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The Muon $g-2$ experiment at FermilabMay 01 2019May 03 2019The current $\sim3.5\sigma$ discrepancy between the experimental measurement and theoretical prediction of the muon magnetic anomaly, $a_{\mu}$, stands as a potential indication of the existence of new physics. The Muon $g-2$ experiment at Fermilab is ... More

The muon $g-2$: a brief overview of hadronic cross section dataMar 22 2019The hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon, $a_{\mu}^{\rm had, VP}$ are evaluated dispersively via a combination of experimentally measured $e^+e^-\rightarrow {\rm hadrons}$ cross section data. Many experiments ... More

The Muon $g-2$ experiment at FermilabMay 01 2019The current $\sim3.5\sigma$ discrepancy between the experimental measurement and theoretical prediction of the muon magnetic anomaly, $a_{\mu}$, stands as a potential indication of the existence of new physics. The Muon $g-2$ experiment at Fermilab is ... More

The muon $g-2$ and $α(M_Z^2)$: a new data-based analysisFeb 08 2018This work presents a complete re-evaluation of the hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon, $a_{\mu}^{\rm had, \, VP}$ and the hadronic contributions to the effective QED coupling at the mass of the $Z$ ... More

The hadronic vacuum polarisation contributions to the muon $g-2$Feb 17 2018The hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon, $a_{\mu}^{\rm had, VP}$ have been re-evaluated from the combination of $e^+e^-\rightarrow {\rm hadrons}$ cross section data. Focus has been placed on the development ... More

The muon $g-2$ and $α(M_Z^2)$: a new data-based analysisFeb 08 2018Jul 13 2018This work presents a complete re-evaluation of the hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon, $a_{\mu}^{\rm had, \, VP}$ and the hadronic contributions to the effective QED coupling at the mass of the $Z$ ... More

On Lorentzian two-symmetric manifolds of dimension fourDec 19 2014We study curvature properties of four-dimensional Lorentzian manifold with two-symmetry property. We then consider Einstein-like metrics, Ricci solitons and homogeneity over these spaces.

Some geometrical properties of the Oscillator groupApr 15 2016We consider the oscillator group equipped with a bi-invariant Lorentzian metric, and then some geometrical properties of this group i.e. homogeneous Ricci solitons and harmonicity properties of invariant vector ?fields are obtained. We also determine ... More

Harmonicity and Minimality of vector fields on four-dimensional Lorentzian lie groupsOct 28 2014Jan 14 2015We consider four dimensional lie groups equipped with left invariant Lorentzian Einstein metrics, and determine the harmonicity properties of vector fields on these spaces. In some cases, all these vector fields are critical points for the energy functional ... More

The strong coupling from $e^+e^-\to$ hadrons below charmMay 21 2018We use a new compilation of the hadronic $R$-ratio from available data for the process $e^+e^-\to\mbox{hadrons}$ to determine the strong coupling, $\alpha_s$. We make use of all data for the $R$-ratio from threshold to a center-of-mass energy of 2 GeV ... More

Conformally flat pseudo Riemannian Homogeneous Ricci Solitons 4 spacesDec 15 2014We consider four dimensional conformally flat homogeneous pseudo Riemannian manifolds. According to forms (Seger types) of the Ricci operator, we provide a full classification of four dimensional pseudo Riemannian conformally flat homogeneous Ricci solitons. ... More

Local pressure of confined fluids inside nanoslit pores -- A density functional theory predictionJul 18 2013In this work, the local pressure of fluids confined inside nanoslit pores is predicted within the framework of the density functional theory. The Euler-Lagrange equation in the density functional theory of statistical mechanics is used to obtain the force ... More

Inhomogeneities and the modeling of radio supernovaeApr 18 2017Observations of radio supernovae often exhibit characteristics not readily accounted for by a homogeneous, spherically symmetric synchrotron model; e.g., flat-topped spectra/lightcurves. It is shown that many of these deviations from the standard model ... More

