Results for "Adrian Ernst"

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Noncontact atomic force microscopy simulator with phase-locked-loop controlled frequency detection and excitationJan 30 2007A simulation of an atomic force microscope operating in the constant amplitude dynamic mode is described. The implementation mimics the electronics of a real setup including a digital phase-locked loop (PLL). The PLL is not only used as a very sensitive ... More
Hard topological versus soft geometrical magnetic particle transportJul 10 2019The transport on top of a periodic two-dimensional hexagonal magnetic pattern of (i) a single macroscopic steel sphere, (ii) a doublet of wax/magnetite composite spheres, and (iii) an immiscible mixture of ferrofluid droplets with a perfluorinated liquid ... More
THz Surface Modes and Electron-Phonon Coupling in Bi$_2$Se$_3$(111)Jul 03 2019We present a study of the surface vibrational modes of the topological insulator (TI) Bi$_2$Se$_3$ using inelastic helium atom scattering (HAS) as well as density functional perturbation theory (DFPT). HAS is used to determine the surface phonon dispersion ... More
The characterization of Co-nanoparticles supported on grapheneNov 13 2014Nov 17 2014The results of density functional theory (DFT) calculations and measurements of X-ray photoelectron (XPS) and X-ray emission (XES) spectra of Co-nanoparticles dispersed on graphene/Cu composites are presented. It is found that for 0.02nm and 0.06nm Co ... More
A Nash-Hormander iteration and boundary elements for the Molodensky problemAug 12 2013We investigate the numerical approximation of the nonlinear Molodensky problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. The method, based on a smoothed Nash-Hormander iteration, solves a sequence ... More
Observation of individual molecules trapped on a nanostructured insulatorNov 22 2005For the first time, ordered polar molecules confined in monolayer-deep rectangular pits produced on an alkali halide surface by electron irradiation have been resolved at room temperature by non-contact atomic force microscopy. Molecules self-assemble ... More
Edge states at the boundary between topologically equivalent latticesSep 18 2018Edge currents of paramagnetic colloidal particles propagate at the edge between two topologically equivalent magnetic lattices of different lattice constant when the system is driven with periodic modulation loops of an external magnetic field. The number ... More
Red Shift from Gravitational Back ReactionMar 30 2007Deviations from geodesic motion caused by gravitational radiation have been discussed in the last decades to describe the motion of particles or photons in strong fields around collapsed objects. On cosmological scale this effect, which in the first order ... More
Extinction by grey dust in the intergalactic mediumJun 23 2003Condensation in the outer regions of decaying supernovae is an efficient source of dust with grain size up to 1 micron. The largest grains leave the parent galaxy, thus forming "grey" intergalactic dust, which can explain the observed dimming of light ... More
Thermal equilibrium under the influence of gravitationJul 30 2003Nov 26 2003Gas clouds under the influence of gravitation in thermodynamic equilibrium cannot be isothermal due to the Dufour effect, the energy flux induced by density gradients. In galaxy clusters this effect may be responsible for most of the "cooling flows" instead ... More
Spectroscopic perspective on the interplay between electronic and magnetic properties of magnetically doped topological insulatorsOct 17 2017Nov 28 2017We combine low energy muon spin rotation (LE-$\mu$SR) and soft-X-ray angle-resolved photoemission spectroscopy (SX-ARPES) to study the magnetic and electronic properties of magnetically doped topological insulators, (Bi,Sb)$_2$Te$_3$. We find that one ... More
Numerical simulations of the nonlinear Molodensky problemAug 12 2013We present a boundary element method to compute numerical approximations to the non-linear Molodensky problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. Our solution procedure solves a sequence ... More
On the lambda Bootis spectroscopic binary hypothesisSep 05 2006It is still a matter of debate if the group of lambda Bootis stars is homogeneously defined. A widely discussed working hypothesis formulates that two apparent solar abundant stars of an undetected spectroscopic binary system mimic a single metal-weak ... More
