Symplectic semifield planes and -linear codes

There are lovely connections between certain characteristic 2 semifields and their associated translation planes and orthogonal spreads on the one hand, and -linear Kerdock and Preparata codes on the other. These inter-relationships lead to the construction of large numbers of objects of each type. In the geometric context we construct and study large numbers of nonisomorphic affine planes coordinatized by semifields; or, equivalently, large numbers of non-isotopic semifields: their numbers are not bounded above by any polynomial in the order of the plane. In the coding theory context we construct and study large numbers of -linear Kerdock and Preparata codes. All of these are obtained using large numbers of orthogonal spreads of orthogonal spaces of maximal Witt index over finite fields of characteristic 2.

We also obtain large numbers of ``boring' affine planes in the sense that the full collineation group fixes the line at infinity pointwise, as well as large numbers of Kerdock codes ``boring' in the sense that each has as small an automorphism group as possible.

The connection with affine planes is a crucial tool used to prove inequivalence theorems concerning the orthogonal spreads and associated codes, and also to determine their full automorphism groups.

     

Computational simulation of the molecular ordering of 3,6-bis(4-butylphenyl)[1,2,4,5]tetrazine at the phase transition temperatures

Computational simulation of 3,6-bis(4-butylphenyl)[1,2,4,5]tetrazine was carried out. Based on the energy of intermolecular interactions of dimers was determined the probability of each configuration (stacking, in-plane and terminal). It was revealed that in the 3,6-bis(4-butylphenyl)[1,2,4,5]tetrazine dimers the sliding of the molecules relative to each other is energetically allowed in the narrow range of distances that provides retaining orientation of the molecules in the mesophase. The relationship between the translational rigidity of the molecules in the dimer and nematic properties was revealed.     

Elastostatic resonances—a new approach to the calculation of the effective elastic constants of composites

A new method is presented for a systematic evaluation of the effective elastic tensor C^(e) in a two-component composite. Both C^(e) and local strain field are expanded in terms of a complete set of elastostatic resonances. The resonances are found by calculating eigenstates of a certain integral operator, and this can be carried out in stages. First one finds the eigenstates of individual, isolated grains or fibers, and only then does one attempt to calculate eigenstates of the entire composite. We apply this procedure to 2D periodic arrays of cylinders—both hexagonal and square. Using simple matrix perturbation techniques we obtain exact expansions for the elastic constants in powers of p, the volume fraction of the cylinders, that go up to the order p¹¹ in the case of bulk modulus of the hexagonal array.     

Theorie der Elementartheiler höherer Stufen

Ohne Zusammenfassung     

Terminal trilinear operations

Translated from Algebra i Logika, Vol. 28, No. 1, pp. 41–60, January–February, 1989.     

High-pressure studies of (Mg0.9Fe0.1)2SiO4 olivine using raman spectroscopy, X-ray diffraction, and mössbauer spectroscopy

High-pressure studies of (Mg(0.9)Fe(0.1))2SiO4 olivine were performed at ambient temperature using X-ray diffraction, Raman spectroscopy, and M?ssbauer spectroscopy. At approximately 40 GPa, a change of compressibility associated with saturation of the anisotropic compression mechanism was detected. This change is interpreted to result from the appearance of Si2O7 dimer defects, as deduced from Raman spectroscopy; the appearance of such defects also accounts for the previously reported pressure-induced amorphization observed for this material upon additional compression. Furthermore, this behavior is followed by a spin crossover of Fe(2+) that occurs over a wide pressure range, as revealed by M?ssbauer spectroscopy.     

List Colorings with Distinct List Sizes,the Case of Complete Bipartite Graphs

Let be a function on the vertex set of the graph . The graph G is f‐choosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. The sum choice number, , is the minimum of , over all functions f such that G is f‐choosable. It is known (Alon, Surveys in Combinatorics, 1993 (Keele), London Mathematical Society Lecture Note Series, Vol. 187, Cambridge University Press, Cambridge, 1993, pp. 1–33, Random Struct Algor 16 (2000), 364–368) that if G has average degree d, then the usual choice number is at least , so they grow simultaneously. In this article, we show that can be bounded while the minimum degree . Our main tool is to give tight estimates for the sum choice number of the unbalanced complete bipartite graph .