On the reduction of the multidimensional Schroedinger equation to a first order equation and its relation to the pseudoanalytic function theory

Given a particular solution of a one-dimensional stationary Schroedinger equation (SE) this equation of second order can be reduced to a first order linear differential equation. This is done with the aid of an auxiliary Riccati equation. We show that a similar fact is true in a multidimensional situation also. We consider the case of two or three independent variables. One particular solution of (SE) allows us to reduce this second order equation to a linear first order quaternionic differential equation. As in one-dimensional case this is done with the aid of an auxiliary Riccati equation. The resulting first order quaternionic equation is equivalent to the static Maxwell system. In the case of two independent variables it is the Vekua equation from theory of generalized analytic functions. We show that even in this case it is necessary to consider not complex valued functions only, solutions of the Vekua equation but complete quaternionic functions. Then the first order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of (SE) and the other can be considered as an auxiliary equation of a simpler structure. For the auxiliary equation we always have the corresponding Bers generating pair, the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of (SE). We obtain an analogue of the Cauchy integral theorem for solutions of (SE). For an ample class of potentials (which includes for instance all radial potentials), this new approach gives us a simple procedure allowing to obtain an infinite sequence of solutions of (SE) from one known particular solution

Study Of Food And Energy Values Of New Gingerbread Types

The article deals with directions of the increase of the food value and decrease of the energetic value of gingerbread products. The results of the studies of the chemical composition of gingerbread products with food additives and changes in their composition were considered.The perspective of the use of vegetable additives in gingerbread technologies was substantiated on the base of the analysis and generalization of theoretical, experimental data and production studies, and the possibility of their use was proved.The use of food additives gives the possibility to raise the food and biological value, to widen the assortment of gingerbread products with prognosticated quality parameters, to form new consumption properties of a product to use the food potential of vegetable additives more full. It was proved, that new types of gingerbread products with vegetable additives have advantages over traditional ones.New types of gingerbread products has the balanced chemical composition, low energetic value, decreased content of sugar and saturated fatty acids and increased content of healthy ingredients of the functional and prophylactic destination.The addition of vegetable additives in the recipe of flour confectionary products leads to the increase of its food value at the expanse of protein quantity, change of food acids ratio in favor of unsaturated ones, enrichment with mineral substances and vitamins

On a factorization of second order elliptic operators and applications

We show that given a nonvanishing particular solution of the equation (divpgrad+q)u=0 (1) the corresponding differential operator can be factorized into a product of two first order operators. The factorization allows us to reduce the equation (1) to a first order equation which in a two-dimensional case is the Vekua equation of a special form. Under quite general conditions on the coefficients p and q we obtain an algorithm which allows us to construct in explicit form the positive formal powers (solutions of the Vekua equation generalizing the usual powers of the variable z). This result means that under quite general conditions one can construct an infinite system of exact solutions of (1) explicitly, and moreover, at least when p and q are real valued this system will be complete in ker(divpgrad+q) in the sense that any solution of (1) in a simply connected domain can be represented as an infinite series of obtained exact solutions which converges uniformly on any compact subset of . Finally we give a similar factorization of the operator (divpgrad+q) in a multidimensional case and obtain a natural generalization of the Vekua equation which is related to second order operators in a similar way as its two-dimensional prototype does

On a complex differential Riccati equation

We consider a nonlinear partial differential equation for complex-valued functions which is related to the two-dimensional stationary Schrodinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation as, e.g., the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical "one-dimensional" results we discuss new features of the considered equation like, e.g., an analogue of the Cauchy integral theorem

Multifractal detrended cross-correlation analysis for two nonstationary signals

It is ubiquitous in natural and social sciences that two variables, recorded temporally or spatially in a complex system, are cross-correlated and possess multifractal features. We propose a new method called multifractal detrended cross-correlation analysis (MF-DXA) to investigate the multifractal behaviors in the power-law cross-correlations between two records in one or higher dimensions. The method is validated with cross-correlated 1D and 2D binomial measures and multifractal random walks. Application to two financial time series is also illustrated.Comment: 4 RevTex pages including 6 eps figure

Superconductivity in correlated disordered two-dimensional electron gas

We calculate the dynamic effective electron-electron interaction potential for a low density disordered two-dimensional electron gas. The disordered response function is used to calculate the effective potential where the scattering rate is taken from typical mobilities from recent experiments. We investigate the development of an effective attractive pair potential for both disordered and disorder free systems with correlations determined from existing numerical simulation data. The effect of disorder and correlations on the superconducting critical temperature Tc is discussed.Comment: 4 pages, RevTeX + epsf, 4 figure

Human appearance and nature features exemplified by English compound adjectives

The article deals with compound English adjectives defining person’s appearance and character. The role of word-composition and affixation is defined. In the article the compound adjectives have been considered semantically according to the connection between the components and the most frequent model of compound adjectives has been define

Modern demographic situation in Ukraine and prospects of its development

У статті розглянуто особливості, форми прояву й причини демографічної кризи в сучасній Україні. Визначено основні чинники, які сприяють погіршенню демографічної ситуації в країні. Обґрунтовано, що сучасна демографічна ситуація характеризується тенденціями депопуляції, зниженням народжуваності, збільшенням смертності у всіх вікових групах, скороченням очікуваної тривалості життя та зміною характеру міграційних процесів. Акцентується увага на найбільш гострих існуючих і можливих в перспективі соціально-демографічних проблемах в Україні. Доводиться, що перспективи і подальший розвиток цієї ситуації в державі потребує проведення цілеспрямованої й ефективної державної демографічної політики.В статье рассмотрены особенности, формы проявления и причины демографического кризиса в современной Украине. Определены основные факторы, которые способствуют ухудшению демографической ситуации в стране. Обосновано, что современная демографическая ситуация характеризуется тенденциями депопуляции, снижением рождаемости, увеличением смертности во всех вековых группах, сокращением ожидаемой продолжительности жизни и изменением характера миграционных процессов. Акцентируется внимание на наиболее острых существующих и возможных в перспективе социально-демографических проблемах в Украине. Доказано, что перспективы и дальнейшее развитие данной ситуации в государстве нуждается в проведении целенаправленной и эффективной государственной демографической политики.The features, forms of display and the reasons of demographic crisis in modern Ukraine are considered in the article. Major factors which promote deterioration of a demographic situation in the country are defined. It is grounded, that a modern demographic situation is characterized by depopulation tendencies, birth rate decrease, death rate increase in all century groups, and reduction of life expectancy and change of character of the migratory processes. The attention is focused on the sharpest existing and possible future social and demographic problems in Ukraine. It is proved, that prospects and the further development of the given situation in the state require carrying out of a targeted and effective state demographic policy

PRACTICAL ISSUES OF SENSOR WEB IMPLEMENTATION AND GRIDIFICATION

In this paper we provide an overview of emerging Sensor Web paradigm and show several practical issues of using Sensor Web technologies for real-world tasks. Issues under study include sensor description using SensorML and database performance for serving observations data. This paper also shows an approach for integrating standard Sensor Observation Service with Globus Toolkit Grid platform.\ud В данной работе представлен обзор развивающейся парадигмы Sensor Web и рассмотрены практические вопросы использования данной технологии для решения прикладных задач. Рассматриваются вопросы описания численных моделей с использованием языка SensorML и оценки производительности баз данных в задачах обслуживания сервисов Sensor Web. Кроме того, в работе описаны подходы к интеграции сервисов Sensor Web с Grid-платформой Globus Toolkit.\u