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Nano-engineering of electron correlation in oxide superlatticesMar 14 2019Oxide heterostructures and superlattices have attracted a great deal of attention in recent years owing to the rich exotic properties encountered at their interfaces. We focus on the potential of tunable correlated oxides by investigating the spectral ... More

Jump Diffusion and α-Stable Techniques for the Markov Switching Approach to Financial Time SeriesMay 19 2016We perform a detailed comparison between a Markov Switching Jump Diffusion Model and a Markov Switching {\alpha}-Stable Distribution Model with respect to the analysis of non-stationary data. We show that the jump diffusion model is extremely robust, ... More

Observation of weakened V-V dimers in the monoclinic metallic phase of strained VO2Mar 13 2019Emergent order at mesoscopic length scales in condensed matter can provide fundamental insight into the underlying competing interactions and their relationship with the order parameter. Using spectromicroscopy, we show that mesoscopic stripe order near ... More

Observation of surface states on heavily indium doped SnTe(111), a superconducting topological crystalline insulatorAug 16 2015Feb 18 2016The topological crystalline insulator tin telluride is known to host superconductivity when doped with indium (Sn$_{1-x}$In$_{x}$Te), and for low indium contents ($x=0.04$) it is known that the topological surface states are preserved. Here we present ... More

Proceedings of the 35th Annual Australian/New Zealand Condensed Matter and Materials MeetingJul 19 2011The 35th Australian/New Zealand Annual Condensed Matter and Materials Meeting was held at the Charles Sturt University campus in Wagga Wagga, NSW, Australia from the 1st to the 4th of February 2011. The conference was attended by 92 delegates from a range ... More

A remark on the Dixmier ConjectureNov 30 2018The Dixmier Conjecture says that every endomorphism of the (first) Weyl algebra $A_1$ (over a field of characteristic zero) is an automorphism, i.e., if $PQ-QP=1$ for some $P, Q \in A_1$ then $A_1 = K \langle P, Q \rangle$. The Weyl algebra $A_1$ is a ... More

Polaron spin echo envelope modulations in an organic semiconducting polymerSep 09 2016Theoretical treatment of the electron spin echo envelope modulation (ESEEM) spectra from polarons in a semiconducting $\pi$- conjugated polymer is presented. The contact hyperfine coupling and the dipolar interaction between the polaron and proton spins ... More

Decay of the rotary echoes for the spin of a nitrogen-vacancy center in diamondMar 25 2014We study dynamics of the electron spin of a nitrogen-vacancy (NV) center subjected to a strong driving field with periodically reversed direction (train of rotary echoes). We use analytical and numerical tools to analyze in detail the form and timescales ... More

Constructing the ultimate theory of grand unificationMay 16 2011Nov 02 2011In accordance with known phenomenological facts on leptons and quarks in the Standard Model as well as on the scale of neutrino masses and introducing the supersymmetry, we logically substantiate the unique composition of fundamental representation for ... More

Theory of the electron relaxation in metals excited by an ultrashort optical pumpAug 20 2013Mar 05 2014The theory of the electron relaxation in metals excited by an ultrashort optical pump is developed on the basis of the solution of the linearized kinetic equation. The kinetic equation includes both the electron-electron and the electron-phonon collision ... More

Morita invariance of the filter dimension and of the inequality of BernsteinOct 29 2006It is proved that the filter dimenion is Morita invariant. A direct consequence of this fact is the Morita invariance of the inequality of Bernstein: if an algebra $A$ is Morita equivalent to the ring $\CD (X)$ of differential operators on a smooth irreducible ... More

Hyperfine-induced spin relaxation of a diffusively moving carrier in low dimensions: implications for spin transport in organic semiconductorsMar 27 2015The hyperfine coupling between the spin of a charge carrier and the nuclear spin bath is a predominant channel for the carrier spin relaxation in many organic semiconductors. We theoretically investigate the hyperfine-induced spin relaxation of a carrier ... More

