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Cesium bright matter-wave solitons and soliton trainsFeb 08 2019Mar 05 2019A study of bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is investigated. Formation of soliton trains ... More

Quasicrystals and Unit-Cell TwinningMar 03 2015The structure and the corresponding electron diffraction patterns of quasicrystals are explained by unit-cell twinning. The twinning operation is applied to the primitive golden rhombohedra, obtained by a slight deformation of a parent cubic close-packed ... More

Nanostructured and Modulated Low-Dimensional SystemsMar 26 2013Charge density wave (CDW) ordering in NbSe3 and the structurally related quasi one-dimensional compounds is reconsidered. Since the modulated ground state is characterized by unstable nano-domains, the structural information obtained from diffraction ... More

Cesium bright matter-wave solitons and soliton trainsFeb 08 2019A setup for studying bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is studied. Formation of soliton ... More

Configurational Electronic States in Layered Metallic DichalcogenidesJan 08 2019Mar 06 2019Mesoscopic irregularly ordered and even amorphous self-assembled electronic structures were recently reported in two-dimensional metallic dichalcogenides (TMDs), created and manipulated with short light pulses or by charge injection. Apart from promising ... More

Correlated Configurational States and a Quantum Charge Liquid in Layered Metallic DichalcogenidesJan 08 2019Two-dimensional metallic dichalcogenides display diverse charge ordering phenomena, but the mechanisms for the formation of low-temperature commensurate order have proven surprisingly controversial. Fermi surface instabilities, the electron-phonon interaction, ... More

Generalized integrands and bond portfolios: Pitfalls and counter examplesSep 12 2009Jan 05 2011We construct Zero-Coupon Bond markets driven by a cylindrical Brownian motion in which the notion of generalized portfolio has important flaws: There exist bounded smooth random variables with generalized hedging portfolios for which the price of their ... More

Detection of a Hypercharge Axion in ATLASMay 28 2001This Master of Science thesis treats the hypercharge axion, which is a hypothetical pseudo-scalar particle with electroweak interactions. First, the theoretical context and the motivations for this study are discussed. In short, the hypercharge axion ... More

Tomography of random social networksSep 15 2005We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at a distance ... More

Limit points of the iterative scaling procedureJul 23 2012The iterative scaling procedure (ISP) is an algorithm which computes a sequence of matrices, starting from some given matrix. The objective is to find a matrix 'proportional' to the given matrix, having given row and column sums. In many cases, for example ... More

Path correlations in a randomly oriented complete bipartite graphFeb 08 2011In a randomly oriented graph containing vertices $x$ and $y$, denote by $\{x\to y\}$ the event that there is a directed path from $x$ to $y$. We study the correlation between the events $\{x\to y\}$ and $\{y\to z\}$ for a (large) oriented complete bipartite ... More

Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz PotentialSep 27 2010The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or "Hele- Shaw") problem in the plane. The guiding principle in this connection is the fact that "non-physical" ... More

Characterizing the Set of Coherent Lower Previsions with a Finite Number of Constraints or VerticesMar 15 2012The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a reformulation ... More

Outbursts of WZ Sge stars/TOADs: a phenomenological comparison with soft X-ray transientsDec 01 1998The outbursts of WZ Sge stars (or TOADs), are compared to those seen in the (soft) X-ray transients. Both types of outbursts exhibit strong similarities: large amplitudes, long recurrence times, occurrence of superhumps, and of rebrightenings or reflares ... More

Towards 4U 1630-47: a black-hole soft X-ray transient odysseyJul 27 1998Aug 12 19984U 1630-47 is a black-hole X-ray transient with one of the shortest recurrence times. Despite its regular outburst behaviour little is known about this source. Only recently has attention to this system increased. I discuss there the basic known (X-ray) ... More

Askey-Wilson polynomials and the quantum SU(2) group: survey and applicationsJul 25 1994Generalised matrix elements of the irreducible representations of the quantum $SU(2)$ group are defined using certain orthonormal bases of the representation space. The generalised matrix elements are relatively infinitesimal invariant with respect to ... More

