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Symbiotic stars and other Halpha emission line stars towards the Galactic BulgeMay 21 2013Symbiotic stars are interacting binaries with the longest orbital periods and their multi-component structure makes them rich astrophysical laboratories. The accretion of a high mass loss rate red giant wind on to a white dwarf (WD) makes them promising ... More

Ongoing surveys for close binary central stars and wider implicationsOct 09 2011Binary central stars have long been invoked to explain the vexing shapes of planetary nebulae (PNe) despite there being scant direct evidence to support this hypothesis. Modern large-scale surveys and improved observing strategies have allowed us to significantly ... More

A D'-type symbiotic binary in the planetary nebula SMP LMC 88Feb 08 2018SMP LMC 88 is one of the planetary nebulae (PN) in the Large Magellanic Cloud. We identify in its spectrum Raman scattered O VI lines at 6825 and 7083A. This unambiguously classifies the central object of the nebula as a symbiotic star (SySt). We identified ... More

LMC S63: a historical reappraisal of the outburst behaviour of a deeply eclipsing Magellanic symbiotic starMay 28 2015We present an analysis of multi-epoch low-resolution spectrophotometry, complemented by the light curves provided by massive photometric surveys spanning over 100 years, of the symbiotic binary LMC S63. We showed that it is an eclipsing binary with the ... More

Identification of new Galactic symbiotic stars with SALT. I. Initial discoveries and other emission line objectsNov 04 2013Feb 10 2014We introduce the first results from an ongoing, systematic survey for new symbiotic stars selected from the AAO/UKST SuperCOSMOS H$\alpha$ Survey (SHS). The survey aims to identify and characterise the fainter population of symbiotic stars underrepresented ... More

IC4663: the first unambiguous [WN] Wolf-Rayet central star of a planetary nebulaOct 01 2012Several [WC]-type central stars of planetary nebulae (PNe) are known to mimic the spectroscopic appearance of massive carbon-rich or WC-type Wolf-Rayet stars. In stark contrast, no [WN]-type central stars have yet been identified as clear-cut analogues ... More

Post-common-envelope Wolf-Rayet central stars of planetary nebulaeJul 28 2015Nearly 50 post-common-envelope (post-CE) close binary central stars of planetary nebulae (CSPNe) are now known. Most contain either main sequence or white dwarf (WD) companions that orbit the WD primary in around 0.1-1.0 days. Only PN~G222.8-04.2 and ... More

When asymmetric cosmic bubbles betray a difficult marriage: the study of binary central stars of Planetary NebulaeAug 01 2011Aug 05 2011Planetary Nebulae represent a powerful window into the evolution of low-intermediate mass stars that have undergone extensive mass-loss. The nebula manifests itself in an extremely wide variety of shapes, but exactly how the mass lost is shaped into such ... More

OGLE-SMC-LPV-00861 (LIN 9): the first proven Z And outburst in a Magellanic symbiotic starJun 18 2014We report on the discovery of a new Small Magellanic Cloud (SMC) symbiotic star, OGLE-SMC-LPV-00861, previously catalogued as H$\alpha$ emission line source LIN 9. The OGLE light curve shows multiple-maxima outburst behaviour over $\sim$1200 d with a ... More

A radial velocity survey for post-common-envelope Wolf-Rayet central stars of planetary nebulae: First results and discovery of the close binary nucleus of NGC 5189Jan 14 2015Jan 15 2015The formation of Wolf-Rayet central stars of planetary nebulae ([WR] CSPNe) whose spectroscopic appearance mimics massive WR stars remains poorly understood. Least understood is the nature and frequency of binary companions to [WR] CSPNe that may explain ... More

A remarkable sample of new symbiotic stars towards the Galactic BulgeMay 21 2013Symbiotic stars are the longest orbital period interacting binaries, where nova-like outbursts are generated by the accretion of a high mass loss rate red giant wind onto a white dwarf companion. Long-term photometric monitoring surveys such as OGLE and ... More

