total 140742took 0.13s

Index-p abelianization data of p-class tower groups, IIJan 02 2016Let \(p\) be a prime and \(K\) be a number field with non-trivial \(p\)-class group \(\mathrm{Cl}_p(K)\). An important step in identifying the Galois group \(G=\mathrm{G}_p^\infty(K)\) of the maximal unramified pro-\(p\) extension of \(K\) is to determine ... More

Normal lattice of certain metabelian p-groups G with \(G/G^\prime\simeq (p,p)\)Mar 16 2014Let p be an odd prime. The lattice of all normal subgroups and the terms of the lower and upper central series are determined for all metabelian p-groups with generator rank d=2 having abelianization of type (p,p) and minimal defect of commutativity k=0. ... More

The distribution of second p-class groups on coclass graphsMar 15 2014General concepts and strategies are developed for identifying the isomorphism type of the second p-class group \(G=Gal(F_p^2(K) | K)\), that is the Galois group of the second Hilbert p-class field \(F_p^2(K)\), of a number field K, for a prime p. The ... More

Deep transfers of p-class tower groupsJul 02 2017Let p be a prime. For any finite p-group G, the deep transfers T(H,G'):H/H' --> G'/G'' from the maximal subgroups H of index (G:H)=p in G to the derived subgroup G' are introduced as an innovative tool for identifying G uniquely by means of the family ... More

Three stage towers of 5-class fieldsApr 23 2016With K=Q((3812377)^(1/2)) we give the first example of an algebraic number field possessing a 5-class tower of exact length L(5,K)=3. The rigorous proof is conducted by means of the p-group generation algorithm, showing the existence of a unique finite ... More

Differential principal factors and Polya property of pure metacyclic fieldsDec 06 2018Barrucand and Cohn's theory of principal factorizations in pure cubic fields \(\mathbb{Q}(\sqrt[3]{D})\) and their Galois closures \(\mathbb{Q}(\zeta_3,\sqrt[3]{D})\) with \(3\) types is generalized to pure quintic fields \(L=\mathbb{Q}(\sqrt[5]{D})\) ... More

Annihilator ideals of two-generated metabelian p-groupsMar 30 2016For a metabelian p-group G = <x,y> with two generators x and y, the annihilator A < Z[X,Y] of the main commutator [y,x] of G, as an ideal of bivariate polynomials with integer coefficients, is determined by means of a presentation for G. Furtw\"angler's ... More

Generalized Artin pattern of heterogeneous multiplets of dihedral fields and proof of Scholz's conjectureApr 12 2019The concept of Artin transfer pattern $((\ker(T_{K,N_i}))_i,(\mathrm{Cl}_p(N_i))_i)$ for homogeneous multiplets $(N_1,\ldots,N_m)$ of unramified cyclic prime degree p extensions $N_i/K$ of a base field K with p-class transfer homomorphisms$T_{K,N_i}:\,\mathrm{Cl}_p(K)\to\mathrm{Cl}_p(N_i)$ ... More

Recent progress in determining p-class field towersMay 31 2016For a fixed prime p, the p-class tower F(p,infinity,K) of a number field K is considered to be known if a pro-p presentation of the Galois group H = Gal( F(p,infinity,K)/K ) is given. In the last few years, it turned out that the Artin pattern AP(K) = ... More

Criteria for three-stage towers of p-class fieldsJan 02 2016Nov 28 2016Let p be a prime and K be a number field with non-trivial p-class group Cl(p,K). A crucial step in identifying the Galois group G=G(p,K) of the maximal unramified pro-p extension of K is to determine its two-stage approximation M=G(p,2,K), that is the ... More

The second p-class group of a number fieldMar 16 2014For a prime \(p\ge 2\) and a number field K with p-class group of type (p,p) it is shown that the class, coclass, and further invariants of the metabelian Galois group \(G=Gal(F_p^2(K) | K)\) of the second Hilbert p-class field \(F_p^2(K)\) of K are determined ... More

