On the convergence properties of the orthogonal similarity transformations to tridiagonal and semiseparable (plus diagonal) form

In this paper, we will compare the convergence properties of three basic reduction methods, by placing them in a general framework. It covers the reduction to tridiagonal, semiseparable and semiseparable plus diagonal form. These reductions are often used as the first step in the computation of the eigenvalues and/or eigenvectors of arbitrary matrices. In this way, the calculation of the eigenvalues using, for example, the QR-algorithm reduces in complexity. First we will investigate the convergence properties of these three reduction algorithms. It will be shown that for the partially reduced matrices at step k of any of these reduction algorithms, the lower right k × k (already reduced) sub-block will have the Lanczos–Ritz values, w.r.t. a certain starting vector. It will also be shown that the reductions to semiseparable and to semiseparable plus diagonal form have an extra convergence behavior a special type of subspace iteration is performed on the lower right k × k submatrix, which contains these Ritz-values. Secondly we look in more detail at the behavior of the involved subspace iteration. It will be shown that the reduction method can be interpreted as a nested type of multi-shift iteration. Theoretical results will be presented, making it possible to predict the convergence behavior of these reduction algorithms. Also a theoretical bound on the convergence rate is presented. Finally we illustrate by means of numerical examples, how it is possible to tune the convergence behavior such that it can become a powerful tool for certain applications.     

Regge pole plus cut model for proton-antiproton elastic scattering at collider and tevatron energies

The Regge pole plus cut model has been used to explain the data at the collider energies √s=546 and 630 GeV and the most recent differential cross-section results at √s=1.8 TeV. Predictions of the model at 1.8 and 40 TeV are compared with those of Bourrelyet al.     

“互联网+”时代高校智慧校园建设与应用探析

"互联网+"智慧校园建设与应用意味着互联网与传统高校教学、管理、服务等方面更为深度的有效融合,本文积极构建了"互联网+"时代高校智慧校园"4F+6P"建设与应用驱动模型,4F(Form)为"互联网+"智慧校园建设策略需要构建新的数据形态、技术形态、组织形态与关系形态,6P(Program)"互联网+"智慧校园应用内容需要打造的6项工程,通过构建"形态+工程"模型驱动"互联网+"智慧校园建设与应用进入新的发展阶段。     

面向新工科的“电工电子学”多模态实验探索

为了顺应新工科学习趋势、增强师生的互动性和培养学生的自主学习创新能力，四川大学电工电子学课程组试行了基于互联网+的雨课堂x“雷实验”方式，选取少数几组同学，用“雨课堂”和A+D Lab实验装置相结合进行电工电子学多模态实验。实验方式较为灵活多变，能更好地调动学生的积极性、培养学生的创新性。     

Nonlinear optical rectification of GaAs/Ga1-xAlxAs quantum dots with Hulthén plus Hellmann confining potential

We investigate the nonlinear optical rectification (NOR) of spherical quantum dots (QDs) under Hulthén plus Hellmann confining potential with the external tuning elements. Energy and wavefunction are determined by using the Nikiforov-Uvarov method. Expression for the NOR coefficient is derived by the density matrix theory. The results show that the applied external elements and internal parameters of this system have a strong influence on intraband nonlinear optical properties. It is hopeful that this tuning of the nonlinear optical properties of GaAs/Ga_1-xAl_xAs QDs can make a greater contribution to preparation of new functional optical devices.     

Relative plus constructions

Let $h$ be a connective homology theory. We construct a functorial relative plus construction as a Bousfield localization functor in the category of maps of spaces. It allows us to associate to a pair $(X,H)$, consisting of a connected space $X$ and an $h$-perfect normal subgroup $H$ of the fundamental group ${\pi }_1\left(X\right)$, an $h$-acyclic map $X\to X_H^{+h}$ inducing the quotient by $H$ on the fundamental group. We show that this map is terminal among the $h$-acyclic maps that kill a subgroup of $H$. When $h$ is an ordinary homology theory with coefficients in a commutative ring with unit $R$, this provides a functorial and well-defined counterpart to a construction by cell attachment introduced by Broto, Levi, and Oliver in the spirit of Quillen’s plus construction. We also clarify the necessity to use a strongly $R$-perfect group $H$ in characteristic zero.