The role of binarity in Wolf-Rayet central stars of planetary nebulaeJul 28 2015Jul 30 2015Over a hundred planetary nebulae (PNe) are known to have H-deficient central stars that mimic the spectroscopic appearance of massive Wolf-Rayet stars. The formation of these low-mass Wolf-Rayet stars, denoted [WR] stars, remains poorly understood. While ... More

The enigmatic central star of the planetary nebula PRTM 1Aug 16 2012The central star of the planetary nebula PRTM 1 (PN G243.8-37.1) was previously found to be variable by M. Pena and colleagues. As part of a larger programme aimed towards finding post common-envelope binary central stars we have monitored the central ... More

Active phases and flickering of a symbiotic recurrent nova T CrBJul 22 2016T CrB is a symbiotic recurrent nova known to exhibit active phases, characterised by apparent increases in the hot component temperature and the appearance of flickering, i.e. changes in the observed flux on the time-scale of minutes. Historical UV observations ... More

An X-Shooter view of the symbiotic star [JD2002] 11Aug 01 2015We aimed to verify the nature and derive the basic parameters of the symbiotic star candidate [JD2002] 11. For this purpose, we obtained and analysed an X-Shooter spectrum of [JD2002] 11. We also used optical and infrared photometry available for the ... More

Improved prospects for the detection of new Large Magellanic Cloud planetary nebulaeMar 10 2011The Large Magellanic Cloud (LMC) contains the nearest large extragalactic population of planetary nebulae (PNe). A shallow viewing angle and low interstellar reddening towards the LMC potentially means a larger, more complete flux-limited population can ... More

A carbon dwarf wearing a Necklace: first proof of accretion in a post-common-envelope binary central star of a planetary nebula with jetsOct 04 2012The formation of collimated outflows or jets in planetary nebulae (PNe) is not well understood. There is no evidence for active accretion disks in PNe making it difficult to decide which of several proposed jet formation scenarios may be correct. A handful ... More

3-Manifolds from Platonic SolidsApr 18 2001The problem of classifying, upto isometry (or similarity), the orientable spherical, Euclidean and hyperbolic 3-manifolds that arise by identifying the faces of a Platonic solid is formulated in the language of Coxeter groups. In the spherical and hyperbolic ... More

Elliptic singularities on log symplectic manifolds and Feigin--Odesskii Poisson bracketsJul 20 2015A log symplectic manifold is a complex manifold equipped with a complex symplectic form that has simple poles on a hypersurface. The possible singularities of such a hypersurface are heavily constrained. We introduce the notion of an elliptic point of ... More

On Linear Landau Damping for Relativistic Plasmas via Gevrey RegularityFeb 05 2014Apr 30 2015We examine the phenomenon of Landau Damping in relativistic plasmas via a study of the relativistic Vlasov-Poisson system (both on the torus and on $\mathbb{R}^3$) linearized around a sufficiently nice, spatially uniform kinetic equilibrium. We find that ... More

Graphs of partitions and Ramanujan's tau-functionMay 05 2004May 31 2004The invariant z_{lambda} attached to a partition lambda sits in the denominator of the Girard-Waring solution to Newton's symmetric function relations. We interpret Ramanujan's tau-function in terms of z_lambda, and interpret z_lambda in terms of the ... More

On the diameter of Hochster-Huneke graphs of Stanley-Reisner rings with Serre $(S_2)$ property and Hirsch type bounds on abstractions of polytopesNov 22 2016Let $R$ be a Noetherian commutative ring of positive dimension. The Hochster-Huneke graph of $R$ (sometimes called the dual graph of Spec $R$ and denoted by $\mathcal{G} (R)$) is defined as follows: the vertices are the minimal prime ideals of $R$, and ... More

