Synthesis of Palladium and Nickel Complexes with Octaphenyltetraazaporphyrins

Palladium(II) and nickel(II) complexes with octaphenyltetraazaporphyrin, octakis(4-bromophenyl)tetraazaporphyrin, and octakis(4-nitrophenyl)tetraazaporphyrin were obtained by reactions of octaphenyltetraazaporphyrin, Mg octaphenyltetraazaporphyrin, octakis(4-bromophenyl)tetraazaporphyrin, and octakis(4-nitrophenyl)tetraazaporphyrin with palladium(II) and nickel(II) chlorides in DMF.     

Pattern Search Method for Discrete <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>–Approximation

We propose a pattern search method to solve a classical nonsmooth optimization problem. In a deep analogy with pattern search methods for linear constrained optimization, the set of search directions at each iteration is defined in such a way that it conforms to the local geometry of the set of points of nondifferentiability near the current iterate. This is crucial to ensure convergence. The approach presented here can be extended to wider classes of nonsmooth optimization problems. Numerical experiments seem to be encouraging. This work was supported by M.U.R.S.T., Rome, Italy.     

Remark on minimization of depth of Boolean circuits

It is shown that Lozhkin’s method (1981) for minimization of the depth of formulas with a bounded number of changing types of elements in paths from input to output and Hoover-Klawe-Pippenger’s method (technical report in 1981, journal publication in 1984) for minimization of the depth of circuits with unbounded branching by insertion of trees from buffers with bounded branching of outputs for each buffer are dual to each other and can be proved by one and the same method.     

Complex projections of completely positive quaternionic maps

We show that the complex projection of a completely positive quaternionic map of quaternionic density matrices is a positive map in the space of complex density matrices, and we briefly outline some of its properties. To illustrate this result, we study the complex projection of a one-parameter quaternionic unitary dynamics of a spin-1/2 quantum system. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 360–370, June, 2007.     

Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions

In this paper we develop an integer-affine classification of three-dimensional multistory, completely empty convex marked pyramids. We apply it to obtain the complete lists of compact two-dimensional faces of multidimensional continued fractions lying in planes at integer distances 2, 3, 4, …  to the origin. The faces are considered up to the action of the group of integer-linear transformations.     

Influence of ionizing radiation on the magnetically sensitive properties of planar triacs

Changes in the magnetically sensitive properties of multilayer semiconductors devices, such as planar diffusion triacs, that are related to atomic-displacement-induced defects and ionization by irradiation are considered. It is shown that irradiation may significantly raise the magnetic sensitivity of the triacs. Processes and underlying mechanisms responsible for the improvement of the magnetic sensitivity under the action of a number of galvanomagnetic effects are studied.