Quinazolines. 4*. Acylation of quinazoline-2,4-diones with aromatic acids chlorides in the presence of ferric chloride hexahydrate

The interaction of quinazoline-2,4-diones with aromatic acids chlorides in nitrobenzene has been investigated in the presence of FeCl₃·6H₂O. Optimum conditions for the acylation reaction have been developed, the used 4-substituted benzoyl chlorides have been put in order of relative activity, depending on the degree of their electrophilicity.     

A polynomial <Emphasis Type="Italic">p</Emphasis>-adic dynamical system

We completely describe the Siegel discs and attractors for the p-adic dynamical system f(x) = x ²ⁿ⁺¹ + axⁿ⁺¹ on the space of complex p-adic numbers.     

Clustering Property of Quantum Markov Chain Associated to XY-model with Competing Ising Interactions on the Cayley Tree of Order Two

Mathematical Physics, Analysis and Geometry - In this paper, we obtain a lower bound for the generalized normalized δ-Casorati curvatures of submanifolds in pointwise Kenmotsu space forms,...     

Weakly Periodic Ground States for the λ-Model

Ukrainian Mathematical Journal - For the λ-model on a Cayley tree of order k ≥ 2, we describe the set of periodic and weakly periodic ground states corresponding to normal divisors of...     

Solvability of nonlinear integral equations and surjectivity of nonlinear Markov operators

In the present paper, we consider integral equations, which are associated with nonlinear Markov operators acting on an infinite-dimensional space. The solvability of these equations is examined by investigating nonlinear Markov operators. Notions of orthogonal preserving and surjective nonlinear Markov operators defined on infinite dimension are introduced, and their relations are studied, which will be used to prove the main results. We show that orthogonal preserving nonlinear Markov operators are not necessarily satisfied surjective property (unlike finite case). Thus, sufficient conditions for the operators to be surjective are described. Using these notions and results, we prove the solvability of Hammerstein equations in terms of surjective nonlinear Markov operators.     

On the Uniqueness of Gibbs Measures for <Emphasis Type="Italic">p</Emphasis>-Adic Nonhomogeneous λ-Model on the Cayley Tree

We consider a nearest-neighbor p-adic -model with spin values ±1 on a Cayley tree of order k 1. We prove for the model there is no phase transition and as well as being unique, the p-adic Gibbs measure is bounded if and only if p 3. If p=2, then we find a condition which guarantees the nonexistence of a phase transition. Besides, the results are applied to the p-adic Ising model and we show that for the model there is a unique p-adic Gibbs measure.     

On chaotic behaviour of the p-adic generalized Ising mapping and its application

In the present paper, by conducting research on the dynamics of the p-adic generalized Ising mapping corresponding to renormalization group associated with the p-adic Ising-Vannemenus model on a Cayley tree, we have determined the existence of the fixed points of a given function. Simultaneously, the attractors of the dynamical system have been found. We have come to a conclusion that the considered mapping is topologically conjugate to the symbolic shift which implies its chaoticity and as an application, we have established the existence of periodic p-adic Gibbs measures for the p-adic Ising-Vannemenus model.     

Benzazoles: III. Synthesis and Transformations of 6-(Chlorosulfonyl)-1,3-benzothiazol-2(3H)-ones

Russian Journal of Organic Chemistry - Treatment of 1,3-benzothiazol-2(3H)-one and its 3-methyl derivative with chlorosulfonic acid afforded the corresponding...     

Antioxidant Hydrolysate of Sericin from Bombyx mori Cocoons

Chemistry of Natural Compounds - Sericin was obtained from Bombyx mori cocoons in 28% yield with 92.06% purity. Its hydrolysate was produced by an enzymatic method. A fraction with molecular mass...