Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.     

The Choquet-Deny convolution equation μ=μ*σ for probability measures on Abelian semigroups

In this note, we characterize the regular probability measures satisfying the Choquet-Deny convolution equation =* on Abelian topological semigroups for a given probability measure .     

Disintegration and perfectness of measure spaces

For every finite measure space (X,A,P) we find a unique representation P=Q₁+Q₂+Q₃ such that Q₁ is compact, Q₂ is perfect and purely noncompact and Q₃ is purely nonperfect. We show that every Pachl-_O-disintegrable probability space is Ramachandran-_O-disintegrable and therefore perfect and under a certain condition we prove the equivalence between compactness and Ramachandran-_O-disintegrability.     

Evidence for the poisson distribution for quasi-energies in the quantum kicked-rotator model

A transformation on the two-dimensional torus which is related to the problem of limit distribution for the distance between the levels in the kicked-rotator model is considered. The first four moments of the r.w. which describe the numbers of visits of a point in a rectangle of measure are calculated. It is shown that when 0 they converge to the first four moments of a Poisson r.w.     

6AZO-CONTAINING SELF-ASSEMBLY ULTRA-THIN FILMS AND THEIR PHOTOVOLTAIC PROPERTIES

A kind of azo-containing resin (Azo-R) was synthesized by a simple way through the coupling reaction of 2-nitro-N-methyldiphenylamine-4-diazoresin (NDR) with phenol, and a new covalentely attached multilayer film from Azo-R as H-donor and photosensitive diazoresin, diphenylamine-4-diazoresin (DR) as H-acceptor via H-bonding attraction by selfassembly technique has been fabricated. Following the decomposition of diazonium group of DR under exposure to UV light, the H-bonds between the layers of the film convert to covalent bonds and the film becomes very stable toward polar solvents or electrolyte aqueous solutions. Thus the UV-irradiated azo-containing films can be used to measure photocurrent in a conventional three-electrode photoelectrochemical cell using KCl as supporting electrolyte. It was confirmed that the azo-containing multilayer film is responsible for the photocurrent generation.     

Optimization of auxiliary basis sets for the LEDO expansion and a projection technique for LEDO-DFT

We present a systematic procedure for the optimization of the expansion basis for the limited expansion of diatomic overlap density functional theory (LEDO-DFT) and report on optimized auxiliary orbitals for the Ahlrichs split valence plus polarization basis set (SVP) for the elements H, Li--F, and Na--Cl. A new method to deal with near-linear dependences in the LEDO expansion basis is introduced, which greatly reduces the computational effort of LEDO-DFT calculations. Numerical results for a test set of small molecules demonstrate the accuracy of electronic energies, structural parameters, dipole moments, and harmonic frequencies. For larger molecular systems the numerical errors introduced by the LEDO approximation can lead to an uncontrollable behavior of the self-consistent field (SCF) process. A projection technique suggested by L?wdin is presented in the framework of LEDO-DFT, which guarantees for SCF convergence. Numerical results on some critical test molecules suggest the general applicability of the auxiliary orbitals presented in combination with this projection technique. Timing results indicate that LEDO-DFT is competitive with conventional density fitting methods.     

环状高分子对胶体稳定性影响的理论研究

将改进的基本度量理论与热力学微扰理论相结合,提出了胶体/高分子系统排空相互作用的IRDFT理论。该理论解释了在实际胶体系统中起重要作用的排斥体积效应和高分子链内相关性的竞争机制。应用该IRDFT,分别以线性链状和环状结构的高分子及其单体为排空元,计算了不同排空元条件下的胶体间排空相互作用。研究表明:对于絮凝破坏,自由环状高分子具有更大的优势。     

有限型的首次返回例外集的测度和维数北大核心CSCD

设M=(m_(ij))是一个b×b阶矩阵且m_(ij)∈{0,1},∑_(M)是矩阵M=(m_(ij))诱导产生的有限型,σ是其上左推移算子.本文主要研究的是有限型动力系统(∑_(M),σ)上的首次返回速度问题.令τ_(k)(x)是点x∈∑_(M)首次返回到包含x的k阶柱集时间,且E_(α,β)={x∈∑_(M):lim inf_(k→∞)(logτ_(k)(x))/k=α,lim sup_(k→∞)(logτ_(k)(x))/k=β}.我们证明了:当M是不可约矩阵时,对任意0≤α≤β≤+∞,集合E_(α,β)的Markov测度要么等于0要么等于1并且具有满的Hausdorff维数.     

On Existence of the Even Lp Gaussian Minkowski Problem for p > n∗

This paper concerns the even Lp Gaussian Minkowski problem in n-dimensional Euclidean space R n . The existence of the solution to the even Lp Guassian Minkowski problem for p > n is obtained.     

基于三阶段SBM模型的中国节能服务上市企业效率研究

节能服务企业效率对于推动节能服务产业发展和确保国家“双碳”目标实现具有重要意义。运用三阶段SBM模型,对2020年60家中国节能服务上市企业的综合效率进行实证研究,并分析效率的影响因素。研究结果表明,经济发展水平对综合效率具有双重影响,合适的产业结构和较高的投入资本回报率有利于综合效率提升,而政府补贴与企业存续时间制约了综合效率改进;剔除环境因素与随机误差影响后,多数企业综合效率下降,整体效率偏低;提高规模效率是提升综合效率的关键,且绝大部分企业处于规模收益递增状态。研究最后提出创新补贴方式、建立企业认证制度、开展综合能源服务和推动企业间兼并重组等可行建议,以提升节能服务企业的综合效率。