The Spherical Tensor Gradient OperatorMay 06 2005The spherical tensor gradient operator ${\mathcal{Y}}_{\ell}^{m} (\nabla)$, which is obtained by replacing the Cartesian components of $\bm{r}$ by the Cartesian components of $\nabla$ in the regular solid harmonic ${\mathcal{Y}}_{\ell}^{m} (\bm{r})$, ... More
Is the Lorentz Transformation Distance-Dependent?Nov 12 1999An analysis of the Lorentz transformation shows that the unchangeability of the space-time coordinates of the inertial systems under consideration and the possibility of a direct projection of those coordinates onto another are the underlying assumptions ... More
Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by Čížek, Zamastil, and Skála. I. Algebraic TheoryJun 25 2003\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962 - 968 (2003)] introduced in connection with the summation of the divergent perturbation expansion of the hydrogen atom in an external magnetic field a new sequence transformation ... More
Properties of the Ideal Ginzburg-Landau Vortex LatticeApr 10 2003The magnetization curves M(H) for ideal type-II superconductors and the maximum, minimum, and saddle point magnetic fields of the vortex lattice are calculated from Ginzburg-Landau theory for the entire ranges of applied magnetic fields Hc1 <= H < Hc2 ... More
Electrodynamics of Superconductors Exposed to High Frequency FieldsAug 12 2010The electric losses in a bulk or film superconductor exposed to a parallel radio-frequency magnetic field may have three origins: In homogeneous vortex-free superconductors losses proportional to the frequency squared originate from the oscillating normal-conducting ... More
The Vortex Lattice in Ginzburg-Landau SuperconductorsJun 05 2008Abrikosov's solution of the linearized Ginzburg-Landau theory describing a periodic lattice of vortex lines in type-II superconductors at large inductions, is generalized to non-periodic vortex arrangements, e.g., to lattices with a vacancy surrounded ... More
Thin Ohmic or superconducting strip with an applied ac electric currentMar 15 2006The complex impedance, currents, and electric and magnetic fields are calculated as functions of resistivity and frequency or London depth for a long thin strip with applied ac current. Both Ohmic and superconducting strips are considered. While the inductance ... More
Diagram calculus for a type affine $C$ Temperley--Lieb algebra, IOct 06 2009Jun 24 2015In this paper, we present an infinite dimensional associative diagram algebra that satisfies the relations of the generalized Temperley--Lieb algebra having a basis indexed by the fully commutative elements (in the sense of Stembridge) of the Coxeter ... More
Using Coalgebras and the Giry Monad for Interpreting Game Logics --- A TutorialJan 01 2017The stochastic interpretation of Parikh's game logic should not follow the usual pattern of Kripke models, which in turn are based on the Kleisli morphisms for the Giry monad, rather, a specific and more general approach to probabilistic nondeterminism ... More
Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent seriesJun 19 2003Slowly convergent series and sequences as well as divergent series occur quite frequently in the mathematical treatment of scientific problems. In this report, a large number of mainly nonlinear sequence transformations for the acceleration of convergence ... More
Non-cancellable elements in type affine $C$ Coxeter groupsOct 06 2009Jun 04 2015Let $(W,S)$ be a Coxeter system and suppose that $w \in W$ is fully commutative (in the sense of Stembridge) and has a reduced expression beginning (respectively, ending) with $s \in S$. If there exists $t\in S$ such that $s$ and $t$ do not commute and ... More
Sets, the Axiom of Choice, And All That: A TutorialAug 26 2014Aug 29 2014This tutorial deal with the Axiom of Choice and some of its applications to topics related to Computer Science. We will see that the Axiom of Choice is equivalent to some well-known proof principles like Zorn's Lemma or Tuckey's Maximality Principle. ... More
Nonlinear Sequence Transformations: Computational Tools for the Acceleration of Convergence and the Summation of Divergent SeriesJul 10 2001Convergence problems occur abundantly in all branches of mathematics or in the mathematical treatment of the sciences. Sequence transformations are principal tools to overcome convergence problems of the kind. They accomplish this by converting a slowly ... More
