Account of interactions in frameworks of Standard Model leads to appearence of γ5 terms in a dressed fermion propagator. In this case the standard spin projectors do not commute with propagator and should be modified...
Account of interactions in frameworks of Standard Model leads to appearence of γ5 terms in a dressed fermion propagator. In this case the standard spin projectors do not commute with propagator and should be modified. Starting point of our discussion is the eigenvalue problem for inverse propagator S(p). Having the solutions of this problem, one can understand the necessary modification of spin projectors. The same generalized spin projector appears at propagation of neutrino in a moving matter, but in contrast to vacuum case, corresponding polarization vector is not arbitrary. This spin projector commute with neutrino propagator and all dispersion laws for neutrino in media are classified according to spin projection onto this fixed axis.
The article is devoted to optimal covering and packing prob- lems for a bounded set in a two-dimensional metric space with a given amount of congruous circles. Such problems are of both theoretical interest and practi...
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The article is devoted to optimal covering and packing prob- lems for a bounded set in a two-dimensional metric space with a given amount of congruous circles. Such problems are of both theoretical interest and practical relevance. For instance, such statements appear in logistics when one needs to locate a given number of commercial or social facilities. A numerical algorithm based on fundamental physical principles due to Fermat and Huygens is suggested and implemented. It allows us to solve the problems for the cases of non-convex sets and non-Euclidean metrics. The results of numerical experiments are presented and discussed. Calculations show the applicability of the proposed approach its high efficiency for covering of a convex set in the Euclidean space by a sufficiently large amount of circles.
In this study, a GPU-enabled implementation of an algorithm for the solution of a real-life optimization problem arising in the geoacoustic inversion is proposed. In the inversion algorithm, a single-hydrophone record...
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We consider a linear nonstationary system of first order partial differential equations that is not resolved with respect to the derivatives and identically degenerates in the domain. Without using the change of varia...
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We complete our derivation of upper limits on the CP violating ηππ and η0ππ couplings from an analysis of their two-loop contributions to the neutron electric dipole moment (nEDM). We use a phenomenological Lagr...
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The exact solutions of the nonlinear heat (porous medium) equation are constructed. We obtain a new class of the heat wave type solutions the construction of which is reduced to the Cauchy problems for nonlinear secon...
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The exact solutions of the nonlinear heat (porous medium) equation are constructed. We obtain a new class of the heat wave type solutions the construction of which is reduced to the Cauchy problems for nonlinear second order differential equations with a singularity. For these problems we prove a new existence and uniqueness theorem in the class of analytic functions. A special case of the heat wave front is considered in details. The results of numerical experiments are presented and discussed.
A new way of formalizing and solving various control problems for the important class of dynamic systems known as DES is suggested. The formalization is based on the original first-order logic calculus of the positive...
A new way of formalizing and solving various control problems for the important class of dynamic systems known as DES is suggested. The formalization is based on the original first-order logic calculus of the positively-constructed formulas (PCF). A PCF-based algorithm for checking the co-observability property of a specification language restricting DES behavior is presented. Co-observable languages serve as specifications for the decentralized supervisors, which are necessary to implement group control tasks. The approach is demonstrated on the example of a discrete-event model of an autonomous underwater vehicle, which describes AUV’s high-level operation modes switching while following the leader, in a surveillance mission, performed by the AUV group.
The problem of constructing solutions to the nonlinear heat equation with power nonlinearity is considered. The solutions have the form of a traveling wave and simulate the propagation of disturbances over a cold back...
The problem of constructing solutions to the nonlinear heat equation with power nonlinearity is considered. The solutions have the form of a traveling wave and simulate the propagation of disturbances over a cold background with a finite velocity. It is shown that the construction can be reduced to the Cauchy problem for an ordinary second- order differential equation with a singularity multiplying the highest derivative. Its solutions are constructed using the boundary element method based on the dual reciprocity method. A computational experiment is carried out. The results are compared with the solutions of the same problems by the power series method. The calculations have shown the correctness of the developed boundary element algorithm and its advantage compared to the power series segments and the step-by-step method previously proposed by the authors.
We provide model-independent bounds on the rates of rare decays η(η′)→ππ based on experimental limits on the neutron electric dipole moment (nEDM). Starting from phenomenological η(η′)ππ couplings, the nEDM...
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We provide model-independent bounds on the rates of rare decays η(η′)→ππ based on experimental limits on the neutron electric dipole moment (nEDM). Starting from phenomenological η(η′)ππ couplings, the nEDM arises at the two-loop level. The leading-order relativistic chiral perturbation theory calculation with the minimal photon coupling to charged pions and a proton inside the loops leads to a finite, counterterm-free result. This is an improvement upon previous estimates which used approximations in evaluating the two-loop contribution and were plagued by divergences. While constraints on the η(η′)ππ couplings in our phenomenological approach are somewhat milder than in the picture with the QCD θ term, our calculation means that whatever the origin of these couplings, the decays η(η′)→2π will remain unobservable in the near future.
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