最小化非光滑复合函数的投影Hessian校正算法的收敛性

本文考虑复合函数 F(x)=f(x)+h(c(x))最小化问题,给出了校正矩阵逼近 Langrangian 函数的“单边投影 Hessian”的 Broyden-类型方法;此方法是 Q-超线性收敛的.文中还叙述了两个校正算法,并且证明了在合理的条件下,这两种算法都具有局部的两步 Q-超线性收敛性.     

Approximation algorithms for scheduling unrelated parallel machines

We consider the following scheduling problem. There arem parallel machines andn independent jobs. Each job is to be assigned to one of the machines. The processing of jobj on machinei requires timep _ij . The objective is to find a schedule that minimizes the makespan.Our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum. We also present a polynomial approximation scheme for the case that the number of machines is fixed. Both approximation results are corollaries of a theorem about the relationship of a class of integer programming problems and their linear programming relaxations. In particular, we give a polynomial method to round the fractional extreme points of the linear program to integral points that nearly satisfy the constraints.In contrast to our main result, we prove that no polynomial algorithm can achieve a worst-case ratio less than 3/2 unlessP = NP. We finally obtain a complexity classification for all special cases with a fixed number of processing times.A preliminary version of this paper appeared in theProceedings of the 28th Annual IEEE Symposium on the Foundations of Computer Science (Computer Society Press of the IEEE, Washington, D.C., 1987) pp. 217–224.     

A Monte Carlo method for an objective Bayesian procedure

This paper describes a method for an objective selection of the optimal prior distribution, or for adjusting its hyper-parameter, among the competing priors for a variety of Bayesian models. In order to implement this method, the integration of very high dimensional functions is required to get the normalizing constants of the posterior and even of the prior distribution. The logarithm of the high dimensional integral is reduced to the one-dimensional integration of a cerain function with respect to the scalar parameter over the range of the unit interval. Having decided the prior, the Bayes estimate or the posterior mean is used mainly here in addition to the posterior mode. All of these are based on the simulation of Gibbs distributions such as Metropolis' Monte Carlo algorithm. The improvement of the integration's accuracy is substantial in comparison with the conventional crude Monte Carlo integration. In the present method, we have essentially no practical restrictions in modeling the prior and the likelihood. Illustrative artificial data of the lattice system are given to show the practicability of the present procedure.     

The Perturbation of the Interface of the Two-dimensional Diffraction Problem and an Approximating Muskat Modal

ln this paper, a new transformation is found out to straighten the interface Γ_2 x = f(y), f ∈ C^{2+a}([0, a]), f_y|_y =0, δ < f < l-δ,δ > 0,δ,l=constants and a perturbation of the interface is considered for a two dimensional diffraction problem. And the existence, uniqueness and regularity of an appeoximating Muskat model are proved.     

COF-42:一种理想的锂硫电池锚定材料

寻找理想的锚定材料抑制穿梭效应是锂硫电池面临的重要问题之一.本文采用密度泛函方法,研究了四种共价有机框架COFs材料(COF-1,CTF-1,COF-LZU1和COF-42)和硫锂化合物(Li_2S_n)的作用机理.通过分析吸附构型、吸附能、电子密度差分以及态密度等性质,发现COFs材料与硫锂化合物的化学吸附作用主要源于COFs表面极性N和O原子与Li之间的静电作用力.在COF-42/Li_2S_n吸附构型中,N和O原子与Li之间形成双重类离子键;电子密度差分和Bader电荷差分表明,与其他COFs材料相比,Li_2S_n和COF-42之间电荷转量最多,因此,COF-42具有最强的锚定作用.比较Li_2S_n和COF-42以及常用电解质分子1,3-二氧戊环(DOL)和二甲氧基乙烷(DME)的吸附能,证明COF-42可以抑制电解质分子的溶剂化作用; COF-42与COF-1,CTF-1和COF-LZU1相比较,具有良好导电性.因此,COF-42可能是一种理想的锂硫电池锚定材料.     

Ab initio方法研究~(40)Ca~(35)Cl分子的自旋轨道耦合效应和跃迁性质

本文研究了~(40)Ca~(35)Cl分子低态的自旋轨道耦合分裂以及获得更精确的光谱常数和更高的激发态.以从头算理论为基础,使用多参考组态相互作用方法获得了该分子的势能曲线和自旋轨道分裂,之后求解径向一维薛定谔方程获得光谱常数.得到了~(40)Ca~(35)Cl分子7个Λ-S低电子态的势能曲线和永久偶极矩,以及A~2Π→~2Σ~+,1~2Δ和C~2Π→~2Σ~+,1~2Δ跃迁的跃迁偶极矩,得到的光谱常数(不管是考虑了自旋轨道耦合(SOC)还是没有考虑SOC)与实验值非常符合,且要好于之前的理论计算结果 .值得注意的是,目前的计算还首次得到了C~2Π→~2Σ+,1~2Δ跃迁的跃迁性质,为之后实验观察~(40)Ca~(35)Cl分子的高激发态光谱和跃迁性质提供有益的理论参考.     

A general Hsu-Robbins-Erdős Type estimate of tail probabilities of sums of independent identically distributed random variables

Periodica Mathematica Hungarica - Let X 1,X 2,... be a sequence of independent and identically distributed random variables, and put % MATHTYPE!MTEF!2!1!+-%...     

Function Spaces of Posets with Projections

This paper investigates function spaces of structures consisting of a partially ordered set together with some directed family of projections.More precisely, given a fixed directed index set (I,), we consider triples (D,,(p _i ) _iI ) with (D,) a poset and (p _i ) _iI a monotone net of projections of D. We call them (I,)-pop's (posets with projections). Our main purpose is to study structure preserving maps between (I,)-pop's. Such homomorphisms respect both order and projections.Any (I,)-pop is known to induce a uniformity and thus a topology. The set of all homomorphisms between two (I,)-pop's turns out to form an (I,)-pop itself. We show that its uniformity is the uniformity of uniform convergence. This enables us to prove that properties such as completeness and compactness transfer to function pop's.Concerning categorical properties of (I,)-pop's, we will see that we are in a lucky situation from a computer scientist's point of view: we obtain Cartesian closed categories. Moreover, by a D -construction we get (I,)-pop's that are isomorphic to their own exponent. This yields new models for the untyped -calculus.     

Dynamic Global Constraints in Backtracking Based Environments

Global constraints provide strong filtering algorithms to reduce the search space when solving large combinatorial problems. In this paper we propose to make the global constraints dynamic, i.e., to allow extending the set of constrained variables during search. We describe a generic dynamisation technique for an arbitrary monotonic global constraint and we compare it with the semantic-based dynamisation for the alldifferent constraint. At the end we sketch a dynamisation technique for non-monotonic global constraints. A comparison with existing methods to model dynamic problems is given as well.