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Thermal noise in optical cavities revisitedNov 21 2011Thermal noise of optical reference cavities sets a fundamental limit to the frequency instability of ultra-stable lasers. Using Levin's formulation of the fluctuation-dissipation theorem we correct the analytical estimate for the spacer contribution given ... More

Tuning the Thermal Expansion Properties of Optical Reference Cavities with Fused Silica MirrorsFeb 10 2010We investigate the thermal expansion of low thermal noise Fabry-Perot cavities made of Low Thermal Expansion (LTE) glass spacers and Fused Silica (FS) mirrors. The different thermal expansion of mirror and spacer deforms the mirror. This deformation strongly ... More

On the relation between uncertainties of weighted frequency averages and the various types of Allan deviationsApr 02 2015Apr 27 2015The power spectral density in Fourier frequency domain, and the different variants of the Allan deviation (ADEV) in dependence on the averaging time are well established tools to analyse the fluctuation properties and frequency instability of an oscillatory ... More

Long range transport of ultra cold atoms in a far-detuned 1D optical latticeApr 16 2012We present a novel method to transport ultra cold atoms in a focused optical lattice over macroscopic distances of many Rayleigh ranges. With this method ultra cold atoms were transported over 5 cm in 250 ms without significant atom loss or heating. By ... More

High accuracy photoassociation of $^{40}$Ca near the ${^3P_1}+{^1S_0}$ asymptote and its Zeeman effectJun 27 2013We report on the first measurement of narrow photoassociation lines of $^{40}$Ca near the ${^3P_1}+{^1S_0}$ asymptote related to the molecular states $^3\Pi_u$ and $^3\Sigma^+_u$. The highly accurate binding energies and Zeeman splittings are well described ... More

Nonlinear Zeeman effect in photoassociation spectra of $^{40}$Ca near the $^3$P$_1$+$^1$S$_0$ asymptoteJun 12 2015We present calculations of the Zeeman effect of narrow photoassociation lines of $^{40}$Ca near the $^3$P$_1$ + $^1$S$_0$ asymptote. Using a coupled-channel model we find a nonlinear Zeeman effect that even at low fields of a few mT amounts to several ... More

High accuracy correction of blackbody radiation shift in an optical lattice clockAug 14 2012Oct 29 2012We have determined the frequency shift that blackbody radiation is inducing on the $5s^2$ $^1$S$_0$ -- $5s5p$ $^3$P$_0$ clock transition in strontium. Previously its uncertainty limited the uncertainty of strontium lattice clocks to $1\times10^{-16}$. ... More

Bose-Einstein condensation of alkaline earth atoms: $^{40}${Ca}Aug 03 2009Sep 02 2009We have achieved Bose-Einstein condensation of $^{40}$Ca, the first for an alkaline earth element. The influence of elastic and inelastic collisions associated with the large ground state s-wave scattering length of $^{40}$Ca was measured. From these ... More

Delivering pulsed and phase stable light to atoms of an optical clockAug 18 2011Feb 10 2012In optical clocks, transitions of ions or neutral atoms are interrogated using pulsed ultra-narrow laser fields. Systematic phase chirps of the laser or changes of the optical path length during the measurement cause a shift of the frequency seen by the ... More

Reducing the effect of thermal noise in optical cavitiesDec 14 2012Dec 17 2013Thermal noise in optical cavities imposes a severe limitation in the stability of the most advanced frequency standards at a level of a few 10^(-16) (s/t)^(1/2) for long averaging times t. In this paper we describe two schemes for reducing the effect ... More

Phase- coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber linkJun 18 2009We have explored the performance of two "dark fibers" of a commercial telecommunication fiber link for a remote comparison of optical clocks. The two fibers, linking the Leibniz University of Hanover (LUH) with the Physi-kalisch-Technische Bundesanstalt ... More

A compact and efficient strontium oven for laser-cooling experimentsSep 25 2012Here we describe a compact and efficient strontium oven well suited for laser-cooling experiments. Novel design solutions allowed us to produce a collimated strontium atomic beam with a flux of 1.0\times10^13 s^-1 cm^-2 at the oven temperature of 450 ... More

