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Bees with attitude: the effect of gusts on flight dynamicsFeb 10 2018Flight is a complicated task at small scales in part due to the ubiquitous unsteady air which contains it. Flying organisms deal with these difficulties using active and passive control mechanisms to steer their body motion. Body attitudes of flapping ... More

Leading-edge vortex shedding from rotating wingsMay 19 2014The paper presents a numerical investigation of the leading-edge vortices generated by rotating triangular wings at Reynolds number $Re=250$. A series of three-dimensional numerical simulations have been carried out using a Fourier pseudo-spectral method ... More

Added costs of insect-scale flapping flight in unsteady airflowsOct 28 2016The aerial environment in the operating domain of small-scale natural and artificial flapping wing fliers is highly complex, unsteady and generally turbulent. Considering flapping flight in an unsteady wind environment with a periodically varying lateral ... More

Adaptive gradient-augmented level set method with multiresolution error estimationJan 28 2014Mar 19 2015A space-time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value multiresolution ... More

FluSI: A novel parallel simulation tool for flapping insect flight using a Fourier method with volume penalizationJun 22 2015Dec 24 2015FluSI, a fully parallel open source software for pseudo-spectral simulations of three-dimensional flapping flight in viscous flows, is presented. It is freely available for non-commercial use under [https://github.com/pseudospectators/FLUSI]. The computational ... More

Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpointMay 31 2012We report the results of a detailed study of the spectral properties of Laplace and Stokes operators, modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, $\eta$, tends to zero. ... More

Analysis and discretization of the volume penalized Laplace operator with Neumann boundary conditionsMar 24 2014Mar 25 2014We study the properties of an approximation of the Laplace operator with Neumann boundary conditions using volume penalization. For the one-dimensional Poisson equation we compute explicitly the exact solution of the penalized equation and quantify the ... More

Bumblebees minimize control challenges by combining active and passive modes in unsteady windsMar 01 2016Mar 02 2016The natural wind environment that volant insects encounter is unsteady and highly complex, posing significant flight control and stability challenges. Unsteady airflows can range from structured chains of discrete vortices shed in the wake of an object ... More

Aerodynamic ground effect in fruitfly sized insect takeoffApr 17 2015Feb 26 2016Aerodynamic ground effect in flapping-wing insect flight is of importance to comparative morphologies and of interest to the micro-air-vehicle (MAV) community. Recent studies, however, show apparently contradictory results of either some significant extra ... More

Metastable states and macroscopic quantum tunneling in a cold atom Josephson ringSep 18 2009We study macroscopic properties of a system of weakly interacting neutral bosons confined in a ring-shaped potential with a Josephson junction. We derive an effective low energy action for this system and evaluate its properties. In particular we find ... More

On Small Gaps in the Length SpectrumFeb 15 2016We discuss upper and lower bounds for the size of gaps in the length spectrum of negatively curved manifolds. For manifolds with algebraic generators for the fundamental group, we establish the existence of exponential lower bounds for the gaps. On the ... More

Coherent phase slips in superconducting nanoringsJul 15 2011We study quantum fluctuations of persistent current in a small superconducting ring. Based on a microscopic model of the ring we argue that under certain conditions such ring will exhibit coherent quantum phase slips, similar to those in a flux qubit. ... More

Kinetics of the Phase Separation Transition in Cold-Atom Boson-Fermion MixturesDec 04 2007Apr 16 2008We study the kinetics of the first order phase separation transition in boson-fermion cold-atom mixtures. At sufficiently low temperatures such a transition is driven by quantum fluctuations responsible for the formation of critical nuclei of a stable ... More

Cold Atom QubitsMay 29 2010Dec 20 2010We discuss a laser-trapped cold-atom superfluid qubit system. Each qubit is proposed as a macroscopic two-state system based on a set of Bose-Einstein condensate (BEC) currents circulating in a ring, cut with a Josephson barrier. We review the effective ... More

