Results for "Pavel D. Grigoriev"

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Random linear combinations of functions from $L_1$Oct 22 2002In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are established. ... More
Estimates for Norms of Random PolynomialsOct 22 2002This paper contains some estimates for the {\it integral-uniform} norm and the uniform norm of a wide class of random polynomials. The family of integral-uniform norms introduced by Kasin and Tzafriri is a natural generalization of the maximum norm taken ... More
Linear magnetoresistance in the charge density wave state of quasi-two-dimensional rare-earth tritelluridesDec 08 2017We report measurements of the magnetoresistance in the charge density wave (CDW) state of rare-earth tritellurides, namely TbTe$_3$ and HoTe$_3$. The magnetic field dependence of magnetoresistance exhibits a temperature dependent crossover between a conventional ... More
The evolution of electron dispersion in the series of rare-earth tritelluride compounds obtained from their charge-density-wave properties and susceptibility calculationsJul 10 2019We calculated electron susceptibility of rare-earth tritelluride compounds RTe$_3$ as a function of temperature, wave vector and electron-dispersion parameters. Comparison of results obtained with the available experimental data on the transition temperature ... More
Public-key cryptography and invariant theoryJul 23 2002Public-key cryptosystems are suggested based on invariants of groups. We give also an overview of the known cryptosystems which involve groups.
Temperature dependence of resistivity at the transition to a charge density wave state in rare-earth tritelluridesDec 16 2018About a half of the Fermi surface in rare-earth tritellurides RT e3 becomes gapped below the transition to a charge-density-wave (CDW) state, as revealed by ARPES data. However, the observed jump in resistivity during the CDW transition is less than 20%. ... More
Bilayer splitting versus Fermi-surface warping as an origin of slow oscillations of in-plane magnetoresistance in rare-earth tritelluridesJun 17 2016Slow oscillations (SlO) of the in-plane magnetoresistance with a frequency less than 4 T are observed in the rare-earth tritellurides and proposed as an effective tool to explore the electronic structure in various strongly anisotropic quasi-two-dimensional ... More
Unstable Spiral Waves and Local Euclidean Symmetry in a Model of Cardiac TissueDec 15 2014Jun 02 2015This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study ... More
Exponential suppression of interlayer conductivity in very anisotropic quasi-two-dimensional compounds in high magnetic fieldNov 10 2011It is shown that in rather strong magnetic field the interlayer electron conductivity is exponentially damped by the Coulomb barrier arising from the formation of polaron around each localized electron state. The theoretical model is developed to describe ... More
Weakly incoherent magnetotransport in layered metalsOct 05 2010We investigate the conductivity in layered metals in magnetic field in the weakly incoherent limit, when the interlayer transfer integral is smaller than the Landau level broadening due to the impurity potential, but the interlayer electron tunnelling ... More
Crossover from the weak to strong-field behavior of the longitudinal interlayer magnetoresistance in quasi-two-dimensional conductorsOct 26 2013Dec 03 2014We investigate the monotonic growth of longitudinal interlayer magnetoresistance $\bar{R}_{zz}(B_z) $, analytically and numerically in the self-consistent Born approximation. We show that in a weak magnetic field the monotonic part of $\bar{R}_{zz}(B_z)$ ... More
Slow quantum oscillations without fine-grained Fermi Surface Reconstruction in Cuprate SuperconductorsJun 13 2016Oct 26 2017The Fourier transform of the observed magnetic quantum oscillations (MQO) in YBa$_{2}$Cu$_{3}$O$_{6+\delta }$ high-temperature superconductors has a prominent low-frequency peak with two smaller neighbouring peaks. The separation and positions of these ... More
Slow quantum oscillations without Fermi Surface Reconstruction in Cuprate SuperconductorsJun 13 2016The Fourier transform of the observed magnetic quantum oscillations (MQO) in YBa$_{2}$Cu$_{3}$O$_{6+\delta }$ high-temperature superconductors has a prominent low-frequency peak with two smaller neighbouring peaks. The separation and even the position ... More
