The completely positive and doubly nonnegative completion problems

We prove the following. Let G be an undirected graph. Every partially specified symmetric matrix, the graph of whose specified entries is G and each of whose fully specified submatrices is completely positive (equal to BB^T for some entrywise nonnegative matrix B), may be completed to a completely positive matrix if and only if G is a block-clique graph (a chordal graph in which distinct maximal cliques overlap in at most one vertex). The same result holds for matrices that are doubly nonnegative (entrywise nonnegative and positive semidefinite).     

Biosynthetic Studies on Antibiotics

The intricacies of the synthetic chemistry executed by living cells in the assembly of complex organic natural products can be probed in great detail by stable-isotope labeling in conjunction with sophisticated 2D and multiple-quantum NMR methods of analysis. Mechanistic details are revealed by unraveling the “cryptic” stereochemistry of biosynthetic reactions with the aid of stereospecific isotope labeling. Analysis of blocked mutants and cloning of biosynthetic genes provides new tools for the study of biosynthetic pathways and for the exploitation of the chemical capabilities of living organisms.     

The Nature of Community OR

This paper outlines the results of a study undertaken to investigate the nature of Community Operational Research (COR). The objective was to contact the people involved in COR through a series of personal interviews and a questionnaire survey, in order to clarify many of the issues that have emerged within the profession relating to the practice of OR within the community and voluntary sector. A total of 20 individuals were successfully contacted, and they have been responsible for at least two-thirds of the projects in the COR area.     

An Experimental Evaluation of Interactive MCDM Methods and the Decision Making Process

Increasingly, it is becoming recognized that interactive solution methods should provide not only a solution to a multiple criteria decision making (MCDM) problem, but also the opportunity for decision makers to learn about their own preferences. In this paper, we describe an experiment that examines three MCDM solution methods and the process of converging on a final solution. Twenty-four management students participated in the experiment and were required to solve two completely different MCDM problems. Within this experimental framework, we examined the use of a two-stage approach to decision making. Both quantitative and qualitative results are presented. Preferences among the different solution methods vary significantly. Several conclusions are drawn concerning the desirable features of interactive MCDM solution methods.     

Fiber formation via solution spinning of the cellulose/ammonia/ammonium thiocyanate system

Fiber formation via the cellulose/ammonia/ammonium thiocyanate system by wet spinning has been investigated. This report presents a characterization of the structure and tensile properties of fibers spun under various coagulation conditions. Microscopic observations showed that the molecular size of coagulant was the dominant factor governing the crosssectional shape of the fibers. Density, birefringence, and crystallinity data indicated that a higher cellulose concentration and lower coagulation temperature favored development of a fiber with a denser and more oriented structure. Under optimum conditions, a welldefined fibrillar structure was obtained. Fiber tensile property measurements suggested the existence of a linear relationship between the fiber breaking tenacity and the product of the square of the Hermans' orientation factor and the infrared crystallinity index.     

Laser-induced breakdown of soda-lime glass microspheres using Nd:YAG laser

The Nd:YAG laser-induced breakdown of 20 μm glass microspheres was investigated using time-resolved optical shadow and Schlieren images. Time-resolved imaging showed the location of the initial breakdown and the shockwave motion over its first 400 μm of expansion. Measured shockwave velocities were in the range of 1–10 km/s and showed a linear dependency on laser fluence within 30 ns.     

Regular simple geodesic loops on a tetrahedron

A regular simple geodesic loop on a tetrahedron is a simple geodesic loop which does not pass through any vertex of the tetrahedron. It is evident that such loops meet each face of the tetrahedron. Among these loops, the minimal loops are those which meet each face exactly once. Necessary and sufficient conditions for the existence of minimal loops are obtained. These conditions fall naturally into two categories, conditions in the first category being called coherence conditions and conditions in the second category being called separation conditions. It is shown that for the existence of three distinct minimal loops through any point on the face of a tetrahedron it is necessary and sufficient that the tetrahedron be isosceles, which, in turn, amounts to the tetrahedron satisfying three coherence conditions. All other regular simple geodesic loops on an isosceles tetrahedron are then classified. Finally, coherence conditions for the existence of similar loops on an arbitrary tetrahedron are found.     

3‐(3‐Oxo‐1,3‐dihydroisobenzofuran‐1‐ylidene)pentane‐2,4‐dione

In the title compound, C₁₃H₁₀O₄, prepared by the condensation reaction between phthalic anhydride and pentane‐2,4‐dione, one of the acetyl groups in the pentane‐2,4‐dione fragment is almost coplanar with the isobenzofuran ring system, while the other group is twisted out of this plane by almost 80°. The corresponding C—C and C—O distances in the two acetyl units are consistent with dipolar delocalization into the coplanar unit only. There is no supramolecular aggregation of the molecules, but a number of rather short intermolecular contacts of C—H...O, O...O and O...C types occur.