Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...

the second law of thermodynamic (entropy principle) is of special theo-philosophical importance. it seems that this law, which is renowned as “the death of software design” and despite the order in the world, is like an incompatible universal. this article examines the concept of entropy in the three temperature, statistic, and information applications and addresses the contradiction of the sec...

In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

The free energies of adsorption of the monomer or dimer of the cationic beta-hairpin antimicrobial peptide protegrin-1 (PG1) in a specific binding orientation on a lipid bilayer are determined using molecular dynamics (MD) simulations and Poisson-Boltzmann calculations. The bilayer is composed of anionic palmitoyl-oleoyl-phosphatidylglycerol (POPG) and palmitoyl-oleoyl-phosphatidylethanolamine ...

let denote the unit circle in the complex plane. given a function , one uses t usual (harmonic) poisson kernel for the unit disk to define the poisson integral of , namely . here we consider the biharmonic poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . we then consider the dilations for and . the ...

This lecture is a short review on the role entropy plays in those classical dissipative systems whose equations of motion may be expressed via a Leibniz Bracket Algebra (LBA). This means that the time derivative of any physical observable f of the system is calculated by putting this f in a “bracket” together with a “special observable” F, referred to as a Leibniz generator of the dynamics. Whi...

This paper explores how entropy and other information theoretic quantities may be used to reverseengineer genetic regulatory networks from repeated microarray data. The problem of differentiating genes that undergo direct coregulation from genes whose expression is similar because they belong to the same regulatory pathway is studied from a graphical modeling viewpoint. This leads to the criter...

We present a novel class of high-order space–time finite element schemes for the Poisson–Nernst–Planck (PNP) equations. prove that our are mass conservative, positivity preserving, and unconditionally energy stable any order approximation. To best knowledge, this is first (arbitrarily) accurate PNP equations simultaneously achieve all these three properties. This accomplished via (1) using elem...

By taking a Poisson limit for sequence of rare quantum objects, I derive simple formulas the Uhlmann fidelity, Chernoff quantity, relative entropy, and Helstrom information. also present analogous in classical information theory model. An operator called intensity emerges as central quantity formalism to describe states. It behaves like density but is unnormalized. The terms operators not only ...