Principalization algorithm via class group structureMar 15 2014For an algebraic number field K with 3-class group \(Cl_3(K)\) of type (3,3), the structure of the 3-class groups \(Cl_3(N_i)\) of the four unramified cyclic cubic extension fields \(N_i\), \(1\le i\le 4\), of K is calculated with the aid of presentations ... More

Modeling rooted in-trees by finite p-groupsJan 27 2017The aim of this chapter is to provide an adequate graph theoretic framework for the description of periodic bifurcations which have recently been discovered in descendant trees of finite p-groups. The graph theoretic concepts of rooted in-trees with weighted ... More

Coarse cohomology types of pure meta cyclic fieldsDec 24 2018An unexpected behavior of pure septic fields L = Q(D^1/7) with certain prime radicands D congruent to 2 or 4 modulo 7, which split in the cyclotomic field of seventh roots of unity, is proved by direct computation. Whereas the Galois closures N = Q(zeta_7, ... More

Periodic bifurcations in descendant trees of finite (p)-groupsFeb 11 2015Theoretical background and an implementation of the (p)-group generation algorithm by Newman and O'Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite (p)-groups.

p-Capitulation over number fields with p-class rank twoMay 12 2016Theoretical foundations of a new algorithm for determining the p-capitulation type kappa(K) of a number field K with p-class rank rho=2 are presented. Since kappa(K) alone is insufficient for identifying the second p-class group G=Gal(F(p,2,K) | K) of ... More

Quadratic p-ring spaces for counting dihedral fieldsMar 16 2014Let p denote an odd prime. For all p-admissible conductors c over a quadratic number field \(K=\mathbb{Q}(\sqrt{d})\), p-ring spaces \(V_p(c)\) modulo c are introduced by defining a morphism \(\psi:\,f\mapsto V_p(f)\) from the divisor lattice \(\mathbb{N}\) ... More

New number fields with known p-class towerOct 02 2015The p-class tower $F_p^\infty(k)$ of a number field k is its maximal unramified pro-p extension. It is considered to be known when the p-tower group, that is the Galois group $G:=Gal(F_p^\infty(k)/k)$, can be identified by an explicit presentation. The ... More

Co-periodicity isomorphisms between forests of finite p-groupsFeb 09 2018Based on a general theory of descendant trees of finite p-groups and the virtual periodicity isomorphisms between the branches of a coclass subtree, the behavior of algebraic invariants of the tree vertices and their automorphism groups under these isomorphisms ... More

Periodic sequences of p-class tower groupsApr 03 2015Recent examples of periodic bifurcations in descendant trees of finite p-groups with p in {2,3} are used to show that the possible p-class tower groups G of certain multiquadratic fields K with p-class group of type (2,2,2), resp. (3,3), form periodic ... More

Index-\(p\) abelianization data of \(p\)-class tower groupsFeb 11 2015Given a fixed prime number \(p\), the multiplet of abelian type invariants of the \(p\)-class groups of all unramified cyclic degree \(p\) extensions of a number field \(K\) is called its IPAD (index-\(p\) abelianization data). These invariants have proved ... More

The strategy of pattern recognition via Artin transfers applied to finite towers of 2-class fieldsJun 02 2019The isomorphism type of the Galois group of the 2-class field tower of quadratic number fields having a 2-class group with abelian type invariants (4,4) is determined by means of information on the transfer of 2-classes to unramified abelian 2-extensions, ... More

Tables of pure quintic fieldsDec 06 2018By making use of our generalization of Barrucand and Cohn's theory of principal factorizations in pure cubic fields $\mathbb{Q}(\sqrt[3]{D})$ and their Galois closures $\mathbb{Q}(\zeta_3,\sqrt[3]{D})$ with 3 possible types to pure quintic fields $L=\mathbb{Q}(\sqrt[5]{D})$ ... More

