Vibrational spectrum of uridine obtained by means of nonresonant-background-free CARS spectroscopy

Received: 18 June 1996/Revised version: 3 January 1997     

Global Optimization of a Quadratic Functional with Quadratic Equality Constraints, Part 2

In this paper, we investigate a constrained optimization problem with a quadratic cost functional and two quadratic equality constraints. It is assumed that the cost functional is positive definite and that the constraints are both feasible and regular (but otherwise they are unrestricted quadratic functions). Thus, the existence of a global constrained minimum is assured. We develop a necessary and sufficient condition that completely characterizes the global minimum cost. Such a condition is of essential importance in iterative numerical methods for solving the constrained minimization problem, because it readily distinguishes between local minima and global minima and thus provides a stopping criterion for the computation. The result is similar to one obtained previously by the authors. In the previous result, we gave a characterization of the global minimum of a constrained quadratic minimization problem in which the cost functional was an arbitrary quadratic functional (as opposed to positive-definite here) and the constraints were at least positive-semidefinite quadratic functions (as opposed to essentially unrestricted here).     

A compact shock-assisted free-piston driver for impulse facilities

A free-piston driver that employs entropy-raising shock processes with diaphragm rupture has been constructed, which promises significant theoretical advantages over isentropic compression. Results from a range of conditions with helium and argon driver gases are reported. Significant performance gains were achieved in some test cases. Heat losses are shown to have a strong effect on driver processes. Measurements compare well with predictions from a quasi-one-dimensional numerical code. Received 7 September 1996 / Accepted 5 October 1996     

Critical fields and currents in a weakly nonlinear medium near the percolation threshold

For fields above a critical value the expansion of the conductivity in powers of the field ceases to be valid and the weak-nonlinearity approximation no longer works. The density behavior of the critical fields in strongly inhomogeneous media near the percolation threshold is found on the basis of two criteria—an average criterion and a local criterion. The parameter values of the medium for which crossover—a change of the critical behavior—occurs are determined. Similar calculations are performed for the critical currents. Zh. Tekh. Fiz. 68, 5–8 (June 1998)     

Transfer theorems and the algebra of modal operators

A set theory ZFI′ which does not employ the Law of the Excluded Middle φ ∀ ⊥ φ, for all φ, retians the stock of expressive capacities of the classical set theory ZF, on the one hand, and has many of the features of an effective theory on the other. In the article, a broad class of formulas σ is constructed for which ZF ⊥ σ implies ZFI′ ⊥ σ. This result provides a generalization of Friedman's theorem on AE-arithmetic formulas. Besides, we prove transfer theorems of classical logic for the case of rings; in particular, Hilbert's theorem on zeros and Artin's theorem on ordered fields are extended to the case of regular f-rings, and we bring in appropriate upper bounds for them. Supported by RFFR grant No. 93-012-1027. Translated fromAlgebra i Logika, Vol. 36, No. 3, pp. 282–303, May–June, 1997.     

Thermal diffusivity measurements in porous ceramics by photothermal methods

Received: 16 September 1996/Accepted: 6 January 1997     

Chain of BBGKY equations for bimolecular chemical reactions

A dynamically verified statistical theory of moderately dense gases developed by Bogoliubov and others is generalized to the case of bimolecular chemical reactions in a gas. The corresponding chain of BBGKY equations is derived. From this chain, the kinetic equations for one-molecule distribution functions are obtained in the approximation of bimolecular and trimolecular interactions. Deceased. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 2, pp. 163–178, May, 1997.