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Results for "Bernd Schmidt"

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Helical Symmetry in Linear SystemsMar 28 2008We investigate properties of solutions of the scalar wave equation and Maxwell's equations on Minkowski space with helical symmetry. Existence of local and global solutions with this symmetry is demonstrated with and without sources. The asymptotic properties ... More
MIP Formulations for the Steiner Forest ProblemSep 04 2017The Steiner Forest problem is among the fundamental network design problems. Finding tight linear programming bounds for the problem is the key for both fast Branch-and-Bound algorithms and good primal-dual approximations. On the theoretical side, the ... More
A variational approach to Navier-StokesFeb 19 2018Oct 24 2018We present a variational resolution of the incompressible Navier-Stokes system by means of stabilized Weighted-Inertia-Dissipation-Energy (WIDE) functionals. The minimization of these parameter-dependent functionals corresponds to an elliptic-in-time ... More
Localized spectral asymptotics for boundary value problems and correlation effects in the free Fermi gas in general domainsJun 07 2010We rigorously derive explicit formulae for the pair correlation function of the ground state of the free Fermi gas in the thermodynamic limit for general geometries of the macroscopic regions occupied by the particles and arbitrary dimension. As a consequence ... More
Ground states of the 2D sticky disc model: fine properties and $N^{3/4}$ law for the deviation from the asymptotic Wulff shapeFeb 26 2013Mar 05 2013We investigate ground state configurations for a general finite number $N$ of particles of the Heitmann-Radin sticky disc pair potential model in two dimensions. Exact energy minimizers are shown to exhibit large microscopic fluctuations about the asymptotic ... More
On the infinite particle limit in Lagrangian dynamics and convergence of optimal transportation meshfree methodsJan 15 2013We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Gamma-converge to a continuum action functional acting on probability measures of particle trajectories. Also the ... More
A Griffith-Euler-Bernoulli theory for thin brittle beams derived from nonlinear models in variational fracture mechanicsFeb 24 2016We study a planar thin brittle beam subject to elastic deformations and cracks described in terms of a nonlinear Griffith energy functional acting on $SBV$ deformations of the beam. In particular we consider the case in which elastic bulk contributions ... More
A quantitative geometric rigidity result in SBDMar 23 2015Jun 02 2015We present a quantitative geometric rigidity estimate for special functions of bounded deformation in a planar setting generalizing the result by Friesecke, James, M\"uller obtained in nonlinear elasticity theory and the piecewise rigidity result by Chambolle, ... More
On the passage from atomistic systems to nonlinear elasticity theoryJul 21 2011May 30 2012We derive continuum limits of atomistic models in the realm of nonlinear elasticity theory rigorously as the interatomic distances tend to zero. In particular we obtain an integral functional acting on the deformation gradient in the continuum theory ... More
Closure and commutability results for Gamma-limits and the geometric linearization and homogenization of multi-well energy functionalsAug 05 2013Under a suitable notion of equivalence of integral densities we prove a $\Gamma$-closure theorem for integral functionals: The limit of a sequence of $\Gamma$-convergent families of such functionals is again a $\Gamma$-convergent family. Its $\Gamma$-limit ... More
Homogenization and the limit of vanishing hardening in Hencky plasticity with non-convex potentialsMar 28 2017We prove a homogenization result for Hencky plasticity functionals with non-convex potentials. We also investigate the influence of a small hardening parameter and show that homogenization and taking the vanishing hardening limit commute.
A sharp version of Ehrenfest's theorem for general self-adjoint operatorsMar 17 2010We prove the Ehrenfest theorem of quantum mechanics under sharp assumptions on the operators involved.