Macroscopic two-state systems in trapped atomic condensatesSep 09 2010We consider a macroscopic two-sate system based on persistent current states of a Bose-Einstein condensate (BEC) of interacting neutral atoms confined in a ring with a weak Josephson link. We demonstrate that macroscopic superpositions of different BEC ... More

Quantum Nucleation and Macroscopic Quantum Tunneling in Cold-Atom Boson-Fermion MixturesOct 17 2008Kinetics of phase separation transition in boson-fermion cold atom mixtures is investigated. We identify the parameters at which the transition is governed by quantum nucleation mechanism, responsible for the formation of critical nuclei of a stable phase. ... More

Accurate solution of near-colliding Prony systems via decimation and homotopy continuationDec 31 2014Oct 21 2016We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the system is a-priori ... More

Faster Lightweight Lempel-Ziv ParsingApr 25 2015Jun 08 2015We present an algorithm that computes the Lempel-Ziv decomposition in $O(n(\log\sigma + \log\log n))$ time and $n\log\sigma + \epsilon n$ bits of space, where $\epsilon$ is a constant rational parameter, $n$ is the length of the input string, and $\sigma$ ... More

QCD measurements at the TevatronNov 30 2011Dec 30 2011Selected quantum chromodynamics (QCD) measurements performed at the Fermilab Run II Tevatron ppbar collider running at sqrt{s} = 1.96 TeV by CDF and D0 Collaborations are presented. The inclusive jet, dijet production and three-jet cross section measurements ... More

Sums with convolution of Dirichlet charactersApr 02 2011We improve a recent result by Shparlinski and Banks related to sums with convolution of Dirichlet characters.

Elimination of generalised imaginaries and Galois cohomologyDec 08 2013Nov 12 2014The objective of this article is to characterise elimination of finite generalised imaginaries (as defined by Hrushovski) in terms of group cohomology. As an application, I consider series of Zariski geometries constructed by Hrushovski and Zilber, and ... More

Quantum Predictive Learning and Communication Complexity with Single InputDec 17 2008Mar 15 2012We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate a relational ... More

On the Role of Shared EntanglementApr 08 2006Aug 22 2006Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement analogue" for ... More

A question about Parisi functionalDec 22 2004We conjecture that the Parisi functional in the SK model is convex in the functional order parameter and prove a partial result that shows the convexity along one-sided directions. A consequence of this result is log-convexity of L_1 norm for a class ... More

A central limit theorem for weighted averages of spins in the high temperature region of the Sherrington-Kirkpatrick modelMay 18 2004In this paper we prove that in the high temperature region of the Sherrington-Kirkpatrick model for a typical realization of the disorder the weighted average of spins $\sum_{i\leq N} t_i \sigma_i$ will be approximately Gaussian provided that $\max_{i\leq ... More

The free energy in a multi-species Sherrington-Kirkpatrick modelOct 24 2013Dec 22 2015The authors of [Ann. Henri Poincar\'{e} 16 (2015) 691-708] introduced a multi-species version of the Sherrington-Kirkpatrick model and suggested the analogue of the Parisi formula for the free energy. Using a variant of Guerra's replica symmetry breaking ... More

Parametric Estimation of the Ultimate Size of HypercomputersNov 18 2011The performance of the emerging petaflops-scale supercomputers of the nearest future (hypercomputers) will be governed not only by the clock frequency of the processing nodes or by the width of the system bus, but also by such factors as the overall power ... More

On solutions of the reduced model for the dynamical evolution of contact linesFeb 05 2013We solve the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a hydrodynamic flow at a 180 contact ... More

Survey on global existence in the nonlinear Dirac equations in one dimensionNov 26 2010We consider the nonlinear Dirac equations in one dimension and review various results on global existence of solutions in H1. Depending on the character of the nonlinear terms, existence of the large-norm solutions can be extended for all times. Global ... More