One-parameter orthogonality relations for basic hypergeometric seriesMay 27 2003The second order hypergeometric q-difference operator is studied for the value c=-q. For certain parameter regimes the corresponding recurrence relation can be related to a symmetric operator on the Hilbert space l^2(Z). The operator has deficiency indices ... More

Static overscreening and nonlinear response in the Hubbard ModelMay 29 2001We investigate the static charge response for the Hubbard model. Using the Slave-Boson method in the saddle-point approximation we calculate the charge susceptibility. We find that RPA works quite well close to half-filling, breaking, of course, down ... More

Equity Allocation and Portfolio Selection in Insurance: A simplified Portfolio ModelJul 22 1999A quadratic discrete time probabilistic model, for optimal portfolio selection in (re-)insurance is studied. For positive values of underwriting levels, the expected value of the accumulated result is optimized, under constraints on its variance and on ... More

The observers' view of (very) long X-ray bursts: they are super!Oct 15 2003In many X-ray point sources on the sky, the X-ray emission arises because hydrogen and/or helium is accreted onto a neutron star from a nearby donor star. When this matter settles on the neutron star surface, it will undergo nuclear fusion. For a large ... More

Bootstrap percolation on the Hamming torus with threshold 2Jul 09 2014Oct 15 2016This paper analyzes various questions pertaining to bootstrap percolation on the $d$-dimensional Hamming torus where each node is open with probability $p$ and the percolation threshold is 2. For each $d'<d$ we find the critical exponent for the event ... More

A decomposition of the Schur block product on matrices of operatorsNov 08 2018Given two $m \times n $ matrices $A = (a_{ij})$ and $B=(b_{ij}) $ with entries in $B(H)$ for some Hilbert space $H,$ the Schur block product is the $m \times n$ matrix $ A\square B := (a_{ij}b_{ij}).$ There exists an $m \times n$ matrix $S = (s_{ij})$ ... More

Quantal interferometry with dissipative internal motionJun 02 2004Nov 16 2004In presence of dissipation, quantal states may acquire complex-valued phase effects. We suggest a notion of dissipative interferometry that accommodates this complex-valued structure and that may serve as a tool for analyzing the effect of certain kinds ... More

Astrometry for DynamicsAug 14 2014In May 2013, I responded with the present paper to ESA's call for White Papers for the definition of Large missions. This was half a year before the launch of ESA's large astrometry mission Gaia. The present proposal for a Gaia successor mission is similar ... More

Normal forms for the G_2-action on the real symmetric 7x7-matrices by conjugationMar 12 2007Jun 08 2007The exceptional Lie group G_2 acts on the set of real symmetric 7x7-matrices by conjugation. We solve the normal form problem for this group action. In view of earlier results, this gives rise to a classification of all finite-dimensional real flexible ... More

Isotopes of Hurwitz algebrasDec 08 2010Aug 10 2018We study the class of all algebras that are isotopic to a Hurwitz algebra. Isomorphism classes of such algebras are shown to correspond to orbits of a certain group action. A complete, geometrically intuitive description of the category of isotopes of ... More

Estimates of the remainder in Taylor's theorem using the Henstock--Kurzweil integralJun 18 2004When a real-valued function of one variable is approximated by its $n^{th}$ degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue $p$-norms in cases where $f^{(n)}$ or $f^{(n+1)}$ are Henstock--Kurzweil integrable. When ... More

Estimates of Henstock--Kurzweil Poisson integralsJun 18 2004If $f$ is a real-valued function on $[-\pi,\pi]$ that is Henstock--Kurzweil integrable, let $u_r(\theta)$ be its Poisson integral. It is shown that $\|u_r\|_p=o(1/(1-r))$ as $r\to 1$ and this estimate is sharp for $1\leq p\leq\infty$. If $\mu$ is a finite ... More

Rapidly growing Fourier integralsJan 02 2001The Riemann-Lebesgue Lemma says that the Fourier transform of an absolutely integrable function on the real line tends to zero as the transform parameter tends to infinity. When the integral is allowed to converge conditionally, the transform can have ... More

Constructivist and Structuralist Foundations: Bishop's and Lawvere's Theories of SetsJan 30 2012Bishop's informal set theory is briefly discussed and compared to Lawvere's Elementary Theory of the Category of Sets (ETCS). We then present a constructive and predicative version of ETCS, whose standard model is based on the constructive type theory ... More