An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problemAug 18 2011Oct 12 2012A two-dimensional atomic mass spring system is investigated for critical fracture loads and its crack path geometry. We rigorously prove that, in the discrete-to-continuum limit, the minimal energy of a crystal under uniaxial tension leads to a universal ... More
An analysis of crystal cleavage in the passage from atomistic models to continuum theoryDec 29 2013Dec 04 2014We study the behavior of atomistic models in general dimensions under uniaxial tension and investigate the system for critical fracture loads. We rigorously prove that in the discrete-to-continuum limit the minimal energy satisfies a particular cleavage ... More
Universal formulae for the limiting elastic energy of membrane networksFeb 07 2011Aug 15 2011We provide universal formulae for the limiting stretching and bending energies of triangulated membrane networks endowed with nearest neighbor bond potentials and cosine-type dihedral angle potentials. The given formulae account for finite elasticity ... More
Existence and Convergence of Solutions of the Boundary Value Problem in Atomistic and Continuum Nonlinear Elasticity TheoryApr 01 2016Jun 29 2016We show existence of solutions for the equations of static atomistic nonlinear elasticity theory on a bounded domain with prescribed boundary values. We also show their convergence to the solutions of continuum nonlinear elasticity theory, with energy ... More
On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regimeMar 03 2014We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Gamma-convergence. We also analyze the ... More
Induction Mapping of the 3D-Modulated Spin Texture of Skyrmions in Thin HelimagnetsOct 23 2017Mar 29 2018Envisaged applications of skyrmions in magnetic memory and logic devices crucially depend on the stability and mobility of these topologically non-trivial magnetic textures in thin films. We present for the first time quantitative maps of the magnetic ... More
Time-Independent Gravitational FieldsMay 13 2000This article reviews, from a global point of view, rigorous results on time independent spacetimes. Throughout attention is confined to isolated bodies at rest or in uniform rotation in an otherwise empty universe. The discussion starts from first principles ... More
How to bypass Birkhoff through extra dimensions (a simple framework for investigating the gravitational collapse in vacuum)May 21 2006It is fair to say that our current mathematical understanding of the dynamics of gravitational collapse to a black hole is limited to the spherically symmetric situation and, in fact, even in this case much remains to be learned. The reason is that Einstein's ... More
Static, Self-Gravitating Elastic BodiesFeb 07 2002Jul 17 2002There is proved an existence theorem, in the Newtonian theory, for static, self-gravitating bodies composed of elastic material. The theorem covers the case where these bodies are small, but allows them to have arbitrary shape.
Celestial mechanics of elastic bodiesDec 29 2006Jul 27 2009We construct time independent configurations of two gravitating elastic bodies. These configurations either correspond to the two bodies moving in a circular orbit around their center of mass or strictly static configurations.
Existence of families of spacetimes with a Newtonian limitAug 19 2009J\"urgen Ehlers developed \emph{frame theory} to better understand the relationship between general relativity and Newtonian gravity. Frame theory contains a parameter $\lambda$, which can be thought of as $1/c^2$, where $c$ is the speed of light. By ... More
Celestial mechanics of elastic bodies IIOct 14 2016Mar 25 2017We construct time independent configurations describing a small elastic body moving in a circular orbit in the Schwarzschild spacetime. These configurations are relativistic versions of Newtonian solutions constructed previously by us. In the process ... More
Tracking Dark Excitons with Exciton Polaritons in Semiconductor MicrocavitiesJun 25 2018Feb 13 2019Dark excitons are of fundamental importance for a wide variety of processes in semiconductors, but are difficult to investigate using optical techniques due to their weak interaction with light fields. We reveal and characterize dark excitons injected ... More
Helical Solutions in Scalar GravityMay 15 2009We construct solutions, for small values of $G$ and angular frequency $\Omega$, of special relativistic scalar gravity coupled to ideally elastic matter which have helical but no stationary or axial symmetry. They correspond to a body without any symmetries ... More
Relativistic ElasticityNov 14 2002Apr 28 2003Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially frame-indifferent ... More
