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The Barut Second-Order Equation, Dynamical Invariants and InteractionsMar 06 2005The second-order equation in the (1/2,0)+(0,1/2) representation of the Lorentz group has been proposed by A. Barut in the beginning of the 70s. It permits to explain the mass splitting of leptons e,mu,tau. Recently, the interest has grown to this model ... More

Stability, chaos and entrapment of stars in very wide pairsNov 18 2011Dec 12 2011The relative motion of stars and other celestial objects in very wide pairs, separated by distances of the order of 1 pc, is strongly influenced by the tidal gravitational potential of the Galaxy. The Coriolis component of the horizontal tidal force in ... More

Equilibrium rotation of semiliquid exoplanets and satellitesJul 27 2015A wide range of exoplanet and exomoon models are characterized by a finite average rigidity and a viscosity much lower than the typical values for terrestrials. Such semiliquid bodies may or may not have rigid crusts with permanent figures. Unlike planets ... More

How terrestrial planets traverse spin-orbit resonances: A camel goes through a needle's eyeOct 12 2011Apr 04 2012The dynamical evolution of terrestrial planets resembling Mercury in the vicinity of spin-orbit resonances is investigated using comprehensive harmonic expansions of the tidal torque taking into account the frequency-dependent quality factors and Love ... More

Absolute Nuv magnitudes of Gaia DR1 astrometric stars and a search for hot companions in nearby systemsMay 02 2017Sep 15 2017Accurate parallaxes from Gaia DR1 (TGAS) are combined with GALEX visual Nuv magnitudes to produce absolute Mnuv magnitudes and an ultraviolet HR diagram for a large sample of astrometric stars. A functional fit is derived of the lower envelope main sequence ... More

Variability of surface flows on the Sun and the implications for exoplanet detectionApr 08 2010The published Mount Wilson Doppler-shift measurements of the solar velocity field taken in 1967--1982 are revisited with a more accurate model, which includes two terms representing the meridional flow and three terms corresponding to the convective limb ... More

Why is the Moon synchronously rotating?May 23 2013If the Moon's spin evolved from faster prograde rates, it could have been captured into a higher spin-orbit resonance than the current 1:1 resonance. At the current value of orbital eccentricity, the probability of capture into the 3:2 resonance is as ... More

On the weak and ergodic limit of the spectral shift functionNov 19 2009We discuss convergence properties of the spectral shift functions associated with a pair of Schrodinger operators with Dirichlet boundary conditions at the end points of a finite interval (0, r) as the length of interval approaches infinity.

No pseudosynchronous rotation for terrestrial planets and moonsSep 07 2012Jan 19 2013We reexamine the popular belief that a telluric planet or satellite on an eccentric orbit can, outside a spin-orbit resonance, be captured in a quasi-static tidal equilibrium called pseudosynchronous rotation. The existence of such configurations was ... More

Tidal dissipation in a homogeneous spherical body. II. Three examples: Mercury, Io, and Kepler-10 bJun 09 2014Oct 08 2014In Efroimsky & Makarov (2014), we derived from the first principles a formula for the tidal heating rate in a tidally perturbed homogeneous sphere. We compared it with the formulae used in the literature, and pointed out the differences. Using this result, ... More

Chaotic rotation and evolution of asteroids and small planets in high-eccentricity orbits around white dwarfsAug 13 2019Observed planetary debris in white dwarf atmospheres predominately originate from the destruction of small bodies on highly eccentric ($>0.99$) orbits. Despite their importance, these minor planets have coupled physical and orbital evolution which has ... More

Photometric and astrometric vagaries of the enigma star KIC 8462852Sep 13 2016Sep 26 2016We apply a PCA-based pre-whitening method to the entire collection of main Kepler mission long-cadence data for KIC 8462852 spanning four years. This technique removes the correlated variations of instrumental origin in both the detected light curves ... More

Dynamical evolution and spin-orbit resonances of potentially habitable exoplanets. The case of GJ 667CNov 19 2013We investigate the dynamical evolution of the potentially habitable super-earth GJ 667Cc in the multiple system of at least two exoplanets orbiting a nearby M dwarf, paying special attention to its spin-orbital state. The published radial velocities for ... More

