On Quantum Markov Chains on Cayley Tree II: Phase Transitions for the Associated Chain with XY-Model on the Cayley Tree of Order Three

In the present paper, we study forward quantum Markov chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY-model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two distinct QMC for the given family of interaction operators {K_áx,y?}{\{K_{\langle x,y\rangle}\}}.     

Catalytic acylation of benzoxazolin-2-ones in the presence of zinc chloride

In the acylation of benzoxazolin-2-ones by aromatic acid chlorides in the presence of 10^-2 mole of ZnCl₂, the yields of the corresponding 6-aroylbenzoxazolin-2-ones depend on the electronegativity of the acylating agent and the nucleophilicity of the benzoxazolin-2-ones.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1136–1138, August, 1994.     

Solvability of cubic equations in p-ADIC integers (p > 3)

We give a criterion for the existence of solutions to an equation of the form x ³ + ax = b, where a, b ∈ ? _p , in p-adic integers for p > 3. Moreover, in the case when the equation x ³ + ax = b is solvable, we give necessary and sufficient recurrent conditions on a p-adic number x ∈ ?* _p under which x is a solution to the equation.     

IR spectroscopic study of structure of matrix pqlyconcondensation products of urea and formaldehyde on carboxymethylcellulose

Translated from Zhurnal Prlkladnoi Spektroskopii, Vol. 49, No. 6, pp. 974–978, December, 1988.     

Vasoactive peptides from venom of the wasp Polistes gallicus. Isolation and physicochemical and functional properties

Six vasoactive peptides have been isolated in the homogeneous form from the venom of the waspPolistes gallicus. Their physicochemical characteristics have been investigated. The wasp kinins exhibit myotropic and hypotensive effects. One of the kinins shows a prolonged hypotensive action. A. S. Sadykov Institute of Bioorganic Chemistry, Uzbek SSR Academy of Sciences, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 564–568, July–August, 1989.     

On periodic Gibbs measures of <Emphasis Type="Italic">p</Emphasis>-adic Potts model on a Cayley tree

In the present paper, we study the existence of periodic p-adic quasi Gibbs measures of p-adic Potts model over the Cayley tree of order two. We first prove that the renormalized dynamical system associated with the model is conjugate to the symbolic shift. As a consequence of this result we obtain the existence of countably many periodic p-adic Gibbs measures for the model.     

Phase diagram of the three states Potts model with next nearest neighbour interactions on the Bethe lattice

We have found an exact phase diagram of the Potts model with competing nearest neighbor and next nearest neighbor interactions on the Bethe lattice of order two. The diagram consists of five phases: ferromagnetic, paramagnetic, modulated, antiphase and paramodulated, all meeting at the multicritical point . We report on a new phase which we denote as paramodulated, found at low temperatures and characterized by zero average magnetization lying inside the modulated phase. Such a phase, inherent in the Potts model has no analogues in the Ising setting.