The Baum-Connes conjecture and proper group actions on affine buildingsMar 30 2007We study the possibility of applying a finite-dimensionality argument in order to address parts of the Baum-Connes conjecture for finitely generated linear groups. This gives an alternative approach to the results of Guentner, Higson, and Weinberger concerning ... More

Enumeration of uni-singular algebraic hypersurfacesMay 18 2005Apr 21 2009We enumerate complex algebraic hypersurfaces in $P^n$, of a given (high) degree with one singular point of a given singularity type. Our approach is to compute the (co)homology classes of the corresponding equi-singular strata in the parameter space of ... More

The Delsarte Method in the Problem of the Antipodal Contact Numbers of Euclidean Spaces of High DimensionsJun 28 2003We study the Delsarte problem for even functions continuous on [-1,1], nonpositive on [-1/2,1/2], and representable as series with respect to the ultraspherical polynomials. The value of the Delsarte problem gives an upper bound for the largest power ... More

On the norm of inverses of confluent Vandermonde matricesDec 02 2012Dec 04 2012In this note we present a simple upper bound for the row-wise norm of the inverses of general confluent Vandermonde matrices.

Embedding punctured n-manifolds in Euclidean (2n-1)-spaceOct 20 2010Let $N$ be a closed orientable connected $n$-manifold, $n\ge 4$. We classify embeddings of the punctured manifold $N_0$ into $\R^{2n-1}$ up to isotopy. Our result in some sense extends results of J.C. Becker -- H.H. Glover (1971) and O. Saeki (1999).

Sequential Covariance Calculation for Exoplanet Image ProcessingJan 05 2015Direct imaging of exoplanets involves the extraction of very faint signals from highly noisy data sets, with noise that often exhibits significant spatial, spectral and temporal correlations. As a results, a large number of post-processing algorithms ... More

Application of the quadratures method to the NLS with saturationJan 19 2009The solution of nonlinear Schroedinger equation with saturation was found by means the quadratures method in terms of degeneracy theory. It was shown the existence conditions for soliton solutions.

The transversality conditions in infinite horizon problems and the stability of adjoint variableAug 12 2011This paper investigates the necessary conditions of optimality for uni- formly overtaking optimal control on infinite horizon with free right endpoint. Clarke's form of the Pontryagin Maximum Principle is proved without the as- sumption on boundedness ... More

On the equi-normalizable deformations of singularities of complex plane curvesMay 27 2008Apr 21 2009We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or equi-generic deformations. We ... More

A discrete analogue of the modified Novikov-Veselov hierarchyApr 23 2009Jun 15 2012We construct a discrete analogue of the integrable two-dimensional Dirac operator and describe the spectral properties of its eigenfunctions. We construct an integrable discrete analogue of the modified Novikov-Veselov hierarchy. We derive the first two ... More

Tauberian theorem for value functionsJul 20 2016Jul 22 2016For two-person dynamic zero-sum games (both discrete and continuous settings), we investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity and the limit of value functions of $\lambda$-discounted ... More

Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation ProcedureNov 01 2016Nov 10 2016We study the consistency conditions for interactions of massless fields of any spin in four-dimensional flat space using the light-cone approach. We show that they can be equivalently rewritten as the Ward identities for the off-shell light-cone amplitudes ... More

On $c_2$ invariants of 4-regular Feynman graphsOct 03 2016The obstruction for application of effective techniques like denominator reduction for the computation of the $c_2$ invariant of Feynman graphs in general is the absence of a 3-valent vertex for the initial steps. In this paper such a formula for a 4-valent ... More

Exponential energy growth due to slow parameter oscillations in quantum mechanical systemsJan 09 2016It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantum mechanical system subjected to a slow periodic variation of parameters. The main example is given by systems (e.g., ... More

Spectral components analysis of diffuse emission processesFeb 06 2012We develop a novel method to separate the components of a diffuse emission process based on an association with the energy spectra. Most of the existing methods use some information about the spatial distribution of components, e.g., closeness to an external ... More

