arXiv subjects

V. Abramov

Publications and source records attributed to V. Abramov.

12 recordsLinked to original sources

arXiv2024

Technical Design Report of the Spin Physics Detector at NICA

The Spin Physics Detector collaboration proposes to install a universal detector in the second interaction point of the NICA collider under construction (JINR, Dubna) to study the spin structure of the proton and deuteron and other spin-related phenomena using a unique possibility to operate with polarized proton and deuteron beams at a collision energy up to 27 GeV and a luminosity up to $10^{32}$ cm$^{-2}$ s$^{-1}$. As the main goal, the experiment aims to provide access to the gluon TMD PDFs in the proton and deuteron, as well as the gluon transversity distribution and tensor PDFs in the deuteron, via the measurement of specific single and double spin asymmetries using different complementary probes such as charmonia, open charm, and prompt photon production processes. Other polarized and unpolarized physics is possible, especially at the first stage of NICA operation with reduced luminosity and collision energy of the proton and ion beams. This document is dedicated exclusively to technical issues of the SPD setup construction.

hep-ex↗

arXiv2022

Conceptual design of the Spin Physics Detector

The Spin Physics Detector, a universal facility for studying the nucleon spin structure and other spin-related phenomena with polarized proton and deuteron beams, is proposed to be placed in one of the two interaction points of the NICA collider that is under construction at the Joint Institute for Nuclear Research (Dubna, Russia). At the heart of the project there is huge experience with polarized beams at JINR. The main objective of the proposed experiment is the comprehensive study of the unpolarized and polarized gluon content of the nucleon. Spin measurements at the Spin Physics Detector at the NICA collider have bright perspectives to make a unique contribution and challenge our understanding of the spin structure of the nucleon. In this document the Conceptual Design of the Spin Physics Detector is presented.

hep-ex↗

arXiv2015

Algebras with ternary law of composition combining Z_2 and Z_3 gradings

In the present article we investigate the possibility of combining the usual Grassmann algebras with their ternary Z_3-graded counterpart, thus creating a more general algebra with coexisting quadratic and cubic constitutive relations. We recall the classification of ternary and cubic algebras according to the symmetry properties of ternary products under the action of the S_3 permutation group. Instead of only two kinds of binary algebras, symmetric or antisymmetric, here we get four different generalizations of each of these two cases. Then we study a particular case of algebras generated by two types of variables, the generators of Grassmann algebra and generators of ternary analog of Grassmann algebra, satisfying quadratic and cubic relations respectively, i.e. the generators of Grassmann algebra anticommute and a triple product of any three generators of a ternary analog of Grassmann algebra is equal to cyclic permutation of generators in this product multiplied by a primitive 3rd root of unity. The invariance group of the generalized algebra is introduced and investigated.

math.RA↗

arXiv2010

The Euler-Maruyama approximations for the CEV model

The CEV model is given by the stochastic differential equation $X_t=X_0+\int_0^tμX_sds+\int_0^tσ(X^+_s)^pdW_s$, $\frac{1}{2}\le p<1$. It features a non-Lipschitz diffusion coefficient and gets absorbed at zero with a positive probability. We show the weak convergence of Euler-Maruyama approximations $X_t^n$ to the process $X_t$, $0\le t\le T$, in the Skorokhod metric. We give a new approximation by continuous processes which allows to relax some technical conditions in the proof of weak convergence in \cite{HZa} done in terms of discrete time martingale problem. We calculate ruin probabilities as an example of such approximation. We establish that the ruin probability evaluated by simulations is not guaranteed to converge to the theoretical one, because the point zero is a discontinuity point of the limiting distribution. To establish such convergence we use the Levy metric, and also confirm the convergence numerically. Although the result is given for the specific model, our method works in a more general case of non-Lipschitz diffusion with absorbtion.

math.PR↗

arXiv2009

Algebras with ternary law of composition and their realization by cubic matrices

We study partially and totally associative ternary algebras of first and second kind. Assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle. We find the sufficient and necessary condition for a ternary multiplication to induce a structure of associative binary algebra in each fiber of this vector bundle. Given two modules over the algebras with involutions we construct a ternary algebra which is used as a building block for a Lie algebra. We construct ternary algebras of cubic matrices and find four different totally associative ternary multiplications of second kind of cubic matrices. It is proved that these are the only totally associative ternary multiplications of second kind in the case of cubic matrices. We describe a ternary analog of Lie algebra of cubic matrices of second order which is based on a notion of j-commutator and find all commutation relations of generators of this algebra.

