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Rings of $SL_2({\mathbb C})$-Characters and the Kauffman Bracket Skein ModuleApr 20 1996Let $M$ be a compact orientable 3-manifold. The set of characters of $SL_2({\mathbb C})$ representations of the fundamental group of $M$ forms a closed affine algebraic set. We show that its coordinate ring is isomorphic to a specialization of the Kauffman ... More

On Evaluating the Renaissance Benchmarking Suite: Variety, Performance, and ComplexityMar 25 2019The recently proposed Renaissance suite is composed of modern, real-world, concurrent, and object-oriented workloads that exercise various concurrency primitives of the JVM. Renaissance was used to compare performance of two stateof-the-art, production-quality ... More

Homogeneous Poisson structures on symmetric spacesOct 24 2007Jul 03 2008We calculate, in a relatively explicit way, the Hamiltonian systems which arise from the Evens-Lu construction of homogeneous Poisson structures on both compact and noncompact type symmetric spaces. A corollary is that the Hamiltonian system arising in ... More

Werner's Measure on Self-Avoiding Loops and WeldingJan 12 2014Aug 04 2014Werner's conformally invariant family of measures on self-avoiding loops on Riemann surfaces is determined by a single measure $\mu_0$ on self-avoiding loops in ${\mathbb C} \setminus\{0\}$ which surround $0$. Our first major objective is to show that ... More

Continuum Variability of Deeply Embedded Protostars as a Probe of Envelope StructureJan 30 2013Stars may be assembled in large growth spurts, however the evidence for this hypothesis is circumstantial. Directly studying the accretion at the earliest phases of stellar growth is challenging because young stars are deeply embedded in optically thick ... More

Non-isotopic Symplectic Tori in the Same Homology ClassDec 27 2002For any pair of integers $n\geq 1$ and $q\geq 2$, we construct an infinite family of mutually non-isotopic symplectic tori representing the homology class $q[F]$ of an elliptic surface E(n), where $[F]$ is the homology class of the fiber. We also show ... More

Multiplicative structure of Kauffman bracket skein module quantizationsFeb 20 1999We describe, for a few small examples, the Kauffman bracket skein algebra of a surface crossed with an interval. If the surface is a punctured torus the result is a quantization of the symmetric algebra in three variables (and an algebra closely related ... More

Homologous Non-isotopic Symplectic Tori in Homotopy Rational Elliptic SurfacesJul 02 2003Let E(1)_K denote the closed 4-manifold that is homotopy equivalent (hence homeomorphic) to the rational elliptic surface E(1) and is obtained by performing Fintushel-Stern knot surgery on E(1) using a knot K in S^3. We construct an infinite family of ... More

Homologous non-isotopic symplectic tori in a K3-surfaceMay 14 2003Jul 14 2003For each member of an infinite family of homology classes in the K3-surface E(2), we construct infinitely many non-isotopic symplectic tori representing this homology class. This family has an infinite subset of primitive classes. We also explain how ... More

Exotic Smooth Structures on Small 4-Manifolds with Odd SignaturesJan 29 2007Sep 10 2009Let $M$ be $\CP#2\CPb$, $3\CP#4\CPb$ or $(2n-1)\CP#2n\CPb$ for any integer $n\geq 3$. We construct an irreducible symplectic 4-manifold homeomorphic to $M$ and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic 4-manifolds ... More

Random walks with badly approximable numbersFeb 27 2001Using the discrepancy metric, we analyze the rate of convergence of a random walk on the circle generated by d rotations, and establish sharp rates that show that badly approximable d-tuples in R^d give rise to walks with the fastest convergence. We use ... More

Symplectic tori in rational elliptic surfacesAug 28 2003Let E(1)_p denote the rational elliptic surface with a single multiple fiber f_p of multiplicity p. We construct an infinite family of homologous non-isotopic symplectic tori representing the primitive class [f_p] in E(1)_p when p>1. As a consequence, ... More

Kuiper Belt Object Occultations: Expected Rates, False Positives, and Survey DesignFeb 19 2009A novel method of generating artificial scintillation noise is developed and used to evaluate occultation rates and false positive rates for surveys probing the Kuiper Belt with the method of serendipitous stellar occultations. A thorough examination ... More

