On Primitive Cellular Algebras

First we define and study the exponentiation of a cellular algebra by a permutation group that is similar to the corresponding operation (the wreath product in primitive action) in permutation group theory. Necessary and sufficient conditions for the resulting cellular algebra to be primitive and Schurian are given. This enables us to construct infinite series of primitive non-Schurian algebras. Also we define and study, for cellular algebras, the notion of a base, which is similar to that for permutation groups. We present an upper bound for the size of an irredundant base of a primitive cellular algebra in terms of the parameters of its standard representation. This produces new upper bounds for the order of the automorphism group of such an algebra and in particular for the order of a primitive permutation group. Finally, we generalize to 2-closed primitive algebras some classical theorems for primitive groups and show that the hypothesis for a primitive algebra to be 2-closed is essential. Bibliography: 16 titles.     

Aryliodine (III) Diacetates as Substrates for Pd-Ag Catalyzed Arylation of Alkenes

An unprecedented application of aryliodine(III) diacetates as substrates in Pd-Ag catalyzed arylation of alkenes is described. The mechanistic studies revealed that the binary Pd-Ag catalysis leads to the decomposition of aryliodine(III) diacetates to oxygen and aryl iodides followed by arylation of alkenes forming Heck-type products. Under optimized conditions both electron-rich and electron-deficient alkenes undergo arylation in high yields. Advantageously, the reaction proceeds smoothly in water as a solvent and neither organic ligands nor inert atmosphere are required.     

Solubility of potassium and sodium orthophosphates in ethylene glycol

Solubility of potassium and sodium orthophosphates in ethylene glycol was determined.     

On the problem of characterizing the diversity vectors of balls

Under study are the diversity vectors of balls (the ith entry of the vector is equal to the number of different balls of radius i) for ordinary connected graphs. The problem is solved of characterizing the diversity vectors of balls in graphs of small diameter.     

Swelling of acrylate hydrogels filled with brushite and octacalcium phosphate

Hydrogels filled with CaHPO₄ · 2H₂O and Ca₈(HPO₄)₂(PO₄)4 · 5H₂O were synthesized from the acrylate derivatives of poly(ethylene glycol) by the photopolymerization method. The swelling behaviour of the filled and unfilled hydrogels in water was studied. The solubility of the photoinitiator in water and in the monomers was estimated.

     

Electronic structure of clusters of 3d elements in layered oxide systems

Sverdlovak State Pedagogical Institute. Institute of Chemistry, Ural Branch, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 1, pp. 20–25, January–February, 1991.     

Some general questions of fast-electron transport

An inverse problem of fast-electron transport in a dielectric is proposed. This problem consists of determining the field distribution in the dielectric from the measured variations of functionals caused by an electric field within the dielectric. A method for solving the inverse problem on the basis of the general theory of variations in transport functionals is examined. It is shown that the distribution of the information functionals throughout the sample is required in order to determine the appropriate set of sources and functionals. The condition for the independence of the information functionals is obtained. It is also shown that if the variations of the transport functionals are measured and if the information functionals are known, the inverse problem of determining the field distribution reduces to the solution of a system of algebraic equations. Equations are derived for determining the value of the information required to calculate the information functionals.Translated from Izvestiya VUZ. Fizika, No. 6, pp. 25–29, June, 1973.