Linearly ordered compacts and co-Namioka spacesJan 25 2016It is shown that for any Baire space $X$, linearly ordered compact $Y$ and separately continuous mapping $f:X\times Y\to\mathbb R$ there exists a dense in $X$ $G_\delta$-set $A\subseteq X$ such that $f$ is jointly continuous at every point of $A\times ... More

Metrizable compacta in the space of continuous functions with the topology of pointwise convergenceDec 23 2015We prove that every point-finite family of nonempty functionally open sets in a topological space $X$ has the cardinality at most an infinite cardinal $\kappa$ if and only if $w(X)\leq\kappa$ for every Valdivia compact space $Y\subseteq C_p(X)$. Correspondingly ... More

The Gould BeltJul 23 2015This review is devoted to studies of the Gould belt and the Local system. Since the Gould belt is the giant stellar-gas complex closest to the sun, its stellar component is characterized, along with the stellar associations and diffuse clusters, cold ... More

SO(10) model of standard and dark matterSep 07 2016We consider a novel model for three standard families of left chiral states of quarks and leptons conjointly with a new family of dark matter fermionic particles and a sterile neutrino. It is suggested to use a SO(10) symmetry for description of these ... More

Generalized kinematical symmetries of quantum phase spaceJul 16 2008Continuous symmetries generated with observables of a quantum theory in the Minkowski spacetime are discussed. An example of an originated in this way algebra of observables is the algebra of observables of the canonical quantum theory, that is contained ... More

Confinement and U(1,3) symmetry of color particles in a complex phase spaceNov 26 2003Jul 01 2004It is shown that a universal confining potential for hadron constituents can be obtained with the help of U(1,3) symmetry in a complex phase space. Parameters of this potential are determined on the basis of spectroscopic data for hadrons and results ... More

Left localizable rings and their characterizationsMay 18 2014A new class of rings, the class of left localizable rings, is introduced. A ring $R$ is left localizable if each nonzero element of $R$ is invertible in some left localization $S^{-1}R$ of the ring $R$. Explicit criteria are given for a ring to be a left ... More

Left localizations of left Artinian ringsMay 01 2014For an arbitrary left Artinian ring $R$, explicit descriptions are given of all the left denominator sets $S$ of $R$ and left localizations $S^{-1}R$ of $R$. It is proved that, up to $R$-isomorphism, there are only finitely many left localizations and ... More

Zeros of the order parameter of d_{x^2-y^2} superconducting film in the presence of uniform currentJul 09 2003Jul 17 2003We show that additional p-wave component is generated in the pure d-wave superconductor in the presence of the uniform current. When the current flows in the antinodal direction the spectrum has a gap over all Fermi surface. If the current flows in the ... More

Nonlinear regimes in mean-field full-sphere dynamoSep 04 2016Sep 15 2016The mean-field dynamo model is employed to study the non-linear dynamo regimes in a fully convective star of mass 0.3$M_{\odot}$ rotating with period of 10 days. For the intermediate value of the parameter of the turbulent magnetic Prandl number, $Pm_{T}=3$ ... More

Helicity--vorticity turbulent pumping of magnetic fields in the solar dynamoNov 11 2012The interaction of helical convective motions and differential rotation in the solar convection zone results in turbulent drift of a large-scale magnetic field. We discuss the pumping mechanism and its impact on the solar dynamo.

Convergence of quantum electrodynamics on the Poincare groupOct 06 2011Extended particles are considered in terms of the fields on the Poincar\'{e} group. Dirac like wave equations for extended particles of any spin are defined on the various homogeneous spaces of the Poincar\'{e} group. Free fields of the spin 1/2 and 1 ... More

Extragalactic background light absorption signal in the TeV gamma-ray spectra of blazarsAug 09 1999Recent observations of the TeV gamma-ray spectra of the two closest active galactic nuclei (AGNs), Markarian 501 (Mrk 501) and Markarian 421 (Mrk 421), by the Whipple and HEGRA collaborations have stimulated efforts to estimate or limit the spectral energy ... More