Magnetic oscillations measure interlayer coupling in cuprate superconductorsOct 26 2017The magnetic oscillations in YBCO high-temperature superconductors have been widely studied over the last decade and consist of three equidistant low frequencies with a central frequency several times more intense than its two shoulders. This remains ... More
Effect of incoherent pump on two-mode entanglement in optical parametric generationMay 13 2019Pumping a nonlinear crystal by an intense radiation results in the optical parametric generation of photons in two modes (the signal and the idler). Quantized electromagnetic field in these modes is described by a continuous-variable quantum state, which ... More
Tropical differential equationsFeb 27 2015Tropical differential equations are introduced and an algorithm is designed which tests solvability of a system of tropical linear differential equations within the complexity polynomial in the size of the system and in its coefficients. Moreover, we ... More
The influence of the oscillations of the chemical potential on the de Haas - van Alphen effect in quasi-two-dimensional compoundsFeb 09 2001The de Haas - van Alphen effect in quasi-two-dimensional metals is studied at arbitrary parameters. The oscillations of the chemical potential may substantially change the temperature dependence of harmonic amplitudes that is usually used to determine ... More
Angular dependence of magnetoresistance in strongly anisotropic quasi-two-dimensional metals for various Landau-level shapesSep 12 2013We present the quantum-mechanical calculations of the angular dependence of interlayer conductivity $\sigma _{zz}(\theta )$ in a tilted magnetic field in quasi-2D layered metals. Our calculation shows that the LL shape is important for this angular dependence. ... More
Off-shell Gauge Fields from BRST QuantizationMay 09 2006We propose a construction for nonlinear off-shell gauge field theories based on a constrained system quantized in the sense of deformation quantization. The key idea is to consider the star-product BFV--BRST master equation as an equation of motion. The ... More
Decomposing tropical rational functionsJan 04 2019Mar 01 2019An algorithm is designed which decomposes a tropical univariate rational function into a composition of tropical binomials and trinomials. When a function is monotone, the composition consists just of binomials. Similar algorithms are designed for decomposing ... More
Tropical recurrent sequencesJul 27 2018Mar 22 2019Tropical recurrent sequences are introduced satisfying a given vector (being a tropical counterpart of classical linear recurrent sequences). We consider the case when Newton polygon of the vector has a single (bounded) edge. In this case there are periodic ... More
Tropical Newton-Puiseux polynomialsApr 12 2017Aug 27 2018We introduce tropical Newton-Puiseux polynomials admitting rational exponents. A resolution of a tropical hypersurface is defined by means of a tropical Newton-Puiseux polynomial. A polynomial complexity algorithm for resolubility of a tropical curve ... More
Parent form for higher spin fields on anti-de Sitter spaceFeb 17 2006Apr 10 2006We construct a first order parent field theory for free higher spin gauge fields on constant curvature spaces. As in the previously considered flat case, both Fronsdal's and Vasiliev's unfolded formulations can be reached by two different straightforward ... More
Hamiltonian BRST and Batalin-Vilkovisky formalisms for second quantization of gauge theoriesOct 08 2003Gauge theories that have been first quantized using the Hamiltonian BRST operator formalism are described as classical Hamiltonian BRST systems with a BRST charge of the form <\Psi,\Omega\Psi>_{even} and with natural ghost and parity degrees for all fields. ... More
Zero Locus Reduction of the BRST DifferentialJun 28 1999I point out an unexpected relation between the BV (Batalin-Vilkovisky) and the BFV (Batalin-Fradkin-Vilkovisky) formulations of the same pure gauge (topological) theory. The nonminimal sector in the BV formulation of the topological theory allows one ... More
Tropical cryptography II: extensions by homomorphismsNov 14 2018We use extensions of tropical algebras as platforms for very efficient public key exchange protocols.
