Mirrorless lasers

Experimental realization of mirrorless lasers in the last decade have resulted in hectic activity in this field, due to their novelty, simplicity and ruggedness and their great potential for application. In this article, I will review the various developments in this field in roughly chronological order, and discuss some possible applications of this exciting phenomenon, also termed as ‘random lasing’.     

模糊数据的线性回归模型

研究观测数据为模糊数据的统计线性回归模型 ,由该模型所得回归系数非模糊 ,易于应用。对于对称三角模糊数据一元线性回归给出最优解的解析表达式 ;将对称三角模糊数多元线性回归问题给出转化为一类二次规划问题的方法 ;证明了最优解的存在性和估计量的无偏性。     

局部Lipschitz条件下的布朗运动和泊松过程混合驱动的正倒向随机微分方程

本文得到在局部Lipschiz条件下的布朗运动和泊松过程混合驱动的倒向随机微分方程的存在唯一性；同时也证明了布朗运动和泊松过程混合驱动的完全藕合的正倒向随机微分方程在局部Lipschitz条件下的解的存在唯一性。     

Almost-sure central limit theorem for a Markov model of random walk in dynamical random environment

Summary We consider a model of random walk on ℤ^ν, ν≥2, in a dynamical random environment described by a field ξ={ξ _t (x): (t,x)∈ℤ^ν+1}. The random walk transition probabilities are taken as P(X _{t +1}= y|X _t = x,ξ _t =η) =P ₀( y−x)+ c(y−x;η(x)). We assume that the variables {ξ _t (x):(t,x) ∈ℤ^ν+1} are i.i.d., that both P ₀(u) and c(u;s) are finite range in u, and that the random term c(u;·) is small and with zero average. We prove that the C.L.T. holds almost-surely, with the same parameters as for P ₀, for all ν≥2. For ν≥3 there is a finite random (i.e., dependent on ξ) correction to the average of X _t , and there is a corresponding random correction of order to the C.L.T.. For ν≥5 there is a finite random correction to the covariance matrix of X _t and a corresponding correction of order to the C.L.T.. Proofs are based on some new L ^p estimates for a class of functionals of the field. Received: 4 January 1996/In revised form: 26 May 1997     

Persistent convergence on randomly deleted sets

At time t_k, a unit with magnitude X_k and lifetime L_k enters a system. Let λ be a real valued function on the finite real sequences. One such sequence, B*_t, consists of the X_k's for which t_k t < t_k + L_k. When λ(X₁,…, X_n) converges (in some sense) to φ, we find conditions under which λ(B*_t) converges or fails to converge to φ in the same sense.     

Exact analysis of asymmetric random polling systems with single buffers and correlated input process

We introduce a simple approach for modeling and analyzing asymmetric random polling systems with single buffers and correlated input process. We consider two variations of single buffers system: the conventional system and the buffer relaxation system. In the conventional system, at most one customer may be resided in any queue at any time. In the buffer relaxation system, a buffer becomes available to new customers as soon as the current customer is being served. Previous studies concentrate on conventional single buffer system with independent Poisson process input process. It has been shown that the asymmetric system requires the solution ofm 2 ^m –1) linear equations; and the symmetric system requires the solution of 2 ^m–1–1 linear equations, wherem is the number of stations in the system. For both the conventional system and the buffer relaxation system, we give the exact solution to the more general case and show that our analysis requires the solution of 2 ^m –1 linear equations. For the symmetric case, we obtain explicit expressions for several performance measures of the system. These performance measures include the mean and second moment of the cycle time, loss probability, throughput, and the expected delay observed by a customer.     

From sum rules to RPA: 1. Nuclei

We take up the flexible formulation of RPA in subspaces of coordinate-like and momentum-like 1 ph operators which was developed in the preceeding paper. We draw the connection to many of the known collective approximations to RPA by proper choice of the subspace of operators. We finally apply the newly developed scheme to comparative studies of a hierarchy of approaches for the RPA spectra of doubly magic nuclei described with Skyrme forces.     

COLLISION AND MEETING OF STABLE PROCESSES

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Lifshitz tails for random perturbations of periodic Schrödinger operators

The present paper is a non-exhaustive review of Lifshitz tails for random perturbations of periodic Schrödinger operators. It is not our goal to review the whole literature on Lifshitz tails; we will concentrate on a single model, the continuous Anderson model.     

Random walks on highly symmetric graphs

We consider uniform random walks on finite graphs withn nodes. When the hitting times are symmetric, the expected covering time is at least 1/2n logn-O(n log logn) uniformly over all such graphs. We also obtain bounds for the covering times in terms of the eigenvalues of the transition matrix of the Markov chain. For distance-regular graphs, a general lower bound of (n-1) logn is obtained. For hypercubes and binomial coefficient graphs, the limit law of the covering time is obtained as well.