On finite free Fisher information for eigenvectors of a modular operatorApr 13 2016Suppose $M$ is a von Neumann algebra equipped with a faithful normal state $\varphi$ and generated by a finite set $G=G^*$, $|G|\geq 3$. We show that if $G$ consists of eigenvectors of the modular operator $\Delta_\varphi$ with finite free Fisher information, ... More

Some results on large cardinals and the continuum functionSep 05 2012Given a Woodin cardinal $\delta$, I show that if $F$ is any Easton function with $F"\delta\subseteq\delta$ and $\GCH$ holds, then there is a cofinality-preserving forcing extension in which $2^\gamma= F(\gamma)$ for each regular cardinal $\gamma<\delta$, ... More

Landau Damping in Relativistic PlasmasAug 12 2014Oct 10 2014We examine the phenomenon of Landau Damping in relativistic plasmas via a study of the relativistic Vlasov-Poisson system (rVP) on the torus for initial data sufficiently close to a spatially uniform steady state. We find that if the steady state is regular ... More

Free transport for finite depth subfactor planar algebrasJun 18 2014Dec 16 2014Given a finite depth subfactor planar algebra $\mathcal{P}$ endowed with the graded $*$-algebra structures $\{Gr_k^+ \mathcal{P}\}_{k\in\mathbb{N}}$ of Guionnet, Jones, and Shlyakhtenko, there is a sequence of canonical traces $Tr_{k,+}$ on $Gr_k^+\mathcal{P}$ ... More

Free monotone transport without a traceNov 05 2013Apr 07 2014We adapt the free monotone transport results of Guionnet and Shlyakhtenko to the type $\text{III}$ case. As a direct application, we obtain that the $q$-deformed Araki-Woods algebras are isomorphic (for sufficiently small $|q|$).

Quadratic minima and modular forms IIJan 14 2000Jan 15 2000We give upper bounds on the size of the gap between a non-zero constant term and the next non-zero Fourier coefficient of an entire level two modular form. We give upper bounds for the minimum positive integer represented by a level two even positive-definite ... More

Multi-Object Spectroscopy Field Configuration by Simulated AnnealingJul 07 2006Multi-object spectroscopy (MOS) instruments, such as the Two-degree Field (2dF) facility of the Anglo-Australian Observatory (AAO), have facilitated large-scale redshift surveys. Yet despite their acclaim, instrument design has been suspected of introducing ... More

The Narrow Line Region: Current Models and Future QuestionsDec 12 2006I present a broad overview of modelling of the Narrow Line Region (NLR) of active galaxies, and discuss some of the more recent models we currently have for the emission from the NLR. I show why the emission line ratios from the NLR are constrained to ... More

Easton's Theorem in the presence of Woodin cardinalsJul 24 2012Jul 27 2012Under the assumption that $\delta$ is a Woodin cardinal and $\GCH$ holds, I show that if $F$ is any class function from the regular cardinals to the cardinals such that (1) $\kappa<\cf(F(\kappa))$, (2) $\kappa<\lambda$ implies $F(\kappa)\leq F(\lambda)$, ... More

The failure of GCH at a degree of supercompactnessOct 24 2011Jul 26 2012We determine the large cardinal consistency strength of the existence of a $\lambda$-supercompact cardinal $\kappa$ such that GCH fails at $\lambda$. Indeed, we show that the existence of a $\lambda$-supercompact cardinal $\kappa$ such that $2^\lambda ... More

On finite free Fisher information for eigenvectors of a modular operatorApr 13 2016Oct 17 2016Suppose $M$ is a von Neumann algebra equipped with a faithful normal state $\varphi$ and generated by a finite set $G=G^*$, $|G|\geq 2$. We show that if $G$ consists of eigenvectors of the modular operator $\Delta_\varphi$ with finite free Fisher information, ... More

Quadratic minima and modular formsJan 14 1998Mar 01 1998We give upper bounds on the size of the gap between the constant term and the next non-zero Fourier coefficient of an entire modular form of given weight for \Gamma_0(2). Numerical evidence indicates that a sharper bound holds for the weights h \equiv ... More

