Том 81, № 6 (2018)

In this paper, we study polytopes generated by three reflections groups. Each polytope is generated from a single point in the real Euclidean space, called a dominant point, by means of a series of reflections with respect to mirrors specifically defined for each of the reflection groups. It is shown that three different polytopes having the same number of vertices but with different dominant points may be synthesized for each of these groups.

We estimate the accuracy of the reconstruction of the structure function xF₃(x,Q²) and the non-singlet combination for the fragmentation function \(D_{u_v }^{\pi ^ + } \) (z, Q²) used in description of the deep inelastic scattering by the Mellin inverse transformation method with the parabolic shape of contour running from the saddle point proposed by Kosower. We demonstrate the applicability of this contour calculated at some fixed value of momentum transfer squared Q²₀ for the evaluation of the non-singlet structure functions at any experimental Q² values.

Chiral spinors and self dual tensors of the Lie superalgebra osp(m|n) are infinite-dimensional representations belonging to the class of representations with Dynkin labels [0,..., 0, p]. We show that the superdimension of [0,..., 0, p] coincides with the dimension of a so(m − n) representation. When the superdimension is finite, these representations could play a role in supergravity models. Our technique is based on expansions of characters in terms of supersymmetric Schur functions. In the process of studying these representations, we obtain new character expansions.

In this paper we are concernedwith integrability of geodesic motions in Sasaki–Einstein space T^1,1 and its Calabi–Yau metric cone. There are enough functionally independent integrals of motions to ensure the complete integrability for geodesics in T^1,1 space and its metric cone. The singularity at the apex of the metric cone can be smoothed out in two different ways. In the case of the small resolution the geodesic motions on the resolved conifold remain completely integrable. However, in the case of the deformation of the conifold the complete integrability is lost.

The possibility of studying the anisotropy of the total fluxes of electrons and positrons of high-energy (10 GeV to 1 TeV) cosmic rays in the PAMELA satellite-borne experiment by means of a calorimeter is considered. The procedure developed with aim of performing searches for this anisotropy is described along with the results of applying it to a test data sample.

The inclusive decays of doubly heavy baryons are studied on the basis of the operator-productexpansion method. The lifetimes of these particles are calculated, and the dependence of the respective theoretical predictions on the quark masses is studied. Theoretical uncertainties that arise in the predictions of the widths with respect to different channels and of the total lifetimes owing to the aforementioned dependence are also estimated.

We propose a new Standard Model (SM) extension based on D₄ flavor symmetry in which all of SM quarks have consistent masses and the observed quark mixing pattern can be explained at the first order of perturbation theory with re-normalizable interactions.

A binary classification of solar wind types is given according to three main hydrodynamic parameters—the proton speed, the proton temperature, and the proton density. Boundaries between the fast–hot–dense, fast–hot–rarefied, fast–cold–dense, fast–cold–rarefied, slow–hot–dense, slow–hot–rarefied, slow–cold–dense, and slow–cold–rarefied solar wind types are specified in the space of these variables. These types arise at different frequencies and originate from different sorts of solar activity. An analysis of 1-minute data from the OMNIWeb database is performed over the period from January 1, 2016, to September 30, 2017. In some cases, this classification scheme, which is quite simple and clear, allows one to identify the sources of the solar wind (coronal holes and coronal mass ejections), as well as to reveal long-term trends. The proposed scheme is compared with the methods used earlier in the literature to classify solar wind types.

The temperature effect is studied for the muon detectors of the Yakutsk cosmic-ray spectrograph, which consists of an ionization chamber and ground-level and undergroundmuon counter telescope deployed at depths of 0, 7, 20, 40, and 60 mwe. This array makes it possible to study muon fluxes over a wide energy range (from 2 to 200 GeV). The dependence of the temperature effect for muon component on the depth and on the zenith angle (that is, on the energy of detected particles, as well as on the solar-activity cycle) is studied. A brief description of the muon detector database (mddb) created at IZMIRAN is given. This database includes observational data from muon detectors and data on the atmospheric pressure and vertical profiles of the atmospheric temperature at standard isobaric levels.

