High‐resolution methods for preserving the sum of mass fractions: improved χ‐scheme and an alternative

When high resolution convection schemes are used for discretizing chemical species mass balance equations, the mass fractions are not guaranteed to add to one. We show that a proposed remedy called χ —scheme (Darwish and Moukalled, Comput. Methods Appl. Mech. Engrg. 192 (2003): 1711) will degrade to a diffusive first‐order scheme when a chemical species vanishes from the mixture, for example, because of chemical reactions. We propose an improvement to the χ ‐scheme to overcome this problem. Furthermore, a computationally efficient alternative scheme is proposed and evaluated with several examples, to quantify the improvements in the accuracy and the computational time. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.     

Facilitating quality control for spectra assignments of small organic molecules: nmrshiftdb2 – a free in‐house NMR database with integrated LIMS for academic service laboratories

nmrshiftdb2 supports with its laboratory information management system the integration of an electronic lab administration and management into academic NMR facilities. Also, it offers the setup of a local database, while full access to nmrshiftdb2's World Wide Web database is granted. This freely available system allows on the one hand the submission of orders for measurement, transfers recorded data automatically or manually, and enables download of spectra via web interface, as well as the integrated access to prediction, search, and assignment tools of the NMR database for lab users. On the other hand, for the staff and lab administration, flow of all orders can be supervised; administrative tools also include user and hardware management, a statistic functionality for accounting purposes, and a ‘QuickCheck’ function for assignment control, to facilitate quality control of assignments submitted to the (local) database. Laboratory information management system and database are based on a web interface as front end and are therefore independent of the operating system in use. Copyright © 2015 John Wiley & Sons, Ltd.     

从纸上到躬行:基于有机化学理论和文献的实验设计及优化之低年级本科教学初探

国际公认化学类本科生的培养目标是能够胜任化学专业技术职务,或具备相关的科研能力,而核心考核因素之一被认为是能否以纸上所学理论和文献助力实验方案的设计,并躬行实现。我们在有机化学基础实验教学中融合以上理念,初步探索出适合低年级本科生的以理论知识和文献指导实验设计和优化的教学策略。以乙酰二茂铁的合成为例,以问题-讨论为主线,引导学生从文献、底物的电子结构、傅-克酰基化反应机理和重要的物理化学性质等进行综合分析,设计乙酰二茂铁的合成路线,鼓励学生对教材提出质疑并自主设计和开展验证实验,对教材中的经典方法持续优化。学生深度参与实验路线设计和关键参数设置,沉浸学术研究氛围,敢于质疑并验证,提升了将已学理论转化为解决实际问题的能力,一定程度上有利于其科学思维和科研执行力的培养,提高其从事化学专业技术职务或相关科研工作的核心竞争力。     

NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS

In this article, we describe on a state of the art of validated numerical computations for solutions of differential equations. A brief overview of the main techniques for self-validating numerics for initial and boundary value problems in ordinary and partial differential equations including eigenvalue problems will be presented. A fairly detailed introductions are given for the author's own method related to second-order elliptic boundary value problems. Many references which seem to be useful for readers are supplied at the end of the article.     

A mathematical approach to the study of the United States Code

The United States Code (Code) is a document containing over 22 million words that represents a large and important source of Federal statutory law. Scholars and policy advocates often discuss the direction and magnitude of changes in various aspects of the Code. However, few have mathematically formalized the notions behind these discussions or directly measured the resulting representations. This paper addresses the current state of the literature in two ways. First, we formalize a representation of the United States Code as the union of a hierarchical network and a citation network over vertices containing the language of the Code. This representation reflects the fact that the Code is a hierarchically organized document containing language and explicit citations between provisions. Second, we use this formalization to measure aspects of the Code as codified in October 2008, November 2009, and March 2010. These measurements allow for a characterization of the actual changes in the Code over time. Our findings indicate that in the recent past, the Code has grown in its amount of structure, interdependence, and language.     

(6,3)-MDS Codes over an Alphabet of Size 4

An (n,k)_q-MDS code C over an alphabet (of size q) is a collection of q^k n–tuples over such that no two words of C agree in as many as k coordinate positions. It follows that n ≤ q+k−1. By elementary combinatorial means we show that every (6,3)₄-MDS code, linear or not, turns out to be a linear (6,3)₄-MDS code or else a code equivalent to a linear code with these parameters. It follows that every (5,3)₄-MDS code over must also be equivalent to linear.