Wide Field CCD Surface Photometry of the Giant Elliptical Galaxy NGC 4472 in the Virgo ClusterJan 03 2000We present deep wide field (16'.4 x 16'.4) Washington CT1 CCD surface photometry of the giant elliptical galaxy NGC 4472, the brightest member in the Virgo cluster. Our data cover a wider field than any previous CCD photometry as well as going deeper. ... More

Skein HomologyJan 17 1997For each skein module we describe a homology theory which, for any three manifold recovers the skein module at its zero level. The theory measures skein-like relations among skein relations, mimicking Hilbert's theory of syzygies. We work explicit examples ... More

Homologous Non-isotopic Symplectic Surfaces of Higher GenusJan 31 2006We construct an infinite family of homologous, non-isotopic, symplectic surfaces of any genus greater than one in a certain class of closed, simply connected, symplectic four-manifolds. Our construction is the first example of this phenomenon for surfaces ... More

Young Star Clusters in the Dwarf Irregular Galaxy, UGC 7636, Interacting with the Giant Elliptical Galaxy NGC 4472Aug 24 1997We present integrated Washington CT1 photometry of 18 bright blue objects discovered in the dwarf galaxy UGC 7636 which is located 5'.5 southeast of the giant elliptical galaxy NGC 4472, the brightest galaxy in the Virgo cluster. Several lines of evidence ... More

The Formation and Evolution of Planetary Systems: The Search for and Characterization of Young PlanetsFeb 17 2009Despite the revolution in our knowledge resulting from the detection of planets around mature stars, we know almost nothing about planets orbiting young stars because rapid rotation and active photospheres preclude detection by radial velocities or transits ... More

Tests of the Las Campanas Distant Cluster Survey from Confirmation Observations for the ESO Distant Cluster SurveyJul 11 2002The ESO Distant Cluster Survey (EDisCS) is a photometric and spectroscopic study of the galaxy cluster population at two epochs, z~0.5 and z~0.8, drawn from the Las Campanas Distant Cluster Survey (LCDCS). We report results from the initial candidate ... More

Maunakea Spectroscopic Explorer Advancing from Conceptual DesignJul 20 2018The Maunakea Spectroscopic Explorer (MSE) project has completed its Conceptual Design Phase. This paper is a status report of the MSE project regarding its technical and programmatic progress. The technical status includes its conceptual design and system ... More

The Maunakea Spectroscopic ExplorerJul 16 2019The Maunakea Spectroscopic Explorer is a next-generation massively multiplexed spectroscopic facility currently under development in Hawaii. It is completely dedicated to large-scale spectroscopic surveys and will enable transformative science. In this ... More

The ice composition in the disk around V883 Ori revealed by its stellar outburstSep 02 2018Feb 07 2019Complex organic molecules (COMs), which are the seeds of prebiotic material and precursors of amino acids and sugars, form in the icy mantles of circumstellar dust grains but cannot be detected remotely unless they are heated and released to the gas phase. ... More

Continued fraction digit averages an Maclaurin's inequalitiesFeb 02 2014Jul 28 2014A classical result of Khinchin says that for almost all real numbers $\alpha$, the geometric mean of the first $n$ digits $a_i(\alpha)$ in the continued fraction expansion of $\alpha$ converges to a number $K = 2.6854520\ldots$ (Khinchin's constant) as ... More

On Estimating Many Means, Selection Bias, and the BootstrapNov 15 2013With recent advances in high throughput technology, researchers often find themselves running a large number of hypothesis tests (thousands+) and esti- mating a large number of effect-sizes. Generally there is particular interest in those effects estimated ... More

Asymptotic freedom of general relativity and its possible consequencesMay 24 2000The formation of singularities in certain situations, such as the collapse of massive stars, is one of the unresolved issues in classical general relativity. Although no complete theory of quantum gravity exists it is often suggested that quantum gravity ... More

Complex groups and root subgroup factorizationJul 24 2017Dec 26 2017Root subgroup factorization is a refinement of triangular (or LDU) factorization. For a complex reductive Lie group, and a choice of reduced factorization of the longest Weyl group element, the forward map from root subgroup coordinates to triangular ... More

Solving for Root Subgroup Coordinates: The SU(2) CaseSep 19 2015Previously we showed that a loop in a simply connected compact Lie group K has a unique triangular factorization if and only if the loop has a unique root subgroup factorization (relative to a choice of a reduced sequence of simple reflections in the ... More

An invariant measure for the loop space of a simply connected compact symmetric spaceSep 04 2004Let X denote a simply connected compact Riemannian symmetric space, U the universal covering of the identity component of the group of automorphisms of X, and LU the loop group of U. In this paper we prove the existence (and conjecture the uniqueness) ... More

The radial part of the zero-mode Hamiltonian for sigma models with group target spaceMar 28 2004We use geometric arguments to derive a possible form for the radial part of the ``zero-mode Hamiltonian'' for the two dimensional sigma model with target space S^3, or more generally a compact simply connected Lie group.