Brain-Computer Interface in Virtual RealityNov 13 2018We study the performance of brain computer interface (BCI) system in a virtual reality (VR) environment and compare it to 2D regular displays. First, we design a headset that consists of three components: a wearable electroencephalography (EEG) device, ... More

A Fast Concurrent Power-Thermal Model for Sub-100nm Digital ICsOct 25 2007As technology scales down, the static power is expected to become a significant fraction of the total power. The exponential dependence of static power with the operating temperature makes the thermal profile estimation of high-performance ICs a key issue ... More

Magnetic susceptibility of the quark condensate via holographyFeb 11 2009Jan 13 2010We discuss the holographic derivation of the magnetic susceptibility of the quark condensate. It is found that the susceptibility emerges upon the account of the Chern-Simons term in the holographic action. We demonstrate that Vainshtein's relation is ... More

On Beurling's sampling theorem in $\R^n$Jun 03 2011We present an elementary proof of the classical Beurling sampling theorem which gives a sufficient condition for sampling of multi-dimensional band-limited functions.

Regenerative compositions in the case of slow variation: A renewal theory approachSep 27 2011Sep 01 2012A regenerative composition structure is a sequence of ordered partitions derived from the range of a subordinator by a natural sampling procedure. In this paper, we extend previous studies Barbour and Gnedin (2006), Gnedin, Iksanov and Marynych (2010) ... More

Derived categories of Gushel-Mukai varietiesMay 21 2016We study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety ... More

Mild and viscosity solutions to quasilinear parabolic path-dependent PDEsNov 24 2016We study and compare two different concepts for weak solutions to quasilinear parabolic path-dependent partial differential equations (PPDEs). The first concept is that of a mild solution as it appears, e.g., in the Laplace functionals of historical superprocesses. ... More

Derived categories of cyclic covers and their branch divisorsNov 07 2014Dec 17 2015Given a variety $Y$ with a rectangular Lefschetz decomposition of its derived category, we consider a degree $n$ cyclic cover $X \to Y$ ramified over a divisor $Z \subset Y$. We construct semiorthogonal decompositions of $\mathrm{D^b}(X)$ and $\mathrm{D^b}(Z)$ ... More

Paramagnetic tunneling state concept of the magnetic anomalies of amorphous insulatorsSep 05 2005A generalized tunneling model of insulating glasses is formulated, considering tunneling states to be paramagnetic centers of spin 1/2. The expression for magnetic field dependent contribution into the free energy is obtained. The derivation is made of ... More

Spherical structures on torus knots and linksAug 02 2010Jul 07 2011The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found ... More

On the Duality between Sampling and InterpolationDec 04 2015We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.

Evaluation of the Einstein's strength of difference schemes for some chemical reaction-diffusion equationsMar 10 2018In this paper we present a difference algebraic technique for the evaluation of the Einstein's strength of a system of partial difference equations and apply this technique to the comparative analysis of difference schemes for chemical reaction-diffusion ... More

When is a Schubert variety Gorenstein?Sep 25 2004Nov 21 2005A (normal) variety is Gorenstein if it is Cohen-Macualay and its canonical sheaf is a line bundle. This property, which measures the ``pathology'' of the singularities of a variety, is thus stronger than Cohen-Macualayness, but is also weaker than smoothness. ... More

Discrete Translates in Function SpacesDec 02 2016Mar 16 2017We construct a Schwartz function $\varphi$ such that for every exponentially small perturbation of integers $\Lambda$, the set of translates $\{\varphi(t-\lambda), \lambda\in\Lambda\}$ spans the space $L^p(R)$, for every $p > 1$. This result remains true ... More

String center of mass operator and its effect on BRST cohomologyNov 15 1995We consider the theory of bosonic closed strings on the flat background R(25,1). We show how the BRST complex can be extended to a complex where the string center of mass operator, x^mu_0, is well defined. We investigate the cohomology of the extended ... More

An ICT-Based Real-Time Surveillance System for Controlling Dengue in Sri LankaMay 16 2014Dengue is a notifiable communicable disease in Sri Lanka since 1996. Dengue fever spread rapidly among people living in most of the districts of Sri Lanka. The present notification system of dengue communicable diseases which is enforced by law is a passive ... More

