Results for "Erik Zupanič"

total 2904took 0.08s
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
Heavy and Excited Leptons in the OPAL Detector?Sep 20 2002Dec 02 2002This M.Sc. thesis describes a search for exotic leptons. The search has been performed using data from the OPAL detector at the Large Electron Positron collider at CERN. The total integrated luminosity was 663 pb$^{-1}$ with center of mass energies in ... More
Random Networks with Tunable Degree Distribution and ClusteringMay 17 2004Jun 04 2004We present an algorithm for generating random networks with arbitrary degree distribution and Clustering (frequency of triadic closure). We use this algorithm to generate networks with exponential, power law, and poisson degree distributions with variable ... More
Warped black holes in 3D general massive gravityJun 17 2010Jun 29 2010We study regular spacelike warped black holes in the three dimensional general massive gravity model, which contains both the gravitational Chern-Simons term and the linear combination of curvature squared terms characterizing the new massive gravity ... More
A superburst from GX 3+1Dec 20 2001I found one long X-ray flare from the X-ray burster GX 3+1 in almost 6 years of observations with the RXTE All Sky Monitor (ASM). The event had a peak flux of about 1.1 Crab (1.5-12 keV), lasted between 4.4 and 16.2 hours and exhibited a fluence of more ... More
Addition formula for big q-Legendre polynomialsApr 26 1994From Koornwinder's interpretation of big $q$-Legendre polynomials as spherical elements on the quantum $SU(2)$ group an addition formula is derived for the big $q$-Legendre polynomial. The formula involves Al-Salam--Carlitz polynomials, little $q$-Jacobi ... More
Critical properties of the three-dimensional equivalent-neighbor model and crossover scaling in finite systemsNov 24 1998Feb 23 1999Accurate numerical results are presented for the three-dimensional equivalent-neighbor model on a cubic lattice, for twelve different interaction ranges (coordination number between 18 and 250). These results allow the determination of the range dependences ... More
On the Holographic Principle in a Radiation Dominated UniverseAug 17 2000Aug 24 2000The holographic principle is studied in the context of a $n+1$ dimensional radiation dominated closed Friedman-Robertson-Walker (FRW) universe. The radiation is represented by a conformal field theory with a large central charge. Following recent ideas ... More
Absolute astrometry in the next 50 yearsAug 10 2014Dec 14 2015With 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
Astrosociology: Interviews about an infinite universeAug 21 2014If the universe is infinite now it has always been infinite. This is the opinion of many astronomers today as can be concluded from the following series of interviews, but the opinions differ much more than I had expected. Many astronomers do not have ... More
Enumeration of three term arithmetic progressions in fixed density setsAug 05 2014Nov 10 2014Additive combinatorics is built around the famous theorem by Szemer\'edi which asserts existence of arithmetic progressions of any length among the integers. There exist several different proofs of the theorem based on very different techniques. Szemer\'edi's ... More
Renormalization, Hopf algebras and Mellin transformsJul 18 2014This article aims to give a short introduction into Hopf-algebraic aspects of renormalization, enjoying growing attention for more than a decade by now. As most available literature is concerned with the minimal subtraction scheme, we like to point out ... More
A global view of quantum computation with noisy componentsJun 30 2016Nov 25 2016The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over the histories ... More
Another proof of Moon's theorem on generalised tournament score sequencesMay 20 2016Jul 13 2016Landau \cite{Landau1953} showed that a sequence $(d_i)_{i=1}^n$ of integers is the score sequence of some tournament if and only if $\sum_{i\in J}d_i \geq \binom{|J|}{2}$ for all $J\subseteq \{1,2,\dots, n\}$, with equality if $|J|=n$. Moon \cite{Moon63} ... More
Revised Elements and Blazhko Effect of the RR Lyrae Star AR HerculisJun 10 2016AR Herculis is an RR Lyrae star of type RRab whose spectral type ranges from A7 to F3. Its visual brightness varies between 10.59 mag and 11.63 mag (V). By analysis of 34,000 measurements from the AAVSO International Database and additional data from ... More
Kinematics, Dynamics, and the Structure of Physical TheoryMar 09 2016Every physical theory has (at least) two different forms of mathematical equations to represent its target systems: the dynamical (equations of motion) and the kinematical (kinematical constraints). Kinematical constraints are differentiated from equations ... More
A Weyl-Type Theorem for Geometrized Newtonian GravityOct 07 2015Mar 09 2016I state and prove, in the context of a space having only the metrical and affine structure imposed by the geometrized version of Newtonian gravitational theory, a theorem analagous to that of Weyl's for a Lorentz manifold. The theorem says that a projective ... More
Tunable liquid-liquid critical point in an ionic model of silicaOct 27 2015Recently it was shown that the WAC model for liquid silica [L. V. Woodcock, C. A. Angell, and P. Cheeseman, J. Chem. Phys. 65, 1565 (1976)] is remarkably close to having a liquid-liquid critical point (LLCP). We demonstrate that increasing the ion charge ... More
Localization and a generalization of MacDonald's inner productMay 03 2013We find a limit formula for a generalization of MacDonald's inner product in finitely many variables, using equivariant localization on the Grassmannian variety, and the main lemma from \cite{Car}, which bounds the torus characters of the higher \c{C}ech ... More
An absorbed view of a new class of INTEGRAL sourcesApr 28 2005The European gamma-ray observatory INTEGRAL has found a group of hard X-ray sources which are highly absorbed, i.e., with column densities higher than about 10^{23}/cm^2. Here I give an overview of this class of INTEGRAL sources. The X-ray, as well as ... More
Simple Non Linear Klein-Gordon Equations in 2 space dimensions, with long range scatteringOct 27 2006Jan 30 2007We establish that solutions, to the most simple NLKG equations in 2 space dimensions with mass resonance, exhibits long range scattering phenomena. Modified wave operators and solutions are constructed for these equations. We also show that the modified ... More
AGT and the Segal-Sugawara constructionAug 31 2015The conjectures of Alday, Gaiotto and Tachikawa and its generalizations have been mathematically formulated as the existence of an action of a $W$-algebra on the cohomology or $K$-theory of the instanton moduli space, together with a Whitakker vector. ... More
$K$-theory of moduli spaces of sheaves and large GrassmanniansFeb 13 2012Mar 20 2012We prove a theorem classifying the equivariant $K$-theoretic pushforwards of the product of arbitrary Schur functors applied to the tautological bundle on the moduli space of framed rank $r$ torsion-free sheaves on $\mathbb{P}^2$, and its dual. This is ... More
Complete vector fields on (C-0)^nAug 19 1998We prove necessary and sufficient conditions for completeness of a rational vector field on C^n minus n hyperplanes in general position (n>1).
Eplett's theorem for self-converse generalised tournamentsJun 07 2016The converse of a tournament is obtained by reversing all arcs. If a tournament is isomorphic to its converse, it is called self--converse. Eplett provided a necessary and sufficient condition for a sequence of integers to be realisable as the score sequence ... 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