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A Qualitative Post-Experience Method for Evaluating Changes in VR Presence Experience Over TimeMay 14 2019A particular measure to evaluate a head-mounted display (HMD) based experience is the state of feeling present in virtual reality. Interruptions of a presence experience - break in presence (BIP) - appearing over time, need to be detected to assess and ... More

Frontal Screens on Head-Mounted Displays to Increase Awareness of the HMD Users' State in Mixed Presence CollaborationMay 15 2019In the everyday context, e.g., a household, HMD users remain a part of the social life for Non-HMD users being co-located with them. Due to the social context situations arise that demand interaction between the HMD and the Non-HMD user. We focus on the ... More

The present-day mass function of the Quintuplet clusterAug 22 2011Context: The stellar mass function is a probe for a potential dependence of star formation on the environment. Only a few young clusters are known to reside within the Central Molecular Zone and can serve as testbeds for star formation under the extreme ... More

Enhanced quantum tunnelling induced by disorderMay 09 2008We reconsider the problem of the enhancement of tunnelling of a quantum particle induced by disorder of a one-dimensional tunnel barrier of length $L$, using two different approximate analytic solutions of the invariant imbedding equations of wave propagation ... More

Mean Free Path in Disordered Multichannel Tight-Binding WiresMar 13 2007Transport in a disordered tight-binding wire involves a collection of different mean free paths resulting from the distinct fermi points, which correspond to the various scattering channels of the wire. The generalization of Thouless' relation between ... More

Exact transmission moments in one-dimensional weak localization and single-parameter scalingJul 23 2003We obtain for the first time the expressions for the mean and the variance of the transmission coefficient for an Anderson chain in the weak localization regime, using exact expansions of the complex transmission- and reflection coefficients to fourth ... More

On structure-stabilizing electronic interferences in bcc-related phases. A research reportMar 24 2019This study deals with cubic crystals where the contents of the simple cubic unit cells are close to n$\times$n$\times$n-bcc sublattices ($n$ = 2: diamond- and zinc-blende type, $n$ = 3: $\gamma$-brasses). First-principle results on the electronic structure ... More

Period- and mirror-maps for the quartic K3Jan 24 2011We study in detail mirror symmetry for the quartic K3 surface in P3 and the mirror family obtained by the orbifold construction. As explained by Aspinwall and Morrison, mirror symmetry for K3 surfaces can be entirely described in terms of Hodge structures. ... More

Quantum Lower Bounds by Entropy NumbersNov 30 2006We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on quantum approximation ... More

From Monte Carlo to Quantum ComputationDec 23 2001Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring over classical ... More

On structure-stabilizing electronic interferences in bcc-related phases. A research reportMar 24 2019Mar 27 2019This study deals with cubic crystals where the contents of the simple cubic unit cells are close to n$\times$n$\times$n-bcc sublattices ($n$ = 2: diamond- and zinc-blende type, $n$ = 3: $\gamma$-brasses). First-principle results on the electronic structure ... More

QCD and High Energy Interactions: Moriond 2018 Theory SummaryJun 13 2018Jun 27 2018The highlights of the theory developments presented at the Rencontres de Moriond 2018 on QCD and High Energy Interactions are summarised and put into perspective.

Quantum Summation with an Application to IntegrationMay 23 2001We study summation of sequences and integration in the quantum model of computation. We develop quantum algorithms for computing the mean of sequences which satisfy a p-summability condition and for integration of functions from Lebesgue spaces L_p([0,1]^d) ... More

The basic physical Lie operationsOct 13 2004Quantum theory can be formulated as a theory of operations, more specific, of complex represented operations from real Lie groups. Hilbert space eigenvectors of acting Lie operations are used as states or particles. The simplest simple Lie groups have ... More

Matter as Spectrum of Spacetime RepresentationsApr 04 2003Bound and scattering state Schr\"odinger functions of nonrelativistic quantum mechanics as representation matrix elements of space and time are embedded into residual representations of spacetime as generalizations of Feynman propagators. The representation ... More

Spacetime as the Manifold of the Internal Symmetry Orbits in the External SymmetriesMar 07 2001Interactions and particles in the standard model are characterized by the action of internal and external symmetry groups. The four symmetry regimes involved are related to each other in the context of induced group representations. In addition to Wigner's ... More