Approximation of discrete functions and size of spectrumApr 02 2013Let $\Lambda$ be a uniformly discrete set and $S$ be a compact set in $R$. We prove that if there exists a bounded sequence of functions in Paley--Wiener space $PW_S$, which approximates $\delta-$functions on $\Lambda$ with $l^2-$error $d$, then measure($S$)$\geq ... More

Kazhdan-Laumon representations of finite Chevalley groups, character sheaves and some generalization of the Lefschetz-Verdeier trace formulaOct 01 1998In this paper we investigate the representations of reductive groups over a finite field, introduced in 1987 by D.Kazhdan and G.Laumon. We show that generically these representations are irreducible and that their character is equal to the function obtained ... More

Discrete Translates in $L^2(R)$Dec 02 2016A set $\Lambda\subset R$ is called $p$-spectral, if there is a function $\varphi\in L^p(R)$ whose $\Lambda$-translates $\{\varphi(t-\lambda),\lambda\in\Lambda\}$ span $L^p(R)$. We prove that exponentially small non-zero perturbations of the integers are ... More

$L^2-$interpolation with error and size of spectraJun 18 2008Given a compact set $S$ and a uniformly discrete sequence $\La$, we show that "approximate interpolation" of delta--functions on $\La$ by a bounded sequence of $L^2-$functions with spectra in $S$ implies an estimate on measure of $S$ through the density ... More

Moments of random sums and Robbins' problem of optimal stoppingJul 17 2011Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal in the sense ... More

Homological projective duality for quadricsFeb 26 2019We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of ... More

Categorical cones and quadratic homological projective dualityFeb 26 2019We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction ... More

Categorical joinsMar 31 2018Feb 26 2019We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical projective duality. ... More

Fast gradient descent method for convex optimization problems with an oracle that generates a $(δ,L)$-model of a function in a requested pointNov 07 2017Feb 02 2019In this article we propose a new concept of a $(\delta,L)$-model of a function which generalizes the concept of the $(\delta,L)$-oracle (Devolder-Glineur-Nesterov). Using this concept we describe the gradient descent method and the fast gradient descent ... More

Scattering theory and Banach space valued singular integralsNov 28 2012We give a new sufficient condition for existence and completeness of wave operators in abstract scattering theory. This condition generalises both trace class and smooth approaches to scattering theory. Our construction is based on estimates for the Cauchy ... More

Diagonalization of the Finite Hilbert Transform on two adjacent intervalsNov 06 2015We study the interior problem of tomography. The starting point is the Gelfand-Graev formula, which converts the tomographic data into the finite Hilbert transform (FHT) of an unknown function $f$ along a collection of lines. Pick one such line, call ... More

Subtle Characteristic ClassesJan 26 2014We construct new subtle Stiefel--Whitney classes of quadratic forms. These classes are much more informative than the ones introduced by Milnor. In particular, they see all the powers of the fundamental ideal of the Witt ring, contain the Arason invariant ... More

Governing Singularities of Schubert VarietiesMar 12 2006Jun 29 2006We present a combinatorial and computational commutative algebra methodology for studying singularities of Schubert varieties of flag manifolds. We define the combinatorial notion of *interval pattern avoidance*. For "reasonable" invariants P of singularities, ... More

Affordance Analysis of Virtual and Augmented Reality Mediated CommunicationApr 09 2019Virtual and augmented reality communication platforms are seen as promising modalities for next-generation remote face-to-face interactions. Our study attempts to explore non-verbal communication features in relation to their conversation context for ... More

A Gröbner basis for Kazhdan-Lusztig idealsSep 03 2009Nov 11 2011Kazhdan-Lusztig ideals, a family of generalized determinantal ideals investigated in [Woo-Yong '08], provide an explicit choice of coordinates and equations encoding a neighbourhood of a torus-fixed point of a Schubert variety on a type A flag variety. ... More