Cayley Automatic Groups and Numerical Characteristics of Turing TransducersJun 27 2016This paper is devoted to the problem of finding characterizations for Cayley automatic groups. The concept of Cayley automatic groups was recently introduced by Kharlampovich, Khoussainov and Miasnikov. We address this problem by introducing three numerical ... More

Dual Graph Polynomials and a 4-face FormulaAug 14 2015We study the dual graph polynomials and the case when a Feynman graph has no triangles but has a 4-face. This leads to the proof of the duality-admissibility of all graphs up to 18 loops. As a consequence, the $c_2$ invariant is the same for all 4 Feynman ... More

Reduction of a problem of finiteness of Tate-Shafarevich group to a result of Zagier typeNov 15 2004Aug 11 2005Kolyvagin proved that the Tate-Shafarevich group of an elliptic curve over Q of analytic rank 0 or 1 is finite, and that its algebraic rank is equal to its analytic rank. A program of generalisation of this result to the case of some motives which are ... More

Tight Lower Bounds for the Longest Common Extension ProblemNov 09 2016We prove that in the non-uniform cell probe model the trade-off $S(n)T(n) = \Omega(n\log n)$ holds for any data structure solving the longest common extension problem on strings of length $n$ in $S(n) = \Omega(n)$ bits of space with queries working in ... More

Positivity of Toeplitz determinants formed by rising factorial series and properties of related polynomialsMar 07 2012In this note we prove positivity of Maclaurin coefficients of polynomials written in terms of rising factorials and arbitrary log-concave sequences. These polynomials arise naturally when studying log-concavity of rising factorial series. We propose several ... More

Lipschitz inverse shadowing for nonsingular flowsFeb 27 2013We prove that Lipschitz inverse shadowing for nonsingular flows is equivalent to structural stability.

Generalizations of analogs of theorems of Maizel and Pliss and their application in Shadowing TheoryFeb 20 2012Nov 28 2012We generalize two classical results of Maizel and Pliss that describe relations between hyperbolicity properties of linear system of difference equations and its ability to have a bounded solution for every bounded inhomogeneity. We also apply one of ... More

On subexponential tails for the maxima of negatively driven compound renewal and Lévy processesAug 31 2016Nov 20 2016We study subexponential tail asymptotics for the distribution of the maximum $M_t:=\sup_{u\in[0,t]}X_u$ of a process $X_t$ with negative drift for the entire range of $t>0$. We consider compound renewal processes with linear drift and L\'evy processes. ... More

A connection between the Ghirlanda--Guerra identities and ultrametricityOct 04 2008Jan 27 2010We consider a symmetric positive definite weakly exchangeable infinite random matrix and show that, under the technical condition that its elements take a finite number of values, the Ghirlanda--Guerra identities imply ultrametricity.

Exponential control of overlap in the replica method for p-spin Sherrington-Kirkpatrick modelJan 30 2007Recently, Michel Talagrand computed the large deviations limit $\lim_{N\to\infty}(Na)^{-1}\log \e Z_N^a$ for the moments of the partition function $Z_N$ in the Sherrington-Kirkpatrick model for all real $a\geq 0.$ For $a\geq 1$ the limit is given by Guerra's ... More

Scattering of wave packets with phasesNov 24 2016A general problem of $2\rightarrow N_f$ scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in $(3+1)$ D, vortex particles with orbital angular momentum, the Airy ... More

Hierarchical exchangeability of pure states in mean field spin glass modelsJul 08 2013The main result in this paper is motivated by the M\'ezard-Parisi ansatz which predicts a very special structure for the distribution of spins in diluted mean field spin glass models, such as the random K-sat model. Using the fact that one can safely ... More

Multidimensional Random Polymers : A Renewal ApproachNov 30 2014In these lecture notes, which are based on the mini-course given at 2013 Prague School on Mathematical Statistical Physics, we discuss ballistic phase of quenched and annealed stretched polymers in random environment on ${\mathbb Z}^d$ with an emphasis ... More