Demonstration of a Transportable 1 Hz-Linewidth LaserOct 13 2010May 18 2011We present the setup and test of a transportable clock laser at 698 nm for a strontium lattice clock. A master-slave diode laser system is stabilized to a rigidly mounted optical reference cavity. The setup was transported by truck over 400 km from Braunschweig ... More

Lattice-induced photon scattering in an optical lattice clockFeb 08 2018Jul 19 2018We investigate scattering of lattice laser radiation in a strontium optical lattice clock and its implications for operating clocks at interrogation times up to several tens of seconds. Rayleigh scattering does not cause significant decoherence of the ... More

Ground-state properties of Ca$_2$ from narrow line two-color photoassociationFeb 02 2017May 23 2017By two-color photoassociation of $^{40}$Ca four weakly bound vibrational levels in the Ca$_2$ \Xpot ground state potential were measured, using highly spin-forbidden transitions to intermediate states of the coupled system $^3\Pi_{u}$ and $^3\Sigma^+ ... More

Noise and instability of an optical lattice clockJul 17 2015Nov 03 2015We present an analysis of the different types of noise from the detection and interrogation laser in our strontium lattice clock. We develop a noise model showing that in our setup quantum projection noise--limited detection is possible if more than 130~atoms ... More

Tackling the blackbody shift in a strontium optical lattice clockSep 10 2010A major obstacle for optical clocks is the frequency shift due to black body radiation. We discuss how one can tackle this problem in an optical lattice clock; in our case 87-Sr: firstly, by a measurement of the dc Stark shift of the clock transition ... More

8E-17 fractional laser frequency instability with a long room-temperature cavityFeb 09 2015Mar 31 2015We present a laser system based on a 48 cm long optical glass resonator. The large size requires a sophisticated thermal control and optimized mounting design. A self balancing mounting was essential to reliably reach sensitivities to acceleration of ... More

Ultra-stable laser with average fractional frequency drift rate below $5\times10^{-19}/\mathrm{s}$May 07 2014Cryogenic single-crystal optical cavities have the potential to provide highest dimensional stability. We have investigated the long-term performance of an ultra-stable laser system which is stabilized to a single-crystal silicon cavity operated at 124 ... More

A compact, robust, and transportable ultra-stable laser with a fractional frequency instability of $1\times10^{-15}$Oct 20 2014We present a compact and robust transportable ultra-stable laser system with minimum fractional frequency instability of $1\times10^{-15}$ at integration times between 1 to 10 s. The system was conceived as a prototype of a subsystem of a microwave-optical ... More

Crystalline optical cavity at 4 K with thermal noise limited instability and ultralow driftDec 06 2018Crystalline optical cavities are the foundation of today's state-of-the-art ultrastable lasers. Building on our previous silicon cavity effort, we now achieve the fundamental thermal noise-limited stability for a 6 cm long silicon cavity cooled to 4 Kelvin, ... More

A strontium lattice clock with $3 \times 10^{-17}$ inaccuracy and its frequencyDec 12 2013Aug 15 2014We have measured the absolute frequency of the optical lattice clock based on $^{87}$Sr at PTB with an uncertainty of $3.9\times 10^{-16}$ using two caesium fountain clocks. This is close to the accuracy of today's best realizations of the SI second. ... More

A high-performance optical lattice clock based on bosonic atomsMar 08 2018Optical lattice clocks with uncertainty and instability in the $10^{-17}$-range and below have so far been demonstrated exclusively using fermions. Here, we demonstrate a bosonic optical lattice clock with $3\times 10^{-18}$ instability and $2.0\times ... More

Wavelength dependent ac-Stark shift of the 1S0 - 3P1 transition at 657 nm in CaJun 04 2004We have measured the ac-Stark shift of the 4s2 1S0 - 4s4p 3P1 line in 40Ca for perturbing laser wavelengths between 780 nm and 1064 nm with a time domain Ramsey-Borde atom interferometer. We found a zero crossing of the shift for the mS = 0 - mP = 0 transition ... More

Geodesy and metrology with a transportable optical clockMay 11 2017The advent of novel measurement instrumentation can lead to paradigm shifts in scientific research. Optical atomic clocks, due to their unprecedented stability and uncertainty, are already being used to test physical theories and herald a revision of ... More

