Point processes and multivariate extreme values

A new model for point processes is developed which assumes that the interarrival times are exponentially distributed and follow joint multivariate extreme value distributions. It is shown that such processes may arise via natural generating procedures, and that, under very weak assumptions, that they can be approximated as closely as desired by appropriate finite models.     

Some asymptotic expansions of moments of order statistics

Series expansions of moments of order statistics are obtained from expansions of the inverse of the distribution function. They are valid for certain types of distributions with regularly varying tails. We show that the expansions converge quickly when the sample size is moderate to large, and we obtain bounds on the rate of convergence. The special case of the Cauchy distribution is treated in more detail.     

Deterministic optimal control,given only a partial observation of the initial state

The deterministic linear-system, quadratic-cost optimal control problem is considered when the only state information available is a partial linear observation of the initial statex ₀. Thus, it is only known that the initial condition belongs to a particular linear variety. A control function is found which is optimal, in the sense (roughly) that (i) it can be computed using available information aboutx ₀ and (ii) no other control function which can be found using that information gives lower cost than it does for every initial condition that could have given rise to the information. The optimal control can be found easily from the conventional Riccati equation of optimal control. Applications are considered in the presence of unknown exponential disturbances and to the case with a sequence of partial state observations.     

Michael reaction. IV. NaNH2 catalyzed one stage reaction between phenylacetic acid dialkylamides and cinnamic acid methyl ester or dialkylamides. Influence of reaction conditions on the stereochemistry

The NaNH₂ catalyzed one stage reaction between phenylacetic acid dialkylamides and cinnamic acid methyl ester or dialkylamides was studied under various conditions. Conditions were found for easy preparation of each of the both possible diastereomeric derivatives of 2,3-diphenylglutaric acid. It was proved that catalytic amounts of NaNH₂ take part in the reaction. It is assumed that the observederythro/threo equilibrium ratios are determined by an isomerization via two different carbanions (at C₂ and C₄) of the reaction products.Part III:J. Stefanovsky andL. Viteva, Comun. Dept. Chem. Bulg. Acad. Sci.4, 159 (1971).     

Partial fractions expansion: a review of computational methodology and efficiency

Nine methods for expressing a proper rational function in terms of partial fractions are presented for the case where the denominator polynomial has been reduced to linear factors. Only those methods which are amenable to computation algorithms are considered. To the extent possible, Newton's divided difference formula is used to provide a uniform derivational tool. Each method is illustrated numerically. The efficiency of the methods are compared on the basis of the number of multiplications and divisions required in the computation.     

Atomic short-range order in CuMn alloys

The establishment of atomic short-range order (SRO) has been investigated in CuMn alloys (5, 8,13,16,20 at. % Mn) by measurement of the electrical resistivity during isochronal and isothermal annealing. An increasing degree of SRO is accompanied by a reduction of resistivity; this effect increases with Mn concentration. For 8,13 and 16 at. % Mn SRO kinetics turn out to deviate significantly from single exponential behavior with a maximum at 13 at. % Mn, whereas at 5 and 20 at. % Mn SRO is adjusted in a single exponential process. For data analysis three methods are used: a sum of two and three exponentials as well as a log-normal spectrum of relaxation times. The strong interaction between second-nearest-neighbor atoms in CuMn seems to be essential for SRO kinetics but of minor importance for the value of SRO-induced resistivity change.     

Neutron scattering by anharmonic crystals and the effect of sublattice displacements

A theory has been given for the scattering of neutrons by anharmonic crystals, for which terms of the typeV ⁽³⁾ (k _1j1; —k _1j1;o _j) which contribute to the sublattice displacements are not neglected. Using the standard perturbation theory in the interaction picture or Green’s function method, an expression has been derived for the differential scattering cross-section which brings in the shift and the width of the phonons in one-phonon energy exchange processes. It is shown that the sublattice displacements will modify the phase factor arising from the scattering by any atom in the unit cell, and the Debye-Waller factor also gets altered both by the sublattice displacements as well as by higher order terms arising from anharmonicity. It is shown that the differential scattering cross-section contains a term linearly depending on the third order anharmonicity coefficientV ⁽³⁾ (k _1j1;k _2j2;k _3j3) and neutron scattering by crystals should provide a useful method for evaluating the third order anharmonicity coefficients.     

Global solutions of the Boltzmann equation on a lattice

The nonlinear Boltzmann equation with a discretized spatial variable is studied in a Banach space of absolutely integrable functions of the velocity variables. Conservation laws and positivity are utilized to extend weak local solutions to a global solution. This is shown to be a strong solution by analytic semigroup techniques.Supported by National Science Foundation Grant ENG-7515882.     

A gasdynamic jet carrying excited metal atoms as a spectral light source and a chemical reactor

A gasdynamic jet is described, which carries excited metal atoms in subsonic or supersonic flow. The excitation is performed by a hot hollow cathode discharge. The jet expands parallel into an atmosphere of a few mbar. Its use will be in atomic and molecular spectroscopy, in chemistry and spectroscopy of free radicals, and in electronic-transition chemical laser design.