Evolution of quantum states of array of quantum dots is analyzed by means of numerical solution of the von Neumann equation. For two qubit system with dipole–dipole interaction and common phonon bath the evolution of the symmetric state \(\frac{{ \uparrow \downarrow + \downarrow \uparrow }}{{\sqrt 2 }}\) leads to the mixture of the triplet states, leaving the singlet decoupled. For three qubit system \(\left( {D_{1/2}^{ \otimes 3} = D_{3/2} + 2D_{1/2} } \right)\) with common phonon bath we observed similar effects within the quartet state D_3/2 if all qubits were symmetrically connected.

The isoscaling behavior of the fragment production cross section was studied for reactions with deuterons on enriched lead targets (²⁰⁴Pb, ²⁰⁶Pb, ²⁰⁷Pb, ²⁰⁸Pb). The information about the reaction mechanism as well as the origin of the residues in the mass range 20 ≤ A ≤ 100 were obtained. During the analysis it was found the same behavior of the reactionmechanism as in the reactions with deuteron on enriched tin isotopes (¹¹²Sn, ¹¹⁸Sn, ¹²⁰Sn, ¹²⁴Sn). In the present article the estimation of the temperature and the symmetry energy coefficient of composite systems was done.

I study the solutions, symmetry, and the map under time inversion (t ↦ 1/t) of the following generalized squeeze equation (GSQE)

\(_{n,m} u \equiv \left[ {\frac{\partial }{{\partial t}} - k\left( {\sum\limits_{k = 1}^n {\frac{{\partial ^2 }}{{\partial x_k^2 }} - \frac{\gamma }{{t^2 }}\sum\limits_{r = 1}^m {\frac{{\partial ^2 }}{{\partial p_r^2 }}} } }\right)} \right]u\left( {t,x_k ,p_r } \right) = 0,\)

\(Q \equiv \left[ {\partial t - \frac{1}{4}\partial x^2 + \frac{1}{{4t^2 }}\partial p^2 } \right]Q\left( {t,x,p} \right) = 0.\)

We construct representations of the quantum algebras U_q,q(gl(n)) and U_q,q(sl(n)) which are in duality with the multiparameter quantum groups GL_qq(n), SL_qq(n), respectively. These objects depend on n(n − 1)/2+ 1 deformation parameters q, q_ij (1 ≤ i< j ≤ n) which is the maximal possible number in the case of GL(n). The representations are labelled by n − 1 complex numbers r_i and are acting in the space of formal power series of n(n − 1)/2 non-commuting variables. These variables generate quantum flag manifolds of GL_qq(n), SL_qq(n). The case n = 3 is treated in more detail.

We have considered the possibility of formation of a massless particles with spin 1 in the region of negative energies, within the framework of the Weyl-type equation for neutrinos. It is proved that the represented approach allows to get a stable structural formation in the ground state, which can be interpreted as a fundamental massless particle. The structure and properties of this vector boson are studied in detail. The problem of entangling two vector bosons with projections of spins +1 and −1 and, accordingly, the formation of a zero-spin boson is studied within the framework of a complex stochastic matrix equations of the Langevin type. The paper discusses the structure of the Bose particle of a scalar field and the space–time properties of an empty space (quantum vacuum).

Using a D = 1 supergravity framework I construct a super-Friedmann equation for an isotropic and homogenous universe including dynamical scalar fields. In the context of quantum theory this becomes an equation for a wave function of the universe of spinorial type, the Wheeler–DeWitt–Dirac equation. It is argued that a cosmological constant breaks a certain chiral symmetry of this equation, a symmetry in the Hilbert space of universe states, which could protect a small cosmological constant from being affected by large quantum corrections.

We introduce a biconfluent Heun potential well for the one-dimensional stationary Schrödinger equation which is composed of a confining fraction-power term and a repulsive centrifugal-barrier core. This is a conditionally integrable potential in that the strength of the centrifugal barrier is fixed to a constant. The potential supports a countable infinite number of bound states. We present the general solution of the Schrödinger equation, deduce the exact equation for the energy spectrumand derive a highly accurate approximation for energy levels. The bound state wave functions are written as irreducible linear combinations with constant coefficients of two Hermite functions of a scaled and shifted argument.

