Some New Results on Circulant Weighing Matrices

We obtain a few structural theorems for circulant weighing matrices whose weight is the square of a prime number. Our results provide new schemes to search for these objects. We also establish the existence status of several previously open cases of circulant weighing matrices. More specifically we show their nonexistence for the parameter pairs (n, k) (here n is the order of the matrix and k its weight) = (147, 49), (125, 25), (200, 25), (55, 25), (95, 25), (133, 49), (195, 25), (11 w, 121) for w < 62.     

多变量双曲方程组初值问题一类变系数差分格式的稳定性

熟知,P.D.Lax和H.O.Kreiss)对一类对称双曲方程组的“耗散型”差分格式的稳定性得到了比较完善的结果。但由于条件稍严,实际应用受到限制。朱幼兰等对一个空间变量情形,取消对称和耗散的限制,建立了较广的一类差分格式的稳定性判别准则,并对大部分常用格式给出了与常系数情形相当的稳定性条件。本文把[3]中这一主要结果推广     

Hopf bifurcation in doubly fed induction generator under vector control

This paper first presents the Hopf bifurcation phenomena of a vector-controlled doubly fed induction generator (DFIG) which is a competitive choice in wind power industry. Using three-phase back-to-back pulse-width-modulated (PWM) converters, DFIG can keep stator frequency constant under variable rotor speed and provide independent control of active and reactive power output. Main results are illustrated by “exact” cycle-by-cycle simulations. The detailed mathematical model of the closed-loop system is derived and used to analyze the observed bifurcation phenomena. The loci of the Jacobian’s eigenvalues are computed and the analysis shows that the system loses stability via a Hopf bifurcation. Moreover, the boundaries of Hopf bifurcation are also given to facilitate the selection of practical parameters for guaranteeing stable operation.     

Trilinear equations, Bell polynomials, and resonant solutions

A class of trilinear differential operators is introduced through a technique of assigning signs to derivatives and used to create trilinear differential equations. The resulting trilinear differential operators and equations are characterized by the Bell polynomials, and the superposition principle is applied to the construction of resonant solutions of exponential waves. Two illustrative examples are made by an algorithm using weights of dependent variables.     

Broadening of Cr nanostructures in laser-focused atomic deposition

This paper presents the experimental progress of laser-focused Cr atomic deposition and the experimental condition.The result is an accurate array of lines with a periodicity of 212.8±0.2 nm and mean full-width at half maximum as approximately 95 nm.Surface growth in laser-focused Cr atomic deposition is modeled and studied by kinetic Monte Carlo simulation including two events:the one is that atom trajectories in laser standing wave are simulated with the semiclassical equations of motion to obtain the deposition position;the other is that adatom diffuses by considering two major diffusion processes,namely,terrace diffusion and step-edge descending.Comparing with experimental results(Anderson W R,Bradley C C,McClelland J J and Celotta R J 1999 Phys.Rev.A 59 2476),it finds that the simulated trend of dependence on feature width is in agreement with the power of standing wave,the other two simulated trends are the same in the initial stage.These results demonstrate that some surface diffusion processes play important role in feature width broadening.Numerical result also shows that high incoming beam flux of atoms deposited redounds to decrease the distance between adatoms which can diffuse to minimize the feature width and enhance the contrast.     

Hydrothermal preparation and photoluminescence of bundle-like structure of ZnWO4 nanorods

ZnWO₄ nanorods with a bundle-like structure were synthesized at 180°C for 12 h by a hydrothermal technology from Na₂WO₄⋅2H₂O and ZnSO₄⋅7H₂O in the presence of sodium dodecyl sulfate (SDS). The as-synthesized bundle-like structure of ZnWO₄ nanorods was characterized by various techniques: TEM, XRD and EDS. The luminescence properties of the bundle-like structure of the ZnWO₄ nanorods were investigated by photoluminescence (PL) spectroscopy.     

Infinite horizon H_2/H_\infty optimal control for discrete-time Markov jump systems with (x,u,v)-dependent noise

In this paper, an infinite horizon $H_2/H_\infty $ control problem is addressed for a broad class of discrete-time Markov jump systems with ( $x,u,v$ )-dependent noises. First of all, under the condition of exact detectability, the stochastic Popov–Belevich–Hautus (PBH) criterion is utilized to establish an extended Lyapunov theorem for a generalized Lyapunov equation. Further, a necessary and sufficient condition is presented for the existence of state-feedback $H_2/H_\infty $ optimal controller on the basis of two coupled matrix Riccati equations, which may be solved by a backward iterative algorithm. A numerical example with simulations is supplied to illustrate the proposed theoretical results.     

Nonlinear Saturation Amplitude in Classical Planar Richtmyer–Meshkov Instability

The classical planar Richtmyer–Meshkov instability(RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order,and then according to definition of nonlinear saturation amplitude(NSA) in Rayleigh–Taylor instability(RTI),the NSA in planar RMI is obtained explicitly.It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface,while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength.Without marginal influence of the initial amplitude,the NSA increases linearly with wavelength.The NSA normalized by the wavelength in planar RMI is about 0.11,larger than that corresponding to RTI.     

Global periodicity and complete integrability of discrete dynamical systems

Consider the discrete dynamical system generated by a map F. It is said that it is globally periodic if there exists a natural number p such that F ^p (x)=x for all x in the phase space. On the other hand, it is called completely integrable if it has as many functionally independent first integrals as the dimension of the phase space. In this paper, we relate both concepts. We also give a large list of globally periodic dynamical systems together with a complete set of their first integrals, emphasizing the ones coming from difference equations.