The Cohen-Macaulay space of twisted cubicsMar 25 2014In this work, we describe the Cohen-Macaulay space CM of twisted cubics parameterizing curves $C$ together with a finite map $i: C \to \mathbb{P}^3$ that is generically a closed immersion and such that $C$ has Hilbert polynomial $p(t)=3t+1$ with respect ... More

Absence of localization in a disordered one-dimensional ring threaded by an Aharonov-Bohm fluxJul 03 2009Absence of localization is demonstrated analytically to leading order in weak disorder in a one-dimensional Anderson model of a ring threaded by an Aharonov-Bohm (A-B) flux. The result follows from adapting an earlier perturbation treatment of disorder ... More

Anomalous scaling of conductance cumulants in one-dimensional Anderson localizationNov 23 2007The mean and the variance of the logarithm of the conductance ($ln g$) in the localized regime in the one-dimensional Anderson model are calculated analytically for weak disorder, starting from the recursion relations for the complex reflection- and transmission ... More

Transmission, reflection and localization in a random medium with absorption or gainMay 23 2005Oct 28 2005We study reflection and transmission of waves in a random tight-binding system with absorption or gain for weak disorder, using a scattering matrix formalism. Our aim is to discuss analytically the effects of absorption or gain on the statistics of wave ... More

Flux Dependence of Persistent Current in a Mesoscopic Disordered Tight Binding RingJun 21 2001We reconsider the study of persistent currents in a disordered one-dimensional ring threaded by a magnetic flux, using he one-band tight-binding model for a ring of N-sites with random site energies. The secular equation for the eigenenergies expressed ... More

Enhancement of Persistent Current in Metal Rings by Correlated DisorderNov 14 2007Aug 22 2008We study analytically the effect of a correlated random potential on the persistent current in a one-dimensional ring threaded by a magnetic flux $\phi$, using an Anderson tight-binding model. In our model, the system of $N=2M$ atomic sites of the ring ... More

Public Key Infrastructure based on Authentication of Media AttestmentsNov 28 2013Many users would prefer the privacy of end-to-end encryption in their online communications if it can be done without significant inconvenience. However, because existing key distribution methods cannot be fully trusted enough for automatic use, key management ... More

Persistence, Change, and the Integration of Objects and Processes in the Framework of the General Formal OntologyNov 07 2013Dec 06 2013In this paper we discuss various problems, associated to temporal phenomena. These problems include persistence and change, the integration of objects and processes, and truth-makers for temporal propositions. We propose an approach which interprets persistence ... More

Sector DecompositionMar 28 2008May 16 2008Sector decomposition is a constructive method to isolate divergences from parameter integrals occurring in perturbative quantum field theory. We explain the general algorithm in detail and review its application to multi-loop Feynman parameter integrals ... More

Prompt photon production in photoproduction, DIS and hadronic collisionsNov 15 2007Recent results on prompt photon production in photoproduction, deeply inelastic scattering and hadronic collisions are reviewed and the importance of photons for LHC experiments is briefly discussed.

A numerical approach to infrared divergent multi-parton phase space integralsJun 30 2004It is described how the method of sector decomposition can serve to disentangle overlapping infrared singularities, in particular those occurring in the calculation of the real emission part of e+e- to 2 jets and e+e- to 3 jets at NNLO.

Gamma-Ray Astronomy of Cosmic RaysFeb 22 2002Many of the basic problems in the astrophysics of charged Cosmic Rays remain on principle unresolved by in situ observations in the Solar System due to the chaotic nature of the propagation of these particles in Interstellar space. This concerns the existence ... More

Towards e+e- --> 3 jets at NNLO by sector decompositionJan 09 2006Jan 09 2006A method based on sector decomposition has been developed to calculate the double real radiation part of the process e+e- to 3 jets at next-to-next-to-leading order. It is shown in an example that the numerical cancellation of soft and collinear poles ... More

The Quantum Query Complexity of Elliptic PDEDec 27 2005The complexity of the following numerical problem is studied in the quantum model of computation: Consider a general elliptic partial differential equation of order 2m in a smooth, bounded domain Q\subset \R^d with smooth coefficients and homogeneous ... More

