
The Fourier method, symmetries and the Green function of the Dirichlet problem
The article offers the deduction of expressions for the Greene function of the Dirichlet problem for a strip and a rectangle by means of
three methods: the Fourier method and methods involving the factorized variant of the symmetry principle and conform maps.
1.
Лаврентьев М.А, Шабат Б.
В.
Методы теории функции комплексного переменного. М., 1973.
2.
Привалов И.
И.
Введение в теорию функций комплексного переменного. М., 1999.
3.
Шабат Б.
В.
Введение в комплексный анализ. М., 1969. ...

Characteristics of communicativetextual functions of complex propertense German sentences
The article analyses complex propertense sentences from the point of view of their role in the text generating process. The article describes the systemformation function of this kind of sentences. The author identifies certain types of derivatory symmetry / asymmetry of the described type of sentences, being the main scenarios of the text generating process.
1.
Тарасов
Е.
Ф.
Тенденции развития психолингвистики.
М.,
1987
.
2.
Степанов Ю.
С.
Методы и принципы современной лингвистики....

Algebra method of the construction of the Maxwell equations in a 2D inhomogeneous dielectric
We study discrete isospectral symmetries for the linear problem in spatial dimensions two, by developing a Darboux (Moutard) transformation formalism for this problem. As an application, we construct some singular and nonsingular integrable potentials (dielectric permitivity) for ...

On the relations between the integrable hierarchies
We demonstrate that such distinct equations as the KdV, mKdV, NLS as well as the Calogero–Degasperis, Toda and Volterra equations can generated from each other via the discrete symmetries chains. Interestingly, the key ingredient in this process is none other but the famous KP equations.
1. Веселов А. П., Шабат А. Б. Одевающая цепочка и спектральная теория оператора ...

Symmetry and asymmetry of higher education in the conditions of globalisation
This article deals with the territorial features of higher education and the development of poles in world education as one of the problems of asymmetry in global economy.
1. Academic Ranking of World Universities — 2010. URL: http://www.arwu.org/ ARWU2010.jsp
2. АзиатскоТихоокеанское экономическое сотрудничество (АТЭС) // Википедия. URL: http://ru.wikipedia.org/wiki
3. Бадарч Д., Сазонов Б. А. Актуальные вопросы интернациональной гармонизации образовательных систем : моногр. М., 2007....

Why is the space around us three dimensional
We note that it is no accident that modern science cannot answer to the question why our space we exist in and which we see is threedimensional. Therefore, it is believed that attempts to find an answer to this question, by remaining only within the mathematics, are bound to fail. On the contrary, it is in the present math study that it is shown that why space is threedimensional can only be explained only by means of higher arithmetic. This is followed by an answer to the following important...

Closed lattice of Toda equations
The method of closed chains of discrete symmetries is used to multiply Toda lattices in one and two spatial dimensions. Using the modified Toda equations m0TCand m1TC as an example, it is shown that the combination of the Darboux and Schlesinger transformations leads to closed dressing chains....

System analysis and methodology for developing a software product of a mathematical model of physical processes for the aviation industry
The method of closed chains of discrete symmetries is used to multiply Toda lattices in one and two spatial dimensions. Using the modified Toda equations m0TCand m1TC as an example, it is shown that the combination of the Darboux and Schlesinger transformations leads to closed dressing chains....

The statement of the problem of scattering of band electrons in an atomic chain by impurities in the approximation of potentials of zero radius
In this work the problem of electron bound to 3d linear atom chain scattering on impurity atoms is considered. In order to describe zone electrons the Bloch functions are constructed with respect to symmetry consideration. In addition, zero range potential approximation is used to model both atoms in chain and impurity atoms.
Botman S. A., Leble S. B.
Bloch wavefunction, scattering, impurity, zero range potential
2934

The calculation of the spectrum of nuclear quadrupole resonance deuterium replaced methyl group
Values for quadrupole energy levels of CD3 molecule are obtained. Besides the energy values stationary states of this system is marked by total spin projection on the molecular symmetry axis. Nuclear selection rule for radiative transitions is M 1. The radiative transition frequencies are calculated and it is obtained, that spectrum have a dublet and triplet structure.
1. Варшалович Д. А., Москалев А. Н., Херсонский В. К. Квантовая теория углового момента. Л., 1975.
2. Иванов А. А., Иванов...

Towards a Theory of Barotropic Geostrophic Currents
In this article, we examine barotropic geostrophic currents in a Cartesian and the polar coordinate system. The polar system is preferable for analysing geostrophic currents, since radial symmetry is intrinsic to these currents. We obtained ratios between the general hydrodynamic properties. The expressions of geostrophic current velocity components in terms of pressure were the most important among them. The procedure of deriving the expression of vorticity in terms of pressure was carried out....