Dynamics of the Optical Spin Hall EffectAug 28 2017We study the time evolution of the Optical Spin Hall Effect (OSHE), which occurs when exciton-polaritons undergo resonant Rayleigh scattering. The resulting spin pattern in momentum space is quantified by calculating the degree of circular polarization ... More
Behavior of Einstein-Rosen Waves at Null InfinityAug 16 1996The asymptotic behavior of Einstein-Rosen waves at null infinity in 4 dimensions is investigated in {\it all} directions by exploiting the relation between the 4-dimensional space-time and the 3-dimensional symmetry reduction thereof. Somewhat surprisingly, ... More
Fermionisation dynamics of a strongly interacting 1D Bose gas after an interaction quenchOct 09 2009Sep 01 2010We study the dynamics of a one-dimensional Bose gas after a sudden change of the interaction strength from zero to a finite value using the numerical time-evolving block decimation (TEBD) algorithm. It is shown that despite the integrability of the system, ... More
Quasi-Normal Modes of Stars and Black HolesSep 20 1999Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present ... More
Discretized vs. continuous models of p-wave interacting fermions in 1DApr 23 2010We present a general mapping between continuous and lattice models of Bose- and Fermi-gases in one dimension, interacting via local two-body interactions. For s-wave interacting bosons we arrive at the Bose-Hubbard model in the weakly interacting, low ... More
Convergence Analysis of Meshfree Approximation SchemesJul 29 2011This work is concerned with the formulation of a general framework for the analysis of meshfree approximation schemes and with the convergence analysis of the Local Maximum-Entropy (LME) scheme as a particular example. We provide conditions for the convergence ... More
Critical behavior in vacuum gravitational collapse in 4+1 dimensionsJun 13 2005We show that the 4+1 dimensional vacuum Einstein equations admit gravitational waves with radial symmetry. The dynamical degrees of freedom correspond to deformations of the three-sphere orthogonal to the $(t,r)$ plane. Gravitational collapse of such ... More
Codimension-two critical behavior in vacuum gravitational collapseAug 22 2006Jan 30 2007We consider the critical behavior at the threshold of black hole formation for the five dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi IX ansatz. Exploiting a discrete symmetry present in this model we predict ... More
Static self-gravitating elastic bodies in Einstein gravityNov 20 2006Jan 12 2009We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution constructed ... More
Boundary conditions in linearized harmonic gravityJun 07 2001Nov 28 2001We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a set of six wave ... More
Asymptotic Structure of Symmetry Reduced General RelativityAug 16 1996Gravitational waves with a space-translation Killing field are considered. In this case, the 4-dimensional Einstein vacuum equations are equivalent to the 3-dimensional Einstein equations with certain matter sources. This interplay between 4- and 3- dimensional ... More
Celestial mechanics of elastic bodies IIOct 14 2016We construct time independent configurations describing a small elastic body moving in a circular orbit in the Schwarzschild spacetime. These configurations are relativistic versions of Newtonian solutions constructed by two of us (R.B.,B.G.S.). In the ... More
Elastic deformations of compact starsFeb 26 2014We prove existence of solutions for an elastic body interacting with itself through its Newtonian gravitational field. Our construction works for configurations near one given by a self-gravitating ball of perfect fluid. We use an implicit function argument. ... More
Rotating elastic bodies in Einstein gravityNov 06 2008We prove that, given a stress-free, axially symmetric elastic body, there exists, for sufficiently small values of the gravitational constant and of the angular frequency, a unique stationary axisymmetric solution to the Einstein equations coupled to ... More
Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shapeSep 04 2009We investigate ground state configurations of atomic systems in two dimensions interacting via short range pair potentials. As the number of particles tends to infinity, we show that low-energy configurations converge to a macroscopic cluster of finite ... More
Methods for the construction of generators of algebraic curvature tensorsJul 20 2005We demonstrate the use of several tools from Algebraic Combinatorics such as Young tableaux, symmetry operators, the Littlewood-Richardson rule and discrete Fourier transforms of symmetric groups in investigations of algebraic curvature tensors.