Robust error estimates for stabilized finite element approximations of the two dimensional Navier-Stokes equations with application to implicit large eddy simulationMar 08 2013Apr 12 2013We consider error estimates in weak parametrised norms for stabilized finite element approximations of the two-dimensional Navier-Stokes' equations. These weak norms can be related to the norms of certain filtered quantities, where the parameter of the ... More

Error estimates for shock capturing finite element approximations of the one dimensional Burgers' equationNov 04 2011May 07 2014We propose an error analysis in weak norms of a shock capturing finite element method for the Burgers' equation. The estimates can be related to estimates of certain filtered quantities and are robust in the inviscid limit. Using a total variation apriori ... More

Fourier series with the continuous primitive integralMay 27 2011Fourier series are considered on the one-dimensional torus for the space of periodic distributions that are the distributional derivative of a continuous function. This space of distributions is denoted $\alext$ and is a Banach space under the Alexiewicz ... More

A simplified characteristic functions of quantum heatApr 06 2019This paper presents a simplified structure of the characteristic function of the distribution of energy changes in a bosonic environment interacting linearly with a quantum system. This characteristic function of quantum heat can be expressed using the ... More

Hölder estimates for viscosity solutions of equations of fractional $p$-Laplace typeMay 26 2014Jun 24 2014We prove H\"older estimates for viscosity solutions of a class of possibly degenerate and singular equations modelled by the fractional $p$-Laplace equation $$ \text{PV} \int_{\mathbb{R}^n}\frac{|u(x)-u(x+y)|^{p-2}(u(x)-u(x+y))}{|y|^{n+sp}}\, dy =0, $$ ... More

A unified picture of strong coupling stochastic thermodynamics and time reversalsDec 21 2017Jan 02 2018Strong-coupling statistical thermodynamics is formulated as Hamiltonian dynamics of an observed system interacting with another unobserved system (a bath). It is shown that the entropy production functional of stochastic thermodynamics, defined as the ... More

On work and heat in time-dependent strong couplingMay 22 2017This paper revisits the classical problem of representing a thermal bath interacting with a system as a large collection of harmonic oscillators initially in thermal equilibrium. As is well known the system then obeys an equation, which in the bulk and ... More

Signatures of hit and run collisionsOct 13 2018Terrestrial planets grew in a series of similar-sized collisions that swept up most of the next-largest bodies. Theia was accreted by the Earth to form the Moon according to the theory. Planetesimals likewise may have finished their accretion in a sequence ... More

Understanding AI Data Repositories with Automatic Query GenerationApr 20 2018We describe a set of techniques to generate queries automatically based on one or more ingested, input corpuses. These queries require no a priori domain knowledge, and hence no human domain experts. Thus, these auto-generated queries help address the ... More

Jigsaw Percolation on Erdos-Renyi Random GraphsMar 21 2015Mar 28 2015We extend the jigsaw percolation model to analyze graphs where both underlying people and puzzle graphs are Erd\H{o}s-R\'enyi random graphs. Let $p_{\text{ppl}}$ and $p_{\text{puz}}$ denote the probability that an edge exists in the respective people ... More

Del Pezzo Surfaces in Weighted Projective SpacesJan 23 2013Nov 15 2016We study singular del Pezzo surfaces that are quasi-smooth and well-formed weighted hypersurfaces. We give an algorithm how to classify all of them.

Upper and Lower Bounds on Zero-Sum Generalized Schur NumbersAug 11 2018Let $S_{\mathfrak{z}}(k,r)$ be the least positive integer such that for any $r$-coloring $\chi : \{1,2,\dots,S_{\mathfrak{z}}(k,r)\} \longrightarrow \{1, 2, \dots, r\}$, there is a sequence $x_1, x_2, \dots, x_k$ such that $\sum_{i=1}^{k-1} x_i = x_k$, ... More

Bounds on the Mordell--Weil rank of elliptic curves over imaginary quadratic number fields with class number 1Nov 19 2018We generalize the lemmas of Thomas Kretschmer to arbitrary number fields, and apply them with a 2-descent argument to obtain bounds for families of elliptic curves over certain imaginary quadratic number fields with class number 1. One such family occurs ... More