Monitoring of Traffic Manoeuvres with Imprecise InformationSep 08 2017In monitoring, we algorithmically check if a single behavior satisfies a property. Here, we consider monitoring for Multi-Lane Spatial Logic (MLSL). The behavior is given as a finite transition sequence of MLSL and the property is that a spatial MLSL ... More

Can the Many-Worlds-Interpretation be probed in Psychology?Sep 15 2016Jan 17 2017A minimal approach to the measurement problem and the quantum-to-classical transition assumes a universally valid quantum formalism, i.e. unitary time evolution governed by a Schr\"odinger-type equation. As had been pointed out long ago, in this view ... More

QCD calculations for the LHC: status and prospectsOct 13 2017We briefly review the status of high precision QCD predictions available for LHC processes, focusing on corrections beyond NLO and ways to make the latter available in a convenient format. As a phenomenological example we discuss the two-loop corrections ... More

Reconstructing a two-color scenery by observing it along a simple random walk pathMar 24 2005Let {\xi (n)}_{n\in Z} be a two-color random scenery, that is, a random coloring of Z in two colors, such that the \xi (i)'s are i.i.d. Bernoulli variables with parameter \tfrac12. Let {S(n)}_{n\in N} be a symmetric random walk starting at 0. Our main ... More

On the Consistency of Quick ShiftOct 29 2017Dec 23 2017Quick Shift is a popular mode-seeking and clustering algorithm. We present finite sample statistical consistency guarantees for Quick Shift on mode and cluster recovery under mild distributional assumptions. We then apply our results to construct a consistent ... More

Representations of Spacetime as Unitary Operation Classes or Against the Monoculture of Particle FieldsJan 18 1999Spacetime is modelled as a homogeneous manifold given by the classes of unitary $\U(2)$ operations in the general complex operations $\GL(\C^2)$. The residual representations of this noncompact symmetric space of rank two are characterized by two continuous ... More

The External-Internal Group Quotient Structure for the Standard Model in Analogy to General RelativityMay 11 1998In analogy to the class structure $\GL(\R^4)/\O(1,3)$ for general relativity with a local Lorentz group as stabilizer and a basic tetrad field for the parametrization, a corresponding class structure $\GL(\C^2)/\U(2)$ is investigated for the standard ... More

The Central Correlations of Hypercharge, Isospin, Colour and Chirality in the Standard ModelFeb 16 1998The correlation of the fractionally represented hypercharge group with the isospin and colour group in the standard model determines as faithfully represented internal group the quotient group ${\U(1)\x\SU(2)\x\SU(3)\over\Z_2\x\Z_3}$. The discrete cyclic ... More

The Coupling Constants and Masses of the Standard Model as Symmetry NormalizationsAug 08 1996The numerical input for the quantitative consequences of the electroweak standard model, the hypercharge and isospin coupling constants and the Higgs field ground state mass value, are interpreted as normalizations of the symmetries involved. Using an ... More

Harmonic analysis of spacetime with hypercharge and isospinDec 09 2003In analogy to the harmonic analysis for the Poincar\'e group with its irreducible representations characterizing free particles, the harmonic analysis for a nonlinear spacetime model as homogenous space of the extended Lorentz group GL(C^2) is given. ... More

Probability Collectives for Unstable ParticlesMay 07 2002Unstable particles, together with their stable decay products, constitute probability collectives which are defined as Hilbert spaces with dimension higher than one, nondecomposable in a particle basis. Their structure is considered in the framework of ... More

Definite and Indefinite Unitary Time Representations for Hilbert and Non-Hilbert SpacesDec 21 2001Stable states (particles), ghosts and unstables states (particles) are discussed with respect to the time representations involved, their unitary groups and the induced Hilbert spaces. Unstable particles with their decay channels are treated as higher ... More

Diophantine Approximation on varieties V: Algebraic independence criteriaJan 10 2010For a tuple $(\theta_1,..,\theta_M)$ of complex number, buliding on the approximation techniques in earlier papers of this series, this paper engages in deducing lower estimates on the transcendence degree of the field generated by $\theta_1, ..., \theta_M$ ... More

