Solutions to arithmetic convolution equations

In the -algebra of arithmetic functions , endowed with the usual pointwise linear operations and the Dirichlet convolution, let denote the convolution power with factors . We investigate the solvability of polynomial equations of the form

with fixed coefficients . In some cases the solutions have specific properties and can be determined explicitly. We show that the property of the coefficients to belong to convergent Dirichlet series transfers to those solutions , whose values are simple zeros of the polynomial . We extend this to systems of convolution equations, which need not be of polynomial-type.

     

卷积反投影法重建温度场

电子散斑干涉技术是近年发展起来的一门新兴的测量技术,它由光干涉原理测量物理场的密度、温度分布等,这种测量技术是由物理场在不同截面、不同方向上的投影值反求场分布,这非常类似于CT技术。简述二维重建的基本原理,着重介绍卷积反投影重建算法。依此原理,模拟了双高斯分布函数的投影,并由平行束卷积法重建出模拟的温度场。为了指导电子散斑干涉实验,模拟了三种可能实验误差,并分别给出了重建结果。由于电子散斑干涉测量(投影)的方向个数小,提出了双线性滤波算法,使在测量值稀疏的条件下得到较好重建结果。     

基于一维卷积神经网络的雌激素粉末拉曼光谱定性分类

拉曼光谱物质定性鉴别已被广泛应用于诸多行业和研究领域,但传统拉曼光谱分析过程中的预处理主要依赖人为经验,光谱特征提取虽然能够降低信号维度,同时也会造成部分光谱信息损失。特性相近物质本身光谱相似度较高,受到测量过程中环境干扰和分析过程中多种误差影响,导致最终分类效果并不理想。针对此问题,提出基于一维卷积神经网络（one-dimensional convolution neural network,1D-CNN）的拉曼光谱定性分类方法。实验采集雌酮（Estrone）、雌二醇（Estradiol）,雌三醇（Estriol）三种不同雌性激素粉末的拉曼光谱,设计随机平移、添加噪声和随机加权三种光谱数据增强方法,构建数量充足的拉曼光谱数据库用于神经网络模型训练与测试;基于拉曼光谱数据特点提出一维卷积神经网络分类模型,将光谱预处理、特征提取和定性分类的全过程融为一体。通过大量仿真实验,优化所提出的神经网络模型超参数和训练过程并测试分类效果,从预处理对光谱分类结果的影响和模型抗干扰性能两个方面与多种传统拉曼光谱分类算法对比,评价模型性能。实验结果表明,本文提出的一维卷积神经网络模型可实现三类雌性激素粉末拉曼光谱快速准确分类,分类正确率最高可达98.26%,分析过程中无需光谱预处理和特征提取步骤,简化了光谱分析流程,并能保留更多有效信息。同时,当模拟测量噪声强度达到60 dBW时,传统方法分类正确率均明显出现不同程度明显降低,卷积神经网络模型依然能够取得96.81%的分类正确率,说明相比对传统拉曼光谱分类方法,所提出方法受光谱测量噪声影响更小,鲁棒性更强,适用于分析更复杂现场测量的强噪声拉曼光谱信号。该研究结果表明深度学习方法在拉曼光谱的分析与处理领域具有很大的应用潜力和研究价值。     

Regularity and convergence of stochastic convolutions in duals of nuclear Fréchet spaces

Let Φ′ be the strong dual of a nuclear Fréchet space Φ. In this paper we present regularity properties, weak convergence, and convergence in probability and in mean square of Φ′-valued stochastic evolution equations and convolutions with respect to Φ′-valued cadlag martingales.     

On a class of analytic functions related to conic domains and associated with Carlson-Shaffer operator

Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigat inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.     

On the Distribution of the Sum of n Non-Identically Distributed Uniform Random Variables

The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit formulae for the distribution of the sum of n non-identically distributed uniform random variables in both the continuous and the discrete case. The results, though involved, have a certain elegance. As examples, we derive from our general formulae some special cases which have appeared in the literature.     

Certain subclasses of p-valently analytic functions involving a generalized fractional differintegral operator

By making use of the principle of subordination between analytic functions and the generalized fractional differintegral operator, we introduce and investigate some new subclasses of p-valently analytic functions in the open unit disk. Such results as inclusion relationships, integral-preserving properties, convolution properties, subordination and superordination properties, and sandwich theorems for these classes are derived.     

卷积型最小二乘法求解梁的动力学问题

提出了卷积型最小二乘法,并用其计算了不同初始条件和不同边界条件下梁的动力学问题,算例表明,方法概念简单,计算方便,精度高,计算工作量少,卷积型最小二乘法是计算结构动力学问题的一种简单、高效的方法,试函数可以不满足边界条件.     

Finite tchebycheff transformations of generalized functions

By using Hilbert space techniques, the finite Tchebycheff transformations of the first and the second kind are defined on appropriate spaces of generalized functions. The inversion theorems are established and some operation transform formulas are obtained. These results are applied in solving certain distributional differential equations.     

ON CERTAIN CLASS OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS

In the present investigation we define a new class of meromorphic functions on the punctured unit disk △*:= {z ∈ C : 0 < |z| < 1} by making use of the generalized Dziok-Srivastava operator H l m [α1 ]. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.