Novel approach to a perfect lensNov 26 2008Feb 19 2009Within the framework of an exact analytical solution of Maxwell equations in a space domain, it is shown that optical scheme based on a slab with negative refractive index ($n=-1$) (Veselago lens or Pendry lens) does not possess focusing properties in ... More

Search for TeV annihilation radiation from supersymmetric dark matter in nearby galaxiesMay 29 2003During the 2002-2003 observing season the Whipple 10m imaging atmospheric Cerenkov telescope was used to search for dark matter annihilation radiation in four nearby galaxies: M32, M33, Draco, and Ursa Minor. Scientific motivations for this choice of ... More

Constraints for quasi-elastic neutron reflections in the range dE~10^(-12)-10^(-9) eVFeb 10 2005A restrictive constraint for any quasi-elastic process was obtained in the previously inaccessible energy range dE~10^(-12)-3x10^(-10) eV for reflections of ultracold neutrons from surfaces in the experiement on neutron quantum states in the earth's gravitational ... More

Electric fields at the quark surface of strange stars in the color-flavor locked phaseAug 12 2004Oct 14 2004It is shown that extremely strong electric fields may be generated at the surface of strange quark matter in the color-flavor locked phase because of the surface effects. Some properties of strange stars made of this matter are briefly discussed.

On the persistent X-ray emission from the soft gamma-ray repeatersDec 10 1996It is suggested that the persistent X-ray emission from the soft gamma-ray repeaters is the thermal radiation of neutron stars which is enhanced by a factor of 10 or more due to the effect of a very strong magnetic field on the thermal structure of the ... More

Experimental study of a transformer with superconducting elements for fault current limitation and energy redistributionApr 19 2005Numerous proposed and developed superconducting fault current limiters and self-limiting transformers limit successfully fault currents but do not provide uninterrupted supplying of consumers. A design investigated in the work combines the functions of ... More

Young Stars in the Camelopardalis Dust and Molecular Clouds. I. The Cam OB1 AssociationMar 17 2008Mar 31 2008The distribution of dust and molecular clouds in the direction of Galactic longitudes 132--158 deg and latitudes pm 12 deg is investigated. The maps of dust distribution in the area were plotted from the following surveys: the star counts in the DSS I ... More

A narrow plane cut near the crystal surface increases the probability of capture into the stable channeling motion up to 99 percentMar 07 2007It is shown that a narrow plane cut near the crystal surface considerably increases the probability of capture into the stable channeling motion of positively charged particles entering a crystal at angles smaller than a quarter of the critical channeling ... More

On the instability of classical dynamics in theories with higher derivativesDec 25 2006Jan 09 2007The development of instability in the dynamics of theories with higher derivatives is traced in detail in the framework of the Pais-Uhlenbeck fourth oder oscillator. For this aim the external friction force is introduced in the model and the relevant ... More

Boundary conditions at spatial infinity for fields in Casimir calculationsNov 02 2005The importance of imposing proper boundary conditions for fields at spatial infinity in the Casimir calculations is elucidated.

The Association of PSR B1757-24 and the SNR G5.4-1.2Oct 14 2003The association of PSR B1757-24 and the supernova remnant (SNR) G5.4-1.2 was recently questioned by Thorsett et al. (2002) on the basis of proper motion measurements of the pulsar and the "incorrect" orientation of the vector of pulsar transverse velocity ... More

On the origin of the hypervelocity runaway star HD271791Sep 27 2009We discuss the origin of the runaway early B-type star HD271791 and show that its extremely high velocity (\simeq 530-920 km/s) cannot be explained within the framework of the binary-supernova ejection scenario. Instead, we suggest that HD271791 attained ... More

Neutron Stars in Supernova Remnants and BeyondDec 26 2002We discuss a concept of off-centred cavity supernova explosion as applied to neutron star/supernova remnant associations and show how this concept could be used to preclude the anti-humane decapitating the Duck (G5.4-1.2 + G5.27-0.9) and dismembering ... More

