On Indirect Approach to the Solvability of Quasi-Linear Dirichlet Elliptic Boundary Value Problem with BMO-Anisotropic p-Laplacian

We study here Dirichlet boundary value problem for a quasi-linear elliptic equation with anisotropic p-Laplace operator in its principle part and L^1-control in coefficient of the low-order term. As characteristic feature of such problem  is a specification of the matrix of anisotropy A=A^{sym}+A^{skew} in BMO-space. Since we cannot expect to have a solution of the state equation in the classical Sobolev space W^{1,p}_0(\Omega), we specify a suitable functional class in which we look for solutions and prove existence of weak solutions in the sense of Minty using a non standard approximation procedure and compactness arguments in variable spaces

On Optimization of a Highly Re-Entrant Production System

We discuss the optimal control problem stated as the minimization in the $L^2$-sense of the mismatch between the actual out-flux and a demand forecast for a hyperbolic conservation law that models a highly re-entrant production system. The output of the factory is described as a function of the work in progress and the position of the switch dispatch point (SDP) where we separate the beginning of the factory employing a push policy from the end of the factory, which uses a quasi-pull policy. The main question we discuss in this paper is about the optimal choice of the input in-flux, push and quasi-pull constituents, and the position of SDP

Definition of Strange Attractor in Benard problem for Generalized Couette Cell

For movements of the viscous continuous flow in generalized Couette cell the dynamic system describing the central limiting variety is received.Comment: 6 pages, exposed on 2nd "European Conference on Computer Science and Applications" - XA2008, Timisoara, Romani

Pathologies of Quenched Lattice QCD at non--zero Density and its Effective Potential

We simulate lattice QCD at non--zero baryon density and zero temperature in the quenched approximation, both in the scaling region and in the infinite coupling limit. We investigate the nature of the forbidden region -- the range of chemical potential where the simulations grow prohibitively expensive, and the results, when available, are puzzling if not unphysical. At weak coupling we have explored the sensitivity of these pathologies to the lattice size, and found that using a large lattice ($64 \times 16^3$) does not remove them. The effective potential sheds considerable light on the problems in the simulations, and gives a clear interpretation of the forbidden region. The strong coupling simulations were particularly illuminating on this point.Comment: 49 pages, uu-encoded expanding to postscript;also available at ftp://hlrz36.hlrz.kfa-juelich.de/pub/mpl/hlrz72_95.p

On Increasing of Resolution of Satellite Images via Their Fusion with Imagery at Higher Resolution

In this paper we propose a new statement of the spatial increasing resolution problem of MODIS-like multi-spectral images via their fusion with Lansat-like imagery at higher resolution. We give a precise definition of the solution to the indicated problem, postulate assumptions that we impose at the initial data, establish existence and uniqueness result, and derive the corresponding necessary optimality conditions. For illustration, we supply the proposed approach by results of numerical simulations with real-life satellite images.In this paper we propose a new statement of the spatial increasing resolution problem of MODIS-like multi-spectral images via their fusion with Lansat-like imagery at higher resolution. We give a precise definition of the solution to the indicated problem, postulate assumptions that we impose at the initial data, establish existence and uniqueness result, and derive the corresponding necessary optimality conditions. For illustration, we supply the proposed approach by results of numerical simulations with real-life satellite images

Trying to understand confinement in the Schroedinger picture

We study the gauge-invariant gaussian ansatz for the vacuum wave functional and show that it potentially possesses many desirable features of the Yang--Mills theory, like asymptotic freedom, mass generation through the transmutation of dimensions and a linear potential between static quarks. We point out that these (and other) features can be studied in a systematic way by combining perturbative and 1/n expansions. Contrary to the euclidean approach, confinement can be easily formulated and easily built in, if not derived, in the variational Schroedinger approach.Comment: 21 pages, 1 figure. Lecture given at the 4th St.Petersburg Winter School in Theoretical Physics, Feb. 22-28, 199

Quenched QCD at finite density

Simulations of quenched $QCD$ at relatively small but {\it nonzero} chemical potential $\mu$ on $32 \times 16^3$ lattices indicate that the nucleon screening mass decreases linearly as $\mu$ increases predicting a critical chemical potential of one third the nucleon mass, $m_N/3$, by extrapolation. The meson spectrum does not change as $\mu$ increases over the same range, from zero to $m_\pi/2$. Past studies of quenched lattice QCD have suggested that there is phase transition at $\mu = m_\pi/2$. We provide alternative explanations for these results, and find a number of technical reasons why standard lattice simulation techniques suffer from greatly enhanced fluctuations and finite size effects for $\mu$ ranging from $m_\pi/2$ to $m_N/3$. We find evidence for such problems in our simulations, and suggest that they can be surmounted by improved measurement techniques.Comment: 23 pages, Revte

A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS

In this paper we discuss some issues related to Poincar´e’s inequality for aspecial class of weighted Sobolev spaces. A common feature of these spaces is that they can be naturally associated with differential operators with variable diffusion coefficients that are not uniformly elliptic. We give a classification of these spaces in the 1-D case bases on a measure of degeneracy of the corresponding weight coefficient and study their key properties

Chiral Magnetic Effect on the Lattice

We review recent progress on the lattice simulations of the chiral magnetic effect. There are two different approaches to analyze the chiral magnetic effect on the lattice. In one approach, the charge density distribution or the current fluctuation is measured under a topological background of the gluon field. In the other approach, the topological effect is mimicked by the chiral chemical potential, and the induced current is directly measured. Both approaches are now developing toward the exact analysis of the chiral magnetic effect.Comment: to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

QCD at finite isospin density

QCD at finite isospin chemical potential mu_I has no fermion sign problem and can be studied on the lattice. We solve this theory analytically in two limits: at low mu_I where chiral perturbation theory is applicable, and at asymptotically high mu_I where perturbative QCD works. At low isospin density the ground state is a pion condensate, whereas at high density it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum numbers as the pion. This leads us to a conjecture that the transition from hadron to quark matter is smooth, which passes several tests. Our results imply a nontrivial phase diagram in the space of temperature and chemical potentials of isospin and baryon number.Comment: 4 pages, 1 figure, version to appear in PR