Artin transfer patterns on descendant trees of finite p-groupsNov 24 2015Based on a thorough theory of the Artin transfer homomorphism \(T_{G,H}:\,G\to H/H^\prime\) from a group \(G\) to the abelianization \(H/H^\prime\) of a subgroup \(H\le G\) of finite index \(n=(G:H)\), and its connection with the permutation representation ... More

Successive approximation of p-class towersOct 11 2017Let F be a number field and p be a prime. In the Successive Approximation Theorem, we prove that, for each positive integer n, finitely many candidates for the Galois group G(p,n,F) of the n-th stage F(p,n) of the p-class tower F(p,infinity) over F are ... More

Transfers of metabelian p-groupsMar 16 2014Explicit expressions for the transfers \(V_i\) from a metabelian p-group G of coclass cc(G)=1 to its maximal normal subgroups \(M_i\) \((1\le i\le p+1)\) are derived by means of relations for generators. The expressions for the exceptional case p=2 differ ... More

$3$-class field towers of exact length $3$Dec 01 2013The $p$-group generation algorithm is used to verify that the Hilbert $3$-class field tower has length $3$ for certain imaginary quadratic fields $K$ with $3$-class group $\mathrm{Cl}_3(K) \cong [3,3]$. Our results provide the first examples of finite ... More

Principalization of $2$-class groups of type $(2,2,2)$ of biquadratic fields $\mathbb{Q}\left(\sqrt{\strut p_1p_2q},\sqrt{\strut -1}\right)$Apr 14 2014Let $p_1\equiv p_2\equiv -q\equiv1 \pmod4$ be different primes such that $\displaystyle\left(\frac{2}{p_1}\right)= \displaystyle\left(\frac{2}{p_2}\right)=\displaystyle\left(\frac{p_1}{q}\right)=\displaystyle\left(\frac{p_2}{q}\right)=-1$. Put $d=p_1p_2q$ ... More

Structure of relative genus fields of cubic Kummer extensionsAug 14 2018Let $\mathrm{k}=\mathbb{Q}(\sqrt[3]{d},\zeta_3)$, where $d>1$ is a cube-free positive integer, $\mathrm{k}_0=\mathbb{Q}(\zeta_3)$ be the cyclotomic field containing a primitive cube root of unity $\zeta_3$, and $\mathrm{k}^{*}$ be the relative genus field ... More

$3$-rank of ambiguous class groups in cubic Kummer extensionsApr 03 2018Aug 09 2018Let $\mathrm{k}=\mathbb{Q}(\sqrt[3]{d},\zeta_3)$ be the Galois closure of a pure cubic field $\mathbb{Q}(\sqrt[3]{d})$, where $d>1$ is a cube-free positive integer and $\zeta_3$ is a primitive third root of unity. Denote by $C_{\mathrm{k},3}^{(\sigma)}$ ... More

$3$-rank of ambiguous class groups of cubic Kummer extensionsApr 03 2018Apr 01 2019Let $k=k_0(\sqrt[3]{d})$ be a cubic Kummer extension of $k_0=\mathbb{Q}(\zeta_3)$ with $d>1$ a cube-free integer and $\zeta_3$ a primitive third root of unity. Denote by $C_{k,3}^{(\sigma)}$ the $3$-group of ambiguous classes of the extension $k/k_0$ ... More

Errors induced by the neglect of polarization in radiance calculations for three-dimensional cloudy atmospheresJan 07 2019Remote sensing instruments observe radiation being scattered and absorbed by molecules, aerosol particles, cloud droplets and ice crystals. In order to interpret and accurately model such observations, the vector radiative transfer equation needs to be ... More

Distributive Gruppen endlicher Ordnung [Finite Distributive Groups]Mar 25 2014This is a translation. I have added translations for (possibly) outdated definitions in an appendix at the end. In this paper, we define distributive groups and show some properties of them. We then concern ourselves with the homogeinity of distributive ... More