Installing of cosmological constantAug 05 2013Jan 14 2014An artificial scale of observable cosmological constant is dynamically related to its natural bare value due to an installation of relevant coherent state for the inflationary field in a finite volume of early Universe, because of exponential suppression ... More

Extra charmonium states as bag-quarkoniaMay 28 2008Jun 06 2008Exotic states in the charmonium family are systematically treated in the framework of simplest model with an effective coulomb-like interaction of heavy quark and antiquark in the presence of static excitation of quark-gluon modes responsible for a nonperturbative ... More

A quantum mass-spectrum of Kerr black hole: superstringsDec 23 2004Jan 12 2005Using thermal quantization of geodesics confined under horizons and reasonable conjecture on massless modes, we evaluate quantum spectrum of Kerr black hole masses compatible with superstring symmetries.

Radial geodesics as a microscopic origin of black hole entropy. II: Features of Reissner--Nordstrom black holeDec 21 2004Jan 04 2005The entropy of charged black hole is calculated by using the partition function evaluated at radial geodesics confined under horizons. We establish two quantum phase states inside the black hole and a transition between them.

CP-violation in the heavy quark systemsSep 11 2001We present a review of general picture in the sector of electroweak symmetry breaking with the CP-violation in the heavy quark interactions.

A gluon condensate term in a heavy quark massJul 19 1999Apr 09 2003We investigate a connection between a renormalon ambiguity of heavy quark mass and the gluon condensate contribution into the quark dispersion law related with a virtuality defining a displacement of the heavy quark from the perturbative mass-shell, which ... More

Lambda-bar from QCD sum rules for heavy quarkoniumSep 08 1994Sep 09 1994Using a specific scheme of the QCD sum rules for heavy quarkonium in the leading approximation over the inverse heavy quark mass, one gets the estimate of the difference between the masses of the heavy meson and heavy quark $\bar \Lambda = 0.59\pm 0.02$ ... More

Entropy of BTZ black hole and its spectrum by quantum radial geodesics behind horizonsJun 09 2005In the framework of thermal quantization of radial geodesics completely confined behind the horizons we calculate the entropy of BTZ black hole in agreement with the Bekenstein--Hawking relation. Particles in the BTZ black hole occupy the only quantum ... More

Quintessential solution of dark matter rotation curves and its simulation by extra dimensionsMar 09 2003Apr 07 2003On the base of an exact solution for the static spherically symmetric Einstein equations with the quintessential dark matter, we explain the asymptotic behavior of rotation curves in spiral galaxies. The parameter of the quintessence state, i.e. the ratio ... More

Spinor algebra transformations as gauge symmetry: limit to Einstein gravityApr 23 2001Mar 19 2002We construct a Lagrangian of Weyl spinors and gauge fields, which is invariant under the action of equivalent local transformations on the spinor algebra representations. A model of vacuum with a nontrivial gauge strength-tensor setting a scale and spontaneously ... More

Perturbative Fragmentation of Leptoquark into Heavy Lepto-QuarkoniumOct 22 1997The fragmentation function of a scalar leptoquark into possible S-wave bound states with a heavy anti-quark is calculated to the leading order in perturbative QCD for the high energy processes at large transverse momenta. The one-loop equations for the ... More

Hard-soft factorization in B_c--> psi pi decayJul 05 1995Jul 06 1995The width of $B_c^+\to \psi \pi^+$ decay is calculated in the framework of factorization of a hard gluon exchange and a soft binding of quarks in the heavy quarkonium, so that ${\rm BR}(B_c^+\to \psi \pi^+) = 2.0\pm 0.5$ \%.