Homeomorphism of S^1 and FactorizationAug 23 2014For each $n > 0$ there is a one complex parameter family of homeomorphisms of the circle consisting of linear fractional transformations `conjugated by $z \to z^n$'. We show that these families are free of relations, which determines the structure of ... More

On invariant measures for the group of diffeomorphisms of the circleDec 29 1996In a previous paper the author constructed biinvariant measures (possibly having values in a line bundle) for a loop group LK (with compact simply connected K) acting on the formal completion of its complexification LG. One motivation for this was to ... More

Spectrum Results with Kogut-Susskind QuarksOct 04 2001Nov 27 2001I summarize recent developments in spectrum calculations using Kogut-Susskind quarks. Theoretical developments include one-loop computations with improved actions. I present some recent simulation results, mostly from a MILC collaboration project using ... More

Scaling functions for O(4) in three dimensionsJul 31 1996Monte Carlo simulation using a cluster algorithm is used to compute the scaling part of the free energy for a three dimensional O(4) spin model. The results are relevant for analysis of lattice studies of high temperature QCD.

Invariant measures for unitary forms of Kac-Moody groups, Parts I-IIIOct 09 1995The purpose of this paper is to describe some conjectures and results on the existence and uniqueness of invariant measures on formal completions of Kac-Moody groups and associated homogeneous spaces. Existence is rigorously established in all affine ... More

Glueball SpinDec 15 1999Apr 02 2001The spin of a glueball is usually taken as coming from the spin (and possibly the orbital angular momentum) of its constituent gluons. In light of the difficulties in accounting for the spin of the proton from its constituent quarks, the spin of glueballs ... More

Variability of Deeply Embedded Protostars: A New Direction for Star Formation?Dec 07 2017The formation of a star is a dynamic process fed by the gravitational collapse of a molecular cloud core. Theoretical models and observations suggest that the majority of this infalling material settles into a protoplanetary disk before reaching the (proto)star ... More

Zero-Bias States and the Mechanism of the Surface d->d+is TransitionAug 28 2000We study the physical mechanism of the surface d->d+is transition proposed as the interpretation of results of tunneling experiments into ab planes. We base our argument on first-order perturbation theory and show that the zero-bias states drive the transition. ... More

Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noiseFeb 14 2014Apr 05 2015We investigate the macroscopic behavior of the disordered harmonic chain of oscillators, through energy diffusion. The Hamiltonian dynamics of the system is perturbed by a degenerate conservative noise. After rescaling space and time diffusively, we prove ... More

Correlated radiative electron capture in ion-atom collisionsAug 30 2010Radiative double electron capture (RDEC) is a one-step process where two free (or quasi-free) target electrons are captured into a bound state of the projectile, e.g. into an empty K-shell, and the energy excess is released as a single photon. This process ... More

Impact of Theory Uncertainties on the Precision of the Top Quark Mass in a Threshold Scan at Future e+e- CollidersNov 10 2016Future energy-frontier electron-positron colliders will be capable of high-precision studies of top quark properties. The measurement of the top-pair production cross section around the threshold provides access to the mass of the top quark in theoretically ... More

Topological constraints in magnetic field relaxationMar 17 2013Stability and reconnection of magnetic fields play a fundamental role in natural and man-made plasma. In these applications the field's topology determines the stability of the magnetic field. Here I will describe the importance of one topology quantifier, ... More

Local Asymptotic Normality for Shape and Periodicity in the Drift of a Time Inhomogeneous DiffusionOct 13 2016We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity $T$ and carrying some unknown $d$-dimensional shape parameter $\theta$. We prove Local Asymptotic Normality (LAN) jointly in $\theta$ ... More

Defending the future: An MSc module in End User Computing Risk ManagementSep 28 2010This paper describes the rationale, curriculum and subject matter of a new MSc module being taught on an MSc Finance and Information Management course at the University of Wales Institute in Cardiff. Academic research on spreadsheet risks now has some ... More

Complementarity and Scientific RationalityDec 24 2004Bohr's interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr's influence, in the pre-war period of 1927-1939, is the harder to explain, and the acceptance of his ... More

The Classical Moment Problem as a Self-Adjoint Finite Difference OperatorJun 08 1999This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence ... More

Four Fermion Models at Non-Zero DensityJun 22 1998I review the properties of the three-dimensional Gross-Neveu model formulated with non-zero chemical potential and temperature, focussing on results obtained by lattice Monte Carlo simulation.

