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Dirac and Normal Fermions in Graphite and Graphene: Implications to the Quantum Hall EffectSep 02 2006Jan 12 2007Spectral analysis of Shubnikov de Haas (SdH) oscillations of magnetoresistance and of Quantum Hall Effect (QHE) measured in quasi-2D highly oriented pyrolytic graphite (HOPG) [Phys. Rev. Lett. 90, 156402 (2003)] reveals two types of carriers: normal (massive) ... More

Magnetization Measurement of a Possible High-Temperature Superconducting State in Amorphous Carbon Doped with SulfurFeb 26 2009Magnetization M(T,H) measurements performed on thoroughly characterized commercial amorphous carbon powder doped with sulfur (AC-S), revealed the occurrence of an inhomogeneous superconductivity (SC) below T_c = 38 K. The constructed magnetic field-temperature ... More

Graphene Physics in GraphiteDec 24 2007Jan 05 2008Single layers of carbon dubbed "graphenes", from which graphite is built, have attracted broad interest in the scientific community because of recent exciting experimental results. Graphene is interesting from a fundamental research perspective, as well ... More

Phase analysis of quantum oscillations in graphiteFeb 02 2004Nov 04 2004The quantum de Haas van Alphen (dHvA) and Shubnikov de Haas (SdH) oscillations measured in graphite were decomposed by pass-band filtering onto contributions from three different groups of carriers. We develop the two-dimensional phase analysis method ... More

Graphite vs graphene: scientific backgroundNov 21 2010Nobel Prize in Physics 2010 was given for "groundbreaking experiments regarding the two-dimensional material graphene." In fact, before graphene has been extracted from graphite and measured, some of its fundamental physical properties have already been ... More

Comment on "Consistent Interpretation of the Low-Temperature Magnetotransport in Graphite Using the Slonczewski-Weiss-McClure 3D Band-Structure Calculations" (arXiv:0902.1925)Jul 12 2009Nov 12 2009In 2004 we have shown that substantial part of conductivity in graphite is provided by holes with massless linear spectrum - Dirac Fermions that coexist with massive normal carriers - electrons. In a recent Letter [Phys. Rev. Lett. 102, 166403 (2009), ... More

Nernst effect in semi-metals: the meritorious heaviness of electronsNov 06 2006Feb 21 2007We present a study of electric, thermal and thermoelectric transport in elemental Bismuth, which presents a Nernst coefficient much larger than what was found in correlated metals. We argue that this is due to the combination of an exceptionally low carrier ... More

Signatures of Electron Fractionalization in Ultraquantum BismuthFeb 14 2008Because of the long Fermi wavelength of itinerant electrons, the quantum limit of elemental bismuth (unlike most metals) can be attained with a moderate magnetic field. The quantized orbits of electrons shrink with increasing magnetic field. Beyond the ... More

Oscillating Nernst-Ettingshausen effect in Bismuth across the quantum limitDec 05 2006Apr 27 2007In elemental Bismuth, 10$^5$ atoms share a single itinerant electron. Therefore, a moderate magnetic field can confine electrons to the lowest Landau level. We report on the first study of metallic thermoelectricity in this regime. The main thermoelectric ... More

Effect of structural disorder on quantum oscillations in graphiteFeb 06 2017We have studied the effect of structural disorder on the de Haas van Alphen (dHvA) and Shubnikov de Haas (SdH) quantum oscillations measured in single-crystal and highly oriented pyrolytic graphite samples at temperatures down to 30 mK and at magnetic ... More

Nernst effect and dimensionality in the quantum limitSep 11 2009Nernst effect, the transverse voltage generated by a longitudinal thermal gradient in presence of magnetic field has recently emerged as a very sensitive, yet poorly understood, probe of electron organization in solids. Here we report on an experiment ... More

Local and Global Superconductivity in BismuthSep 14 2011We performed magnetization M(H,T) and magnetoresistance R(T,H) measurements on powdered (grain size ~ 149 micrometers) as well as highly oriented rhombohedral (A7) bismuth (Bi) samples consisting of single crystalline blocks of size ~ 1x1 mm2 in the plane ... More