Photometric and astrometric vagaries of the enigma star KIC 8462852Sep 13 2016Dec 26 2016We apply a PCA-based pre-whitening method to the entire collection of main Kepler mission long-cadence data for KIC 8462852 spanning four years. This technique removes the correlated variations of instrumental origin in both the detected light curves ... More

Tidal dissipation in a homogeneous spherical body. I. MethodsJun 09 2014Dec 21 2015A formula for the tidal dissipation rate in a spherical body is derived from first principles, to correct some mathematical inaccuracies found in the literature. The development is combined with the Darwin-Kaula formalism for tides. Our intermediate results ... More

Observations of red giants with suspected massive companionsFeb 08 2019Mar 21 2019Motivated by the existence of binary systems where a stellar-mass black hole is bound to a normal star, we selected four red giants with large radial velocity (RV) variation from the survey of SIM grid stars and monitored their RVs for several months. ... More

Observations of red giants with suspected massive companionsFeb 08 2019Motivated by the existence of binary systems where a stellar-mass black hole is bound to a normal star, we selected four red giants with large radial velocity (RV) variation from the survey of SIM grid stars and monitored their RVs for several months. ... More

Kepler data on KIC 7341653, a nearby M dwarf with monster flares and a phase-coherent variabilityJul 03 2017KIC 7341653 is one of several late-type M dwarfs observed in the main mission of Kepler with peculiar infrared colors placing them in the domain of suspected young stellar objects (YSO). It is likely associated with a powerful X-ray emitter with X-ray ... More

Variability induced motion in Kepler dataMar 22 2016Variability induced motion (VIM) is an observable effect in simultaneous astrometric and photometric measurements caused by brightness variation in one of the components of a double source or blended image, which manifests itself as a strongly correlated ... More

Tidal Friction and Tidal Lagging. Applicability Limitations of a Popular Formula for the Tidal TorqueSep 07 2012Jan 19 2013Tidal torques play a key role in rotational dynamics of celestial bodies. They govern these bodies' tidal despinning, and also participate in the subtle process of entrapment of these bodies into spin-orbit resonances. This makes tidal torques directly ... More

Rigidly rotating ZAMO surfaces in the Kerr spacetimeAug 27 2014A stationary observer in the Kerr spacetime has zero angular momentum if his/her angular velocity $\omega$ has a particular value, which depends on the position of the observer. Worldlines of such zero angular momentum observers (ZAMOs) with the same ... More

Black Holes in a Compactified SpacetimeFeb 13 2003Apr 03 2003We discuss properties of a 4-dimensional Schwarzschild black hole in a spacetime where one of the spatial dimensions is compactified. As a result of the compactification the event horizon of the black hole is distorted. We use Weyl coordinates to obtain ... More

Forced libration of tidally synchronized planets and moonsNov 19 2015Tidal dissipation of kinetic energy, when it is strong enough, tends to synchronize the rotation of planets and moons with the mean orbital motion, or drive it into long-term stable spin-orbit resonances. As the orbital motion undergoes periodic acceleration ... More

Radial velocities and binarity of southern SIM grid starsOct 29 2014We present analysis of precision radial velocities (RV) of 1134 mostly red giant stars in the southern sky, selected as candidate astrometric grid objects for the Space Interferometry Mission (SIM). Only a few (typically, 2 or 3) spectroscopic observations ... More

Astrometric Effects of Secular AberrationAug 24 2005One of the main endeavors of fundamental astrometry is to establish a practical realization of an inertial reference frame anchored to celestial objects whose positions are defined in the barycentric coordinates of the solar system. The development of ... More

Dynamical evolution and spin-orbit resonances of potentially habitable exoplanets. The case of GJ 581dAug 03 2012Jan 21 2013GJ 581d is a potentially habitable super-Earth in the multiple system of exoplanets orbiting a nearby M dwarf. We investigate this planet's long-term dynamics, with an emphasis on its probable final rotation states acquired via tidal interaction with ... More

Double stars and astrometric uncertainties in Gaia DR1Apr 02 2017A significant number of double stars with separations up to 2.5 arcsec are present in the Gaia Data Release 1 astrometric catalogs. Limiting our analysis to a well-studied sample of 1124 doubles resolved by Hipparcos, provided with individual Tycho component ... More

