Extensions of the Borel–Cantelli lemma in general measure spaces

In this paper, an important bilateral inequality for a sequence of nonnegative measurable functions on a measure space \((S,\mathcal {B}_S,\mu )\) is obtained, and some sufficient conditions for \(\mu \left( \limsup \limits _{n\rightarrow \infty }A_n\right) =\mu (S)\) are given. In addition, a weighted version of the Borel–Cantelli Lemma on the measure space is obtained. Our results generalize the corresponding ones for bounded random sequences to the case of unbounded measurable functions.     

Breakdown-quenching characteristics and mechanisms for silicon photomultipliers

Some deviant breakdown-quenching characteristics of silicon photomultipliers are demonstrated and their physical mechanisms are explored. “Twice breakdown” phenomenon, “flat-topped” avalanche pulses and the determination method of the real breakdown voltage of the detector are analyzed. These characteristics are explained by the integration model in terms of avalanche threshold current based on the Haitz's equivalent circuit model. The reasoning results show that the maximum over-voltage for a normal operating silicon photomultiplier equals the product of the avalanche threshold current and the quenching resistor of the avalanche photo-diode (APD) pixel, approximately. Moreover, the model and results can be extended to other small avalanche junctions with quenching resistor.     

Multi-scales association modeling of membrane water resistance indexes

In order to quantify and predict the water resistance of membrane, a multi-scales association model was built up based on the Fick’s second law. Two water resistance indexes, balance time and seepage velocity, were put forward and calculated by the model for measuring the property of membrane water resistance. The association model linked macro-scale factors and micro-scale parameters together. The influence of macro-scale factors, environmental temperature and membrane thickness, and micro-scale parameters, water molecules diffusivity, membrane saturated water absorption rate and water escape concentration, were discussed. The properties of water resistances for two groups including 10 waterborne acrylate membranes samples were measured for validating the indexes calculated by the model. The well consistency between the results of calculations and experiments proved that the method of multi-scales association modeling for quantifying and predicting the membrane water resistance was feasible.     

单位球上F(p,q,s)空间到Bloch型空间的复合算子

该文分别给出了单位球B上空间F(p, q, s)到空间β^α之复合算子C_{varphi}为有界算子和紧算子的充要条件.同时作为推论获得了Bloch型空间的相应结果.     

螺旋管锅炉反应器管内汽液两相流压力降脉动研究

本又根据闭式循环热动力推进系统中锅炉反应器的各种可能的航行方向及运行参数，对螺旋管内汽液两相流压力降脉动特性进行了系统的试验研究，首次区分了两类不同特征的压力降脉动并得到了各主要因素的影响现律和发生脉动的界限准则。     

On the GLY Conjecture of upper estimate of positive integral points in real right-angled simplices

The GLY (Granville-Lin-Yau) Conjecture is a generalization of Lin, Xu and Yau's results. An important application of GLY is its use in characterizing an affine hypersurface in Cn as a cone over a nonsingular projective variety. In addition, the Rough Upper Estimate Conjecture in GLY, recently proved by Yau and Zhang, implies the Durfee Conjecture in singularity theory. This paper develops a unified approach to prove the Sharp Upper Estimate Conjecture for general n. Using this unified approach, we prove that the Sharp Upper Estimate Conjecture is true for n=4,5,6. After giving a counter-example to show that the Sharp Upper Estimate Conjecture is not true for n=7, we propose a Modified GLY Conjecture. For each fixed n, our unified approach can be used to prove this Modified GLY Conjecture.     

The Mixed Norm Spaces of Polyharmonic Functions

Let be a bounded domain with C ² boundary. And let H _k be the set of all polyharmonic functions f with order k on Ω. For 0<p, q≤∞ and ϕ a normal weight, the mixed-norm space consists of all function f in H _k for which the mixed-norm ||·|| _{p, q, ϕ} <∞. The main result of the paper is the norm equivalence:

移动的线源平稳随机荷载激励下梁的随机响应

利用广义Ｄｕｈａｍｅｌ积分和积分变换，研究了粘弹性Ｋｅｌｖｉｎ地基上无限长梁在运动的线源平稳随机荷载作用下的随机响应．发现此时梁的挠度响应为非平稳随机过程．通过引入随动坐标系，建立了有明确物理意义的随动谱分析方法，使随机位移响应在随动坐标系下成为平稳随机过程     

利用铝＋氮或钛＋氮离子束辅助沉积改善纯铁摩擦学性能的研究

离子束辅助沉积是近几年发展起来的一种将离子注入与薄膜沉积融为一体的材料表面改性新技术。利用Ａｌ＋Ｎ＋或Ｔｉ＋Ｎ＋离子束辅助沉积对工业纯铁进行了表面改性处理，并且就其摩擦学性能与未经表面改性处理之纯铁试样的作了对比试验研究，同时还利用俄歇电子能谱仪、掠角Ｘ射线衍射仪和扫描电子显微镜等分析测试手段对离子束改性层的成分深度分布和微观组织结构，以及磨痕的表面形貌和元素面分布进行了分析。结果表明，Ａｌ＋Ｎ＋或Ｔｉ＋Ｎ＋离子束辅助沉积可以在纯铁表面形成Ｆｅ４Ｎ、Ｆｅ３Ａｌ或Ｆｅ２Ｎ、Ｆｅ２Ｔｉ等强化相，因而使材料的表层显微硬度分别提高了２１．５％和５８．４％，稳态摩擦下的摩擦系数分别降低约８０％和８３％，平均磨损量分别降低约７１％和８６％；磨损形式主要由纯铁严重的粘着磨损转化为轻微的氧化磨损。