Computing an eigenvector of an inverse Monge matrix in max-plus algebra

The problem of computing an eigenvector of an inverse Monge matrix in max-plus algebra is addressed. For a general matrix, the problem can be solved in at most O(n³) time. This note presents an O(n²) algorithm for computing one max-plus algebraic eigenvector of an inverse Monge matrix . It is assumed that is irreducible.     

Quantum reflection of bright matter-wave solitons

We propose the use of bright matter-wave solitons formed from Bose-Einstein condensates with attractive interactions to probe and study quantum reflection from a solid surface at normal incidence. We demonstrate that the presence of attractive interatomic interactions leads to a number of advantages for the study of quantum reflection. The absence of dispersion as the soliton propagates allows precise control of the velocity normal to the surface and for much lower velocities to be achieved. Numerical modelling shows that the robust, self-trapped nature of bright solitons leads to a clean reflection from the surface, limiting the disruption of the density profile and permitting accurate measurements of the reflection probability.     

Comment on the reply by T. Ozawa

Journal of Thermal Analysis and Calorimetry -     

The determination of kinetic parameters for some solid state reactions

The kinetics of many solid state reactions can best be explained in terms of an order of reaction; this is particularly true in the case of polymer degradation. The methods currently available for the determination ofn andk, from isothermal data, are either limited in the range of which can be used or are difference-difference techniques where the data must of necessity be highly accurate. This paper presents a review of these methods and introduces a new approach by whichn andk can be obtained directly, giving results which are unique and objective in that they provide a best fit to the experimental data.

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Zusammenfassung Die Kinetik vieler Reaktionen in fester Phase kann am besten an Hand einer Reaktions-Ordnung erklärt werden; dies besteht besonders bei dem Abbau von Polymeren. Die für die Bestimmung vonn undk aus isothermen Daten zur Verfügung stehenden Methoden sind entweder auf den verwendbaren Bereich von beschränkt oder sind Differenz-Differenz-Methoden, bei welchen es äußerst genauer Angaben bedarf. Die vorliegende Veröffentlichung gibt eine übersicht dieser Methoden und führt eine neue Annäherung ein, durch welchen undk unmittelbar erhalten werden können. Diese Methode ergibt einzigartige und zielgerechte Ergebnisse, indem diese sich den Versuchsdaten am besten anpassen.

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Résumé Pour de nombreuses réactions dans l'état solide l'ordre de réaction constitue un très bon moyen pour exprimer leur cinétique; c'est le cas, en particulier, de la dégradation des polymères. Les différentes méthodes dont on dispose pour déterminern et k à partir des données isothermes sont limitées à l'intervalle d'utilisation de ou opèrent par différences successives ce qui nécessite des données très précises. L'article présente une revue de ces méthodes et introduit une nouvelle approche oùn etk peuvent Être obtenus directement, en donnant des résultats uniques et objectifs qui assurent un meilleur accord avec les données expérimentales.

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; . , n ,k . , « — », . , n k. .

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The calculations presented in this paper were performed on an ICL 4130 computer using the program SOLITER. This program was written in ALGOL 60.     

Energy of activation for the decomposition of the alkaline-earth carbonates from thermogravimetric data

Activation energies for the vacuum thermal decomposition of calcium, strontium and barium carbonates have been determined from thermogravimetric data, using the Coats and Redfern equation. A computer program, written in 4100 Algol, was used to process the data and to obtain the order (n) of the decomposition reactions. In all three cases, a value ofn=2/3 was in closest agreement with the experimental results, suggesting that decomposition occurs at a progressively shrinking spherical interface. The energies of activation obtained were in close agreement with the corresponding values of the enthalpy of decomposition, calculated at the temperature at which half of the sample had decomposed.     

Polyoxometalate HIV-1 protease inhibitors. A new mode of protease inhibition.

