A kinetic model for beer production is proposed. The model takes into account five responses: biomass, sugar, ethanol, diacetyl and ethyl acetate. In contrast with previously published models, this model segregates biomass into three components: lag, active and dead cells and considers the...

It is well known that low-discrepancy sequences and their discrepancy play essential roles in quasi Monte Carlo methods [5]. In this paper, a new class of low-discrepancy sequences Nβ is constructed by using the ergodic theoretical transformation which is called β-adic transformation [7, 8]....

A modelling approach that will facilitate an in-depth understanding of the inter-relations of the different phenomena, human interactions and environmental factors constituting “real world” industrial processes is presented. Important industrial systems such as aluminium smelters, nuclear...

This paper presents the numerical approach of the free boundary by using shape optimization method. The numerical simulation field effect transistor MESFET is possible with the Laplace–Poisson model, which introduces two regions, respectively, known by “charge neutrality region” and...

We calculated numerically the energy interaction of two point charged particles. The integral has simple analytical result but is not easily solved numerically. Commercial programs as Mathematica 3.0™ and Maple V™ could not evaluate the integral and Gauss–Legendre method gave poor results....

In this paper a special class of k-step methods of order k+1 with two free parameters up to order 9 are established. The stability analysis of the P–C scheme is investigated. The coefficients of our class and the values of the parameters for getting A0-stable schemes are tabulated. The...

Three Monte Carlo methods for matrix inversion (MI) and finding a solution vector of a system of linear algebraic equations (SLAE) are considered: with absorption, without absorption with uniform transition frequency function, and without absorption with almost optimal transition frequency...

Linear systems with a derivation of non-integer order are examined as a special case of systems described by Mikusiński operators. Controllability and observability are examined using the theory of modules, as well as regulation of finite-dimensional systems. A stability result is obtained...

We discuss the capabilities of MathLie in supporting the symmetry analysis of differential equations. MathLie is a computer algebra program written in Mathematica 3.0 and capable to carry out different types of symmetry calculations for ordinary as well as for partial differential equations....

Regulations for the long-term disposal of high-level radioactive wastes command that the performance of the disposal facility be assessed for very long periods of time and quite extensive spatial scales. By nature, then, the analysis of the performance of a disposal facility relies on the...