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Lattice-induced photon scattering in an optical lattice clockFeb 08 2018We investigate scattering of lattice laser radiation in a strontium optical lattice clock and its implications for operating clocks at interrogation times up to several ten seconds. Rayleigh scattering does not cause significant decoherence of the atomic ... More

Low-Noise YBa$_2$Cu$_3$O$_7$ NanoSQUIDs for Performing Magnetization-Reversal Measurements on Magnetic NanoparticlesMar 20 2015We fabricated YBa$_2$Cu$_3$O$_7$ (YBCO) direct current (dc) nano superconducting quantum interference devices (nanoSQUIDs) based on grain boundary Josephson junctions by focused ion beam patterning. Characterization of electric transport and noise properties ... More

Brill-Noether theory for cyclic coversMar 16 2016The Brill-Noether Theorem gives necessary and sufficient conditions for the existence of a linear series. Here we consider a general n-fold, etale cyclic cover p of a curve C of genus g and investigate for which numbers r,d a linear series of dimension ... More

Hilbert series of nearly holomorphic sections on generalized flag manifoldsMar 12 2014Apr 09 2014Let X=G/P be a complex flag manifold and E->X be a G-homogeneous holomorphic vector bundle. Fix a U-invariant Kaehler metric on X with U in G maximal compact. We study the sheaf of nearly holomorphic sections and show that the space of global nearly holomorphic ... More

A-model and generalized Chern-Simons theoryJan 16 2005Jan 30 2005The relation between open topological strings and Chern-Simons theory was discovered by E. Witten. He proved that A-model on T*M where M is a three-dimensional manifold is equivalent to Chern-Simons theory on M and that A-model on arbitrary Calabi-Yau ... More

Gauge theories on noncommutative spacesNov 29 2000I review my results about noncommutative gauge theories and about the relation of these theories to M(atrix) theory following my lecture on ICMP 2000.

Symmetry transformations in Batalin-Vilkovisky formalismOct 19 1993This short note is closely related to Sen-Zwiebach paper on gauge transformations in Batalin-Vilkovisky theory (hep-th 9309027). We formulate some conditions of physical equivalence of solutions to the quantum master equation and use these conditions ... More

Equivalences for Morse homologyMay 25 1999An explicit isomorphism between Morse homology and singular homology is constructed via the technique of pseudo-cycles. Given a Morse cycle as a formal sum of critical points of a Morse function, the unstable manifolds for the negative gradient flow are ... More

Normalizers of solvable spherical subgroupsJul 26 2011Jun 18 2012For an arbitrary connected solvable spherical subgroup H of a connected semisimple algebraic group G we compute the group N_G(H), the normalizer of H in G. Thereby we complete a classification of all (not necessarily connected) solvable spherical subgroups ... More

On solvable spherical subgroups of semisimple algebraic groups (report version)Jun 23 2010Nov 26 2010A new approach to classification of solvable spherical subgroups of semisimple algebraic groups is considered. This approach is completely different from the known approach by D. Luna and provides an explicit classification.

Homological Invariants and Quasi-IsometryDec 05 2003Oct 18 2004Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated to a topological coupling. As an application we obtain estimates of the (co)homological dimension of groups G and H, where ... More

An infinite-dimensional generalization of Zenger's lemmaNov 11 2011We prove an infinite-dimensional generalization of Zenger's lemma that was used in the proof of the fact that the convex hull of the point spectrum of a linear operator is contained in its numerical range. Two relevant examples are given, and possible ... More

Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potentialSep 29 2004For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background ... More

Weighted Radon transforms for which the Chang approximate inversion formula is preciseJan 10 2011Jan 17 2011We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given.

On semi-infinite cohomology of finite dimensional algebrasMay 15 2000Nov 03 2000We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups at a root of ... More

Amenable covers, volume and L2-Betti numbers of aspherical manifoldsMay 23 2006Jun 30 2008We provide a proof for an inequality between volume and L2-Betti numbers of aspherical manifolds for which Gromov outlined a strategy based on general ideas of Connes. The implementation of that strategy involves measured equivalence relations, Gaboriau's ... More

Realistic collapse model of bosonic stringsJun 05 2012Jun 07 2012In this paper we will utilize the non-trivial shapes of the strings in order to come up with realistic definition of probability amplitudes in a lot more natural way than could be done in point particle counterpart. We then go on to "translate" GRW model ... More

Can Bohmian particle be a source of "continuous collapse" in GRW-type theoriesMar 15 2011The purpose of this paper is to unite Pilot Wave model with GRW ideas through a proposal that Bohmian particle serves as a source of continuous collapse. The continuous trajectory of a particle allows the particle-centered collapse mechanism to be continuous ... More

Can gravity be added to Pilot Wave models?Sep 30 2010The purpose of this paper is to come up with one of the many possible schemes of "adding" gravity to Pilot Wave models.

