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Synthesis and Compression study of orthorhombic $Fe_7(C,Si)_3$: A possible constituent of the Earth's coreMay 27 2019Orthorhombic phase of $Si$-doped $Fe$ carbide is synthesized at high pressures and temperatures using laser-heated diamond anvil cell ($LHDAC$), followed by its characterization using Transmission Electron Microscopy ($TEM$), Raman spectroscopy, and X-ray ... More

The Lonely Vertex ProblemOct 25 2007In a locally finite tiling of n-dim Euclidean space by convex polytopes, each point of the space is either a vertex of at least two tiles, or no vertex at all.

Repeated minimizers of $p$-frame energiesJan 18 2019Aug 12 2019For a collection of $N$ unit vectors $\mathbf{X}=\{x_i\}_{i=1}^N$, define the $p$-frame energy of $\mathbf{X}$ as the quantity $\sum_{i\neq j} |\langle x_i,x_j \rangle|^p$. In this paper, we connect the problem of minimizing this value to another optimization ... More

Detection of melting by in-situ observation of spherical-drop formation in laser-heated diamond-anvil cellsApr 07 2011A simple method for detection of melting event in laser-heated diamond anvil cells (DACs) is introduced. The melting is registered optically by the formation of spherical drops of the investigated material as heated in an inert pressure transmitting medium. ... More

First non-icosahedral boron allotrope synthesized at high pressure and high temperatureFeb 13 2017Theoretical predictions of pressure-induced phase transformations often become long-standing enigmas because of limitations of contemporary available experimental possibilities. Hitherto the existence of a non-icosahedral boron allotrope has been one ... More

Coulomb corrections and thermo-conductivity of a dense plasmaJul 02 2009Feb 06 2010We point out that confusion sometimes arises when using a chemical potential in plasma with Coulomb interactions. The results of our consideration are applied to the discussion of nuclear reactions screening. Finally, we present a transparent derivation ... More

B1-B2 phase transition in MgO at ultra-high static pressureMar 31 2019Studies of the behaviour of solids at ultra-high pressures, those beyond 200 GPa, contribute to our fundamental understanding of materials properties and allow an insight into the processes happening at such extreme conditions relevant for terrestrial ... More

Lower bounds for the simplexity of the n-cubeOct 21 2009Dec 23 2012In this paper we prove a new asymptotic lower bound for the minimal number of simplices in simplicial dissections of $n$-dimensional cubes. In particular we show that the number of simplices in dissections of $n$-cubes without additional vertices is at ... More

Covering by homothets and illuminating convex bodiesMay 25 2019The paper is devoted to coverings by translative homothets and illuminations of convex bodies. For a given positive number $\alpha$ and a convex body $B$, $g_{\alpha}(B)$ is the infimum of $\alpha$-powers of finitely many homothety coefficients less than ... More

Covering by homothets and illuminating convex bodiesMay 25 2019Jun 02 2019The paper is devoted to coverings by translative homothets and illuminations of convex bodies. For a given positive number $\alpha$ and a convex body $B$, $g_{\alpha}(B)$ is the infimum of $\alpha$-powers of finitely many homothety coefficients less than ... More

Optimal measures for p-frame energies on spheresAug 02 2019We provide new answers about the placement of mass on spheres so as to minimize energies of pairwise interactions. We find optimal measures for the $p$-frame energies, i.e. energies with the kernel given by the absolute value of the inner product raised ... More

Minimizing the $p$-frame potentialJan 18 2019For a set of $N$ unit vectors $\{x_1,x_2,\ldots,x_N\}$ in $\mathbb{R}^d$, by a $p$-frame potential we mean $\sum_{i\neq j} |\langle x_i,x_j \rangle|^p$. In this note, we connect the minimization problem of the $p$-frame potential to a certain optimization ... More

Moments of isotropic measures and optimal projective codesApr 25 2019In this paper, we use the linear programming approach to find new upper bounds for the moments of isotropic measures. These bounds are then utilized for finding lower packing bounds and energy bounds for projective codes. We also show that the obtained ... More

A high speed unsupervised speaker retrieval using vector quantization and second-order statisticsAug 27 2010Sep 09 2010This paper describes an effective unsupervised method for query-by-example speaker retrieval. We suppose that only one speaker is in each audio file or in audio segment. The audio data are modeled using a common universal codebook. The codebook is based ... More

On time change equivalence of Borel flowsSep 19 2016This paper addresses the notion of time change equivalence for Borel multidimensional flows. We show that all free flows are time change equivalent up to a compressible set. An appropriate version of this result for non-free flows is also given.