Irregular Input Data in Convergence Acceleration and Summation Processes: General Considerations and Some Special Gaussian Hypergeometric Series as Model ProblemsMar 31 2000Sequence transformations accomplish an acceleration of convergence or a summation in the case of divergence by detecting and utilizing regularities of the elements of the sequence to be transformed. For sufficiently large indices, certain asymptotic regularities ... More
Prediction Properties of Aitken's Iterated Delta^2 Process, of Wynn's Epsilon Algorithm, and of Brezinski's Iterated Theta AlgorithmFeb 14 2000The prediction properties of Aitken's iterated Delta^2 process, Wynn's epsilon algorithm, and Brezinski's iterated theta algorithm for (formal) power series are analyzed. As a first step, the defining recursive schemes of these transformations are suitably ... More
Muon Spin Rotation and the Vortex Lattice in SuperconductorsJun 03 2008The magnetic field probability P(B) is calculated from the Ginzburg-Landau theory for various lattices of vortex lines in type-II superconductors: Ideal triangular lattices, lattices with various shear strains and with a super lattice of vacancies, and ... More
Summation of Divergent Power Series by Means of Factorial SeriesMay 04 2010Factorial series played a major role in Stirling's classic book "Methodus Differentialis" (1730), but now only a few specialists still use them. This article wants to show that this neglect is unjustified, and that factorial series are useful numerical ... More
A fuzzy-set theoretical framework for computing exit rates of rare events in potential-driven diffusion processesAug 02 2017This article is about molecular simulation. However, the theoretical results apply for general overdamped Langevin dynamics simulations. Molecular simulation is often used for determining the stability of a complex (e.g., ligand-receptor). The stability ... More
Finite order automorphisms and real forms of affine Kac-Moody algebras in the smooth and algebraic categoryMar 31 2009Automorphisms of finite order and real forms of "smooth" affine Kac-Moody algebras are studied, i.e. of 2-dimensional extensions of the algebra of smooth loops in a simple Lie algebra. It is shown that they can be parametrized by certain invariants and ... More
Efficient long division via Montgomery multiplyMar 02 2013Aug 21 2016We present a novel right-to-left long division algorithm based on the Montgomery modular multiply, consisting of separate highly efficient loops with simply carry structure for computing first the remainder (x mod q) and then the quotient floor(x/q). ... More
Fully Electrified Neugebauer SpacetimesJul 20 1994Jul 29 1994Generalizing a method presented in an earlier paper, we express the complex potentials E and Phi of all stationary axisymmetric electrovac spacetimes that correspond to axis data of the form E(z,0) = (U-W)/(U+W) , Phi(z,0) = V/(U+W) , where U = z^{2} ... More
State-space modeling of dynamic genetic networksAug 16 2013Oct 05 2013The genomic reality is a highly complex and dynamic system. The recent development of high-throughput technologies has enabled researchers to measure the abundance of many genes (in the order of thousands) simultaneously. The challenge is to unravel from ... More
Algebraic Properties of Stochastic Effectivity FunctionsMar 30 2014Effectivity functions are the basic formalism for investigating the semantics game logic. We discuss algebraic properties of stochastic effectivity functions, in particular the relationship to stochastic relations, morphisms and congruences are defined, ... More
Cell Complexes for Arrangements with Group ActionsMay 27 2009For a real oriented hyperplane arrangement, we show that the corresponding Salvetti complex is homotopy equivalent to the complement of the complexified arrangement. This result was originally proved by M. Salvetti. Our proof follows the framework of ... More
Invertible functions on non-archimedean symmetric spacesApr 01 2019Let $u$ be a nowhere vanishing holomorphic function on the Drinfeld space $\Omega^{r}$ of dimension $r-1$, where $r \geq 2$. The logarithm $\log_{q}\lvert u \rvert$ of its absolute value may be regarded as an affine function on the attached Bruhat-Tits ... More
Charged and Neutral Currents in a 3-3-1 Model with Right-Handed NeutrinosDec 29 2007The charged and the neutral currents are obtained by using a formal algebraical approach (developed and applied by the author) within the exact solution of a 3-3-1 gauge model with right-handed neutrinos. The entire Standard Model phenomenology is recovered ... More
Book review of SUPERSTITION by Robert ParkJan 13 2009The 2008 book Superstition: Belief in the age of science, by Robert Park, published by Princeton University Press is briefly reviewed.