Completely local interpretation of quantum field theoryApr 16 2010Sep 05 2010The purpose of this paper is to come up with a framework that "converts" existing concepts from configuration space to ordinary one. This is done by modeling our universe as a big "computer" that simulates configuration space. If that "computer" exists ... More

Extremal graphs for clique-pathsNov 30 2011In this paper we deal with a Tur\'an-type problem: given a positive integer n and a forbidden graph H, how many edges can there be in a graph on n vertices without a subgraph H? How does a graph look like if it has this extremal edge number? The forbidden ... More

A Field Guide to Recent Work on the Foundations of Statistical MechanicsApr 02 2008This is an extensive review of recent work on the foundations of statistical mechanics. Subject matters discussed include: interpretation of probability, typicality, recurrence, reversibility, ergodicity, mixing, coarse graining, past hypothesis, reductionism, ... More

Multivariate discrete copulas, with applications in probabilistic weather forecastingDec 17 2015In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. We introduce the concept of multivariate discrete copulas, discuss their equivalence to stochastic arrays, ... More

On One Function Defined on the Cartesian Product and Guinness NumbersSep 03 2013New numbers, called Guinness numbers, are introduced using certain function of natural argument. Few problems related to these numbers are formulated.

Mensky's path integral and photon massJul 19 2013Aug 10 2016It is commonly assumed that zero and non-zero photon mass would lead to qualitatively different physics. For example, massless photon has two polarization degrees of freedom, while massive photon at least three. This feature seems counter-intuitive. In ... More

Multiplicative orders of elements in Conway towers of finite fieldsSep 07 2015We give a lower bound on multiplicative orders of some elements in defined by Conway towers of finite fields of characteristic two and also formulate a condition under that these elements are primitive

On a multiplicative order of Gauss periods and related questionsAug 05 2010Dec 19 2010We obtain explicit lower bounds on multiplicative order of elements that have more general form than finite field Gauss period. In a partial case of Gauss period this bound improves the previous bound of O.Ahmadi, I.E.Shparlinski and J.F.Voloch

A Note on the Area Requirement of Euclidean Greedy Embeddings of Christmas Cactus GraphsMay 30 2016An Euclidean greedy embedding of a graph is a straight-line embedding in the plane, such that for every pair of vertices $s$ and $t$, the vertex $s$ has a neighbor $v$ with smaller distance to $t$ than $s$. This drawing style is motivated by greedy geometric ... More

On an inequality of different metrics for algebraic polynomialsJun 20 2016We establish an inequality of different metrics for algebraic polynomials.

Invariant subspaces for operator semigroups with commutators of rank at most oneMar 31 2009Let X be a complex Banach space of dimension at least 2, and let S be a multiplicative semigroup of operators on X such that the rank of AB - BA is at most 1 for all pairs {A,B} in S. We prove that S has a non-trivial invariant subspace provided it is ... More

On continuity of correspondences of probability measures in the category of Tychonov spacesFeb 23 2005We consider the correspondence assigning to every Radon measure on two Tychonoff coordinate spaces the set of probability measures with these marginals. It is proved that this correspondence is continuous.

Security and Privacy in Future Internet Architectures - Benefits and Challenges of Content Centric NetworksJan 06 2016Jan 13 2016As the shortcomings of our current Internet become more and more obvious, researchers have started creating alternative approaches for the Internet of the future. Their design goals are mainly content-orientation, security, support for mobility and cloud ... More

Fantasy Football PredictionMay 26 2015The ubiquity of professional sports and specifically the NFL have lead to an increase in popularity for Fantasy Football. Users have many tools at their disposal: statistics, predictions, rankings of experts and even recommendations of peers. There are ... More

Nonlinear propagation of planet-generated tidal wavesOct 22 2001The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to the shock formation and wake dissipation, is followed in the weakly nonlinear regime. The local approach of Goodman ... More

Reversible Denoising and Lifting Based Color Component Transformation for Lossless Image CompressionAug 25 2015Apr 06 2016An undesirable side effect of reversible color space transformation, which consists of lifting steps, is that while removing correlation it contaminates transformed components with noise from other components. To remove correlation without increasing ... More

