On non-linear Markov operators: surjectivity vs orthogonal preserving property

In the present paper, we consider non-linear Markov operators, namely polynomial stochastic operators. We introduce a notion of orthogonal preserving polynomial stochastic operators. The purpose of this study is to show that surjectivity of non-linear Markov operators is equivalent to their orthogonal preserving property.     

On the Blum-Hanson theorem for quantum quadratic processes

In this paper an analog of the Blum-Hanson theorem for quantum quadratic processes on the von Neumann algebra is proved, i.e., it is established that the following conditions are equivalent:

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.     

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.     

Reaction of deoxyvasicinone with organolithium compounds

4-Butyl-4-hydroxydeoxypeganine was prepared by lithiation of deoxyvasicinone. Deoxypeganine and 1,2-dihydrodeoxypeganine were produced by reduction of deoxyvasicinone with lithium aluminum hydride.     

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.     

Ground States and Phase Transition of the λ Model on the Cayley Tree

We consider the λ model, a generalization of the Potts model, with spin values {1, 2, 3} on the order-two Cayley tree. We describe the model ground states and prove that translation-invariant Gibb measures exist, which means that a phase transition exists. We establish that two-periodic Gibbs measures exist.     

The p-adic Potts model on the Cayley tree of order three

We study a phase transition problem for the q-state p-adic Potts model on the Cayley tree of order three. We find certain conditions for the existence of p-adic Gibbs measures and then establish the existence of a phase transition.