On a tropical version of the Jacobian conjectureFeb 20 2019We prove for a tropical rational map that if for any point the convex hull of Jacobian matrices at smooth points in a neighborhood of the point does not contain singular matrices then the map is an isomorphism. We also show that a tropical polynomial ... More
Noise residuals for GW150914 using maximum likelihood and numerical relativity templatesMar 06 2019May 13 2019We reexamine the results presented in a recent work by Nielsen et al. [1], in which the properties of the noise residuals in the 40\,ms chirp domain of GW150914 were investigated. This paper confirmed the presence of strong (i.e., about 0.80) correlations ... More
On the Question of Effective Sample Size in Network Modeling: An Asymptotic InquiryDec 05 2011Aug 05 2015The modeling and analysis of networks and network data has seen an explosion of interest in recent years and represents an exciting direction for potential growth in statistics. Despite the already substantial amount of work done in this area to date ... More
HII Region Driven Galactic Bubbles and Their Relationship to the Galactic Magnetic FieldOct 15 2012The relative alignments of mid-infrared traced Galactic bubbles are compared to the orientation of the mean Galactic magnetic field in the disk. The orientations of bubbles in the northern Galactic plane were measured and are consistent with random orientations ... More
Identification and Control of Symmetric SystemsNov 08 1998Jan 25 1999In a recent paper [Phys. Rev. E 57, p. 1550 (1998)] we demonstrated that the symmetries of the evolution equation and the target state have a profound effect on the selection of the admissible control parameters. In the present paper we extend these results ... More
Boundary values of mixed-symmetry massless fields in AdS spaceDec 20 2015Oct 24 2016We elaborate on the ambient space approach to boundary values of $AdS_{d+1}$ gauge fields and apply it to massless fields of mixed-symmetry type. In the most interesting case of odd-dimensional bulk the respective leading boundary values are conformal ... More
First order parent formulation for generic gauge field theoriesSep 01 2010Nov 28 2010We show how a generic gauge field theory described by a BRST differential can systematically be reformulated as a first order parent system whose spacetime part is determined by the de Rham differential. In the spirit of Vasiliev's unfolded approach, ... More
BRST Extension of the Non-Linear Unfolded FormalismApr 13 2005May 05 2005We review the construction of gauge field theories from BRST first-quantized systems and its relation to the unfolded formalism. In particular, the BRST extension of the non linear unfolded formalism is discussed in some details.
Bounds on the number of connected components for tropical prevarietiesNov 20 2015For a tropical prevariety in ${R}^n$ given by a system of $k$ tropical polynomials in $n$ variables with degrees at most $d$, we prove that its number of connected components is less than ${k+7n-1 \choose 3n} \cdot \frac{d^{3n}}{k+n+1}$. On a number of ... More
Gauge PDE and AKSZ-type Sigma ModelsMar 07 2019Apr 22 2019A gauge PDE is a natural notion which arises by abstracting what physicists call a local gauge field theory defined in terms of BV-BRST differential (not necessarily Lagrangian). We study supergeometry of gauge PDEs paying particular attention to globally ... More
A Lack of Resolved Near-Infrared Polarization Across the Face of M51Nov 18 2012The galaxy M51 was observed using the Mimir instrument on the Perkins telescope to constrain the resolved H-band (1.6 $\mu$m) polarization across the galaxy. These observations place an upper limit of $P_H<0.05%$ on the $H$-band polarization across the ... More
Chiral criticality in doped Mn$_{1-y}$Fe$_y$Si compoundsApr 06 2011Apr 11 2011The critical spin fluctuations in doped compounds Mn$_{1-y}$Fe$_y$Si have been studied by means of ac-susceptibility measurements, polarized neutron small angle scattering and spin echo spectroscopy. It is shown that these compounds undergo the transition ... More
Tropical cryptographyJan 07 2013We employ tropical algebras as platforms for several cryptographic schemes that would be vulnerable to linear algebra attacks were they based on "usual" algebras as platforms.