Unstable and elusive superconductorsMay 28 2015We briefly review earlier and report original experimental results in the context of metastable or possible superconducting materials. We show that applied electric field induces conducting state in Copper Chloride (CuCl) whose characteristics resemble ... More

Ferromagnetism and Superconductivity in Carbon-Based SystemsSep 20 2006In this article we shortly review previous and recently published experimental results that provide evidence for intrinsic, magnetic-impurity-free ferromagnetism and for high-temperature superconductivity in carbon-based materials. The available data ... More

Comment on "Quantum Melting of the Quasi-Two-Dimensional Vortex Lattice in $κ-(ET)_2Cu(NCS)_2$"Jul 04 2001In a recent Letter Mola et al. \cite{mola} reported magnetization measurements $M(H,\theta)$ performed on the organic superconductor $\kappa-$(ET)$_2$Cu(NCS)$_2 (T_c = 9.1$ K) as a function of the magnetic field $H$ applied at different angles $\theta$ ... More

Searching in Dynamic Catalogs on a TreeJul 20 2010In this paper we consider the following modification of the iterative search problem. We are given a tree $T$, so that a dynamic catalog $C(v)$ is associated with every tree node $v$. For any $x$ and for any node-to-root path $\pi$ in $T$, we must find ... More

Infinite-dimensional Lie algebras and the period map for curvesJun 23 1994Jun 29 1994We compute higher-order differentials of the period map for curves and show how they factor through the corresponding higher Kodaira-Spencer classes. Our approach is based on the infinitesimal equivariance of the period map, due to Arbarello and De Concini ... More

Quadratic invariants of the elasticity tensorSep 08 2015We study the quadratic invariants of the elasticity tensor in the framework of its unique irreducible decomposition. The key point is that this decomposition generates the direct sum reduction of the elasticity tensor space. The corresponding subspaces ... More

On skewon modification of light cone structureJul 24 2014Jan 08 2015Electromagnetic media with generic linear response provide a rich class of Lorentz violation models. In the framework of a general covariant metric-free approach, we study electromagnetic wave propagation in these media. We define the notion of an optic ... More

Skewon no-go theoremOct 30 2013Axion modification of the electrodynamics can be considered as produced by an irreducible part of the constitutive pseudotensor. In this paper, we study the modification of wave propagation produced by the second irreducible part called skewon. We introduce ... More

Large deviations of U-empirical Kolmogorov-Smirnov tests, and their efficiencyJun 02 2009Non-degenerate U-empirical Kolmogorov-Smirnov tests are studied and their large deviation asymptotics under the null-hypothesis is described. Several examples of such statistics used for testing goodness-of-fit and symmetry are considered. It is shown ... More

Weinstein manifolds revisitedJul 11 2017Aug 29 2017This is a very biased and incomplete survey of some basic notions, old and new results, as well as open problems concerning Weinstein symplectic manifolds.

p-adic uniformization of unitary Shimura varieties IISep 23 1999In this paper we show that certain Shimura varieties, uniformized by the product of complex unit balls, can be p-adically uniformized by the product (of equivariant coverings) of Drinfeld upper half-spaces. We also extend a p-adic uniformization to automorphic ... More

Test compatible metrics and 2-branesNov 14 1999We propose a sufficient condition for a general spherical symmetric static metric to be compatible with classical tests of gravity. A 1-parametric class of such metrics are constructed. The Schwarzschild metric as well as the Yilmaz-Rosen metric are in ... More

p-adic uniformization of unitary Shimura varietiesSep 23 1999In this paper we generalize Cherednik's method and prove that certain Shimura varieties corresponding to groups of unitary similitudes and automorphic vector bundles over them have p-adic uniformization. This is proved for Shimura varieties, uniformized ... More

Lefschetz-Verdier trace formula and a generalization of a theorem of FujiwaraMay 26 2005Nov 25 2005The goal of this paper is to generalize a theorem of Fujiwara (formerly Deligne's conjecture) to the situation appearing in a joint work [KV] with David Kazhdan on the global Langlands correspondence over function fields. Moreover, our proof is more elementary ... More

