Asymptotic formulae for bivariate Mellin convolution operators

In this paper some Voronovskaya approximation formulae for a class of Mellin convolution operators of the type (Tw f)(x,y) = ∫R2+ Kw(tx-1,vy-1)f(t,v)tvdtdv are given. Moreover, various examples are discussed.     

Certain Sub classes of Analytic Functions Involving the Generalized Dziok-Srivastava Op erator

The generalized Dziok-Srivastava operator is used here to introduce a class of analytic functions in the open unit disc. We provide convolution properties, some subordi-nation relations and the problem of radius. The results presented here extend some of the earlier results.     

基于高斯锐化法的重叠峰分解方法研究

在放射性能谱测量中,由于探测器分辨率较低、待测样品中原子能级相近,往往会出现全能峰的重叠现象,对放射性核素的定性或定量检测带来较大的困难;常规的分离算法一般需要复杂的谱变换或大量的标准谱样本,不适用于现场测量中重叠峰的实时分解。因此,提出一种基于高斯锐化法的能谱重叠峰解析方法(GSM),结合峰锐化法的分辨率增强能力和褶积滑动变换法的平滑特性,可快速地识别、定位和解析γ能谱中的重叠峰。该方法首先对高斯函数进行锐化并做归一化处理,并以此作为变换算子,选择合适的高斯参数及窗宽度,通过对原始γ能谱数据进行褶积滑动变换,达到滤波和提高重叠峰分离度的目的;然后求解GSM成形处理后的谱线近似函数作为目标函数,并选取峰位中心附近若干点作为初始参数,最后以非线性拟合的方法进行重叠峰特征峰参数的解析。实验中,首先验证了该方法变换前后峰位、峰面积特征值的不变性,其次分别对重叠峰能谱段以及MCNP模拟的131I,137Cs,214Bi,206Bi和26Al混合放射源γ能谱进行方法验证。实验结果表明,该方法对于分离度大于0.375、信噪比大于40 dB的重叠峰具有较好分解效果,分解前后的峰位和峰面积的相对误差分别在1%和4.5%以内;对于γ能谱进行全谱解析后,重叠峰的峰位分离相对误差在1%以内,单峰的分离相对误差约为0.1%以内,且当变换算子的半宽度接近探测器能量分辨率时,重叠峰的分解结果更准确。该方法具备较好的噪声抑制性能,在全谱解析中无需进行能谱光滑及本底扣除等谱线预处理操作,且计算资源耗费少,分解精确度较高,便于能谱测量系统的嵌入式实时解谱应用,对放射性测量中能谱的现场快速解析具有实用性。     

Convolution complementarity problems with application to impact problems

^** Email: dstewart{at}math.uiowa.edu. Part of this work was carried out while visiting CMAF at the University of Lisbon and while visiting the University of Lyons 1. Convolution complementarity problems (CCPs) have the followingform: given a matrix-valued function k and a vector-valued functionq, find a vector-valued function u satisfying 0 u(t) (k*u)(t)+ q(t) 0 for all t. In this paper CCPs are applied to a mechanicalimpact problem, but they can also be applied to other dynamicproblems with hard constraints. CCPs are shown to have solutionsprovided q(0) 0 and q is sufficiently regular, k has locallybounded variation and k(0⁺) is a P-matrix. Uniqueness also holdsprovided, in addition, k(0⁺) is symmetric positive definite.This theory shows that the impact problem studied here has aunique solution, and that energy is conserved. Numerical methodshave been devised and implemented for the impact problem, andthe results are presented.     

Asymptotic behavior of generalized convolutions

We study the behavior of a class of convolution-type nonlinear transformations. Under some smallness conditions we prove the existence of fixed points and analyze the spectrum of the associated linearized operator.      

Kernel based approximation in Sobolev spaces with radial basis functions

In this paper, we study several radial basis function approximation schemes in Sobolev spaces. We obtain an optional error estimate by using a class of smoothing operators. We also discussed sufficient conditions for the smoothing operators to attain the desired approximation order. We then construct the smoothing operators by some compactly supported radial kernels, and use them to approximate Sobolev space functions with optimal convergence order. These kernels can be simply constructed and readily applied to practical problems. The results show that the approximation power depends on the precision of the sampling instrument and the density of the available data.     

LAMOST现场光纤位置检测方法研究

LAMOST(大天区多目标光纤光谱天文望远镜)要求通过非接触测量快速准确地获得光纤端部的中心位置。在研究光斑中心提取技术的过程中,提出了一种改进的光重心方法,包括图像卷积预处理、用标准差迭代的方法取背景值和减背景后非线性加权获得光斑特征点。有效地抑制了边缘点对中心位置的影响,提高了在大视场多目标光纤条件下提取光斑特征点的精度,并通过数据模拟、实验室和现场实验进行了验证。     

基于Transformer的普通话语声识别模型位置编码选择

具有自注意机制的Transformer网络在语声识别研究领域渐渐得到广泛关注.该文围绕着将位置信息嵌入与语声特征相结合的方向,研究更加适合普通话语声识别模型的位置编码方法.实验结果得出,采用卷积编码的输入表示代替正弦位置编码,可以更好地融合语声特征上下文联系和相对位置信息,获得较好的识别效果.训练的语声识别系统是在Tr...