Neutrino energy quantization in rotating mediumSep 30 2008Exact solution of the modified Dirac equation in rotating medium is found in polar coordinates in the limit of vanishing neutrino mass. The solution for the active left-handed particle exhibit properties similar to those peculiar for the charged particle ... More

General Conditions for Lepton Flavour Violation at Tree- and 1-Loop LevelSep 20 2007In this work, we compile the necessary and sufficient conditions a theory has to fulfill in order to ensure general lepton flavour conservation, in the spirit of the Glashow-Weinberg criteria for the absence of flavour-changing neutral currents. At tree-level, ... More

Discrete Uniqueness Sets for Functions with Spectral GapsSep 15 2016It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular, Sobolev spaces ... More

Derived categories of Gushel-Mukai varietiesMay 21 2016Oct 25 2017We study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety ... More

Spectral perturbation theory and the two weights problemJun 08 2013The famous two weights problem consists in characterising all possible pairs of weights such that the Hardy projection is bounded between the corresponding weighted $L^2$ spaces. Koosis' theorem of 1980 gives a way to construct a certain class of pairs ... More

Exponential-Uniform Identities Related to RecordsJun 05 2012We consider a rectangular grid induced by the south-west records from the planar Poisson point process in $R^2_+$. A random symmetry property of the matrix whose entries are the areas of tiles of the grid implies cute multivariate distributional identities ... More

Yet again on polynomial convergence for SDEs with a gradient-type driftJun 28 2017Jul 23 2017Bounds on convergence rate to the invariant distribution for a class of stochastic differential equations (SDEs) with a gradient-type drift are obtained.

Mild and viscosity solutions to semilinear parabolic path-dependent PDEsNov 24 2016Nov 14 2018We study and compare two concepts for weak solutions to semilinear parabolic path-dependent partial differential equations (PPDEs). The first is that of mild solutions as it appears, e.g., in the log-Laplace functionals of historical superprocesses. The ... More

Full exceptional collections on the Lagrangian Grassmannians LG(4,8) and LG(5,10)Oct 13 2009We construct full exceptional collections of vector bundles on the Lagrangian Grassmannians LG(4,8) and LG(5,10).

Cauchy independent measures and super-additivity of analytic capacityNov 12 2012We show that, given a family of discs centered at a nice curve, the analytic capacities of arbitrary subsets of these discs add up. However we need that the discs in question would be slightly separated, and it is not clear whether the separation condition ... More

Random "dyadic" lattice in geometrically doubling metric space and $A_2$ conjectureMar 27 2011Apr 21 2011Recently three proofs of the $A_2$-conjecture were obtained. All of them are "glued" to euclidian space and a special choice of one random dyadic lattice. We build a random "dyadic" lattice in any doubling metric space which have properties that are enough ... More

Reachability in Higher-Order-CountersJun 05 2013Higher-order counter automata (\HOCS) can be either seen as a restriction of higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an extension of counter automata to higher levels. We distinguish two principal kinds of \HOCS: those ... More

Exceptional collections on isotropic GrassmanniansOct 25 2011Sep 13 2015We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the ... More

Paramagnetic tunneling state concept of the low-temperature magnetic anomalies of multicomponent insulating glassesMar 17 2006A generalized tunneling model of multicomponent insulating glasses is formulated, considering tunneling states to be paramagnetic centers of the electronic hole type. The expression for magnetic field dependent contribution into the free energy is obtained. ... More

On multi-dimensional sampling and interpolationApr 02 2013The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from above (from ... More

Conduct and Correctness in Mathematical PublishingAug 10 2012"We risk sliding down toward the standards where the validity of action is decided by whether one can get away with it." (P. Doty) "We do not 'risk' sliding down toward such standards; we have reached them." (S. Lang) This is an essay in which I try to ... More

Autocorrelated errors explain the apparent relationship between disapproval of the US Congress and prosocial languageJun 08 2015Recently, it has been claimed by Frimer et al. (2015) that there is a linear relationship between the level of prosocial language and the level of public disapproval of US Congress. A re-analysis demonstrates that this relationship is the result of a ... More