Torsion, topology and CPT anomaly in two-dimensional chiral U(1) gauge theoryMay 30 2001Sep 07 2001We consider the CPT anomaly of two-dimensional chiral U(1) gauge theory on a torus with topologically nontrivial zweibeins corresponding to the presence of spacetime torsion. The resulting chiral determinant can be expressed in terms of the standard chiral ... More

Forensic Similarity for Digital ImagesFeb 13 2019In this paper we introduce a new digital image forensics approach called forensic similarity, which determines whether two image patches contain the same forensic trace or different forensic traces. One benefit of this approach is that prior knowledge, ... More

The Life of a Free Soap FilmOct 12 2010"The Life of a Free Soap Film" is a fluid dynamics video for the Gallery of Fluid Motion intended to showcase the novel experimental techniques that we have developed in our laboratory to study the retraction of planar liquid films of various shapes and ... More

Selectron Pair Production in Electron-Electron-ScatteringSep 20 2001We investigate pair production of selectrons in electron-electron-scattering with subsequent decay into an electron and the LSP including ISR and beamstrahlung. This process can be used at a linear collider to measure the selectron masses and the gaugino ... More

The Hubble Sequence in Groups: The Birth of the Early-Type GalaxiesAug 19 2010May 26 2011The physical mechanisms and timescales that determine the morphological signatures and the quenching of star formation of typical (~L*) elliptical galaxies are not well understood. To address this issue, we have simulated the formation of a group of galaxies ... More

ALIS: An efficient method to compute high spectral resolution polarized solar radiances using the Monte Carlo approachJan 07 2019An efficient method to compute accurate polarized solar radiance spectra using the (three-dimensional) Monte Carlo model MYSTIC has been developed. Such high resolution spectra are measured by various satellite instruments for remote sensing of atmospheric ... More

Buried Points in Julia SetsOct 23 2008We give an introduction to buried points in Julia sets and a list of questions about buried points, written to encourage aficionados of topology and dynamics to work on these questions.

The Formation of Galaxy DisksJan 11 2008Jan 14 2008We present a new set of multi-million particle SPH simulations of the formation of disk dominated galaxies in a cosmological context. Some of these galaxies are higher resolution versions of the models already described in Governato et al (2007). To correctly ... More

Tidal debris in elliptical galaxies as tracers of mergers with disksJan 30 2008Aug 20 2008We use a set of high-resolution N-body simulations of binary galaxy mergers to show that the morphologies of the tidal features that are seen around a large fraction of nearby, massive ellipticals in the field, cannot be reproduced by equal-mass dissipationless ... More

Quantum spin dynamics of individual neutral impurities coupled to a Bose-Einstein condensateFeb 23 2018Aug 31 2018We report on spin dynamics of individual, localized neutral impurities immersed in a Bose-Einstein condensate. Single Cesium atoms are transported into a cloud of Rubidium atoms, thermalize with the bath, and the ensuing spin-exchange between localized ... More

Single-atom quantum probes for ultracold gases using nonequilibrium spin dynamicsJun 03 2019Quantum probes are atomic-sized devices mapping information of their environment to quantum mechanical states. By improving measurements and at the same time minimizing perturbation of the environment, they form a central asset for quantum technologies. ... More

Using nonequilibrium thermodynamics to optimize the cooling of a dilute atomic gasJan 18 2019Optimizing thermodynamic processes far from equilibrium is a challenge. We report the experimental optimization of cooling and thermalization of a gas of few noninteracting Cesium atoms confined in a nonharmonic optical dipole trap. To this end, we combine ... More

Tailored single-atom collisions at ultra-low energiesSep 21 2018Jan 02 2019We employ collisions of individual atomic cesium (Cs) impurities with an ultracold rubidium (Rb) gas to probe atomic interaction with hyperfine- and Zeeman-state sensitivity. Controlling the Rb bath's internal state yields access to novel phenomena observed ... More

Dust capture and long-lived density enhancements triggered by vortices in 2D protoplanetary disksJan 22 2016We study dust capture by vortices and its long-term consequences in global two-fluid inviscid disk simulations using a new polar grid code RoSSBi. We perform the longest integrations so far, several hundred disk orbits, at the highest resolution attainable ... More

