Tools for Assigning Resonance Structures in Collisions of Few-Body Quantum Systems

The complex dilated Mittag-Leffler, the T-matrix, and the Siegert pseudostate methods are briefly reviewed. Their respective strengths and weaknesses and some recent results are discussed. Permanent address: V. Fock Institute of Physics, St. Petersburg State University, St. Petersburg, 198504 Russia Permanent address: Department of Mathematical and Computational Physics, St. Petersburg State University, St. Petersburg, Russia Permanent address: Department of Physics, University of South Africa, P.O. Box 392, Pretoria, South Africa     

��-Homogeneity of Borel sets

We give an affirmative answer to the following question: Is any Borel subset of a Cantor set C a sum of a countable number of pairwise disjoint h-homogeneous subspaces that are closed in X? It follows that every Borel set ${X \subset {\bf R}^n}$ can be partitioned into countably many h-homogeneous subspaces that are G _?? -sets in X.     

Multichannel detection of signals and estimation of signal parameters in non-Gaussian clutter

Multichannel asymptotically optimal signal detectors and signal parameter meters are synthesized in non-Gaussian clutter. The estimates of the detection and measurement efficiency of synthesized structures are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 8, pp. 1044–1056, August, 1996.     

Maps of Borel sets

Questions concerning the structure of Borel sets were raised in special cases by Luzin, Aleksandrov, and Uryson as the problems of distinguishing the sets with certain homogeneous properties in Borel classes and determining the number of such pairwise nonhomemorphic sets. The universal homogeneity, i.e., the property to contain an everywhere closed copy of any Borel set of the same or smaller class, was considered by L.V. Keldysh. She called the sets of classes Π _α ⁰ , α > 2, of first category in themselves that possess this homogeneity property canonical and proved their uniqueness. Thus she revealed the central role of the universality property when describing homeomorphic Borel sets. These investigations led her to the problem of universality of Borel sets and to the problem of finding conditions under which there exists an open map between Borel sets. In this paper, such conditions are presented and similar questions are considered for closed, compact-covering, harmonious, and other stable maps.     

Origin of the single chain magnet behavior of the Co(H2L)(H2O) compound with a 1D structure

The paper is aimed at the elucidation of the main factors responsible for the single-chain magnet behavior of the cobalt(II) disphosphonate compound Co(H2L)(H2O) with a 1D structure. The model takes into account the spin-orbit interaction, the axial component of the octahedral crystal field acting on the ground-state cubic 4T1 terms of the Co(II) ions, the antiferromagnetic exchange interaction between Co(II) ions as well as the difference in the crystallographic positions of these ions. The conditions that favor the single-chain magnet behavior based on spin canting in a 1D chain containing inequivalent Co(II) centers are discussed. The peculiarities of this behavior in chains containing orbitally degenerate ions are revealed. The qualitative explanation of the experimental data is given.     

Composite particles of polyethylene @ silica

Polyethylene (PE) and silica are perhaps the simplest and most common organic and inorganic polymers, respectively. We describe, for the first time, a physically interpenetrating nanocomposite between these two elementary polymers. While polymer-silica composites are well known, the nanometric physical blending of PE and silica has remained a challenge. A method for the preparation of such materials, which is based on the entrapment of dissolved PE in a polymerizing tetraethoxysilane (TEOS) system, has been developed. Specifically, the preparation of submicron particles of low-density PE@silica and high-density PE@silica is detailed, which is based on carrying out a silica sol-gel polycondensation process within emulsion droplets of TEOS dissolved PE, at elevated temperatures. The key to the successful preparation of this new composite has been the identification of a surfactant, PE-b-PEG, that is capable of stabilizing the emulsion and promoting the dissolution of the PE. A mechanism for the formation of the particles as well as their inner structure are proposed, based on a large battery of analyses, including transmission electron microscopy (TEM) and scanning electron microscopies (SEM), surface area and porosity analyses, various thermal analyses including thermal gravimetric analysis (TGA/DTA) and differential scanning calorimetry (DSC) measurements, small-angle X-ray scattering (SAXS) measurements and solid-state NMR spectroscopy.     

The Linear-Array Conjecture in Communication Complexity Is False

linear array network consists of k+1 processors with links only between and (0≤i<k). It is required to compute some boolean function f(x,y) in this network, where initially x is stored at and y is stored at . Let be the (total) number of bits that must be exchanged to compute f in worst case. Clearly, , where D(f) is the standard two-party communication complexity of f. Tiwari proved that for almost all functions and conjectured that this is true for all functions. In this paper we disprove Tiwari's conjecture, by exhibiting an infinite family of functions for which is essentially at most . Our construction also leads to progress on another major problem in this area: It is easy to bound the two-party communication complexity of any function, given the least number of monochromatic rectangles in any partition of the input space. How tight are such bounds? We exhibit certain functions, for which the (two-party) communication complexity is twice as large as the best lower bound obtainable this way. Received: March 1, 1996     

Synthesis of Fused Heterocycles Based on 1-Amino-1H-tetrazole-5-thiol and α,β-Unsaturated Aldehydes

Russian Journal of General Chemistry - 8-Phenyltetrazolo[5,1-b][1,3,4]thiadiazepine was obtained as a result of intermolecular cyclization of 1-amino-1H-tetrazole-5-thiol and 3-phenyl-2-propynal....