real matrices is the interference of electroactive species present in the sample under investigation. Several approaches have been attempted to overcome this problem in the past ten years but the best results were achieved by using mediated based electrochemical biosensors. Despite this, the kinetic of the redox mediators‐enzymatic proteins interaction has not been studied deeply enough. In this work we have developed a theoretical‐methodological approach for the characterization of the kinetic of interaction between redox enzymes and substrates and/or redox mediators. Particularly, the interaction of glucose oxidase (GOx) with several commercially available redox mediators has been studied by means of amperometry and cyclic voltammetry. The main kinetic parameters for different mediators were exploited and discussed with the aim of finding the best mediator for a glucose biosensor to be used on real samples.     

Periods for flat algebraic connections

In previous work (Hien, Math. Ann. 337, 631–669, 2007), we established a duality between the algebraic de Rham cohomology of a flat algebraic connection on a smooth quasi-projective surface over the complex numbers and the rapid decay homology of the dual connection relying on a conjecture by C. Sabbah. In the present article, we generalize this result to arbitrary dimensions unconditionally using recent results of T. Mochizuki.     

Hessian orders and multinormal distributions

Several well known integral stochastic orders (like the convex order, the supermodular order, etc.) can be defined in terms of the Hessian matrix of a class of functions. Here we consider a generic Hessian order, i.e., an integral stochastic order defined through a convex cone of Hessian matrices, and we prove that if two random vectors are ordered by the Hessian order, then their means are equal and the difference of their covariance matrices belongs to the dual of . Then we show that the same conditions are also sufficient for multinormal random vectors. We study several particular cases of this general result.     

Linking solutions for p-Laplace equations with nonlinearity at critical growth

Under a suitable condition on n and p, the quasilinear equation at critical growth −Δpu=λ|u|^p−2u+|u|^p∗−2u is shown to admit a nontrivial weak solution for any λ?λ₁. Nonstandard linking structures, for the associated functional, are recognized.