Abstract: Abstract
We determine the extension of an ideal liquid by “thermodynamic forces,” that is, forces related to entropy growth. We show that the negative pressure corresponds to the case of at most two degrees of freedom. PubDate: 2015-10-01

Abstract: Abstract
The system of conservation laws
\({u_t} + {\left( {\frac{{{u^2} + {v^2}}}{2}} \right)_x} = 0\)
, v
t + (uv − v)x = 0 with the initial conditions u(x, 0) = l
0 + b
0
H(x), v(x, 0) = k
0 + c
0
H(x), where H is the Heaviside function is studied. This strictly hyperbolic system was introduced by M. Brio in 1988 and provides a simplified model for the magnetohydrodynamics equations. Under certain compatibility conditions for the constants l
0, b
0, k
0, c
0, an explicit solution containing a Dirac mass is given and we prove the uniqueness of this solution within a convenient class of distributions which includes Dirac-delta measures. Our concept of solution is defined within the framework of a distributional product, and it is a consistent extension of the concept of a classical solution. This direct method seems considerably simpler than the weak asymptotic method usually used in the study of delta-shocks emergence in nonlinear conservation laws. PubDate: 2015-10-01

Abstract: Abstract
In this paper, we develop the method of Chaplygin’s reducing multiplier; using this method, we obtain a conformally Hamiltonian representation for three nonholonomic systems, namely, for the nonholonomic oscillator, for the Heisenberg system, and for the Chaplygin sleigh. Furthermore, in the case of oscillator and nonholonomic Chaplygin sleigh, we show that the problem reduces to the study of motion of a mass point (in a potential field) on a plane and, in the case of Heisenberg system, on the sphere. Moreover, we consider an example of a nonholonomic system (suggested by Blackall) to which one cannot apply the method of reducing multiplier. PubDate: 2015-10-01

Abstract: Abstract
In the paper, an unexpected correspondence between the automorphisms of 5D real uniformly 2-nondegenerate hypersurfaces of the space C3 and the automorphisms of the 3D hypersphere in C2 is constructed. In a certain sense, the 3D hypersphere, which is, as is known, a model surface for the class of nondegenerate 3D hypersurfaces in C2, has this status also with respect to the above class of 5D hypersurfaces in C3. PubDate: 2015-10-01

Abstract: Abstract
In the paper, we discuss relationships between the existence of Hilbert supports of countably additive measures on a locally convex space (LCS) and the continuity of their Fourier transforms in the Gross–Sazonov topology (which is defined below) on the dual space. In particular, it follows from the theorem proved in the paper that the Fourier transform of the Wiener measure on C[0, 1] is not continuous in the Gross–Sazonov topology on the dual space
\({\left( {C\left[ {0,1} \right]} \right)^\prime }\)
endowed with the Mackey topology (the strongest locally convex topology among those consistent with the duality between
\({\left( {C\left[ {0,1} \right]} \right)^\prime }\)
and C[0, 1]). PubDate: 2015-10-01

Abstract: Abstract
We study a stationary kinetic equation describing the electron component of nonequilibrium plasma in crossed electric and magnetic fields. The collision integral is taken in the so-called relaxation (BGK) approximation. It is assumed that the plasma parameters vary only along the electric field. Using the Laplace method, asymptotic formulas for the moments of the distribution function including components of the stress tensor and heat flux vector are obtained with a qualified estimate of the remainder. PubDate: 2015-10-01

Abstract: Abstract
Recently, T. Kim considered an Euler zeta function which interpolates Euler polynomials at negative integers (see [3]). In this paper, we study the degenerate Euler zeta function which is holomorphic on the complex s-plane and is associated with degenerate Euler polynomials at negative integers. PubDate: 2015-10-01

Abstract: Abstract
An analog of the Freudenthal–Weil theorem holds for some discontinuous homomorphisms of a connected pro-Lie group into a compact group. PubDate: 2015-10-01

Abstract: Abstract
We study the lattice point counting problem for a class of families of domains in a Euclidean space. This class consists of anisotropically expanding bounded domains that remain unchanged along some fixed linear subspace and expand in directions orthogonal to this subspace. We find the leading term in the asymptotics of the number of lattice points in such family of domains and prove remainder estimates in this asymptotics under various conditions on the lattice and the family of domains. As a consequence, we prove an asymptotic formula for the eigenvalue distribution function of the Laplace operator on a flat torus in adiabatic limit determined by a linear foliation with a nontrivial remainder estimate. PubDate: 2015-10-01

Abstract: Abstract
We study the behavior of a wave diffracted by a wedge wave near its front in the two-dimensional scattering of an incident plane harmonic wave with a Heaviside type profile. We find the asymptotics of the cylindrical wave diffracted by the edge of a wedge near the front in two cases: near the critical rays and far from the critical rays. The asymptotics turns out to be nonuniform and depends on the magnitude of the wedge. The cases of Dirichlet–Dirichlet, Dirichlet–Neumann and Neumann–Neumann boundary conditions are considered. PubDate: 2015-10-01