Scaling behaviour of leptonic decay constants for heavy quarkonia and heavy mesonsJun 07 1994In the framework of QCD sum rules one uses a scheme, allowing one to apply the conditions of both nonrelativistic heavy quark motion inside mesons and independence of nonsplitting nS-state density on the heavy quark flavours. In the leading order an analitic ... More

Scaling law for the $Υ(4S) \to B \bar B$ and $ψ(3770) \to D \bar D$ decay constants from effective sum rulesJan 27 1994Sum rules for exclusive production of heavy meson pairs in $e^+e^-$ annihilation are used to evaluate the $\Upsilon(4S) \to B \bar B$ and $\psi(3770) \to D \bar D$ decay widths. Infinitely heavy quark limit is discussed, so that scaling law for the quarkonium-meson ... More

Scaling Relations in Phenomenology of QCD Sum Rules for Heavy QuarkoniumApr 17 1995In the framework of a specific scheme of the QCD sum rules for $S$-wave levels of the heavy quarkonium, one derives expressions, relating the leptonic constants, the energetic density of quarkonium states and universal characteristics in the heavy quarkonium ... More

Asymptotical photon distributions in the dissipative Dynamical Casimir EffectFeb 09 2010Asymptotical formulas for the photon distribution function of a quantum oscillator with time-dependent frequency and damping coefficients, interacting with a thermal reservoir, are derived in the case of a large mean number of quanta. Different regimes ... More

Variation of fundamental constantsAug 25 2006We present a review of recent works devoted to the variation of the fine structure constant alpha, strong interaction and fundamental masses. There are some hints for the variation in quasar absorption spectra, Big Bang nucleosynthesis, and Oklo natural ... More

Limits on temporal variation of fine structure constant, quark masses and strong interaction from atomic clock experimentsSep 26 2003We perform calculations of the dependence of nuclear magnetic moments on quark masses and obtain limits on the variation of the ratio of quark mass and strong interaction scale (m_q/Lambda_{QCD}) from recent atomic clock experiments with hyperfine transitions ... More

Comment on "Black holes constrain varying constants"Aug 20 2002A recent paper [DDL] claims that the increase of the proton electric charge e leads to a (forbidden) decrease of black hole entropy, therefore, possible evidence for variation of $\alpha=e^2/\hbar c$ [alpha] must be interpreted as a decrease of the speed ... More

Comment on "Black hole constraints on varying fundamental constants"Aug 19 2008In the Letter [1] (also [2]) there is a claim that the generalised second law of thermodynamics (entropy increase) for black holes provides some limits on the rate of variation of the fundamental constants of nature (electric charge e, speed of light ... More

Long-Range Rapidity Correlations in the Model with Independent EmittersDec 01 2010The correlation between multiplicities in two separated rapidity windows, the so-called long-range correlation (LRC), is studied in the framework of the model with independent identical emitters. It's shown that the LRC coefficient, defined for the scaled ... More

Hardy-Littlewood inequality for primesApr 27 2015May 07 2015In the article we establish the Hardy-Littlewood inequality $ \pi (x + y) \leq \pi (x) + \pi (y) $. We also prove that the naturally ordered primes $p_1=2,p_2=3,p_3=5,p_4=7,\dots$ satisfy the inequality $ p_ {a + b}> p_a + p_b $ for all $a, \ b \geq 2$. ... More

Community Detection in Complex Networks by Dynamical Simplex EvolutionOct 02 2007We benchmark the dynamical simplex evolution (DSE) method with several of the currently available algorithms to detect communities in complex networks by comparing the fraction of correctly identified nodes for different levels of ``fuzziness'' of random ... More

On the inverse braid and reflection monoids of type $B$Feb 28 2009There are well known relations between braid groups and symmetric groups, between Artin-Briskorn braid groups and Coxeter groups. Inverse braid monoid the same way is related to the inverse symmetric monoid. In the paper we show that similar relations ... More

One sided conformal collars and the reflection principleDec 01 2016If a Jordan curve {\sigma} has a one-sided conformal collar with "good" properties, then, using the Reflection principle, we show that any other conformal collar of {\sigma} from the same side has the same "good" properties. A particular use of this fact ... More