Computational complexity and approximability of guarding of proximity graphsMay 01 2016Jul 26 2016Computational complexity and approximability are studied for a problem of intersecting a set of straight line segments with the smallest cardinality set of disks of fixed radii $r\geq 0$ where the set of segments forms a straight line drawing $G=(V,E,F)$ ... More

Generating News Headlines with Recurrent Neural NetworksDec 05 2015We describe an application of an encoder-decoder recurrent neural network with LSTM units and attention to generating headlines from the text of news articles. We find that the model is quite effective at concisely paraphrasing news articles. Furthermore, ... More

Regular cross sections of Borel flowsJul 08 2015Jul 15 2015Any free Borel flow is shown to admit a cross section with only two possible distances between adjacent points. Non smooth flows are proved to be Lebesgue orbit equivalent if and only if they admit the same number of invariant ergodic probability measures. ... More

An Efficient Local Approach to Convexity Testing of Piecewise-Linear HypersurfacesMar 07 2007We show that a closed piecewise-linear hypersurface immersed in $R^n$ ($n\ge 3$) is the boundary of a convex body if and only if every point in the interior of each $(n-3)$-face has a neighborhood that lies on the boundary of some convex body; no assumptions ... More

On the asymptotics of the principal eigenvalue for a Robin problem with a large parameter in planar domainsMay 14 2013Let $\Omega\subset \RR^2$ be a domain having a compact boundary $\Sigma$ which is Lipschitz and piecewise $C^4$ smooth, and let $\nu$ denote the inward unit normal vector on $\Sigma$. We study the principal eigenvalue $E(\beta)$ of the Laplacian in $\Omega$ ... More

Quasiperiodic surface Maryland models on quantum graphsNov 20 2008We study quantum graphs corresponding to isotropic lattices with quasiperiodic coupling constants given by the same expressions as the coefficients of the discrete surface Maryland model. The absolutely continuous and the pure point spectra are described. ... More

Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory DualitiesDec 20 2012This review covers a number of applications of conformal field theory methods for perturbative calculations in N=4 Super Yang-Mills and ABJM theory. After motivating the role of superconformal symmetry for elementary particle physics research, we review ... More

Note on the question of SikoraNov 01 2007A natural topology on the set of left orderings on free abelian groups and free groups $F_n$, $n>1$ has studied in [1]. It has been proven already that in the abelian case the resulted topological space is a Cantor set. There was a conjecture: this is ... More

Full Groups and Orbit Equivalence in Cantor DynamicsJun 06 2010Jul 15 2010In this note we consider dynamical systems $(X,G)$ on a Cantor set $X$ satisfying some mild technical conditions. The considered class includes, in particular, minimal and transitive aperiodic systems. We prove that two such systems $(X_1,G_1)$ and $(X_2,G_2)$ ... More

On the distribution of the Brownian motion process on its way to hitting zeroJan 05 2010Apr 07 2010We present functional versions of recent results on the univariate distributions of the process $V_{x,u} = x + W_{u\tau(x)},$ $0\le u\le 1$, where $W_\bullet$ is the standard Brownian motion process, $x>0$ and $\tau (x) =\inf\{t>0 : W_{t}=-x\}$.

Equivariant $\mathcal{D}$-modules on rigid analytic spacesAug 24 2017We define coadmissible equivariant $\mathcal{D}$-modules on smooth rigid analytic spaces and relate them to admissible locally analytic representations of semisimple $p$-adic Lie groups.

