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The sum of log-normal variates in geometric Brownian motionFeb 08 2018Geometric Brownian motion (GBM) is a key model for representing self-reproducing entities. Self-reproduction may be considered the definition of life [5], and the dynamics it induces are of interest to those concerned with living systems from biology ... More

Rational insurance with linear utility and perfect informationJul 16 2015We present a mathematical solution to the insurance puzzle. Our solution only uses time-average growth rates and makes no reference to risk preferences. The insurance puzzle is this: according to the expectation value of wealth, buying insurance is only ... More

The evolutionary advantage of cooperationJun 10 2015The present study asks how cooperation and consequently structure can emerge in many different evolutionary contexts. Cooperation, here, is a persistent behavioural pattern of individual entities pooling and sharing resources. Examples are: individual ... More

Stochastic Market EfficiencyJan 24 2011It is argued that the simple trading strategy of leveraging or deleveraging an investment in the market portfolio cannot outperform the market. Such stochastic market efficiency places strong constraints on the possible stochastic properties of the market. ... More

Far from equilibrium: Wealth reallocation in the United StatesMay 18 2016Studies of wealth inequality often assume that an observed wealth distribution reflects a system in equilibrium. This constraint is rarely tested empirically. We introduce a simple model that allows equilibrium but does not assume it. To geometric Brownian ... More

A Discontinuous Galerkin - Front Tracking Scheme and its Optimal$^2$ Error EstimationDec 09 2013In [11] and [5], an error estimate of optimal convergence rates and optimal error propagation (optimal^2) was given for the Runge-Kutta discontinuous Galerkin (RKDG) method solving the scalar nonlinear conservation laws in the case of smooth solutions. ... 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

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

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

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

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

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

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

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

Homological projective duality for quadricsFeb 26 2019Mar 01 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 2019Mar 01 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

Bayesian design of experiments for generalised linear models and dimensional analysis with industrial and scientific applicationJun 19 2016Oct 26 2016The design of an experiment can be always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the explanatory variables ... 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

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

Concepts and evolution of research in the field of wireless sensor networksFeb 12 2015May 13 2015The field of Wireless Sensor Networks (WSNs) is experiencing a resurgence of interest and a continuous evolution in the scientific and industrial community. The use of this particular type of ad hoc network is becoming increasingly important in many contexts, ... More

The Bernoulli sieve: an overviewMay 31 2010The Bernoulli sieve is a version of the classical balls-in-boxes occupancy scheme, in which random frequencies of infinitely many boxes are produced by a multiplicative random walk, also known as the residual allocation model or stick-breaking. We give ... More

Bayesian design of experiments for generalised linear models and dimensional analysis with industrial and scientific applicationJun 19 2016Sep 02 2016The design of an experiment can be always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the explanatory variables ... 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

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.

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

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 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

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

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

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

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

Meromorphic Solutions to a Differential--Difference Equation Describing Certain Self-Similar PotentialsMar 23 2001In this paper we prove the existence of meromorphic solutions to a nonlinear differential difference equation that describe certain self-similar potentials for the Schroedinger operator.

Note on Malmstèn's paper De Integralibus quibusdam definitis seriebusque infinitisJun 16 2013We present a proof of the functional equation of the Riemann zeta-function or more precisely the Dirichlet eta-function, which proof seems to be new but follows almost immediately from Malmst\`en's paper ``De integralibus quibusdam definitis seriebusque ... More

Quantization of geometry associated to the quantized Knizhnik-Zamolodchikov equationsJun 05 1996It is known that solutions of the Knizhnik-Zamolodchikov differential equations are given by integrals of closed differential forms over suitable cycles. In this paper a quantization of this geometric construction is described leading to solution of the ... More

Critical set of the master function and characteristic variety of the associated Gauss-Manin differential equationsOct 09 2014Aug 30 2016We consider a weighted family of $n$ parallelly transported hyperplanes in a $k$-dimensioinal affine space and describe the characteristic variety of the Gauss-Manin differential equations for associated hypergeometric integrals. The characteristic variety ... More