Metric inequalities for polygonsDec 19 2009Jun 21 2012Let $A_1,A_2,...,A_n$ be the vertices of a polygon with unit perimeter, that is $\sum_{i=1}^n |A_i A_{i+1}|=1$. We derive various tight estimates on the minimum and maximum values of the sum of pairwise distances, and respectively sum of pairwise squared ... More
Initial Conditions and Global Event Properties from Color Glass CondensateAug 30 2010Perturbative unitarization from non-linear effects is thought to deplete the gluon density for transverse momenta below the saturation scale. Such effects also modify the distribution of gluons produced in heavy-ion collisions in transverse impact parameter ... More
Beable-Guided Quantum Theories: Generalising Quantum Probability LawsApr 26 2012We introduce the idea of a {\it beable-guided quantum theory}. Beable-guided quantum theories (BGQT) are generalisations of quantum theory, inspired by Bell's concept of beables. They modify the quantum probabilities for some specified set of fundamental ... More
A derivation of Witten's conjecture relating Donaldson and Seiberg-Witten invariantsMar 23 2000May 02 2000We generalize Witten's conjectured formula relating Donaldson and Seiberg-Witten invariants to manifolds of non-simple type, via equivariant localization techniques. This approach does not use the theory of non-abelian monopoles, but works directly on ... More
On the Spectrum of the Generalised Petersen GraphsDec 11 2014Apr 10 2015We show that the gap between the two greatest eigenvalues of the generalised Petersen graphs $P(n,k)$ tends to zero as $n \rightarrow \infty$. Moreover, we provide explicit upper bounds on the size of this gap. It follows that these graphs have poor expansion ... More
On the Riemann Hypothesis and the Difference Between PrimesFeb 26 2014May 20 2014We prove some results concerning the distribution of primes on the Riemann hypothesis. First, we prove the explicit result that there exists a prime in the interval $(x-\frac{4}{\pi} \sqrt{x} \log x,x]$ for all $x \geq 2$; this improves a result of Ramar\'{e} ... More
Depth and Stanley Depth of the Canonical Form of a factor of monomial idealsFeb 24 2014Apr 05 2014In this paper we show that the depth and the Stanley depth of the factor of two monomial ideals is invariant under taking a so called canonical form. It follows easily that the Stanley Conjecture holds for the factor if and only if it holds for its canonical ... More
Orbit equivalence and Borel reducibility rigidity for profinite actions with spectral gapSep 12 2013Jul 30 2015We study equivalence relations $\mathcal R(\Gamma\curvearrowright G)$ that arise from left translation actions of countable groups on their profinite completions. Under the assumption that the action $\Gamma\curvearrowright G$ is free and has spectral ... More
On deriving nonreflecting boundary conditions in generalized curvilinear coordinatesJan 20 2015In this work, nonreflecting boundary conditions in generalized three-dimensional curvilinear coordinates are derived, relying on the original analysis that was done in Cartesian two-dimensional coordinates by Giles (AIAA Journal, 28.12, 2050-2058, 1990). ... More
Lorentzian Quantum Reality: Postulates and Toy ModelsNov 11 2014We describe postulates for a novel realist version of relativistic quantum theory or quantum field theory in Minkowski space or other background spacetimes with suitable asymptotic properties. We illustrate their application in toy models.
Scaling Behaviour of the Maximal Growth Rate in the Rosensweig InstabilityJul 16 2001The dependence of the maximal growth rate of the modes of the Rosensweig instability on the properties of the magnetic fluid and the external magnetic induction is studied. An expansion and a fit procedure are applied in the appropriate ranges of the ... More
Dynamic Markov BasesMar 25 2011We present a computational approach for generating Markov bases for multi-way contingency tables whose cells counts might be constrained by fixed marginals and by lower and upper bounds. Our framework includes tables with structural zeros as a particular ... More
A note on k-jet ampleness on surfacesFeb 20 1998We prove Reider type criterions for k-jet spannedness and k-jet ampleness of adjoint bundles for surfaces with at most rational singularities. Moreover, we prove that on smooth surfaces [n(n+4)/4]-very ampleness implies n-jet ampleness.
A Wiki for Business Rules in Open Vocabulary, Executable EnglishMar 03 2011The problem of business-IT alignment is of widespread economic concern. As one way of addressing the problem, this paper describes an online system that functions as a kind of Wiki -- one that supports the collaborative writing and running of business ... More
Algebraic structures in quantum gravitySep 30 2009Mar 01 2010Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with quantum field ... More
Generalization of the Bollobás-Riordan polynomial for tensor graphsDec 08 2010Jul 19 2011Tensor models are used nowadays for implementing a fundamental theory of quantum gravity. We define here a polynomial $\mathcal T$ encoding the supplementary topological information. This polynomial is a natural generalization of the Bollob\'as-Riordan ... More
Extension of the Poincaré Symmetry and Its Field Theoretical ImplementationOct 31 2005May 29 2006We define a new algebraic extension of the Poincar\'e symmetry; this algebra is used to implement a field theoretical model. Free Lagrangians are explicitly constructed; several discussions regarding degrees of freedom, compatibility with Abelian gauge ... More
Shape universality classes in the random sequential addition of non-spherical particlesNov 09 2016Random sequential addition (RSA) models are used in a large variety of contexts to model particle aggregation and jamming. A key feature of these models is the algebraic time dependence of the asymptotic jamming coverage as $t\to\infty$. For the RSA of ... More
The circular $k$-partite crossing number of $K_{m,n}$May 09 2006We define a new kind of crossing number which generalizes both the bipartite crossing number and the outerplanar crossing number. We calculate exact values of this crossing number for many complete bipartite graphs and also give a lower bound.