A Coincidence Formula for Foliated ManifoldsJun 02 2003The main result of the present paper is a coincidence formula for foliated manifolds. To prove this we establish Kuenneth formula, Poincare duality and intersection product in the context of tangential de Rham cohomology and homology of tangential currents. ... More
Short formulas for algebraic covariant derivative curvature tensors via Algebraic CombinatoricsDec 08 2003We consider generators of algebraic covariant derivative curvature tensors R' which can be constructed by a Young symmetrization of product tensors W*U or U*W, where W and U are covariant tensors of order 2 and 3. W is a symmetric or alternating tensor ... More
Iterated Function Systems in Mixed Euclidean and p-adic SpacesOct 23 2006We investigate graph-directed iterated function systems in mixed Euclidean and p-adic spaces. Hausdorff measure and Hausdorff dimension in such spaces are defined, and an upper bound for the Hausdorff dimension is obtained. The relation between the Haar ... More
$β$-Boundedness, Semipassivity, and the KMS-ConditionNov 19 2001Nov 26 2001The proof of a recent result by Guido and Longo establishing the equivalence of the KMS-condition with complete $\beta$-boundedness is shortcut and generalized in such a way that a covariant version of the theorem is obtained.
More Kolakoski SequencesSep 21 2010Our goal in this article is to review the known properties of the mysterious Kolakoski sequence and at the same time look at generalizations of it over arbitrary two letter alphabets. Our primary focus will here be the case where one of the letters is ... More
An effective medium approach to the asymptotics of the statistical moments of the parabolic Anderson model and Lifshitz tailsJun 28 2011Originally introduced in solid state physics to model amorphous materials and alloys exhibiting disorder induced metal-insulator transitions, the Anderson model $H_{\omega}= -\Delta + V_{\omega} $ on $l^2(\bZ^d)$ has become in mathematical physics as ... More
Self-adjoint symmetry operators connected with the magnetic Heisenberg ringOct 02 2009We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in the paper) and ... More
Stationary or static space-times and Young tableauxOct 14 2005Algebraic curvature tensors possess generators which can be formed from symmetric or alternating tensors S, A or tensors \theta with an irreducible (2,1)-symmetry. In differential geometry examples of curvature formulas are known which contain generators ... More
Generators of algebraic curvature tensors based on a (2,1)-symmetryNov 02 2004We consider generators of algebraic curvature tensors R which can be constructed by a Young symmetrization of product tensors U*w or w*U, where U and w are covariant tensors of order 3 and 1. We assume that U belongs to a class of the infinite set S of ... More
Symmetry classes connected with the magnetic Heisenberg ringSep 02 2007We define symmetry classes and commutation symmetries in the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites and investigate them by means of tools from the representation theory of symmetric groups S_N such as decompositions ... More
Quantum liquid of repulsively bound pairs of particles in a latticeOct 07 2006Mar 31 2008Repulsively interacting particles in a periodic potential can form bound composite objects, whose dissociation is suppressed by a band gap. Nearly pure samples of such repulsively bound pairs of cold atoms -- "dimers" -- have recently been prepared by ... More
Attractively bound pairs of atoms in the Bose-Hubbard model and antiferromagnetismFeb 25 2009We consider a periodic lattice loaded with pairs of bosonic atoms tightly bound to each other via strong attractive on-site interaction that exceeds the inter-site tunneling rate. An ensemble of such lattice-dimers is accurately described by an effective ... More
Carbon nanotubes in electric and magnetic fieldsJun 16 2011We derive an effective low-energy theory for metallic (armchair and non-armchair) single-wall nanotubes in the presence of an electric field perpendicular to the nanotube axis, and in the presence of magnetic fields, taking into account spin-orbit interactions ... More
Surface energy and boundary layers for a chain of atoms at low temperatureApr 12 2019We analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard-Jones type. The pressure (stress) is assumed small but positive and bounded away from zero, while the temperature $\beta^{-1}$ ... More