Astro2020 Activity, Project of State of the Profession Consideration (APC) White Paper: All-Sky Near Infrared Space Astrometry. State of the Profession Considerations: Development of Scanning NIR Detectors for AstronomyJul 11 2019Gaia is a revolutionary space mission developed by ESA and is delivering 5 parameter astrometry, photometry and radial velocities over the whole sky with astrometric accuracies down to a few tens of micro-arcseconds. A weakness of Gaia is that it only ... More

Static Internal Representation Of Dynamic Situations Reveals Time Compaction In Human CognitionJun 27 2018The time-changing nature of our world demands processing of huge amounts of information in fast and reliable way to generate successful behaviors. Therefore, significant brain resources are devoted to process spatiotemporal information. Neural basis of ... More

Revealing companions to nearby stars with astrometric accelerationApr 18 2012A subset of 51 Hipparcos astrometric binaries among FG dwarfs within 67pc has been surveyed with the NICI adaptive optics system at Gemini-S, directly resolving for the first time 17 sub-arcsecond companions and 7 wider ones. Using these data together ... More

Unconstrained Astrometric Orbits for Hipparcos Stars with Stochastic SolutionsJun 13 2006A considerable number of astrometric binaries whose positions on the sky do not obey the standard model of mean position, parallax and linear proper motion, were observed by the Hipparcos satellite. Some of them remain non-discovered, and their observational ... More

Gravitational bending of light by planetary multipolesDec 04 2007General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived in the approximation of the linearized Einstein equations. All terms of order 1 microarcsecond ... More

Spin-orbital tidal dynamics and tidal heating in the TRAPPIST-1 multi-planet systemMar 20 2018Apr 27 2018We perform numerical simulations of the TRAPPIST-1 system of seven exoplanets orbiting a nearby M dwarf, starting with a previously suggested stable configuration. The long-term stability of this configuration is confirmed, but the motion of planets is ... More

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometersNov 11 2006Feb 08 2007General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived. All terms of order 1 microarcsecond are taken into account, parametrized, and classified ... More

Taking the Measure of the Universe: Precision Astrometry with SIM PlanetQuestAug 28 2007Nov 07 2007Precision astrometry at microarcsecond accuracy has application to a wide range of astrophysical problems. This paper is a study of the science questions that can be addressed using an instrument that delivers parallaxes at about 4 microarcsec on targets ... More

Mechanism of epitaxial self-assembly of Fe nanowedge islands on Mo(110)May 07 2004The deposition of ultrathin Fe films on the Mo(110) surface at elevated temperatures results in the formation of distinctive nanowedge islands supported on a pseudomorphic Fe layer. We propose a model explaining the growth mode of these wedge-shaped Fe ... More

Exoplanet Science Priorities from the Perspective of Internal and Surface Processes for Silicate and Ice Dominated WorldsApr 13 2018The geophysics of extrasolar planets is a scientific topic often regarded as standing largely beyond the reach of near-term observations. This reality in no way diminishes the central role of geophysical phenomena in shaping planetary outcomes, from formation, ... More

A list of peculiar velocities of RFGC galaxiesJul 03 2001A list of radial velocities, HI line widths and peculiar velocities of 1327 galaxies from the RFGC catalogue has been compiled using actual observations and literature data. The list can be used for studying bulk motions of galaxies, construction of the ... More

Micromagnetic Theory of Curvilinear Ferromagnetic ShellsApr 04 2019Here, we present a micromagnetic theory of curvilinear ferromagnets, which allows discovering novel fundamental physical effects which were amiss. In spite of the firm confidence for more than 70 years, we demonstrate that there is an intimate coupling ... More

The precious set of radio-optical reference frame objects in the light of Gaia DR2 dataNov 25 2018Feb 07 2019We investigate a sample of 3412 {\it International Celestial Reference Frame} (ICRF3) extragalactic radio-loud sources with accurate positions determined by VLBI in the S/X band, mostly active galactic nuclei (AGN) and quasars, which are cross-matched ... More

Towards the ICRF3: astrometric comparison of the USNO 2016A VLBI solution with ICRF2 and Gaia DR1Apr 26 2018The VLBI USNO 2016A (U16A) solution is part of a work-in-progress effort by USNO towards the preparation of the ICRF3. Most of the astrometric improvement with respect to the ICRF2 is due to the re-observation of the VCS sources. Our objective in this ... More

