Abstract: Abstract
An approximate solution of the inverse problem of tsunami is given. For the initial data, the marigram with the first registration of the Japanese tsunami of March 11, 2011 on the DART station 21418 and the first registration of the tsunami on the South Ivate GPS buoy are taken. The potential model of tsunami with a simple source of the piston type is used, and estimates for the geographical coordinates of the epicenter and the two characteristic parameters tsunami source are given. PubDate: 2014-10-01

Abstract: Abstract
Let g be a finite-dimensional Lie algebra and L be a Lie algebra bundle (LAB). A given coupling Ξ between the LAB L and the tangent bundle TM of a manifold M generates the so-called Mackenzie obstruction Obs(Ξ) ∈ H
3 (M; ZL) to the existence of a transitive Lie algebroid (K. Mackenzie, General Theory of Lie Groupoids and Lie Algebroids, 2005, p. 279). We present two cases of evaluating the Mackenzie obstruction.
In the case of a commutative algebra g, the group Aut(g)
δ
is isomorphic to the group of all matrices GL(g) with the discrete topology. We show that the Mackenzie obstruction for coupling Obs(Ξ) vanishes.
The other case describes the Mackenzie obstruction for simply connected manifolds. We prove that, for simply connected manifolds, the Mackenzie obstruction is also trivial, i.e. Obs(Ξ) = 0 ∈ H
3(M; ZL; ∇
Z
). PubDate: 2014-10-01

Abstract: Abstract
A class of quasirepresentations is introduced. For an amenable group, every (not necessarily bounded) quasirepresentation in this class with sufficiently small defect admits an ordinary representation of the same group for which the distance from the given quasirepresentation can be estimated using the defect. PubDate: 2014-10-01

Abstract: Abstract
We define the notions of distribution half-forms (also called quantum states) on an infinite-dimensional space, and differential operators (also called quantum observables) on the space of these half-forms. This definition depends on the dimensional constant h (the Planck constant). In the limit h → 0, this construction turns into the construction of the Poisson algebra of classical field theory observables (defined earlier) and Maslov-Shvedov’s theory of complex germ. Using these definitions, we give a definition of mathematical quantization of a classical field theory given by a variational principle. PubDate: 2014-10-01

Abstract: Abstract
We consider birth-and-death stochastic evolution of genotypes with different lengths. The genotypes might mutate, which provides a stochastic changing of lengths by a free diffusion law. The birth and death rates are length dependent, which corresponds to a selection effect. We study an asymptotic behavior of a density for an infinite collection of genotypes. The cases of space homogeneous and space heterogeneous densities are considered. PubDate: 2014-10-01

Abstract: Abstract
In this paper, general questions concerning equilibrium and non-equilibrium states are discussed. Using the Van-der-Waals model, the relationship between Gentile statistics and non-ideal gas is demonstrated. The second virial coefficient is expressed in terms of collective degrees of freedom. The admissible cluster size at given temperature is determined. PubDate: 2014-10-01

Abstract: Abstract
In this paper, we present several new expansion formulas for a class of generalized Hurwitz-Lerch zeta functions which were introduced by Raina and Chhajed [R. K. Raina and P. K. Chhajed, “Certain Results Involving a Class of Functions Associated with the Hurwitz Zeta Function,” Acta Math. Univ. Comenian. 73, 89–100 (2004)] and (more recently) by Srivastava et al. [H. M. Srivastava, M.-J. Luo, and R. K. Raina, “New Results Involving a Class of Generalized Hurwitz-Lerch Zeta Functions and Their Applications,” Turkish J. Anal. Number Theory 1, 26–35 (2013)]. These expansion formulas are obtained with the help of some fractional calculus theorems such as the generalized Leibniz rules, the Taylorlike expansions in terms of different functions and the generalized chain rule. Several (known or new) special cases are also considered. PubDate: 2014-10-01

Abstract: Abstract
In this paper, we study some properties of several polynomials arising from umbral calculus. In particular, we investigate the properties of orthogonality type of the Frobeniustype Eulerian polynomials which are derived from umbral calculus. By using our properties, we can derive many interesting identities of special polynomials associated with Frobeniustype Eulerian polynomials. An application to normal ordering is presented. PubDate: 2014-10-01

Abstract: Abstract
This paper is a report on the results of computer experiments with an algorithm that takes classical knots to what we call their “normal form” (and so can be used to identify the knot). The algorithm is implemented in a computer animation that shows the isotopy joining the given knot diagram to its normal form. We describe the algorithm, which is a kind of gradient descent along a functional that we define, present a table of normal forms of prime knots with 7 crossings or less, compare it to the knot table of normal forms of wire knots (obtained in [1] by mechanical experiments with real wire models) and (regretfully) present simple examples showing that normal forms obtained by our algorithm are not unique for a given knot type (sometimes isotopic knots can have different normal forms). PubDate: 2014-10-01

Abstract: Abstract
The Cauchy problem for a parabolic equation with a small parameter multiplying the highest derivatives is considered. The dynamical system corresponding to the limit equation of the first order has an asymptotically stable equilibrium. A Lyapunov function known in a neighborhood of this equilibrium is used to construct a barrier in the Cauchy problem for the original parabolic equation. This result is applied to study the dynamical system with respect to random perturbations of the “white noise” type. PubDate: 2014-10-01