Higher Weak Derivatives and Reflexive Algebras of OperatorsApr 14 2015Jul 09 2015Let D be a self-adjoint operator on a Hilbert space H and x a bounded operator on H. We say that x is n-times weakly D-differentiable, if for any pair of vectors a, b from H the function < exp(itD)x exp(-itD) a, b> is n-times differentiable. We give several ... More

Monte Carlo simulation of spin models with long-range interactionsJun 15 1999An efficient Monte Carlo algorithm for the simulation of spin models with long-range interactions is discussed. Its central feature is that the number of operations required to flip a spin is independent of the number of interactions between this spin ... More

Attractors and the Holomorphic AnomalyDec 14 2004Motivated by the recently proposed connection between N=2 BPS black holes and topological strings, I study the attractor equations and their interplay with the holomorphic anomaly equation. The topological string partition function is interpreted as a ... More

Entanglement-induced geometric phase of quantum statesMar 18 2008Mar 09 2010The concept of relative state is used to introduce geometric phases that originate from correlations in states of composite quantum systems. In particular, we identify an entanglement-induced geometric phase in terms of a weighted average of geometric ... More

On the alleged nonlocal and topological nature of the molecular Aharonov-Bohm effectOct 31 2003Sep 09 2004The nonlocal and topological nature of the molecular Aharonov-Bohm (MAB) effect is examined for real electronic Hamiltonians. A notion of preferred gauge for MAB is suggested. The MAB effect in the linear + quadratic $E\otimes \epsilon$ Jahn-Teller system ... More

More on functional and quantitative versions of the isoperimetric inequalitySep 14 2016This paper deals with the famous isoperimetric inequality. In a first part, we give some new functional form of the isoperimetric inequality, and in a second part, we give a quantitative form with a remainder term involving Wasserstein distance of the ... More

On determinacy/indeterminacy of Moment ProblemsApr 21 2016This paper treat determinacy of strong moment problems in part I and indeterminacy of strong moment problems in part II. This paper is a summary of the following papers: [1] Ald\'en. E., Determinacy of Strong Moment Problems. [2] On Indeterminacy of Strong ... More

A Simple Proof of the Uniqueness of the Einstein Field Equation in All DimensionsJan 12 2016The standard argument for the uniqueness of the Einstein field equation is based on Lovelock's Theorem, the relevant statement of which is restricted to four dimensions. I prove a theorem similar to Lovelock's, with a physically modified assumption: that ... More

The parity theorem for multiple polylogarithmsDec 14 2015Oct 03 2016We generalize the well-known parity theorem for multiple zeta values (MZV) to functional equations of multiple polylogarithms (MPL). This reproves the parity theorem for MZV with an additional integrality statement, and also provides parity theorems for ... More

Feynman integrals and hyperlogarithmsJun 24 2015We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we prove that in ... More

Error estimates for stabilized finite element methods applied to ill-posed problemsJun 17 2014We propose an analysis for the stabilized finite element methods proposed in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: Elliptic equations. SIAM J. Sci. Comput., 35(6) 2013, valid in the ... More

On T-duality transformations for the three-sphereAug 07 2014Mar 25 2015We study collective T-duality transformations along one, two and three directions of isometry for the three-sphere with H-flux. Our aim is to obtain new non-geometric backgrounds along lines similar to the example of the three-torus. However, the resulting ... More

Enumeration of monochromatic three term arithmetic progressions in two-colorings of any finite groupAug 05 2014Nov 10 2014There are many extremely challenging problems about existence of monochromatic arithmetic progressions in colorings of groups. Many theorems hold only for abelian groups as results on non-abelian groups are often much more difficult to obtain. In this ... More

Anisotropic diffusive transport: connecting microscopic scattering and macroscopic transport propertiesNov 14 2013Aug 12 2014This work concerns the modeling of radiative transfer in anisotropic turbid media using diffusion theory. A theory for the relationship between microscopic scattering properties (i.e., an arbitrary differential scattering cross-section) and the macroscopic ... More

T-duality revisitedOct 15 2013Jan 29 2014We revisit the transformation rules of the metric and Kalb-Ramond field under T-duality, and express the corresponding relations in terms of the metric G and the field strength H=dB. In the course of the derivation, we find an explanation for potential ... More