Quantum Tests of the Einstein Equivalence Principle with the STE-QUEST Space MissionApr 16 2014Sep 25 2014We present in detail the scientific objectives in fundamental physics of the Space-Time Explorer and QUantum Equivalence Space Test (STE-QUEST) space mission. STE-QUEST was pre-selected by the European Space Agency together with four other missions for ... More

Lattice-induced photon scattering in an optical lattice clockFeb 08 2018We investigate scattering of lattice laser radiation in a strontium optical lattice clock and its implications for operating clocks at interrogation times up to several ten seconds. Rayleigh scattering does not cause significant decoherence of the atomic ... More

Dilute Birman--Wenzl--Murakami Algebra and $D^{(2)}_{n+1}$ modelsFeb 14 1994A ``dilute'' generalisation of the Birman--Wenzl--Murakami algebra is considered. It can be ``Baxterised'' to a solution of the Yang--Baxter algebra. The $D^{(2)}_{n+1}$ vertex models are examples of corresponding solvable lattice models and can be regarded ... More

Co-Indexing Labelled DRSs to Represent and Reason with AmbiguitiesJul 25 1995The paper addresses the problem of representing ambiguities in a way that allows for monotonic disambiguation and for direct deductive computation. The paper focuses on an extension of the formalism of underspecified DRSs to ambiguities introduced by ... More

A short-key one-time pad cipherAug 18 2016A process for the secure transmission of data is presented that has to a certain degree the advantages of the one-time pad (OTP) cipher, that is, simplicity, speed, and information-theoretically security, but overcomes its fundamental weakness, the necessity ... More

Recent advances in and future challenges for mesoscopic hydrodynamic modelling of complex wettingMar 14 2018Jul 21 2018We highlight some recent developments that widen the scope and reach of mesoscopic thin-film (or long-wave) hydrodynamic models employed to describe the dynamics of thin films, drops and contact lines of simple and complex liquids on solid substrates. ... More

Long Time Stability of the Energy Scale Calibration of a Quantum 2000Jun 10 2015According to the international standard ISO 15472 the energy scale of an XPS instrument, type Physical Electronics Quantum 2000, was calibrated. It is shown, how the procedures of the ISO 15472 were adapted to the hardware and software design of the Quantum ... More

Patterned deposition at moving contact linesJul 03 2013When a simple or complex liquid recedes from a smooth solid substrate it often leaves a homogeneous or structured deposit behind. In the case of a receding non-volatile pure liquid the deposit might be a liquid film or an arrangement of droplets depending ... More

Dienstplanerstellung in Krankenhaeusern mittels genetischer AlgorithmenMay 30 2013This thesis investigates the use of problem-specific knowledge to enhance a genetic algorithm approach to multiple-choice optimisation problems. It shows that such information can significantly enhance performance, but that the choice of information and ... More

Technical Report: Artificial DNA - a Concept for Self-Building Embedded SystemsJul 24 2017This technical report deals with the concept of an artificial DNA which contains a blueprint of the structure and organization of an embedded system. This blueprint can be used to build up the embedded system in a self-organizing manner at run-time. The ... More

Multiplicative monotone convolutionsMar 25 2005Recently, Bercovici has introduced multiplicative convolutions based on Muraki's monotone independence and shown that these convolution of probability measures correspond to the composition of some function of their Cauchy transforms. We provide a new ... More

Reducing the Aspect Ratio of Contact Holes by In-Situ Low-Angle Cross SectioningApr 16 2015Auger analysis of high-aspect ratio contact holes of integrated microelectronic devices is a challenging analytical task. Due to geometrical shadowing the primary electron beam and the energy analyser have not the required direct line of sight to the ... More

Rigidity theorems for K- and H-cohomology and other functorsMar 30 2015Apr 26 2018Suslin proved that for an extension K/k of algebraically closed fields the induced maps K_m(k)[n] --> K_m(K)[n] and K_m(k)/n ---> K_m(K)/n for the higher K-groups are isomorphisms, where A[n] is the subgroup of n-torsion in an abelien group, and A/n = ... More

Hitting probabilities for random convex bodies and lattices of trianglesDec 18 2013In the first part of this paper, we obtain symmetric formulae for the probabilities that a plane convex body hits exactly 1, 2, 3, 4, 5 or 6 triangles of a lattice of congruent triangles in the plane. Furthermore, a very simple formula for the expectation ... More