Nuclear structure and composition in ultra-strong magnetic fields relevant for heavy-ion collisions, supernovae, andmagnetar crusts are analyzed. For field intensities exceeding 0.1 teratesla (TT) nuclear magnetic response is represented as combined reactivity of valent outer-shell nucleons, exhibits linear regime up to a strength of ~10 TT and exceeds significantly nuclear g factor. The Zeeman effect leads to an increase of binding energies for open shell nuclei and a decrease for closed-shell nuclei. Noticeable enhancement and suppression in a yield of corresponding explosive nucleosynthesis products with antimagic and magic numbers corroborate with observational results.

In this paper we present an independent scheme for constructing fractional parentage coefficients using symmetry group apparatus in translationally invariantmodel space, suitable for the six-particle system composed of three-particle bi-clusters, where the presented subsystems have their own intrinsic clusterization. Simple expressions for corresponding antisymmetrization procedure are presented as well as computational results.

A new method of employing A(n, n′γ)A reactions of inelastic tagged-neutron scattering is proposed for revealing hidden substances. In contrast to the well-known method where substances are identified by measuring the spectrum of gamma rays, the new method consists in identifying substances by measuring the spectrum of neutrons. The neutron energy is measured by the time-of-flight method via detecting a (γ, n) pair and invoking the parameters of tagged neutrons. The detection of a neutron in a pair with a photon is also a factor that reduces the rate of accumulation of useful events. As is shown in the present study, however, the method in question possesses a number of important special features owing to which it boasts high precision and efficiency, as well as the ability of revealing a broad range of elements and hidden substances of small volume. A numerical simulation of both methods is performed. It is shown that the required time of measurements within the proposed method is one order of magnitude shorter, which makes it possible to circumvent that main difficulty encountered in applying the known method and associated with a low resource and a high cost of neutron sources.

A stack of track-photoemulsion layers was exposed to a beam of ¹²C ions accelerated to a momentum of 4.5 GeV/c per nucleon at the synchrophasotron of the Laboratory of High Energies at the Joint Institute for Nuclear Research (JINR, Dubna). The mean free path of relativistic ¹²C nuclei was measured for the reaction of their coherent fragmentation to three alpha particles in BR-2 nuclear track photoemulsion filled with lead nuclei in proportion of one lead atom per five silver atoms. The result was λ_(Em+Pb) = (11±3) m. The cross section of σ_(Em+Pb) = (18±3) mb averaged over all track-photoemulsion nuclei corresponds to this value of λ_(Em+Pb). From a comparison of the value obtained in the present study for λ_(Em+Pb) with the mean free path of ¹²C nuclei in a standard BR-2 track photoemulsion, (10.3 ± 1.5) m, it follows that, in this channel, a nuclear fragmentation mechanism is dominant in the fragmentation of ¹²C nuclei both off lead nuclei and off track-photoemulsion nuclei.

A brief survey of self-consistent models used to perform global calculations of β-decay properties of neutron-rich nuclei is given. These models include the continuum quasiparticle randomphase approximation (CQRPA) based on the energy density functional (DF) proposed by Fayans and his colleagues (DF + CQRPA), relativistic quasiparticle random-phase approximation (RQRPA), and the finite-amplitude method (FAM). These models take into account allowed Gamow–Teller transitions and first-forbidden transitions. Models that allow for complex configurations beyond the QRPA framework are also analyzed. The β-decay properties of heavy calcium, potassium, and scandium isotopes in the vicinity of the N = 32 and 34 neutron subshells, which are new magic subshells for neutrons, are calculated on the basis of the self-consistent DF + CQRPA approach. The predicted high probability for two-neutron emission is found to be correlated with the anomalous nuclear radii measured for potassium and calcium isotopes in the region around N = 32. The results ofDF3 + CQRPA calculations are compared with their counterparts obtained within the self-consistent models implemented with the SkO’ Skyrme functional and the D3C* relativistic functional.

In the present paper, the double-differential cross sections (d²σ/dΩdε) of emission spectra for the ¹⁹F(n, xn) and ¹⁹F(n, xp) structural fusion materials (contained in FLiBe) were calculated by using the Hybrid Monte-Carlo Simulation at 14.2-MeV incident neutron energy in emission angles ranging from 30◦ to 150◦. Theoretical model calculations were carried out by using ALICE-2011, EMPIRE, and TALYS computer codes. Theoretically calculated results of the double-differential cross section for neutron and proton emission are presented and compared with the existing experimental data taken from the international nuclear reaction EXFOR database.