Asymptotically Safe Gravitons in Electroweak Precision PhysicsDec 06 2010Nov 11 2011Asymptotic safety offers a field theory based UV completion to gravity. For low Planck scales, gravitational effects on low-energy precision observables cannot be neglected. We compute the contribution to the rho parameter from asymptotically safe gravitons ... More

Spin-orbit interactions in a helical Luttinger liquid with a Kondo impurityMar 14 2013Jun 17 2013The combined effect of Rashba and Dresselhaus spin-orbit interactions on the physics of a helical Luttinger liquid coupled to a Kondo impurity is studied. A Rashba coupling can potentially destroy the Kondo singlet formation in certain parameter regimes ... More

Stationary probability of the identity for the TASEP on a ringDec 27 2012Consider the following Markov chain on permutations of length $n$. At each time step we choose a random position. If the letter at that position is smaller than the letter immediately to the left (cyclically) then these letters swap positions. Otherwise ... More

Holographic entanglement entropy: near horizon geometry and disconnected regionsOct 31 2010We study the finite term of the holographic entanglement entropy for the charged black hole in AdS(d+2) and other examples of black holes when the spatial region in the boundary theory is given by one or two parallel strips. For one large strip it scales ... More

A `superoutburst' in XTE J1118+480Feb 05 2001Feb 14 2001I propose that the properties of the two outbursts observed in the X-ray transient XTE J1118+480 in 2000 are akin to superoutbursts of SU UMa stars. In these systems a `normal' outburst immediately precedes a 5-10 times longer (`super')outburst. The optical ... More

A0620-00 revisited: a black-hole transient case-studyMay 05 1998For the first time we have performed a detailed study of the X-ray, optical and infra-red light curves of the 1975/1976 outburst of the famous black-hole transient A0620-00 (Nova Mon 1975, V616 Mon). During the various stages of its outburst the X-rays ... More

Del Pezzo Surfaces in Weighted Projective SpacesJan 23 2013Apr 13 2016We study singular del Pezzo surfaces that are quasi-smooth and well-formed weighted hypersurfaces. We give an algorithm how to classify all of them.

Review of "Garden of integrals"Feb 06 2008This is a review of the book "Garden of integrals" by Frank Burk.

Isotopes of Hurwitz algebrasDec 08 2010Sep 22 2015We study the class of all algebras that are isotopic to a Hurwitz algebra. Isomorphism classes of such algebras are shown to correspond to orbits of a certain group action. A complete, geometrically intuitive description of the category of isotopes of ... More

Spectral theory and special functionsJul 05 2001A short introduction to the use of the spectral theorem for self-adjoint operators in the theory of special functions is given. As the first example, the spectral theorem is applied to Jacobi operators, i.e. tridiagonal operators, on l^2(N), leading to ... More

8 Lectures on quantum groups and q-special functionsAug 22 1996Lecture notes for an eight hour course on quantum groups and $q$-special functions at the fourth Summer School in Differential Equations and Related Areas, Universidad Nacional de Colombia and Universidad de los Andes, Bogot\'a, Colombia, July 22 -- August ... More

On Jacobi and continuous Hahn polynomialsSep 21 1994Jacobi polynomials are mapped onto the continuous Hahn polynomials by the Fourier transform and the orthogonality relations for the continuous Hahn polynomials then follow from the orthogonality relations for the Jacobi polynomials and the Parseval formula. ... More

Yet another basic analogue of Graf's addition formulaSep 21 1994An identity involving basic Bessel functions and Al-Salam--Chihara polynomials is proved for which we recover Graf's addition formula for the Bessel function as the base $q$ tends to $1$. The corresponding product formula is derived. Some known identities ... More

Addition formulas for q-special functionsJun 15 1995A general addition formula for a two-parameter family of Askey-Wilson polynomials is derived from the quantum $SU(2)$ group theoretic interpretation. This formula contains most of the previously known addition formulas for $q$-Legendre polynomials as ... More

Periodic orbit theory for realistic cluster potentials: The leptodermous expansionMar 25 1998The formation of supershells observed in large metal clusters can be qualitatively understood from a periodic-orbit-expansion for a spherical cavity. To describe the changes in the supershell structure for different materials, one has, however, to go ... More

