The six semifield planes associated with a semifield flock

In 1965 Knuth (J. Algebra 2 (1965) 182) noticed that a finite semifield was determined by a 3-cube array (a_ijk) and that any permutation of the indices would give another semifield. In this article we explain the geometrical significance of these permutations. It is known that a pair of functions (f,g) where f and g are functions from GF(q) to GF(q) with the property that f and g are linear over some subfield and g(x)²+4xf(x) is a non-square for all x∈GF(q)∗, q odd, give rise to certain semifields, one of which is commutative of rank 2 over its middle nucleus, one of which arises from a semifield flock of the quadratic cone, and another that comes from a translation ovoid of Q(4,q). We show that there are in fact six non-isotopic semifields that can be constructed from such a pair of functions, which will give rise to six non-isomorphic semifield planes, unless (f,g) are of linear type or of Dickson-Kantor-Knuth type. These six semifields fall into two sets of three semifields related by Knuth operations.     

New sources of “active” halogen bis(dialkylamide)hydrogen dibromobromates, efficient reagents for destruction of ecotoxicants

Bis(dialkylamide)hydrogen dibromobromates were synthesized and their reactivity was investigated in decomposition of diethylphosphonic, diethylphosphoric, and 4-toluenesulfonic acids 4-nitrophenyl esters. The nucleophilic reactivity of a typical α-nucleophile, hypobromite ion, is independent of the source of the active bromine. The cetyltrimethylammonium dibromobromate is a unique reagent for destruction of ecotoxicants. In weakly alkaline media the half-life of 4-nitrophenyl diethylphosphonate did not exceed 6 s at [BrO^?] 0.02 mol l^?1, and the apparent reaction rate compared to water increased ～40-fold. The main factor governing the micellar effects of surfactants is concentrating the substrate in the micellar pseudophase.     

Ionization of two-electron atom in ultrashort laser pulse

The method of numerical integration of the classical equations of motion was used to study interaction of a model two-electron atom with ultrashort laser pulses. Mechanisms and specific features of the ionization process were analyzed in a broad range of laser-field parameters.     

Direct chemical ionization mass silylated iridoid glucosides

The direct chemical ionization mass spectra with isobutane of 14 silylated iridoid glucosides of different structural types were studied. The dependence of the intensity of different peaks on the structure and stereochemistry of the investigated compounds is discussed.     

Helmholtz potentiality conditions for systems of difference-differential equations

For operators corresponding to systems ofμth-order difference-differential equations of neutral type, necessary and sufficient conditions for potentiality with respect to the classical bilinear form are obtained. These results are applied to first-order quasilinear systems. Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 437–442, September, 1998. The author wishes to express his thanks to V. M. Savchin for fruitful discussions and useful remarks.