Oscillator with random trichotomous mass

In addition to the case usually considered of a stochastic harmonic oscillator subject to an external random force (Brownian motion in a parabolic potential) or to a random frequency and random damping, we consider an oscillator with random mass subject to an external periodic force, where the molecules of a surrounding medium, which collide with a Brownian particle are able to adhere to the oscillator for a random time, changing thereby the oscillator mass. The fluctuations of mass are modelled as trichotomous noise. Using the Shapiro–Loginov procedure for splitting the correlators, we found the first two moments. It turns out that the second moment is a non-monotonic function of the characteristics of noise and periodic signal, and for some values of these parameters, the oscillator becomes unstable.     

Stieltjes moment problem and fractional moments

Stieltjes moment problem is considered and a solution, consisting of the use of fractional moments, is proposed. More precisely, a determinate Stieltjes moment problem, whose corresponding Hamburger moment problem is determinate too, is investigated in the setup of Maximum Entropy. Condition number in entropy calculation is provided endowing both Stieltjes moment problem existence conditions and Hamburger moment problem determinacy conditions by a geometric meaning. Then the resorting to fractional moments is considered; numerical aspects are investigated and a stable algorithm for calculating fractional moments from integer moments is proposed.     

Numerical Comparison of Controls and Verification of Optimality for Stochastic Control Problems

We provide two approaches to the numerical analysis of stochastic control problems. The analyses rely on linear programming formulations of the control problem and allow numerical comparison between controls and numerical verification of optimality. The formulations characterize the processes through the moments of the induced occupation measures. We deal directly with the processes rather than with some approximation to the processes. Excellent software is readily available, since the computations involve finite-dimensional linear programs.     

Rayleigh–Ritz variation method and connected‐moments polynomial approach

We show that the connected‐moments polynomial approach proposed recently is equivalent to the well known Rayleigh–Ritz variation method in the Krylov space. We compare the latter with one of the original connected‐moments methods by means of a numerical test on an anharmonic oscillator. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Boltzmann-Poisson系统解的动量及能量估计

In this paper, the properties of the solutions of Boltzmann-Poisson system in three dimensions are considered. The estimates of the energies (the kinetic and the potential energies) and the γ-th moments with γ∈[2,3) are obtained. The latter answers an open problem.     

The summarized equation for functions which are holomorphic in the exterior of a triangle

We consider the six-element summarized equation in the class of functions which are holomorphic in the exterior of a regular triangle and vanishing at infinity. We apply the method of integral equations and the theory of elliptic functions. Using the obtained results, we construct biorthogonal systems of holomorphic functions and study the problem of moments for integer functions of a finite degree.     

Energy dependence of non-linear dynamical features in e^＋e^- collisions

A study of the d.ynamical fluctuation properties at various c.m.energies in e~ e~- collisions is performed using the Monte Carlo method.The results suggest that,after the normalized factorial moments of 3-dimensional phase space are analyzed using an isotropical phase space partition,the NFM describing non- linear dynamical properties show a power-law scaling,i.e.,the dynamical fluctuations in higher dimensional phase space are isotropic.For c.m.energies s~(1/2)≤80 GeV,the scaling exponentsφ_q increase rapidly with the c.m.energy and for c.m.energies s~(1/2)>80 GeV,theφ_q gradually saturate.     

Application of possibility theory to investment decisions

Carlson and Fuller (2001, Fuzzy Sets and Systems, 122, 315–326) introduced the concept of possibilistic mean, variance and covariance of fuzzy numbers. In this paper, we extend some of these results to a nonlinear type of fuzzy numbers called adaptive fuzzy numbers (see Bodjanova (2005, Information Science, 172, 73–89) for detail). We then discuss the application of these results to decision making problems in which the parameters may involve uncertainty and vagueness. As an application, we develop expression for fuzzy net present value (FNPV) of future cash flows involving adaptive fuzzy numbers by using their possibilistic moments. An illustrative numerical example is given to illustrate the results.     

Nucleon octet in a relativistic logarithmic potential

A simple independent-quark-model based on the Dirac equation with logarithmic potential is used to calculate several properties of octet baryons such as magnetic moment, the axial vector coupling constantg _A (n) for neutronβ-decay and the charge radius of the proton. In view of the simplicity of the model, the results obtained are quite good.     

Magnetic moments of hindered rotators by off‐center impurity ions

Off‐center impurity ions in solids often perform rotations around their regular lattice sites. Unlike quasifree rotors with rotational line spectra subject to textbook attention in quantum mechanics, the off‐center species are hindered rotors with spectra quantized in rotational bands. These bands occur because of tunneling through barriers arising along the orbital path. For an off‐center ion rotating along a planar orbit, such as the Li⁺ impurity nearest‐neighboring an F center in alkali halide, the hindered rotation will give rise to specific magnetic moments that couple to and quantize external magnetic fields normal to the orbital plane. We present a simple theory and estimates of Li⁺ magnetic dipoles and rotational bands to find conditions for an experimental verification. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002