Locality and topology in the molecular Aharonov-Bohm effectDec 21 2001Nov 05 2002It is shown that the molecular Aharonov-Bohm effect is neither nonlocal nor topological in the sense of the standard magnetic Aharonov-Bohm effect. It is further argued that there is a close relationship between the molecular Aharonov-Bohm effect and ... More

Absolute astrometry in the next 50 yearsAug 10 2014Aug 03 2017With Gaia in orbit since December 2013 it is time to look at the future of fundamental astrometry and a time frame of 50 years is needed in this matter. A space mission with Gaia-like astrometric performance is required, but not necessarily a Gaia-like ... More

Interferometry from Space: A Great DreamAug 20 2014During some thirty years, 1980-2010, technical studies of optical interferometry from instruments in space were pursued as promising for higher spatial resolution and for higher astrometric accuracy. Nulling interferometry was studied for both high spatial ... More

Applications of spectral theory to special functionsDec 21 2016Lecture notes for one of the courses at the OPSFA Summerschool 6, July 11-15, 2016. All the results in these notes have appeared in the literature. Many special functions are eigenfunctions to explicit operators, such as difference and differential operators, ... More

Self-Correcting Models for Model-Based Reinforcement LearningDec 19 2016Jul 26 2017When an agent cannot represent a perfectly accurate model of its environment's dynamics, model-based reinforcement learning (MBRL) can fail catastrophically. Planning involves composing the predictions of the model; when flawed predictions are composed, ... More

The $\infty$-harmonic potential is not always an $\infty$-eigenfunctionOct 11 2012Oct 26 2012In this note we prove that there is a convex domain for which the $\infty$-harmonic potential is not a first $\infty$-eigenfunction.

The one-dimensional heat equation in the Alexiewicz normJan 18 2015A distribution on the real line has a continuous primitive integral if it is the distributional derivative of a function that is continuous on the extended real line. The space of distributions integrable in this sense is a Banach space that includes ... More

The distributional Denjoy integralJun 21 2006Dec 07 2007Let $f$ be a distribution (generalised function) on the real line. If there is a continuous function $F$ with real limits at infinity such that $F'=f$ (distributional derivative) then the distributional integral of $f$ is defined as $\int_{-\infty}^\infty ... More

Higher order corrected trapezoidal rules in Lebesgue and Alexiewicz spacesApr 28 2016If $f\!:\![a,b]\to\R$ such that $f^{(n)}$ is integrable then integration by parts gives the formula \begin{align*} &\intab f(x)\,dx = &\frac{(-1)^n}{n!}\sum_{k=0}^{n-1}(-1)^{n-k-1}\left[ \phi_n^{(n-k-1)}(a)f^{(k)}(a)- \phi_n^{(n-k-1)}(b)f^{(k)}(b)\right] ... More

Vector product algebrasOct 30 2008Vector products can be defined on spaces of dimensions 0, 1, 3 and 7 only, and their isomorphism types are determined entirely by their adherent symmetric bilinear forms. We present a short and elementary proof for this classical result.

Symmetric Functions and CapsAug 21 2008Given a finite subset S in F_p^d, let a(S) be the number of distinct r-tuples (x_1,...,x_r) in S such that x_1+...+x_r = 0. We consider the "moments" F(m,n) = sum_|S|=n a(S)^m. Specifically, we present an explicit formula for F(m,n) as a product of two ... More

The $h$-vectors of 1-dimensional Matroid Complexes and a Conjecture of StanleyMar 20 2009A matroid complex is a pure complex such that every restriction is again pure. It is a long-standing open problem to classify all possible $h$-vectors of such complexes. In the case when the complex has dimension 1 we completely resolve this question. ... More

Fourier transform inversion using an elementary differential equation and a contour integralAug 13 2018Let $f$ be a function on the real line. The Fourier transform inversion theorem is proved under the assumption that $f$ is absolutely continuous such that $f$ and $f'$ are Lebesgue integrable. A function $g$ is defined by $f'(t)-iwf(t)=g(t)$. This differential ... More

