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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

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

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

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.

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

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

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.

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

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.

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

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

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

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

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

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

$L^2-$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

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

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

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

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

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

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

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

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

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

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

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

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).

A Pareto Optimal D* Search Algorithm for Multiobjective Path PlanningNov 03 2015Path planning is one of the most vital elements of mobile robotics, providing the agent with a collision-free route through the workspace. The global path plan can be calculated with a variety of informed search algorithms, most notably the A* search ... More

Extending the Learning by Teaching Canvas System: Maximising Academic Learning TimeMar 15 2016Time plays an integral role in the realm of e-learning modules. plaimi previously described a canvas for composing e-learning modules. By transitivity, time needs to play an integral role in this canvas. This paper investigates some of the ways it can ... More

Existence and regularity for a class of infinite-measure $(ξ,ψ,K)$-superprocessesFeb 23 1998We extend the class of $(\xi,\psi,K)$-superprocesses known so far by applying a simple transformation induced by a \lq\lq weight function\rq\rq\ for the one-particle motion. These transformed superprocesses may exist under weak conditions on the branching ... More

Generalized Carleson--Newman inner functionsMar 21 2012We study a class of inner functions introduced by Gorkin, Mortini, and Nikolski, and motivated by Banach algebras and functional calculus applications. Answering their question, we produce a singular function that cannot be multiplied into this generalized ... More

Intrinsic vs. Extrinsic Spin Currents. Old Ideas in a New LightDec 19 2005We have described the electron spin dynamics in the presence of Rashba 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

Intrinsic spin current for an arbitrary Hamiltonian and scattering potentialOct 31 2005Nov 15 2005We have described electron spin dynamics in the presence of the spin-orbit interaction and disorder using the spin-density matrix method. Exact solution is obtained for an arbitrary 2D spin-orbit Hamiltonian and arbitrary smoothness of the disorder potential. ... More

SuperspinorsMar 09 2006We propose to replace the classical Lorentz group with a compact semisimple Lie group. The results are rendered via the formalism of superspinors - objects identifiable as particles or antiparticles, and governed by the Fermi-Dirac statistics.

Deninger's conjecture on $L$-function of elliptic curves at $s=3$Dec 25 1995Feb 02 1996I compute explicitly the regulator map on $K_4(X)$ for an arbitrary curve $X$ over a number field. Using this and Beilinson's theorem about regulators for modular curves ([B2]) I prove a formula expressing the value of the $L$-function $L(E,s)$ of a modular ... More

A Note on Markov Normalized Magnetic EigenmapsAug 15 2016Sep 23 2016We note that building a magnetic Laplacian from the Markov transition matrix, rather than the graph adjacency matrix, yields several benefits for the magnetic eigenmaps algorithm. The two largest benefits are that the embedding becomes more stable as ... More

Science of Cyber Security as a System of Models and ProblemsNov 29 2015Terms like "Science of Cyber" or "Cyber Science" have been appearing in literature with growing frequency, and influential organizations initiated research initiatives toward developing such a science even though it is not clearly defined. We propose ... More

Searching for a Compressed Polyline with a Minimum Number of VerticesApr 24 2015There are many practical applications that require simplification of polylines. Some of the goals are to reduce the amount of information necessary to store, improve processing time, or simplify editing. The simplification is usually done by removing ... More

Approximate Fitting of Circular Arcs when Two Points are KnownApr 24 2015May 05 2015The task of approximation of points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, development of algorithms that perform a significant amount of circular arcs fitting ... More

Notes on the horizontal cohomologyMar 24 1998This paper is devoted to the horizontal (``characteristic'') cohomology of systems of differential equations. Recent results on computing the horizontal cohomology via the compatibility complex are generalized. New results on the Vinogradov C-spectral ... More

The Joseph Greenberg problem: combinatorics and comparative linguisticsSep 23 2013Sep 30 2013We correct a 1957 combinatorial enumeration by the linguist J. Greenberg. The desired count, the Bell number B(25), supported using his Mass Comparison method for language classification. In 1987, he used this method to classify indigenous languages of ... More

A simple model of cerebral blood flow dependence on arterial blood pressureMar 28 2011It is shown that the dependence of the cerebral blood flow (CBF) on mean arterial blood pressure (MABP) can be described with a simple model having the following assumptions. Below certain MABP (denoted as MABP1) there are no autoregulatory or feedback ... More