Log Triviality in the Nambu -- Jona-Lasinio ModelSep 15 1997Results are presented from a Monte Carlo simulation of the Nambu -- Jona-Lasinio model with SU(2)xSU(2) chiral symmetry and N_f=2 flavors of fermion. We show that fits to the equation of state are sensitive to the shape and extent of the assumed scaling ... More

O(1/N_f) Corrections to the Thirring Model in 2<d<4Nov 02 1994Nov 10 1994The Thirring model, that is, a relativistic field theory of fermions with a contact interaction between vector currents, is studied for dimensionalities 2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species. The model is found to ... More

The Noncommutative Topology of Anti-Self-Dual Gauge FieldsMar 07 2013May 09 2013Through techniques afforded by $C^*$-algebras and Hilbert modules, we study the topology of spaces which parametrize families of instanton gauge fields on noncommutative Euclidean four-spheres $S^4_\sigma$. By deforming the ADHM construction of instantons ... More

The long history of the Rossiter-McLaughlin effect and its recent applicationsSep 08 2011Nov 21 2011In this paper I will review the Rossiter-McLaughlin (RM) effect; its history, how it manifests itself during stellar eclipses and planetary transits, and the increasingly important role its measurements play in guiding our understanding of the formation ... More

Rethinking Newton's $\textit{Principia}$Sep 20 2016It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying $\text{Newton's}$ methods in $\textit{Principia}$ is neo-Newtonian or Galilean space-time. I argue to the ... More

Spectral Theory Sum Rules, Meromorphic Herglotz Functions and Large DeviationsAug 17 2016Short blurb for invited talk at AMS annual meeting in Atlanta; will appear in January AMS Notices

Right Amenable Left Group Sets and the Tarski-Følner TheoremMar 21 2016Mar 24 2016We introduce right amenability, right F{\o}lner nets, and right paradoxical decompositions for left homogeneous spaces and prove the Tarski-F{\o}lner theorem for left homogeneous spaces with finite stabilisers. It states that right amenability, the existence ... More

The Garden of Eden Theorem for Cellular Automata on Group SetsMar 21 2016Sep 05 2016We prove the Garden of Eden theorem for cellular automata with finite set of states and finite neighbourhood on right amenable left homogeneous spaces with finite stabilisers. It states that the global transition function of such an automaton is surjective ... More

Resolved observations of transition disksFeb 21 2016Resolved observations are bringing new constraints on the origin of radial gaps in protoplanetary disks. The kinematics, sampled in detail in one case-study, are indicative of non-Keplerian flows, corresponding to warped structures and accretion which ... More

FreeSASA: An open source C library for solvent accessible surface area calculationsJan 25 2016Calculating solvent accessible surface areas (SASA) is a run-of-the-mill calculation in structural biology. Although there are many programs available for this calculation, there are no free-standing, open-source tools designed for easy tool-chain integration. ... More

RAMBO on dietAug 13 2013We describe a phase space generator which is flat for massless particles, and approximately flat for massive particles of masses much smaller than the typical mometum scales involved in the process. The same goal is achieved by the RAMBO algorithm, contrary ... More

Inclusive Cross Sections in ME+PS MergingJul 02 2013We discuss an extension of matrix element plus parton shower merging at leading and next-to-leading order. The algorithm does preserve inclusive cross sections at the respective input order. This constraint avoids potentially large logarithmic contributions, ... More

Improvement and generalisation of Papasoglu's lemmaAug 31 2017We improve an isoperimetric inequality due to Panos Papasoglu. We also generalize this inequality to the Finsler case by proving an optimal Finsler version of the Besicovitch's lemma which holds for any notion of Finsler volume.