Asymptotics for some combinatorial characteristics of the convex hull of a Poisson point process in the Clifford torusOct 28 2010Nov 29 2012N. Dolbilin and M. Tanemura studied the convex hulls of finite subsets of the Clifford torus $T$ in $E^4$. They have completely studied the combinatorial structure of the convex hull for a periodic point set. Moreover, there was performed a numerical ... More

Nonexistence of intrinsic spin currentsAug 06 2004We have described the electron spin dynamics in the presence of the spin-orbit interaction and disorder using the spin-density matrix method. We showed that in the Born approximation in the scattering amplitude the spin current is zero for an arbitrary ... More

On acceleration of Krylov-subspace-based Newton and Arnoldi iterations for incompressible CFD: replacing time steppers and generation of initial guessApr 01 2016We propose two techniques aimed at improving the convergence rate of steady state and eigenvalue solvers preconditioned by the inverse Stokes operator and realized via time-stepping. First, we suggest a generalization of the Stokes operator so that the ... More

Reduction of the graph isomorphism problem to equality checking of $n$-variables polynomials and the algorithms that use the reductionDec 10 2015Jun 07 2016The graph isomorphism problem is considered. We assign modified characteristic polynomials for graphs and reduce the graph isomorphism problem to the following one. It is required to find out, is there such an enumeration of the graphs vertices that the ... More

Enumeration and Random Generation of Unlabeled Classes of Graphs: A Practical Study of Cycle Pointing and the Dissymmetry TheoremNov 19 2015Our work studies the enumeration and random generation of unlabeled combinatorial classes of unrooted graphs. While the technique of vertex pointing provides a straightforward procedure for analyzing a labeled class of unrooted graphs by first studying ... More

Optimal Compression of a Polyline with Segments and ArcsApr 25 2016Oct 19 2016This paper describes an efficient approach to constructing a resultant polyline with a minimum number of segments and arcs. While fitting an arc can be done with complexity O(1) (see [1] and [2]), the main complexity is in checking that the resultant ... More

A control problem with fuel constraint and Dawson-Watanabe superprocessesJul 24 2012Dec 05 2013We solve a class of control problems with fuel constraint by means of the log-Laplace transforms of $J$-functionals of Dawson-Watanabe superprocesses. This solution is related to the superprocess solution of quasilinear parabolic PDEs with singular terminal ... More

Statistics-Free Sports PredictionDec 21 2015Sep 19 2016We use a simple machine learning model, logistically-weighted regularized linear least squares regression, in order to predict baseball, basketball, football, and hockey games. We do so using only the thirty-year record of which visiting teams played ... More

Geometric phase in the G3+ quantum state evolutionOct 23 2015When quantum mechanical qubits as elements of two dimensional complex Hilbert space are generalized to elements of even subalgebra of geometric algebra over three dimensional Euclidian space, geometrically formal complex plane becomes explicitly defined ... More

Determinant bundles for abelian schemesMar 18 1997Jun 06 1997To a symmetric, relatively ample line bundle on an abelian scheme one can associate a linear combination of the determinant bundle and the relative canonical bundle, which is a torsion element in the Picard group of the base. We improve the bound on the ... More

Symplectic biextensions and a generalization of the Fourier-Mukai transformNov 28 1995Dec 01 1995A generalization of the Fourier-Mukai transform is proposed. The construction is based on analogy with the classical picture of representations of the Heisenberg group.

Is the world made of loops?Sep 28 2013Nov 18 2013In discussions of the Aharonov-Bohm effect, Healey and Lyre have attributed reality to loops $\sigma_0$ (or hoops $[\sigma_0]$), since the electromagnetic potential $A$ is currently unmeasurable and can therefore be transformed. I argue that $[A]=[A+d\lambda]_{\lambda}$ ... More

A Pareto Front-Based Multiobjective Path Planning AlgorithmMay 22 2015Path planning is one of the most vital elements of mobile robotics. With a priori knowledge of the environment, global path planning provides a collision-free route through the workspace. The global path plan can be calculated with a variety of informed ... More