Topological Test SpacesMay 28 2004A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with incommensurable ... More

Twist deformations of module homomorphisms and connectionsOct 03 2012Let H be a Hopf algebra, A a left H-module algebra and V a left H-module A-bimodule. We study the behavior of the right A-linear endomorphisms of V under twist deformation. We in particular construct a bijective quantization map to the right A_\star-linear ... More

Is There a Relationship between the Density of Primordial Black Holes in a Galaxy and the Rate of Cosmological Gamma-Ray Bursts?Oct 28 2007The rate of accretion of matter from a solar-type star onto a primordial black hole (PBH) that passes through it is calculated. The probability that a PBH is captured into an orbit around a star in a galaxy is found. The mean lifetime of the PBH in such ... More

Invitation to higher local fields, Part II, section 8: Higher local skew fieldsDec 18 2000This work studies two dimensional local skew fields and their automorphisms.

Remarks on perturbation theory for Hamiltonian systemsJan 04 2001A comparative discussion of the normal form and action angle variable method is presented in a tutorial way. Normal forms are introduced by Lie series which avoid mixed variable canonical transformations. The main interest is focused on establishing a ... More

Integral Representations of Holomorphic Functions on Coverings of Pseudoconvex Domains in Stein ManifoldsApr 02 2005The classical integral representation formulas for holomorphic functions defined on pseudoconvex domains in Stein manifolds play an important role in the constructive theory of functions of several complex variables. In this paper we construct similar ... More

Explicit formulas for orthogonal polynomials derived from their difference equationJun 20 2015We solve the difference equation with linear coefficients by the Momentenansatz to obtain explicit formulas for orthogonal polynomials.

Notes and Remarks on certain logarithmic integralsJul 22 2013Logarithmic integrals revisited. We consider integrals of the form $\int_0^1 \ln{\ln{(\frac{1}{x})}}R{(x)}{\rm d}x$ again, where $R{(x)}$ is a rational function, and we will explain a way to obtain their values.

On proving some of Ramanujan's formulas for $\frac{1}π$ with an elementary methodSep 04 2013Sep 05 2013In this paper we want to prove some formulas listed by S. Ramanujan in his paper "Modular equations and approximations to $\pi$" \cite{24} with an elementary method.

Arrangements and Frobenius like structuresOct 14 2012Sep 19 2014We consider a family of generic weighted arrangements of $n$ hyperplanes in $\C^k$ and show that the Gauss-Manin connection for the associated hypergeometric integrals, the contravariant form on the space of singular vectors, and the algebra of functions ... More

Characteristic variety of the Gauss-Manin differential equations of a generic parallelly translated arrangementFeb 05 2014We consider a weighted family of $n$ generic parallelly translated hyperplanes in $\C^k$ and describe the characteristic variety of the Gauss-Manin differential equations for associated hypergeometric integrals. The characteristic variety is given as ... More

Feynman Equation in Hamiltonian Quantum Field TheoryMay 26 2000May 26 2000Functional Schr\"{o}dinger equations for interacting fields are solved via rigorous non-perturbative Feynman type integrals.

Subconvexity for a double Dirichlet series and non-vanishing of $L$-functionsOct 31 2015Jun 15 2016We study a double Dirichlet series of the form $\sum_{d}L(s,\chi_{d}\chi)\chi'(d)d^{-w}$, where $\chi$ and $\chi'$ are quadratic Dirichlet characters with prime conductors $N$ and $M$ respectively. A functional equation group isomorphic to the dihedral ... More

Banach-valued Holomorphic Functions on the Maximal Ideal Space of H^\inftyMar 11 2011We study Banach-valued holomorphic functions defined on open subsets of the maximal ideal space of the Banach algebra H^\infty of bounded holomorphic functions on the unit disk D\subset C with pointwise multiplication and supremum norm. In particular, ... More

Extension of Matrices with Entries in H^{\infty} on Coverings of Riemann Surfaces of Finite TypeJan 11 2008In the present paper continuing our previous work we prove an extension theorem for matrices with entries in the algebra of bounded holomorphic functions defined on an unbranched covering of a Caratheodory hyperbolic Riemann surface of finite type.