Abstract: Abstract
In this paper, we study the wave equation on the simplest hybrid spaces of constant curvature, namely, on Euclidean space or a sphere with a glued ray. We obtain explicit formulas for solutions of the Cauchy problem, which are the simplest nontrivial analogs of Kirchhoff or Herglotz-Petrovsky formulas; especially simple formulas are obtained in the case of three-dimensional Euclidean space with a glued ray. The solutions depend on the boundary conditions at the point of gluing, and these conditions determine the choice of the domain of the Laplace operator; the conditions ensuring the full reflection or full passage of waves are described separately. PubDate: 2014-10-01

Abstract: Abstract
We consider the Shallow Water Equations on the sphere in the basin with nonuniform bottom. Using recently developed approach based on generalized Maslov canonical operator we construct quite explicit asymptotic formulas for the solutions to the Cauchy problem with spatially localized initial data. These solutions in particular describe propagation of tsunami waves in frame of so-called piston model. We discuss the following question: to what extent can the spherical property of the Earth influence the front and the profile (amplitude) of the wave generated by spatially localized momentary sources. We also discuss the problem concerning the influence of the Coriolis force into the solution. PubDate: 2014-10-01

Abstract: Abstract
The integral law of thermal radiation by finite-size emitters is studied. Two geometrical characteristics of a radiating body or a cavity, its volume and its boundary area, define two terms in its radiance. The term defined by the volume corresponds to the Stefan-Boltzmann law. The term defined by the boundary area is proportional to the third power of temperature and inversely proportional to emitter’s effective size, which is defined as the ratio of its volume to its boundary area. This generalized law is valid for arbitrary temperature and effective size. It is shown that the cubic temperature contribution is observed in experiments. This term explains the intrinsic uncertainty of the NPL experiment on radiometric determination of the Stefan-Boltzmann constant. It is also quantitatively confirmed by data from the NIST calibration of cryogenic blackbodies. Its relevance to the size of source effect in optical radiometry is proposed and supported by the experiments on thermal emission from nano-heaters. PubDate: 2014-10-01

Abstract: Abstract
In classical information theory, one of the most important theorems are the coding theorems, which were discussed by calculating the mean entropy and the mean mutual entropy defined by the classical dynamical entropy (Kolmogorov-Sinai). The quantum dynamical entropy was first studied by Emch [13] and Connes-Stormer [11]. After that, several approaches for introducing the quantum dynamical entropy are done [10, 3, 8, 39, 15, 44, 9, 27, 28, 2, 19, 45]. The efficiency of information transmission for the quantum processes is investigated by using the von Neumann entropy [22] and the Ohya mutual entropy [24]. These entropies were extended to S- mixing entropy by Ohya [26, 27] in general quantum systems. The mean entropy and the mean mutual entropy for the quantum dynamical systems were introduced based on the S- mixing entropy. In this paper, we discuss the efficiency of information transmission to calculate the mean mutual entropy with respect to the modulated initial states and the connected channel for the quantum dynamical systems. PubDate: 2014-07-01

Abstract: Abstract
In this paper, we formulate limit Zeno dynamics of general open systems as the adiabatic elimination of fast components. We are able to exploit previous work on adiabatic elimination of quantum stochastic models to give explicitly the conditions under which open Zeno dynamics will exist. The open systems formulation is further developed as a framework for Zeno master equations, and Zeno filtering (that is, quantum trajectories based on a limit Zeno dynamical model). We discuss several models from the point of view of quantum control. For the case of linear quantum stochastic systems, we present a condition for stability of the asymptotic Zeno dynamics. PubDate: 2014-07-01

Abstract: Abstract
Boyle temperature is interpreted as the temperature at which the formation of dimers becomes impossible. To Irving Fisher’s correspondence principle we assign two more quantities: the number of degrees of freedom, and credit. We determine the danger level of the mass of money M when the mutual trust between economic agents begins to fall. PubDate: 2014-07-01

Abstract: Abstract
We analyze the unravelling of the quantum optical master equation at finite temperature due to direct, continuous, general-dyne detection of the environment. We first express the general-dyne Positive Operator Valued Measure (POVM) in terms of the eigenstates of a non-Hermitian operator associated to the general-dyne measurement. Then we derive the stochastic master equation obtained by considering the interaction between the system and a reservoir at thermal equilibrium, which is measured according to the POVM previously determined. Finally, we present a feasible measurement scheme, which reproduces general-dyne detection for any value of the parameter characterizing the stochastic master equation. PubDate: 2014-07-01

Abstract: Abstract
Theorem 4.1 of the author’s paper “Quantum Yang-Mills-Weyl dynamics in the Schroedinger paradigm”, RJMP 21 (2), 169–188 (2014) claims the relative ellipticity of cutoff Yang-Mills quantum energy-mass operators in von Neumann algebras with regular traces. This implies that the spectra of cutoff self-adjoint Yang-Mills energy-mass operators in a nonperturbative quantum Yang-Mills theory (with an arbitrary compact simple gauge group) are nonnegative sequences of the eigenvalues converging to +∞. The spectra are self-similar in the inverse proportion to the running coupling constant. In particular, they have self-similar positive spectral mass gaps. Presumably, this is a solution of the Yang-Mills Millennium problem.
The present note shows that the fundamental spectral value of a cutoff quantum Yang-Mills energy-mass operator is the simple zero eigenvalue with the vacuum eigenvector. The direct proof (without von Neumann algebras) is based on the domination over the number operator (with simple fundamental eigenvalue) and the standard spectral variational principle. PubDate: 2014-07-01

Abstract: Abstract
We show that there is a unique C*-algebra for the transverse quantum electromagnetic field obeying the Maxwell equations with any classical charge-current. For nonzero charge, the representation of the C*-algebra differs from the representation with zero charge. PubDate: 2014-07-01