Relaxation Patterns in Supercooled Liquids from Generalized Mode-Coupling TheoryJan 28 2014Nov 25 2014The mode-coupling theory of the glass transition treats the dynamics of supercooled liquids in terms of two-point density correlation functions. Here we consider a generalized, hierarchical formulation of schematic mode-coupling equations in which the ... More

Frequency-domain nonlinear optics in two-dimensionally patterned quasi-phase-matching mediaSep 21 2015Advances in the amplification and manipulation of ultrashort laser pulses has led to revolutions in several areas. Examples include chirped pulse amplification for generating high peak-power lasers, power-scalable amplification techniques, pulse shaping ... More

The Properties of Prestellar Discs in Isolated and Multiple Prestellar SystemsMar 12 2010Jul 07 2011We present high-resolution 3D smoothed particle hydrodynamics simulations of the formation and evolution of protostellar discs in a turbulent molecular cloud. Using a piecewise polytropic equation of state, we perform two sets of simulations. In both ... More

Quantum gate teleportation between separated zones of a trapped-ion processorFeb 08 2019Large-scale quantum computers will inevitably require quantum gate operations between widely separated qubits, even within a single quantum information processing device. Nearly two decades ago, Gottesman and Chuang proposed a method for implementing ... More

Conferences with Internet Web-Casting as Binding Events in a Global Brain: Example Data From Complexity DigestMar 22 2003There is likeness of the Internet to human brains which has led to the metaphor of the world-wide computer network as a `Global Brain'. We consider conferences as 'binding events' in the Global Brain that can lead to metacognitive structures on a global ... More

Characterizing indecomposable plane continua from their complementsMay 21 2008We show that a plane continuum X is indecomposable iff X has a sequence (U_n) of not necessarily distinct complementary domains satisfying what we call the double-pass condition: If one draws an open arc A_n in each U_n whose ends limit into the boundary ... More

Bulges or Bars from Secular Evolution?Feb 20 2004Mar 03 2004We use high resolution collisionless $N$-body simulations to study the secular evolution of disk galaxies and in particular the final properties of disks that suffer a bar and perhaps a bar-buckling instability. Although we find that bars are not destroyed ... More

Clumps in the Outer Disk by Disk Instability: Why They are Initially Gas Giants and the Legacy of DisruptionSep 24 2009Jan 11 2010We explore the initial conditions for fragments in the extended regions ($r\gtrsim 50$ AU) of gravitationally unstable disks. We combine analytic estimates for the fragmentation of spiral arms with 3D SPH simulations to show that initial fragment masses ... More

Generalized mode-coupling theory of the glass transition: schematic results at finite and infinite orderOct 26 2015We present an extensive treatment of the generalized mode-coupling theory (GMCT) of the glass transition, which seeks to describe the dynamics of glass-forming liquids using only static structural information as input. This theory amounts to an infinite ... More

Analysis of Galaxy Morphology and Evolution using the Pointwise DimensionOct 30 1995In this paper we explore the application of the pointwise dimension (PD) analysis as a large-scale structure descriptor to the RC3 catalog of galaxies (de Vaucouleurs et al. 1991). This technique, which originated in the field of fractal geometry (Mandelbrot ... More

Determination of the Gaugino Mass Parameter M_1 in Different Linear Collider ModesJan 16 2001We study the different linear collider modes with regard to the determination of the gaugino mass parameter M_1. In a specific mSUGRA inspired scenario we compare four processes with polarized beams: (a) e+ e- --> neutralino_1 neutralino_2 --> neutralino_1 ... More

Stringent and efficient assessment of Boson-Sampling devicesDec 11 2013Jul 11 2014Boson-Sampling holds the potential to experimentally falsify the Extended Church Turing thesis. The computational hardness of Boson-Sampling, however, complicates the certification that an experimental device yields correct results in the regime in which ... More