Boundary orbit strata and faces of invariant cones and complex Olshanskii semigroupsAug 24 2009Let D=G/K be an irreducible Hermitian symmetric domain. Then G is contained in a complexification, and there exists a closed complex subsemigroup, the so-called minimal Olshanskii semigroup, of the complexification characterised by the fact that all holomorphic ... More

Divide and conquer the Hilbert space of translation-symmetric spin systemsOct 05 2012Apr 21 2013Iterative methods that operate with the full Hamiltonian matrix in the untrimmed Hilbert space of a finite system continue to be important tools for the study of one- and two-dimensional quantum spin models, in particular in the presence of frustration. ... More

Densities of primes and realization of local extensionsSep 30 2013Apr 11 2014In this paper we introduce new densities on the set of primes of a number field. If $K/K_0$ is a Galois extension of number fields, we associate to any element $x \in {\rm Gal}_{K/K_0}$ a density $\delta_{K/K_0,x}$ on primes of $K$. In particular, the ... More

Framed correspondences and the Milnor-Witt K-theoryOct 27 2014Nov 24 2015The article is to construct a graded ring isomorphism between $H_0(ZF(\Delta^{\bullet}_k,\mathbb{G}_m^{\wedge *}))$ and the Milnor-Witt K-theory ring $K^{MW}_{*\geqslant 0}(k)$, where $k$ is a field of characteristic zero and $ZF_*(k)$ is the category ... More

Arithmetic and intermediate Jacobians of some rigid Calabi-Yau threefoldsFeb 10 2015Jun 12 2015We construct Calabi-Yau threefolds defined over $\mathbb{Q}$ via quotients of abelian threefolds, and re-verify the rigid Calabi-Yau threefolds in this construction are modular by computing their L-series, without \cite{Dieulefait} or \cite{GouveaYui}. ... More

An infinite server system with general packing constraintsMay 18 2012Jun 01 2012We consider a service system model primarily motivated by the problem of efficient assignment of virtual machines to physical host machines in a network cloud, so that the number of occupied hosts is minimized. There are multiple input flows of different ... More

No interesting sequential groupsApr 29 2016We prove that it is consistent with ZFC that no sequential topological groups of intermediate sequential orders exist. This shows that the answer to a 1981 question of P.~Nyikos is independent of the standard axioms of set theory. The model constructed ... More

Hilbert spaces with generic groups of automorphismsNov 28 2004Let G be a countable group. We proof that there is a model companion for the approximate theory of a Hilbert space with a group G of automorphisms. We show that G is amenable if and only if the structure induced by countable copies of the regular representation ... More

Branes and integrability in the N=2 SUSY YM theoryDec 26 1996Sep 05 1997We suggest the brane interpretation of the integrable dynamics behind the exact solution to the N=2 SUSY YM theory. Degrees of freedom of the Calogero type integrable system responsible for the appearance of the spectral Riemann surfaces originate from ... More

On equivalence of thinning fluids used for hydraulic fracturingAug 09 2012The paper aims to answer the question: if and how non-Newtonian fluids may be compared in their mechanical action when used for hydraulic fracturing? By employing the modified formulation of the PKN problem we obtain its simple analytical solutions in ... More

Dynamical canonical systems and their explicit solutionsMar 29 2016Apr 20 2016Dynamical canonical systems and their connections with the classical (spectral) canonical systems are considered. We construct B\"acklund-Darboux transformation and explicit solutions of the dynamical canonical systems. We study also those properties ... More

Sine-Gordon theory in a semi-stripJan 23 2010Initial-boundary value problems for complex sine-Gordon and sine-Gordon equations in a semi--strip are treated. The evolution of the Weyl function and a uniqueness result are obtained for complex sine-Gordon equation. The evolution of the Weyl function ... More

Discrete canonical system and non-Abelian Toda lattice: Backlund-Darboux transformation and Weyl functionsNov 02 2003Jan 31 2004A version of the iterated B\"acklund-Darboux transformation, where Darboux matrix takes a form of the transfer matrix function from the system theory, is constructed for the discrete canonical system and Non-Abelian Toda lattice. Results on the transformations ... More

Perturbative Heavy Quark Fragmentation Function through O(α_s^2): Gluon Initiated ContributionOct 14 2004Jul 07 2005We derive the gluon initiated contribution to the initial condition for the perturbative fragmentation function of a heavy quark through order O(\alpha_s^2) in the MS-bar scheme. This result is needed for the resummation with next-to-next-to-leading logarithmic ... More