Special functions, KZ type equations and Representation theoryMay 29 2002May 29 2002This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without proofs) of ... More

Optimal Compression of a Polyline with Segments and ArcsApr 25 2016May 23 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

Geometry of the high energy limit of differential operators on vector bundlesSep 09 2011At high energies relativistic quantum systems describing scalar particles behave classically. This observation plays an important role in the investigation of eigenfunctions of the Laplace operator on manifolds for large energies and allows to establish ... More

A Pythagoras proof of Szemerédi's regularity lemmaDec 14 2012Dec 21 2012We give a short proof of Szemer\'edi's regularity lemma, based on elementary Euclidean geometry. The general line of the proof is that of the standard proof (in fact, of Szemer\'edi's original proof), but most technicalities are swallowed by applying ... More

Traces of creation-annihilation operators and Fredholm's formulasMar 09 1997Dec 21 1997We prove the formula for the traces of certain class of operators in bosonic and fermionic Fock spaces. Vertex operators belong to this class. Traces of vertex operators can be used for calculation of correlation functions and formfactors of integrable ... More

Nonequilibrium Critical PhenomenaOct 05 2000We discuss the non-equilibrium critical phenomena in liquids, and the models for these phenomena based on local equilibrium and extended scaling assumptions. Special situations are proposed for experimental tests of the theory. Near-critical steady and ... More

On some possible features of motion of a polaron in gyrotropic mediumFeb 20 2014Dec 08 2014We predict the possibility of asymmetric dynamics of polaron in gyrotropic medium and give approximate quantitative estimate of the effect.

Green-Function-Based Monte Carlo Method for Classical Fields Coupled to FermionsApr 20 2009Microscopic models of classical degrees of freedom coupled to non-interacting fermions occur in many different contexts. Prominent examples from solid state physics are descriptions of colossal magnetoresistance manganites and diluted magnetic semiconductors, ... More

The Reeh-Schlieder Property for the Dirac Field on Static SpacetimesNov 17 1999We prove the Reeh-Schlieder property for the ground- and KMS-states states of the massive Dirac Quantum field on a static globally hyperbolic 4 dimensional spacetime.

From Complex to Stochastic Potential: Heavy Quarkonia in the Quark-Gluon PlasmaFeb 25 2013The in-medium physics of heavy quarkonium is an ideal proving ground for our ability to connect knowledge about the fundamental laws of physics to phenomenological predictions. One possible route to take is to attempt a description of heavy quark bound ... More

Improved Maximum Entropy Method with an Extended Search SpaceAug 25 2012We report on an improvement to the implementation of the Maximum Entropy Method (MEM). It amounts to departing from the search space obtained through a singular value decomposition (SVD) of the Kernel. Based on the shape of the SVD basis functions we ... More

On quantum flag algebrasNov 17 1994Let g be a semisimple Lie algebra over an algebraically closed field k of characteristic 0. Let V be a simple finite-dimensional g-module and let y\in V be a highest weight vector. It is a classical result of B. Kostant that the algebra of functions on ... More

Permutohedra, associahedra, and beyondJul 07 2005The volume and the number of lattice points of the permutohedron P_n are given by certain multivariate polynomials that have remarkable combinatorial properties. We give several different formulas for these polynomials. We also study a more general class ... More

Condensates near the Argyres-Douglas point in SU(2) gauge theory with broken N=2 supersymmetrySep 26 2000The behaviour of the chiral condensates in the SU(2) gauge theory with broken N=2 supersymmetry is reviewed. The calculation of monopole, dyon, and charge condensates is described. It is shown that the monopole and charge condensates vanish at the Argyres-Douglas ... More

Integrable many-body problems from the field theoriesOct 29 1994We review recent results which clarify the role of the integrable many-body problems in the quantum field theory framework.They describe the dynamics of the topological degrees of freedom in the theories which are obtained by perturbing the topological ... More

The Heavy Quark Fragmentation Function at NNLOOct 20 2005We present a general discussion of collider processes with not-completely inclusive production of heavy flavors. We review the Perturbative Fragmentation Functions formalism as the appropriate tool for studying such processes and detail the extension ... More

Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutionsOct 11 2007Auxiliary systems for matrix nonisospectral equations, including coupled NLS with external potential and KdV with variable coefficients, were introduced. Explicit solutions of nonisospectral equations were constructed using the GBDT version of the B\"acklund-Darboux ... More

Weyl functions and the boundary value problem for a matrix nonlinear Schrödinger equation on a semi-stripMar 24 2014Rectangular matrix solutions of the defocusing nonlinear Schr\"odinger equation (dNLS) are considered on a semi-strip. Evolution of the corresponding Weyl function is described in terms of the initial-boundary conditions. Then initial condition is recovered ... More

Classifying terminal weighted projective spaceApr 10 2013We present a classification of all weighted projective spaces with at worst terminal or canonical singularities in dimension four. As a corollary we also classify all four-dimensional one-point lattice simplices up to equivalence. Finally, we classify ... More

Light Vector MesonsSep 23 2008Dec 21 2008This article reviews the current status of experimental results obtained in the measurement of light vector mesons produced in proton-proton and heavy ion collisions at different energies. The review is focused on two phenomena related to the light vector ... More

Operations and poly-operations in Algebraic CobordismSep 02 2014Sep 03 2014We describe all operations from a theory A^* obtained from Algebraic Cobordism of M.Levine-F.Morel by change of coefficients to any oriented cohomology theory B^*. We prove that such an operation can be reconstructed out of it's action on the products ... More

Algebraic Cobordism as a module over the Lazard ringAug 30 2014Dec 19 2014In this paper we study the structure of the Algebraic Cobordism ring of a variety as a module over the Lazard ring, and show that it has relations in positive codimensions. We actually prove the stronger graded version. This extends the result of M.Levine-F.Morel ... More

G-convergence and homogenization of viscoelastic flowsJun 07 2007Jun 22 2007The paper is devoted to homogenization of two-phase incompressible viscoelastic flows with disordered microstructure. We study two cases. In the first case, both phases are modeled as Kelvin-Voight viscoelastic materials. In the second case, one phase ... More

Usage of Liquid Metals in the Positron Production System of Linear ColliderNov 11 2015In this publication we collected descriptions of some installations with liquid metals which could be used for high-energy colliders, ILC particularly, for the purposes of targeting, collimation, cooling, collection of secondary particles etc. Some important ... More

S-duality constraints on 1D patterns associated with fractional quantum Hall statesFeb 12 2010Using the modular invariance of the torus, constraints on the 1D patterns are derived that are associated with various fractional quantum Hall ground states, e.g. through the thin torus limit. In the simplest case, these constraints enforce the well known ... More

Cosmic connections: from cosmic rays to gamma rays, to cosmic backgrounds and magnetic fieldsJul 16 2012Combined data from gamma-ray telescopes and cosmic-ray detectors have produced some new surprising insights regarding intergalactic and galactic magnetic fields, as well as extragalactic background light. We review some recent advances, including a theory ... More

Pulsar kicks from neutrino oscillationsSep 21 2004Sep 27 2004Neutrino oscillations in a core-collapse supernova may be responsible for the observed rapid motions of pulsars. Given the present bounds on the neutrino masses, the pulsar kicks require a sterile neutrino with mass 2-20 keV and a small mixing with active ... More

Interactions of ultrahigh-energy neutrinosDec 16 2002Future detection of ultrahigh-energy neutrinos will open a new window on physics at center-of-mass energy 10^5 GeV and higher. In particular, observations of neutrino-initiated showers will help test the Standard Model predictions for the neutrino-nucleon ... More

Cosmology of Q-ballsJan 18 2000Supersymmetric extensions of the Standard Model predict the existence of Q-balls, some of which can be entirely stable. Both stable and unstable Q-balls can play an important role in cosmology. In particular, Affleck-Dine baryogenesis can result in a ... More

Sterile neutrinosMar 12 2007Neutrino masses are usually described by adding to the Standard Model some SU(2)-singlet fermions that have the Yukawa couplings, as well as some Majorana mass terms. The number of such fields and the scales of their Majorana masses are not known. Several ... More

