Diagonalization and Jordan Normal Form – motivation through Maple

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package Maple®.

Enhancing the selenium content of bovine milk through alteration of the form and concentration of selenium in the diet of the dairy cow

Since estimated dietary selenium intake in the UK has declined steadily from around 60 mug day(-1) in 1975 to 34 mug day(-1) in 1997, there is a need to increase selenium intake from staple foods such as milk and milk products. An experiment was therefore done to investigate the relationship between dietary source and concentration of selenium and the selenium content of bovine milk. In a 3 x 3 factorial design, 90 mid-lactation Holstein dairy cows were supplemented over 8 weeks with either sodium selenite (S), a chelated selenium product (Selenium Metasolate(TM)) (C) or a selenium yeast (Sel-plex(TM)) (Y) at three different dietary inclusion levels of 0.38 (L), 0.76 (M) and 1.14 (H) mg kg(-1) dry matter (DM). Significant increases in milk selenium concentration were observed for all three sources with increasing inclusion level in the diet, but Y gave a much greater response (up to +65 mug l(-1)) than the other two sources of selenium (S and C up to +4 and +6 mug l(-1) respectively). The Y source also resulted in a substantially higher apparent efficiency of transfer of selenium from diet to milk than S or C. Feeding Y at the lowest dietary concentration, and thus within the maximum level permitted under EU regulations, resulted in milk with a selenium concentration of 28 mug l(-1). If the selenium concentration of milk in the UK was increased to this value, it would, at current consumption rates, provide an extra 8.7 mug selenium day(-1), or 11 and 14% of daily recommended national intake for men and women respectively. (C) 2004 Society of Chemical Industry.

Crystal structure of a monomeric form of SARS-CoV endonuclease nsp15 suggests a role for hexamerization as an allosteric switch

Mature nonstructural protein-15 (nsp15) from the severe acute respiratory syndrome coronavirus (SARS-CoV) contains a novel uridylate-specific Mn2+-dependent endoribonuclease (NendoU). Structure studies of the full-length form of the obligate hexameric enzyme from two CoVs, SARS-CoV and murine hepatitis virus, and its monomeric homologue, XendoU from Xenopus laevis, combined with mutagenesis studies have implicated several residues in enzymatic activity and the N-terminal domain as the major determinant of hexamerization. However, the tight link between hexamerization and enzyme activity in NendoUs has remained an enigma. Here, we report the structure of a trimmed, monomeric form of SARS-CoV nsp15 (residues 28 to 335) determined to a resolution of 2.9 A. The catalytic loop (residues 234 to 249) with its two reactive histidines (His 234 and His 249) is dramatically flipped by approximately 120 degrees into the active site cleft. Furthermore, the catalytic nucleophile Lys 289 points in a diametrically opposite direction, a consequence of an outward displacement of the supporting loop (residues 276 to 295). In the full-length hexameric forms, these two loops are packed against each other and are stabilized by intimate intersubunit interactions. Our results support the hypothesis that absence of an adjacent monomer due to deletion of the hexamerization domain is the most likely cause for disruption of the active site, offering a structural basis for why only the hexameric form of this enzyme is active.

A reaction surface Hamiltonian study of malonaldehyde

We report calculations using a reaction surface Hamiltonian for which the vibrations of a molecule are represented by 3N-8 normal coordinates, Q, and two large amplitude motions, s(1) and s(2). The exact form of the kinetic energy operator is derived in these coordinates. The potential surface is first represented as a quadratic in Q, the coefficients of which depend upon the values of s(1),s(2) and then extended to include up to Q(6) diagonal anharmonic terms. The vibrational energy levels are evaluated by solving the variational secular equations, using a basis of products of Hermite polynomials and appropriate functions of s(1),s(2). Our selected example is malonaldehyde (N=9) and we choose as surface parameters two OH distances of the migrating H in the internal hydrogen transfer. The reaction surface Hamiltonian is ideally suited to the study of the kind of tunneling dynamics present in malonaldehyde. Our results are in good agreement with previous calculations of the zero point tunneling splitting and in general agreement with observed data. Interpretation of our two-dimensional reaction surface states suggests that the OH stretching fundamental is incorrectly assigned in the infrared spectrum. This mode appears at a much lower frequency in our calculations due to substantial transition state character. (c) 2006 American Institute of Physics.