Recent theoretical progress in top quark pair production at hadron collidersMar 05 2013This is a writeup of a plenary talk given at the conference {\it HCP 2012} held November 2012 in Kyoto, Japan. This writeup reviews recent theoretical developments in the following areas of top quark physics at hadron colliders: (a) the forward-backward ... More

Extended Itô calculus for symmetric Markov processesNov 22 2012Chen, Fitzsimmons, Kuwae and Zhang (Ann. Probab. 36 (2008) 931-970) have established an Ito formula consisting in the development of F(u(X)) for a symmetric Markov process X, a function u in the Dirichlet space of X and any $\mathcal{C}^2$-function F. ... More

Stochastic integration with respect to additive functionals of zero quadratic variationDec 06 2011Dec 17 2013We consider a Markov process $X$ associated to a nonnecessarily symmetric Dirichlet form $\mathcal{E}$. We define a stochastic integral with respect to a class of additive functionals of zero quadratic variation and then we obtain an It\^{o} formula for ... More

Stellar spindown: From the ONC to the SunOct 07 2008Rotation is a key parameter in the evolution of stars. From 1 Myr (the age of the ONC) to 4.5 Gyr (the age of the Sun), solar-like stars lose about 1-2 orders of specific angular momentum. The main agents for this rotational braking are believed to be ... More

Single solenoidal magnetic system for Iron-free detectorJul 23 2015We consider a single solenoidal system for possible usage in Iron-free detectors for future linear colliders

Constructive description of Hardy-Sobolev spaces in $\mathbb{C}^n$Jan 13 2016Nov 09 2016In this paper we study the polynomial approximations in Hardy-Sobolev spaces on for convex domains. We use the method of pseudoanalytical continuation to obtain the characterization of these spaces in terms of polynomial approximations.

Gravitational strings beyond quantum theory: Electron as a closed heterotic stringSep 18 2011Mar 12 2012The observable parameters of the electron indicate unambiguously that its gravitational background should be the Kerr-Newman solution without horizons. This background is not flat and has a non-trivial topology created by the Kerr singular ring. This ... More

Kerr-Schild Photonlike Metric SolutionsApr 24 2007Mar 20 2008The charged and spinning lightlike solutions are obtained in the Kerr-Schild formalism. In particular, one of them may be considered as an ultrarelativistic boost of the Kerr-Newman solution along the direction of angular momentum. The Kerr singular ring ... More

Wonderful Consequences of the Kerr TheoremJun 01 2005Oct 18 2005Kerr's multi-particle solution is obtained on the base of the Kerr theorem. Choosing generating function of the Kerr theorem $F$ as a product of partial functions $F_i$ for spinning particles i=1,...k, we obtain a multi-sheeted, multi-twistorial space-time ... More

Complex Structure of Kerr Geometry and Rotating `Photon Rocket' SolutionsOct 03 2002Jan 31 2003In the frame of the Kerr-Schild approach, we obtain a generalization of the Kerr solution to a nonstationary case corresponding to a rotating source moving with arbitrary acceleration. Similar to the Kerr solution, the solutions obtained have the geodesic ... More

Superconducting Source of the Kerr-Newman ElectronOct 28 2009Nov 08 2009Regular superconducting solution for interior of the Kerr-Newman (KN) spinning particle is obtained. For parameters of electron it represents a highly oblated rotating bubble formed by Higgs field which expels the electromagnetic (em) field and currents ... More

The Kerr Theorem, Multisheeted Twistor Spaces and Multiparticle Kerr-Schild SolutionsDec 29 2006Kerr-Schild formalism is generalized by incorporation of the Kerr Theorem with polynomials of higher degrees in $Y\in CP^1.$ It leads to multisheeted twistor spaces and multiparticle solutions.

Axial Stringy System of the Kerr Spinning ParticleMar 22 2004Mar 31 2004The structure of classical spinning particle based on the Kerr-Newman black hole (BH) solution is investigated. For large angular momentum, $|a|>>m$, the BH horizons disappear exposing a naked ringlike source which is a circular relativistic string. It ... More

Supersymmetric Bag Model as a Development of the Witten Superconducting StringOct 01 2001Nov 27 2001We consider particlelike solutions to supergravity based on the Kerr-Newman BH solution. The BH singularity is regularized by means of a phase transition to a new superconducting vacuum state near the core region. We show that this phase transition can ... More