Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields

Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.     

Fredholm theory for pseudoholomorphic curves with brake symmetry

We study the pseudoholomorphic curves with brake symmetry in symplectization of a closed contact manifold. We introduce the pseudo-holomorphic curves with brake symmetry and the corresponding moduli space. Then we get the virtual dimension of the moduli space.     

经典一维装箱问题近似算法的研究进展

自20世纪70年代开始,随着计算复杂性理论的建立,近似算法逐渐成为组合优化的重要研究方向。作为第一批研究对象,装箱问题引起了组合优化领域学者的极大关注。装箱问题模型简单、拓展性强,广泛出现在各种带容量约束的资源分配问题中。除了在物流装载和材料切割等方面愈来愈重要的应用外,装箱算法的任何理论突破都关乎到整个组合优化领域的发展。直到今天,对装箱问题近似算法的研究仍如火如荼。本文主要针对一维模型,简述若干经典Fit算法的发展历程,分析基于线性规划松弛的近似方案的主要思路,总结当前的研究现状并对未来的研究提供一些参考建议。     

Gr-凝聚环的分次FP-内射维数

引进了分次FP-内射维数，对Gr-凝聚环的分次FP-内射维数作了刻划，将Stentrom等人的若干工作推广到分次环上．     

A fixed-parameter-tractable algorithm for set packing

1. IntroductionIt is a useful and challenging task to find efficient algorithms for many computationalhard problems. Recently, the research on Fixed-Parameter nactable Theory arouses muchinterest. FOr example, different fixed- p ax amet er- t rac t ab le- algori t hms for many well- knowndecisio11 pruble11ls illc1udi11g 3-dimellsio11al IIlatchiIlg: a11d vertex--cover Problen1 have beenPrese11ted in [1 8]. Jia11er Chen, DoIlald K. FYiesen al1d Weijia Jia proPosed a coll1pletelynew appro…     

An Exploratory Study on the Complexity and Machine Learning Predictability of Stock Market Data

This paper shows if and how the predictability and complexity of stock market data changed over the last half-century and what influence the M1 money supply has. We use three different machine learning algorithms, i.e., a stochastic gradient descent linear regression, a lasso regression, and an XGBoost tree regression, to test the predictability of two stock market indices, the Dow Jones Industrial Average and the NASDAQ (National Association of Securities Dealers Automated Quotations) Composite. In addition, all data under study are discussed in the context of a variety of measures of signal complexity. The results of this complexity analysis are then linked with the machine learning results to discover trends and correlations between predictability and complexity. Our results show a decrease in predictability and an increase in complexity for more recent years. We find a correlation between approximate entropy, sample entropy, and the predictability of the employed machine learning algorithms on the data under study. This link between the predictability of machine learning algorithms and the mentioned entropy measures has not been shown before. It should be considered when analyzing and predicting complex time series data, e.g., stock market data, to e.g., identify regions of increased predictability.     

基于概率密度演化的输电塔-线体系抗风可靠性分析

以三线两塔直线段输电塔-线体系为工程对象,应用有限元数值模拟,建立了基于概率密度演化的输电塔-线体系抗风可靠性分析方法。首先,应用谱表示-降维方法模拟结构脉动风场,生成风荷载的代表性样本集合。然后,结合概率密度演化理论,分析了输电塔-线体系考虑气弹效应的随机动力反应。最后,应用等价极值思想构建了风荷载作用下输电塔-线体系失效准则,进而对输电塔-线体系的抗风可靠性进行精细化分析。本文结合谱表示-降维方法与概率密度演化理论,实现了仅用较少数量的代表性样本来精细地分析结构的抗风可靠性,为工程实践提供参考。     

End-capped Thiophene Modulated Molecular Packing in 2,8-Dibenzothiophene-based Materials：from Face-to-face to Edge-to-face Stacking

Two new organic crystals of 2,8-bisthienyldibenzothiophene(BTDT) and 2,8-bis-dithienyldibenzothiophene(BDTDT) compounds were successfully obtained.The change of end-capped group from thiophene to dithiophene causes big differences in molecular packing and carrier-transport property.The adjacent molecules of compound BTDT adopt face-to-face π stacking and exhibit two-dimensional interchain interactions.On the contrary,BDTDT molecules are arranged in an edge-to-face motif and show mainly one-dimensional interacting character.The packing mode exerts dramatic effect on the carrier-transport property.The crystal of BTDT belongs to the orthorhombic system,space group P21212 with a = 20.1427(11),b = 4.6016(3),c = 8.6340(5) ,V = 800.27(8) 3,Z = 2,Dc = 1.446 g/cm3,F(000) = 360,S = 1.019,the final R = 0.0491 and wR = 0.0960 for 1605 reflections with I > 2σ(I).The crystal of BDTDT belongs to the orthorhombic system,space group P212121 with a = 7.2636(15),b = 25.359(5),c = 25.359 ?,V = 4670.9(14) ?3,Z = 8,Dc = 1.458 g/cm3,F(000) = 2112,S = 0.880,the final R = 0.0597 and wR = 0.1318 for 8047 reflections with I > 2σ(I).     

The global dimensions of crossed products and crossed coproducts

In this paper, we show that if H is a finite-dimensional Hopf algebra such that H and H^＊ are semisimple, then gl.dim（A#σH）=gl.dim（A）, where a is a convolution invertible cocycle. We also discuss the relationship of global dimensions between the crossed product A^#σH and the algebra A, where A is coacted by H. Dually, we give a sufficient condition for a finite dimensional coalgebra C and a finite dimensional semisimple Hopf algebra H such that gl.dim（C α H）=gl.dim（C）.