Elliptic Quadratic Operator Equations

The paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations. The iterative Newton-Kantorovich method for stable solutions is also presented.

     

Crystal structure of α-(N-benzoxazoline-2-one) acetic acid hydrate,solvate, and salts

The crystal structure of α-(N-benzoxazoline-2-one) acetic acid is studied in the following forms: hydrate, solvate with formic acid, organic monoethanolammonium salt (NН₂(CH₂)₂OH) in two polymorphs produced by minor changes in the crystallization temperature, and also its ethylenediammonium salt (NН₂(CH₂)₂NH₂) in the 2:1 ratio, where amino groups participate in the deprotonation of two molecules of α-(N-benzoxazoline-2-one) acetic acid. Weak intermolecular hydrogen and dative bonds in the crystals consisting of different molecules are analyzed.     

Benzazoles. 4. Synthesis and chemical reactions of 6-chlorosulfonylbenzoxazolin-2-ones

The corresponding 6-chlorosulfonyl derivatives were synthesized from benzoxazolin-2-one and its 3-methyl derivative by treatment with chlorosulfonic acid. By treatment of the compounds obtained with water and other nucleophilic reagents (aliphatic and heterocyclic amines) 2-oxobenzoxazoline-6-sulfonic acids and a series of their amides were obtained, while reduction with SnCl₂·2H₂O gave 6-mercaptobenzoxazolin-2-ones.     

Uniqueness of quantum Markov chains associated with an XY-model on a cayley tree of order 2

We propose the construction of a quantum Markov chain that corresponds to a “forward” quantum Markov chain. In the given construction, the quantum Markov chain is defined as the limit of finite-dimensional states depending on the boundary conditions. A similar construction is widely used in the definition of Gibbs states in classical statistical mechanics. Using this construction, we study the quantum Markov chain associated with an XY-model on a Cayley tree. For this model, within the framework of the given construction, we prove the uniqueness of the quantum Markov chain, i.e., we show that the state is independent of the boundary conditions.     

On the existence of generalized gibbs measures for the one-dimensional <Emphasis Type="Italic">p</Emphasis>-adic countable state Potts model

We consider the one-dimensional countable state p-adic Potts model. A construction of generalized p-adic Gibbs measures depending on weights λ is given, and an investigation of such measures is reduced to the examination of a p-adic dynamical system. This dynamical system has a form of series of rational functions. Studying such a dynamical system, under some condition concerning weights, we prove the existence of generalized p-adic Gibbs measures. Note that the condition found does not depend on the values of the prime p, and therefore an analogous fact is not true when the number of states is finite. It is also shown that under the condition there may occur a phase transition.     

On One Regularity Condition for Quantum Quadratic Stochastic Processes

We present necessary and sufficient conditions for the validity of a regularity condition for homogeneous quantum quadratic stochastic processes defined on von Neumann algebras.     

Two crystalline polymorphic forms of α-(<Emphasis Type="Italic">N</Emphasis>-benzoxazolin-2-one)acetic acid

Two crystalline polymorphic forms of α-(N-benzoxazolin-2-one)acetic acid (BAA) are prepared by changing the temperature of its crystallization from solution in ethanol. Crystallographic data of the α-form are determined: a = 12.7769(17) Å, b = 8.2574(9) Å, c = 16.7390(19) Å, β = 105.087(13)°, space group C2/c, V = 1705.2(4) ų, and Z = 8, while those of β form are a = 5.2854(4) Å, b = 5.9880(4) Å, c = 13.4509(5) Å, β = 94.666(4)°, space group P2₁, V = 424.30(4) ų, and Z = 2. It is found that BAA molecules of the α form combine into infinite one-dimensional chains arranged along axis b by means of O?H···O and C?H···O hydrogen bonds, and these chains are crosslinked via C?H···O hydrogen bonds to form a threedimensional structure. The β form has another system of hydrogen bonds, one of which is bifurcated (O4···O2, O4···O3), and the π–π-interactions between the benzoxazolinone fragments of BAA molecules combined into a chain also arranged along axis b are observed. Calorimetric analysis shows that the polymorphic transition from the α form to the β form occurs at 129°C.     

On Quantum Markov Chains on Cayley Tree III: Ising Model

In this paper, we consider the classical Ising model on the Cayley tree of order \(k\) ( \(k\ge 2\) ), and show the existence of the phase transition in the following sense: there exists two quantum Markov states which are not quasi-equivalent. It turns out that the found critical temperature coincides with the classical critical temperature.     

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.     

Vasoactive peptides from venom of the hornet Vespa orientalis physiochemical and functional characterization

Two peptides having kinin activity have been isolated from hornet venom. The peptides isolated exhibit hypotensive action and a myotropic effect, and they also liberate histamine from mast cells. One of the peptides is a close structural analog of bradykinin while the other differs considerably from it.Institute of Bioorganic Chemistry of the Uzbek SSR Academy of Sciences, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 255–258, March–April, 1988.