One kind of spinor techniques for massive fermionsNov 12 1999In the work we have considered the reduction techniques matrix element of the reaction interaction of elementary particles for massive fermions to spinor products . The our procedure is not more complex than CALCUL spinor techniques for massless fermions. ... More

Decay Constant of Pseudoscalar Meson in the Heavy Mass LimitDec 09 1999The leptonic decay constant of the pseudoscalar mesons a calculated by use of the relativistic constituent quark model constructed on the point form of Poincare-covariant quantum mechanics. We discuss the role relativistic corrections for decay constants ... More

Local Rank of Ergodic Symmetric $n$-Powers does not exceed $n!n^{-n}$Aug 29 2011We prove that local rank of an ergodic symmetric power $T^{\odot n}$ does not exceed $n!n^{-n}$. A. Katok's old results show that this upper bound is exact. We prove also that $T^{\odot n}$ has infinite Rank as $n>1$.

Weak Closure Theorem for Double Staircase ActionsAug 02 2011We introduce a double staircase construction $T$ and show that the weak closure of $\{T^n\}$ is $\{\int, 2^{-m}T^n+(1-2^{-m})\int \ : m\in\N,\ n\in \Z\}.$

The Galaxy Kinematics from the Cepheids with the Proper Motions from the GAIA DR1 CatalogNov 06 2016The sample of classic Cepheids with known distances and line-of-sight velocities is supplemented by the proper motions from the Gaia DR1 catalog. From spatial velocities of 260 stars the components of the peculiar Solar velocity: (U,V,W)_\odot=(7.90,11.73,7.39)+/-(0.65,0.77,0.62) ... More

Rapid and Inexpensive Reconstruction of 3D Structures for Micro-Objects Using Common Optical MicroscopyApr 13 2009A simple method of constructing the 3D surface of non-transparent micro-objects by extending the depth-of-field on the whole attainable surface is presented. The series of images of a sample are recorded by the sequential movement of the sample with respect ... More

Mass of nonrelativistic meson from leading twist distribution amplitudesDec 09 2009In this paper distribution amplitudes of pseudoscalar and vector nonrelativistic mesons are considered. Using equations of motion for the distribution amplitudes, it is derived relations which allow one to calculate the masses of nonrelativistic pseudoscalar ... More

The study of leading twist light cone wave functions of J/Psi mesonJan 27 2007This paper is devoted to the study of leading twist light cone wave functions of J/Psi meson. The moments of these wave functions have been calculated within three approaches: potential models, nonrelativistic QCD and QCD sum rules. Using the results ... More

Transverse positron polarization in the $μ^+ \to e^+ \bar{ν_μ} ν_e$ decay in SMJun 11 2005Jun 14 2005In this paper transverse positron polarization in the $\mu^+ \to e^+ \bar {\nu_{\mu}} \nu_e$ decay in the framework of SM is considered. It is shown that the final state interaction effect leads to nonzero transverse polarization. Numerical value of the ... More

Evidence for a Supernova in the Ic Band Light Curve of the Optical Transient of GRB 970508Feb 28 2001Unique data on $BVRI$ brightness curves of the OT of GRB 970508 obtained with the 6-m telescope have been interpreted in the framework of the GRB-SN (supernovae) connection. The effect must be maximal in the I_c band as OT GRB 970228. The peak absolute ... More

On the GRB progenitors: possible consequences for supernovae connection with gamma-ray burstsJul 20 2001Unique data on $BVRI$ light curves of the optical transient (OT) of GRB 970508 obtained with the 6-m telescope have been interpreted in the framework of the idea of a straightforward link between supernovae (SNe) and long duration gamma-ray bursts (GRBs). ... More

Multiplicities of Singular Points in Schubert Varieties of GrassmanniansAug 09 2001We give a closed-form formula for the Hilbert function of the tangent cone at the identity of a Schubert variety X in the Grassmannian in both group theoretic and combinatorial terms. We also give a formula for the multiplicity of X at the identity, and ... More

Primary Decompositions for Left Noetherian RingsFeb 01 2007Two constructions are given that describe respectively all shortest primary decompositions and all shortest uniform decompositions for left Noetherian rings. They show that these decompositions are, in general, highly non-unique.

