During recent years the authors and collaborators have been involved in an activity related to the construction and analysis of large time step operator splitting algorithms for the numerical simulation of multi-phase ow in heterogeneous porous media. The purpose of these lecture notes is to review some of this activity. We illustrate the main ideas behind these novel operator splitting algorit...

Understanding the behavior of basic biomolecular components as parts of larger systems is one of the goals of the developing field of synthetic biology. A multidisciplinary approach, involving mathematical and computational modeling in parallel with experimentation, is often crucial for gaining such insights and improving the efficiency of artificial gene network design. Here we used such an ap...

Commutator structure of operator ideals Ken Dykema, ,1 Tadeusz Figiel, Gary Weiss, and Mariusz Wodzicki Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA b Instytut Matematyczny Polskiej Akademii Nauk, 81-825 Sopot, Poland Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA Department of Mathematics, University of Cali...

The spectral representation for stochastic integration operators with respect to the Wiener process is proposed in form of a composition characteristics used mathematical description control systems. This can be defined relative various orthonormal bases. For given deterministic square-integrable kernels, characteristic operator determined as an infinite random matrix. main applications such su...

and Applied Analysis 3 operator, the chromatic aberration Canny operator was used instead to extract the coastline. (1) Calculation of the Chromatic Aberration Amplitude by Means of Chromatic Aberration Canny Operator. In order to improve on deficiencies of the traditional Canny operator, an improved Canny operator was used based on the LAB color model as the main technical route in this paper,...

This paper is an introduction to rule-based programming in Maude. We illustrate in particular the use of operator attributes to structure the state of a system, and the difference between equations and rules. We use well-known mathematical games and puzzles for our examples illustrating the expressive power of Maude.

In this paper we propose a method for generating OWA weighting vectors from the individual assessments on a set of alternatives in such a way that these weights maximize the consensus among individual assessments with respect to the outcome provided by the OWA operator. Keywords—OWA operators; consensus; distances; mathematical programming.

We consider algebraic structure of Quantum Theory and provide its combinatorial representation. It is shown that by lifting to the richer algebra of graphs operator calculus gains simple interpretation as the shadow of natural operations on graphs. This provides insights into the algebraic structure of the theory and sheds light on the combinatorial nature and philosophy hidden behind its forma...

A new recombination operator, called Gene Pool Recombination (GPR) is introduced. In GPR, the genes are randomly picked from the gene pool defined by the selected parents. The mathematical analysis of GPR is easier than for two-parent recombination (TPR) normally used in genetic algorithms. There are n difference equations for the marginal gene frequencies that describe the evolution of a popul...

The purpose of this paper is to provide a mathematical analysis of the Adler-Wiser formula relating the macroscopic relative permittivity tensor to the microscopic structure of the crystal at the atomic level. The technical level of the presentation is kept at its minimum to emphasize the mathematical structure of the results. We also briefly review some models describing the electronic structu...