Stochastic systems with cross-correlated Gaussian white noises

This paper theoretically investigates three stochastic systems with cross-correlation Gaussian white noises.Both steady state properties of the stochastic nonlinear systems and the nonequilibrium transitions induced by the cross-correlated noises are studied.The stationary solutions of the Fokker-Planck equation for three specific examples are analysed.It is shown explicitly that the cross-correlation of white noises can induce nonequilibrium transitions.     

Phase diagram and tricritical behavior of an metamagnet in uniform and random fields

A two-sublattice Ising metamagnet in both uniform and random fields is studied within the mean-field approach based on Bogoliubov’s inequality for the Gibbs free energy. We show that the qualitative features of the phase diagrams are dependent on the parameters of the model and the uniform field values. The tricritical point and reentrant phenomenon can be observed on the phase diagram. The reentrance is due to the competition between uniform and random interactions.     

Easy axis reorientation and magneto-crystalline anisotropic resistance of tensile strained (Ga,Mn)As films

We present a study of magnetic anisotropy by using magneto-transport and direct magnetization measurements on tensile strained (Ga,Mn)As films. The magnetic easy axis of the films is in-plane at low temperatures, while the easy axis flips to out-of-plane when temperature is raised or hole concentration is increased. This easy axis reorientation is explained qualitatively in a simple physical picture by Zener’s p-d model. In addition, the magneto-crystalline anisotropic resistance was also investigated experimentally and theoretically based on the single magnetic domain model. The dependence of sheet resistance on the angle between the magnetic field and [1 0 0] direction was measured. It is found that the magnetization vector M in the single-domain state deviates from the external magnetic field H direction at low magnetic field, while for high magnetic field, M continuously moves following the field direction, which leads to different resistivity function behaviors.     

Global existence for some radial, low regularity nonlinear Schrödinger equations

We prove the nonlinear Schrödinger equation has a local solution for any energy - subcritical nonlinearity when u₀ is the characteristic function of a ball in Rn. Additionally, we establish the existence of a global solution for n?3 when and α?2. Finally, we establish the existence of a global solution when the initial function is radial, the nonlinear Schrödinger equation has an energy subcritical nonlinearity, and the initial function lies in Hρ+?(Rn)∩H1/2+?(Rn)∩H1/2+?,1(Rn).     

Small prime solutions of a pair of linear equations in five prime variables

Assume an additional congruent condition on the coefficients. We prove that the pair 5 of linear equations ∑j=1^5 αλjpj = bλ （λ= 1, 2） has solutions in primes pj satisfying pj 〈〈 （｜b1｜＋｜b2｜＋1） maxλ,j ｜αλj｜^2318＋ε. This improves the exponent 79680 without assuming the additional condition of the second author＇s.     

Nonlinear study of a rotor–AMB system under simultaneous primary-internal resonance

A rotor–active magnetic bearing (AMB) system subjected to a periodically time-varying stiffness with quadratic and cubic non-linearities under multi-parametric excitations is studied and solved. The method of multiple scales is applied to analyze the response of two modes of a rotor–AMB system with multi-parametric excitations and time-varying stiffness near the simultaneous primary and internal resonance. The stability of the steady state solution for that resonance is determined and studied using Rung–Kutta method of fourth order. It is shown that the system exhibits many typical non-linear behaviors including multiple-valued solutions, jump phenomenon, hardening and softening non-linearities and chaos in the second mode of the system. The effects of the different parameters on the steady state solutions are investigated and discussed also. A comparison to published work is reported.     

What types of investors generate the two-phase phenomenon?

We examine the two-phase phenomenon described by Plerou, Gopikrishnan, and Stanley (2003)  [1] in the KOSPI 200 options market, one of the most liquid options markets in the world. By analysing a unique intraday dataset that contains information about investor type for each trade and quote, we find that the two-phase phenomenon is generated primarily by domestic individual investors, who are generally considered to be uninformed and noisy traders. In contrast, our empirical results indicate that trades by foreign institutions, who are generally considered informed and sophisticated investors, do not exhibit two-phase behaviour.     

Random doubly stochastic tridiagonal matrices

Let \begin{align*}{\mathcal T}\end{align*}n be the compact convex set of tridiagonal doubly stochastic matrices. These arise naturally in probability problems as birth and death chains with a uniform stationary distribution. We study ‘typical’ matrices T∈ \begin{align*}{\mathcal T}\end{align*}n chosen uniformly at random in the set \begin{align*}{\mathcal T}\end{align*}n. A simple algorithm is presented to allow direct sampling from the uniform distribution on \begin{align*}{\mathcal T}\end{align*}n. Using this algorithm, the elements above the diagonal in T are shown to form a Markov chain. For large n, the limiting Markov chain is reversible and explicitly diagonalizable with transformed Jacobi polynomials as eigenfunctions. These results are used to study the limiting behavior of such typical birth and death chains, including their eigenvalues and mixing times. The results on a uniform random tridiagonal doubly stochastic matrices are related to the distribution of alternating permutations chosen uniformly at random.© 2012 Wiley Periodicals, Inc. Random Struct. Alg., 42, 403–437, 2013