Dunkl harmonic analysis and fundamental sets of continuous functions on the unit sphereFeb 15 2016We establish a necessary and sufficient condition on a continuous function on $[-1,1]$ under which the family of functions on the unit sphere $\mathbb{S}^{d-1}$ constructed in the described manner is fundamental in $C(\mathbb{S}^{d-1})$. In our construction ... More

Covering dimension using toric varietiesJul 12 2013In this paper we deduce the Lebesgue and the Knaster--Kuratowski--Mazurkiewicz theorems on the covering dimension, as well as their certain generalizations, from some simple facts of toric geometry. This provides a new point of view on this circle of ... More

On non-overdetermined inverse scattering at zero energy in three dimensionsMay 31 2006We develop the d-bar -approach to inverse scattering at zero energy in dimensions d>=3 of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability ... More

Absence of exponentially localized solitons for the Novikov-Veselov equation at positive energyOct 05 2010Jan 24 2011In this note we show that the Novikov-Veselov equation at positive energy (an analog of KdV in 2+1 dimensions) has no exponentially localized solitons ( in the two-dimensional sense).

Understanding Gravitational Clustering with Non-Linear Perturbation TheoryFeb 21 1997I discuss new results concerning the evolution of the bispectrum due to gravitational instability from gaussian initial conditions using one-loop perturbation theory (PT). Particular attention is paid to the transition from weakly non-linear scales to ... More

Large-Scale Structure in Brane-Induced Gravity I. Perturbation TheoryJun 24 2009Jul 19 2009We study the growth of subhorizon perturbations in brane-induced gravity using perturbation theory. We solve for the linear evolution of perturbations taking advantage of the symmetry under gauge transformations along the extra-dimension to decouple the ... More

Cosmological Perturbations: Entering the Non-Linear RegimeDec 21 1996We consider one-loop corrections to the bispectrum and skewness of cosmological density fluctuations induced by gravitational evolution. As has been established by comparison with numerical simulations, tree-level perturbation theory (PT) describes these ... More

Canonical bases for sl(2,C)-modules of spherical monogenics in dimension 3Mar 29 2010Jun 17 2010Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as sl(2,C)-modules. As finite-dimensional irreducible sl(2,C)-modules, they have canonical bases which are, by construction, orthogonal. In this note, we show that these ... More

Conservation laws of semidiscrete canonical Hamiltonian equationsFeb 25 2004There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs. The same result holds for semidiscrete Hamiltonian ... More

Pilot Wave model that includes creation and annihilation of particlesNov 12 2010Nov 16 2010The purpose of this paper is to come up with a Pilot Wave model of quantum field theory that incorporates particle creation and annihilation without sacrificing determinism. This has been previously attempted in an article by the same author titled "Incorporating ... More

Spinor fields in Causal Set TheoryAug 21 2008The goal of this paper is to define fermionic fields on causal set. This is done by the use of holonomies to define vierbines, and then defining spinor fields by taking advantage of the leftover degrees of freedom of holonomies plus additional scalar ... More

Universal geometric entanglement close to quantum phase transitionsNov 16 2007Mar 24 2008Under successive Renormalization Group transformations applied to a quantum state $\ket{\Psi}$ of finite correlation length $\xi$, there is typically a loss of entanglement after each iteration. How good it is then to replace $\ket{\Psi}$ by a product ... More

On rational approximations of algebraic numbers of higher orders and certain parametrization for generalized Pell's equationsMar 29 2011A new algebraic object is introduced - recurrent fractions, which is an n-dimensional generalization of continued fractions. It is used to describe an algorithm for rational approximations of algebraic irrational numbers. Some parametrization for generalized ... More

On the solutions of generalized discrete Poisson equationJun 19 2007The set of common numerical and analytical problems is introduced in the form of the generalized multidimensional discrete Poisson equation. It is shown that its solutions with square-summable discrete derivatives are unique up to a constant. The proof ... More

Proving Craig and Lyndon Interpolation Using Labelled Sequent CalculiJan 21 2016We have recently presented a general method of proving the fundamental logical properties of Craig and Lyndon Interpolation (IPs) by induction on derivations in a wide class of internal sequent calculi, including sequents, hypersequents, and nested sequents. ... More

Falsification or Confirmation: From Logic to PsychologyOct 30 2015Corroboration or confirmation is a prominent philosophical debate of the 20th century. Many philosophers have been involved in this debate most notably the proponents of confirmation led by Hempel and its most powerful criticism by the falsificationists ... More