Tame Decompositions and CollisionsFeb 24 2014A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small minority among all polynomials over a finite field. The tame case, where ... More

On the chromatic number of a simplicial complexJun 20 2013Nov 17 2015In [Ho] A.J. Hoffman proved a lower bound on the chromatic number of a graph in the terms of the largest and the smallest eigenvalues of its adjacency matrix. In this paper, we prove a higher dimensional version of this result and give a lower bound on ... More

Graev ultrametrics and free products of Polish groupsDec 12 2012Oct 10 2013We construct Graev ultrametrics on free products of groups with two-sided invariant ultrametrics and HNN extensions of such groups. We also introduce a notion of a free product of general Polish groups and prove, in particular, that two Polish groups ... More

On the asymptotic behaviour of a dynamic version of the Neyman contagious point processAug 27 2013May 14 2014We consider a dynamic version of the Neyman contagious point process that can be used for modelling the spacial dynamics of biological populations, including species invasion scenarios. Starting with an arbitrary finite initial configuration of points ... More

Measurements of Diffractive Processes at CDFJun 10 2003We review the results of measurements on hard diffractive processes performed by the CDF Collaboration and report preliminary CDF results on two soft diffractive processes with a leading antiproton and a rapidity gap in addition to that associated with ... More

Aspects of Diffraction at the TevatronAug 18 2003Results on soft and hard diffraction obtained by the CDF Collaboration at the Fermilab Tevatron proton-antiproton Collider are reviewed with emphasis on aspects of the data that point to the underlying QCD mechanism for diffraction. The results are interpreted ... More

Surface Curvature Effects on Reflectance from Translucent MaterialsOct 13 2010Nov 15 2010Most of the physically based techniques for rendering translucent objects use the diffusion theory of light scattering in turbid media. The widely used dipole diffusion model (Jensen et al. 2001) applies the diffusion-theory formula derived for a planar ... More

Sample covariance matrices of heavy-tailed distributionsJun 11 2016Let $p>2$, $B\geq 1$, $N\geq n$ and let $X$ be a centered $n$-dimensional random vector with the identity covariance matrix such that $\sup\limits_{a\in S^{n-1}}{\mathrm E}|\langle X,a\rangle|^p\leq B$. Further, let $X_1,X_2,\dots,X_N$ be independent ... More

Capture of Planets Into Mean Motion Resonances and the Origins of Extrasolar Orbital ArchitecturesMay 07 2015The early stages of dynamical evolution of planetary systems are often shaped by dissipative processes that drive orbital migration. In multi-planet systems, convergent amassing of orbits inevitably leads to encounters with rational period ratios, which ... More

Theory of 2D metal-insulator transition I: Zero Magnetic fieldDec 26 2000We propose a scaling theory of 2D metal insulator transition discovered by Kravchenko and coworkers. In this theory conductance/resistance duality is an exact relation. The exponent of the stretched exponential in $\sigma(T)$ is determined by the temperature ... More

On some upper bounds for spin velocity and instability of gapless state of 1-d Heisenberg chainsOct 19 1999We derive upper bounds for spin velocity in half-integer-spin Heisenberg antiferromagnetic chains. We relate these upper bounds to the instability of the gapless state, which is observed in frustrated systems.

Statistical InferenceMar 16 2016What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly reporting p-values ... More

TASI Lectures on Precision Electroweak PhysicsFeb 03 2004These notes are a written version of a set of lectures given at TASI-02 on the topic of precision electroweak physics.

The Classification of Rigid Irregular $G_2$-ConnectionsSep 12 2016Sep 28 2016Using the Katz-Arinkin algorithm we give a complete classification of irreducible rigid irregular connections on a punctured $\mathbb{P}^1_{\mathbb{C}}$ having differential Galois group $G_2$, the exceptional simple algebraic group. In addition to hypergeometric ... More

On the spectrum of a waveguide with periodic cracksJul 21 2010The spectral problem on a periodic domain with cracks is studied. An asymptotic form of dispersion relations is calculated under assumption that the opening of the cracks is small.

Strongly normal cones and the midpoint locally uniform rotundityDec 06 2011We give the method of construction of normal but not strongly normal positive cones in Banach space.