Vector-scalar mixing to all orders, for an arbitrary gauge model in the generic linear gaugeMar 22 2019May 07 2019I give explicit fromulae for full propagators of vector and scalar fields in a generic spin-1 gauge model quantized in an arbitrary linear covariant gauge. The propagators, expressed in terms of all-order one-particle-irreducible correlation functions, ... More
Learning Representations of Social Media UsersDec 02 2018User representations are routinely used in recommendation systems by platform developers, targeted advertisements by marketers, and by public policy researchers to gauge public opinion across demographic groups. Computer scientists consider the problem ... More
A new realization of the Langlands correspondence for PGL(2,F)Oct 11 2012In this paper, we give a new realization of the local Langlands correspondence for PGL(2,F), where F is a p-adic field of odd residual characteristic. In this case, supercuspidal representations of PGL(2,F) are parameterized by characters of elliptic ... More
Good Reductions of Shimura Varieties of Hodge Type in Arbitrary Unramified Mixed Characteristic, Part IIDec 10 2007Jul 24 2012We prove a conjecture of Milne pertaining to the existence of integral canonical models of Shimura varieties of abelian type in arbitrary unramified mixed characteristic $(0,p)$. As an application we prove for $p=2$ a motivic conjecture of Milne pertaining ... More
Deformation subspaces of p-divisible groups as formal Lie groups associated to p-divisible groupsJul 20 2006Jun 15 2010Let $k$ be an algebraically closed field of characteristic $p>0$. Let $D$ be a $p$-divisible group over $k$ which is not isoclinic. Let $\scrD$ (resp. $\scrD_k$) be the formal deformation space of $D$ over $\Spf(W(k))$ (resp. over $\Spf(k)$). We use axioms ... More
Integral models in unramified mixed characteristic (0,2) of hermitian orthogonal Shimura varieties of PEL type, Part IJul 15 2003Mar 27 2012Let $(G,X)$ be a Shimura variety of PEL type such that $G_{{\bf Q}_2}$ is a split ${\bf GSO}_{2n}$ group with $n\ge 2$. We prove the existence of the integral canonical models of ${\rm Sh}(G,X)/H_2$ in unramified mixed characteristic $(0,2)$, where $H_2$ ... More
On the Tate and Langlands--Rapoport conjectures for special fibres of integral canonical models of Shimura varieties of abelian typeOct 24 2012We prove the isogeny property for special fibres of integral canonical models of compact Shimura varieties of $A_n$, $B_n$, $C_n$, and $D_n^{\dbR}$ type. The approach used also shows that many crystalline cycles on abelian varieties over finite fields ... More
Nef line bundles over finite fieldsNov 27 2011We use Totaro's examples of non-semiample nef line bundles on smooth projective surfaces over finite fields to construct nef line bundles for which the first cohomology group cannot be killed by any generically finite covers. This is used to show a similar ... More
Integral Canonical Models of Shimura Varieties of Preabelian TypeJul 08 2003We prove the existence of integral canonical models of Shimura varieties of preabelian type with respect to primes of characteristic at least 5.