Compact OrthoalgebrasMay 28 2004We initiate a study of topological orthoalgebras (TOAs), concentrating on the compact case. Examples of TOAs include topological orthomodular lattices, and also the projection lattice of a Hilbert space. As the latter example illustrates, a lattice-ordered ... More

On axioms of Frobenius like structure in the theory of arrangementsJan 10 2016Jul 04 2016A Frobenius manifold is a manifold with a flat metric and a Frobenius algebra structure on tangent spaces at points of the manifold such that the structure constants of multiplication are given by third derivatives of a potential function on the manifold ... More

Selberg IntegralsAug 23 2004Oct 11 2004The paper is written for Kluwer's Encyclopaedia of Mathematics.

Critical Points of the Product of Powers of Linear Functions and Families of Bases of Singular VectorsDec 14 1993The quasiclassical asymptotics of the Knizhnik-Zamolodchikov equation with values in the tensor product of sl(2)- representations are considered. The first term of asymptotics is an eigenvector of a system of commuting operators. We show that the norm ... More

Quantum Field Theory on Curved Noncommutative SpacetimesJan 18 2011Jan 24 2011We summarize our recently proposed approach to quantum field theory on noncommutative curved spacetimes. We make use of the Drinfel'd twist deformed differential geometry of Julius Wess and his group in order to define an action functional for a real ... More

Global stability of systems related to the Navier-Stokes equationsJan 04 2001A generalized Lyapunov method is outlined which predicts global stability of a broad class of dissipative dynamical systems. The method is applied to the complex Lorenz model and to the Navier-Stokes equations. In both cases one finds compact domains ... More

Reconstruction algorithms for a class of restricted ray transforms without added singularitiesMar 17 2016Let $X$ and $X^*$ denote a restricted ray transform along curves and a corresponding backprojection operator, respectively. Theoretical analysis of reconstruction from the data $Xf$ is usually based on a study of the composition $X^* D X$, where $D$ is ... More

Instanton counting via affine Lie algebras I: Equivariant J-functions of (affine) flag manifolds and Whittaker vectorsJan 29 2004Oct 15 2004For a semi-simple simply connected algebraic group G we introduce certain parabolic analogues of the Nekrasov partition function (introduced by Nekrasov and studied recently by Nekrasov-Okounkov and Nakajima-Yoshioka for G=SL(n)). These functions count ... More

In-medium heavy-quarkonium from lattice QCD spectral functionsSep 12 2015We discuss recent progress in the study of in-medium heavy quarkonium using first-principles lattice QCD calculations and effective field theory. In particular our focus lies on real-time information carried by QCD spectral functions and we report on ... More

Chebyshev expansion approach to the AC conductivity of the Anderson modelFeb 20 2004Aug 12 2004We propose an advanced Chebyshev expansion method for the numerical calculation of linear response functions at finite temperature. Its high stability and the small required resources allow for a comprehensive study of the optical conductivity $\sigma(\omega)$ ... More

Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum SpaceMay 13 2009Nov 08 2009We discuss multiloop MHV amplitudes in the N=4 SYM theory in terms of effective gravity in the momentum space with IR regulator branes as degrees of freedom. Kinematical invariants of external particles yield the moduli spaces of complex or Kahler structures ... More

Peierls model and vacuum structure in N=2 supersymmetric gauge theoriesMay 20 1996We suggest the quasiparticle picture behind the integrable structure of N=2 SYM theory,which arises if the Lax operator is considered as a Hamiltonian for the fermionic system. We compare the meaning of BPS states with the one coming from the D-brane ... More

On the higher-dimensional harmonic analog of the Levinson log log theoremJul 18 2014Aug 05 2014Let $M\colon (0,1) \to [e,+\infty)$ be a decreasing function such that $\int\limits_{0}^{1}\log\log M(y)dy<+\infty$. Consider the set $H_M$ of all functions $u$ harmonic in $P:=\{(x,y)\in \mathbb{R}^n: x\in \mathbb{R}^{n-1}, y\in \mathbb{R}, |x|<1, |y|<1 ... More

On the regularity of CR mappings in higher codimensionAug 13 2002We give a proof of the regularity of Holder CR homeomorphisms of strictly pseudo convex CR manifolds of higher codimension.