math.RA↗

arXiv2007

Scalability and Optimisation of a Committee of Agents Using Genetic Algorithm

A population of committees of agents that learn by using neural networks is implemented to simulate the stock market. Each committee of agents, which is regarded as a player in a game, is optimised by continually adapting the architecture of the agents using genetic algorithms. The committees of agents buy and sell stocks by following this procedure: (1) obtain the current price of stocks; (2) predict the future price of stocks; (3) and for a given price trade until all the players are mutually satisfied. The trading of stocks is conducted by following these rules: (1) if a player expects an increase in price then it tries to buy the stock; (2) else if it expects a drop in the price, it sells the stock; (3)and the order in which a player participates in the game is random. The proposed procedure is implemented to simulate trading of three stocks, namely, the Dow Jones, the Nasdaq and the S&P 500. A linear relationship between the number of players and agents versus the computational time to run the complete simulation is observed. It is also found that no player has a monopolistic advantage.

cs.MA↗

arXiv2005

Asymmetry measurement of charged hadron production in pA collisions at 40 GeV

The single spin asymmetry of charge hadron production by a 40 GeV/c proton beam with 39% transverse polarization incident on nuclei (C, Cu) has been measured using the Focusing Double Arm Spectrometer (FODS). The measurements were carried out for hadrons with high Xt (82 deg. in c.m.) and with high Xf (one arm at 51 deg. and the other arm at 99 deg. in c.m.). The results are presented for charged pions, kaons, protons and antiprotons with high Xt.

hep-ex↗

arXiv2005

On the development of differential geometry in Estonia

We give a brief review of a research made in the field of differential geometry in Estonia in the period from the beginning of the 19th century to the present time. The biographic data of mathematicians who made a valuable contribution to the development of differential geometry in Estonia in mentioned period are presented. The material presented in the introduction covers the period from the beginning of the 19th century to the middle of the 20th century and it can be considered as a brief historical sketch of the development of differential geometry in Estonia in this period. The next sections give an idea of the modern trends of development of differential geometry in Estonia.

math.HO↗

arXiv2005

On a graded q-differential algebra

Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differential algebra in the case of a reduced quantum plane which can be endowed with a structure of a graded algebra. We consider the differential d satisfying d to power N equals zero as an analog of an exterior differential and study the first order differential calculus induced by this differential.

math.QA↗

arXiv2000

Exterior differentials of higher order and their covariant generalization

We investigate a particular realization of generalized q-differential calculus of exterior forms on a smooth manifold based on the assumption that the N-th power (N>2) of exterior differential is equal to zero. It implies the existence of cyclic commutation relations for the differentials of first order and their generalization for the differentials of higher order. Special attention is paid to the cases N=3 and N=4. A covariant basis of the algebra of such q-grade forms is introduced, and the analogues of torsion and curvature of higher order are considered. We also study a graded exterior calculus on a generalized Clifford algebra.

math.QA↗

arXiv2000

Algebra of differential forms with exterior differential $d^3=0$ in dimension one

In this work, we construct the algebra of differential forms with the cube of exterior differential equal to zero on one-dimensional space. We prove that this algebra is a graded q-differential algebra where q is a cubic root of unity. Since the square of differential is not equal to zero the algebra of differential forms is generated not only by the first order differential but also by the second order differential of a coordinate. We study the bimodule generated by this second order differential, and show that its structure is similar to the structure of bimodule generated by the first order differential in the case of anyonic line.

math-ph↗

arXiv1996

$Z_3$-graded analogues of Clifford algebras and generalization of supersymmetry

We define and study the ternary analogues of Clifford algebras. It is proved that the ternary Clifford algebra with $N$ generators is isomorphic to the subalgebra of the elements of grade zero of the ternary Clifford algebra with $N+1$ generators. In the case $N=3$ the ternary commutator of cubic matrices induced by the ternary commutator of the elements of grade zero is derived. We apply the ternary Clifford algebra with one generator to construct the $Z_3$-graded generalization of the simplest algebra of supersymmetries.

hep-th↗