Electroweak Nucleon Decays in a Superstrong Magnetic Field

We study the influence of a magnetic field on the electroweak processes of nucleon decay in a degenerate ideal gas of neutrons, protons, and electrons situated in an external superstrong constant and homogeneous magnetic field with effects due to the interaction of nucleon anomalous magnetic moments with the magnetic field taken into account. For different values of the chemical potentials of degenerate fermions, we obtain expressions for probabilities of electroweak processes, which are assumed to be responsible for the chemical equilibrium in the central domain of a neutron star with a frozen superstrong magnetic field. We show that the difference between the neutron decay probabilities in the presence of a magnetic field B ≪ 10¹⁷ G and without this field is completely determined by changing the phase volume of electron states. We discuss the process of proton decay into a neutron, positron, and neutrino. This process is energetically allowed only when the interaction of nucleon anomalous magnetic moments with a superstrong magnetic field is taken into account. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 1, pp. 108–122, October, 2005.     

A Possibility for Studying Gravitational Properties of the Neutrino

We consider the effect that the gravitational field of a neutrino pulse radiated in the collapse of presupernova nuclei has on the observable optical radiation spectra of atoms at the supernova surface. We show that at the modern level of development of experimental methods, neutrino monitoring supplemented by optical monitoring of supernova candidates provides a unique possibility to check whether the Einstein equivalence principle is satisfied for neutrinos of each of the three types (electron, muon, and tau-lepton) and their antiparticles, to estimate the change of the gravitational potential at the surface of the star at the instant of the neutrino radiation pulse, and to obtain upper limits on the mass values of these neutrinos in a new way.     

Evaluation of high energy natural neutrino experiments

The directional intensities of neutrinos of various types produced in the decay of cosmic ray secondaries in the earth’s atmosphere have been estimated. The calculated energy spectra are believed to be uncertain by <20% for neutrino energies up to 100 GeV. Using these fluxes and making various assumptions about the behaviour of neutrino cross-section with energy, the energy spectra of neutrino-induced muons at large depths underground have been calculated. It is shown that a cross-section increasing only linearly with energy up to ～ 100 GeV. would account only for about one-fifth of the preliminary counting rate observed in a recent underground experiment. A more rapid increase in cross-section is indicated somewhere between 10 GeV. and 100 GeV. and this is shown to be quantitatively consistent with the existence of a charged intermediate boson of mass 2 GeV. ～ M_w < 5 GeV. (However see the note added in proof.) The question of detecting high energy neutrino signals from extra-terrestrial sources is briefly discussed.     

Neutrino emission from a one-dimensional hydrogen-like atom

We find the probability and intensity of the neutrino emission from a hydrogen-like atom in a strong magnetic field. We analyze the dependence of the neutrino emission intensity on the temperature of the ensemble of atoms.     

A Large Deviation Principle of Retarded Ornstein-Uhlenbeck Processes Driven by Lévy Noise

In this article, we develop a large deviation principle (LDP) for a class of retarded Ornstein-Uhlenbeck processes driven by Lévy processes. We first present a LDP result for time delay systems driven by cylindrical Wiener processes based on the large deviations of Gaussian processes. By using a contraction technique and passing on a finite-dimensional approximation, an LDP is obtained for stochastic time delay evolution equations driven by additive Lévy noise, whose solutions are generally not Lévy processes any more.     

Smoothness of certain functions in two kinds of risk models with a barrier dividend strategy

In this paper,we study the smoothness of certain functions in two kinds of risk models with a barrier dividend strategy.Mainly using technique from the piecewise deterministic Markov processes theory,we prove that the function is continuously differentiable in the first risk model.Using the weak infinitesimal generator method of Markov processes,we prove that the function is twice continuously differentiable in the second risk model.Intego-differential equations satisfied by them are derived.     

