We study the master equation with time-dependent coefficients, a linear kinetic equation for the Markov chains or for the monomolecular chemical kinetics. For the solution of this equation a path summation formula is proved. This formula represents the solution as a sum of solutions for simple kinetic schemes (kinetic paths), which are available in explicit analytical form. The relaxation rate ...

A computation-oriented representation of uncertain kinetic systems is introduced and analysed in this paper. It is assumed that the monomial coefficients of the ODEs belong to a polytopic set, which defines a set of dynamical systems for an uncertain model. An optimization-based computation model is proposed for the structural analysis of uncertain models. It is shown that the so-called dense r...

Background: Investigating the performance of naturally operated treatment plants may be due to the fact that they cannot be operated as desired, or that they should be modified to achieve good performance e.g. for nutrients removal. The advantage of kinetic coefficient determination is that the model can be adjusted to fit data and then used for analyzing alternatives to improve the process. Th...

Many features of granular media can be modelled as a fluid of hard spheres with inelastic collisions. Under rapid flow conditions, the macroscopic behavior of grains can be described through hydrodynamic equations. At lowdensity, a fundamental basis for the derivation of the hydrodynamic equations and explicit expressions for the transport coefficients appearing in them is provided by the Boltz...

Accurate measurements of kinetic rate constants for interacting biomolecules are crucial for understanding the mechanisms underlying intracellular signalling pathways. The magnitude of binding rates plays a very important molecular regulatory role which can lead to very different cellular physiological responses under different conditions. Here, we extend the k-space image correlation spectrosc...

A sensitive fixed-time kinetic enzymatic method for the measurement of high density lipoprotein cholesterol is described, as adapted for the Cobas Bio centrifugal analyser (Hoffmann LaRoche). The Boehringer Mannheim cholesterol esterase/cholesterol oxidase/peroxidase/3,4-dichlorophenol kinetic reagent was modified by the inclusion of 2,4,6-tribromo-3-hydroxybenzoic acid which reacts with hydrog...

The Boltzmann equation is a fundamental kinetic that describes the dynamics of dilute gas. In this paper we study regularity both dynamical and steady in strictly convex domain with Cercignani-Lampis (C-L) boundary condition. C-L condition intermediate reflection law between diffuse specular via two accommodation coefficients. We construct local weighted $C^1$ solution using repeated interactio...

The decomposition of the tensor product of a positive and a negative discrete series representation of the Lie algebra su(1, 1) is a direct integral over the principal unitary series representations. In the decomposition discrete terms can occur, and the discrete terms are a finite number of discrete series representations or one complementary series representation. The interpretation of Meixne...

This paper characterizes the first cohomology group H(G,M) where M is a Banach space (with norm || ||M) that is also a left CG module such that the elements of G act onM as continuous C-linear transformations. We study this group for G an infinite, finitely generated group. Of particular interest are the implications of the vanishing of the group H(G,M). The first result is that H(G,CG) imbeds ...