Can the Many-Worlds-Interpretation be probed in Psychology?Sep 15 2016A minimal approach to the measurement problem and the quantum-to-classical transition assumes a universally valid quantum formalism, i.e. unitary time evolution governed by a Schr\"odinger-type equation. As had been pointed out long ago, in this view ... More

Analytic Study of Persistent Current in a Two-Channel Disordered Mesoscopic RingFeb 04 2011Jun 20 2011We present an extensive analytical study of persistent current in a weakly disordered two-chain cylindrical ring threaded by an Aharonov-Bohm flux $0 < \phi <\phi_0/2$ (with $\phi_0$ the flux quantum) and described by the Anderson model. The effect of ... More

Cusps of the Kähler moduli space and stability conditions on K3 surfacesDec 14 2010In [Ma1] S. Ma established a bijection between Fourier--Mukai partners of a K3 surface and cusps of the K\"ahler moduli space. The K\"ahler moduli space can be described as a quotient of Bridgeland's stability manifold. We study the relation between stability ... More

Pitfalls of Goodness-of-Fit from LikelihoodOct 31 2003The value of the likelihood is occasionally used by high energy physicists as a statistic to measure goodness-of-fit in unbinned maximum likelihood fits. Simple examples are presented that illustrate why this (seemingly intuitive) method fails in practice ... More

Quantum Approximation I. Embeddings of Finite Dimensional L_p SpacesMay 06 2003We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The results show ... More

A numerical approach to the double real radiation part of e+e- to 3 jets at NNLOJul 04 2006We report on the sector decomposition approach to the double real radiation part of e^+e^- to 3 jets at NNLO.

Constraining the gluon in the proton via photoproduction reactionsApr 16 2003Two reactions, the photoproduction of a direct photon plus a jet and the photoproduction of a charged hadron plus a jet, are studied in view of their potential to constrain the gluon distribution in the proton. The results are based on a program of partonic ... More

Asymptotic Goodness-of-Fit Tests for Point Processes Based on Scaled Empirical K-FunctionsJun 04 2017We study sequences of scaled edge-corrected empirical (generalized) K-functions (modifying Ripley's K-function) each of them constructed from a single observation of a $d$-dimensional fourth-order stationary point process in a sampling window W_n which ... More

Relativities and Homogeneous Spaces I -- Finite dimensional relativity representationsFeb 13 2006Special relativity, the symmetry breakdown in the electroweak standard model, and the dichotomy of the spacetime related transformations with the Lorentz group, on the one side, and the chargelike transformations with the hypercharge and isospin group, ... More

Gauge coupling constants as residues of spacetime representationsMay 06 2005The gauge coupling constants in the electroweak standard model can be written as mass ratios, e.g. the coupling constant for isospin interactions $g_2^2=2{m_W^2\over m^2}\sim 2({80\over169})^2\sim{1\over 2.3}$ with the mass of the charged weak boson and ... More

Duality Induced Reflections and CPTOct 28 1999The linear particle-antiparticle conjugation $\ty C$ and position space reflection $\ty P$ as well as the antilinear time reflection $\ty T$ are shown to be inducable by the selfduality of representations for the operation groups $\SU(2)$, $\SL(\C^2)$ ... More

The Analysis of Time-Space Translations in Quantum FieldsJan 30 1996I discuss the indefinite metrical structure of the time-space translations as realized in the indefinite inner products for relativistic quantum fields, familiar in the example of quantum gauge fields. The arising indefinite unitary nondiagonalizable ... More

The space of Cohen-Macaulay curvesMar 24 2014One can consider the Hilbert scheme as a natural compactification of the space of smooth projective curves with fixed Hilbert polynomial. Here we consider a different modular compactification, namely the functor CM parameterizing curves together with ... More

The scaling of conductance in the Anderson model of localization in one dimension is a two-parameter scalingJul 23 2003The cumulants of the logarithm of the conductance (lng) in the localized regime in the one-dimensional Anderson model are calculated exactly in the second Born approximation for weak disorder. Only the first two cumulants turn out to ne non-zero since ... More