Moduli spaces of principal F-bundlesMay 13 2002Aug 31 2004In this paper we construct certain moduli spaces, which we call moduli spaces of (principal) $F$-bundles, and study their basic properties. These spaces are associated to triples consisting of a smooth projective geometrically connected curve over a finite ... More

The Lie algebra associated with the lower central series of a right-angled Coxeter groupJan 21 2019We study the lower central series of a right-angled Coxeter group $RC_K$ and the associated Lie algebra $L(RC_K)$. The latter is related to the graph Lie algebra $L_K$. We give an explicit combinatorial description of the first three consecutive factors ... More

Gravity on a parallelizable manifold. Exact solutionsJun 28 1998The wave type field equation $\square \vt^a=\la \vt^a$, where $\vt^a$ is a coframe field on a space-time, was recently proposed to describe the gravity field. This equation has a unique static, spherical-symmetric, asymptotically-flat solution, which ... More

G-Graded Central Polynomials and G-Graded Posner's TheoremOct 13 2016Let F be characteristic zero field, G a residually finite group and W a G-prime and PI F-algebra. By constructing G-graded central polynomials for W, we prove the G-graded version of Posner's theorem. More precisely, if S denotes all non-zero degree e ... More

On the characterization of complex Shimura varietiesSep 23 1999In this paper we recall the construction and basic properties of complex Shimura varieties and show that these properties actually characterize them. This characterization immediately implies the explicit form of Kazhdan's theorem on the conjugation of ... More

Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covarianceJan 26 2009Nov 22 2009We argue that the holographic principle may be hinted at already from low-energy considerations, assuming diffeomorphism invariance, quantum mechanics and Minkowski-like causality. We consider the states of finite spacelike hypersurfaces in a diffeomorphism-invariant ... More

Proximity and Josephson effects in superconducting hybrid structuresNov 17 2003Chapter 1: Superconductivity in thin SN bilayers. Chapter 2: Proximity effect in SF systems. Chapter 3: Josephson effect in SFS junctions. Chapter 4: Decoherence due to nodal quasiparticles in d-wave Josephson junctions.

A Fast Algorithm for Three-Dimensional Layers of Maxima ProblemJul 09 2010May 03 2011We show that the three-dimensional layers-of-maxima problem can be solved in $o(n\log n)$ time in the word RAM model. Our algorithm runs in $O(n(\log \log n)^3)$ deterministic time or $O(n(\log\log n)^2)$ expected time and uses O(n) space. We also describe ... More

A class of quasi-linear equations in coframe gravityNov 24 1998Jul 07 1999We have shown recently that the gravity field phenomena can be described by a traceless part of the wave-type field equation. This is an essentially non-Einsteinian gravity model. It has an exact spherically-symmetric static solution, that yields to the ... More

A few remarks about symplectic fillingNov 26 2003Feb 27 2004We show that any compact symplectic manifold (W,\omega) with boundary embeds as a domain into a closed symplectic manifold, provided that there exists a contact plane \xi on dW which is weakly compatible with omega, i.e. the restriction \omega |\xi does ... More

A proof of a generalization of Deligne's conjectureMay 15 2005Sep 28 2005The goal of this paper is to give a simple proof of Deligne's conjecture (proven by Fujiwara) and to generalize it to the situation appearing in our joint project with David Kazhdan on the global Langlands correspondence over function fields. Our proof ... More

Charge Ordering in Amorphous WO$_{x}$ FilmsJan 11 2007We report on the observation of highly anisotropic viscous electronic conducting phase in amorphous WO$_{1.55}$ films that occurs below a current (I)- and frequency (f)- dependent temperature T*(I, f). At T < T*(I, f) the rotational symmetry of randomly ... More

Submillimeter - sized proximity effect in graphite and bismuthFeb 08 2019In this work, we probe the electrical properties of macroscopic graphite and bismuth in which the electrical current is injected via superconducting electrodes, few millimeters apart from each other. Results reveal the induction of a partial superconducting-like ... More

On the derivation of the equations of motion in theories of gravityJan 02 2001The equations of motion of massive particles in GR are completely determined by the field equation. We utilize the particular form of Einstein's field equation and propose for the $N$-body problem of the equations that are Lorentz invariant a novel algorithm ... More

On the derivation of the equation of motion in a scalar modelDec 12 2000A new method for derivation of the equation of motion from the field equation is proposed. The problem of embedding the singularities in a field satisfying the field equations is discussed.

