A New kHz Velocity Map Ion/Electron Imaging Spectrometer for Femtosecond Time-Resolved Molecular Reaction Dynamics Studies

A new velocity map imaging spectrometer is constructed for molecular reaction dynamics studies using time-resolved photoelectron/ion spectroscopy method.By combining a kHz pulsed valve and an ICCD camera,this velocity map imaging spectrometer can be run at a repetition rate of 1 kHz,totally compatible with the fs Ti:Sapphire laser system,facilitating time-resolved studies in gas phase which are usually time-consuming.Time-resolved velocity map imaging study of NH₃ photodissociation at 200 nm was performed and the time-resolved total kinetic energy release spectrum of H+NH₂ products provides rich information about the dissociation dynamics of NH₃.These results show that this new apparatus is a powerful tool for investigating the molecular reaction dynamics using time-resolved methods.     

A novel size independent symplectic analytical singular element for inclined crack terminating at bimaterial interface

Cracks often exist in composite structures, especially at the interface of two different materials. These cracks can significantly affect the load bearing capacity of the structure and lead to premature failure of the structure. In this paper, a novel element for modeling the singular stress state around the inclined interface crack which terminates at the interface is developed. This new singular element is derived based on the explicit form of the high order eigen solution which is, for the first time, determined by using a symplectic approach. The developed singular element is then applied in finite element analysis and the stress intensity factors (SIFs) for a number of crack configurations are derived. It has been concluded that composites with complex geometric configurations of inclined interface cracks can be accurately simulated by the developed method, according to comparison of the results against benchmarks. It has been found that the stiffness matrix of the proposed singular element is independent of the element size and the SIFs of the crack can be solved directly without any post-processing.     

捕食者和食饵均带有扩散的随机捕食-食饵模型动力学分析

考虑了斑块环境下捕食者种群和食饵种群分别在n个斑块扩散的随机捕食 食饵模型.利用Lyapunov函数法证明了对任意给定的初始值,随机系统全局正解的存在唯一性,并对其进行了有界性分析.此外给出了食饵种群及整个系统灭绝的充分条件.最后通过数值模拟验证了所得理论的正确性.     

Generalized harmonic number summation formulae via hypergeometric series and digamma functions

By computing the derivatives of five classical hypergeometric summation theorems, and applying the related properties of the digamma function, we derive a large number of closed summation formulae for generalized harmonic numbers.     

海洋立管涡激损伤分析的虚拟激励法概述

立管是连接海底钻井和海上平台的重要系统.涡激振动是造成立管疲劳损伤的主要因素.受海流的随机作用,立管涡激振动表现出不确定性,对这种随机振动进行快速有效地分析,对于立管的工程设计具有非常重要的意义.考虑随机激励作用,要比确定性激励困难得多,虚拟激励法对于克服这种困难具有很好的效果.近年来,应用虚拟激励法分析立管的涡激损伤问题,取得一些成果,该文对此作一概略的叙述.     

An alternating direction and projection algorithm for structure-enforced matrix factorization

Structure-enforced matrix factorization (SeMF) represents a large class of mathematical models appearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning techniques useful in many applications including neuroscience and signal processing. In this paper, we present a unified algorithm framework, based on the classic alternating direction method of multipliers (ADMM), for solving a wide range of SeMF problems whose constraint sets permit low-complexity projections. We propose a strategy to adaptively adjust the penalty parameters which is the key to achieving good performance for ADMM. We conduct extensive numerical experiments to compare the proposed algorithm with a number of state-of-the-art special-purpose algorithms on test problems including dictionary learning for sparse representation and sparse nonnegative matrix factorization. Results show that our unified SeMF algorithm can solve different types of factorization problems as reliably and as efficiently as special-purpose algorithms. In particular, our SeMF algorithm provides the ability to explicitly enforce various combinatorial sparsity patterns that, to our knowledge, has not been considered in existing approaches.     

Geometry of spacelike generalized constant ratio surfaces in Minkowski 3-space

Generalized constant ratio surfaces are defined by the property that the tangential component of the position vector is a principal direction on the surfaces. In this work, we study these class of surfaces in the 3-dimensional Minkowski space L³. We achieve a complete classification of spacelike generalized constant ratio surfaces in L³.     

Precise large deviations for sums of random vectors with dependent components of consistently varying tails

Let {X _i = (X _1,i ,...,X _m,i )^?, i ≥ 1} be a sequence of independent and identically distributed nonnegative m-dimensional random vectors. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Here, the components of X ₁ are allowed to be generally dependent. Moreover, let N(·) be a nonnegative integer-valued process, independent of the sequence {X _i , i ≥ 1}. Under several mild assumptions, precise large deviations for S _n = Σ _i=1 ⁿ X _i and S _N(t) = Σ _i=1 ^N(t) X _i are investigated. Meanwhile, some simulation examples are also given to illustrate the results.     

An unexpected Ramanujan-type congruence modulo 7 for 4-colored generalized Frobenius partitions

In this paper, we present an unexpected Ramanujan-type congruence modulo 7 for \(c\phi _4(n)\), which denotes the number of generalized Frobenius partitions of n with 4 colors. This work extends the recent work of Lin on \(c\phi _4\) modulo 7.     

Uniform bound for the effective Bogomolov conjecture

We obtain a uniform bound for the effective Bogomolov conjecture, which depends only on the genus g of the curve. The bound grows as $O(g^{?3})$ as g tends to infinity.