Conductance and localization in disordered wires: role of evanescent statesJul 23 2003This paper extends an earlier analytical scattering matrix treatment of conductance and localization in coupled two- and three Anderson chain systems for weak disorder when evanescent states are present at the Fermi level. Such states exist typically ... More

Localization fom conductance in few-channel disordered wiresJun 17 2002We study localization in two- and three channel quasi-1D systems using multichain tight-binding Anderson models with nearest-neighbour interchain hopping. In the three chain case we discuss both the case of free- and that of periodic boundary conditions ... More

The Relativity of ExistenceFeb 21 2012Aug 23 2012Despite the success of modern physics in formulating mathematical theories that can predict the outcome of experiments, we have made remarkably little progress towards answering the most fundamental question of: why is there a universe at all, as opposed ... More

Inverses of Motzkin and Schröder PathsMay 18 2011We suggest three applications for the inverses: For the inverse Motzkin matrix we look at Hankel determinants, and counting the paths inside a horizontal band, and for the inverse Schr\"oder matrix we look at the paths inside the same band, but ending ... More

Quantum Approximation II. Sobolev EmbeddingsMay 06 2003A basic problem of approximation theory, the approximation of functions from the Sobolev space W_p^r([0,1]^d) in the norm of L_q([0,1]^d), is considered from the point of view of quantum computation. We determine the quantum query complexity of this problem ... More

Neutrino masses and particle physics beyond the standard modelSep 02 2002Oct 28 2002The evidence for non-vanishing neutrino masses from solar and atmospheric neutrinos provides the first solid hint towards physics beyond the standard model. A full reconstruction of the neutrino spectrum may well provide a key to the theoretical structures ... More

Physics Beyond the Multiverse - Naturalness and the Quest for a Fundamental TheorySep 17 2018Mar 15 2019Finetuning and Naturalness are extra-empirical theory assessments that reflect our expectation how scientific theories should provide an intuitive understanding about the foundations underlying the observed phenomena. Recently, the absence of new physics ... More

Godunov Variables in Relativistic Fluid DynamicsJun 20 2017This note presents Godunov variables and 4-potentials for the relativistic Euler equations of barotropic fluids. The associated additional conservation/ production law has different interpretations for different fluids. In particular it refers to ENTROPY ... More

New option for solving the climatic problems with non-thermal laser driven boron fusion and ultrahigh magnetic fieldsDec 13 2014In contrast to the broad stream of sustainable developments on fusion energy, new aspects are developed now by applying ultra-short, ultra-powerful laser pulses in a plasma-block ignition scheme by avoiding the well known difficulties of thermal-pressure ... More

Laser Plasma Physics - Forces and Nonlinear PrincipleAug 20 2014This work is an electronic pre-publication of a book manuscript being under consideration in order to provide information to interested researchers about a review of mechanical forces in plasmas by electro-dynamic fields. Beginning with Kelvin's ponderomotive ... More

Physical Relativism as an Interpretation of ExistenceJun 23 2013Dec 05 2013Despite the success of modern physics in formulating mathematical theories that can predict the outcome of quantum-scale experiments, the physical interpretations of these theories remain controversial. In this manuscript, we propose a new interpretation ... More

Photoproduction of prompt photons at NLOMay 15 2001A numerical program to calculate the photoproduction of prompt photons is presented. The code includes full next-to-leading order corrections to all subprocesses. The results are compared to recent ZEUS data.

The Hilbert spaces for stable and unstable particlesJan 11 2005The Hilbert spaces for stable scattering states and particles are determined by the representations of the characterizing Euclidean and Poincar\'e group and given, respectively, by the square integrable functions on the momentum 2-spheres for a fixed ... More

The Symmetry Reduction from Interactions to ParticlesNov 29 2000The hypercharge-isospin-color symmetry of the standard model interaction is drastically reduced to a remaining Abelian electromagnetic $\U(1)$-symmetry for the particles. It is shown that such a symmetry reduction comes as a consequence of the central ... More

Diophantine Approximation on varieties III: Approximation of non-algebraic points by algebraic pointsNov 23 2007For $\theta$ a non-algebraic point on a quasi projective variety over a number field, I prove that $\theta$ has an approximation by a series of algebraic points of bounded height and degree which is essentially best possible. Applications of this result ... More