The Worst Distortions of Astrometric Instruments and Orthonormal Models for Rectangular Fields of ViewOct 13 2011The non-orthogonality of algebraic polynomials of field coordinates traditionally used to model field-dependent corrections to astrometric measurements, gives rise to subtle adverse effects. In particular, certain field dependent perturbations in the ... More

UrHip Proper Motion CatalogSep 18 2015Proper motions are computed and collected in a catalog using the Hipparcos positions (epoch 1991.25) and URAT1 positions (epoch 2012.3 to 2014.6). The goal is to obtain a significant improvement on the proper motion accuracy of single stars in the northern ... More

The field of Loden 112Jul 20 2011Based on the available uvbybeta photometry of OB stars in the longitude range 281 - 285 deg in the Galactic disk, we identify a feature of young stars at 1630+/-82 pc, that is probably connected to the compact cluster candidate Loden 112 and the open ... More

MasterPVA and WAlg: Mathematica packages for Poisson vertex algebras and classical affine $\mathcal{W}$-algebrasMar 16 2016Feb 06 2017We give an introduction to the Mathematica packages "MasterPVA" and "MasterPVAmulti used to compute lambda-brackets in Poisson vertex algebras, which play an important role in the theory of infinite-dimensional Hamiltonian systems. As an application, ... More

All-Sky Near Infrared Space AstrometryApr 18 2019Gaia is currently revolutionizing modern astronomy. However, much of the Galactic plane, center and the spiral arm regions are obscured by interstellar extinction, rendering them inaccessible because Gaia is an optical instrument. An all-sky near infrared ... More

Chaos and hyperchaos in driven interacting quantum systemsJul 08 2019We investigate theoretically the dynamics of one-dimensional coupled quantum systems with energy pumping and dissipation. Our study focusses on coupled Rydberg atoms driven by an external laser field and undergoing spontaneous emission. We show that this ... More

All-optical nanoscale heating and thermometry with resonant dielectric nanoparticles for photoinduced tumor treatmentJun 13 2019All-dielectric nanophotonics becomes a versatile tool for various optical applications, including nanothermometry and optical heating. Its general concept includes excitation of Mie resonances in nonplasmonic nanoparticles. However, the potential of resonant ... More

Hipparcos red stars in the HpV_{T2} and VI_C systemsNov 04 2002For Hipparcos M, S, and C spectral type stars, we provide calibrated instantaneous (epoch) Cousins $V-I$ color indices using newly derived $HpV_{T2}$ photometry. Three new sets of ground-based Cousins $VI$ data have been obtained for more than 170 carbon ... More

Gaussian free field and conformal field theoryJan 05 2011Jun 19 2013In these mostly expository lectures, we give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. We consider statistical fields, and define Ward functionals in terms of their Lie derivatives. ... More

Discovery of an unusual bright eclipsing binary with the longest known period: TYC 2505-672-1 / MASTER OT J095310.04+335352.8Feb 19 2016Mar 27 2016We report on the MASTER Global Robotic Net discovery of an eclipsing binary, MASTER OT J095310.04+335352.8, previously known as unremarkable star TYC 2505-672-1, which displays extreme orbital parameters. The orbital period P=69.1 yr is more than 2.5 ... More

Symphony of high-dimensional brainJun 27 2019This paper is the final part of the scientific discussion organised by the Journal "Physics of Life Rviews" about the simplicity revolution in neuroscience and AI. This discussion was initiated by the review paper "The unreasonable effectiveness of small ... More

Spin-orbit evolution of Mercury revisitedJun 29 2013Aug 24 2014While it is accepted that the eccentricity of Mercury (0.206) favours entrapment into the 3:2 spin-orbit resonance, open is the question how and when the capture took place. A recent work by Makarov (2012) has demonstrated that trapping into this resonance ... More

Some Applications of the Spectral Shift OperatorMar 31 1999The recently introduced concept of a spectral shift operator is applied in several instances. Explicit applications include Krein's trace formula for pairs of self-adjoint operators, the Birman-Solomyak spectral averaging formula and its operator-valued ... More

Antisymmetric Tensor Fields, 4-Potentials and Indefinite MetricsFeb 18 2004We generalize the Stueckelberg formalism in the (1/2,1/2) representation of the Lorentz Group. Some relations to other modern-physics models are found.