Random chords and point distances in regular polygonsApr 12 2012Sep 05 2012In this paper we obtain the chord length distribution function for any regular polygon. From this function we conclude the density function and the distribution function of the distance between two uniformly and independently distributed random points ... More

An Indirect Genetic Algorithm for Set Covering ProblemsMar 20 2008This paper presents a new type of genetic algorithm for the set covering problem. It differs from previous evolutionary approaches first because it is an indirect algorithm, i.e. the actual solutions are found by an external decoder function. The genetic ... More

Artificial Immune Systems (AIS) - A New Paradigm for Heuristic Decision MakingJan 28 2008May 16 2008Over the last few years, more and more heuristic decision making techniques have been inspired by nature, e.g. evolutionary algorithms, ant colony optimisation and simulated annealing. More recently, a novel computational intelligence technique inspired ... More

Measures and geometric probabilities for ellipses intersecting circlesDec 06 2016Santal\'o calculated the measures for all positions of a moving line segment in which it lies inside a fixed circle and intersects this circle in one or two points. From these measures he concluded hitting probabilities for a line segment thrown randomly ... More

Liaison classes of modulesSep 25 2004We propose a concept of module liaison that extends Gorenstein liaison of ideals and provides an equivalence relation among unmixed modules over a commutative Gorenstein ring. Analyzing the resulting equivalence classes we show that several results known ... More

Comparing Castelnuovo-Mumford regularity and extended degree: the borderline casesNov 28 2003Castelnuovo-Mumford regularity and any extended degree function can be thought of as complexity measures for the structure of finitely generated graded modules. A recent result of Doering, Gunston, Vasconcelos shows that both can be compared in case of ... More

Free Lévy Processes on Dual GroupsMar 23 2002We give a short introduction to the theory of L\'evy processes on dual groups. As examples we consider L\'evy processes with additive increments and L\'evy processes on the dual affine group.

LIL type behaviour of multivariate Levy processes at zeroJun 19 2018Jan 14 2019We study the almost sure behaviour of suitably normalised multivariate Levy processes as t goes to zero. Among other results we find necessary and sufficient conditions for a law of a very slowly varying function which includes a general law of the iterated ... More

Aperiodic crystals and beyondJun 17 2015Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order, encompassing ... More

Influence of the SIPG penalisation on the numerical properties of linear systems for elastic wave propagationDec 15 2017Interior penalty discontinuous Galerkin discretisations (IPDG) and especially the symmetric variant (SIPG) for time-domain wave propagation problems are broadly accepted and widely used due to their advantageous properties. Linear systems with block structure ... More

Monotone and Boolean Convolutions for Non-compactly Supported Probability MeasuresMar 14 2007Jul 03 2009The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the multiplicative boolean ... More

Minimal free resolutions of projective subschemes of small degreeMay 16 2005We discuss the minimal free resolution of an irreducible projective subscheme X. If X is also reduced, we focus on the case when its degree equals two plus the codimension. The set of all possible graded Betti numbers is described if the codimension is ... More

Improved Sputter Depth Resolution in Auger Thin Film Analysis Using In Situ Low Angle Cross-SectionsFeb 17 2015A none conventional approach for depth profiling of thin film systems with enhanced depth resolution has been developed using standard Auger microprobe instruments. For the preparation of an in situ low angle cross-section, the sample is partly covered ... More

Siegel Modular Varieties and the Eisenstein Cohomology of $\PGL_{2g+1}$Feb 01 2013Mar 14 2013We use the twisted topological trace formula developed in an earlier paper to understand liftings from symplectic to general linear groups. We analyse the lift from $\SP_{2g}$ to $\PGL_{2g+1}$ over the ground field $\Q$ in further detail, and we get a ... More

Bench Measurements and Simulations of Beam Coupling ImpedanceMay 04 2018After a general introduction, the basic principles of wake-field and beamcoupling- impedance computations are explained. This includes time domain, frequency domain, and methods that do not include excitations by means of a particle beam. The second part ... More

On Undetected Redundancy in the Burrows-Wheeler TransformApr 05 2018The Burrows-Wheeler-Transform (BWT) is an invertible permutation of a text known to be highly compressible but also useful for sequence analysis, what makes the BWT highly attractive for lossless data compression. In this paper, we present a new technique ... More