On a property of random-oriented percolation in a quadrantMay 26 2012Jun 08 2012Grimmett's random-orientation percolation is formulated as follows. The square lattice is used to generate an oriented graph such that each edge is oriented rightwards (resp. upwards) with probability $p$ and leftwards (resp. downwards) otherwise. We ... More

The Sherrington-Kirkpatrick model: an overviewNov 06 2012The goal of this paper is to review some of the main ideas that emerged from the attempts to confirm mathematically the predictions of the celebrated Parisi ansatz in the Sherrington-Kirkpatrick model. We try to focus on the big picture while sketching ... More

A unified stability property in spin glassesJun 20 2011Nov 03 2011Gibbs' measures in the Sherrington-Kirkpatrick type models satisfy two asymptotic stability properties, the Aizenman-Contucci stochastic stability and the Ghirlanda-Guerra identities, which play a fundamental role in our current understanding of these ... More

Enumeration of singular algebraic curvesJul 21 2004Oct 04 2006We enumerate plane complex algebraic curves of a given degree with one singularity of any given topological type. Our approach is to compute the homology classes of the corresponding equisingular strata in the parameter spaces of plane curves. We suggest ... More

A method of quaternion typification of Clifford algebra elementsJun 26 2008Mar 07 2009We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method of analysis of commutators and anticommutators of Clifford algebra elements. This ... More

Application of the method of quaternion typification for finding subalgebras and Lie subalgebras of Clifford algebrasApr 11 2009In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous papers. On the basis of new classification of Clifford algebra elements it is possible to find out and prove a ... More

Microlocal condition for non-displaceablilitySep 09 2008We formulate a sufficient condition for non-displaceability (by Hamiltonian symplectomorphisms which are identity outside of a compact) of a pair of subsets in a cotangent bundle. This condition is based on micro-local analysis of sheaves on manifolds ... More

Contact integral geometry and the Heisenberg algebraDec 26 2017Jan 03 2018Generalizing Weyl's tube formula and building on Chern's work, Alesker reinterpreted the Lipschitz-Killing curvature integrals as a family of valuations (finitely-additive measures with good analytic properties), attached canonically to any Riemannian ... More

A remark on approximation of open sets with regular bounded onesDec 08 2010We show that any open set in $\R^n$ is a union of an ascending sequence of bounded open sets with analytic boundary. This is just a technical result, which is probably known. We believe, however, that it can be useful for studing BVPs on irregular open ... More

Topological Semantics and DecidabilityMar 05 2007Jun 01 2007It is well-known that the basic modal logic of all topological spaces is $S4$. However, the structure of basic modal and hybrid logics of classes of spaces satisfying various separation axioms was until present unclear. We prove that modal logics of $T_0$, ... More

On the derivative of two functions from Denjoy-Tichy-Uitz familyFeb 14 2013Dec 01 2013The family of functions, we investigate in this article, was originally introduced by A.Denjoy and later rediscovered by R Tichy and J. Uitz. We denote the functions of the family by $g_{\lambda}(x),$ where $\lambda\in(0,1)$. The definition will be given ... More

Asymptotic dimension of one relator groupsJul 21 2006We show that one relator groups viewed as metric spaces with respect to the word-length metric have finite asymptotic dimension in the sense of Gromov and give an estimate of their asymptotic dimension in terms of the relator length.

On subexponential tails for the maxima of negatively driven compound renewal and Lévy processesAug 31 2016We study subexponential tail asymptotics for the distribution of the maximum $M_t:=\sup_{u\in[0,t]}X_u$ of a process $X_t$ with negative drift for the entire range of $t>0$. We consider compound renewal processes with linear drift and L\'evy processes. ... More

Unbalanced Renormalization of Tunneling in MOSFET-type Structures in Strong High-Frequency Electric FieldsAug 12 2007Two-dimensional electron gas coupled to adjacent impurity sites in high-frequency out-of-plane ac control electric field is investigated. Modification of tunneling rates as a function of the field amplitude is calculated. Nonlinear dependence on the ac ... More