Dual Stochastic Transformations of Solvable DiffusionsJul 16 2009Dec 02 2014We present new extensions to a method for constructing several families of solvable one-dimensional time-homogeneous diffusions whose transition densities are obtainable in analytically closed-form. Our approach is based on a dual application of the so-called ... More

(Modified) Fredholm Determinants for Operators with Matrix-Valued Semi-Separable Integral Kernels RevisitedDec 12 2003We revisit the computation of (2-modified) Fredholm determinants for operators with matrix-valued semi-separable integral kernels. The latter occur, for instance, in the form of Green's functions associated with closed ordinary differential operators ... More

Orbital relaxation and excitation of planets tidally interacting with white dwarfsApr 05 2019Observational evidence of white dwarf planetary systems is dominated by the remains of exo-asteroids through accreted metals, debris discs, and orbiting planetesimals. However, exo-planets in these systems play crucial roles as perturbing agents, and ... More

Separation of variables in Maxwell equations in Plebanski-Demianski spacetimeFeb 26 2018Mar 09 2018A new method for separating variables in Maxwell's equations in four- and higher-dimensional Kerr-(A)dS spacetimes proposed recently by Lunin is generalized to any off-shell metric that admits a principal Killing-Yano tensor. The key observation is that ... More

Astrometric evidence for a population of dislodged AGNDec 20 2016Jan 12 2017We investigate a sample of 2293 ICRF2 extragalactic radio-loud sources with accurate positions determined by VLBI, mostly active galactic nuclei (AGN) and quasars, which are cross-matched with optical sources in the first Gaia release (Gaia DR1). The ... More

QFT's With Action of Degree 3 and Higher and Degeneracy of TensorsMay 31 1997In this paper we develop a technique of computation of correlation functions in theories with action being cubic or higher degree form in terms of discriminants of corresponding tensors. These are analogues of formula $\int \exp (iT(x))dx\sim \det T^{-1/2}$ ... More

Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equationFeb 20 2015Feb 01 2016We study the one dimensional periodic derivative nonlinear Schr\"odinger (DNLS) equation. This is known to be a completely integrable system, in the sense that there is an infinite sequence of formal integrals of motion $\int h_k$, $k\in \mathbb{Z}_{+}$. ... More

On Invariant TheoryDec 14 1995Jun 28 1997Here we develop a technique of computing the invariants of $n-$ary forms and systems of forms using the discriminants of corresponding multilinear forms built of their partial derivatives, which should be cosidered as analogues of classical discriminants ... More

Antisymmetric Tensor Fields, 4-Vector Fields, Indefinite Metrics and NormalizationNov 14 2007On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the Ogievetskii-Polubarinov notoph ... More

The Structure and the Distance of Collinder 121 from Hipparcos and Photometry: Resolving the DiscrepancyAug 24 2007We present further arguments that the Hipparcos parallaxes for some of the clusters and associations represented in the Hipparcos catalog should be used with caution in the study of the Galactic structure. It has been already shown that the discrepancy ... More

Scattering of a Long Cosmic String by a Rotating Black HoleAug 03 2002Nov 03 2002The scattering of a straight, infinitely long string by a rotating black hole is considered. We assume that a string is moving with velocity v and that initially the string is parallel to the axis of rotation of the black hole. We demonstrate that as ... More

Massive mimetic cosmologyFeb 21 2019May 29 2019We study the first cosmological implications of the mimetic theory of massive gravity recently proposed by Chamseddine and Mukhanov. This is a novel theory of ghost-free massive gravity which additionally contains a mimetic dark matter component. In an ... More

Pricing Step Options under the CEV and other Solvable Diffusion ModelsFeb 15 2013We consider a special family of occupation-time derivatives, namely proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96 (1999)]. We develop new closed-form spectral expansions for pricing such options under a class of nonlinear ... More

Univalent Polynomials and Hubbard TreesAug 16 2019We study rational functions $f$ of degree $d$, univalent in the exterior unit disc, with $f(\mathbb{T})$ having the maximal number of cusps ($d+1$) and double points $(d-2)$. We introduce a bi-angled tree associated to any such $f$. It is proven that ... More

Fluctuations of eigenvalues of random normal matricesJul 02 2008Jun 13 2010In this note, we prove Gaussian field convergence of fluctuations of eigenvalues of random normal matrices in the interior of a quantum droplet.