Simple evaluation of one of Malmstén's integralsSep 25 2017The logarithmic integral no. 4.325.7 from Gradshteyn and Ryzhik's tables of integrals was first evaluated by Malmst\'en. Recently, Blagouchine used contour integration methods to evaluate a family of logarithmic integrals that contains this integral. ... More

Orientations of 1-Factorizations and the List Chromatic Index of Small GraphsMay 01 2017As starting point, we formulate a corollary to the Quantitative Combinatorial Nullstellensatz. This corollary does not require the consideration of any coefficients of polynomials, only evaluations of polynomial functions. In certain situations, our corollary ... More

Vacuum Quality Monitoring of Analytical Sputter Depth Profile Equipment by Recontamination Measurements of a Sputtered Ti SurfaceJan 01 2017Often a surface sensitive analytical technique in combination with sample erosion by inert ion sputtering is used for compositional in-depth analysis of solid state samples. Layer by layer the sample gets eroded and then the composition of the actual ... More

An ensemble related to discrete orthogonal polynomials and its application to tilings of a half-hexagonJan 19 2011Jun 28 2013We discuss asymptotic properties of a family of discrete probability measures which may be used to model particle configurations with a wall on a set of discrete nodes. The correlations are shown to be determinantal and are expressed in terms of discrete ... More

Weights in arithmetic geometryMar 03 2010The concept of weights on the cohomology of algebraic varieties was initiated by fundamental ideas and work of A. Grothendieck and P. Deligne. It is deeply connected with the concept of motives and appeared first on the singular cohomology as the weights ... More

Volume Laws for Boxed Plane Partitions and Area Laws for Ferrers DiagramsApr 28 2008Jan 27 2009We asymptotically analyse the volume-random variables of general, symmetric and cyclically symmetric plane partitions fitting inside a box. We consider the respective symmetry class equipped with the uniform distribution. We also prove area limit laws ... More

On Reasoning with AmbiguitiesFeb 21 1995Feb 22 1995The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations and different ... More

Trigonometric R Matrices related to `Dilute' Birman--Wenzl--Murakami AlgebraFeb 16 1994Explicit expressions for three series of $R$ matrices which are related to a ``dilute'' generalisation of the Birman--Wenzl--Murakami are presented. Of those, one series is equivalent to the quantum $R$ matrices of the $D^{(2)}_{n+1}$ generalised Toda ... More

On Dirichlet Products Evaluated at Fibonacci NumbersJun 06 2016In this work we discuss Dirichlet products evaluated at Fibonacci numbers. As first applications of the results we get a representation of Fibonacci numbers in terms of Euler's totient function, an upper bound on the number of primitive prime divisors ... More

Buffon's problem with a star of needles and a lattice of parallelogramsSep 24 2012A star of n (n greater than or equal to 2) line segments (needles) of equal length with common endpoint and constant angular spacing is randomly placed onto a lattice which is the union of two families of equidistant lines in the plane with angle alpha ... More

Nurse Rostering with Genetic AlgorithmsMar 19 2010In recent years genetic algorithms have emerged as a useful tool for the heuristic solution of complex discrete optimisation problems. In particular there has been considerable interest in their use in tackling problems arising in the areas of scheduling ... More

Hasse principles for higher-dimensional fieldsOct 15 2009Dec 04 2014For schemes X over global or local fields, or over their rings of integers, K. Kato stated several conjectures on certain complexes of Gersten-Bloch-Ogus type, generalizing the fundamental exact sequence of Brauer groups for a global field. He proved ... More

Space-Time-Parallel Poroelasticity SimulationDec 20 2017The accurate, reliable and efficient numerical approximation of multi-physics processes in heterogeneous porous media with varying media coefficients that include fluid flow and structure interactions is of fundamental importance in energy, environmental, ... More

A Pyramidal Evolutionary Algorithm with Different Inter-Agent Partnering Strategies for Scheduling ProblemsJan 21 2008Mar 03 2008This paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. Cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of ... More

The mean width of the oloid and integral geometric applications of itApr 25 2016The oloid is the convex hull of two circles with equal radius in perpendicular planes so that the center of each circle lies on the other circle. We calculate the mean width of the oloid in two ways, first via the integral of mean curvature, and then ... More

Buffon's problem with a pivot needleJan 14 2014Jan 16 2014In this paper, we solve Buffon's needle problem for a needle consisting of two line segments connected in a pivot point.

