The Factorization of Queueing Equations and Their Interpretation

There are many queueing systems, including the M ^x /M ^y /c queue, the GI ^x /M/c queue and the M/D/c queue, in which the distribution of the queue length at certain epochs is determined by a Markov chain with the following structure. Except for a number of boundary states, all columns of the transition matrix are identical except for a shift which assures that there is always the same element occupying the main diagonal. This paper describes how one can find the equilibrium distribution for such Markov chains. Typically, this problem is solved by factorizing of a certain expression characterizing the repeated columns. In this paper, we show that this factorization has a probabilistic significance and we use this result to develop new approaches for finding the equilibrium distribution in question.     

The mass spectra of 2- and 4-monohydroxy- and 2, 4-dihydroxy-1, X-naphthyridines

The mass spectra of 2-and 4-monohydroxy-and 2, 4-dihydroxy-1, 5-, -1, 6-, -1, 7-and 1, 8-naphthyridines are reported. Fragmentation mechanisms are proposed and discussed.     

Untersuchungen an reagenzien zur photometrischen zinnbestimmung

The formation of complexes between tin(IV) and o-diphenols, and o-hydroxyquinones, has been studied spectrophotometrically. Simple o-hydroxyquinones do not react with tin(IV), chloranilic acid gives an SnR₂ complex, and o-diphenols give SnR₃ complexes. The reactions of tin(IV) with hydroxyxanthene dyes to give coloured products were considered for their possible analytical utility: the pH range, absorption spectrum, solubility and composition of the complexes were investigated, and the stability constants determined. Analytical procedures have been developed for tin and checked for precision and sensitivity: gallein and hydroxyhydroquinonephthalein (dihydroxyfluorescein) are to be recommended.     

The effect of dipole-dipole interaction on zero-THz frequency polarisation

The effect of intramolecular dipole-dipole interaction on polarisation at frequencies from 0 – 10¹² Hz in dipolar media is investigated using a numerical solution of the Sturm-Liouville eigenvalue problem to which the governing Smoluchowski equation reduces. The results of Budó for the long-wavelength limit are extended to all frequencies up to the far infrared, where the predominant inertial effects are treated using a preliminary first-order correction. The numerical method of Pryce may be used to investigate much more realistic interaction potentials than the simple harmonic and cosine form considered by Budó. These simple forms are, however, sufficient to indicate that the integrated absorption intensity per molecule in the far infrared is very sensitive to dipole-dipole interaction and relative hydrodynamic drag on both interacting groups. Applications of the theory to the disordered solid and nematic phases are considered.     

Stereoelectronic control of exo/endo rate ratios in the solvolysis of 2-norbornyl p-toluenesulfonates

The variable exo/endo rate ratios observed in the solvolysis of 6-exo-substituted exo- and endo-2-norbornyl p-toluenesulfonates are due to differential transmission of polar effects in the transition state for ionization.     

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