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Results for "Bernd Schmidt"

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An atomistic derivation of von-Kármán plate theoryJun 29 2019We derive von-K\'arm\'an plate theory from three dimensional, purely atomistic models with classical particle interaction. This derivation is established as a $\Gamma$-limit when considering the limit where the interatomic distance $\varepsilon$ as well ... More
Energy minimising configurations of pre-strained multilayersJun 30 2019We investigate energetically optimal configurations of thin structures with a pre-strain. Depending on the strength of the pre-strain we consider a whole hierarchy of effective plate theories with a spontaneous curvature term, ranging from linearised ... 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
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
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
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
$N^{3/4}$ 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
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 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
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.
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
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
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
Dynamical arrest of ultracold lattice fermionsMay 17 2012Mar 10 2013We theoretically investigate the thermodynamics of an interacting inhomogeneous two-component Fermi gas in an optical lattice. Motivated by a recent experiment by L. Hackerm\"uller et al., Science, 327, 1621 (2010), we study the effect of the interplay ... 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
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
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.
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
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
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
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
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
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
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
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
A hierarchy of multilayered plate modelsMay 27 2019We derive a hierarchy of plate theories for heterogeneous multilayers from three dimensional nonlinear elasticity by means of $\Gamma$-convergence. We allow for layers composed of different materials whose constitutive assumptions may vary significantly ... 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
ILP formulations for the two-stage stochastic Steiner tree problemNov 14 2016We give an overview of new and existing cut- and flow-based ILP formulations for the two-stage stochastic Steiner tree problem and compare the strength of the LP relaxations.
The smallest Dirac eigenvalue in a spin-conformal class and cmc-immersionsSep 03 2003Apr 26 2006Let us fix a conformal class $[g_0]$ and a spin structure $\sigma$ on a compact manifold $M$. For any $g\in [g_0]$, let $\lambda^+_1(g)$ be the smallest positive eigenvalue of the Dirac operator $D$ on $(M,g,\sigma)$. In a previous paper we have shown ... 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
Part-of-Speech-Tagging using morphological informationJun 04 1996This paper presents the results of an experiment to decide the question of authenticity of the supposedly spurious Rhesus - a attic tragedy sometimes credited to Euripides. The experiment involves use of statistics in order to test whether significant ... More
The Willmore Conjecture for immersed tori with small curvature integralJun 10 1999Nov 16 1999The Willmore conjecture states that any immersion F:T^2 -> R^n of a 2-torus into flat euclidean space satisfies $\int_{T^2} H^2\geq 2\pi^2$. We prove it under the condition that the L^p-norm of the Gaussian curvature is sufficiently small.
Waste forms for actinides: borosilicate glassesApr 28 2019Apr 30 2019This high level liquid radioactive reprocessing waste will become vitrified in order to obtain a stable borosilicate waste glass matrix that provides protection against environmental dispersion. Since vitrified waste is in a solid form, transportation, ... 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
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
Equations Defining Toric VarietiesOct 26 1996This article will appear in the proceedings of the AMS Summer Institute in Algebraic Geometry at Santa Cruz, July 1995. The topic is toric ideals, by which I mean the defining ideals of subvarieties of affine or projective space which are parametrized ... More
Nonisomorphic Ordered Sets with Arbitrarily Many Ranks That Produce Equal DecksSep 25 2006We prove that for any $n$ there is a pair $(P_1 ^n , P_2 ^n )$ of nonisomorphic ordered sets such that $P_1 ^n $ and $P_2 ^n $ have equal maximal and minimal decks, equal neighborhood decks, and there are $n+1$ ranks $k_0 , \ldots , k_n $ such that for ... More
Symmetric versions of Laman's TheoremJul 11 2009Recent work has shown that if an isostatic bar and joint framework possesses non-trivial symmetries, then it must satisfy some very simply stated restrictions on the number of joints and bars that are `fixed' by various symmetry operations of the framework. ... More
Injective and non-injective realizations with symmetryAug 13 2008In this paper, we introduce a natural classification of bar and joint frameworks that possess symmetry. This classification establishes the mathematical foundation for extending a variety of results in rigidity, as well as infinitesimal or static rigidity, ... More