A Model Structure On The Category Of Small Acyclic CategoriesAug 05 2015In this paper, we show that the Thomason model structure restricts to a Quillen equivalent cofibrantly generated model structure on the category of acyclic categories, whose generating cofibrations are the same as those generating the Thomason model structure. ... More

Formulas for phase recovering from phaseless scattering data at fixed frequencyFeb 08 2015Feb 14 2015We consider quantum and acoustic wave propagation at fixed frequency for compactly supported scatterers in dimension $d\ge 2$. In these framework we give explicit formulas for phase recovering from appropriate phaseless scattering data. As a corollary, ... More

Explicit formulas and global uniqueness for phaseless inverse scattering in multidimensionsDec 16 2014We consider phaseless inverse scattering for the Schr\"odinger equation with compactly supported potential in dimension $d\ge 2$. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we give also a ... More

Expressing QFT in terms of QM with single extra dimension and classical hidden variable fieldSep 12 2013Oct 30 2015The goal of this paper is to re-express QFT in terms of two "classical" fields living in ordinary space with single extra dimension. The role of the first classical field is to set up an injection from the set of values of extra dimension into the set ... More

Strongly solvable spherical subgroups and their combinatorial invariantsDec 13 2012Mar 26 2015A subgroup H of an algebraic group G is said to be strongly solvable if H is contained in a Borel subgroup of G. This paper is devoted to establishing relationships between the following three combinatorial classifications of strongly solvable spherical ... More

Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spacesNov 03 2011Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly described for the spaces of k-homogeneous polynomial solutions of the Hodge-de Rham system in the Euclidean space R^m which take values in the space of s-vectors. In this ... More

The Fischer Decomposition for the H-action and Its ApplicationsFeb 02 2010Recently the Fischer decomposition for the H-action of the Pin group on Clifford algebra valued polynomials has been obtained. We apply this tool to get various decompositions of special monogenic and inframonogenic polynomials in terms of two sided monogenic ... More

On the sharpness of one inequality of different metrics for algebraic polynomialsJul 05 2016We prove that the previously established inequality of different metrics for algebraic polynomials is sharp in the sense of order.

Second order variational problem and 2-dimensional concircular geometryJul 23 2014Apr 22 2016It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description is proved. A ... More

Finite speed of propagation for the thin film equation in spherical geometryFeb 06 2018We show that a double degenerate thin film equation, which originated from modeling of viscous coating flow on a spherical surface, has finite speed of propagation for nonnegative strong solutions and hence there exists an interface or free boundary separating ... More

A study of energy concentration and drain in incompressible fluidsMay 07 2012May 22 2012In this paper we examine two opposite scenarios of energy behavior for solutions of the Euler equation. We show that if $u$ is a regular solution on a time interval $[0,T)$ and if $u \in L^rL^\infty$ for some $r\geq \frac{2}{N}+1$, where $N$ is the dimension ... More

On tensor categories attached to cells in affine Weyl groupsOct 10 2000Dec 31 2011We prove a conjecture by Lusztig, which describes the tensor categories of perverse sheaves on affine flag manifolds, with tensor structure provided by truncated convolution, in terms of the Langlands dual group. We also give a geometric (categorical) ... More

Koszul Property and Frobenius Splitting of Schubert VarietiesFeb 20 1995We show how the Frobenius splitting method of Mehta-Ramanathan implies the Koszul property of projective coordinate rings of Schubert varieties.

On iterative reconstruction in the nonlinearized polarization tomographyApr 16 2009We give uniqueness theorem and reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomography data. We assume that the medium has uniform background parameters ... More

An effectivization of the global reconstruction in the Gel'fand-Calderon inverse problem in three dimensionsOct 20 2008By developing the d-bar approach to global "inverse scattering" at zero energy we give a principal effectivization of the global reconstruction method for the Gel'fand-Calderon inverse boundary value problem in three dimensions. This work goes back to ... More

On stable determination of potential by boundary measurementsDec 06 2007We give new stability estimates for the Gel'fand-Calderon inverse boundary value problem

New global stability estimates for the Gel'fand-Calderon inverse problemJan 31 2010Aug 06 2010We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D. For sufficiently regular potentials this result of the present work is a principal improvement of the result of [G. Alessandrini, Stable determination of conductivity ... More