On a class of invariant coframe operators with application to gravityJul 06 1999Let a differential 4D-manifold with a smooth coframe field be given. Consider the operators on it that are linear in the second order derivatives or quadratic in the first order derivatives of the coframe, both with coefficients that depend on the coframe ... More

Interaction of a Supernova Shock with the other Star in a Binary SystemSep 07 2008Interaction of a fast shock wave generated during a supernova explosion with a magnetized star-companion of the supernova precursor produces a current sheet. We consider the evolution of this current sheet and show that a singularity (shock) is formed ... More

Yoneda lemma for complete Segal spacesJan 22 2014Feb 07 2014In this note we formulate and give a self-contained proof of the Yoneda lemma for infinity categories in the language of complete Segal spaces.

Isorotating Baby SkyrmionsSep 17 2013Oct 11 2013We discuss how internal rotation with fixed angular frequency can affect the solitons in the baby Skyrme model in which the global O(3) symmetry is broken to the SO(2). Two particular choices of the potential term are considered, the "old" potential and ... More

Spinning gravitating Skyrmions in generalized Einstein-Skyrme modelOct 17 2017Dec 15 2017We investigate properties of self-gravitating isorotating Skyrmions in the generalized Einstein-Skyrme model with higher-derivative terms in the matter field sector. These stationary solutions are axially symmetric, regular and asymptotically flat. We ... More

Crystal structures in generalized Skyrme modelMar 30 2017Apr 04 2017We investigate the properties of triply-periodic Skyrme crystals in the generalized Skyrme model $\mathcal{L}_6 + \mathcal{L}_4 + \mathcal{L}_2+ \mathcal{L}_0$ with higher-derivative terms up to sixth order. Three different symmetry breaking potential ... More

Generalized Skyrmions and hairy black holes in asymptotically AdS$_4$ spacetimeDec 06 2016We investigate the properties of spherically symmetric black hole solutions in the generalized Einstein-Skyrme model theory in four-dimensional asymptotically anti-de Sitter space-time. The dependencies of the Skyrmion fields on the cosmological constant ... More

Cooper like paring and energy gap induced by ion electronic polarizabilityJan 24 2016We explore the possibility that the ionic electron polarizabilities of the oxygen ions in the cuprates and the bismutates and the polarizabilities of As and Se ions in the iron pnictides contribute to charge carrier pairing leading to high Tc superconductivity. ... More

The entropy of the Angenent torus is approximately 1.85122Aug 24 2018To study the singularities that appear in mean curvature flow, one must understand self-shrinkers, surfaces that shrink by dilations under mean curvature flow. The simplest examples of self-shrinkers are spheres and cylinders. In 1989, Angenent constructed ... More

Oscillons in the presence of external potentialJun 28 2017Dec 29 2017We discuss similarity between oscillons and oscillational mode in perturbed $\phi^4$. For small depths of the perturbing potential it is difficult to distinguish between oscillons and the mode in moderately long time evolution, moreover one can transform ... More

Yang-Mills ReplacementAug 24 2016Nov 28 2017We develop an analog of harmonic replacement in the gauge theory context. The idea behind harmonic replacement dates back to Schwarz and Perron. The technique, as introduced by Jost and further developed by Colding and Minicozzi, involves taking a map ... More

Lagrangian capsMar 04 2013We establish an $h$-principle for exact Lagrangian embeddings with concave Legendrian boundary. We prove, in particular, that in the complement of the unit ball $B$ in the standard symplectic $\R^{2n}, 2n\geq 6$, there exists an embedded Lagrangian $n$-disc ... More

Path connectedness and entropy density of the space of ergodic hyperbolic measuresMay 09 2015Jun 08 2017We show that the space of hyperbolic ergodic measures of a given index supported on an isolated homoclinic class is path connected and entropy dense provided that any two hyperbolic periodic points in this class are homoclinically related. As a corollary ... More