Measuring chemical composition and particle cross-section of ultra-high energy cosmic rays by a ground radio arrayDec 02 2013We present a technique to measure chemical composition and particle cross-section of ultra-high energy cosmic rays using radio data. We relate the geometry of the radio footprint on the ground to the depth of the extensive air shower maximum. We suggest ... More

The Arithmetic Katz-Arinkin Algorithm and Wildly Ramified Rigid $G_2$-Local SystemsJul 26 2018We employ the arithmetic version of the Katz-Arinkin algorithm to give a classification of wildly ramified irreducible rigid $\ell$-adic local systems on open subsets of $\mathbb{P}^1_k$, $k$ the algebraic closure of a finite field, with monodromy group ... More

Bordism classes of the multiple points manifoldsAug 07 2000Let $f:V^n\looparrowright M^m$ be a smooth generic immersion. Then the set of points, that have at least $k$ preimages is an image of a (non-generic) immersion. If the manifolds $V^n$ and $M^m$ are oriented and $m-n$ is even, then the manifold of $k$-fold ... More

Variational principle for Hamiltonians with degenerate bottomOct 25 2007We consider perturbations of Hamiltonians whose Fourier symbol attains its minimum along a hypersurface. Such operators arise in several domains, like spintronics, theory of supercondictivity, or theory of superfluidity. Variational estimates for the ... More

Automatic continuity for homomorphisms into free productsDec 07 2012Jun 11 2013A homomorphism from a completely metrizable topological group into a free product of groups whose image is not contained in a factor of the free product is shown to be continuous with respect to the discrete topology on the range. In particular, any completely ... More

Dynamics of infinite-multivalued transformationsDec 08 2004We consider a transformation of a normalized measure space such that the image of any point is a finite set. We call such transformation $m$-transformation. In this case the orbit of any point looks like a tree. In the study of $m$-transformations we ... More

Invertibility via distance for non-centered random matrices with continuous distributionsJul 30 2017Oct 10 2017Let $A$ be an $n\times n$ random matrix with independent rows $R_1(A),\dots,R_n(A)$, and assume that for any $i\leq n$ and any three-dimensional linear subspace $F\subset {\mathbb R}^n$ the orthogonal projection of $R_i(A)$ onto $F$ has distribution density ... More

An inequality for the maximum curvature through a geometric flowJan 15 2015Jul 29 2015We provide a new proof of the following inequality: the maximum curvature $k_\mathrm{max}$ and the enclosed area $A$ of a smooth Jordan curve satisfy $k_\mathrm{max}\ge \sqrt{\pi/A}$. The feature of our proof is the use of the curve shortening flow.

On Scales of Sobolev spaces associated to generalized Hardy operatorsApr 16 2019We consider the fractional Laplacian with Hardy potential and study the scale of homogeneous $L^p$ Sobolev spaces generated by this operator. Besides generalized and reversed Hardy inequalities, the analysis relies on a H\"ormander multiplier theorem ... More

Reducible boundary conditions in coupled channelsJun 03 2005Sep 07 2005We study Hamiltonians with point interactions in spaces of vector-valued functions. Using some information from the theory of quantum graphs we describe a class of the operators which can be reduced to the direct sum of several one-dimensional problems. ... More

Particle Dark Matter from Physics Beyond the Standard ModelFeb 09 2004In this talk I contrast three different particle dark matter candidates, all motivated by new physics beyond the Standard Model: supersymmetric dark matter, Kaluza-Klein dark matter, and scalar dark matter. I then discuss the prospects for their discovery ... More

Fast Verification of Convexity of Piecewise-linear SurfacesSep 23 2003Nov 24 2003We show that a realization of a closed connected PL-manifold of dimension n-1 in n-dimensional Euclidean space (n>2) is the boundary of a convex polyhedron (finite or infinite) if and only if the interior of each (n-3)-face has a point, which has a neighborhood ... More

A Fast Audio Clustering Using Vector Quantization and Second Order StatisticsSep 23 2010This paper describes an effective unsupervised speaker indexing approach. We suggest a two stage algorithm to speed-up the state-of-the-art algorithm based on the Bayesian Information Criterion (BIC). In the first stage of the merging process a computationally ... More

Einstein-Podolsky-Rosen paradox and measurement of quantum systemFeb 13 1999Einstein-Podolsky-Rosen (EPR) paradox is considered in a relation to a measurement of an arbitrary quantum system . It is shown that the EPR paradox always appears in a gedanken experiment with two successively joined measuring devices.