The Carlitz AlgebrasMay 18 2005The Carlitz $\mathbb{F}_q$-algebra $C=C_\nu$, $\nu \in \mathbb{N}$, is generated by an algebraically closed field $\CK $ (which contains a non-discrete locally compact field of positive characteristic $p>0$, i.e. $K\simeq \mathbb{F}_q[[ x,x^{-1}]]$, $q=p^\nu$), ... More

Thick brane solutions supported by two spinor fieldsApr 14 2011Stationary thick brane solutions supported by two spinor fields are considered. Two spinor fields are used here to exclude the off-diagonal components of the energy-momentum tensor of the spinor fields. The trapping of a test scalar field on the brane ... More

Derivations and skew derivations of the Grassmann algebrasApr 29 2007Surprisingly, skew derivations rather than ordinary derivations are more basic (important) object in study of the Grassmann algebras. Let $\L_n = K\lfloor x_1, ..., x_n\rfloor$ be the Grassmann algebra over a commutative ring $K$ with ${1/2}\in K$, and ... More

${\rm K}_1(\mS_1)$ and the group of automorphisms of the algebra $\mS_2$ of one-sided inverses of a polynomial algebra in two variablesJun 02 2009Apr 18 2010Explicit generators are found for the group $G_2$ of automorphisms of the algebra $\mS_2$ of one-sided inverses of a polynomial algebra in two variables over a field of characteristic zero. Moreover, it is proved that $$ G_2\simeq S_2\ltimes \mT^2\ltimes ... More

Hyperspherical Functions and Harmonic Analysis on the Lorentz GroupAug 28 2003May 21 2004Matrix elements of spinor and principal series representations of the Lorentz group are studied in the basis of complex angular momentum (helicity basis). It is shown that matrix elements are expressed via hyperspherical functions (relativistic spherical ... More

Relativistic Wave Equations in the Helicity BasisNov 14 2002The principal series of unitary representations of the Lorentz group has been considered in the helicity basis. Decompositions of tensor products of the spinspaces are studied in the framework of projective representations of the symmetric group. Higher-spin ... More

Explicit solution of the problem of equivalence for some Painleve equationsSep 10 2009For an arbitrary ordinary second order differential equation a test is constructed that checks if this equation is equivalent to Painleve I, II or Painleve III with three zero parameters equations under the substitutions of variables. If it is true then ... More

Generators and defining relations for the ring of differential operators on a smooth affine algebraic varietyApr 22 2005For the ring of differential operators on a smooth affine algebraic variety $X$ over a field of characteristic zero a finite set of algebra generators and a finite set of defining relations are found explicitly. As a consequence, a finite set of generators ... More

Dense families of selections and finite-dimensional spacesNov 26 2001A characterization of $n$-dimensional spaces via continuous selections avoiding $Z_n$-sets is given, and a selection theorem for strongly countable-dimensional spaces is established. We apply these results to prove a generalized Ostrand's theorem and ... More

Orthogonal Polynomials and Generalized Oscillator AlgebrasFeb 26 2000For any orthogonal polynomials system on real line we construct an appropriate oscillator algebra such that the polynomials make up the eigenfunctions system of the oscillator hamiltonian. The general scheme is divided into two types: a symmetric scheme ... More

Inverse spectral problem for GK integrable systemMar 01 2015A.Goncharov and R.Kenyon has defined a class of integrable system on a cluster varieties constructed out of a Newton polygon on the plane. In the present note we show that thiest cluster varieties coincides with the configuration spaces of collections ... More