Potentials of filtration flows in an angle area
The new theorem which generalizing the theorems of a straight line and a circle is formulated and proved.With their help complex potentials of filtration flows in the two — component media filling angle area are received.
1.
Голубева О.
В.
Курс механики сплошных сред. М., 1972.
2.
Зайцев А.А, Шпилевой А.
Я.
Теория стационарных физических полей в кусочнооднородных средах. Калининград, 2001.
3.
Волянская И.
К., Зайцев А.
А., Шпилевой А.
Я.
Комплексные потенциалы фильтрационных течений...

The application of effective Hamiltonian method for open quantum system
The article shows that the Lindblad Master Equation for finitedimensional Hilbert space can be presented as a Schrödinger Equation on a Hilbert space of greater dimension. This equation can be considered as an equation of the evolution of an integrated system consisting of two subsystems: observational and auxiliary ones. This equation allows solutions in the form of entangled states.
1.
Lindblad
G.
Communications Mathematical Physics
.
1976
.
Vol. 48
.
P. 119
.
2.
Helstrom
C.
W.
Quantum...

A Lax pair for the (1+3) nonlinear equation
... systems of nonlinear partial differential equations in mathematical sciences. The search for a systematic approach to developing exact solutions of such systems has become one of the main problems in the theory of integrable systems.
1. Fokas A. S. Symmetries and integrability // Stud. Appl. Math. 77. 1987. No. 3. P. 253—299.
2. Солитоны и метод обратной задачи / пер. с англ. M., 1987.
3. Matveev V. B., Salle M. A. Darboux Transformation and Solitons. Berlin,...

The asymmetry of small and medium business development at a regional level
This article proposes a practical method for estimating the regional asymmetry of small and medium business development and presents the results of its approbation in the Northwestern Federal District of Russia. The author makes a conclusion that small and medium business is developing unevenly. The author's method can be used in studying other aspects of the asymmetry of economic development as well as in drawing up small and medium enterprise stimulations programs.
1. Бухарова Е. Б. Оценка стратегического...

Generalized Evans function for continuous spectrum
The task is to define a function EH(λ), such that if { n } are the points of the continuous spectrum of operator H and n λ λ , then EH(λ) is defined and is nonzero.
1.
Evans J.
W.
Nerve axon equations. Stability of the nerve impulse // Indiana Univ. Math. J. 1972/73. 22. P. 577—593.
2.
Leble S.
B., Salle M.
A., Yurov A.
V.
Darboux transforms for Davey — Stewartson equations and solitons in multidimensions // Inverse Problems. 1992. Vol. 8, №
2. P. 207—218.
3.
Bordag M...

The dynamics of localized pulse as solutions of Davey — Stewartson II equations
A class of spatially localized solutions of Davey — Stewartson II equation is examined; it is shown that such solutions tend to lose the locality properties with time scale corresponding to a characteristic space scale of initial localization. The locality loss manifests itself with emergence of resonance spikes, whose total number is determined by the asymptotic behavior of support function on infinity. In particular, the exponentially localized perturbations split into an infinite number of the...

The diagnostics of regional asymmetry of innovative development of small enterprises
The subject of this study is the influence of area factors on the innovation activities of small enterprises. The main theoretical aspects of regional asymmetry of economic development are analyzed. The article presents the author’s method of assessing regional asymmetry of small enterprise innovation development and the mechanism of its diagnostics tested in the case of the regions of the Northwestern Federal District of the Russian Federation. The most meaningful factors affecting innovation activities...

Twodimensional supersymmetric quantum mechanics and the Moutard transformations
This is a treatise on a twodimensional supersymmetric hamiltonian H whose components consists of two scalar (h0, h1) and one matrixvalued hml quantummechanical Hamiltonians with constant terms added to the mix. In particular, the article discusses the ways to utilize a known solution of the spectral problem for operator h0 in the multidimensional generalization of the factorization method in order to produce such hml and h1 that their groundstate eigenvalues will be identical to each...

Rhythm and Metaphor in the Art of the Icon
Using art history interpretation methods and the methods of historical cultural studies, the author demonstrates the role of rhythm and metaphor as the most expressive artistic means of icon painting. The interaction of rhythm and metaphor is an integral part of the imagery and semantics of icon painting. It is stressed that the entire theological and aesthetic image of icons, which is based on rhythm and metaphor, expresses the cosmogonic ideas of the Church Fathers. However, the practical realisation...

The apologia of reason in J. Chr. Gottsched’s classicistic system: On the 250th anniversary of the philosopher’s death
This article revisits the ratiocentric system developed by the prominent exponent of the German enlightenment J. Chr. Gottsched (1700—1766). The authors examine the problem of the ontological argument in the context of the current civilizational crisis of consciousness, which arose against the background of the 20th century crisis of objectivist methodology of modern natural sciences. Such a methodology is incapable of solving the problem of an accurate description of the reality, in particular...