The entropy of the Angenent torus is approximately 1.85122Aug 24 2018Aug 05 2019To study the singularities that appear in mean curvature flow, one must understand self-shrinkers, surfaces that shrink by dilations under mean curvature flow. The simplest examples of self-shrinkers are spheres and cylinders. In 1989, Angenent constructed ... More

Distance in the Ellipticity GraphJun 24 2010Aug 08 2013The ellipticity graph of a free group $F$ was defined by I. Kapovich and M. Lustig in order to study the outer automorphism group of $F$, which acts on this graph. The graph was constructed to be analogous to the curve complex of a surface. It is a bipartite ... More

Communication complexity of approximate Nash equilibriaAug 23 2016Sep 13 2016For a constant $\epsilon$, we prove a poly(N) lower bound on the (randomized) communication complexity of $\epsilon$-Nash equilibrium in two-player NxN games. For n-player binary-action games we prove an exp(n) lower bound for the (randomized) communication ... More

Path connectedness and entropy density of the space of ergodic hyperbolic measuresMay 09 2015We show that the space of hyperbolic ergodic measures of a given index supported on an isolated homoclinic class is path connected and entropy dense provided that any two hyperbolic periodic points in this class are homoclinically related. As a corollary ... More

Optimal Top-k Document RetrievalJul 25 2013Jul 31 2013Let $\mathcal{D}$ be a collection of $D$ documents, which are strings over an alphabet of size $\sigma$, of total length $n$. We describe a data structure that uses linear space and and reports $k$ most relevant documents that contain a query pattern ... More

Full-fledged Real-Time Indexing for Constant Size AlphabetsFeb 17 2013Jul 06 2013In this paper we describe a data structure that supports pattern matching queries on a dynamically arriving text over an alphabet ofconstant size. Each new symbol can be prepended to $T$ in O(1) worst-case time. At any moment, we can report all occurrences ... More

Computational Aspects of Private Bayesian PersuasionMar 04 2016We study computational questions in a game-theoretic model that, in particular, aims to capture advertising/persuasion applications such as viral marketing. Specifically, we consider a multi-agent Bayesian persuasion model where an informed sender (marketer) ... More

Query Complexity of Correlated EquilibriumJun 11 2013Jul 12 2013We study lower bounds on the query complexity of determining correlated equilibrium. In particular, we consider a query model in which an n-player game is specified via a black box that returns players' utilities at pure action profiles. In this model ... More

Learning of Optimal Forecast Aggregation in Partial Evidence EnvironmentsFeb 20 2018We consider the forecast aggregation problem in repeated settings, where the forecasts are done on a binary event. At each period multiple experts provide forecasts about an event. The goal of the aggregator is to aggregate those forecasts into a subjective ... More

Thermodynamical Formalism Associated with Inducing Schemes for One-dimensional MapsNov 24 2005For a smooth map f of a compact interval I admitting an inducing scheme we establish a thermodynamical formalism, i.e., describe a class of real-valued potential functions $\phi$ on I which admit a unique equilibrium measure $\mu_\phi$. Our results apply ... More

On the commutator subgroup of a right-angled Artin groupFeb 01 2017Dec 19 2018We use polyhedral product models to analyse the structure of the commutator subgroup of a right-angled Artin group. In particular, we provide a minimal set of generators for the commutator subgroup, consisting of special iterated commutators of canonical ... More

Tight Bounds for Online Stable SortingJul 04 2009Although many authors have considered how many ternary comparisons it takes to sort a multiset $S$ of size $n$, the best known upper and lower bounds still differ by a term linear in $n$. In this paper we restrict our attention to online stable sorting ... More

A Way to Measure Very Large Δm for B_s MesonsDec 05 1996While present vertex technology cannot measure x_s much beyond 20, the Standard Model accomodates significantly larger x_s values. This note presents a method to determine very large x_s with present technology. The determination is based upon subtle ... More

Verbally prime T-ideals and graded division algebrasOct 14 2016The notion of verbally prime $T$-ideal or verbally prime algebra is naturally extended to the context of $G$-graded algebras where $G$ is a finite group. It turns out that equivalent definitions for ungraded verbally prime algebras extend to nonequivalent ... More

Graphical potential gamesMay 07 2014Mar 23 2016We study the class of potential games that are also graphical games with respect to a given graph $G$ of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of Markov random fields ... More

Making cobordisms symplecticApr 23 2015May 14 2015We establish an existence $h$-principle for symplectic cobordisms of dimension $2n>4$ with concave overtwisted contact boundary.