Mod p classification of Shimura F-crystalsApr 02 2003Jan 20 2010Let $k$ be an algebraically closed field of positive characteristic $p$. We first classify the $D$-truncations mod $p$ of Shimura $F$-crystals over $k$ and then we study stratifications defined by inner isomorphism classes of these $D$-truncations. This ... More
Kolmogorov bounds for the normal approximation of the number of triangles in the Erdos-Renyi random graphApr 03 2017We bound the error for the normal approximation of the number of triangles in the Erdos-Renyi random graph with respect to the Kolmogorov metric. Our bounds match the best available Wasserstein-bounds obtained by Barbour, Karonski and Rucinski (1989), ... More
Lifting zero-dimensional schemes and divided powersNov 14 2017Mar 07 2018We study divided power structures on finitely generated $k$-algebras, where $k$ is a field of positive characteristic $p$. As an application we show examples of $0$-dimensional Gorenstein $k$-schemes that do not lift to a fixed noetherian local ring of ... More
Two-loop effects of enhanced electroweak strength in the Higgs sectorJul 28 1996Aug 11 1996The selfcoupling of the Higgs field grows with the mass of the Higgs particle and induces potentially large radiative corrections in the electroweak model. The technical aspects of performing multiloop calculations in the massive case are discussed briefly. ... More
The traveling salesman problem for lines and rays in the planeApr 26 2012In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of $n$ regions (neighborhoods) and we seek a shortest tour that visits each region. In the path variant, we seek a shortest path that visits each region. We present several linear-time ... More
Quantum Reality via Late Time PhotodetectionAug 16 2016We further investigate postulates for realist versions of relativistic quantum theory and quantum field theory in Minkowski space and other background space-times. According to these postulates, quantum theory is supplemented by local variables that depend ... More
Color Glass Condensate at RHIC ?Mar 14 2002Heavy-ion collisions at the BNL-RHIC collider can probe whether gluon saturation effects in nuclei at small x have set in, or whether leading-twist perturbative estimates of particle production are still applicable. I discuss that soon to come data from ... More
Abc of SUSYMay 28 2009This article is a very basic introduction to supersymmetry. It introduces the two kinds of superfields needed for supersymmetric extensions of the Standard Model, the chiral superfield and the vector superfield, and discusses in detail how to construct ... More
A theoretical update on t \bar{t} production near thresholdApr 04 2006We present an evaluation of the t\bar{t} cross section near threshold at next-to-next-to-leading logarithmic accuracy, using a two-step matching procedure. QED corrections are taken into account as well and are shown to be numerically important. Finally ... More
The Physics Programme at SuperBDec 06 2011SuperB is a next generation high luminosity $e^+e^-$ collider that will be built at the Cabibbo Laboratory, Tor Vergata, in Italy. The physics goals of this experiment are to search for signs of physics beyond the Standard Model through precision studies ... More
On the Ext Ring of Koszul RingsJun 01 2015Sep 04 2015The aim of this article is to study the Ext ring associated to a Koszul $R$-ring and to use it to provide further characterisations of the former. As such, for $R$ being a semisimple ring and $A$ a graded Koszul $R$-ring, we will prove that there is an ... More
Graphical Modeling of Spatial Health DataNov 24 2014The literature on Gaussian graphical models (GGMs) contains two equally rich and equally significant domains of research efforts and interests. The first research domain relates to the problem of graph determination. That is, the underlying graph is unknown ... More
An Explicit Result for $|L(1+it,χ)|$Sep 08 2014We give an explicit upper bound for non-principal Dirichlet $L$-functions on the line $s=1+it$. This result can be applied to improve the error in the zero-counting formulae for these functions.
Strong ergodicity, property (T), and orbit equivalence rigidity for translation actionsJun 25 2014We study equivalence relations that arise from translation actions $\Gamma\curvearrowright G$ which are associated to dense embeddings $\Gamma<G$ of countable groups into second countable locally compact groups. Assuming that $G$ is simply connected and ... More
Almost-Ramanujan Graphs and Prime GapsFeb 04 2014The method of Murty and Cioab\u{a} shows how one can use results about gaps between primes to construct families of almost-Ramanujan graphs. In this paper we give a simpler construction which avoids the search for perfect matchings and thus eliminates ... More
An Explicit Result for Primes Between CubesJan 17 2014We prove that there is a prime between $n^3$ and $(n+1)^3$ for all $n \geq \exp(\exp(33.217))$. Our new tool which we derive is a version of Landau's explicit formula for the Riemann zeta-function with explicit bounds on the error term. We use this along ... More
A remark on the Kottwitz homomorphismAug 11 2016Aug 15 2016We prove that for any split connected reductive group G over a p-adic field F, the Kottwitz homomorphism exhibits a homomorphic section.