The quotient girth of normed spaces, and an extension of Schäffer's dual girth conjecture to GrassmanniansNov 22 2011Dec 01 2011In this note we introduce a natural Finsler structure on convex surfaces, referred to as the projective Finsler structure, which is dual in a sense to the obvious inclusion of a convex surface in a normed space. It has an associated projective girth, ... More

Clown: a Microprocessor Simulator for Operating System StudiesJul 21 2012In this paper, I present the design and implementation of Clown--a simulator of a microprocessor-based computer system specifically optimized for teaching operating system courses at undergraduate or graduate levels. The package includes the simulator ... More

Error bounds for approximations with deep ReLU networksOct 03 2016We study how approximation errors of neural networks with ReLU activation functions depend on the depth of the network. We establish rigorous error bounds showing that deep ReLU networks are significantly more expressive than shallow ones as long as approximations ... More

Commuting symplectomorphisms and Dehn twists in divisorsMay 18 2014Jun 02 2016Two commuting symplectomorphisms of a symplectic manifold give rise to actions on Floer cohomologies of each other. We prove the elliptic relation saying that the supertraces of these two actions are equal. In the case when a symplectomorphism $f$ commutes ... More

A Theory of Intermittency Renormalization of 1D Gaussian Multiplicative Chaos MeasuresSep 29 2016A theory of intermittency differentiation is developed for a general class of 1D Gaussian Multiplicative Chaos measures including the measure of Bacry and Muzy on the interval and circle as special cases. An exact, non-local functional equation is derived ... More

New models of income distribution, graduation as the explanation of Gini coefficientSep 15 2013The paper covers the new model of wage distribution in typical group of people. The model provides the opportunity to reparameterize applicable income distribution model: Pareto, logarithmically normal, logarithmically logistic, Dagum etc. The model ensures ... More

Attainable numbers and the Lagrange spectrumJun 06 2016Oct 14 2016The paper is devoted to the properties of the Lagrange spectrum left endpoints and so-called attainable numbers.

Storage option an Analytic approachNov 04 2010May 28 2012The mathematical problem of the static storage optimisation is formulated and solved by means of a variational analysis. The solution obtained in implicit form is shedding light on the most important features of the optimal exercise strategy. We show ... More

On extension for infinite horizon game of pursuit-evasionDec 16 2010The extension of a conflict control problem with infinite horizon is constructed. This extension is the projective limit of restricted games. Relations between "sensitivity to target set" and the existence of the optimal control are studied. Special attention ... More

Classical Interaction Cannot Replace Quantum NonlocalityJan 08 2009We present a two-player communication task that can be solved by a protocol of polylogarithmic cost in the simultaneous message passing model with classical communication and shared entanglement, but requires exponentially more communication in the classical ... More

Classical Interaction Cannot Replace a Quantum MessageMar 23 2007Feb 21 2008We demonstrate a two-player communication problem that can be solved in the one-way quantum model by a 0-error protocol of cost O (log n) but requires exponentially more communication in the classical interactive (bounded error) model.

Free energy in the Sherrington-Kirkpatrick model with constrained magnetizationMay 18 2004Oct 12 2004This paper has been withdrawn since a trivial proof of the result has been pointed out to the author.

Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation ProcedureNov 01 2016We study the consistency conditions for interactions of massless fields of any spin in four-dimensional flat space using the light-cone approach. We show that they can be equivalently rewritten as the Ward identities for the off-shell light-cone amplitudes ... More

Enstrophy growth in the viscous Burgers equationFeb 09 2012We study bounds on the enstrophy growth for solutions of the viscous Burgers equation on the unit circle. Using the variational formulation of Lu and Doering, we prove that the maximizer of the enstrophy's rate of change is sharp in the limit of large ... More