Architect and user interaction: The spoken representation of form and functional meaning

The paper is an investigation of the exchange of ideas and information between an architect and building users in the early stages of the building design process before the design brief or any drawings have been produced. The purpose of the research is to gain insight into the type of information users exchange with architects in early design conversations and to better understand the influence the format of design interactions and interactional behaviours have on the exchange of information. We report an empirical study of pre-briefing conversations in which the overwhelming majority of the exchanges were about the functional or structural attributes of space, discussion that touched on the phenomenological, perceptual and the symbolic meanings of space were rare. We explore the contextual features of meetings and the conversational strategies taken by the architect to prompt the users for information and the influence these had on the information provided. Recommendations are made on the format and structure of pre-briefing conversations and on designers' strategies for raising the level of information provided by the user beyond the functional or structural attributes of space.

Responsiveness to change by standard-form contract drafters: A case study of the FIDIC White Book

Purpose – The purpose of this paper is to focus on the Fédération Internationale des Ingénieurs-Conseils (FIDIC) White Book standard form of building contract. It tracks the changes to this contract over its four editions, and seeks to identify their underlying causes. Design/methodology/approach – The changes made to the White Book are quantified using a specific type of quantitative content analysis. The amended clauses are then examined to understand the nature of the changes made. Findings – The length of the contract increased by 34 per cent between 1990 and 2006. A large proportion of the overall increase can be attributed to the clauses dealing with “conflict of interest/corruption” and “dispute resolution”. In both instances, the FIDIC drafting committees have responded to international developments to discourage corruption, and to encourage the use of alternative dispute resolution. Between 1998 and 2006, the average length of the sentences increased slightly, raising the question of whether long sentences are easily understood by users of contracts. Research limitations/implications – Quantification of text appears to be particularly useful for the analysis of documents which are regularly updated because changes can be clearly identified and the length of sentences can be determined, leading to conclusions about the readability of the text. However, caution is needed because changes of great relevance can be made to contract clauses without actually affecting their length. Practical implications – The paper will be instructive for contract drafters and informative for users of FIDIC's White Book. Originality/value – Quantifying text has been rarely used regarding standard-form contracts in the field of construction.

Treatment response in child anxiety is differentially related to the form of maternal anxiety disorder

An examination was made of the extent to which maternal anxiety predicted response to treatment of children presenting with an anxiety disorder. In a sample of 55 children referred to a local NHS CAMH service for treatment of an anxiety disorder, systematic mental state interview assessment was made of both mothers and children, and both completed self-report questionnaires to assess aspects of anxiety, both immediately before the children received treatment and following treatment. Children of mothers with anxiety disorder overall responded less well to treatment than children of mothers with no anxiety disorder. There was some diagnostic specificity in this in that children of mothers with GAD did as well in treatment as children whose mothers had no anxiety, whereas children of mothers with social phobia did poorly. The outcome for children with anxiety appears to be related to the presence and nature of maternal anxiety. It would seem prudent that treatment of children with anxiety involves assessment of maternal anxiety. It is important to establish in systematic investigation whether treatment of maternal anxiety improves the outcome for child anxiety.

Instance generators and test suites for the multiobjective quadratic assignment problem

We describe, and make publicly available, two problem instance generators for a multiobjective version of the well-known quadratic assignment problem (QAP). The generators allow a number of instance parameters to be set, including those controlling epistasis and inter-objective correlations. Based on these generators, several initial test suites are provided and described. For each test instance we measure some global properties and, for the smallest ones, make some initial observations of the Pareto optimal sets/fronts. Our purpose in providing these tools is to facilitate the ongoing study of problem structure in multiobjective (combinatorial) optimization, and its effects on search landscape and algorithm performance.

Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

Integrable quadratic Hamiltonians on the Euclidean group of motions

In this paper, we discuss the problem of globally computing sub-Riemannian curves on the Euclidean group of motions SE(3). In particular, we derive a global result for special sub-Riemannian curves whose Hamiltonian satisfies a particular condition. In this paper, sub-Riemannian curves are defined in the context of a constrained optimal control problem. The maximum principle is then applied to this problem to yield an appropriate left-invariant quadratic Hamiltonian. A number of integrable quadratic Hamiltonians are identified. We then proceed to derive convenient expressions for sub-Riemannian curves in SE(3) that correspond to particular extremal curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles.