Stationary probability distributions for multiresponse linear learning models

A necessary and sufficient condition is given for the existence of stationary probability distributions of a non-Markovian model with linear transition rule. Similar to the Markovian case, stationary probability distributions are characterized as eigenvectors of nonnegative matrices. The model studied includes as special cases the Markovian model as well as the linear learning model and has applications in psychological and biological research, in control theory, and in adaption theory.     

Models having the thermodynamic properties of aqueous alkaline earth halides and NaCl-MgCl2 mixtures

A model studied earlier in relation to aqueous 1–1 electrolytes has been applied to the interpretation of the excess free energies of aqueous solutions of the alkaline earth halides up to 1 M ionic strength. Several variations on the model could be fitted to the data. In the one which seems most consistent with the other observations, the cospheres (hydration layers) on the M⁺⁺ ions were two water molecules thick rather than one as for the alkali metal, tetraalkylammonium, and halide ions. The overlap of cospheres of an M⁺⁺, M⁺⁺ pair was found to make a small attractive contribution to the interionic force, while the overlap of cospheres of an M⁺⁺, X^– pair makes a small positive contribution which is almost the same for X^–=Cl^–, Br^–, or I^–. Thus, ionic hydration shells which are not penetrated by other ions are not required to account for the observed excess free energies. The model is also fitted to NaCl-MgCl₂ mixtures to see whether the new cosphereoverlap parameter which must be determined is consistent with the others. The calculation also shows how the thermodynamic behavior of the mixtures is consistent with the mixture limiting law for unsymmetrical mixtures. The singularities in the mixing coefficients g₀ and w₀ at infinite dilution dominate their concentration dependence only up to ionic strengths of about 0.01 M in models which fit the data.Most of this report is abstracted from a thesis presented by A. Smitherman to the Graduate School of the State University of New York at Stony Brook in partial fulfillment of the requirements for the M.S. degree, August 1972.     

Biomimetic hydrolysis of penicillin G catalyzed by dinuclear zinc(II) complexes: structure-activity correlations in beta-lactamase model systems

A series of highly preorganized pyrazolate-based dinuclear zinc complexes has been studied as functional synthetic analogues of metallo-beta-lactamases, a class of bacterial enzymes that cause serious clinical problems because of their degradation of common beta-lactam antibiotics. We have investigated the hydrolytic cleavage of penicillin G mediated by the different dinuclear zinc complexes, and have deduced structure-activity correlations. While cooperative effects of the adjacent metal ions might be operative, these are found to either enhance or diminish beta-lactamase activity with respect to a single free zinc. Drastic differences in activity are ascribed to a lack of accessible binding sites after incorporation of the substrate within the bimetallic pocket of 2 and 4, whereas partial detachment of hemilabile ligand side arms in 1 and 3 opens up available coordination sites for nucleophile activation and/or for binding and polarisation of the beta-lactam amide oxygen atom. This interpretation has been corroborated by NMR spectroscopic and mass spectrometric evidence as well as by X-ray crystallography of several adducts formed between the pyrazolate-based dinuclear zinc scaffolds and the small substrate analogue oxazetidinylacetate (oaa), 5-7. In all adducts, the carboxylate group of oaa is the primary anchoring site and is nested in a bridging position within the bimetallic pocket. However, zinc binding of the beta-lactam amide oxygen atom has been confirmed crystallographically for the first time in 7, in which additional open-site coordination sites are available.     

On standardized models of isogenous elliptic curves

Let be isogenous elliptic curves over given by standardized Weierstrass models. We show that (in the obvious notation)

and, moreover, that there are integers such that

where .

     

Sieve likelihood ratio inference on general parameter space

In this paper,a theory on sieve likelihood ratio inference on general parameterspaces(including infinite dimensional)is studied.Under fairly general regularity conditions,the sieve log-likelihood ratio statistic is proved to be asymptotically X~2 distributed,whichcan be viewed as a generalization of the well-known Wilks' theorem.As an example,asemiparametric partial linear model is investigated.     

Adaptive quasi-likelihood estimate in generalized linear models

This paper gives a thorough theoretical treatment on the adaptive quasi-likelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.     

First-order kinetic approximation for a reactive gas mixture

A multicomponent reacting gas with an arbitrary number of chemical species and one reversible reaction is studied at a kinetic level in the frame of discrete velocity models of the Boltzmann equation, with the main objective of deriving the reactive Navier Stokes equations of the model, and characterizing the dissipative terms related to shear viscosity, thermal conductivity and thermal diffusion. The closure of the system formed by conservation and chemical rate equations is based on a first-order Chapman-Enskog method, to be applied in the strong reaction regime, and on a convenient representation of the density vector space in terms of the macroscopic variables. A mathematical procedure is proposed which leads to identification of the transport coefficients, and may be applied to a quite large variety of reactive gas flows. Moreover, it allows characterization of the functional form of the transport coefficients in dependence on the local gas concentrations, once the model is specified.Received: 4 October 2004, Accepted: 3 December 2004, Published online: 18 March 2005PACS: 51.10. + y, 51.20. + d, 47.70.Fw Correspondence to: A.J. Soares     

WKB method for the Dirac equation with a scalar-vector coupling

We outline a recursive method for obtaining WKB expansions of solutions of the Dirac equation in an external centrally symmetric field with a scalar-vector Lorentz structure of the interaction potentials. We obtain semiclassical formulas for radial functions in the classically allowed and forbidden regions and find conditions for matching them in passing through the turning points. We generalize the Bohr-Sommerfeld quantization rule to the relativistic case where a spin-1/2 particle interacts simultaneously with a scalar and an electrostatic external field. We obtain a general expression in the semiclassical approximation for the width of quasistationary levels, which was earlier known only for barrier-type electrostatic potentials (the Gamow formula). We show that the obtained quantization rule exactly produces the energy spectrum for Coulomb- and oscillatory-type potentials. We use an example of the funnel potential to demonstrate that the proposed version of the WKB method not only extends the possibilities for studying the spectrum of energies and wave functions analytically but also ensures an appropriate accuracy of calculations even for states with n_r 1.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 1, pp. 83–111, April, 2005.     

$${\cal K}$$-Convexity1 in $$\Re^{n}$$

We generalize the concept of K-convexity to an n-dimensional Euclidean space. The resulting concept of -convexity is useful in addressing production and inventory problems where there are individual product setup costs and/or joint setup costs. We derive some basic properties of -convex functions. We conclude the paper with some suggestions for future research. Support from Columbia University and University of Texas at Dallas is gratefully acknowledged. Helpful comments from Qi Feng are appreciated.