A New Method for Calculating Differential Distributions Directly in Mellin SpaceNov 30 2005We present a new method for the calculation of differential distributions directly in Mellin space without recourse to the usual momentum-fraction (or z-) space. The method is completely general and can be applied to any process. It is based on solving ... More

Applications of Perturbative Quantum Chromodynamics to Processes with Heavy QuarksNov 07 2003In this thesis we study the b-quark fragmentation in top decay as well as the effect of the threshold resummation on heavy quark production in charged-current DIS. To predict the spectrum of b-flavored hadrons in top decay, we calculate at NLO the QCD ... More

Bäcklund-Darboux Transformation for Non-Isospectral Canonical System and Riemann-Hilbert ProblemMar 25 2007A GBDT version of the Backlund-Darboux transformation is constructed for a non-isospectral canonical system, which plays essential role in the theory of random matrix models. The corresponding Riemann-Hilbert problem is treated and some explicit formulas ... More

Second harmonic generation: Goursat problem on the semi-strip and explicit solutionsFeb 27 2004A rigorous and complete solution of the initial-boundary-value (Goursat) problem for second harmonic generation (and its matrix analog) on the semi-strip is given in terms of the Weyl functions. A wide class of the explicit solutions and their Weyl functions ... More

Linear independence of nearest neighbor valence bond states on the kagome lattice and construction of SU(2)-invariant spin-1/2-Hamiltonian with a Sutherland-Rokhsar-Kivelson quantum liquid ground stateJun 02 2009Nov 07 2009A class of local SU(2)-invariant spin-1/2 Hamiltonians is studied that has ground states within the space of nearest neighbor valence bond states on the kagome lattice. Cases include "generalized Klein'' models without obvious non-valence bond ground ... More

Ultrahigh-energy nuclei, photons, and magnetic fieldsOct 23 2010Oct 27 2010Combined recent data from cosmic-ray detectors and gamma-ray detectors have produced some surprising insights regarding the sources of ultrahigh-energy cosmic rays (UHECRs), magnetic fields inside and outside the Milky Way, and the universal photon backgrounds. ... More

Properties and signatures of supersymmetric Q-ballsDec 13 2006Supersymmetric extensions of the Standard Model predict the existence of Q-balls with baryon and lepton numbers. Stable Q-balls can form at the end of inflation from the fragmentation of the Affleck-Dine condensate and can exist as dark matter. The best ... More

Dark matter's X-filesNov 19 2007Nov 26 2007Sterile neutrinos with keV masses can constitute all or part of the cosmological dark matter. The electroweak-singlet fermions, which are usually introduced to explain the masses of active neutrinos, need not be heavier than the electroweak scale; if ... More

Pulsar velocities and dark matter hint at a singlet neutrinoNov 11 2003Nov 12 2003Two astrophysical puzzles, the origin of pulsar velocities and that of dark matter, may have a simultaneous explanation if there exists a sterile neutrino with a mass in the 1-20 keV range and a small mixing (of order 10^{-4}) with the electron neutrino. ... More

Superball dark matterAug 10 1998Supersymmetric models predict a natural dark-matter candidate, stable baryonic Q-balls. They could be copiously produced in the early Universe as a by-product of the Affleck-Dine baryogenesis. I review the cosmological and astrophysical implications, ... More

Hyperdiffusion of quantum waves in random photonic latticesAug 24 2015A quantum-mechanical analysis of hyper-fast (faster than ballistic) diffusion of a quantum wave packet in random optical lattices is presented. The main motivation of the presented analysis is experimental demonstrations of hyper-diffusive spreading of ... More

The First Order Effect of the Quantum Weyl Algebra on a Harmonic OscillatorApr 05 2010We examine a concrete realization of the quantum Weyl algebra and expand it to first order. From here we apply the resulting algebra to a quantum harmonic oscillator in its ground state and observe how a slightly noncommutative space affects the physical ... More