Signal Machine And Cellular Automaton Time-Optimal Quasi-Solutions Of The Firing Squad/Mob Synchronisation Problem On Connected GraphsJun 19 2017We construct a time-optimal quasi-solution of the firing mob synchronisation problem over finite, connected, and undirected multigraphs whose maximum degrees are uniformly bounded by a constant. It is only a quasi-solution because its number of states ... More

Mean squared displacement and sinuosity of three-dimensional random search movementsJan 08 2018Correlated random walks (CRW) have been used for a long time as a null model for animal's random search movement in two dimensions (2D). An increasing number of studies focus on animals' movement in three dimensions (3D), but the key properties of CRW, ... More

The Petersen graph has no quantum symmetryJan 09 2018Jan 17 2018In 2007, Banica and Bichon asked whether the well-known Petersen graph has quantum symmetry. In this article, we show that the Petersen graph has no quantum symmetry, i.e. the quantum automorphism group of the Petersen graph is its usual automorphism ... More

Liouville type theorem for the stationary equations of magneto-hydrodynamicsOct 19 2017Feb 01 2018We show that any sufficiently smooth solution $(\mathbf{u},\mathbf{H})$ to the stationary equations of magneto-hydrodynamics (MHD) belonging to both spaces $L^6 (\mathbb{R}^3)$ and $BMO^{-1}(\mathbb{R}^3)$ must be identically zero. This is an extension ... More

Radio Observations of Two Isolated Neutron Stars, RXJ0720.4-3125 and RX J0806.4-4132Feb 24 2003Radio observations of two isolated neutron stars, RXJ0720.4-3125 and RX J0806.4-4132, have been made with the Australia Telescope Compact Array at a frequency of 1.4 GHz. No continuum emission is detected from either object with a 3 sigma upper limit ... More

Relative Zeta Determinants and the Quillen MetricOct 27 1999We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over the boundary ... More

Badly approximable systems of linear forms over a field of formal seriesJun 26 2003Aug 05 2004We prove that the Hausdorff dimension of the set of badly approximable systems of m linear forms in n variables over the field of Laurent series with coefficients from a finite field is maximal. This is a analogue of Schmidt's multi-dimensional generalisation ... More

Remarks on $G_{2}$-manifolds with boundaryFeb 27 2018This article is based on a lecture at the Journal of Differential Geometry Conference, Harvard 2017. We discuss closed and torsion-free $G_{2}$-structures on a 7-manifold with boundary, with prescribed $3$-form on the boundary. Much of the article is ... More

The exact number of r-regular elements in finite exceptional groupsJan 26 2013We calculate the precise number of r-regular elements in the finite exceptional groups. As a corollary we find that the proportion of r-regular elements is at least 3577/18432 and for all \epsilon>0, there are infinitely finite simple exceptional groups ... More

Feedback control of charged ideal fluidsMay 12 2019The theory of controlled mechanical systems of [6, 3, 4] is extended to the case of ideal incompressible fluids consisting of charged particles in the presence of an external magnetic field. The resulting control is of feedback type and depends on the ... More

Extensions to Justification TheoryMay 09 2019Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge representation languages ... More

A Homogeneous Function Constant along the Leaves of a FoliationJul 03 2018Given a smooth foliation by complex curves (locally around a point $x\in\mathbb{C}^2\setminus\{0\}$) which is "compatible" with the foliation by spheres centered at the origin, we construct a smooth real-valued function $g$ in a neighborhood of said point, ... More

Schrodinger Operators with Purely Discrete SpectrumOct 17 2008We prove $-\Delta +V$ has purely discrete spectrum if $V\geq 0$ and, for all $M$, $|\{x\mid V(x)<M\}|<\infty$ and various extensions.

Fine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two PicturesNov 17 2004Mhaskar-Saff found a kind of universal behavior for the bulk structure of the zeros of orthogonal polynomials for large $n$. Motivated by two plots, we look at the finer structure for the case of random Verblunsky coefficients and for what we call the ... More

Molecular Labor Division: Its Cause and ConsequenceDec 04 2007Aug 21 2011Both external environmental selection and internal lower-level evolution are essential for an integral picture of evolution. This paper proposes that the division of internal evolution into DNA/RNA pattern formation (genotype) and protein functional action ... More