The Kinematic Signature of Face-On Peanut-Shaped BulgesApr 24 2005We present a kinematic diagnostic for peanut-shaped bulges in nearly face-on galaxies. The face-on view provides a novel perspective on peanuts which would allow study of their relation to bars and disks in greater detail than hitherto possible. The diagnostic ... More

Chargino Production and Decay in Photon-Photon-CollisionsSep 10 2002Nov 04 2002We discuss the pair production of charginos in collisions of polarized photons $\gamma\gamma \to \tilde{\chi}_i^+ \tilde{\chi}_i^-$, ($i=1,2$) and the subsequent leptonic decay of the lighter chargino $\tilde{\chi}_1^+ \to \tilde{\chi}_1^0 e^+ \nu_e$ ... More

On the formation of the Magellanic StreamSep 09 2003We use high resolution N-Body/SPH simulations to study the hydro-dynamical and gravitational interaction between the Large Magellanic Cloud and the Milky Way. We model the dark and hot extended halo components as well as the stellar/gaseous disks of the ... More

Gravitational waves from intermediate-mass black holes in young clustersJun 08 2010Massive young clusters (YCs) are expected to host intermediate-mass black holes (IMBHs) born via runaway collapse. These IMBHs are likely in binaries and can undergo mergers with other compact objects, such as stellar mass black holes (BHs) and neutron ... More

Observation of individual tracer atoms in an ultracold dilute gasNov 04 2016Understanding the motion of a tracer particle in a rarefied gas is of fundamental and practical importance. We report the experimental investigation of individual Cs atoms impinging on a dilute cloud of ultracold Rb atoms with variable density. We study ... More

Nonergodic Diffusion of Single Atoms in a Periodic PotentialJan 25 2016Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic potential. We engineer ... More

Precision Measurement of the 87-Rb Tune-Out Wavelength in the Hyperfine Ground State F=1 at 790 nmDec 11 2015We report on a precision measurement of the $D$ line tune-out wavelength of $^{87}$Rubidium in the hyperfine ground state $|F=1, m_F=0,\pm1 \rangle$ manifold at 790 nm, where the scalar ac Stark shifts of the $D_1$ and the $D_2$ lines cancel. This wavelength ... More

Neutral Impurities in a Bose-Einstein Condensate for Simulation of the Fröhlich-PolaronAug 11 2015We present an experimental system to study the Bose polaron by immersion of single, well-controllable neutral Cs impurities into a Rb Bose-Einstein condensate (BEC). We show that, by proper optical traps, independent control over impurity and BEC allows ... More

On the stellar masses of giant clumps in distant star-forming galaxiesJan 31 2017We analyse stellar masses of clumps drawn from a compilation of star-forming galaxies at 1.1<z<3.6. Comparing clumps selected in different ways, and in lensed or blank field galaxies, we examine the effects of spatial resolution and sensitivity on the ... More

A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow EstimationDec 07 2015Recent work has shown that optical flow estimation can be formulated as a supervised learning task and can be successfully solved with convolutional networks. Training of the so-called FlowNet was enabled by a large synthetically generated dataset. The ... More

Extreme Event Statistics in a Drifting Markov ChainFeb 24 2017We analyse extreme event statistics of experimentally realized Markov chains with various drifts. Our Markov chains are individual trajectories of a single atom diffusing in a one dimensional periodic potential. Based on more than 500 individual atomic ... More

Clumpy galaxies seen in H-alpha: inflated observed clump properties due to limited spatial resolution and sensitivityOct 17 2016High-resolution simulations of star-forming massive galactic discs have shown that clumps form with a characteristic baryonic mass in the range $10^7-10^8~M_{\odot}$, with a small tail exceeding $10^9~M_{\odot}$ produced by clump-clump mergers. This is ... More

A Single Atom Thermometer for Ultracold GasesJan 22 2016We use single or few Cs atoms as thermometer for an ultracold, thermal Rb cloud. Observing the thermometer atoms' thermalization with the cold gas using spatially resolved fluorescence detection, we find an interesting situation, where a fraction of thermometer ... More