Homological Mirror Symmetry in Dimension OneDec 04 2000In this paper we complete the proof began by A. Polishchuk and E. Zaslow (math.AG/9801119) of a weak version of Kontsevich's homological mirror symmetry conjecture for elliptic curves. The main difference to the work of Polishchuk and Zaslow is that we ... More
Spectral estimates on 2-toriJan 08 2001We prove upper and lower bounds for the eigenvalues of the Dirac operator and the Laplace operator on 2-dimensional tori. In particluar we give a lower bound for the first eigenvalue of the Dirac operator for non-trivial spin structures. It is the only ... More
Open Problems in Algebraic StatisticsJul 31 2007Nov 10 2007Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field, with main emphasis ... More
Gromov-Witten invariants of general symplectic manifoldsAug 12 1996Oct 12 1998We present an approach to Gromov-Witten invariants that works on arbitrary (closed) symplectic manifolds. We avoid genericity arguments and take into account singular curves in the very formulation. The method is by first endowing mapping spaces from ... More
The Hurwitz Form of a Projective VarietyOct 24 2014Jul 18 2016The Hurwitz form of a variety is the discriminant that characterizes linear spaces of complementary dimension which intersect the variety in fewer than degree many points. We study computational aspects of the Hurwitz form, relate this to the dual variety ... More
Idealistic exponents and their characteristic polyhedraOct 24 2014In this paper we study Hironaka's idealistic exponents in the situation over $ Spec ( \mathbb{Z} ) $. In particular we give an idealistic interpretation of the tangent cone, the directrix, and the ridge. The main purpose is to introduce the notion of ... More
Recent results of high-energy spin phenomena of gluons and sea-quarks in polarized proton-proton collisions at RHIC at BNLOct 29 2013The STAR experiment at the Relativistic Heavy-Ion Collider at Brookhaven National Laboratory is carrying out a spin physics program in high-energy polarized proton collisions at $\sqrt{s}=200\,$GeV and $\sqrt{s}=500\,$GeV to gain a deeper insight into ... More
SocioAware Content Distribution using P2P solutions in Hybrid NetworksApr 10 2014The growing online traffic that is bringing the infrastructure to its limits induces an urgent demand for an efficient content delivery model. Capitalizing social networks and using advanced delivery networks potentially can help to solve this problem. ... More
An Achievable Rate Region for Three-Pair Interference Channels with NoiseMay 22 2012An achievable rate region for certain noisy three-user-pair interference channels is proposed. The channel class under consideration generalizes the three-pair deterministic interference channel (3-DIC) in the same way as the Telatar-Tse noisy two-pair ... More
Gauged Sigma Models and Magnetic SkyrmionsMay 15 2019We define a gauged non-linear sigma model for a 2-sphere valued field and a $su(2)$ connection on an arbitrary Riemann surface whose energy functional reduces to that for critically coupled magnetic skyrmions in the plane for a particular choice of the ... 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.
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
Description of Helson-Szegö measures in terms of the Schur parameter sequences of associated Schur functionsMar 08 2010Mar 30 2010Let mu be a probability measure on the Borelian sigma-algebra of the unit circle. Then we associate a Schur function theta in the unit disk with mu and give characterizations of the case that mu is a Helson-Szeg\"o measure in terms of the sequence of ... 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
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
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
Shift Operators Contained in Contractions, Pseudocontinuable Schur Functions and Orthogonal Systems on the Unit CircleNov 06 2009The main aim of this paper is to establish the connection between well-known criteria for the pseudocontinuability of a non-inner Schur function Theta in the unit disk. In a canonical way we associate a probability measure mu on the unit circle with Theta. ... More
On a Simultaneous Approach to the Even and Odd Truncated Matricial Stieltjes Moment Problem II. An $α$-Schur-Stieltjes-type algorithm for sequences of holomorphic matrix-valued functionsApr 26 2016The main goal of this paper is to achieve a simultaneous treatment of the even and odd truncated matricial Stieltjes moment problems in the most general case. These results are generalizations of results of Chen and Hu [5,17] which considered the particular ... More
The effect of a modulated flux on the growth of thin filmsNov 14 1997Thin films are usually obtained by depositing atoms with a continuous flux. We show that using a chopped flux changes the growth and the morphology of the film. A simple scaling analysis predicts how the island densities change as a function of the frequency ... More
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
Reactive Synthesis: Towards Output-Sensitive AlgorithmsMar 27 2018Reactive synthesis is a technology for the automatic construction of reactive systems from logical specifications. In these lecture notes, we study different algorithms for the reactive synthesis problem of linear-time temporal logic (LTL). The classic ... More
A formula for the core of an idealOct 14 2004The core of an ideal is the intersection of all its reductions. For large classes of ideals I we explicitly describe the core as a colon ideal of a power of a single reduction and a power of I.
