On random walks arising in queueing systems: ergodicity and transience via quadratic forms as lyapounov functions — Part I

A simple and quite general approach is proposed to derive criteria for transience and ergodicity of a certain class of irreducibleN-dimensional Markov chains in ₊ ^N assuming a boundedness condition on the second moment of the jumps. The method consists in constructing convenient smooth supermartingales outside some compact set. The Lyapounov functions introduced belong to the set of quadratic forms in ₊ ^N and do not always have a definite sign. Existence and construction of these forms is shown to be basically equivalent to finding vectors satisfying a system of linear inequalities.Part I is restricted toN=2, in which case a complete characterization is obtained for the type of random walks analyzed by Malyshev and Mensikov, thus relaxing their condition of boundedness of the jumps. The motivation for this work is partly from a large class of queueing systems that give rise to random walks in ₊ ^N      

Purification and partial characterization of two lectin isoforms fromCratylia mollis mart. (camaratu bean)

Two additional electrophoretically distinct molecular forms, isoforms (iso) 2 and 3, with lectin properties were isolated fromCratylia mollis Mart, seeds (FABACEAE), by extraction with 0.15M NaCl and ammonium sulfate fractionation, followed by chromatography on Sephadex G-75 and Bio-Gel P-200 (iso 2), as well as CM-Cellulose and Sephadex G-75 (iso 3). Both isoforms were human group nonspecific and showed distinct specificity. Polyacrylamide gel electrophoresis resolved iso 2 and 3 in polypeptides of apparent mol wts 60 and 31 kDa, respectively; a distinct isoelectric focusing pattern was obtained for iso 2 and 3, under denaturing and reducing conditions.     

On a characterization of the normal distribution by means of identically distributed linear forms

Let X₁, X₂,…, be independent, identically distributed random variables. Suppose that the linear forms L₁ = Σ_j=1^∞a_jX_j and L₂ = Σ_j=1^∞b_jX_j exist with probability one and are identically distributed; necessary and sufficient conditions assuring that X₁ is normally distributed are presented. The result is an extension of a theorem of Linnik (Ukrainian Math. J.5 (1953), 207–243, 247–290) concerning the case that the linear forms L₁ and L₂ have a finite number of nonvanishing components. This proof only makes use of elementary properties of characteristic functions and of meromorphic functions.     

Lifschitz singularities for periodic operators plus random potentials

UsingX-bounding (lower bounds by Laplacians with mixed boundary conditions and discrete analogs), we obtain the Lifschitz exponent at the bottom of the spectrum for random operators of typeH =T+V , withT a (periodic) generator of a positivity-preserving semigroup, extending results by Kirsch and Simon.     

Die multikomponenten Formen von Cellulase (EC 3.2.1.4) ausAspergillus oryzae

The enzyme cellulase fromAspergillus oryzae was resolved into four multiple forms, using anion exchange chromatography on DEAE Sephadex A-50 and gel filtration on Sephadex G-75. The stages of fractionation were followed by electrophoresis on cellulose acetate strips. These enzyme forms are characterized by different enzyme activities and isoelectric points.

Herrn Univ.-Prof. Dr.Hans Tuppy zum 65. Geburtstag herzlichst gewidmet.     

Alkylhydrazides and their protonated forms: Physical methods andab initio calculations

The basicity of hydrazides of the highest aliphatic carboxylic acids RC(O)NHNH₂ (R = C_nH_2n+1,n = 5-12) has been studied by potentiometric titration, and IR and¹H NMR spectroscopy.Ab initio Hartree-Fork calculations using the 6–31G^* basis set with full optimization of geometry were carried out on the simplest acy1hydrazines and their possible protonated forms. Based on these calculations, and the 1R and¹H NMR spectra, the tautomerism of alkylhydrazides and the structures of their protonated forms are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2645–2649, November, 1996.     

Pyrite Genesis During Early Diagenesis in Yellow Sea and East China Sea

The content and isotopic compositions of different sulphur species in pore-water and solid phases have been examined on five sediment cores taken from muddy sediment region in the Yellow Sea and the East China Sea. Relationships among these data have been investigated with the combination of morphology of mineral pyrite and organic matter so as to role out the diagenetic behaviour of sulphur species at the early stage of diagenesis in modern marine sediment and the origin of pyrite formation.     

Fitting complex potential energy surfaces to simple model potentials: application of the simplex-annealing method

A stochastic method of optimization, which combines simulated annealing with simplex, is implemented to fit the parameters of a simple model potential. The main characteristic of the method is that it explores the whole space of the parameters of the model potential, and therefore it is very efficient in locating the global minimum of the cost function, in addition to being independent of the initial guess of the parameters. The method is employed to fit the complex intermolecular potential energy surface of the dimer of water, using as a reference the spectroscopic quality anisotropic site-site potential of Feller et al. The simple model potential chosen for its reparameterization is the MCY model potential of Clementi et al. The quality of the fit is assessed by comparing the geometry of the minimum, the harmonic frequencies, and the second virial coefficients of the parameterized potential with the reference one. Finally, to prove more rigorously the robustness of this method, it is compared with standard nonstochastic methods of optimization.     

Kinetic Spectrophotometric Determination of Ritodrine Hydrochloride in Dosage Forms

A simple and sensitive kinetic method was developed for the determination of ritodrine hydrochloride in pharmaceutical preparations. The method is based upon a kinetic investigation of the oxidation reaction of the drug with alkaline potassium permenganate at room temperature for a fixed 12.5 min; the absorbance of the colored permenganate ion was measured at 609 nm. The absorbance concentration plots were rectilinear over the range of 1.6–11.2 μg mL^?1 (r = 0.9992) with a minimum detectability of 0.096 μgmL^?1 (2.88 × 10^?7 M). The different experimental parameters affecting the development and stability of color were carefully studied and optimized. The determination of ritodrine hydrochloride by the fixed concentration and rate constant methods is also feasible with the calibration equations obtained, but the fixed time method has been found to be more applicable. The proposed method was applied successfully to the determination of ritodrine hydrochloride in tablets and ampoules with average recoveries of 100.37 ± 0.93% and 100.42 ± 0.87%, respectively. The results obtained were in good agreement with those obtained using a reference method for comparison. A proposal of the reaction pathway is also presented.     

Polarographic behaviour and determination of spironolactone

The polarographic behaviour of spironolactone in Britton-Robinson buffers containing 40% methanol as a solubilizer was studied. Over the pH range 3-12 a cathodic wave was produced. The wave was characterized as irreversible, diffusion-controlled and partially affected by adsorption phenomena. The number of electrons involved in the reduction was found by coulometric measurements at a controlled potential. A method was developed for the determination of spironolactone in tablets and the results obtained were in agreement with those obtained by the B.P. 1988 method. The mechanism of the electrode reaction is discussed.AvH scholar: 1989–1991