On the Robin eigenvalues of the Laplacian in the exterior of a convex polygonNov 07 2014Jan 26 2015Let $\Omega\subset \mathbb{R}^2$ be the exterior of a convex polygon whose side lengths are $\ell_1,...,\ell_M$. For $\alpha>0$, let $H^\Omega_\alpha$ denote the Laplacian in $\Omega$, $u\mapsto -\Delta u$, with the Robin boundary conditions $\partial ... More

Spectra of Schroedinger operators on equilateral quantum graphsDec 28 2005Jan 05 2006We consider magnetic Schroedinger operators on quantum graphs with identical edges. The spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the underlying combinatorial graph and a certain Hill operator. In particular, ... More

Stellar explosions: from supernovae to gamma-ray burstsOct 14 2004Current understanding of core collapse and thermonuclear supernovae is reviewed. Recent progress in unveiling the nature of cosmic gamma-ray bursts (GRB) is discussed, with the focus on the apparent link of several GRBs with an energetic subclass of stellar ... More

Computing Entanglement PolytopesAug 09 2018In arXiv:1208.0365 entanglement polytopes where introduced as a coarsening of the SLOCC classification of multipartite entanglement. The advantages of classifying entanglement by entanglement polytopes are a finite hierarchy for all dimensions and a number ... More

Singlet Free Energies of a Static Quark-Antiquark PairSep 01 2004We study the singlet part of the free energy of a static quark anti-quark pair at finite temperature in three flavor QCD with degenerate quark masses using $N_{\tau}=4$ and 6 lattices with Asqtad staggered fermion action. We look at thermodynamics of ... More

A new way to accelerate the D-MORPH method to search for optimal quantum controlSep 12 2017The paper introduces new corrections of different orders of smallness to the D-MORPH method by using the full form of the derivative of the exponential map, defined on a Lie algebra, to search for the optimal control of a quantum system that implements ... More

Radio emission from Air Showers. Comparison of theoretical approachesMar 13 2013While the fluorescence and the ground counter techniques for the detection of ultra-high energy cosmic rays (UHECR) were being developed for decades, the interest in the radio detection diminished after the initial experiments in the 1960s. As a result, ... More

Statistically self-similar fractal setsDec 24 2001In the present paper we define statistically self-similar sets, and, using a modification of method described K.J.Falconer find a Hausdorff dimension of a statistically self-similar set.

Metallurgical processes in AlSi alloy improved by WC nanoparticlesOct 24 2018The influence of a modifier based on WC nanoparticles was investigated using bulk Al in a real industrial process using a commercial AlSi hypoeutectic alloy. The modifier was prepared by hot extrusion approach. Its influence was investigated on Al and ... More

Critical Ising interfaces in multiply-connected domainsSep 20 2013Mar 13 2015We prove a general result on convergence of interfaces in the critical planar Ising model to conformally invariant curves absolutely continuous with respect to SLE(3). Our setup includes multiple interfaces on arbitrary finitely connected domains, and ... More

Centres of skewfields and completely faithful Iwasawa modulesOct 29 2007Let H be a torsionfree compact p-adic analytic group whose Lie algebra is split semisimple. We show that the quotient skewfield of fractions of the Iwasawa algebra \Lambda_H of H has trivial centre and use this result to classify the prime c-ideals in ... More

On approximation of homeomorphisms of a Cantor setOct 03 2005Jan 24 2007We continue to study topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology tau, which was started in the paper (S. Bezuglyi, A.H. Dooley, and J. Kwiatkowski, Topologies on the group of ... More

Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structuresSep 04 2011We consider a class of self-adjoint extensions using the boundary triple technique. Assuming that the associated Weyl function has the special form $M(z)=\big(m(z)\Id-T\big) n(z)^{-1}$ with a bounded self-adjoint operator $T$ and scalar functions $m,n$ ... More

Illumination of convex bodies with many symmetriesJun 29 2016Oct 05 2016Let $n\geq C$ for a large universal constant $C>0$, and let $B$ be a convex body in $R^n$ such that for any $(x_1,x_2,\dots,x_n)\in B$, any choice of signs $\varepsilon_1,\varepsilon_2,\dots,\varepsilon_n\in\{-1,1\}$ and for any permutation $\sigma$ on ... More