Automatic clustering of business processes in business systems planning

In this paper, we apply the technique of hierarchical clustering to business processes identified in business systems planning (BSP) which is an important methodology in information systems planning. A measure based on notions of cohesion and coupling is proposed as a guidance in searching for optimal number of clusters of business processes. By optimality, we mean that the net cohesion is maximized and net coupling is minimized. Moreover, we show that optimal number of clusters occurs at level of 0.5 in the hierarchy of partitions.     

Spontaneous breaking of flavor symmetry and naturalness of nearly degenerate neutrino masses and bi-maximal mixing

The gauge model withSO(3) _F . flavor symmetry and three Higgs triplets is studied. We show how the intriguing nearly degenerate neutrino mass and bi-maximal mixing scenario comes out naturally after spontaneous breaking of the symmetry. The hierarchy between the neutrino mass-squared differences, which is needed for reconciling both solar and atmospheric neutrino data, naturally results from an approximate permutation symmetry. The model can also lead to interesting phenornena on lepton-flavor violations via theSO(3) _F gauge interactions.     

Approximate KMS States for Scalar and Spinor Fields in Friedmann�CRobertson�CWalker Spacetimes

We construct and discuss Hadamard states for both scalar and Dirac spinor fields in a large class of spatially flat Friedmann–Robertson–Walker spacetimes characterised by an initial phase either of exponential or of power-law expansion. The states we obtain can be interpreted as being in thermal equilibrium at the time when the scale factor a has a specific value a = a ₀. In the case a ₀ = 0, these states fulfil a strict KMS condition on the boundary of the spacetime, which is either a cosmological horizon or a Big Bang hypersurface. Furthermore, in the conformally invariant case, they are conformal KMS states on the full spacetime. However, they provide a natural notion of an approximate KMS state also in the remaining cases, especially for massive fields. On the technical side, our results are based on a bulk-to-boundary reconstruction technique already successfully applied in the scalar case and here proven to be suitable also for spinor fields. The potential applications of the states we find range over a broad spectrum, but they appear to be suited to discuss in particular thermal phenomena such as the cosmic neutrino background or the quantum state of dark matter.     

任意加速带电轴对称动态黑洞中Weyl中微子的热辐射

在任意加速带电动态轴对称时空中,采用新Tortoise坐标变换研究、Weyl中微子的量子热效应,得到事件视界的位置以及在视界面附近Weyl中微子的热辐射温度,导出Hawking热谱公式.结果表明视界的位置和辐射温度不仅随时间变化,而且依赖于角度.     

Theory and applications of multivariate self-normalized processes

Multivariate self-normalized processes, for which self-normalization consists of multiplying by the inverse of a positive definite matrix (instead of dividing by a positive random variable as in the scalar case), are ubiquitous in statistical applications. In this paper we make use of a technique called “pseudo-maximization” to derive exponential and moment inequalities, and bounds for boundary crossing probabilities, for these processes. In addition, Strassen-type laws of the iterated logarithm are developed for multivariate martingales, self-normalized by their quadratic or predictable variations.     

Exponential change of measure applied to term structures of interest rates and exchange rates

In this paper, we study the term structures of interest rates and foreign exchange rates through establishing a state-price deflator. The state-price deflator considered here can be viewed as an extension to the potential representation of the state-price density in [Rogers, L.C.G., 1997. The potential approach to the term structure of interest rates and foreign exchange rates. Mathematical Finance 7(2), 157-164]. We identify a risk-neutral probability measure from the state-price deflator by a technique of exponential change of measure for Markov processes proposed by [Palmowski, Z., Rolski, T., 2002. A technique for exponential change of measure for Markov processes. Bernoulli 8(6), 767-785] and present examples of several classes of diffusion processes (jump-diffusions and diffusions with regime-switching) to illustrate the proposed theory. A comparison between the exponential change of measure and the Esscher transform for identifying risk-neutral measures is also presented. Finally, we consider the exchange rate dynamics by virtue of the ratio of the current state-price deflators between two economies and then discuss the pricing of currency options.     