Framework Confirmation by Newtonian AbductionApr 20 2018The analysis of theory-confirmation generally takes the form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theory-confirmation ... More

Selected astrometric cataloguesJun 25 2017Jul 09 2017A selection of astrometric catalogues are presented in three tables for respectively positions, proper motions and trigonometric parallaxes. The tables contain characteristics of each catalogue showing the evolution in optical astrometry, in fact the ... More

GIER: A Danish computer from 1961 with a role in the modern revolution of astronomyApr 19 2017A Danish computer, GIER, from 1961 played a vital role in the development of a new method for astrometric measurement. This method, photon counting astrometry, ultimately led to two satellites with a significant role in the modern revolution of astronomy. ... More

Resolving observable features of galaxy cluster merger 'El Gordo' using idealized cluster models in SPH simulationsAug 18 2017Sep 02 2017The merger scenario of two galaxy subclusters to form the massive galaxy cluster 'El Gordo' is investigated using smoothed particle hydrodynamics (SPH) simulations. Idealized cluster models are used to initialize the states of both subclusters prior to ... More

Yet another category of setoids with equality on objectsApr 21 2013When formalizing mathematics in (generalized predicative) constructive type theories, or more practically in proof assistants such as Coq or Agda, one is often using setoids (types with explicit equivalence relations). In this note we consider two categories ... More

One-point functions in $β$-deformed N = 4 SYM with defectApr 25 2018We generalize earlier results on one-point functions in N = 4 SYM with a co-dimension one defect, dual to the D3-D5-brane setup in type IIB string theory on AdS5xS5, to a similar setup in the $\beta$-deformed version of the theory. The treelevel vacuum ... More

On the complete boundedness of the Schur block productDec 14 2017Nov 08 2018We give a Stinespring representation of the Schur block product, say (*), on pairs of square matrices with entries in a C*-algebra as a completely bounded bilinear operator of the form: A:=(a_{ij}), B:= (b_{ij}): A (*) B := (a_{ij}b_{ij}) = V* pi(A) F ... More

Decompositions of Schur block productsNov 08 2018Feb 17 2019Given two m x n matrices A = (a_{ij}) and B=(b_{ij}) with entries in B(H), the Schur block product is the m x n matrix A \square B := (a_{ij}b_{ij}). There exists an m x n contraction matrix S = (s_{ij}), such that A \square B = diag(AA*)^(1/2) S diag(B*B)^(1/2). ... More

Calculating the Tate local pairing for any odd prime numberOct 04 2016Fisher and Newton have given an explicit description of the Tate local pairing associated with the 3-torsion of an elliptic curve. The present paper summarizes the work from the author's master's thesis and gives an explicit formula for any odd prime ... More

Bond Market Completeness and Attainable Contingent ClaimsFeb 23 2004Mar 03 2005A general class, introduced in [Ekeland et al. 2003], of continuous time bond markets driven by a standard cylindrical Brownian motion $\wienerq{}{}$ in $\ell^{2},$ is considered. We prove that there always exist non-hedgeable random variables in the ... More

A projection formula for the ind-GrassmannianMar 22 2013Jul 29 2013Let $X = \bigcup_k X_k$ be the ind-Grassmannian of codimension $n$ subspaces of an infinite-dimensional torus representation. If $\cE$ is a bundle on $X$, we expect that $\sum_j (-1)^j \Lambda^j(\cE)$ represents the $K$-theoretic fundamental class $[\cO_Y]$ ... More

Trigonometry of The Gold-BugMay 31 2012The classic Edgar Allan Poe story The Gold-Bug involves digging for pirate treasure. Locating the digging sites requires some simple trigonometry.

Addition formula for 2-parameter family of Askey-Wilson polynomialsDec 07 1994For a two parameter family of Askey-Wilson polynomials, that can be regarded as basic analogues of the Legendre polynomials, an addition formula is derived. The addition formula is a two-parameter extension of Koornwinder's addition formula for the little ... More

Enhancing Tc in field-doped Fullerenes by applying uniaxial stressDec 18 2001Capitalizing on the two-dimensional nature of superconductivity in field-effect doped C60, we show that it should be possible to increase the transition temperature Tc by applying uniaxial stress perpendicular to the gate electrode. This method not only ... More