The d-bar approach to approximate inverse scattering at fixed energy in three dimensionsMay 10 2005We develop the d-bar approach to inverse scattering at fixed energy in dimensions $d\ge 3$ of [Beals, Coifman 1985] and [Henkin, Novikov 1987]. As a result we propose a stable method for nonlinear approximate finding a potential $v$ from its scattering ... More

Transients from Initial Conditions: A Perturbative AnalysisNov 17 1997The standard procedure to generate initial conditions (IC) in numerical simulations is to use the Zel'dovich approximation (ZA). Although the ZA correctly reproduces the linear growing modes of density and velocity perturbations, non-linear growth is ... More

Redshift-Space Distortions, Pairwise Velocities and NonlinearitiesJul 12 2004Aug 02 2004We derive the exact relationship, including all non-linearities, between real-space and redshift-space two-point statistics through the pairwise velocity distribution function. We show using numerical simulations that the pairwise velocity PDF is strongly ... More

Homogeneous solutions to the 3D Euler systemOct 12 2015We study stationary homogeneous solutions to the 3D Euler equation. The problem is motivated be recent exclusions of self-similar blowup for Euler and its relation to Onsager conjecture and intermittency. We reveal several new classes of solutions and ... More

Superluminality in dilatationally invariant generalized Galileon theoriesJul 31 2015Mar 25 2016We consider small perturbations about homogeneous backgrounds in dilatationally-invariant Galileon models. The issues we address are stability (absence of ghosts and gradient instabilities) and superluminality. We show that in Minkowski background, it ... More

Fast Estimators for Redshift-Space ClusteringJun 08 2015Jul 18 2015Redshift-space distortions in galaxy surveys happen along the radial direction, breaking statistical translation invariance. We construct estimators for radial distortions that, using only Fast Fourier Transforms (FFTs) of the overdensity field multipoles ... More

Phaseless inverse scattering in the one-dimensional caseMar 07 2015We consider the one-dimensional Schr\"odinger equation with a potential satisfying the standard assumptions of the inverse scattering theory and supported on the half-line $x\ge 0$. For this equation at fixed positive energy we give explicit formulas ... More

On transfinite nilpotence of the Vogel-Levine localizationJun 10 2014We construct a finitely-presented group such that its Vogel-Levine localization is not transfinitely nilpotent. This answers a problem of J. P. Levine.

Ensemble Copula Coupling as a Multivariate Discrete Copula ApproachMay 15 2013May 24 2013In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. In this paper, we introduce the concept of multivariate discrete copulas, discuss their equivalence ... More

Bijective mapping preserving intersecting antichains for k-valued cubesNov 30 2011Generalizing a result of Miyakawa, Nozaki, Pogosyan and Rosenberg, we prove that there is a one-to-one correspondence between the set of intersecting antichains in a subset of the lower half of the k-valued n-cube and the set of intersecting antichains ... More

Squeezed states of light and their applications in laser interferometersNov 12 2016According to quantum theory the interactions between physical systems are quantized. As a direct consequence, measurement sensitivities are fundamentally limited by quantization noise, or just `quantum noise' in short. Furthermore, Heisenberg's Uncertainty ... More

Space-time discretization of the heat equation. A concise Matlab implementationDec 25 2012Sep 25 2013A concise Matlab implementation of a stable parallelizable space-time Petrov-Galerkin discretization for parabolic evolution equations is given. Emphasis is on reusability of spatial finite element codes.

A note on Lagrangian cobordisms between Legendrian submanifolds of R^{2n+1}Aug 18 2011Sep 27 2012We study the relation of an embedded Lagrangian cobordism between two closed, orientable Legendrian submanifolds of R^{2n+1}. More precisely, we investigate the behavior of the Thurston-Bennequin number and (linearized) Legendrian contact homology under ... More

Triangularizability of trace-class operators with increasing spectrumAug 31 2015For any measurable set $E$ of a measure space $(X, \mu)$, let $P_E$ be the (orthogonal) projection on the Hilbert space $L^2(X, \mu)$ with the range $ran \, P_E = \{f \in L^2(X, \mu) : f = 0 \ \ a.e. \ on \ E^c\}$ that is called a standard subspace of ... More

Once More on Positive CommutatorsNov 05 2012Let A and B be bounded operators on a Banach lattice E such that the commutator C=AB-BA and the product BA are positive operators. If the product AB is a power-compact operator, then C is a quasi-nilpotent operator having a triangularizing chain of closed ... More

