Implementation of the operations research/management science process

The aim of this article is to point out some basic aspects of the OR/MS implementation problem and to outline a frame of reference for dealing with the OR/MS process. The model proposed includes a decomposition of the OR/MS process. Phases, interest groups, strategies, and variables in the OR/MS process are considered as being important. The first part of the article is a summary of some important recent contributions by others, whereas the second part represents contributions resulting from the author's own research.     

Properties of nasicon electrolytes prepared from alkoxide derived gels: Ionic conductivity,durability in molten sodium and strength test data

Nasicon ceramics have been prepared from gel-derived raw materials both by conventional sintering and by hot-pressing. For several compositions the ionic conductivity have been determined by the AC-method. The properties of ceramics based on the ZrO₂-poor composition Na_2.94Zr_1.49P_0.8Si_2.2O_10.85 have been studied in greater detail. Durability test in Na/Na-cells so far indicate good stability at 300°C, and corrosion tests in molten sodium (400°–700°C) indicate that at 400°, 350° and 300°C it will take respectively at least 100 h, 7 weeks and 3 years to dissolve a 1 micron thich layer of the ceramic. The fracture strenght of the ceramics have been determined by the three point bending method. Weibul statistics indicate an average fracture strength of 168 MPa and a m-value of 8.3 (sample vol. 0.07 cm³) for the best ceramics prepared so far.     

On single and bimodal optimum buckling loads of clamped columns

We study the problem of determining the optimum shape of a thin, elastic, clamped column of given length and volume, such that the fundamental buckling load is a maximum. The column cross-sections are assumed to be geometrically similar, and a minimum allowable value is specified for the cross-sectional area.Investigating the optimization problem parametrically in terms of this minimum constraint, we reveal a significant feature. There exists a threshold value for the constraint, beyond which the optimum columns are all associated with single mode optimum buckling loads, whereas, for any value of the constraint less than the threshold value, the optimum columns are associated with bimodal fundamental buckling loads.This bimodal behaviour necessitates an extension and a mathematical reformulation of the current optimization problem, which is outlined and solved in the paper. In particular, we revise the result hitherto considered to be the optimum solution for an unconstrained column with clamped ends.     

Finite metric spaces of strictly negative type

We prove that, if a finite metric space is of strictly negative type, then its transfinite diameter is uniquely realized by the infinite extender (load vector). Finite metric spaces that have this property include all spaces on two, three, or four points, all trees, and all finite subspaces of Euclidean spaces. We prove that, if the distance matrix is both hypermetric and regular, then it is of strictly negative type. We show that the strictly negative type finite subspaces of spheres are precisely those which do not contain two pairs of antipodal points. In connection with an open problem raised by Kelly, we conjecture that all finite subspaces of hyperbolic spaces are hypermetric and regular, and hence of strictly negative type.     

Mass spectrometry in structural and stereochemical problems-CCXXIX: Electron-impact-induced fragmentation of boric acid esters

The mass spectral decompositions of cyclic and acyclic borates have been examined. Straight chain trialkyl borates fragment by C? O cleavage reactions accompanied by transfer of one or two hydrogen atoms, whereas tri-(sec-alkyl) borates primarily undergo α-cleavage reactions. Both types of cleavage are observed in the fragmentation of cyclic borates. B? O bonds are not broken in the formation of most major fragment ions. The fragmentations of borates are compared with those of phenylboronates with special emphasis on the rearrangements leading to hydrocarbon ions in the spectra of the latter.