A fast algorithm for the spectral radii of weakly reducible nonnegative tensors

In this paper, we propose a fast algorithm for computing the spectral radii of symmetric nonnegative tensors. In particular, by this proposed algorithm, we are able to obtain the spectral radii of weakly reducible symmetric nonnegative tensors without requiring the partition of the tensors. As we know, it is very costly to determine the partition for large‐sized weakly reducible tensors. Numerical results are reported to show that the proposed algorithm is efficient and also able to compute the spectral radii of large‐sized tensors. As an application, we present an algorithm for testing the positive definiteness of Z‐tensors. By this algorithm, it is guaranteed to determine the positive definiteness for any Z‐tensor.     

The effect of cation size (H+, Li+, Na+, and K+) on McLafferty-type rearrangement of even-electron ions in mass spectrometry

Protonation and alkali-metal cation adduction are the most important ionization processes in soft-ionization mass spectrometry.Studies on the fragmentation mechanism of protonated and alkali-metal-cationized compounds in tandem mass spectrometry are essential and helpful for structural analysis.In some cases,it was often observed that a compound attached by different alkali-metal cations(or proton)exhibits similar fragmentation patterns but the relative abundances of product ions are different.This difference was considered to derive from the different electrostatic interactions of alkali-metal cations(or the bonded effect of proton)with the analyte.The alkali-metal cation with a smaller ionic radius shows stronger electrostatic interaction with the molecule because of its higher charge density.In addition,the bonded effect of the proton is stronger than the electrostatic interaction of the alkali-metal cation.In the present study,which used McLafferty-type rearrangements of even-electron ions([M+Cat]+,Cat=H,Li,Na,K)as model reactions,the effect of cation size in mass spectrometric fragmentation reactions is highlighted.These considerations were also successfully applied to interpret the similar but distinct fragmentation behavior of proton and alkali-metal cation adducts of a synthetic compound(2-(acetamido(phenyl)methyl)-3-oxobutanoate)and a drug(entecavir).     

Experimental research of effects of different rotation radii on the growth rate of potassium dihydrogen phosphate crystals

Comparing with the traditional concentric rotation method (rotation radius is 0 cm), the effects of different rotation radii on the growth rate of KDP crystals were studied by experimental methods. It was found that with the increase of rotation radius from 0 cm, the growth rate of each direction of crystals first increased and then decreased in a size‐unchanged vessel. The smaller the distance between the crystal and vessel wall, the less the growth rate. This phenomenon was named the “wall collision effect”. Also, the value of growth rate reached a maximum when the rotation radius was about half of its allowable largest value in the size‐unchanged vessel. In addition, an increase of the rotation radius could improve the crystal growth rate under the same linear velocity of crystal movement. Finally, the uniformity of crystal growth has also been analyzed compared with the concentric rotation radius. It was found that the uniformity of crystal growth was best when the rotation radius was half of its allowable maximum value, and it was more conducive to the actual application of KDP crystals.     

基于自相关函数的激光散斑统计半径的测量

为了测量激光散斑的统计半径,运用统计光学理论推导了二维近场散斑光强的归一化自相关函数,并提出了通过求解散斑图像自相关拟合函数的系数来计算激光散斑统计半径的一种测量方法,利用该测量方法编制的测量软件可以方便地计算出激光散斑的统计半径.通过对尺寸已知的模拟散斑的测量,测量结果与实际尺寸相吻合,证实了该测量方法的可行性.     

Enhanced nonlinearity in photonic crystal fiber by germanium doping in the core region

Germanium doping in silica can be used as a method for nonlinearity enhancement.Properties of the enhanced nonlinearity in photonic crystal fiber(PCF)with a GeO2-doped core are investigated theoretically by using all-vector finite element method.Numerical result shows that the nonlinear coefficient of PCF is greatly enhanced with increasing doping concentration,furthermore,optimal radius of the doped region should be considered for the desired operating wavelength.     

The independence of initial vectors in the subdivision schemes

Starting with an initial vector λ = (λ(κ))κ∈z ∈ ep(Z), the subdivision scheme generates asequence (Snaλ)∞n=1 of vectors by the subdivision operator Saλ(κ) = ∑λ(j)a(k - 2j), k ∈ Z. j∈zSubdivision schemes play an important role in computer graphics and wavelet analysis. It is very interesting tounderstand under what conditions the sequence (Snaλ)∞n=1 converges to an Lp-function in an appropriate sense.This problem has been studied extensively. In this paper we show that the subdivision scheme converges forany initial vector in ep(Z) provided that it does for one nonzero vector in that space. Moreover, if the integertranslates of the refinable function are stable, the smoothness of the limit function corresponding to the vectorλ is also independent of λ.     

Smooth diameter and eigenvalue rigidity in positive Ricci curvature

A recent injectivity radius estimate and previous sphere theorems yield the following smooth diameter sphere theorem for manifolds of positive Ricci curvature: For any given and there exists a positive constant 0$">such that any -dimensional complete Riemannian manifold with Ricci curvature , sectional curvature and diameter is Lipschitz close and diffeomorphic to the standard unit -sphere. A similar statement holds when the diameter is replaced by the first eigenvalue of the Laplacian.

     

用5种不同的电子光学软件对微波管电子枪进行模拟计算

 对TWTCAD微机版、工作站版本、EGUN，CAMEO以及Orprogr电子光学软件背景和特点作了一个简单介绍，并利用其模拟计算了11支不同结构的电子枪。将计算得到的导流系数、射程和注腰半径与实验数据列表对比，结果表明：不同电子光学软件计算不同类型电子枪其计算精度也不一样。在导流系数方面，EGUN和Orprogr的计算精度较高，绝对平均误差分别为7.18%和7.4%；在射程方面，TWTCAD的计算精度最高，绝对平均误差为5.69%；在注腰半径方面，Orprogr与实验值偏差较大，绝对平均误差为47.43%，而工作站版本的计算精度最高，绝对误差仅为2.29%。     

Some Upper Bounds on the Covering Radii of Linear Codes Over Fq and Their Applications

We show that the covering radius R of an [n,k,d] code over F_q is bounded above by R n-n _q(k, d/q). We strengthen this bound when R d and find conditions under which equality holds.As applications of this and other bounds, we show that all binary linear codes of lengths up to 15, or codimension up to 9, are normal. We also establish the normality of most codes of length 16 and many of codimension 10. These results have applications in the construction of codes that attain t[n,k,/it>], the smallest covering radius of any binary linear [n,k].We also prove some new results on the amalgamated direct sum (ADS) construction of Graham and Sloane. We find new conditions assuring normality of the ADS; covering radius 1 less than previously guaranteed for ADS of codes with even norms; good covering codes as ADS without the hypothesis of normality, from concepts p- stable and s- stable; codes with best known covering radii as ADS of two, often cyclic, codes (thus retaining structure so as to be suitable for practical applications).