Fermions in Rotating Reference FramesDec 02 2015Feb 24 2016Current quantisations of fermions in cylindrical coordinates are shown to be inadequate in calculating some single-particle expectation values. This paper develops an alternate quantisation, applicable to one-particle states, which is generalised to rotating ... More
Data structuring for the ontological modelling of wind energy systemsOct 12 2015Small wind projects encounter difficulties to be efficiently deployed, partly because wrong way data and information are managed. Ontologies can overcome the drawbacks of partially available, noisy, inconsistent, and heterogeneous data sources, by providing ... More
On the relation of three theorems of analysis to the axiom of choiceSep 03 2015Nov 21 2016In what follows, essentially two things will be accomplished: Firstly, it will be proven that a version of the Arzel\`a--Ascoli theorem and the Fr\'echet--Kolmogorov theorem are equivalent to the axiom of countable choice for subsets of real numbers. ... More
Kelvin force in a layer of magnetic fluidApr 09 2002The Kelvin force in a layer of magnetic fluid subjected to a homogeneous magnetic field and local heating is studied. The study is motivated by the question about the corresponding Kelvin force density [M. Liu, Phys. Rev. Lett., 2762 (2000)]. It is shown ... More
The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluidsApr 09 2002The Rosensweig instability is the phenomenon that above a certain threshold of a vertical magnetic field peaks appear on the free surface of a horizontal layer of magnetic fluid. In contrast to almost all classical hydrodynamical systems, the nonlinearities ... More
Approximation of smooth functions using Bernstein polynomials in multiple variablesSep 07 2016In this survey, we use (more or less) elementary means to establish the well-known result that for any given smooth multivariate function, the respective multivariate Bernstein polynomials converge to that function in all derivatives on each compact set. ... More
Parallelisation of PyHEADTAIL, a Collective Beam Dynamics Code for Particle Accelerator PhysicsOct 17 2016The longitudinal tracking engine of the particle accelerator simulation application PyHEADTAIL shows a heavy potential for parallelisation. For basic beam circulation, the tracking functionality with the leap-frog algorithm is extracted and compared between ... More
On the outerplanar crossing numbers of complete multipartite graphsMay 10 2006We calculate the outerplanar crossing numbers of complete multipartite graphs which have $n$ partite sets with $m$ vertices and one partite set with $p$ vertices, where either $p|mn$ or $mn|p$.
Introduction to the Differential Algebra Normal Form Algorithm using the Centrifugal Governor as an ExampleJun 26 2019This paper provides a detailed introduction into the differential algebra (DA) based normal form algorithm using the example of the symplectic one dimensional system of the centrifugal governor. The intention of this paper is to make the single steps ... More
The rate of convergence of some Riemann-Stieltjes sumsMar 13 2014We give the rate of convergence of some optimal lower Riemann-Stieltjes sums toward the integral.
Semistable principal G-bundles in positive characteristicDec 12 2003Sep 27 2004Let $X$ be a normal projective variety defined over an algebraically closed field $k$ of positive characteristic. Let $G$ be a connected reductive group defined over $k$. We prove that some Frobenius pull back of a principal $G$-bundle admits the canonical ... More
CM-lifts for Isogeny Classes of Shimura F-crystals over Finite FieldsApr 09 2003Oct 24 2012We extend to large contexts pertaining to Shimura varieties of Hodge type a result of Zink on the existence of lifts to characteristic 0 of suitable representatives of certain isogeny classes of abelian varieties endowed with Frobenius and other endomorphisms ... More
Projective integral models of Shimura varieties of Hodge type with compact factorsAug 30 2004Mar 27 2007Let $(G,X)$ be a Shimura pair of Hodge type such that $G$ is the Mumford--Tate group of some elements of $X$. We assume that for each simple factor $G_0$ of $G^{\ad}$ there exists a simple factor of $G_{0\dbR}$ which is compact. Let $N\Ge 3$. We show ... More
Shimura Varieties and the Mumford-Tate conjecture, part ISep 14 2001We prove the Mumford-Tate conjecture for those abelian varieties over number fields, whose simple factors of their adjoint Mumford-Tate groups have over $\dbR$ certain (products of) non-compact factors. In particular, we prove this conjecture for the ... More
Some cases of the Mumford--Tate conjecture and Shimura varietiesDec 04 2002Dec 18 2007We prove the Mumford--Tate conjecture for those abelian varieties over number fields whose extensions to C have attached adjoint Shimura varieties that are products of simple, adjoint Shimura varieties of certain Shimura types. In particular, we prove ... More