Orthogonal tropical linear prevarietiesMar 02 2018Jun 04 2018The paper studies the operation $A^\perp$ of tropical orthogonalization, applied to a subset $A$ of a vector space $({\mathbb R} \cup \{ \infty \})^n$, and iterations of this operation. Main results include a criterion and an algorithm, deciding whether ... More
Upper bounds on Betti numbers of tropical prevarietiesSep 25 2017Mar 09 2018We prove upper bounds on the sum of Betti numbers of tropical prevarieties in dense and sparse settings. In the dense setting the bound is in terms of the volume of Minkowski sum of Newton polytopes of defining tropical polynomials, or, alternatively, ... More
Interplay between electron band-anticrossing and charge-density-wave instabilitiesJun 26 2019Our measurements of the Hall coefficient in rare-earth tritelluride compounds reveal a strong hysteresis between cooling and warming in the low temperature range where a second unidirectional charge density wave (CDW) occurs. We show that this effect ... More
The Price of BitCoin: GARCH Evidence from High Frequency DataDec 22 2018This is the first paper that estimates the price determinants of BitCoin in a Generalised Autoregressive Conditional Heteroscedasticity framework using high frequency data. Derived from a theoretical model, we estimate BitCoin transaction demand and speculative ... More
Laboratory characterization of SLS-based infrared detectors for precision photometryJul 28 2018Strained layer superlattice (SLS) detectors are a new class of infrared detectors available in the scientific and commercial markets. The photosensitive bandpass is set by material and engineered properties with typical detectors covering 7.5- 10.5 microns, ... More
Virtual Relationships: Short- and Long-run Evidence from BitCoin and Altcoin MarketsJun 22 2017This study empirically examines interdependencies between BitCoin and altcoin markets in the short- and long-run. We apply time-series analytical mechanisms to daily data of 17 virtual currencies (BitCoin + 16 alternative virtual currencies) and two Altcoin ... More
Analogue of Newton-Puiseux series for non-holonomic D-modules and factoringNov 09 2008We introduce a concept of a fractional-derivatives series and prove that any linear partial differential equation in two independent variables has a fractional-derivatives series solution with coefficients from a differentially closed field of zero characteristic. ... More
On conformal higher spins in curved backgroundSep 29 2016We address the question of how to represent an interacting action for the tower of conformal higher spin fields in a form covariant with respect to a background metric. We use a background metric to define a star product which plays a central role in ... More
On conformal higher spins in curved backgroundSep 29 2016Nov 02 2016We address the question of how to represent an interacting action for the tower of conformal higher spin fields in a form covariant with respect to a background metric. We use a background metric to define a star product which plays a central role in ... More
Frame-like Lagrangians and presymplectic AKSZ-type sigma modelsDec 18 2013Mar 31 2014We study supergeometric structures underlying frame-like Lagrangians. We show that for the theory in n spacetime dimensions both the frame-like Lagrangian and its gauge symmetries are encoded in the target supermanifold equipped with the odd vector field, ... More
Spectral theory for the failure of linear control in a nonlinear stochastic systemSep 30 2002Nov 11 2002We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur in systems ... More
Memory effects, transient growth, and wave breakup in a model of paced atriumApr 11 2017The mechanisms underlying cardiac fibrillation have been investigated for over a century, but we are still finding surprising results that change our view of this phenomenon. The present study focuses on the transition from normal rhythm to atrial fibrillation ... More
On reduced models for superstrings on AdS_n x S^nJun 16 2008Jul 16 2008We review the Pohlmeyer reduction procedure of the superstring sigma model on AdS_n x S^n leading to a gauged WZW model with an integrable potential coupled to 2d fermions. In particular, we consider the case of the Green-Schwarz superstring on AdS_3 ... More
Identifying the Parametric Occurrence of Multiple Steady States for some Biological NetworksFeb 13 2019We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address the problem ... More
A non-invasive ultra-thin luminophore foil detector system for secondary beam monitoringMay 28 2019High-intensity secondary beams play a vital role in today's particle physics and materials science research and require suitable detection techniques to adjust beam characteristics to optimally match experimental conditions. To this end we have developed ... More
Propensity to form amyloid fibrils is encoded as excitations in the free energy landscape of monomeric proteinsJul 07 2014Protein aggregation, linked to many of diseases, is initiated when monomers access rogue conformations that are poised to form amyloid fibrils. We show, using simulations of src SH3 domain, that mechanical force enhances the population of the aggregation ... More
Squeezed Gluon Condensate and Quark Confinement in the Global Color Model of QCDJul 20 1997Dec 17 1998We discuss how the presence of a squeezed gluon vacuum might lead to quark confinement in the framework of the global colour model of QCD. Using reduced phase space quantization of massive vector theory we construct a Lorentz invariant and colourless ... More
