WebProp: Web interface for ab initio calculation of molecular one-electron properties

This note describes the features and implementation issues of WebProp, a web-based interface for evaluating ab initio quality one-electron properties. The interface code is written in HTML and Python, while the backend is handled using Python and our indigenously developed code INDPROP for property evaluation. A novel feature of this setup is that it provides a simple interface for computing first principle one-electron properties of small to medium sized molecules. To facilitate computation of otherwise expensive calculations on large molecular systems, we employ the Molecular Tailoring Approach (MTA) developed in our laboratory to obtain the density matrix (DM). This DM is then employed for computing the one-electron properties of these systems. The backend transparently handles jobs submitted by the user and runs them either on a single machine or over a grid of compute nodes. The results of the calculations, which include the summary and the files necessary for visualization of one-electron properties, are e-mailed to the user. The user can either directly use the data or visualize it using visualization tools such as UNIVIS-2000 or Drishti.     

Rational extrapolation for the PageRank vector

An important problem in web search is to determine the importance of each page. From the mathematical point of view, this problem consists in finding the nonnegative left eigenvector of a matrix corresponding to its dominant eigenvalue 1. Since this matrix is neither stochastic nor irreducible, the power method has convergence problems. So, the matrix is replaced by a convex combination, depending on a parameter , with a rank one matrix. Its left principal eigenvector now depends on , and it is the PageRank vector we are looking for. However, when is close to 1, the problem is ill-conditioned, and the power method converges slowly. So, the idea developed in this paper consists in computing the PageRank vector for several values of , and then to extrapolate them, by a conveniently chosen rational function, at a point near 1. The choice of this extrapolating function is based on the mathematical expression of the PageRank vector as a function of . Numerical experiments end the paper.

     

The n‐ordered graphs: A new graph class

For a positive integer n, we introduce the new graph class of n‐ordered graphs, which generalize partial n‐trees. Several characterizations are given for the finite n‐ordered graphs, including one via a combinatorial game. We introduce new countably infinite graphs R⁽ⁿ⁾, which we name the infinite random n‐ordered graphs. The graphs R⁽ⁿ⁾ play a crucial role in the theory of n‐ordered graphs, and are inspired by recent research on the web graph and the infinite random graph. We characterize R⁽ⁿ⁾ as a limit of a random process, and via an adjacency property and a certain folding operation. We prove that the induced subgraphs of R⁽ⁿ⁾ are exactly the countable n‐ordered graphs. We show that all countable groups embed in the automorphism group of R⁽ⁿ⁾. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 204–218, 2009     

考虑焊接残余应力的波形钢腹板PC梁关键细节疲劳可靠度研究

焊接残余应力对波形钢腹板细节疲劳寿命的影响不可忽略,本文以头道河大桥为工程背景,基于ABAQUS有限元软件,建立波形钢腹板焊接构件数值模型,提出不同波折角度的波形钢腹板残余应力模型。采用瞬态分析方法,分析6种典型车辆作用下波折角区域焊缝细节的应力时程。在此基础上,构建考虑焊接残余应力和车辆荷载共同作用下的波形钢腹板细节疲劳极限状态方程,讨论不同波折角度和交通增长率对疲劳可靠度指标的影响规律。研究表明,翼缘板-波形钢腹板焊接构件斜边两侧的纵向残余应力呈对称分布,焊接细节转角区域圆弧外侧的纵向残余应力整体高于圆弧内侧,随着波折角度的增加,两侧焊缝附近的纵向残余应力变大;在桥梁设计基准期取100年时,30°波折角度焊缝细节疲劳可靠度是60°波折角度的1.05倍;交通量的线性增长对头道河大桥焊缝细节的疲劳可靠度影响较大,不考虑交通增长率的焊缝细节疲劳可靠度是α=5%的1.84倍。