Some D type metric forms for spacetimes with shear,nongeodesic, and nondiverging principal null congruences

In the context of a null tetrad formalism it is assumed that the two real vectors of the tetrad have neither expansion nor rotation and that they are nongeodesic and/or have shear. This assumption is rarely used in search of algebraically special spacetimes. General relations for the connection and for the Ricci and Weyl tensors are presented. An additional assumption that these vectors are principal leads to Petrov type D spacetimes, reducible in some cases to conformally flat ones. Twenty-two explicit metric forms, probably hitherto unknown, are found.     

An Interior Point Heuristic for the Hamiltonian Cycle Problem via Markov Decision Processes

We consider the Hamiltonian cycle problem embedded in a singularly perturbed Markov decision process (MDP). More specifically, we consider the HCP as an optimization problem over the space of long-run state-action frequencies induced by the MDP's stationary policies. We show that Hamiltonian cycles (if any) correspond to the global minima of a suitably constructed indefinite quadratic programming problem over the frequency space. We show that the above indefinite quadratic can be approximated by quadratic functions that are `nearly convex' and as such suitable for the application of logarithmic barrier methods. We develop an interior-point type algorithm that involves an arc elimination heuristic that appears to perform rather well in moderate size graphs. The approach has the potential for further improvements.     

The Gompertzian curve reveals fractal properties of tumor growth

The normalized Gompertzian curve reflecting growth of experimental malignant tumors in time can be fitted by the power function y(t)=at^b with the coefficient of nonlinear regression r0.95, in which the exponent b is a temporal fractal dimension, (i.e., a real number), and time t is a scalar. This curve is a fractal, (i.e., fractal dimension b exists, it changes along the time scale, the Gompertzian function is a contractable mapping of the Banach space R of the real numbers, holds the Banach theorem about the fix point, and its derivative is 1). This denotes that not only space occupied by the interacting cancer cells, but also local, intrasystemic time, in which tumor growth occurs, possesses fractal structure. The value of the mean temporal fractal dimension decreases along the curve approaching eventually integer values; a fact consistent with our hypothesis that the fractal structure is lost during tumor progression.     

An efficient approach to calculation of zero-flux atomic surfaces and generation of atomic integration data

A new robust method for variational determination of atomic zero-flux surfaces is presented. The zero-flux surface sheets are expressed in terms of variational trial functions in prolate spheroidal coordinates. The trial functions are optimized with a Newton procedure to satisfy the zero-flux condition on a grid. The data required for radial integrations are generated by an adaptive quadrature procedure that employs model electron densities and utilizes an original third-order algorithm for linear search. Results of test calculations involving variational determination of atomic surfaces are presented for a representative set of 20 molecules. The new approach is both less time consuming and substantially more accurate than the previously published algorithms. © 1995 John Wiley & Sons, Inc.     

Cyanato-copper(II) complexes with organic ligands—XXIV. Diisocyanato-bis(3,5-dimethylpyrazole)copper(II)—the cyanate member of the coligand isomer

The title compound was prepared, and found to be isomeric with the known bis(1-carbamoyl-3,5-dimethylpyrazolato)copper(II). Its IR, far-IR, electronic