二维卷积在动力学分析中的应用

本文用计算机模拟和二维卷积研究了稀土与间乙酰基偶氮氯膦的显色反应，选择不同的模型参数可描述这类反应的细节，二维卷积则增强对叠合二维谱的分辨。     

用重复卷积法求解物理宽化函数

用重复卷积法求解物理宽化函数吴万国,林嘉　（福州大学中心实验室,福州３５０００２）（中国（福建）对外贸易中心集团,福州３５０００１）关键词Ｘ射线衍射,晶粒度,晶格畸变,重复卷积粉末试样的Ｘ射线衍射谱线一般具有一定的宽度,引起话线宽化的主要原因有仪器致...     

Real-time recursive estimation of statistical parameters

Recursive algorithms for the computation of standard deviation and average deviation are derived and their applications in data acquisition are discussed. The relative speeds and accuracies of the two algorithms are compared for synthetic data. The performance of recursive estimation under shot and proportional noise limitations is also described. As an example of the utility of these algorithms, absorbance data with constant confidence intervals are collected regardless of incident and transmitted intensities. The desired precision is specified prior to data acquisition and used to control signal-averaging of the data in real time.     

How good is CuAAC “click” chemistry for polymer coupling reactions?

¹H NMR and SEC analyses are used to investigate the overall efficiency of Copper Catalyzed Azide Alkyne Cycloaddition (CuAAC) “click” coupling reactions between alkyne‐ and azide‐terminated polymers using polystyrene as a model. Quantitative convolution modeling of the entire molecular weight distribution is applied to characterize the outcomes of the functional polymer synthesis reactions (i.e., by atom transfer radical polymerization), as well as the CuAAC coupling reaction. Incomplete functionality of the azide‐terminated polystyrene (∼92%) proves to be the largest factor compromising the efficacy of the CuAAC coupling reaction and is attributed primarily to the loss of terminal bromide functionality during its synthesis. The efficiency of the S_N2 reaction converting bromide to azide was found to be about 99%. After taking into account the influence of non‐functional polymer, we find that, under the reaction conditions used, the efficiency of the CuAAC coupling reaction determined from both techniques is about 94%. These inefficiencies compromise the fidelity and potential utility of CuAAC coupling reactions for the synthesis of hierarchically structured polymers. While CuAAC efficiency is expected to depend on the specific reaction conditions used, the framework described for determining reaction efficiency does provide a means for ultimately optimizing the reaction conditions for CuAAC coupling reactions. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 75–84     

On effectively computable realizations of choice functions: Dedicated to Professors Kenneth J. Arrow and Anil Nerode

Let X be a compact, convex subset of R_n, and let $\text{〈R(X),}\text{F}{}_{\mathrm{R}}\text{〉}$ be a recursive space of alternatives, where R(X) is the image of X in a recursive metric space, and $\text{F}{}_{\mathrm{R}}$ is the family of all recursive subsets of R(X). If $\text{C:}\text{F}{}_{\mathrm{R}}\text{→}\text{F}{}_{\mathrm{R}}$ is a non-trivial recursively representable choice function that is rational in the sense of Richter, we prove that C has no recursive realization within Church's Thesis. Our proof is not a diagonalization argument and uses no paradoxical statements from formal systems. Instead, the proof is a Kleene-Post reduction style argument and uses the Turing equivalence between mechanical devices of computation and the recursive functions of Gödel and Kleene.     

由从属关系定义的亚纯多叶函数的子类的某些性质

In the present paper, we introduce some new subclasses of meromorphic starlike,convex, close-to-convex and quasi-convex functions of β-reciprocal in terms of the linear operator using subordination. We obtain the coefficient estimates, convolution properties, integral preserving properties and inclusion relationships of the classes. The results presented here include several results as their special cases.     

基于Chebyshev多项式的神经网络中长期负荷预测研究

高精度负荷预测在提高电力系统的安全性和经济性方面有着极其重要的意义,而现有的负荷预测方法因参数有限,难以完全反映其内在规律,因而导致预测结果不够准确.为此提出了一种基于Chebyshev多项式神经网络模型的预测方法.该方法使用递推最小二乘法训练神经网络权值系数,以获得高精度的参数估计,从而实现Chebyshev多项式神经网络模型对负荷量的最优拟合,再利用训练好的Chebyshev多项式神经网络模型实现中长期负荷预测.研究结果表明,该方法能较好模拟负荷变化规律,有效提高了负荷预测精度,在电力系统负荷预测中有较大的应用价值.     

On Fatou Type Convergence of Convolution Type Double Singular Integral Operators

In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a~b ∫_a~b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ∈Λ  [0,∞),(0.1)are given. Here f belongs to the function space L_1( a,b ~2), where a,b is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15].     

两类广泛递归序列的动力特性

We investigate the dynamics of two extensive classes of recursive sequences:xn+1=c∑ k ∑xn-ioxn-i1…xn-i2j+f(xn-io,xn-i1,…,xn-i2k)j=0(i0,i1,…,i2j)∈A2j/c∑ k ∑xn-ioxn-i1…xn-i2j-1+c+f(xn-io,xn-i1,…,xn-i2k)j=1(i0,i1,…,i2j)∈A2j-1 and xn+1=c∑ k ∑xn-ioxn-i1…xn-i2j-1+c+f(xn-io,xn-i1,…,xn-i2k)j=1(i0,i1,…,i2j)∈A2j-1/c∑ k ∑xn-ioxn-i1…xn-i2j+f(xn-io,xn-i1,…,xn-i2k)j=0(i0,i1,…,i2j)∈A2j We prove that their unique positive equilibrium x = 1 is globally asymptotically stable.And a new access is presented to study the theory of recursive sequences.     

CALCULATIONS OF RUIN PROBABILITIES CONCERNING WITH CLAIM OCCURRENCES

In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.