Interpolation of functional by integral continued C-fractionsJan 21 2018The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued fraction contains ... More

Rescaling Ward identities in the random normal matrix modelOct 15 2014Oct 29 2015We study existence and universality of scaling limits for the eigenvalues of a random normal matrix, in particular at points on the boundary of the spectrum. Our approach uses Ward's equation, which is an identity satisfied by the 1-point function.

On a perturbation determinant for accumulative operatorsDec 20 2014For a purely imaginary sign-definite perturbation of a self-adjoint operator, we obtain exponential representations for the perturbation determinant in both upper and lower half-planes and derive respective trace formulas.

Evans Functions, Jost Functions, and Fredholm DeterminantsNov 15 2005The principal results of this paper consist of an intrinsic definition of the Evans function in terms of newly introduced generalized matrix-valued Jost solutions for general first-order matrix-valued differential equations on the real line, and a proof ... More

An Addendum to Krein's FormulaNov 18 1997We provide additional results in connection with Krein's formula, which describes the resolvent difference of two self-adjoint extensions A_1 and A_2 of a densely defined closed symmetric linear operator A with (possibly infinite) equal deficiency indices. ... More

High-dimensional brain. A tool for encoding and rapid learning of memories by single neuronsOct 30 2017Jan 27 2018Codifying memories is one of the fundamental problems of modern Neuroscience. The functional mechanisms behind this phenomenon remain largely unknown. Experimental evidence suggests that some of the memory functions are performed by stratified brain structures ... More

Poisson $λ$-brackets for differential-difference equationsJun 14 2018Jun 18 2018We introduce the notion of a multiplicative Poisson $\lambda$-bracket, which plays the same role in the theory of Hamiltonian differential-difference equations as the usual Poisson $\lambda$-bracket plays in the theory of Hamiltonian PDE. We classify ... More

Dirac reduction for Poisson vertex algebrasJun 27 2013Jul 23 2014We construct an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's reduction of an arbitrary non-local Poisson structure. We apply this construction ... More

Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotentsJun 07 2013Jul 23 2014We derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the corresponding intgerable ... More

Double Poisson vertex algebras and non-commutative Hamiltonian equationsOct 13 2014May 23 2015We develop the formalism of double Poisson vertex algebras (local and non-local) aimed at the study of non-commutative Hamiltionan PDEs. This is a generalization of the theory of double Poisson algebras, developed by Van den Bergh, which is used in the ... More

Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebrasJan 09 2014Jan 16 2014We put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, together with its generalizations and reduction to the N-th KdV hierarchy, ... More

Identification of 1.4 Million AGNs in the Mid-Infrared using WISE DataSep 24 2015We present an all-sky sample of ~ 1.4 million AGNs meeting a two color infrared photometric selection criteria for AGNs as applied to sources from the Wide-Field Infrared Survey Explorer final catalog release (AllWISE). We assess the spatial distribution ... More

Structure of classical (finite and affine) W-algebrasApr 02 2014First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f. On the other hand, ... More

Integrability of Dirac reduced bi-Hamiltonian equationsJan 23 2014Jul 23 2014First, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the remainder of the paper to prove integrability of three hierarchies of bi-Hamiltonian ... More

A new scheme of integrability for (bi)Hamiltonian PDEAug 11 2015Sep 05 2018We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method ... More

Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebrasJul 26 2012Aug 12 2013We provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the ... More

Finite W-algebras for gl_NMay 10 2016We study the quantum finite W-algebras W(gl_N,f), associated to the Lie algebra gl_N, and its arbitrary nilpotent element f. We construct for such an algebra an r_1 x r_1 matrix L(z) of Yangian type, where r_1 is the number of maximal parts of the partition ... More

Early optical follow-up of the nearby active star DG CVn during its 2014 superflareJul 11 2015DG CVn is a binary system in which one of the components is an M type dwarf ultra fast rotator, only three of which are known in the solar neighborhood. Observations of DG CVn by the Swift satellite and several ground-based observatories during its super-flare ... More