Dynamical compact elastic bodies in general relativityOct 18 2014We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
Spectroscopy of fractional orbital angular momentum statesOct 11 2018We present an approach for measuring the orbital angular momentum (OAM) of light tailored towards applications in spectroscopy and non-integer OAM values. It is based on the OAM sorting method (Berkhout et al., Phys. Rev. Lett. 105, 153601 (2010)). We ... More
Helical modes in carbon nanotubes generated by strong electric fieldsNov 16 2010Helical modes, conducting opposite spins in opposite directions, are shown to exist in metallic armchair nanotubes in an all-electric setup. This is a consequence of the interplay between spin-orbit interaction and strong electric fields. The helical ... More
Fetus: the radar of maternal stress, a cohort studyFeb 26 2019Objective: We hypothesized that prenatal stress (PS) exerts lasting impact on fetal heart rate (fHR). We sought to validate the presence of such PS signature in fHR by measuring coupling between maternal HR (mHR) and fHR. Study design: Prospective observational ... More
Matricial Canonical Moments and Parametrization of Matricial Hausdorff Moment SequencesNov 02 2017In this paper we study moment sequences of matrix-valued measures on compact intervals. A complete parametrization of such sequences is obtained via a symmetric version of matricial canonical moments. Furthermore, distinguished extensions of finite moment ... More
Rational $q\times q$ Carathéodory Functions and Central Non-negative Hermitian MeasuresDec 17 2015We give an explicit representation of central measures corresponding to finite Toeplitz non-negative definite sequences of complex $q\times q$ matrices. Such measures are intimately connected to central $q\times q$ Carath\'eodory functions. This enables ... More
On the propagation of jump discontinuities in relativistic cosmologyJul 03 2000Jul 05 2000A recent dynamical formulation at derivative level $\ptl^{3}g$ for fluid spacetime geometries $({\cal M}, {\bf g}, {\bf u})$, that employs the concept of evolution systems in first-order symmetric hyperbolic format, implies the existence in the Weyl curvature ... More
$N^{3/4}$ law in the cubic latticeJul 01 2018We investigate the Edge-Isoperimetric Problem (EIP) for sets with $n$ elements of the cubic lattice by emphasizing its relation with the emergence of the Wulff shape in the crystallization problem. Minimizers $M_n$ of the edge perimeter are shown to deviate ... More
Failure of hydrogenation in protecting polycyclic aromatic hydrocarbons from fragmentationOct 27 2015A recent study of soft X-ray absorption in native and hydrogenated coronene cations, C$_{24}$H$_{12+m}^+$ $m=0-7$, led to the conclusion that additional hydrogen atoms protect (interstellar) Polycyclic Aromatic Hydrocarbon (PAH) molecules from fragmentation ... More
Helically symmetric N-particle solutions in scalar gravityDec 11 2006Mar 13 2007Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded + half-advanced solution of the scalar wave equation, we consider an N-body problem: we investigate configurations of N particles which form ... More
Dynamical elastic bodies in Newtonian gravityJun 20 2011Well-posedness for the initial value problem for a self-gravitating elastic body with free boundary in Newtonian gravity is proved. In the material frame, the Euler-Lagrange equation becomes, assuming suitable constitutive properties for the elastic material, ... More
Flysig: Dataflow Oriented Delay-Insensitive Processor for Rapid Prototyping of Signal ProcessingOct 12 1998As the one-chip integration of HW-modules designed by different companies becomes more and more popular reliability of a HW-design and evaluation of the timing behavior during the prototype stage are absolutely necessary. One way to guarantee reliability ... More
Polynomial relations among principal minors of a 4x4-matrixDec 02 2008Jun 22 2009The image of the principal minor map for n x n-matrices is shown to be closed. In the 19th century, Nansen and Muir studied the implicitization problem of finding all relations among principal minors when n=4. We complete their partial results by constructing ... More
Alexander duality in subdivisions of Lawrence polytopesFeb 12 2002Jul 12 2002The class of simplicial complexes representing triangulations and subdivisions of Lawrence polytopes is closed under Alexander duality. This gives a new geometric model for oriented matroid duality.