$SU(2)$ Yang-Mills solitons in $R^2$ gravityJan 23 2018Mar 06 2018We construct new family of spherically symmetric regular solutions of $SU(2)$ Yang-Mills theory coupled to pure $R^2$ gravity. The particle-like field configurations possess non-integer non-Abelian magnetic charge. A discussion of the main properties ... More

S-Flow GANMay 21 2019This work offers a new method for generating photo-realistic images from semantic label maps and a simulator edge map images. We do so in a conditional manner, where we train a Generative Adversarial network (GAN) given an image and its semantic label ... More

Partially ordered groups and geometry of contact transformationsOct 13 1999We prove, for a class of contact manifolds, that the universal cover of the group of contact diffeomorphisms carries a natural partial order. It leads to a new viewpoint on geometry and dynamics of contactomorphisms. It gives rise to invariants of contactomorphisms ... More

Hadamard-Perron theorems and effective hyperbolicityMar 10 2013We prove several new versions of the Hadamard-Perron Theorem, which relates infinitesimal dynamics to local dynamics for a sequence of local diffeomorphisms, and in particular establishes the existence of local stable and unstable manifolds. Our results ... More

Equilibrium Measures for Maps with Inducing SchemesSep 25 2006Jun 04 2008We introduce a class of continuous maps f of a compact metric space I admitting inducing schemes and describe the tower constructions associated with them. We then establish a thermodynamical formalism, i.e., describe a class of real-valued potential ... More

Integer Quantum Hall Effect in GraphiteMar 07 2006Mar 14 2006We present Hall effect measurements on highly oriented pyrolytic graphite that indicate the occurrence of the integer quantum-Hall-effect. The evidence is given by the observation of regular plateau-like structures in the field dependence of the transverse ... More

Top-K Color Queries for Document RetrievalJul 08 2010Oct 18 2010In this paper we describe a new efficient (in fact optimal) data structure for the {\em top-$K$ color problem}. Each element of an array $A$ is assigned a color $c$ with priority $p(c)$. For a query range $[a,b]$ and a value $K$, we have to report $K$ ... More

Yang-Mills ReplacementAug 24 2016We develop an analog of the harmonic replacement technique of Colding and Minicozzi in the gauge theory context. The idea behind harmonic replacement dates back to Schwarz and Perron, and the technique involves taking a map $v\colon\Sigma\to M$ defined ... More

Optimal Dynamic Sequence RepresentationsJun 29 2012Feb 01 2013We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string $S[1,n]$ over alphabet $[1..\sigma]$ in time $O(\lg n/\lg\lg n)$, which is optimal even on binary sequences and in the ... More

Equidistribution of primitive vectors in $\mathbb{Z}^{n}$Mar 04 2019We prove effective equidistribution of several natural parameters associated to primitive vectors in $\mathbb{Z}^{n}$. These parameters include the direction, the orthogonal lattice, and the length of the shortest solution to the associated $\gcd$ equation. ... More

Approximate Nash Equilibria via SamplingJul 18 2013We prove that in a normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium where each player randomizes uniformly among a set of O(log(m) + log(n)) pure strategies. This result induces an $N^{\log \log N}$ ... More

Some Recent Developments on Kink Collisions and Related TopicsSep 13 2018We review recent works on modeling of dynamics of kinks in 1+1 dimensional $\phi^4$ theory and other related models, like sine-Gordon model or $\phi^6$ theory. We discuss how the spectral structure of small perturbations can affect the dynamics of non-perturbative ... More

Endoscopic decomposition of characters of certain cuspidal representationsSep 18 2003Mar 04 2004We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

Duality in finite element exterior calculus and Hodge duality on the sphereJun 14 2019Finite element exterior calculus refers to the development of finite element methods for differential forms, generalizing several earlier finite element spaces of scalar fields and vector fields to arbitrary dimension $n$, arbitrary polynomial degree ... More

Verbally prime T-ideals and graded division algebrasOct 14 2016May 08 2018Let $F$ be an algebraically closed field of characteristic zero and let $G$ be a finite group. We consider graded Verbally prime $T$-ideals in the free $G$-graded algebra. It turns out that equivalent definitions in the ordinary case (i.e. ungraded) extend ... More

On Generalized Rectangular Fuzzy Model for AssessmentJan 05 2015The article is dedicated to the analysis of the existing models for assessment based of the fuzzy logic centroid technique. A new Generalized Rectangular Model were developed. Some generalizations of the existing models are offered.

