Modeling of the non-equilibrium effects by high electric fields in small semiconductor devices

For the purpose of the future theory of energy and momentum relaxation in semiconductor devices, the introduction of two temperatures and two mean velocities for electron and phonons is required. A new model, based on an asymptotic procedure for solving the generalized kinetic equations of electrons and phonons is proposed, which gives naturally the displaced Maxwellian at the leading order. After that, balance equations for the electron number, energy densities, and momentum densities are constructed, which now constitute a system of five equations for the chemical potential of electrons, the temperatures and the drift velocities. In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered.     

Thermal entanglement of Hubbard dimers in the nonextensive statistics

The thermal entanglement of the Hubbard dimer (two-site Hubbard model) has been studied with the nonextensive statistics. We have calculated the auto-correlation (O_q), pair correlation (L_q), concurrence (Γ_q) and conditional entropy (R_q) as functions of entropic index q and the temperature T. The thermal entanglement is shown to considerably depend on the entropic index. For q<1.0, the threshold temperature where Γ_q vanishes or R_q changes its sign is more increased and the entanglement may survive at higher temperatures than for q=1.0. Relations among L_q, Γ_q and R_q are investigated. The physical meaning of the entropic index q is discussed with the microcanonical and superstatistical approaches. The nonextensive statistics is applied also to Heisenberg dimers.     

A note on the existence of fractional f-factors in random graphs

Let G=Gn,p be a binomial random graph with n vertices and edge probability p=p(n),and f be a nonnegative integer-valued function defined on V(G) such that 0a≤f(x)≤bnp-2np ㏒n for every x ∈V(G). An fractional f-indicator function is an function h that assigns to each edge of a graph G a number h(e) in [0,1] so that for each vertex x,we have dh G(x)=f(x),where dh G(x) = x∈e h(e) is the fractional degree of x in G. Set Eh = {e:e ∈E(G) and h(e)=0}.If Gh is a spanning subgraph of G such that E(Gh)=Eh,then Gh is called an fractional f-factor of G. In this paper,we prove that for any binomial random graph Gn,p with p≥n-23,almost surely Gn,p contains an fractional f-factor.     

Dynamic fuzzy reliability models of degraded hold-down structures for folded solar array

The hold-down structures are of considerable importance to the launch of solar array. Due to the difficulties in obtaining sufficient load specimen, it is imprecise to construct the stress as random variables. Therefore, dynamic fuzzy reliability models are developed in this paper, which resolve the problems in dealing with the interaction between the fuzzy stress process and the stochastic strength process. Even for a deterministic fuzzy stress process, the influences of material statistical properties on reliability can be affected by the level α of fuzzy stress. Meanwhile, the level α relates to investment in the collection of information about the fuzzy stress on hold-down bar. Hence, the models can be used for the economic analysis and optimal design of hold-down bar. Finally, key fuzzy parameters of stress, which have significant influences on both the reliability behavior and the effects of material statistical properties on reliability, are identified and some suggestions for the reliability enhancement of hold-down bar are provided in this paper.     

The finite sample breakdown point of PCS

The Projection Congruent Subset (PCS) is a new method for finding multivariate outliers. PCS returns an outlyingness index which can be used to construct affine equivariant estimates of multivariate location and scatter. In this note, we derive the finite sample breakdown point of these estimators.     

用不确定德尔菲法预测GDP

德尔菲法是一种建立在专家意见基础上的预测评估方法.不确定统计是利用不确定理论收集和整理分析专家数据的一种统计方法,其中关键的一点是如何构造不确定变量的不确定分布.把德尔菲法和不确定统计相结合,就得到了一种估计不确定分布的新方法——不确定德尔菲法.对该方法的估计误差进行了改进,得到了一种预测GDP的新方法,并利用其预测邯郸市的生产总值(GDP).     

Best Fourier Approximation and Application in Efficient Blurred Signal Reconstruction

We expand upon the known results on sharp linear Fourier methods of approximation where the approximation is the best in terms of both rate and constant among all polynomial procedures of approximation. So far these results have been studied due to their mathematical beauty rather than their practical importance. In this paper we show that they are the core mathematics underlying best statistical methods of solving noisy ill-posed problems. In particular, we suggest a procedure for recovery of noisy blurred signals based on samples of small sizes where a traditional statistics concludes that the complexity of such a setting makes the problem not worthy of a further study. Thus, we present a problem where a combination of the classical approximation theory and statistics leads to interesting practical results.     

Positive Semidefinite Rank-Based Correlation Matrix Estimation With Application to Semiparametric Graph Estimation

Many statistical methods gain robustness and flexibility by sacrificing convenient computational structures. In this article, we illustrate this fundamental tradeoff by studying a semiparametric graph estimation problem in high dimensions. We explain how novel computational techniques help to solve this type of problem. In particular, we propose a nonparanormal neighborhood pursuit algorithm to estimate high-dimensional semiparametric graphical models with theoretical guarantees. Moreover, we provide an alternative view to analyze the tradeoff between computational efficiency and statistical error under a smoothing optimization framework. Though this article focuses on the problem of graph estimation, the proposed methodology is widely applicable to other problems with similar structures. We also report thorough experimental results on text, stock, and genomic datasets.