Coupled mass-momenta balance for modeling material failureOct 27 2016Cracks are created by massive breakage of molecular or atomic bonds. The latter, in its turn, leads to the highly localized loss of material, which is the reason why even closed cracks are visible by a naked eye. Thus, fracture can be interpreted as the ... More

CMS results on soft diffractionOct 09 2013We present measurements of soft single- and double-diffractive cross sections, as well as of forward rapidity gap cross sections at 7 TeV at the LHC, and compare the results to other measurements and to theoretical predictions implemented in various Monte ... More

Subset Simulation Method for Rare Event Estimation: An IntroductionMay 13 2015This paper provides a detailed introductory description of Subset Simulation, an advanced stochastic simulation method for estimation of small probabilities of rare failure events. A simple and intuitive derivation of the method is given along with the ... More

A remark on the discriminant of Hill's equation and Herglotz functionsJan 08 2014We establish a link between the basic properties of the discriminant of periodic second-order differential equations and an elementary analysis of Herglotz functions. Some generalizations are presented using the language of self-adjoint extensions.

An example of unitary equivalence between self-adjoint extensions and their parametersDec 31 2012Jan 08 2013The spectral problem for self-adjoint extensions is studied using the machinery of boundary triplets. For a class of symmetric operators having Weyl functions of a special type we calculate explicitly the spectral projections in the form of operator-valued ... More

Localization effects in a periodic quantum graph with magnetic field and spin-orbit interactionJul 18 2006Aug 08 2006A general technique for the study of embedded quantum graphs with magnetic fields and spin-orbit interaction is presented. The analysis is used to understand the contribution of Rashba constant to the extreme localization induced by magnetic field in ... More

Localization in a quasiperiodic model on quantum graphsJul 13 2007We show the presence of a dense pure point spectrum on quantum graphs with Maryland-type quasiperiodic Kirchhoff coupling constants at the vertices.

On one uniqueness theorem for M. Rietz potentialsDec 12 2007We prove that there exists a nonzero holderian real-to-real function vanishing together with its M. Rietz potential in all points of some set of positive length. This result improves the one of D. Beliaev and V. Havin. We also extend the results to multidimensional ... More

Pseudoscalar flavor-singlet mesons from lattice QCDMay 20 2019We investigate the masses and mixing of $\eta$, $\eta'$ mesons in the framework of twisted mass lattice QCD with $N_f=2+1+1$ dynamical quark flavors. For the first time we perform a controlled chiral and continuum extrapolation to obtain physical results. ... More

Convexity of Hypersurfaces in Spherical SpacesAug 23 2007Oct 02 2007A spherical set is called convex if for every pair of its points there is at least one minimal geodesic segment that joins these points and lies in the set. We prove that for n >= 3 a complete locally-convex (topological) immersion of a connected (n-1)-manifold ... More

Strengthening of copper by carbon nanotubesOct 18 2018The influence of a modifier based on multi walled carbon nanotubes (MWCNT) is investigated using C11000 copper alloy. The influence of the modifier addition into the melt was investigated using tensile test, hardness measurements, X-ray diffraction method ... More

On locally convex PL-manifolds and fast verification of convexitySep 23 2003Nov 24 2003We show that a realization of a closed connected PL-manifold of dimension n-1 in Euclidean n-space (n>2) is the boundary of a convex polyhedron if and only if the interior of each (n-3)-face has a point, which has a neighborhood lying on the boundary ... More

Smirnov's observable for free boundary conditions, interfaces and crossing probabilitiesApr 01 2014Dec 11 2014We prove convergence results for variants of Smirnov's fermionic observable in the critical Ising model in presence of free boundary conditions. One application of our analysis is a simple proof of a theorem by Hongler and Kyt\"ol\"a on convergence of ... More

On the orientation of graphsDec 27 2000In this short notice we give a universal definition of $\Z_2$-module $Or(\Gamma)$ of orientations of a graph $\Gamma$ and construct a method, by means of which one can easily verify whenever two such special definitions coincide.

Pressure induced Hydrogen-Hydrogen interaction in metallic FeH revealed by NMRFeb 08 2019Knowledge of the behavior of hydrogen in metal hydrides is the key for understanding their electronic properties. So far, no experimental methods exist to access these properties beyond 100 GPa, where high-Tc superconductivity emerges. Here, we present ... More

Localization and AdS/CFT CorrespondenceAug 09 2016Aug 14 2016An interplay between localization and holography is reviewed with the emphasis on the AdS_5/CFT_4 correspondence.