Polyhedral products and commutator subgroups of right-angled Artin and Coxeter groupsMar 22 2016Sep 01 2016We construct and study polyhedral product models for classifying spaces of right-angled Artin and Coxeter groups, general graph product groups and their commutator subgroups. By way of application, we give a criterion of freeness for the commutator subgroup ... More

Rotation of quantum liquid without singular vortex linesMay 17 2011Dec 03 2011The operator equations for quantum hydrodynamics are discussed and solved in a simple cylindrical geometry. We find a solution with the velocity curl "frozen" into a density of the liquid in the absence of singular vortex lines. The spectrum of small ... More

Sorted Range ReportingApr 20 2012Apr 25 2012In this paper we consider a variant of the orthogonal range reporting problem when all points should be reported in the sorted order of their $x$-coordinates. We show that reporting two-dimensional points with this additional condition can be organized ... More

The Sparse Principal Component Analysis Problem: Optimality Conditions and AlgorithmsJul 29 2015Mar 08 2017Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to interpret the ... More

Symplectic quasi-states on the quadric surface and Lagrangian submanifoldsJun 12 2010The quantum homology of the monotone complex quadric surface splits into the sum of two fields. We outline a proof of the following statement: The unities of these fields give rise to distinct symplectic quasi-states defined by asymptotic spectral invariants. ... More

The topology of rationally and polynomially convex domainsMay 07 2013Feb 27 2014We give in this article necessary and sufficient conditions on the topology of rationally and polynomially convex domains.

Stein structures: existence and flexibilityMay 07 2013This survey on the topology of Stein manifolds is an extract from our recent joint book. It is compiled from two short lecture series given by the first author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred Renyi Institute of Mathematics, ... More

Subgroups of Chevalley groups of types $B_l$ and $C_l$ containing the group over a subring and corresponding carpetsDec 10 2018We continue study of subgroups of a Chevalley group $G_P(\Phi,R)$ over a ring $R$ with a root system $\Phi$ and a weight lattice $P$, containing the elementary subgroup $E_P(\Phi,K)$ over a subring $K$ of $R$. Recently A. Bak and A. Stepanov considered ... More

On endoscopic decomposition of certain depth zero representationsAug 31 2004Nov 25 2005We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

Making cobordisms symplecticApr 23 2015Apr 07 2017We establish an existence $h$-principle for symplectic cobordisms of dimension $2n>4$ with concave overtwisted contact boundary.

Duality in finite element exterior calculusJun 30 2018In order to generalize finite element methods to differential forms, Arnold, Falk, and Winther constructed two families of spaces of polynomial differential forms on a simplex $T$, the $\mathcal P_r\Lambda^k(T)$ spaces and the $\mathcal P_r^-\Lambda^k(T)$ ... More

On the injectivity radius in Hofer's geometryApr 16 2014Apr 19 2014In this note we consider the following conjecture: given any closed symplectic manifold $M$, there is a sufficiently small real positive number $\rho$ such that the open ball of radius $\rho$ in the Hofer metric centered at the identity on the group of ... More

The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagationAug 05 2012In linear anisotropic elasticity, the elastic properties of a medium are described by the fourth rank elasticity tensor C. The decomposition of C into a partially symmetric tensor M and a partially antisymmetric tensors N is often used in the literature. ... More

Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole SpacetimesDec 27 2015In this paper, we provide an elementary, unified treatment of two distinct blue-shift instabilities for the scalar wave equation on a fixed Kerr black hole background: the celebrated blue-shift at the Cauchy horizon (familiar from the strong cosmic censorship ... More