282 research outputs found
On System of Generalized Vector Quasiequilibrium Problems with Applications
We introduce a new system of generalized vector quasiequilibrium problems which
includes system of vector quasiequilibrium problems, system of vector equilibrium problems, and
vector equilibrium problems, and so forth in literature as special cases. We prove the existence of solutions
for this system of generalized vector quasi-equilibrium problems. Consequently, we derive some
existence results of a solution for the system of generalized quasi-equilibrium problems and the generalized
Debreu-type equilibrium problem for both vector-valued functions and scalar-valued functions
Thermo field hydrodynamic and kinetic equations of dense quantum nuclear systems
Basic equations of nonequilibrium thermo field dynamics of dense quantum
systems are presented. A formulation of nonequilibrium thermo field dynamics
has been performed using the nonequilibrium statistical operator method by
D.N.Zubarev. Hydrodynamic equations have been obtained in thermo field
representation. Two levels of the description of kinetics and hydrodynamics of
a dense nuclear matter are considered. The first one is a quantum system with
strongly coupled states, the second one is a quark-gluon plasma. Generalized
transfer equations of a consistent description of kinetics and hydrodynamics
have been obtained, as well as limiting cases are considered.Comment: 37 LaTeX2e pages, special sty-fil
On the stability of solution mapping for parametric generalized vector quasiequilibrium problems
AbstractIn this paper, we study the solution stability for a class of parametric generalized vector quasiequilibrium problems. By virtue of the parametric gap function, we obtain a sufficient and necessary condition for the Hausdorff lower semicontinuity of the solution mapping to the parametric generalized vector quasiequilibrium problem. The results presented in this paper generalize and improve some main results of Chen et al. (2010) [34], and Zhong and Huang (2011) [35]
The Michaelis-Menten-Stueckelberg Theorem
We study chemical reactions with complex mechanisms under two assumptions:
(i) intermediates are present in small amounts (this is the quasi-steady-state
hypothesis or QSS) and (ii) they are in equilibrium relations with substrates
(this is the quasiequilibrium hypothesis or QE). Under these assumptions, we
prove the generalized mass action law together with the basic relations between
kinetic factors, which are sufficient for the positivity of the entropy
production but hold even without microreversibility, when the detailed balance
is not applicable. Even though QE and QSS produce useful approximations by
themselves, only the combination of these assumptions can render the
possibility beyond the "rarefied gas" limit or the "molecular chaos"
hypotheses. We do not use any a priori form of the kinetic law for the chemical
reactions and describe their equilibria by thermodynamic relations. The
transformations of the intermediate compounds can be described by the Markov
kinetics because of their low density ({\em low density of elementary events}).
This combination of assumptions was introduced by Michaelis and Menten in 1913.
In 1952, Stueckelberg used the same assumptions for the gas kinetics and
produced the remarkable semi-detailed balance relations between collision rates
in the Boltzmann equation that are weaker than the detailed balance conditions
but are still sufficient for the Boltzmann -theorem to be valid. Our results
are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.Comment: 54 pages, the final version; correction of a misprint in Attachment
Initial Data for Numerical Relativity
Initial data are the starting point for any numerical simulation. In the case
of numerical relativity, Einstein's equations constrain our choices of these
initial data. We will examine several of the formalisms used for specifying
Cauchy initial data in the 3+1 decomposition of Einstein's equations. We will
then explore how these formalisms have been used in constructing initial data
for spacetimes containing black holes and neutron stars. In the topics
discussed, emphasis is placed on those issues that are important for obtaining
astrophysically realistic initial data for compact binary coalescence.Comment: 50 pages, LaTeX(livrev.cls), Review article for "Living Reviews in
Relativity" (http://www.livingreviews.org/), July 200
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