Integrability of Solutions of Nonlinear Elliptic Equations with Right-Hand Sides from Logarithmic Classes

We establish the existence of a weak solution to the Dirichlet problem belonging to a Sobolev space for nonlinear elliptic equations of second order with right-hand sides from a wide class of functions defined in terms of the logarithmic function.     

Krylov-Bogolyubov averaging of asymptotically autonomous differential equations

We apply the Krylov and Bogolyubov asymptotic integration procedure to asymptotically autonomous systems. First, we consider linear systems with quasi-periodic coefficient matrix multiplied by a scalar factor vanishing at infinity. Next, we study the asymptotically autonomous Van-der-Pol oscillator.

     

Thermoelectric effects in layered conductors in a strong magnetic field

Thermoelectric effects are investigated theoretically in layered conductors with a quasi-two-dimensional electron energy spectrum of arbitrary type in a strong magnetic field. It is shown that, at temperatures sufficiently low for quantization of the orbital motion of charge carriers in a magnetic field to be required, there exist giant quantum oscillations of the thermoelectric field. Thermoelectric emf is studied as a f unction of the orientation of the magnetic field with respect to the layers; experimental investigation of this function allows one to determine the velocity distribution of conduction electrons on the Fermi surface.     

On the transmission rate of classical information through quantum communication channels

The coding of quantum communication channels in real time is considered as applied to the situation when information is coded into continuous quantum degrees of freedom (into the shape of the amplitude of quantum states with an arbitrary number of photons). It is shown that the nonlocalizability of states in quantum field theory requires that the identity of particles should be taken into account. This, together with the finiteness of the limit speed of propagation, leads to the fact that the formulas for the transmission rate of nonrelativistic communication channels have an asymptotic character; i.e., these formulas are formally valid only when the separation between messages is infinite (when the identity of particles can be neglected) and, hence, when the transmission rate in [bit/message s] is infinitely small. A real-time information capacity of a sequential relativistic quantum communication channel is obtained that takes into account the identity of particles for pure signal states with an arbitrary number of photons. An explicit analytic expression is obtained for the transmission rate of a quantum channel of finite bandwidth for one-photon input states.     

Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.     

Remarks on the Regularity to 3-D Ideal Magnetohydrodynamic Equations

In this paper we are interested in the sufficient conditions which guarantee the regularityof solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval [0,T].Fivesufficient conditions are given.Our results are motivated by two main ideas:one is to control theaccumulation of vorticity alone;the other is to generalize the corresponding geometric conditions of3-D Euler equations to 3-D ideal magnetohydrodynamic equations.     

Marking Games and the Oriented Game Chromatic Number of Partial <Emphasis Type="Italic">k</Emphasis>-Trees

 Nešetřil and Sopena introduced the concept of oriented game chromatic number. They asked whether the oriented game chromatic number of partial k-trees was bounded. Here we answer their question positively. Received: January 12, 2001 Final version received: February 25, 2002     

Non-Trivial t-Intersection in the Function Lattice

The function lattice, or generalized Boolean algebra, is the set of ℓ-tuples with the ith coordinate an integer between 0 and a bound n_i. Two ℓ-tuples t-intersect if they have at least t common nonzero coordinates. We prove a Hilton–Milner type theorem for systems of t-intersecting ℓ-tuples.Received September 29, 2004