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Full-Text Articles in Physical Sciences and Mathematics

Translation-Invariant Gibbs Measures Of A Model On Cayley Tree, Golibjon Botirov Sep 2018

Translation-Invariant Gibbs Measures Of A Model On Cayley Tree, Golibjon Botirov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider a model where the spin takes values in the set [0,1]d, and is assigned to the vertexes of the Cayley tree. We reduce the problem of describing the “splitting Gibbs measures” of the model to the description of the solutions of some non-linear integral equation. For a concrete form of the Kernel of the integral equation we show the uniqueness of solution.


Carleman's Formula For The Matrix Upper Half-Plane, Gulmirza Khudayberganov, Zokirbek Matyakubov Mar 2018

Carleman's Formula For The Matrix Upper Half-Plane, Gulmirza Khudayberganov, Zokirbek Matyakubov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this work the Carleman’s formula for the matrix upper half-plane is obtained.


Positive Fixed Points Of Lyapunov Integral Operators And Gibbs Measures, Farkhod Haydarov Mar 2018

Positive Fixed Points Of Lyapunov Integral Operators And Gibbs Measures, Farkhod Haydarov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper it is found fixed points of Lyapunov integral equation and considered the connections between Gibbs measures for four competing interactions of models with uncountable (i.e. $[0,1]$) set of spin values on the Cayley tree of order two.