An operator-based approach to the analysis of ruin-related quantities in jump diffusion risk models

Recent developments in ruin theory have seen the growing popularity of jump diffusion processes in modeling an insurer’s assets and liabilities. Despite the variations of technique, the analysis of ruin-related quantities mostly relies on solutions to certain differential equations. In this paper, we propose in the context of Lévy-type jump diffusion risk models a solution method to a general class of ruin-related quantities. Then we present a novel operator-based approach to solving a particular type of integro-differential equations. Explicit expressions for resolvent densities for jump diffusion processes killed on exit below zero are obtained as by-products of this work.     

On the fluid approximation for a multiclass queue under non-preemptive SBP service discipline

A multi-class single server queue under non-preemptive static buffer priority (SBP) service discipline is considered in this paper. Using a bounding technique, we obtain the fluid approximation for the queue length and busy time processes. Furthermore, we prove that the convergence rate of the fluid approximation for the queue length and busy time processes is exponential for large N. Additionally, a sufficient condition for stability is obtained.     

Laplace's method for the laws of heat processes on loop spaces

In this paper, we will consider Laplace's method for a class of heat processes on loop spaces. We will obtain the first term of the asymptotics under assumptions that the function under consideration attains its minimum at a unique point and that the Hessian at the point is non-degenerate. This kind of process was first introduced by P. Malliavin in 1990 for the loop group case and then gradually generalized by various authors. Our tool is the rough path theory of T. Lyons. This technique was pioneered by S. Aida for finite-dimensional processes in his unpublished paper.     

The construction of operational matrix of fractional derivatives using B-spline functions

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. Here we construct the operational matrix of fractional derivative of order α in the Caputo sense using the linear B-spline functions. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus we can solve directly the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the new technique presented in the current paper.     

Fluid approximation and its convergence Rate for GI/G/1 queue with vacations

A GI/G/1 queue with vacations is considered in this paper.We develop an approximating technique on max function of independent and identically distributed(i.i.d.) random variables,that is max{ηi,1 ≤ i ≤ n}.The approximating technique is used to obtain the fluid approximation for the queue length,workload and busy time processes.Furthermore,under uniform topology,if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate,we prove by the...     

Profiling effects in industrial data mining by non-parametric DOE methods: An application on screening checkweighing systems in packaging operations

There is a growing interest in applying robust techniques for profiling complex processes in industry. In this work, we present an approach for analyzing fractional-factorial data by building distribution-free models suitable for dealing with replicated trials in search of non-linear effects. The technique outlined in this article is synthesized by implementing four key elements: (1) the data collection efficiency of non-linear fractional factorial designs, (2) the data compression capabilities of rank-sums for repetitive sampling schemes, (3) the rank-ordering as a means to transform data, and (4) the non-parametric screening for prominent effects where the normality and sparsity assumptions are waived. The technique is tested on four controlling factors for profiling the packaging weighing operations of a pharmaceutical enterprise. The robust data mining of repeated trials based on an L₉(3⁴) orthogonal array scheme with embedded uncontrolled noise is discussed extensively. The technique has been subjected to quality control as it is tested with well-defined artificial data. Concluding remarks involve contrasting this new technique with mainstream competing schemes.     

Evolution Inclusions Governed by Time-Dependent Maximal Monotone Operators with a Full Domain

In this paper, we study the existence of solutions for evolution inclusions governed by time-dependent maximal monotone operators with a full domain. Without assumptions concerning time-regularity on the time-dependent maximal monotone operators, and by using the Moreau-Yosida regularization technique, we establish the existence of solutions in Hilbert spaces. The theoretical result is applied to prove the existence of solutions for semicoercive sweeping processes with velocity constraint.

     

The cauchy problem for a nonlinear integro-differential transport equation

In the present paper, we study the Cauchy problem for a nonlinear time-dependent kinetic neutrino transport equation. We prove the existence and uniqueness theorem for the solution of the Cauchy problem, establish uniform bounds int for the solution of this problem, and prove the existence and uniqueness of a stationary trajectory and the stabilization ast→∞ of the solution of the time-dependent problem for arbitrary initial data. Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 677–686, May, 1997. Translated by A. M. Chebotarev