Cross sections of Borel flows with restrictions on the distance setApr 08 2016Given a set of positive reals, we provide a necessary and sufficient condition for a free Borel flow to admit a cross section with all distances between adjacent points coming from this set.

Localization and AdS/CFT CorrespondenceAug 09 2016Oct 15 2016An interplay between localization and holography is reviewed with the emphasis on the AdS_5/CFT_4 correspondence.

A Primordial Origin for Misalignments Between Stellar Spin Axes and Planetary OrbitsApr 18 2013The presence of gaseous giant planets whose orbits lie in extreme proximity to their host stars ("hot Jupiters"), can largely be accounted for by planetary migration, associated with viscous evolution of proto-planetary nebulae. Recently, observations ... More

On the lowest energy excitations of one-dimensional strongly correlated electronsMar 06 1998Aug 28 1999It is proven that the lowest excitations $E_{low}(k)$ of one-dimensional half-integer spin generalized Heisenberg models and half-filled extended Hubbard models are $\pi$-periodic functions. For Hubbard models at fractional fillings $E_{low}{(k+ 2 k_f)} ... More

On signal and extraneous roots in Singular Spectrum AnalysisJun 17 2010In the present paper we study properties of roots of characteristic polynomials for the linear recurrent formulae (LRF) that govern time series. We also investigate how the values of these roots affect Singular Spectrum Analysis implications, in what ... More

Eigenvalue inequalities and absence of threshold resonances for waveguide junctionsJun 30 2016Sep 27 2016Let $\Lambda\subset \mathbb{R}^d$ be a domain consisting of several cylinders attached to a bounded center. One says that $\Lambda$ admits a threshold resonance if there exists a non-trivial bounded function $u$ solving $-\Delta u=\nu u$ in $\Lambda$ ... More

Variational proof of the existence of eigenvalues for star graphsNov 30 2015We provide a purely variational proof of the existence of eigenvalues below the bottom of the essential spectrum for the Schr\"odinger operator with an attractive $\delta$-potential supported by a star graph, i.e. by a finite union of rays emanating from ... More

Stellar black hole mass function: determination and possible implications for fundamental gravityJul 10 2003We discuss masses of stellar black holes found in binary systems and errors in their determination. The observed mass distribution has a broad shape within the range $4-16 M_\odot$ without visible concentration to some preferred value. On the other hand, ... More

Equivalence of Wilson Loops in ABJM and N = 4 SYM TheoryOct 06 2011Oct 27 2011In previous investigations, it was found that four-sided polygonal light-like Wilson loops in ABJM theory calculated to two-loop order have the same form as the corresponding Wilson loop in N = 4 SYM at one-loop order. Here we study light-like polygonal ... More

Dimensional reduction of Lattice Gauge Theory in (2+1)DNov 15 2002This is my Ph.D. thesis defended earlier this year. It contains mostly information already presented in previous Bielefeld/Saclay papers on this subject, though in more detailed form. It also includes actual calculations and some unpublished material ... More

On semiclassical dispersion relations of Harper-like operatorsJan 28 2004Oct 20 2004We describe some semiclassical spectral properties of Harper-like operators, i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and position. The spectral region corresponding to the separatrices of the classical Hamiltonian is studied ... More

An improvement of D-MORPH method for finding quantum optimal controlSep 15 2017The paper examines the prominent algorithm D-MORPH to search for the optimal control of a quantum system in order to implement desired unitary evolution of the quantum system at the final time, and reveals new mathematical expressions for various orders' ... More

Classification of Rigid Irregular $G_2$-ConnectionsSep 12 2016Jul 16 2018Using the Katz-Arinkin algorithm we give a classification of irreducible rigid irregular connections on a punctured $\mathbb{P}^1_{\mathbb{C}}$ having differential Galois group $G_2$, the exceptional simple algebraic group, and slopes having numerator ... More

On the discrete spectrum of Robin Laplacians in conical domainsJul 31 2015We discuss several geometric conditions guaranteeing the finiteness or the infiniteness of the discrete spectrum for Robin Laplacians on conical domains.