Optimizing Quantum Gas Production by an Evolutionary AlgorithmJan 22 2016We report on the application of an evolutionary algorithm (EA) to enhance performance of an ultra-cold quantum gas experiment. The production of a $^{87}$Rubidium Bose-Einstein condensate (BEC) can be divided into fundamental cooling steps, specifically ... More

What Makes Good Synthetic Training Data for Learning Disparity and Optical Flow Estimation?Jan 19 2018Mar 22 2018The finding that very large networks can be trained efficiently and reliably has led to a paradigm shift in computer vision from engineered solutions to learning formulations. As a result, the research challenge shifts from devising algorithms to creating ... More

Controlled doping of a bosonic quantum gas with single neutral atomsMay 03 2018We report on the experimental doping of a $^{87}$Rubidium (Rb) Bose-Einstein condensate (BEC) with individual neutral $^{133}$Cesium (Cs) atoms. We discuss the experimental tools and procedures to facilitate Cs-Rb interaction. First, we use degenerate ... More

Algebraic K-theory and sums-of-squares formulasJul 13 2004We prove a result about the non-existence of certain sums-of-squares formulas over a field. This generalizes an old theorem which used topological K-theory to obtain obstruction conditions when the field is the real numbers. Our result applies to arbitrary ... More

Z/2-equivariant and R-motivic stable stemsMar 30 2016We establish an isomorphism between the stable homotopy groups of the 2-completed motivic sphere spectrum over the real numbers and the corresponding stable homotopy groups of the 2-completed Z/2-equivariant sphere spectrum, in a certain range of dimensions. ... More

Motivic Hopf elements and relationsJul 24 2013Jul 26 2013We use Cayley-Dickson algebras to produce Hopf elements eta, nu and sigma in the motivic stable homotopy groups of spheres, and we prove via geometric arguments that the the products eta*nu and nu*sigma both vanish. Along the way we develop several basic ... More

Hypercovers in topologyNov 27 2001We show that if U is a hypercover of a topological space X then the natural map from hocolim U to X is a weak equivalence. This fact is used to construct topological realization functors for the A^1-homotopy theory of schemes over real and complex fields. ... More

Motivic cell structuresOct 13 2003Jul 16 2005An object in motivic homotopy theory is called cellular if it can be built out of motivic spheres using homotopy colimit constructions. We explore some examples and consequences of cellularity. We explain why the algebraic K-theory and algebraic cobordism ... More

Weak equivalences of simplicial presheavesMay 02 2002The usual way of defining weak equivalences for simplicial presheaves is to require an isomorphism on all sheaves of homotopy groups. We unravel some of the machinery here, and give a more concrete description in terms of local homotopy lifting properties. ... More

The Hopf condition for bilinear forms over arbitrary fieldsSep 11 2003We settle an old question about the existence of certain "sums-of-squares" formulas over a field F (which are the simplest examples of composition formulas for quadratic forms). A classical theorem says that if such a formula exists over a field of characteristic ... More

The motivic Adams spectral sequenceJan 12 2009We present some data on the cohomology of the motivic Steenrod algebra over an algebraically closed field. We discuss several features of the associated Adams spectral sequence, including the basic construction and convergence properties. The paper also ... More

Etale homotopy and sums-of-squares formulasSep 11 2006This paper uses a relative of BP-cohomology to prove a theorem in characteristic p algebra. Specifically, we obtain some new necessary conditions for the existence of sums-of-squares formulas over fields of characteristic p > 2. These conditions were ... More

Low dimensional Milnor-Witt stems over RFeb 03 2015This article computes some motivic stable homotopy groups over R. For 0 <= p - q <= 3, we describe the motivic stable homotopy groups of a completion of the motivic sphere spectrum. These are the first four Milnor-Witt stems. We start with the known Ext ... More