Large deviations of the empirical volume fraction for stationary Poisson grain modelsMar 23 2005We study the existence of the (thermodynamic) limit of the scaled cumulant-generating function L_n(z)=|W_n|^{-1}\logE\exp{z|\Xi\cap W_n|} of the empirical volume fraction |\Xi\cap W_n|/|W_n|, where |\cdot| denotes the d-dimensional Lebesgue measure. Here ... More

Localization length in Dorokhov's microscopic model of multichannel wiresMar 10 2003We derive exact quantum expressions for the localization length $L_c$ for weak disorder in two- and three chain tight-binding systems coupled by random nearest-neighbour interchain hopping terms and including random energies of the atomic sites. These ... More

Theory of Localization in a Disordered Ring in a Non-Hermitian FieldJun 21 2001We present an analytical study of the Lyapunov exponent for electronic states in a disordered tight-binding ring, with N sites of spacing c, in the presence of a non-hermitian field component h, for weak disorder. This system has been proposed by Hatano ... More

Relation between Anderson- and Invariant Imbedding Models for Transport in Finite Chains and Study of Phase- and Delay Time Distributions for Strong DisorderJun 21 2001The invariant imbedding evolution equations for the amplitude reflection and transmission coefficients of a disordered 1D chain are shown to follow from the continuum limit, for weak disorder, of recursion relations between reflection (transmission) coefficients ... More

The DMPK equation for mesoscopic quantum transport revisitedFeb 06 2013A recent Drude model description of the metallic regime and of a channel- averaged elastic mean free path (mfp), $\ell_0$, in an $N$-channel tight-binding wire identifies the Thouless localization length, $N\ell_0$, as a proper lower bound of macroscopic ... More

Physics Beyond the Multiverse - Naturalness and the Quest for a Fundamental TheorySep 17 2018Finetuning and Naturalness are extra-empirical theory assessments that reflect our expectation how scientific theories should provide an intuitive understanding about the foundations underlying the observed phenomena. Recently, the absence of new physics ... More

Lensing Bias to CMB Polarization Measurements of Compensated Isocurvature PerturbationsAug 03 2017Compensated isocurvature perturbations are opposite spatial fluctuations in the baryon and dark matter (DM) densities. They arise in the curvaton model and some models of baryogenesis. While the gravitational effects of baryon fluctuations are compensated ... More

Photoproduction of isolated photons, single hadrons and jets at NLODec 04 2003The photoproduction of large-p_T charged hadrons and of prompt photons is discussed, for the inclusive case and with an associated jet, using predictions from the NLO partonic Monte Carlo program EPHOX. Comparisons to recent HERA data are also shown.

Quantum Integration in Sobolev ClassesDec 23 2001We study high dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes $W^r_p([0,1]^d)$ and analyze their convergence rates. We also prove lower bounds which show that ... More

The sector decomposition approach to real radiation at NNLOJan 27 2006A method based on sector decomposition is briefly described which is suitable for the calculation of the double real radiation part of e^+e^- to 3 jets at next-to-next-to-leading order in a fully differential way.

On the Power of Quantum Algorithms for Vector Valued Mean ComputationMar 15 2004We study computation of the mean of sequences with values in finite dimensional normed spaces and compare the computational power of classical randomized with that of quantum algorithms for this problem. It turns out that in contrast to the known superiority ... More

A numerical method for NNLO calculationsNov 11 2002A method to isolate the poles of dimensionally regulated multi-loop integrals and to calculate the pole coefficients numerically is extended to be applicable to phase space integrals as well.

