Explicit Free Parameterization of the Modified Tetrahedron Equation

The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at N-th root of unity is solved by a rational mapping operator which is obtained from the solution of a linear problem. We show that the solutions can be parameterized in terms of eight free parameters and sixteen discrete phase choices, thus providing a broad starting point for the construction of 3-dimensional integrable lattice models. The Fermat curve points parameterizing the representation of the mapping operator in terms of cyclic functions are expressed in terms of the independent parameters. An explicit formula for the density factor of the MTE is derived. For the example N=2 we write the MTE in full detail. We also discuss a solution of the MTE in terms of bosonic continuum functions.Comment: 28 pages, 3 figure

On exact solution of a classical 3D integrable model

We investigate some classical evolution model in the discrete 2+1 space-time. A map, giving an one-step time evolution, may be derived as the compatibility condition for some systems of linear equations for a set of auxiliary linear variables. Dynamical variables for the evolution model are the coefficients of these systems of linear equations. Determinant of any system of linear equations is a polynomial of two numerical quasimomenta of the auxiliary linear variables. For one, this determinant is the generating functions of all integrals of motion for the evolution, and on the other hand it defines a high genus algebraic curve. The dependence of the dynamical variables on the space-time point (exact solution) may be expressed in terms of theta functions on the jacobian of this curve. This is the main result of our paper

Quantum 2+1 evolution model

A quantum evolution model in 2+1 discrete space - time, connected with 3D fundamental map R, is investigated. Map R is derived as a map providing a zero curvature of a two dimensional lattice system called "the current system". In a special case of the local Weyl algebra for dynamical variables the map appears to be canonical one and it corresponds to known operator-valued R-matrix. The current system is a kind of the linear problem for 2+1 evolution model. A generating function for the integrals of motion for the evolution is derived with a help of the current system. The subject of the paper is rather new, and so the perspectives of further investigations are widely discussed.Comment: LaTeX, 37page

Simple Estimation of X- Trion Binding Energy in Semiconductor Quantum Wells

A simple illustrative wave function with only three variational parameters is suggested to calculate the binding energy of negatively charged excitons (X-) as a function of quantum well width. The results of calculations are in agreement with experimental data for GaAs, CdTe and ZnSe quantum wells, which differ considerably in exciton and trion binding energy. The normalized X- binding energy is found to be nearly independent of electron-to-hole mass ratio for any quantum well heterostructure with conventional parameters. Its dependence on quantum well width follows an universal curve. The curve is described by a simple phenomenological equation.Comment: 8 pages, 3 Postscript figure

The modified tetrahedron equation and its solutions

A large class of 3-dimensional integrable lattice spin models is constructed. The starting point is an invertible canonical mapping operator in the space of a triple Weyl algebra. This operator is derived postulating a current branching principle together with a Baxter Z-invariance. The tetrahedron equation for this operator follows without further calculations. If the Weyl parameter is taken to be a root of unity, the mapping operator decomposes into a matrix conjugation and a C-number functional mapping. The operator of the matrix conjugation satisfies a modified tetrahedron equation (MTE) in which the "rapidities" are solutions of a classical integrable Hirota-type equation. The matrix elements of this operator can be represented in terms of the Bazhanov-Baxter Fermat curve cyclic functions, or alternatively in terms of Gauss functions. The paper summarizes several recent publications on the subject.Comment: 24 pages, 6 figures using epic/eepic package, Contribution to the proceedings of the 6th International Conference on CFTs and Integrable Models, Chernogolovka, Spetember 2002, reference adde

Цифровые возможности развития классификации бюджетных расходов страны

The study of the processes of planning and accounting of budget expenditures in the context of digitalization and the development of the processes of classification and coding of costs is an important urgent task of improving public financial management. The purpose of the study is to generalize the classification of the country’s budget expenditures to justify the need for changes in the order of planning and cost accounting on digital platforms. The research methods included: analysis and synthesis; regression analysis; modeling; scientific abstraction; logical method. The novelty lies in the proposed logical justification of the provisions of the theory of financial informatics as a synthesis of two scientific disciplines — the theory of finance and the theory of computer science. The author’s view on the digital content of the classification of budget expenditures is proposed, which represents a multi-dimensional hierarchical system for constructing a graph of budget expenditures. Regression models of the dependence of the resource intensity of the conditional classification budget code of expenditures on the quality of financial management of the GRBS have been developed. The conclusions of the study confirmed the hypothesis that the more detailed the differentiation (classification) of budget expenditures, the more opportunities there are for competent organization and management of their financing processes, which is facilitated by the development of ICT. The recommendations are reduced to the need for further research of the scientific and applied provisions of the development and organization of the functioning of digital platforms in the system of public financial management to improve the efficiency of the use of the country’s budget resources. Further development of scientific and applied methodological provisions for the development of the electronic budget is required in order to turn it into a form of the digital budget of the country.Исследование процессов планирования и учета бюджетных расходов в условиях цифровизации и развития процессов классификации и кодирования затрат является важной и актуальной задачей совершенствования государственного финансового менеджмента. Целью исследования является обоснование положений развития бюджетной классификации расходов на цифровых платформах. Предмет исследования — система классификации бюджетных расходов. Методы исследования включили: анализ и синтез; регрессионный анализ; моделирование; научную абстракцию; логический метод. Новизна заключается в предложенном логическом обосновании положений теории финансовой информатики как синтеза двух научных дисциплин — теории финансов и теории информатики. Предложен авторский взгляд на цифровой контент классификации бюджетных расходов, который представляет многоразмерную иерархическую систему построения графа бюджетных расходов. Разработаны регрессионные модели зависимости ресурсоемкости условного классификационного бюджетного кода расходов от качества финансового менеджмента главных распорядителей бюджетных средств. Выводы исследования подтвердили гипотезу, которая заключается в том, что чем детальнее дифференцировать (классифицировать) бюджетные расходы, тем больше возможностей грамотной организации и управления процессами их финансирования, чему способствует развитие информационно коммуникационных технологий. Рекомендации сводятся к необходимости дальнейшего исследования научно-прикладных положений развития и организации функционирования цифровых платформ в системе государственного финансового менеджмента для повышения эффективности использования бюджетных ресурсов страны. Требуется дальнейшая разработка научно-прикладных методических положений развития электронного бюджета с целью превращения его в форму цифрового бюджета страны