Sputter-Induced Cross-Contaminations in Analytical AES and XPS Instrumentation: Utilization of the effect for the In-situ Deposition of Ultrathin Functional LayersFeb 27 2013Cross contaminations are observed on sample surfaces by AES and XPS, if multiple samples are mounted on one sample holder and a neighbouring sample was sputter depth profiled. During sputter depth profiling sputtered material is deposited on inner surfaces ... More

Limit laws for discrete excursions and meanders and linear functional equations with a catalytic variableMay 26 2011Dec 13 2011We study limit distributions for random variables defined in terms of coefficients of a power series which is determined by a certain linear functional equation. Our technique combines the method of moments with the kernel method of algebraic combinatorics. ... More

Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growthOct 14 2010In the present contribution we review basic mathematical results for three physical systems involving self-organising solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting, evaporation/condensation or epitaxial ... More

Probabilistic properties of the elliptic motionMar 31 2017In this paper we consider the plane elliptic motion which occurs if the moving centrode is a circle of radius $r$ and the fixed centrode a circle of radius $2r$. Every point of the moving plane generates an ellipse in the fixed plane. Let a disk of radius ... More

Towards finding the single-particle content of two-dimensional adjoint QCDJun 26 2015The single-particle content of two-dimensional adjoint QCD remains elusive due to the inability to distinguish single- from multi-particle states. To find a criterion we compare several approximations to the theory. Starting from the asymptotic theory ... More

In-Situ Low-Angle Cross Sectioning: Bevel Slope Flattening due to Self-Alignment EffectsJun 24 2015Low-angle cross sections are produced inside an Auger microprobe using the equipped depth profile ion sputter gun. Simply the sample is partly covered by a mask. Utilizing the edge of this mask the sample is sputtered with ions. Due to the shading of ... More

Boolean convolution of probability measures on the unit circleMar 15 2004Dec 13 2006We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic function and ... More

The Tournament Scheduling Problem with AbsencesSep 01 2015May 20 2016We study time scheduling problems with allowed absences as a new kind of graph coloring problem. One may think of a sport tournament where each player (each team) is permitted a certain number $t$ of absences. We then examine how many rounds are needed ... More

The Benefit of Wide Energy Range Spectrum Acquisition During Sputter Depth Profile MeasurementsNov 26 2017Thin film systems are often analysed by using sputter depth profiling. First the sample gets eroded by inert gas ion impact during sputter depth profiling. Then the elemental composition of the freshly unveiled surface is determined by using a surface ... More

Examples for the improvements in AES Depth Profiling of Multilayer Thin Film Systems by Application of Factor Analysis Data EvaluationFeb 12 2015Factor Analysis has proved to be a powerful tool for the full exploitation of the chemical information included in the peak shapes and peak positions of spectra measured by AES depth profiling. Due to its ability to extract the number of independent chemical ... More

A spectral sequence for Iwasawa adjointsJul 24 2013We establish a purely algebraic tool for studying the Iwasawa adjoints of some natural Iwasawa modules for $p$-adic Lie group extensions of number fields, by relating them to certain continuous Galois cohomology groups via a spectral sequence.

Quantitative Combinatorial NullstellensatzDec 22 2012The main result of this paper is a coefficient formula that sharpens and generalizes Alon and Tarsi's Combinatorial Nullstellensatz, which provides some information about the polynomial map $P|_{\X_1\times...\times\X_n}$ when only incomplete information ... More

Level algebras through Buchsbaum* manifoldsJun 22 2010Stanley-Reisner rings of Buchsbaum* complexes are studied by means of their quotients modulo a linear system of parameters. The socle of these quotients is computed. Extending a recent result by Novik and Swartz for orientable homology manifolds without ... More

Exact solution of two classes of prudent polygonsSep 30 2008Jan 26 2010Prudent walks are self-avoiding walks on the square lattice which never step into the direction of an already occupied vertex. We study the closed version of these walks, called prudent polygons, where the last vertex is adjacent to the first one. More ... More

A generalization of Strassen's functional LILJan 25 2006Aug 25 2006Let X_1,X_2, . . . be a sequence of i.i.d. mean zero random variables and let S_n the sum of the first n random variables. We show that whenever lim sup_n |S_n|/c_n is finite with probability one and the normalizing sequence {c_n} is sufficiently regular, ... More