X-Ray Sources in Multiple StarsAug 25 2009Luminous X-ray stars are very often found in visual double or multiple stars. Binaries with periods of a few days possess the highest degree of coronal X-ray activity among regular, non-relativistic stars because of their fast, tidally driven rotation. ... More

An efficient approach for solving stiff nonlinear boundary value problemsJan 17 2016Apr 19 2018A new method for solving stiff boundary value problems is described and compared to other known approaches using the Troesch's problem as a test example. The method is based on the general idea of alternate approximation of either the unknown function ... More

Schwarz reflections and anti-holomorphic correspondencesJul 22 2019In this paper, we continue exploration of the dynamical and parameter planes of one-parameter families of Schwarz reflections that was initiated in \cite{LLMM1,LLMM2}. Namely, we consider a family of quadrature domains obtained by restricting the Chebyshev ... More

The June 2016 Optical and Gamma-Ray Outburst and Optical Micro-Variability of the Blazar 3C454.3Mar 11 2019The quasar 3C454.3 underwent a uniquely-structured multi-frequency outburst in June 2016. The blazar was observed in the optical $R$ band by several ground-based telescopes in photometric and polarimetric modes, at $\gamma$-ray frequencies by the \emph{Fermi}\ ... More

Notes on Oscillator-Like Interactions of Various Spin Relativistic ParticlesMar 28 1994Mar 30 1994The equations for various spin particles with oscillator-like interactions are discussed in this talk. Contents: 1. Comment on "The Klein-Gordon Oscillator"; 2. The Dirac oscillator in quaternion form; 3. The Dirac-Dowker oscillator; 4. The Weinberg oscillator; ... More

Siegel automorphic form corrections of some Lorentzian Kac--Moody Lie algebrasApr 10 1995Oct 04 1995We find automorphic form corrections which are generalized Lorentzian Kac--Moody superalgebras without odd real simple roots (see R. Borcherds \cite{Bo1} -- \cite{Bo7}, V. Kac \cite{Ka1} -- \cite{Ka3}, R. Moody \cite{Mo} and \S~6 of this paper) for two ... More

A lecture on Arithmetic Mirror Symmetry and Calabi-Yau manifoldsDec 03 1996Feb 11 1997We extend our variant of mirror symmetry for K3 surfaces \cite{GN3} and clarify its relation with mirror symmetry for Calabi-Yau manifolds. We introduce two classes (for the models A and B) of Calabi-Yau manifolds fibrated by K3 surfaces with some special ... More

Automorphic Forms and Lorentzian Kac-Moody Algebras. Part IINov 24 1996Feb 10 1997We give variants of lifting construction, which define new classes of modular forms on the Siegel upper half-space of complex dimension 3 with respect to the full paramodular groups (defining moduli of Abelian surfaces with arbitrary polarization). The ... More

The Igusa modular forms and ``the simplest'' Lorentzian Kac--Moody algebrasMar 13 1996We find automorphic corrections for the Lorentzian Kac--Moody algebras with the simplest generalized Cartan matrices of rank 3: A_{1,0} = 2 0 -1 0 2 -2 -1 -2 2 and A_{1,I} = 2 -2 -1 -2 2 -1 -1 -1 2 For A_{1,0} this correction is given by the Igusa Sp_4(Z)-modular ... More

Zitterbewegung with spin-orbit coupled ultracold atoms in a fluctuating optical latticeDec 13 2015Feb 01 2016Dynamics of non-interacting ultracold atoms with artificial spin-orbit coupling is considered. Spin-orbit coupling is created using two moving optical lattices with orthogonal polarizations. Our main goal is to study influence of lattice noise on Rabi ... More

Question: Negative Group Delays and Action-at-a-DistanceFeb 17 1998We comment on the paper by M. W. Mitchell and R. Y. Chiao, ``Causality and negative group delay in a simple bandpass amplifier", Am. J. Phys. 66 (1), 14-19 (1998).

Automorphic Forms and Lorentzian Kac--Moody Algebras. Part IOct 31 1996Using the general method which was applied to prove finiteness of the set of hyperbolic generalized Cartan matrices of elliptic and parabolic type, we classify all symmetric (and twisted to symmetric) hyperbolic generalized Cartan matrices of elliptic ... More