Local duality in Loewner equationsFeb 10 2012Feb 27 2012Among diversity of frameworks and constructions introduced in Loewner Theory by different authors, one can distinguish two closely related but still different ways of reasoning, which colloquially may be described as "increasing" and "decreasing". In ... More
Loewner chains in the unit diskFeb 18 2009In this paper we introduce a general version of the notion of Loewner chains which comes from the new and unified treatment, given in [arXiv:0807.1594], of the radial and chordal variant of the Loewner differential equation, which is of special interest ... More
Loewner Theory in annulus I: evolution families and differential equationsNov 18 2010Loewner Theory, based on dynamical viewpoint, is a powerful tool in Complex Analysis, which plays a crucial role in such important achievements as the proof of famous Bieberbach's conjecture and well-celebrated Schramm's Stochastic Loewner Evolution (SLE). ... More
Geometry behind chordal Loewner chainsFeb 03 2010Loewner Theory is a deep technique in Complex Analysis affording a basis for many further important developments such as the proof of famous Bieberbach's conjecture and well-celebrated Schramm's Stochastic Loewner Evolution (SLE). It provides analytic ... More
Testing Galactic Magnetic Field Models using Near-Infrared PolarimetryFeb 05 2012This work combines new observations of NIR starlight linear polarimetry with previously simulated observations in order to constrain dynamo models of the Galactic magnetic field. Polarimetric observations were obtained with the Mimir instrument on the ... More
Near-infrared polarimetry of a normal spiral galaxy viewed through the Taurus Molecular Cloud ComplexJan 11 2013Few normal galaxies have been probed using near-infrared polarimetry, even though it reveals magnetic fields in the cool interstellar medium better than either optical or radio polarimetry. Deep H-band (1.6um) linear imaging polarimetry toward Taurus ... More
Boundary regular fixed points in Loewner theoryMar 21 2013We characterize regular fixed points of evolution families in terms of analytical properties of the associated Herglotz vector fields and geometrical properties of the associated Loewner chains. We present several examples showing the r\^ole of the given ... More
Slope problem for trajectories of holomorphic semigroups in the unit discJun 13 2014It has been an open problem for about ten years whether every trajectory of a parabolic one-parameter semigroup in the unit disk tends to the Denjoy-Wolff point with a definite (and common for all trajectories) slope. In this paper, we give the negative ... More
Resolved Magnetic Field Mapping of a Molecular Cloud Using GPIPSAug 30 2012We present the first resolved map of plane-of-sky magnetic field strength for a quiescent molecular cloud. GRSMC 45.60+0.30 subtends 40 x 10 pc at a distance of 1.88 kpc, masses 16,000 M_sun, and exhibits no star formation. Near-infrared background starlight ... More
Self-consistent and Maxwell approximations to describe the excess conductivity anisotropy in FeSe above superconducting transition temperatureJul 05 2018Using the self-consistent approximation we calculate conductivity in an anisotropic heterogeneous media with superconducting inclusions and compare the results with those obtained previously using the Maxwell approximation and with available experimental ... More
Testing Gaussian random hypothesis with the cosmic microwave background temperature anisotropies in the three-year WMAP dataMar 24 2006May 04 2006We test the hypothesis that the temperature of the cosmic microwave background is consistent with a Gaussian random field defined on the celestial sphere, using de-biased internal linear combination (DILC) map produced from the 3-year WMAP data. We test ... More
Loewner Theory in annulus II: Loewner chainsMay 16 2011Loewner Theory, based on dynamical viewpoint, proved itself to be a powerful tool in Complex Analysis and its applications. Recently Bracci et al [Bracci et al, to appear in J. Reine Angew. Math. Available on ArXiv 0807.1594; Bracci et al, Math. Ann. ... More
Symmetry, Rigidity, and Allosteric Signaling: From Monomeric Proteins to Molecular MachinesDec 12 2018Allosteric signaling in biological molecules, which may be viewed as specific action at a distance due to localized perturbation upon binding of ligands or changes in environmental cues, is pervasive in biology. Phenomenological MWC and KNF models galvanized ... More
On non-abelian homomorphic public-key cryptosystemsJul 23 2002Nov 14 2002An important problem of modern cryptography concerns secret public-key computations in algebraic structures. We construct homomorphic cryptosystems being (secret) epimorphisms f:G --> H, where G, H are (publically known) groups and H is finite. A letter ... More
Fedosov Deformation Quantization as a BRST TheoryMar 14 2000Apr 23 2000The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold $\mathcal M$ is presented as a second class ... More
Capacity of several aligned segmentsDec 22 2015In this note we present a universal formula in terms of theta functions for the Log- capacity of several segments on a line. The case of two segments was studied by N.I.Akhiezer (1930); three segments were considered by A.Sebbar and T.Falliero (2001). ... More
Some Trigonometric Polynomials with Extremely Small Uniform NormJun 10 2014An example of trigonometric polynomials with extremely small uniform norm is given. This example demonstrates the potential limits for extension of Sidon's inequality for lacunary polynomials in a certain direction.