Nb-containing polyoxometalates (POMs) of the Wells-Dawson class inhibit HIV-1 protease (HIV-1P) by a new mode based on kinetics, binding, and molecular modeling studies. Reaction of alpha(1)-K(9)Li[P(2)W(17)O(61)] or alpha(2)-K(10)[P(2)W(17)O(61)] with aqueous H(2)O(2) solutions of K(7)H[Nb(6)O(19)] followed by treatment with HCl and KCl and then crystallization affords the complexes alpha(1)-K(7)[P(2)W(17)(NbO(2))O(61)] (alpha(1)()1) and alpha(2)-K(7)[P(2)W(17)(NbO(2))O(61)] (alpha(2)()1) in 63 and 86% isolated yields, respectively. Thermolysis of the crude peroxoniobium compounds (72-96 h in refluxing H(2)O) prior to treatment with KCl converts the peroxoniobium compounds to the corresponding polyoxometalates (POMs), alpha(1)-K(7)[P(2)W(17)NbO(62)] (alpha(1)()2) and alpha(2)-K(7)[P(2)W(17)NbO(62)] (alpha(2)()2), in moderate yields (66 and 52%, respectively). The identity and high purity of all four compounds were confirmed by (31)P NMR and (183)W NMR. The acid-induced dimerization of the oxo complexes differentiates sterically between the cap (alpha(2)) site and the belt (alpha(1)) site in the Wells-Dawson structure (alpha(2)()2 dimerizes in high yield; alpha(1)()2 does not). All four POMs exhibit high activity in cell culture against HIV-1 (EC(50) values of 0.17-0.83 microM), are minimally toxic (IC(50) values of 50 to >100 microM), and selectively inhibit purified HIV-1 protease (HIV-1P) (IC(50) values for alpha(1)()1, alpha(2)()1, alpha(1)()2, and alpha(2)()2 of 2.0, 1.2, 1.5, and 1.8 microM, respectively). Thus, theoretical, binding, and kinetics studies of the POM/HIV-1P interaction(s) were conducted. Parameters for [P(2)W(17)NbO(62)](7)(-) were determined for the Kollman all-atom (KAA) force field in Sybyl 6.2. Charges for the POM were obtained from natural population analysis (NPA) at the HF/LANL2DZ level of theory. AutoDock 2.2 was used to explore possible binding locations for the POM with HIV-1P. These computational studies strongly suggest that the POMs function not by binding to the active site of HIV-1P, the mode of inhibition of all other HIV-1P protease inhibitors, but by binding to a cationic pocket on the "hinge" region of the flaps covering the active site (2 POMs and cationic pockets per active homodimer of HIV-1P). The kinetics and binding studies, conducted after the molecular modeling, are both in remarkable agreement with the modeling results: 2 POMs bind per HIV-1P homodimer with high affinities (K(i) = 1.1 +/- 0.5 and 4.1 +/- 1.8 nM in 0.1 and 1.0 M NaCl, respectively) and inhibition is noncompetitive (k(cat) but not K(m) is affected by the POM concentration).     

Concentration dependent chemical shifts in the NMR spectrum of 3,5-dimethyl-5-nitro-tetrahydro-1,3-oxazine

The marked concentration dependence of the chemical shifts of the C2, C4 and C6 protons in 3,5-dimethyl-5-nitro-tetrahydro-1,3-oxazine is described.     

Spin-orbit matrix elements in the atomic f shell from automorphisms of SO(8)

A scrutiny of the matrix elements within the f shell of the spin-other-orbit interaction H(soo) has revealed many unexpected proportionalities that go beyond an application of the Wigner-Eckart theorem to Racah's groups G2 and SO(7). An explanation is sought by using the automorphisms of SO(8) by means of which the states of the atomic f shell are generated by two alternative SO(7) bases of the type (1 / 21 / 21 / 2)(4), each augmented by two parity labels. Transformations between the bases can be made by reversing the relative phases of the two angular-momentum states 3 and 0 that comprise any one of the four SO(7) spinors. The method is exemplified by the single-electron spin-orbit interaction H(so), for which a component can be found that is invariant under the phase reversal. The extension from H(so) to H(soo) is described for the component z(6) of H(soo), and several examples drawn from the comparatively inaccessible configurations near the middle of the f shell are presented.     

A photo-optical technique for measuring flow-induced vibrations in cantilevered tube bundles

A photo-optical technique has been developed for monitoring the dynamic displacement of cantilevered tubes in fluid flow. The technique employs an optical fiber to transmit light through the tube and a phototransistor array to measure the motion of the light beam that is projected from the end of the tube. The device is simple, inexpensive, and very sensitive to small displacements. Details are given for the development of the technique, analysis of performance, and static calibration. The device was tested by monitoring the dynamic response of a bundle of cantilevered tubes in both single-phase and two-phase Freon 11 flows. The results are compared with those of a standard strain gauge bridge.