Abstract: Abstract
We study the dynamics of a charge in the planar Penning trap in which the direction of the magnetic field does not coincide with the trap axis. Under a certain combined resonance condition on the deviation angle and magnitudes of magnetic and electric fields, the trajectories of a charge are near-periodic.We describe the reduction to a top-like system with one degree of freedom on the space with quadratic Poisson brackets and study the stability of the equilibrium points of this system. PubDate: 2015-10-01

Abstract: Abstract
In the paper, the asymptotic behavior of solutions of the Cauchy problem is described for the linearized Navier–Stokes equation with the initial condition localized in a neighborhood of a curve or a two-dimensional surface in three-dimensional space. In particular, conditions for the growth of the perturbation in plane-parallel, two-dimensional, and helical external flows are obtained. PubDate: 2015-10-01

Abstract: Abstract
In this paper, we study the smoothness of generalized solutions to boundary value problems for strongly elliptic differential-difference equations on a boundary of neighboring subdomains of smoothness. PubDate: 2015-10-01

Abstract: Abstract
The Cauchy problem for the wave equations of Boussinesq type is treated by considering the initial conditions taken from the solution of generalized Cauchy problem for the potential model of tsunami with some “simple” impulsive source under the assumption that the depth of the liquid is constant. The solutions of the problem under consideration are derived in the form of a single integral giving the wave height at every point of observation at any time moment after the pulsed action of the source. The results of comparing the time history of the the height of tsunami waves at different distances from the source for different values of its characteristic radius (these histories are calculated using two solutions, namely, the solution derived here and the solution known for the potential tsunami model) are described. Conclusions concerning the accuracy of the tested solutions are made. PubDate: 2015-10-01

Abstract: Abstract
A Feynman formula for the solving semigroup describing the evolution of the Wigner function (defined on the phase space of a finite-dimensional Hamiltonian system) is obtained. For an information concerning Feynman formulas, see V. A. Dubravina, Feynman formulas for solutions of evolution equations on ramified surfaces, Russ. J. Math. Phys. 21 (2), 285–288 (2014). PubDate: 2015-10-01

Abstract: Abstract
The goal of this paper is to study some cases of not Col-divisible balanced three-dimensional polytopes and to calculate the corresponding E-groups and K-groups. PubDate: 2015-07-01

Abstract: Abstract
We compute the K-theory of noncommutative Bieberbach manifolds, which are fixed point C* subalgebras of a three-dimensional noncommutative torus by a free action of a cyclic group ℤ
N
, N = 2, 3, 4, 6. PubDate: 2015-07-01

Abstract: Abstract
As is known from previous research, the study of the structure and counting of Reidemeister classes (twisted conjugacy classes) of an automorphism ϕ: G → G, i.e., the classes x ∼ gxϕ(g
−1), is closely related to the study of the corresponding twisted inner representation of a discrete group G, i.e., a representation on ℓ2(G) corresponding to the action g ↦ xgϕ(x
−1) (x, g ∈ G) of G on itself. In the present paper, we study twisted inner representations from a more general point of view, but the questions under consideration are still close to important relations with Reidemeister classes. PubDate: 2015-07-01

Abstract: This paper is devoted to analyzing two approaches to characteristic classes of transitive Lie algebroids. The first approach is due to Kubarski [5] and is a version of the Chern-Weil homomorphism. The second approach is related to the so-called categorical characteristic classes (see, e.g., [6]). The construction of transitive Lie algebroids due to Mackenzie [1] can be considered as a homotopy functor T LA
g from the category of smooth manifolds to the transitive Lie algebroids. The functor T LA
g assigns to every smooth manifold M the set T LA
g(M) of all transitive algebroids with a chosen structural finite-dimensional Lie algebra g. Hence, one can construct [2, 3] a classifying space B
g such that the family of all transitive Lie algebroids with the chosen Lie algebra g over the manifold M is in one-to-one correspondence with the family of homotopy classes of continuous maps [M, B
g]: T LA
g(M) ≈ [M, B
g]. This enables us to describe characteristic classes of transitive Lie algebroids from the point of view of a natural transformation of functors similar to the classical abstract characteristic classes for vector bundles and to compare them with those derived from the Chern-Weil type homomorphism by Kubarski [5]. As a matter of fact, we show that the Chern-Weil type homomorphism by Kubarski does not cover all characteristic classes from the categorical point of view. PubDate: 2015-07-01

Abstract: Abstract
We extend the Chern character construction of Neshveyev and Tuset to a map whose values lie in Hopf cyclic homology with coefficients, generalizing their definition of K-theory as well. We also introduce the sheaf of equivariant K-theory (with and without coefficients) similar to the equivariant cohomology of Block and Getzler. This construction is much more geometric (it is defined only for the case in which the Hopf algebra and the Hopfmodule algebra are both algebras of functions on some spaces). Thus, we give a geometric definition of the corresponding Chern character, which takes values in a version of Block—Getzler’s sheaf of equivariant cohomology. PubDate: 2015-07-01