An Illustrated Introduction to the Basic Biological PrinciplesDec 13 2007Dec 14 2009Both external environmental selection and internal lower-level evolution are essential for an integral picture of evolution. This paper proposes that the division of internal evolution into DNA/RNA pattern formation (genotype) and protein functional action ... More

Fusion Rules of the ${\cal W}_{p,q}$ Triplet ModelsJul 26 2009Jan 11 2010In this paper we determine the fusion rules of the logarithmic ${\calW}_{p,q}$ triplet theory and construct the Grothendieck group with subgroups for which consistent product structures can be defined. The fusion rules are then used to determine projective ... More

A Feynman-Kac Formula for Unbounded SemigroupsJul 27 1999We prove a Feynman-Kac formula for Schrodinger operators with potentials V(x) that obey (for all \epsilon > 0): V(x) \geq - \epsilon |x|^2 - C_\epsilon. Even though e^{-tH} is an unbounded operator, any \phi, \psi \in L^2 with compact support lie in D(e^{-tH}) ... More

On small bases which admit countably many expansionsMay 16 2013Let $q\in(1,2)$ and $x\in[0,\frac1{q-1}]$. We say that a sequence $(\epsilon_i)_{i=1}^{\infty}\in\{0,1\}^{\mathbb{N}}$ is an expansion of $x$ in base $q$ (or a $q$-expansion) if x=\sum_{i=1}^{\infty}\epsilon_iq^{-i}. Let $\mathcal{B}_{\aleph_{0}}$ denote ... More

Generalised golden ratios over integer alphabetsOct 31 2012It is a well known result that for $\beta\in(1,\frac{1+\sqrt{5}}{2})$ and $x\in(0,\frac{1}{\beta-1})$ there exists uncountably many $(\epsilon_{i})_{i=1}^{\infty}\in {0,1}^{\mathbb{N}}$ such that $x=\sum_{i=1}^{\infty}\epsilon_{i}\beta^{-i}.$ When $\beta\in(\frac{1+\sqrt{5}}{2},2]$ ... More

Approximation properties of $β$-expansionsSep 09 2014Let $\beta\in(1,2)$ and $x\in [0,\frac{1}{\beta-1}]$. We call a sequence $(\epsilon_{i})_{i=1}^\infty\in\{0,1\}^{\mathbb{N}}$ a $\beta$-expansion for $x$ if $x=\sum_{i=1}^{\infty}\epsilon_{i}\beta^{-i}$. We call a finite sequence $(\epsilon_{i})_{i=1}^{n}\in\{0,1\}^{n}$ ... More

Equidistribution and the shrinking target problem for sequences of polynomialsMay 31 2019Jun 06 2019Let $(f_n)_{n=1}^{\infty}$ be a sequence of polynomials and $\alpha>1$. In this paper we study the distribution of the sequence $(f_n(\alpha))_{n=1}^{\infty}$ modulo one. We give sufficient conditions for a sequence $(f_n)_{n=1}^{\infty}$ to ensure that ... More

A general asymptotic decay lemma for elliptic problemsJun 03 2008We prove a general asymptotic decay lemma which is applicable in various contexts. As an example, the general theorem is shown to give lower growth estimates for entire and exterior solutions of the minimal surface equation.

One-sided asymptotically mean stationary channelsMar 26 2014This paper proposes an analysis of asymptotically mean stationary (AMS) communication channels. A hierarchy based on stability properties (stationarity, quasi-stationarity, recurrence and asymptotically mean stationarity) of channels is identified. Stationary ... More

Weak convergence of CD kernels and applicationsJul 17 2007We prove a general result on equality of the weak limits of the zero counting measure, $d\nu_n$, of orthogonal polynomials (defined by a measure $d\mu$) and $\frac{1}{n} K_n(x,x) d\mu(x)$. By combining this with Mate--Nevai and Totik upper bounds on $n\lambda_n(x)$, ... More

The Gradient Flow of O'Hara's Knot EnergiesJan 12 2016Jun O'Hara invented a family of knot energies $E^{j,p}$, $j,p \in (0, \infty)$. We study the negative gradient flow of the sum of one of the energies $E^\alpha = E^{\alpha,1}$, $\alpha \in (2,3)$, and a positive multiple of the length. Showing that the ... More

Quasidense monotone multifunctionsDec 08 2016Jul 10 2017In this paper, we discuss quasidense multifunctions from a Banach space into its dual, and use the two sum theorems proved in a previous paper to give various characterizations of quasidensity. We investigate the Fitzpatrick extension of such a multifunction. ... More

