Brownian survival and Lifshitz tail in perturbed lattice disorder

We consider the annealed asymptotics for the survival probability of Brownian motion among randomly distributed traps. The configuration of the traps is given by independent displacements of the lattice points. We determine the long time asymptotics of the logarithm of the survival probability up to a multiplicative constant. As applications, we show the Lifshitz tail effect of the density of states of the associated random Schrödinger operator and derive a quantitative estimate for the strength of intermittency in the parabolic Anderson problem.     

Estimating the Gerber–Shiu function in the perturbed compound Poisson model by Laguerre series expansion

In this paper, we study the statistical estimation of the Gerber–Shiu function in the compound Poisson risk model perturbed by diffusion. This problem has been solved in [32] by the Fourier–Sinc series expansion method. Different from [32], we use the Laguerre series to expand the Gerber–Shiu function and propose a relevant estimator. The estimator is easily computed and has fast convergence rate. Various simulation studies are presented to confirm that the estimator performs well when the sample size is finite.     

On admissible perturbations for exponential dichotomy

In this work we obtain an optimal upper bound for exponential dichotomy roughness in infinite-dimensional Banach spaces. Unlike some previous works, we do not assume bounded growth. We consider linear, non-autonomous ordinary differential equations with bounded and unbounded coefficients.     

On the Existence of Towers in Pseudo-Tree Algebras

A tower in a Boolean algebra (BA) is a strictly increasing sequence, of regular order type, of elements of the algebra different from 1 but with sum 1. A pseudo-tree is a partially ordered set T such that the set T↓t = {s ∈ T:s < t} is linearly ordered for every t ∈ T. If that set is well-ordered, then T is a tree. For any pseudo-tree T, the BA Treealg(T) is the algebra of subsets of T generated by all of the sets T↑t = {s ∈ T:t ≤ s}. The main theorem of this note is a characterization in tree terms of when Treealg(T) has a tower of order type κ (given in advance).     

A quantitative notion of redundancy for finite frames

The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy for finite frames in a Hilbert space. This motivates a carefully chosen list of desired properties for upper and lower redundancies. The means to achieve these properties is to consider the maximum and minimum of a redundancy function, which is interesting in itself. The redundancy function is defined on the sphere of the Hilbert space and measures the concentration of frame vectors around each point. A complete characterization of functions on the sphere which coincide with a redundancy function for some frame is given. The upper and lower redundancies obtained from this function are then shown to satisfy all of the intuitively desirable properties. In addition, the range of values they assume is characterized.     

Perturbed recurrence relations III the general case—some new applications

In this paper, we give some new extensions and some new applications of our results on the perturbation of coefficients and the order of a general recurrence relation—for example we will give some new results for the asymptotic properties, for the zeros and for the differential equations of the polynomials which satisfy the perturbed recurrence relation.      

Embedded pair of extended Runge–Kutta–Nyström type methods for perturbed oscillators

A 5(3) pair of extended Runge–Kutta–Nyström type methods for the numerical integration of perturbed oscillators is presented. These methods are based on the order conditions of extended Runge–Kutta–Nyström type methods proposed by Yang et al. [H.L. Yang, X.Y. Wu, X. You, Y.L. Fang, Extended RKN-type methods for numerical integration of perturbed oscillators, Comput. Phys. Commun. 180 (2009) 1777–1794]. The numerical stability and phase properties of the fifth-order methods are analyzed. Numerical experiments are carried out to show the efficiency and robustness of our new methods in comparison with some well known high quality codes proposed in the scientific literature.     

Exact solutions for a nonlinear model

In this paper we show new exact solutions for a type of generalized sine-Gordon equation which is obtained by constructing a Lagrange function for a dynamical coupled system of oscillators. We convert it into a nonlinear system by perturbing the potential energy from a point of view of an approach proposed by Fermi [1].     

Linearly polarized white fluorescence from shish-kebab type liquid crystalline poly(P-phenylenevinvlene)s with (P-phenylene)s as kebab

Liquid crystalline(LC) polymers with a shish-kebab-type moiety on their cross-conjugated(p-phenylene)s-poly(p-phenylenevinylene) s main chains were synthesized through Gilch polymerization in order to develop a kind of polymers available for linearly polarized white-light-emitting from single chain.In this system,the 2,5-bis(4’-alkoxyphenyl)benzene as the "kebabs" connects with poly(p-phenylenevinylene)(PPV) main chain backbone using its molecular gravity center and the PPV as the "shish" or "skewer"(the "shish-kebab").The polymers possess desirable properties such as excellent solubility and liquid crystalline properties.To drop the "kebabs" of the 2,5-bis(4’-alkoxyphenyl)benzene into the orientation microgroove of aligned polyimide film,not only the "shish" of polymer main chain can be aligned by the virtue of orientation of "kebabs" but also the uniform cross-conjugated structure between the "kebabs" and "shish" can be broken. Then,the alignment of the polymer main chain showed yellow light emission and was also accompanied by orientation of the LC side chains showing blue light emission,this gave rise to a notable linearly polarized white fluorescence.     

不同波长的散射介质后向散射光偏振度特性

基于Stockes矢量,通过测量以线偏振光和圆偏振光入射时脂肪乳剂后向散射光的偏振度,研究了532 nm、650 nm和780 nm三个波长的光与散射粒子粒径为325 nm的脂肪乳剂溶液作用后,其后向散射光的偏振度特性.研究结果表明,对于入射线偏振光,780 nm波长后向散射光中的线偏振光成分多于圆偏振光成分,而532 nm波长则相反;对于入射圆偏振光,三个波长后向散射光中的圆偏振光成分均多于线偏振光成分;532 nm波长的总偏振度高于650 nm和780 nm两个波长各自的总偏振度;线偏振光的保偏性优于圆偏振光的保偏性,但偏振光在散射介质中的穿透深度较小.因此,后向散射成像技术适用于物体表层成像,而且选择波长略大于粒径的线偏振光可以提高成像质量.