Non-homogeneous system

All experimentation is prone to human error and, additionally, sampling reproducibility in non-homogenous systems such as enzyme catalyzed trans-... 

The following cultivation modes have been described for production of MAbs in in vitro large-scale systems batch, fed-batch, chemostat and perfusion (Reuveny Lazar, 1989). Batch and fed-batch processes are the most common methods. More demanding are chemostat and perfusion modes, which allow a continuous production of MAbs. All methods are applicable in homogeneous and, with the exception of chemostat, non-homogeneous systems. 

Low cell density compared with perfusion or non-homogeneous systems (at the end, less than 5 x 10 cells mH)... 

In the original article by Kohn and Sham [28] where the LDA was proposed, there was also a suggestion for improvement in the case of non-homogeneous systems. The suggestion was a gradient expansion... 

Wc have omitted the six freciuencies corresponding to rotational and translational motions of the whole cluster. One of the advantages of the INM analysis is that we can perform projections of the density of states. One can decompose the density of states spectrum, c.g., into molecular rotational and translational motion [39]. For molecular clusters it is interesting to explore the localization of the motion described by the Hessian eigenvectors at different frequencies. Even though the harmonic motion is inherently collective, certain motions can be attributed to a limited area. This is the case of non-homogeneous systems, where the spectral characteristics can be quite different for different spatial parts. We define a projector Parea... 

This estimate implies that for un = the equation (2.16) possesses the trivial solution only. Therefore, the matrix Jn(u ) is nonsingular. Then for un = 4 and arbitrary Vn, the non-homogeneous system (2.15) always possesses the unique solution. 

The Boltzmann integro-differential kinetic equation written in terms of statistical physics became the foundation for construction of the structure of physical kinetics that included derivation of equations for transfer of matter, energy and charges, and determination of kinetic coefficients that entered into them, i.e. the coefficients of viscosity, heat conductivity, diffusion, electric conductivity, etc. Though the interpretations of physical kinetics as description of non-equilibrium processes of relaxation towards the state of equilibrium are widespread, the Boltzmann interpretations of the probability and entropy notions as functions of state allow us to consider physical kinetics as a theory of equilibrium trajectories. These trajectories as well as the trajectories of Euler-Lagrange have the properties of extremality (any infinitesimal part of a trajectory has this property) and representability in the form of a continuous sequence of states of rest. These trajectories can be used to describe the behavior of (a) isolated systems that spontaneously proceed to final equilibrium (b) the systems for which the differences of potentials with the environment are fixed (c) and non-homogeneous systems in which different parts have different values of the same intensive parameters. 

One of the major factors affecting the structure and properties of polymer blends is their miscibility. Most polymer pairs exhibit pronounced immiscibility, and only certain pairs are thermodynamically miscible. Generally, polymer blends are at least two-phase non-homogeneous systems. 

The C-J pressures, velocities, and isentropic expansion states of the non-homogeneous systems of explosive and aluminum powder may be reproduced by assuming that the mixture behaves like a homogeneous explosive, and the product molecule AI2O3 is formed as an equilibrium C-J product. Again the computed and experimental C-J pressures and velocities are lower than one might expect from the heats of explosion because of the low particle density of the detonation products. 

Dulnev GN, Novikov VV (1979) Conductivity of non-homogeneous systems. Inz Fiz Zhum 36 900-909... 

Information theory deals with the content of information encoded in a message or inherent to a system. If a system is homogenous, that is, all its elements are identictd, the system has, from the point of view of information theory, little information as compared with a system which is internally non-homogenous. In a non-homogenous system elements can be partitioned in many classes. In 1948 Shannon proposed a measure of the information content of a system by the formula ... 

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