On the quantum symmetry of distance-transitive graphsJun 15 2019In this article, we study quantum automorphism groups of distance-transitive graphs. We show that the odd graphs, the Hamming graphs $H(n,3)$, the Johnson graphs $J(n,2)$ and the Kneser graphs $K(n,2)$ do not have quantum symmetry. We also give a table ... More

The intersection ring of matroidsFeb 23 2016Aug 30 2016We study a particular graded ring structure on the set of all loopfree matroids on a fixed labeled ground set, which occurs naturally in tropical geometry. The product is given by matroid intersection and the additive structure is defined by assigning ... More

An application of continuous logic to fixed point theoryOct 18 2016Jan 25 2019In aiming to apply to a broader class of examples the Avigad-Iovino "ultraproducts and metastability" approach to obtaining uniformity for convergence of sequences, we construct a framework using continuous logic that in particular is able to handle discontinuous ... More

Optimal eigenvalues estimate for the Dirac operator on domains with boundaryMar 21 2006We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the $\MIT$ bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.

Unitaries Permuting Two Orthogonal ProjectionsMar 16 2017Mar 27 2017Let $P$ and $Q$ be two orthogonal projections on a separable Hilbert space, $\calH$. Wang, Du and Dou proved that there exists a unitary, $U$, with $UPU^{-1} =Q, \quad UQU^{-1} = P$ if and only if $\dim(\ker P \cap \ker(1-Q)) = \dim(\ker Q \cap \ker(1-P))$ ... More

VC-sets and generic compact dominationFeb 16 2015Jan 26 2016Let X be a closed subset of a locally compact second countable group G whose family of translates has finite VC-dimension. We show that the topological border of X has Haar measure 0. Under an extra technical hypothesis, this also holds if X is constructible. ... More

Mittag-Leffler functions and complete monotonicityDec 16 2013Dec 17 2013We consider two operations on the Mittag-Leffler function which cancel the exponential term in the expansion at infinity, and generate a completely monotonic function. The first one is the action of a certain differential-difference operator, and leads ... More

Comparing Fréchet and positive stable lawsOct 07 2013Jan 27 2014Let ${\bf L}$ be the unit exponential random variable and ${\bf Z}_\alpha$ the standard positive $\alpha$-stable random variable. We prove that $\{(1-\alpha) \alpha^{\gamma_\alpha} {\bf Z}_\alpha^{-\gamma_\alpha}, 0< \alpha <1\}$ is decreasing for the ... More

Total positivity of a Cauchy kernelMay 06 2013We study the total positivity of the kernel $1/(x^2 + 2 \cos(\pi\a)xy +y^2).$ The case of infinite order is characterized by an application of Schoenberg's theorem. We then give necessary conditions for the cases of any given finite order with the help ... More

Small deviations in p-variation for stable processesMay 31 2003Let $\{Z_t, t\geq 0\}$ be a strictly stable process on $\R$ with index $\alpha\in (0,2]$. We prove that for every $p > \alpha$, there exists $\gamma = \gamma (\alpha, p)$ and $\k = \k (\alpha, p)\in (0, +\infty)$ such that $$\lim_{\ee\downarrow 0}\ee^{\gamma}\log\pb\lcr ... More

Small deviations in p-variation norm for multidimensional Levy processesMay 31 2003Let Z be an Rd-valued Levy process with strong finite p-variation for some p<2. We prove that the ''decompensated'' process Y obtained from Z by annihilating its generalized drift has a small deviations property in p-variation. This property means that ... More

Multiplicative strong unimodality for positive stable lawsFeb 26 2010It is known that real Non-Gaussian stable distributions are unimodal, not additive strongly unimodal, and multiplicative strongly unimodal in the symmetric case. By a theorem of Cuculescu-Theodorescu, the only remaining relevant situation for the multiplicative ... More

Minimal generating sets of non-modular invariant rings of finite groupsMar 01 2007Apr 12 2007It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case. Apart from very ... More

On the magnitude of odd balls via potential functionsApr 06 2018Magnitude is a measure of size defined for certain classes of metric spaces; it arose from ideas in category theory. In particular, magnitude is defined for compact subsets of Euclidean space and, in arXiv:1507.02502, Barcel\'o and Carbery gave a procedure ... More