Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations

We study the conformal vertex algebras which naturally arise in relation to the Nakajima-Yoshioka blow-up equations.Comment: 23 pages v2. 24 pages, references added, proofs in section 3 are expanded, many typos correcte

Priority Events Determination For The Risk-oriented Management Of Electric Power System

The task of risk-oriented management of the electric power system in conditions of multi-criteria choice is considered. To determine the most effective measures, the implementation of which will reduce the magnitude of the risk of an emergency situation, multi-criteria analysis methods are applied. A comparative analysis of the multi-criteria alternative (ELECTRE) ranking method based on utility theory and the Pareto method, which defines a subset of non-dominant alternatives, is carried out. The Pareto method uses in its algorithm only qualitative characteristics of the advantage and allows only to distinguish a group of competitive solutions with the same degrees of non-dominance. Given the large number of evaluation criteria, the Pareto method is ineffective because the resulting subset of activities is in the field of effective trade-offs, when no element of the set of measures can be improved without degrading at least one of the other elements. The ELECTRE method is a pairwise comparison of multi-criteria alternatives based on utility theory. This method allows to identify a subset of the most effective activities. The number of elements of the resultant subset is regulated by taking into account the coefficients of importance of optimization criteria and expert preferences

Conceptual design of elliptical cavities for intensity and position sensitive beam measurements in storage rings

Position sensitive beam monitors are indispensable for the beam diagnostics in storage rings. Apart from their applications in the measurements of beam parameters, they can be used in non-destructive in-ring decay studies of radioactive ion beams as well as enhancing precision in the isochronous mass measurement technique. In this work, we introduce a novel approach based on cavities with elliptical cross-section, in order to compensate for existing limitations in ion storage rings. The design is aimed primarily for future heavy ion storage rings of the FAIR project. The conceptual design is discussed together with simulation results.Comment: Added definition of Uv and Pdiss in the introduction section. Added Mode numbering in table 1 and figure 1 for more clarity. Corrected one wrong figure reference. Other minor typo correction

Integral geometry, hypergroups, and I.M. Gelfand's question

This note is an attempt to give an answer for the following old I.M. Gelfand's question: why some important problems of integral geometry (e.g., the Radon transform and others) are related to harmonic analysis on groups, but for other quite similar problems such relations are not clear? In the note we examine standard problems of integral geometry generating harmonic analysis (the Plancherel theorem etc.) on pairs of commutative hypergroups that are in a duality of Pontryagin's type. As a result new meaningful examples of hypergroups are constructed.Comment: 10 pages, to be published in Doklady Mathematics, 201