Properties of superconductivity on the density wave background with small ungapped Fermi surface pocketsMar 06 2008We investigate the properties and the microscopic structure of superconductivity (SC), coexisting and sharing the common conducting band with density wave (DW). Such coexistence may take place when the nesting of the Fermi surface (FS) is not perfect, ... More
Non-holonomic Ideals in the Plane and Absolute FactoringNov 09 2008We study {\it non-holonomic} overideals of a left differential ideal $J\subset F[\partial_x, \partial_y]$ in two variables where $F$ is a differentially closed field of characteristic zero. The main result states that a principal ideal $J=< P>$ generated ... More
On Decoupling of Functions of Normal Vectors IIJun 10 2014A decoupling type inequality for a sum of functions of Guassian vectors is established.
Longitudinal interlayer magnetoresistance in quasi-2D metalsDec 31 2012The longitudinal interlayer magnetoresistance $R_{zz}(B_{z})$ is calculated in strongly anisotropic layered metals, when the interlayer band width $4t_{z}$ is less than the Landau level separation $\hbar \omega_{c}$. The impurity scattering has much stronger ... More
Angular dependence of magnetoresistance and Fermi-surface shape in quasi-2D metalsMar 02 2010The analytical and numerical study of the angular dependence of magnetoresistance in layered quasi-two-dimensional (Q2D) metals is performed. The harmonic expansion analytical formulas for the angular dependence of Fermi-surface cross-section area in ... More
Construction of universal Thom-Whitney-a stratifications, their functoriality and Sard-type Theorem for singular varietiesNov 09 2008Jul 09 2009{\bf Construction.} For a dominating polynomial mapping {$F: K^n\to K^l$} with an isolated critical value at 0 ($K$ an algebraically closed field of characteristic zero) we construct a closed {\it bundle} $G_F \subset T^{*}K^n $. We restrict $ G_F $ over ... More
Surface charges and dynamical Killing tensors for higher spin gauge fields in constant curvature spacesJul 14 2005Aug 14 2005In the context of massless higher spin gauge fields in constant curvature spaces, we compute the surface charges which generalize the electric charge for spin one, the color charges in Yang-Mills theories and the energy-momentum and angular momentum for ... More
Non-Abelian Conversion and Quantization of Non-scalar Second-Class ConstraintsJan 13 2005We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components of a section ... More
A Kaehler Structure of the Triplectic GeometryJul 02 1998Sep 23 1998We study the geometry of the triplectic quantization of gauge theories. We show that underlying the triplectic geometry is a Kaehler manifold N endowed with a pair of transversal polarizations. The antibrackets can be brought to the canonical form if ... More
Monotonic growth of interlayer magnetoresistance in strong magnetic field in very anisotropic layered metalsApr 27 2011It is shown, that the monotonic part of interlayer electronic conductivity strongly decreases in high magnetic field perpendicular to the conducting layers. We consider only the coherent interlayer tunnelling, and the obtained result strongly contradicts ... More
Superconductivity on the density wave background with soliton-wall structureNov 26 2008Superconductivity (SC) may microscopically coexist with density wave (DW) when the nesting of the Fermi surface (FS) is not perfect. There are, at least, two possible microscopic structures of a DW state with quasi-particle states remaining on the Fermi ... More
Theory of the Shubnikov-de Haas effect in quasi-two-dimensional metalsApr 12 2002The Shubnikov - de Haas effect in quasi-two-dimensional normal metals is studied. The interlayer conductivity is calculated using the Kubo formula. The electron scattering on short-range is considered in the self-consistent Born approximation. The result ... More
Robust Approach for Rotor Mapping in Cardiac TissueDec 26 2018The motion of and interaction between phase singularities that anchor spiral waves captures many qualitative and, in some cases, quantitative features of complex dynamics in excitable systems. Being able to accurately reconstruct their position is thus ... More
Subtraction-free complexity, cluster transformations, and spanning treesJul 31 2013Sep 28 2014Subtraction-free computational complexity is the version of arithmetic circuit complexity that allows only three operations: addition, multiplication, and division. We use cluster transformations to design efficient subtraction-free algorithms for computing ... More
A Solvable Model for Spatiotemporal ChaosJun 06 1997We show that the dynamical behavior of a coupled map lattice where the individual maps are Bernoulli shift maps can be solved analytically for integer couplings. We calculate the invariant density of the system and show that it displays a nontrivial spatial ... More
Bidimensionality of Geometric Intersection GraphsAug 28 2013Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric intersection ... More
Probabilistic solution of Yao's millionaires' problemNov 27 2017We offer a probabilistic solution of Yao's millionaires' problem that gives correct answer with probability (slightly) less than 1 but on the positive side, this solution does not use any one-way functions.