Planetary Nebulae towards the Galactic bulge. I. [OIII] fluxesDec 21 2010We present [OIII]{\lambda}5007 fluxes and angular diameters for 435 Planetary Nebulae (PN) in the central 10' x 10' region towards the Galactic bulge. Our sample is taken from the new discoveries of the MASH PN surveys as well as previously known PN. ... More

Optimal $\mathfrak{L}^β$-Control for the Global Cauchy Problem of the Relativistic Vlasov-Poisson SystemNov 10 2010Recently, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh proved that a unique global classical solution to the relativistic Vlasov-Poisson system exists whenever the positive, integrable initial datum is spherically symmetric, compactly supported in momentum ... More

Existence of Spherical Initial Data with Unit Mass, Zero Energy, and Virial less than - 1/2 for the Relativistic Vlasov-Poisson Equation with Attractive CouplingNov 13 2010May 24 2011In a recent paper, Kiessling and Tahvildar-Zadeh proved that any classical solution of the relativistic Vlasov-Poisson equation with attractive coupling launched by spherically symmetric initial data with zero total energy and virial less than or equal ... More

Asymptotic parameterization in inverse limit spaces of dendritesJun 13 2012In this paper, we study asymptotic behavior arising in inverse limit spaces of dendrites. In particular, the inverse limit is constructed with a single unimodal bonding map, for which points have unique itineraries and the critical point is periodic. ... More

Irreducible polynomials in F_q[x] versus 1 - qz in C[z]Dec 20 2006Dec 21 2006Let q be a prime power and N_n count degree-n monic irreducible polynomials in F_q[x]. We show that prod_{n=1}^{\infty} (1 -z^n)^N_n = 1 - qz for small |z|.

Quantum deformations of projective three-spaceMar 25 2014We describe the possible noncommutative deformations of complex projective three-space by exhibiting the Calabi--Yau algebras that serve as their homogeneous coordinate rings. We prove that the space parametrizing such deformations has exactly six irreducible ... More

Alternating Quotients of Fuchsian GroupsJul 23 1999It is shown that any finitely generated non-elementary Fuchsian group has among its homomorphic images all but finitely many of the alternating groups. This settles in the affirmative a conjecture of Graham Higman.

Automorphism Groups of Schur RingsMay 12 2009In 1993, Muzychuk \cite{muzychuk} showed that the rational Schur rings over a cyclic group $Z_n$ are in one-to-one correspondence with sublattices of the divisor lattice of $n$, or equivalently, with sublattices of the lattice of subgroups of $Z_n$. This ... More

The Morpho-kinematics of Planetary Nebulae with Binary Central StarsJan 16 2014Jan 20 2014It is now clear that a binary formation pathway is responsible for a significant fraction of planetary nebulae, and this increased sample of known binaries means that we are now in a position to begin to constrain their influence on the formation and ... More

Multi-wavelength diagnostic properties of Galactic Planetary Nebulae detected by GLIMPSE-IDec 10 2010We uniformly analyze 136 optically detected PNe and candidates from the GLIMPSE-I survey in order to to develop robust, multi-wavelength, classification criteria to augment existing diagnostics and provide pure PN samples. PNe represent powerful astrophysical ... More

PHR1315-6555: a bipolar planetary nebula in the compact Hyades-age open cluster ESO96-SC04Jan 20 2011We present a detailed study of a bipolar, possible Type I planetary nebula (PN), PHR1315-6555 (PN G305.3-03.1), that was discovered as part of the Macquarie/AAO/Strasbourg H-alpha planetary nebula project (MASH) and that we considered at the time was ... More

The post-common-envelope, binary central star of the planetary nebula Hen 2-11Jan 07 2014We present a detailed photometric study of the central star system of the planetary nebula Hen 2-11, selected for study because of its low-ionisation filaments and bipolar morphology - traits which have been strongly linked with central star binarity. ... More