Non-Asymptotic Uniform Rates of Consistency for k-NN RegressionJul 19 2017Nov 03 2018We derive high-probability finite-sample uniform rates of consistency for $k$-NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that $k$-NN regression adapts to an unknown lower intrinsic dimension automatically. ... More

Realizations of Causal Manifolds by Quantum FieldsJul 08 1997Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the homogenous spaces $\D(n)=\GL(\C^n_\R)/\U(n)$ ... More

Residual Representations of SpacetimeOct 09 2000Spacetime is modelled by binary relations - by the classes of the automorphisms $\GL(\C^2)$ of a complex 2-dimensional vector space with respect to the definite unitary subgroup $\U(2)$. In extension of Feynman propagators for particle quantum fields ... More

Diophantine Approximation on Varieties IV: Derivated algebraic distance and derivative metric Bezout TheoremJan 25 2009The metric Bezout Theorem proved in an earlier paper can be extended to a derivative version that compares derivatives of the algebraic distance of a point $\theta$ to two properly intersecting cycles in projective space with the derivatives of the algebraic ... More

Diophantine Approximation of non-algebraic points on varieties II: Explicit estimates for arithmetic Hilbert FunctionsNov 11 2007Jan 26 2016Because of its ineffectiveness, the usual arithmetic Hilbert-Samuel formula is not applicable in the context of Diophantine Approximation. In order to overcome this difficulty, the present paper presents explicit estimates for arithmetic Hilbert Functions ... More

Diophantine Approximation on projective Varieties I: Algebraic distance and metric Bézout TheoremNov 23 2006Jan 26 2016For two properly intersecting effective cycles in projective space X,Y, and their intersection product Z, the metric Bezout Theorem relates the degrees, heights of X,Y, and Z, as well as their distances and algebraic distances to a given point theta. ... More

Some remarks on biequidimensionality of topological spaces and Noetherian schemesMar 23 2014There are many examples of the fact that dimension and codimension behave somewhat counterintuitively. In EGA it is stated that a topological space is equidimensional, equicodimensional and catenary if and only if every maximal chain of irreducible closed ... More

Entropy, biological evolution and the psychological arrow of timeJan 13 2014Nov 30 2015We argue that in Universes where future and past differ only by the entropy content a psychological arrow of time pointing in the direction of entropy increase can arise from natural selection in biological evolution. We show that this effect can be demonstrated ... More

Massive non-planar two-loop four-point integrals with SecDec 2.1Mar 05 2013Jun 13 2013We present numerical results for massive non-planar two-loop box integrals entering heavy quark pair production at NNLO, some of which are not known analytically yet. The results have been obtained with the program SecDec 2.1, based on sector decomposition ... More

Numerical evaluation of massive multi-loop integrals with SecDecSep 27 2012The program package SecDec is presented, allowing the numerical evaluation of multi-loop integrals. The restriction to Euclidean kinematics of version 1.0 has been lifted: thresholds can be handled by an automated deformation of the integration contour ... More

The Lopatinski determinant of small shocks may vanishFeb 21 2011The Kreiss-Majda Lopatinski determinant encodes a uniform stability property of shock wave solutions to hyperbolic systems of conservation laws in several space variables. This note deals with the Lopatinski determinant for shock waves of sufficiently ... More

Inversion of marine heat flow measurements by expansion of the temperature decay functionMar 25 2008Marine heat flow data, obtained with a Lister-type probe, consists of two temperature decay curves, frictional and heat pulse decay. Both follow the same physical model of a cooling cylinder. The mathematical model describing the decays is non-linear ... More

Gilbert Damping in Magnetic MultilayersJul 19 2002We study the enhancement of the ferromagnetic relaxation rate in thin films due to the adjacent normal metal layers. Using linear response theory, we derive the dissipative torque produced by the s-d exchange interaction at the ferromagnet-normal metal ... More

Optimal Summation and Integration by Deterministic, Randomized, and Quantum AlgorithmsMay 23 2001We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new aspect, which ... More

The Blesgen and Lowengrub-Truskinovsky Descriptions of Two-Phase Compressible Fluid Flow: Interstitial Working and a Reduction to Korteweg TheoryNov 27 2017Formulated by Blesgen and Lowengrub and Truskinovsky, the `Navier-Stokes-Allen-Cahn' (NSAC) equations and the `Navier-Stokes-Cahn-Hilliard' (NSCH) equations describe diphasic fluid flow, combining the conservation laws for mass, momentum, and energy with ... More

Numerical multi-loop calculations with the program SecDecNov 04 2014SecDec is a program which can be used for the evaluation of parametric integrals, in particular multi-loop integrals. For a given set of propagators defining the graph, the program constructs the graph polynomials, factorizes the endpoint singularities, ... More