Hidden Symmetries of the Open N=2 String

It is known for ten years that self-dual Yang-Mills theory is the effective field theory of the open N=2 string in 2+2 dimensional spacetime. We uncover an infinite set of abelian rigid string symmetries, corresponding to the symmetries and integrable hierarchy of the self-dual Yang-Mills equations. The twistor description of the latter naturally connects with the BRST approach to string quantization, providing an interpretation of the picture phenomenon in terms of the moduli space of string backgrounds.Comment: 24 pages, no figures; v2: typos correcte

Group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations

A complete group classification of a class of variable coefficient (1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, is given, by using a compatibility method and additional equivalence transformations. A number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Furthermore, the possible additional equivalence transformations between equations from the class under consideration are investigated. Exact solutions of special forms of these equations are also constructed via classical Lie method and generalized conditional transformations. Local conservation laws with characteristics of order 0 of the class under consideration are classified with respect to the group of equivalence transformations.Comment: 23 page

Group Analysis of Variable Coefficient Diffusion-Convection Equations. I. Enhanced Group Classification

We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear diffusion--convection equations with coefficients depending on the space variable. At first, we construct the usual equivalence group and the extended one including transformations which are nonlocal with respect to arbitrary elements. The extended equivalence group has interesting structure since it contains a non-trivial subgroup of non-local gauge equivalence transformations. The complete group classification of the class under consideration is carried out with respect to the extended equivalence group and with respect to the set of all point transformations. Usage of extended equivalence and correct choice of gauges of arbitrary elements play the major role for simple and clear formulation of the final results. The set of admissible transformations of this class is preliminary investigated.Comment: 25 page

National ideology in a multicultural world

This article attempts a social-philosophical analysis of national ideology as a crucial mechanism for expressing national consciousness in a multicultural world. National ideology is viewed as a specific form of ideology, which expresses the interests, needs, and mentality of a national-ethnic community. The authors stress that this phenomenon is associated with the national specificity of its sociocultural context. National ideology is viewed not only in its traditional interpretation as a rational expression of the political interests of a national community - the article emphasizes a special role of a nation's oftentimes unconscious aspiration toward preserving its ethnic boundaries. The author conducts an analysis of national ideology through the prism of the dissonance of narratives in a multicultural society

Conceptual approach to the development of financial technologies in the context of digitalization of economic processes

The successful introduction of the digital economy into the information space of the Russian Federation involves the solution of several problems associated with the transition to a new paradigm of economic development based on the digitization of social and economic processes. At the same time, the existing regulatory mechanisms and legislation do not create optimal conditions for the development of the market of new financial instruments and technologies in Russia today. There are socio-economic risks, the key ones including an increase in the outflow of capital and innovative projects to other countries, a lack of confidence on the part of potential investors in new financial instruments, a decrease in the stability of traditional financial institutions. On this basis, the following tasks have been set in this article. To consider the terminology in the field of digital economy from the theoretical aspect; to identify trends and justify the need for digitalization of economic processes based on the use of new financial technologies; to reveal the informative characteristics of financial technologies promising for Russia. This article ends with a conclusion that the development of the digital economy in Russia is due to the need to ensure the information and economic security of the state, realize the potential of the new economy to improve the standard of living and national well-being through the introduction of innovative communication and financial technologies. The impact of the “digital economy” on socio-economic processes is multifaceted. It is sustainable and permeates all spheres of life, being an integral part of modern society.peer-reviewe

Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons

We consider a complex vector bundle E endowed with a connection A over the eight-dimensional manifold R^2 x G/H, where G/H = SU(3)/U(1)xU(1) is a homogeneous space provided with a never integrable almost complex structure and a family of SU(3)-structures. We establish an equivalence between G-invariant solutions A of the Spin(7)-instanton equations on R^2 x G/H and general solutions of non-Abelian coupled vortex equations on R^2. These vortices are BPS solitons in a d=4 gauge theory obtained from N=1 supersymmetric Yang-Mills theory in ten dimensions compactified on the coset space G/H with an SU(3)-structure. The novelty of the obtained vortex equations lies in the fact that Higgs fields, defining morphisms of vector bundles over R^2, are not holomorphic in the generic case. Finally, we introduce BPS vortex equations in N=4 super Yang-Mills theory and show that they have the same feature.Comment: 14 pages; v2: typos fixed, published versio

Studying the suspended matter in Antarctic Peninsula coastal waters to understand the local geological and ecological processes

We review comprehensive international studies of the mineral and organic suspended matter in the South Ocean. We suggest an experimental design to monitor these parameters at the Akademik Vernadsky station, where this research will be introduced. Applied aspects of marine suspension's qualitative and quantitative properties are a subject of active research, given its significance for several physical and biochemical processes such as sedimentation. Therefore, geological, biological, and climatological studies of the Antarctic shelf employ continuous observations of the suspension’s distribution. Work in this area is aimed at investigating the qualitative and quantitative properties of the suspension and analysis of its organic and mineral components, determining the dynamics of the currents and transportation of suspended matter, the nature of sedimentation processes, their seasonality and connection with the direction of currents and movement of sea ice. To determine the possibility of researching the suspended matter in the waters around the Akademik Vernadsky station, we analyze our long-term experience of using sedimentation traps to study the suspended matter flows in the seas and rivers of Ukraine. The developed complex of field equipment can be used to sample the suspended matter in waters adjacent to the Akademik Vernadsky station. The light single-cylinder sedimentation traps were transferred to the team of the Ukrainian Antarctic Expedition 2022 for further use at the Vernadsky station

Instantons and Yang-Mills Flows on Coset Spaces

We consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang-Mills equations to phi^4-kink equations on R. Depending on the boundary conditions and torsion, we obtain solutions to the Yang-Mills equations describing instantons, chains of instanton-anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on R x G/H, dyon-type configurations are constructed as well. We also present explicit solutions to the Yang-Mills flow equations and compare them with the Yang-Mills solutions on R x G/H.Comment: 1+12 page