Computing the Integer Programming GapJan 23 2003We determine the maximal gap between the optimal values of an integer program and its linear programming relaxation, where the matrix and cost function are fixed but the right hand side is unspecified. Our formula involves irreducible decomposition of ... More
Tropical Implicitization and Mixed Fiber PolytopesJun 05 2007Jun 20 2010The software TrIm offers implementations of tropical implicitization and tropical elimination, as developed by Tevelev and the authors. Given a polynomial map with generic coefficients, TrIm computes the tropical variety of the image. When the image is ... More
Multigraded Hilbert SchemesJan 28 2002We introduce the multigraded Hilbert scheme, which parametrizes all homogeneous ideals with fixed Hilbert function in a polynomial ring that is graded by any abelian group. Our construction is widely applicable, it provides explicit equations, and it ... More
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical SystemsNov 19 2018The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. ... More
Dirac eigenvalue estimates on surfacesJan 25 2002We prove lower Dirac eigenvalue bounds for closed surfaces with a spin structure whose Arf invariant equals 1. Besides the area only one geometric quantity enters in these estimates, the spin-cut-diameter which depends on the choice of spin structure. ... More
A handy formula for the Fredholm index of Toeplitz plus Hankel operatorsDec 14 2011We consider Toeplitz and Hankel operators with piecewise continuous generating functions on $l^p$-spaces and the Banach algebra generated by them. The goal of this paper is to provide a transparent symbol calculus for the Fredholm property and a handy ... More
Toric degenerations of toric varieties and tropical curvesSep 04 2004Mar 06 2006We show that the counting of rational curves on a complete toric variety that are in general position to the toric prime divisors coincides with the counting of certain tropical curves. The proof is algebraic-geometric and relies on degeneration techniques ... More
Computing j-multiplicityJun 30 2008The j-multiplicity is an invariant that can be defined for any ideal in a Noetherian local ring $(R, m)$. It is equal to the Hilbert-Samuel multiplicity if the ideal is $m$-primary. In this paper we explore the computability of the j-multiplicity, giving ... More
Hyperdeterminantal relations among symmetric principal minorsApr 17 2006Jan 16 2007The principal minors of a symmetric $n{\times}n$-matrix form a vector of length $2^n$. We characterize these vectors in terms of algebraic equations derived from the $ 2{\times}2{\times}2$-hyperdeterminant.
An upper bound on the Kolmogorov widths of a certain family of integral operatorsDec 09 2016We consider the family of integral operators $(K_{\alpha}f)(x)$ from $L^p[0,1]$ to $L^q[0,1]$ given by $$(K_{\alpha}f)(x)=\int_0^1(1-xy)^{\alpha -1}\,f(y)\,\operatorname{d}\!y, \qquad 0<\alpha<1.$$ The main objective is to find upper bounds for the Kolmogorov ... More
Convergence rates of a penalized variational inequality method for nonlinear monotone ill-posed equations in Hilbert spacesJun 03 2018We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized equation on the ... More
Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scalesMay 09 2017Nov 16 2017We study the Tikhonov regularization for ill-posed non-linear operator equations in Hilbert scales. Our focus is on the interplay between the smoothness-promoting properties of the penalty and the smoothness inherent in the solution. The objective is ... More
Errors of regularisation under range inclusions using variable Hilbert scalesMay 21 2010Based on the variable Hilbert scale interpolation inequality bounds for the error of regularisation methods are derived under range inclusions. In this context, new formulae for the modulus of continuity of the inverse of bounded operators with non-closed ... More
Blow-ups of $\mathbb{P}^{n-3}$ at $n$ points and spinor varietiesJun 27 2009Work of Dolgachev and Castravet-Tevelev establishes a bijection between the $2^{n-1}$ weights of the half-spin representations of $\mathfrak{so}_{2n}$ and the generators of the Cox ring of the variety $X_n$ which is obtained by blowing up $\mathbb{P}^{n-3}$ ... More
Kolakoski-(3,1) is a (deformed) model setJun 10 2002Feb 07 2003Unlike the (classical) Kolakoski sequence on the alphabet {1,2}, its analogue on {1,3} can be related to a primitive substitution rule. Using this connection, we prove that the corresponding bi-infinite fixed point is a regular generic model set and thus ... More
