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Ivanov I.P.,University of Liège | Ivanov I.P.,RAS Sobolev Institute of Mathematics
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2011

Photons carrying nonzero orbital angular momentum (twisted photons) are well-known in optics. Recently, using Compton backscattering to boost optical twisted photons to high energies was suggested. Twisted electrons in the intermediate energy range have also been produced recently. Thus, collisions involving energetic twisted particles seem to be feasible and represent a new tool in high-energy physics. Here we discuss some generic features of scattering processes involving twisted particles in the initial and/or final state. In order to avoid additional complications arising from nontrivial polarization states, we focus here on scalar fields only. We show that processes involving twisted particles allow one to perform a Fourier analysis of the plane-wave cross section with respect to the azimuthal angles of the initial particles. In addition, using twisted states, one can probe the autocorrelation function of the amplitude, which is inaccessible in the plane-wave collisions. Finally, we discuss prospects for experimental study of these effects. © 2011 American Physical Society.


Buchbinder I.L.,Tomsk State Pedagogical University | Pletnev N.G.,RAS Sobolev Institute of Mathematics
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2015

We consider a six-dimensional (1, 0) hypermultiplet model coupled to an external field of vector/tensor system and study the structure of the low-energy effective action of this model. Manifestly a (1, 0) supersymmetric procedure of computing the effective action is developed in the framework of the superfield proper-time technique. The leading low-energy contribution to the effective action is calculated. © 2015 The Authors.


Ginzburg I.F.,RAS Sobolev Institute of Mathematics
Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment | Year: 2015

After a collision at the main interaction point the beam of an e+ e- Linear Collider can be utilized to construct a neutrino factory with exceptional parameters. We also briefly discuss possible applications of some elements of the proposed scheme to standard fixed target experiments and new experiments with νμN interactions. © 2014 Elsevier B.V. All rights reserved.


Buchbinder I.L.,Tomsk State Pedagogical University | Pletnev N.G.,RAS Sobolev Institute of Mathematics
Nuclear Physics B | Year: 2015

We consider the six-dimensional hypermultiplet, vector and tensor multiplet models in (1, 0) harmonic superspace and discuss the corresponding superfield actions. The actions for free (2, 0) tensor multiplet and for interacting vector/tensor multiplet system are constructed. Using the superfield formulation of the hypermultiplet coupled to the vector/tensor system we develop an approach to calculation of the one-loop superfield effective action and find its divergent structure. © 2015 The Authors.


Krotov D.S.,RAS Sobolev Institute of Mathematics
Designs, Codes, and Cryptography | Year: 2011

A vertex coloring of a graph is called "perfect" if for any two colors a and b, the number of the color-b neighbors of a color-a vertex x does not depend on the choice of x, that is, depends only on a and b (the corresponding partition of the vertex set is known as "equitable"). A set of vertices is called "completely regular" if the coloring according to the distance from this set is perfect. By the "weight distribution" of some coloring with respect to some set we mean the information about the number of vertices of every color at every distance from the set. We study the weight distribution of a perfect coloring (equitable partition) of a graph with respect to a completely regular set (in particular, with respect to a vertex if the graph is distance-regular). We show how to compute this distribution by the knowledge of the color composition over the set. For some partial cases of completely regular sets, we derive explicit formulas of weight distributions. Since any (other) completely regular set itself generates a perfect coloring, this gives universal formulas for calculating the weight distribution of any completely regular set from its parameters. In the case of Hamming graphs, we prove a very simple formula for the weight enumerator of an arbitrary perfect coloring. © 2010 Springer Science+Business Media, LLC.


Dobrynin A.A.,RAS Sobolev Institute of Mathematics
Match | Year: 2010

The Wiener index is a distance-based topological index defined as the sum of distances between all pairs of vertices in a graph. Fibonacenes are a class of unbranched catacondensed benzenoid hydrocarbons having zig-zag structure. We deal mainly with so-called collective properties of the Wiener index, i. e. the main results don't reflect the property of Wiener index of any particular fibonacene, but a collective property of sets of such graphs. In particular, some results on degeneracy classes of the Wiener index of fibonacenes are presented.


Secchi P.,University of Brescia | Trakhinin Y.,RAS Sobolev Institute of Mathematics
Nonlinearity | Year: 2014

We consider the free-boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the pre-Maxwell dynamics for the magnetic field. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. The plasma-vacuum system is not isolated from the outside world, because of a given surface current on the fixed boundary that forces oscillations. Under a suitable stability condition satisfied at each point of the initial interface, stating that the magnetic fields on either side of the interface are not collinear, we show the existence and uniqueness of the solution to the nonlinear plasma-vacuum interface problem in suitable anisotropic Sobolev spaces. The proof is based on the results proved in the companion paper (Secchi and Trakhinin 2013 Interfaces Free Boundaries 15 323-57), about the well-posedness of the homogeneous linearized problem and the proof of a basic a priori energy estimate. The proof of the resolution of the nonlinear problem given in the present paper follows from the analysis of the elliptic system for the vacuum magnetic field, a suitable tame estimate in Sobolev spaces for the full linearized equations, and a Nash-Moser iteration. © 2014 IOP Publishing Ltd & London Mathematical Society.


Beresnev V.,RAS Sobolev Institute of Mathematics
Computers and Operations Research | Year: 2013

We study a mathematical model generalizing the well-known facility location problem. In this model we consider two competing sides successively placing their facilities and aiming to capture consumers, in order to make maximal profit. We state the problem as a bilevel integer programming problem, regarding optimal noncooperative solutions as optimal solutions. We propose a branch-and-bound algorithm for finding the optimal noncooperative solution. While constructing the algorithm, we represent our problem as the problem of maximizing a pseudo-Boolean function. An important ingredient of the algorithm is a method for calculating an upper bound for the values of the pseudo-Boolean function on subsets of solutions. We present the results of a simulation demonstrating the computational capabilities of the proposed algorithm. © 2013 Elsevier Ltd.


Berikov V.,RAS Sobolev Institute of Mathematics
Pattern Recognition Letters | Year: 2014

This paper considers a problem of clustering complex data composed from various structures. A collection of different algorithms is used for the analysis. The main idea is based on the assumption that each algorithm is "specialized" (as a rule, gives more accurate partition results) on particular types of structures. The degree of algorithm's "competence" is determined by usage of weights attributed to each pair of observations. Optimal weights are specified by the analysis of partial ensemble solutions with use of the proposed model of clustering ensemble. The efficiency of the suggested approach is demonstrated with Monte-Carlo modeling. © 2013 Elsevier B.V. All rights reserved.


Dobrynin A.A.,RAS Sobolev Institute of Mathematics
Match | Year: 2013

The Wiener index is a distance-based topological index defined as the sum of distances between all pairs of vertices in a graph. Fibonacenes form a class of unbranched catacondensed benzenoid hydrocarbons having zig-zag structure. Collective properties of the Wiener index for some classes of fibonacenes have been studied in [4]. We present new families of fibonacenes for which the sum of their Wiener indices can be easily calculated.

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