Asymptotic properties of excited states in the Thomas--Fermi limitNov 24 2009Excited states are stationary localized solutions of the Gross--Pitaevskii equation with a harmonic potential and a repulsive nonlinear term that have zeros on a real axis. Existence and asymptotic properties of excited states are considered in the semi-classical ... More

Artifact-free data recovery system for an ASNOM applicationJul 09 2013A digital signal acquisition system for an Apertureless SNOM (ASNOM) based on a digital signal processing (DSP) card is presented. An electromagnetic wave scattered by an AFM-like tip is initially detected by an optical homodyning in a Michelson interferometer, ... More

An application of the fixed point theorem to the inverse Sturm-Liouville problemOct 27 2009We consider Sturm-Liouville operators $-y''+v(x)y$ on $[0,1]$ with Dirichlet boundary conditions $y(0)=y(1)=0$. For any $1\le p<\infty$, we give a short proof of the characterization theorem for the spectral data corresponding to $v\in L^p(0,1)$.

Baker-Sprindzhuk conjectures for complex analytic manifoldsOct 23 2002We show a large class of analytic submanifolds of C^n to be strongly extremal. This generalizes V. Sprindzhuk's solution of the complex case of Mahler's Problem, and settles complex analogues of conjectures made in the 1970s by Baker and Sprindzhuk. The ... More

New equation on the low dimensional Calabi-Yau metricsApr 29 2011May 02 2011In this paper we introduce a new equation on the compact Kahler manifolds. Solution of this equation corresponds to the Calabi-Yau metric. New equation differs from the Monge--Ampere equation considered by Calabi and Yau.

Retarded action principle and self-financing portfolio dynamicsSep 30 2015Jun 21 2016We derive a consistent differential representation for the dynamics of a self-financing portfolio for different hedging strategies. In the basis of the derivation there is the so called "retarded action principle", which represents the causality in the ... More

Some extensions of an inequality of Vapnik and ChervonenkisMay 18 2004The inequality of Vapnik and Chervonenkis controls the expectation of the function by its sample average uniformly over a VC-major class of functions taking into account the size of the expectation. Using Talagrand's kernel method we prove a similar result ... More

A note on Talagrand's concentration inequality for empirical processesMay 18 2004In this paper we revisit Talagrand's proof of concentration inequality for empirical processes. We give a different shorter proof of the main technical lemma that garantees the existence of a certain kernel. Our proof provides the almost optimal value ... More

Necessity of limiting co-state arc in Bolza-type infinite horizon problemJul 02 2014We investigate necessary conditions of optimality for the Bolza-type infinite horizon problem with free right end. The optimality is understood in the sense of weakly uniformly overtaking optimal control. No previous knowledge in the asymptotic behaviour ... More

Singular Virasoro vectors and Lie algebra cohomologyMay 26 2014We present an explicit formula for a new family of Virasoro singular vectors. As a corrolary we get formulas for differentials of Feigin-Fuchs-Rocha-Carridi-Wallach resolution of the the positive nilpotent part of Virasoro (or Witt) algebra $L_1$.

Geometric Discretization of the EPDiff EquationsMar 13 2015The main objective of this paper is to develop a general method of geometric discretization for infinite-dimensional systems and apply this method to the EPDiff equation. The method described below extends one developed by Pavlov et al. for incompressible ... More

On differentiability of the Parisi formulaSep 11 2007May 04 2008It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using approximate ... More

Discovery of Convoys in Network Proximity LogMar 21 2013This paper describes an algorithm for discovery of convoys in database with proximity log. Traditionally, discovery of convoys covers trajectories databases. This paper presents a model for context-aware browsing application based on the network proximity. ... More

Complex interpolation of couple (X, BMO) for $A_1$-regular latticesMar 25 2013Recent results of A. Lerner concerning certain properties of the Fefferman-Stein maximal function are applied to show that $(\BMO, X)_\theta = X^\theta$, $0 < \theta < 1$, for a Banach lattice $X$ of measurable functions on $\mathbb R^n$ satisfying the ... More