Pulsar kicks and dark matter from a sterile neutrinoApr 26 2004The observed velocities of radio pulsars, which range in the hundreds kilometers per second, and many of which exceed 1000 km/s, are not explained by the standard physics of the supernova explosion. However, if a sterile neutrino with mass in the 1-20 ... More

Spectral and Transport Properties of d-Wave Superconductors With Strong ImpuritiesAug 05 2001One of the remarkable features of disordered d-wave superconductors is strong sensitivity of long range properties to the microscopic realization of the disorder potential. Particularly rich phenomenology is observed for the -- experimentally relevant ... More

Subdiffusion on a Fractal CombAug 31 2011Subdiffusion on a fractal comb is considered. A mechanism of subdiffusion with a transport exponent different from 1/2 is suggested. It is shown that the transport exponent is determined by the fractal geometry of the comb.

Lyapunov exponents in 1d disordered system with long-range memoryFeb 19 2009The Lyapunov exponents for Anderson localization are studied in a one dimensional disordered system. A random Gaussian potential with the power law decay $\sim 1/|x|^q$ of the correlation function is considered. The exponential growth of the moments of ... More

Picture changing operators in supergeometry and superstring theoryJun 04 1997Jun 07 1997Geometrical meaning of superstring pictures is discussed in details. An off-shell generalization of the picture changing operation and its inverse are constructed. It is demonstrated that the generalised operations are inverse to each other on-shell while ... More

Quantum measurements as a control resourceAug 18 2015We discuss the use of back-action of quantum measurements as a resource for controlling quantum systems and review its application to optimal approximation of quantum anti-Zeno effect.

Engineering arbitrary pure and mixed quantum statesOct 08 2012This work addresses a fundamental problem of controllability of open quantum systems, meaning the ability to steer arbitrary initial system density matrix into any final density matrix. We show that under certain general conditions open quantum systems ... More

The multi-time correlation functions, free white noise, and the generalized Poisson statistics in the low density limitJan 22 2007In the present paper the low density limit of the non-chronological multitime correlation functions of boson number type operators is investigated. We prove that the limiting truncated non-chronological correlation can be computed using only a sub-class ... More

MSW effect for large mixing anglesJun 04 2001The traditional physical description of neutrino flavor conversion in the Sun focuses on the notion of resonance. However, the resonance picture is valid only in the limit of small mixing angles theta. For large values of theta, the resonance picture ... More

Source of the Kerr-Newman Solution as a Supersymmetric Domain-Wall Bubble: 50 years of the problemFeb 12 2016We consider the chiral field model of the source of the Kerr-Newman (KN) solution and obtain that it represents a supersymmetric spinning soliton, bounded by the chiral domain wall (DW) of the ellipsoidal form. The known method for transformation of the ... More

Gravitating lepton bag modelApr 30 2015As is known, the gravitational and electromagnetic (EM) field of the Dirac electron is described by an over-extremal Kerr-Newman (KN) black hole (BH) solution which has the naked singular ring and two-sheeted topology. This space is regulated by the formation ... More

Kerr-Newman electron as spinning solitonOct 10 2014Measurable parameters of the electron indicate that its background should be described by the Kerr-Newman (KN) solution. Spin/mass ratio of the electron is extreme large, and the black hole horizons disappear, opening a topological defect of spacetime ... More

Fluctuating Twistor-Beam Solutions and Holographic Pre-Quantum Kerr-Schild GeometryJan 02 2010Jun 02 2010Kerr-Schild (KS) geometry is based on a congruence of twistor null lines which forms a holographic space-time determined by the Kerr theorem. We describe in details integration of the non-stationary Debney-Kerr-Schild equations for electromagnetic excitations ... More

Casimir Energy and Vacua vor Superconducting Ball in SupergravityMay 14 2002Casimir energy for solid conducting ball is considered on the base of some finite models. One model is physical and built of a battery of parallel metallic plates. Two finite models are based on the Higgs model of superconductivity. One of them is supersymmetric ... More