Tunneling spectroscopy between one-dimensional helical conductorsJun 29 2018Sep 24 2018We theoretically investigate the tunneling spectroscopy of a system of two parallel one-dimensional helical conductors in the interacting, Luttinger liquid regime. We calculate the non-linear differential conductance as a function of the voltage bias ... More
On primary Carmichael numbersFeb 28 2019The primary Carmichael numbers were recently introduced as a special subset of the Carmichael numbers. A primary Carmichael number $m$ has the unique property that for each prime factor $p$ the sum of the base-$p$ digits of $m$ equals $p$. The first such ... More
Motions of grid-like reflection frameworksSep 26 2017Combinatorial characterisations are obtained of symmetric and anti-symmetric infinitesimal rigidity for two-dimensional frameworks with reflectional symmetry in the case of norms where the unit ball is a quadrilateral and where the reflection acts freely ... More
Dualities in Convex Algebraic GeometryJun 25 2010Convex algebraic geometry concerns the interplay between optimization theory and real algebraic geometry. Its objects of study include convex semialgebraic sets that arise in semidefinite programming and from sums of squares. This article compares three ... More
Non-commutative waves for gravitational anyonsApr 16 2018Dec 22 2018We revisit the representation theory of the quantum double of the universal cover of the Lorentz group in 2+1 dimensions, motivated by its role as a deformed Poincar\'e symmetry and symmetry algebra in (2+1)-dimensional quantum gravity. We express the ... More
A priori parameter choice in Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problemsApr 03 2019We study Tikhonov regularization for certain classes of non-linear ill-posed operator equations in Hilbert space. Emphasis is on the case where the solution smoothness fails to have a finite penalty value, as in the preceding study 'Tikhonov regularization ... More
Weighted Sobolev spaces and regularity for polyhedral domainsSep 04 2006Oct 27 2015We prove a regularity result for the Poisson problem $-\Delta u = f$, $u |\_{\pa \PP} = g$ on a polyhedral domain $\PP \subset \RR^3$ using the \BK\ spaces $\Kond{m}{a}(\PP)$. These are weighted Sobolev spaces in which the weight is given by the distance ... More
Milnor algebras could be isomorphic to modular algebrasMar 15 2007Apr 10 2008We find and describe unexpected isomorphisms between two very different objects associated to hypersurface singularities. One object is the Milnor algebra of a function, while the other object associated to a singularity is the local ring of the flatness ... More
An irreducibility criterion for power seriesMay 18 2016We prove an irreducibility criterion for polynomials with power series coefficients generalizing previous known results concerning quasi-ordinary polynomials.
Influence of topological excitations on Shapiro steps and microwave dynamical conductance in bilayer exciton condensatesJul 30 2012The quantum Hall state at total filling factor $\nu_T=1$ in bilayer systems realizes an exciton condensate and exhibits a zero-bias tunneling anomaly, similar to the Josephson effect in the presence of fluctuations. In contrast to conventional Josephson ... More
Quantitative description of Josephson-like tunneling in $ν_T=1$ quantum Hall bilayersNov 25 2010At total filling factor $\nu_T=1$, interlayer phase coherence in quantum Hall bilayers can result in a tunneling anomaly resembling the Josephson effect in the presence of strong fluctuations. The most robust experimental signature of this effect is a ... More
On the geometry of the $p$-Laplacian operatorApr 26 2016The $p$-Laplacian operator $\Delta_pu={\rm div }\left(|\nabla u|^{p-2}\nabla u\right)$ is not uniformly elliptic for any $p\in(1,2)\cup(2,\infty)$ and degenerates even more when $p\to \infty$ or $p\to 1$. In those two cases the Dirichlet and eigenvalue ... More
Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic GeometryJun 18 2009We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a spectrahedron, and to ... More
The Convex Hull of a VarietyApr 18 2010Jul 01 2010We present a characterization, in terms of projective biduality, for the hypersurfaces appearing in the boundary of the convex hull of a compact real algebraic variety.