On uniqueness of Gibbs measure for -adic countable state Potts model on the Cayley tree

In the present paper we consider countable state of p-adic Potts model on the tree. Under some condition on weights we establish uniqueness of Gibbs measures for the model. Note that this condition does not depend on values of the prime p. An analogous fact is not true when the number of spins is finite.     

Complexes of acetic acid α-(N-benzoxazolin-2-one) with Zn(II), Cu(II), and Co(II): Syntheses and crystal structures

The results of syntheses and X-ray diffraction analyses of mononuclear complexes [ML₂(H₂O)₄] (M = Co²⁺(I), Cu²⁺(II), and Zn²⁺(III)) containing water molecules and anions of acetic acid α-(N-benzoxazolin-2-one) (L = C₉H₆O₄) are presented. The crystals of complexes I–III are isostructural (space group P2₁/n, Z = 2) and are built of discrete neutral complex molecules. The crystallographic data are as follows: for complex I, a = 6.1470(5), b = 5.3310(3), c = 30.5894(17) Å, β = 95.056(6)°, V = 998.50(11) ų; for complex II, a = 5.9661(6) Å, b = 5.1414(4) Å, c = 32.672(2) Å, β = 92.395(6)°, V = 1001.33(14) ų; and for complex III, a = 6.1404(3) Å, b = 5.3476(2) Å, c = 30.5865(12) Å, β = 94.708(4)°, V = 1000.96(7) ų. The metal atoms (M) of the complexing agents are localized in the crystallographic symmetry centers and have a distorted octahedral environment due to two oxygen atoms of the carboxy groups of two monodentate ligands (L) and four water molecules. The M-O(1w)(H₂O) and M-O(2w)(H₂O) bond lengths for the indicated complexes are 2.088(3) and 2.118(3), 2.446(3) and 1.971(3), and 2.113(4) and 2.093(3) Å for M = Co²⁺, Cu²⁺, and Zn²⁺, respectively. The crystal structures are formed due to packing of chains built of inter-molecular hydrogen bonds O-H…O.     

Quinazolines. 3*. synthesis of 6-bromo-8-chloro-sulfonylquinazoline-2,4(1h,3h)-dione and its interaction with nucleophilic reagents

6-Bromo-8-chlorosulfonylquinazoline-2,4(1H,3H)-dione was obtained from 6-bromoquinazoline-2,4(1H,3H)-dione and chlorosulfonic acid in place of the expected 6-bromo-7-chlorosulfonyl-quinazoline-2,4(1H,3H)-dione. Interaction of the product with water, alcohols, ammonia, aliphatic and heterocyclic amines gave 6-bromo-8X-quinazoline-2,4(1H,3H)-diones (X = SO₂OH, SO₂OAlk, SO₂NR¹R²), and, by reduction with SnCl₂·2H₂O in hydrochloric acid, 6-bromo-8-mercaptoquinazoline-2,4-dione was obtained.     

Quinazolines 1. Synthesis and chemical reactions of 6-chlorosulfonyl-quinazoline-2,4-diones

Treatment of quinazoline-2,4-dione and its symmetrical 1,3-dialkyl derivatives with chlorosulfonic acid gave the corresponding 6-chlorosulfonylquinazoline-2,4-diones. Reaction of the compounds obtained with nucleophilic agents (water, ammonia, aliphatic and cyclic amines) gave the corresponding free 2,4-dioxoquinazoline-6-sulfonic acids, 6-sulfamidoquinazoline-2,4-diones, and 2,4-dioxoquinazoline-6-sulfonic acid amides. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 420–427, March 2008.     

Benzazoles. 3*. Synthesis and arylsulfonylation of 2-substituted benzimidazoles

2-Alkylbenzimidazoles have been obtained from o-nitroaniline and aliphatic carboxylic acids by reductive cyclization. Interaction of the former with arenesulfonyl chlorides led to the synthesis of 2-alkyl-1-arylsulfonylbenzimidazoles, the yield of which depended on the structure of the substituent in position 2.     

Recurrence equations over trees in a non-Archimedean context

In the present paper we study recurrence equations over k-ary trees. Namely, each equation is assigned to a vertex of the tree, and they are generated by contractive functions defined on an arbitrary non-Archimedean algebra. The main result of this paper states that the given equations have at most one solution. Moreover, we also provide the existence of unique solution of the equations. We should stress that the non-Archimedeanity of the algebra is essentially used, therefore, the methods applied in the present paper are not valid in the Archimedean setting.     

Structural analogues of bradykinin and other vasoactive peptides in the venom of the wasp Polistes gallicus

Six vasoactive peptides have been isolated in the homogeneous state from the venom of the waspPolistes gallicus. Their full amino acid sequences have been determined. It has been shown that four of them are structural analogues of bradykinin with additional N- and C-terminal sequences and intramolecular substitutions of amino acids. Some structure-function relationships in bradykinin analogues are discussed.     

Existence of a Phase Transition for the Potts p-adic Model on the Set ℤ

We consider the Potts model on the set in the field Q _p of p-adic numbers. The range of the spin variables (n), , in this model is . We show that there are some values q=q(p) for which phase transitions occur.