Old and young bulges in late-type disk galaxiesOct 20 2006ABRIDGED: We use HSTACS and NICMOS imaging to study the structure and colors of a sample of nine late-type spirals. We find: (1) A correlation between bulge and disks scale-lengths, and a correlation between the colors of the bulges and those of the inner ... More

Closed form Solutions to Some Nonlinear equations by a Generalized Cole-Hopf TransformationJul 20 2014In the first part of this paper we linearize and solve the Van der Pol and Lienard equations with some additional nonlinear terms by the application of a generalized form of Cole-Hopf transformation. We then show that the same transformation can be used ... More

Data management in systems biology I - Overview and bibliographyAug 04 2009Dec 15 2009Large systems biology projects can encompass several workgroups often located in different countries. An overview about existing data standards in systems biology and the management, storage, exchange and integration of the generated data in large distributed ... More

A lower bound of the hyperbolic dimension for meromorphic functions having a logarithmic Hölder tractSep 07 2017We improve existing lower bounds of the hyperbolic dimension for meromophic functions that have a logarithmic tract {\Omega} which is a H\"older domain. These bounds are given in terms of the fractal behavior, measured with integral means, of the boundary ... More

None compactness versus critical points at infinity: an exampleMar 12 2019We illustrate an example of a generic, positive function K on a Riemannian manifold to be conformally prescribed as the scalar curvature, for which the corresponding Yamabe type L2-gradient flow exhibits non compact flow lines, while a slight modification ... More

U-Quantile-StatisticsJun 06 2009In 1948, W. Hoeffding introduced a large class of unbiased estimators called U-statistics, defined as the average value of a real-valued m-variate function h calculated at all possible sets of m points from a random sample. In the present paper, we investigate ... More

Coupled Contact Systems and Rigidity of Maximal Dimensional Variations of Hodge StructureNov 30 1997In this article we prove that locally Griffiths' horizontal distribution on the period domain is given by a generalized version of the familiar contact differential system. As a consequence of this description we obtain strong local rigidity properties ... More

Super-Eddington accretion; flow regimes and conditions in high-z galaxiesJul 17 2018We review and discuss theoretical studies addressing the possibility of gas accretion onto black holes occurring at rates exceeding the Eddington limit. Our focus is on the applications to the growth of black hole seeds at high redshift. We first present ... More

Foreword: Advanced Science Letters (ASL), Special Issue on Computational AstrophysicsJun 24 2009Computational astrophysics has undergone unprecedented development over the last decade, becoming a field of its own. The challenge ahead of us will involve increasingly complex multi-scale simulations. These will bridge the gap between areas of astrophysics ... More

On the Solution of the Van der Pol EquationAug 27 2013We linearize and solve the Van der Pol equation (with additional nonlinear terms) by the application of a generalized form of Cole-Hopf transformation. We classify also Lienard equations with low order polynomial coefficients which can be linearized by ... More

Assessing Turbulence Strength via Lyaponuv ExponentsSep 12 2004In this paper we study the link between `turbulence strength' in a flow and the leading Lyaponuv exponent that characterize it. To this end we use two approaches. The first, analytical, considers the truncated convection equations in 2-dimensions with ... More

Long's Equation in Terrain Following CoordinatesMay 22 2008Aug 08 2008Long's equation describes two dimensional stratified atmospheric flow over terrain which is represented by the geometry of the domain. The solutions of this equation over simple topography were investigated analytically and numerically by many authors. ... More

Data management in Systems biology II - Outlook towards the semantic webDec 15 2009The benefit of using ontologies, defined by the respective data standards, is shown. It is presented how ontologies can be used for the semantic enrichment of data and how this can contribute to the vision of the semantic web to become true. The problems ... More

Quantum Key Distribution and String Oblivious Transfer in Noisy ChannelsJun 04 1996We prove the unconditional security of a quantum key distribution (QKD) protocol on a noisy channel against the most general attack allowed by quantum physics. We use the fact that in a previous paper we have reduced the proof of the unconditionally security ... More