Algebraic Properties of Propositional CalculusJun 11 2009In this short note we relate some known properties of propositional calculus to purely algebraic considerations of a Boolean algebra. Classes of formulas of propositional calculus are considered as elements of a Boolean algebra. As such they can be represented ... More
Manifolds with small Dirac eigenvalues are nilmanifoldsMar 08 2004Mar 10 2004Consider the class of n-dimensional Riemannian spin manifolds with bounded sectional curvatures and diameter, and almost non-negative scalar curvature. Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of the Dirac operator on ... 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
Some remarks on Kurepa's left factorialOct 21 2004We establish a connection between the subfactorial function S(n) and the left factorial function of Kurepa K(n). Some elementary properties and congruences of both functions are described. Finally, we give a calculated distribution of primes below 10000 ... More
Classification of p-adic functions satisfying Kummer type congruencesSep 03 2009Oct 07 2009We introduce $p$-adic Kummer spaces of continuous functions on $\mathbb{Z}_p$ that satisfy certain Kummer type congruences. We will classify these spaces and show their properties, for instance, ring properties and certain decompositions. As a result, ... 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.
Galactic cosmic ray hydrogen spectra and radial gradients in the inner heliosphere measured by the HELIOS Experiment 6May 03 2019Context: The HELIOS solar observation probes provide unique data regarding their orbit and operation time. One of the onboard instruments, the Experiment 6 (E6), is capable of measuring ions from 4 to several hundred MeV/nuc. Aims: In this paper we aim ... 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
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
On the real locus in the Kato-Nakayama space of logarithmic spaces with a view toward toric degenerationsOct 23 2016Apr 17 2018We study the real loci of toric degenerations of complex varieties with reducible central fibre, as introduced in the joint work of the second author with Mark Gross on mirror symmetry. The topology of such degenerations can be explicitly described via ... 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
On a relative Fourier-Mukai transform on genus one fibrationsOct 15 2004Jun 14 2005We study relative Fourier-Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a skew-commutativity relation between this equivalence ... More
Self-stabilizing temperature driven crossover between topological and non-topological ordered phases in one-dimensional conductorsOct 21 2015Dec 30 2015We present a self-consistent analysis of the topological superconductivity arising from the interaction between self-ordered localized magnetic moments and electrons in one-dimensional conductors in contact with a superconductor. We show that due to a ... More
The first conformal Dirac eigenvalue on 2-dimensional toriDec 20 2004Sep 27 2006Let M be a compact manifold with a spin structure \chi and a Riemannian metric g. Let \lambda_g^2 be the smallest eigenvalue of the square of the Dirac operator with respect to g and \chi. The \tau-invariant is defined as \tau(M,\chi):= sup inf \sqrt{\lambda_g^2} ... More
The second Yamabe invariantFeb 04 2005Mar 15 2005Let $(M,g)$ be a compact Riemannian manifold of dimension $n \geq 3$. We define the second Yamabe invariant as the infimum of the second eigenvalue of the Yamabe operator over the metrics conformal to $g$ and of volume 1. We study when it is attained. ... More
A polyhedral characterization of quasi-ordinary singularitiesDec 23 2015May 28 2018Given an irreducible hypersurface singularity of dimension $d$ (defined by a polynomial $f\in K[[ {\bf x} ]][z]$) and the projection to the affine space defined by $K[[ {\bf x} ]]$, we construct an invariant which detects whether the singularity is quasi-ordinary ... More