Unrestricted electron bunching at the helical edgeMar 10 2019A quantum magnetic impurity of spin $S$ at the edge of a two-dimensional time reversal invariant topological insulator may give rise to backscattering. We study here the shot noise associated with the backscattering current for arbitrary $S$. Our full ... More
Nearest Neighbor Distances on a Circle: Multidimensional CaseJul 20 2011Sep 20 2011We study the distances, called spacings, between pairs of neighboring energy levels for the quantum harmonic oscillator. Specifically, we consider all energy levels falling between E and E+1, and study how the spacings between these levels change for ... More
Multilinear commutators in residually finite groupsDec 13 2010Let w be a multilinear commutator and n a positive integer. Suppose that G is a residually finite group in which every product of at most 896 w-values has order dividing n. Then the verbal subgroup w(G) is locally finite.
Nonlocal elliptic problems with nonlinear argument transformations near the points of conjugationApr 18 2014We consider elliptic equations of order $2m$ in a domain $G\subset\mathbb R^n$ with nonlocal conditions that connect the values of the unknown function and its derivatives on $(n-1)$-dimensional submanifolds $\Upsilon_i$ (where $\bigcup_i\Upsilon_i=\partial ... More
On infinite Jacobi matrices with a trace class resolventApr 30 2019Let $\{\hat{P}_{n}(x)\}$ be an orthonormal polynomial sequence and denote by $\{w_{n}(x)\}$ the respective sequence of functions of the second kind. Suppose the Hamburger moment problem for $\{\hat{P}_{n}(x)\}$ is determinate and denote by $J$ the corresponding ... More
On construction of unitary quantum group differential calculusApr 17 2015We develop a construction of the unitary type anti-involution for the quantized differential calculus over $GL_q(n)$ in the case $|q|=1$. To this end, we consider a joint associative algebra of quantized functions, differential forms and Lie derivatives ... More
Extended Quantum MechanicsSep 17 1999Dec 16 2012We are dealing in this work with such formal and conceptual extensions of nonrelativistic quantum mechanics (QM) which contain QM with its standard formalism and interpretation as a subtheory. QM is here primarily equivalently reformulated in the form ... More
The Whitney extension problem and Lipschitz selections of set-valued mappings in jet-spacesJan 29 2006We study a variant of the Whitney extension problem for the space $C^{k,\omega}(R^n)$. We identify this space with a space of Lipschitz mappings from $R^n$ into the space $P_k \times R^n$ of polynomial fields on $R^n$ equipped with a certain metric. This ... More
The graph bottleneck identityMar 20 2010Jan 18 2011A matrix $S=(s_{ij})\in{\mathbb R}^{n\times n}$ is said to determine a \emph{transitional measure} for a digraph $G$ on $n$ vertices if for all $i,j,k\in\{1,\...,n\},$ the \emph{transition inequality} $s_{ij} s_{jk}\le s_{ik} s_{jj}$ holds and reduces ... More
A Class of Graph-Geodetic Distances Generalizing the Shortest-Path and the Resistance DistancesOct 15 2008Jan 18 2011A new class of distances for graph vertices is proposed. This class contains parametric families of distances which reduce to the shortest-path, weighted shortest-path, and the resistance distances at the limiting values of the family parameters. The ... More