Open-multicommutativity of some functors related to the functor of probability measuresSep 28 2004The property of a normal functor to be open-multicommutative proposed by Kozhan and Zarichnyi (2004) is investigated. A number of normal functors related to the functor of probability measures and equipped with convex structure are considered here and ... More

Open-multicommutativity of the functor of upper-continuous capacitiesOct 23 2006The notion of open-multicommutativity, introduced by Kozhan and Zarichnyi (2005), is investigated. The weakly normal covariant functor of upper-continuous capacities is considered. The main result of the paper is that this functor open-multicommutative. ... More

Solutions to a Quantal Gravity-Matter Field Theory on a LineDec 18 1996Solutions to a scalar-tensor (dilaton) quantum gravity theory, interacting with quantized matter, are described. Dirac quantization is frustrated by quantal anomalies in the constraint algebra. Progress is made only after the Wheeler--DeWitt equation ... More

Gauge Theories in the Momentum/Curvature RepresentationApr 08 1996The gauge variance of wave functionals for a gauge theory quantized in the momentum (curvature) representation is described. It is shown that a gauge transformation gives rise to a cocycle, which for theories in two space-time dimensions is related to ... More

The Unreasonable Effectiveness of Quantum Field TheoryFeb 22 1996Quantum field theory offers physicists a tremendously wide range of application; it is both a language with which a vast variety of physical processes can be discussed and also it provides a model for fundamental physics, the so-called ``standard-model,'' ... More

Precision jet measurements at HERA and determination of α_sDec 21 2011Jan 12 2012The status is reviewed of recent high precision measurements of inclusive-jet, dijet and trijet production in deep-inelastic scattering and photoproduction by the HERA experiments H1 and ZEUS. The measurements are in good agreement with perturbative QCD ... More

Propagation Effects in Magnetized Transrelativistic PlasmasAug 29 2008The transfer of polarized radiation in magnetized and non-magnetized relativistic plasmas is an area of research with numerous flaws and gaps. The present paper is aimed at filling some gaps and eliminating the flaws. Starting from a Trubnikov's linear ... More

$\infty$-Open-multicommutativity in the category $\comp$Feb 23 2005In this paper the notion of $\infty$-open-multicommutativity of functors in the category of compact Hausdorff spaces is considered. This property is a generalization of the open-multicommutativity on the case of infinite diagrams. It is proved that every ... More

Factory of realities: on the emergence of virtual spatiotemporal structuresNov 30 2016The ubiquitous nature of modern Information Retrieval and Virtual World give rise to new realities. To what extent are these "realities" real? Which "physics" should be applied to quantitatively describe them? In this essay I dwell on few examples. The ... More

When powers of a matrix coincide with its Hadamard powersSep 01 2015We characterize matrices whose powers coincide with their Hadamard powers.

Additive habit formation: Consumption in incomplete markets with random endowmentsJun 15 2011Sep 23 2011We provide a detailed characterization of the optimal consumption stream for the additive habit-forming utility maximization problem, in a framework of general discrete-time incomplete markets and random endowments. This characterization allows us to ... More

A similarity-based implementation of the Schaake shuffleJul 08 2015Contemporary weather forecasts are typically based on ensemble prediction systems, which consist of multiple runs of numerical weather prediction models that vary with respect to in the initial conditions and/or the the parameterization of the atmosphere. ... More

The tie theoremsNov 15 2014Nov 29 2014Theorem. There are general position points A, B, C, P on the projective plane. Let A_P be the intersection point of lines AP and BC. Analogously define B_P and C_P. Take any points A_1, B_1, C_1 on AP, BP, CP, respectively. Let W_C be the intersection ... More

Quantum State Tomography of a Single Qubit: Comparison of MethodsJul 17 2014Feb 08 2016The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical density matrix ... More

A one-relator group with long lower central seriesJun 10 2014A one-relator group with lower central series of length \omega^2 is constructed. This answers a problem of G. Baumslag.

Endpoint symmetries of helicity amplitudesSep 30 2013We investigate helicity amplitudes (HAs) of $A \to B C$-type decays for arbitrary spin towards the kinematic endpoint. We show that they are proportional to product of Clebsch-Gordan coefficients (CGC) and the velocity to some positive power. The latter ... More

Additive habits with power utility: Estimates, asymptotics and equilibriumAug 14 2011We consider a power utility maximization problem with additive habits in a framework of discrete-time markets and random endowments. For certain classes of incomplete markets, we establish estimates for the optimal consumption stream in terms of the aggregate ... More