The Theory of Quantum Levy ProcessesJul 28 2004Various recent results on quantum L\'evy processes are presented. The first part provides an introduction to the theory of L\'evy processes on involutive bialgebras. The notion of independence used for these processes is tensor independence, which generalizes ... More

Dilute Algebras and Solvable Lattice ModelsNov 24 1995The definition of a dilute braid-monoid algebra is briefly reviewed. The construction of solvable vertex and interaction-round-a-face models built on representations of the dilute Temperley-Lieb and Birman-Wenzl-Murakami algebras is discussed.

Representations of Two-Colour BWM Algebras and Solvable Lattice ModelsDec 03 1996Many of the known solutions of the Yang-Baxter equation, which are related to solvable lattice models of vertex- and IRF-type, yield representations of the Birman-Wenzl-Murakami algebra. From these, representations of a two-colour generalization of the ... More

Note on a Positronium Model from Flow Equations in Front Form DynamicsAug 13 1998Jan 16 2001In this note we address the problem of solving for the positronium mass spectrum. We use front-form dynamics together with the method of flow equations. For a special choice of the similarity function, the calculations can be simplified by analytically ... More

SYM Correlators and the Maldacena ConjectureAug 21 2002We report on progress in evaluating quantum filed theories with supersymmetric discrete light-cone quantization (SDLCQ). We compare the method to lattice gauge theory and point out its relevance for lattice calculations. As an exciting application we ... More

Analytical solution to the Schrodinger equation of a laser-driven correlated two-particle systemJan 31 2002The time-dependent quantum system of two laser-driven electrons in a harmonic oscillator potential is analysed, taking into account the repulsive Coulomb interaction between both particles. The Schrodinger equation of the two-particle system is shown ... More

Improved bounds on the number of ternary square-free wordsMay 29 2001Aug 02 2001Improved upper and lower bounds on the number of square-free ternary words are obtained. The upper bound is based on the enumeration of square-free ternary words up to length 110. The lower bound is derived by constructing generalised Brinkhuis triples. ... More

Testing SDLCQ in 2+1 dimensionsMar 13 2000The SDLCQ regularization is known to explicitly preserve supersymmetry in 1+1 dimensions. To test this property in higher dimensions, we consider supersymmetric Yang-Mills theory on R x S^1 x S^1. In particular, we choose one of the compact directions ... More

Basis Invariants in Non--Abelian Gauge TheoriesJan 23 1997Feb 05 1997A basis of Lorentz and gauge-invariant monomials in non--Abelian gauge theories with matter is described, applicable for the inverse mass expansion of effective actions. An algorithm to convert an arbitrarily given invariant expression into a linear combination ... More

Recent HERA Results and Future ProspectsJun 10 1998A few selected HERA results are presented and the prospects for future measurements with high luminosity are discussed, which will become available after the planned luminosity upgrade of the HERA storage ring planned for 2000.

Killing forms on G2 and Spin7 manifoldsOct 04 2004Killing forms on Riemannian manifolds are differential forms whose covariant derivative is totally skew-symmetric. We show that on a compact manifold with holonomy G2 or Spin7 any Killing form has to be parallel. The main tool is a universal Weitzenboeck ... More

Kinetic Model for Stochastic Heating in the INCA DischargeJun 01 2018Jun 07 2018A novel electron heating mechanism based on periodically structured vortex fields induced in a plane was first proposed in 2014 [U. Czarnetzki and Kh. Tarnev, Physics of Plasmas 21, 123508 (2014)]. This theoretical concept has now been realized in an ... More

On a harmonic solution for two-dimensional adjoint QCDMay 31 2018Two-dimensional QCD with adjoint fermions has many attractive features, yet its single-particle content remains largely unknown. To lay the foundation for a crucially improved approximation of the theory's spectrum, we developed a method to find the basis ... More

Application of the analytical methods REM/EDX, AES and SNMS to a chlorine induced aluminium corrosionFeb 06 2015Scanning electron microscopy - SEM - with energy dispersive X-ray detection - EDX -, Auger electron spectroscopy - AES - and sputtered neutral mass spectrometry - SNMS - have been used to characterize a chlorine induced corrosion of an aluminium metallisation. ... More