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Dynamical Systems of Möbius Transformation: Real, \(p\) -Adic and Complex Variables
In this paper we consider function \(f(x)={x+a\over bx+c}\) , (where
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Synthesis of Methyl 2-O-Benzoyl-3,5-di-O-benzyl-α-L-talofuranoside
Methyl 2-O-benzoyl-3,5-di-O-benzyl-α-L-talofuranoside was synthesized from methyl 3,5-di-O-benzyl-1,2-O-isopropylidene-α-L-talofuranoside which was successively treated with 20% hydrochloric acid in aqueous metha...
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Gibbs Periodic Measures for a Two-State HC-Model on a Cayley Tree
In this paper, we study a two-state Hard-Core (HC) model with activity λ > 0 on a Cayley tree of order k ≥ 2. It is known that there are λcr,
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Behavior of Trajectories of a Quadratic Operator
We consider a two-parametric quadratic stochastic operator (QSO) map** 3-dimensional simplex to itself. To date, for very few QSOs complete description of trajectories (limit points) is known. For our two-pa...
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Synthesis and Phosphonylation of S-Methylthiouracil and Its Derivatives
A series of S-methylated derivatives of 2-thiouracil were prepared and then phosphonylated with diethyl chlorophosphate. The reaction conditions were optimized, the structure of the obtained compounds was determi...
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Gibbs Measures for HC-Model with a Cuountable Set of Spin Values on a Cayley Tree
In this paper, we study the HC-model with a countable set \(\mathbb Z\) Z o...
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Fixed points of an infinite-dimensional operator related to Gibbs measures
We describe fixed points of an infinite-dimensional nonlinear operator related to a hard-core (HC) model with a countable set $$\ma...
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Periodic Points of a \(p\) -Adic Operator and their \(p\) -Adic Gibbs Measures
In this paper we investigate generalized Gibbs measure (GGM) for \(p\) -adic Hard-Core (HC) model with a countable se...
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Mirror Symmetry of Height-Periodic Gradient Gibbs Measures of an SOS Model on Cayley Trees
For the solid-on-solid model with spin values from the set of all integers on a Cayley tree we give gradient Gibbs measures (GGMs). Such a measure corresponds to a boundary law (which is an infinite-dimensiona...
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Dynamical System of a Quadratic Stochastic Operator with Two Discontinuity Points
We consider a population consisting of two species whose dynamics is determined by a quadratic stochastic operator with variable coefficients, which makes it a discontinuous operator at two points. This ope...
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Gibbs measures for the HC Blume–Capel model with countably many states on a Cayley tree
We study the Blume–Capel model with a countable set \(\mathbb Z\) of spin values and a force
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Periodic Gibbs measures for the Potts model in translation-invariant and periodic external fields on the Cayley tree
We study the Potts model in translation-invariant and periodic external fields on the Cayley tree of order \({k\geq 2}\) ...
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Quadratic non-stochastic operators: examples of splitted chaos
There is one-to-one correspondence between quadratic operators (map** \({\mathbb {R}}^m\) ...
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\(p\) -Adic Dynamical Systems of the Function \(a x^{-2}\)
In this paper we study \(p\) -adic dynamical systems generated by the function
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Thermodynamics of interacting systems of DNA molecules
We define a DNA molecule as a sequence of the numbers 1 and 2 and embed it on a path of a Cayley tree such that each vertex of the Cayley tree belongs to only one DNA and each DNA has its own countable set ...
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p-adic boundary laws and Markov chains on trees
In this paper, we consider a potential on general infinite trees with q spin values and nearest-neighbor p-adic interactions given by a stochastic matrix. We show the uniqueness of the associated Markov chain (sp...
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\(p\) -Adic Dynamical Systems of \((3,1)\) -Rational Functions with Unique Fixed Point
We describe the set of all \((3,1)\) -rational functions given on the set of complex \(p\) -adic field \({\mathbb C}_p\) and having a unique fixed point. We study \(p\) -adic dynamical systems generated by ...
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Dynamical Systems of the p-Adic (2, 2)-Rational Functions with Two Fixed Points
We consider a family of (2, 2)-rational functions given on the set of complex p-adic field \(\mathbb C_p\) C p . Each such function f has two distinct fixed points \(x_1=x_1(f)\) x 1 = x 1 ( f ) ,...
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Dynamics of a Population with Two Equal Dominated Species
We consider a population with two equal dominated species, dynamics of which is defined by an one-dimensional piecewise-continuous, two parametric function. It is shown that for any non-zero parameters this fu...
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A Quasi-strictly Non-volterra Quadratic Stochastic Operator
We consider a four-parameter family of non-Volterra operators defined on the two-dimensional simplex and show that, with one exception, each such operator has a unique fixed point. Depending on the parameters,...