The classical left regular left quotient ring of a ring and its semisimplicity criteriaApr 27 2015Let $R$ be a ring, $\CC_R$ and $\pCCR$ be the set of regular and left regular elements of $R$ ($\CC_R\subseteq \pCCR$). Goldie's Theorem is a semisimplicity criterion for the classical left quotient ring $Q_{l,cl}(R):=\CC_R^{-1}R$. Semisimplicity criteria ... More

On subgroups of minimal topological groupsApr 19 2000Mar 15 2007A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. The Roelcke uniformity (or lower uniformity) on a topological group is the greatest lower bound of the left and right uniformities. A group is Roelcke-precompact ... More

Hardy-Littlewood inequality for primesApr 27 2015Jan 13 2017In the article we establish the Hardy-Littlewood inequality $ \pi (x + y) \leq \pi (x) + \pi (y) $. We also prove that the naturally ordered primes $p_1=2,p_2=3,p_3=5,p_4=7,\dots$ satisfy the inequality $ p_ {a + b}> p_a + p_b $ for all $a, \ b \geq 2$. ... More

Dirac matrices as elements of superalgebraic matrix algebraApr 17 2016The paper considers a Clifford extension of the Grassmann algebra, in which operators are built from Grassmann variables and by the derivatives with respect to them. It is shown that a subalgebra which is isomorphic to the usual matrix algebra exists ... More

Evolution of moments of isotropic Brownian stochastic flowsJun 11 2016In this paper we consider the asymptotic behaviour of all moments of the interparticle distance and of all mixed moments of an isotropic Brownian stochastic flow which serves as a smooth approximation of the Arratia flow.

Infinite sequences in the framework of classical logicApr 28 2008Infinite sequences are considered in the framework of classical logic from a new point of view.

Double resonant processes in $χ^{(2)}$ nonlinear periodic mediaAug 07 2000In a one-dimensional periodic nonlinear $\chi^{(2)}$ medium, by choosing a proper material and geometrical parameters of the structure, it is possible to obtain two matching conditions for simultaneous generation of second and third harmonics. This leads ... More

Neutron Diffraction and Optics of a Noncentrosymmetric Crystal. New Feasibility of a Search for Neutron EDMApr 25 2005May 03 2005Recently strong electric fields (up to 10^9 V/cm) have been discovered, which affect the neutrons moving in noncentrosymmetric crystals. Such fields allow new polarization phenomena in neutron diffraction and optics and provide, for instance, a new feasibility ... More

Onepoint discontinuity set of separately continuous functions on the product of two compact spacesJan 12 2016It is investigated the existence of a separately continuous function $f:X\times Y\to \mathbb R$ with an onepoint set of discontinuity for topological spaces $X$ and $Y$ which satisfy compactness type conditions. In particular, it is shown that for compact ... More

The discontinuity points set of separately continuous functions on the products of compactsDec 24 2015It is solved a problem of construction of separately continuous functions on the product of compacts with a given discontinuity points set. We obtaine the following results. 1. For arbitrary \v{C}ech complete spaces $X$, $Y$ and a separable compact perfect ... More

Low voltage transport through a tunneling barrier in Tomonaga-Luttinger liquid constrictionMar 09 1997As voltage decreases d.c. condctivity of a Tomonaga-Luttinger liquid wire collapses to a small value determined by the length of the wire and its contacts with the leads. In condition that voltage drop (V) mostly occurs across a tunnel barrier inside ... More

Statistics of heat generated in a solvable dissipative Landau-Zener modelDec 05 2014Jul 07 2015We consider an adiabatic Landau-Zener model of two-level system diagonally coupled to an Ohmic bosonic bath of large spectral width and derive through fermionization its exact solution at a special value of the coupling constant. From this solution we ... More

Geoneutrinos and the Earth inner parts structureJul 15 2010The connection between geoneutrino registration and the Earth theory test is discussed. We compare standard theory of lithosphere plates and hypothesis of hydride Earth. Last hypothesis adds additional neutrino source $-$ planet core in which the initial ... More