Discovery of New Faint Northern Galactic Planetary NebulaeJun 12 2012We present the discovery of 6 nebular objects made by amateur astronomers. Four of these discoveries are clearly planetary nebulae (PNe), one is a possible PN, and another is a likely H II region. The bipolar nebula Ou4 presents the largest angular extent ... More

The post-common envelope central stars of the planetary nebulae Henize 2-155 and Henize 2-161Jun 04 2015Jun 10 2015We present a study of Hen 2-155 and Hen 2-161, two planetary nebulae which bear striking morphological similarities to other planetary nebulae known to host close-binary central stars. Both central stars are revealed to be photometric variables while ... More

Quantum Entanglement and TeleportationApr 14 2011Even Einstein has to be wrong sometimes. However, when Einstein was wrong he created a 70 year debate about the strange behavior of quantum mechanics. His debate helped prove topics such as the indeterminacy of particle states, quantum entanglement, and ... More

Some comments on C. S. Wallace's random number generatorsMay 13 2010We outline some of Chris Wallace's contributions to pseudo-random number generation. In particular, we consider his idea for generating normally distributed variates without relying on a source of uniform random numbers, and compare it with more conventional ... More

MP users guideApr 19 2010Apr 20 2010MP is a package of ANSI Standard Fortran (ANS X3.9-1966) subroutines for performing multiple-precision floating-point arithmetic and evaluating elementary and special functions. The subroutines are machine independent and the precision is arbitrary, subject ... More

Towards non-reductive geometric invariant theoryMar 05 2007We study linear actions of algebraic groups on smooth projective varieties X. A guiding goal for us is to understand the cohomology of "quotients" under such actions, by generalizing (from reductive to non-reductive group actions) existing methods involving ... More

Environmental Dependencies in the Luminosity Function of GalaxiesMay 03 2005The evidence is becoming strong that the luminosity function of galaxies varies with environment. Higher density, more dynamically evolved regions appear to have more dwarfs per giant. The situation is becoming clearer as a result of wide field imaging ... More

Mass/Light Variations with EnvironmentDec 20 2001In the local part of the universe, a majority of the total mass is in only a small number of groups with short dynamical times. The Virgo Cluster dominates far out of proportion to its contribution in light. Ninety percent of the total mass is in groups ... More

The Luminosity Function in Groups of GalaxisOct 19 2010With targeted imaging of groups in the local volume, the regions of collapse around bright galaxies can be clearly identified by the distribution of dwarfs and luminosity functions can be established to very faint levels. In the case of the M81 Group ... More

Our CMB Motion: The Role of the Local VoidNov 11 2006A database with a high density of accurate distances is used to investigate the contributions to the motion of our Galaxy. It is found that the motion of the Local Group separates remarkably cleanly into 3 components: a large-scale attraction toward structure ... More

Distances from the Correlation between Galaxy Luminosities and Rotation RatesSep 30 1998A large luminosity--linewidth template sample is now available, improved absorption corrections have been derived, and there are a statistically significant number of galaxies with well determined distances to supply the zero point. A revised estimate ... More

Fourier Synthesis Methods for Control of Inhomogeneous Quantum SystemsMay 17 2007Finding control laws (pulse sequences) that can compensate for dispersions in parameters which govern the evolution of a quantum system is an important problem in the fields of coherent spectroscopy, imaging, and quantum information processing. The use ... More

Partial mirror symmetry I: reflection monoidsJan 10 2007Nov 07 2007This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce ... More

Partial symmetry, reflection monoids and Coxeter groupsDec 15 2008Dec 16 2008This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce ... More

Action Model of Infall into the Virgo ClusterMar 31 2004May 26 2004The observed infall of galaxies into the Virgo Cluster puts strong constraints on the mass of the cluster. A non-parametric fully non-linear description of the infall can be made with orbit reconstructions based on Numerical Action Methods. The mass of ... More

Anomaly Mediated Supersymmetry Breaking From a String Theory PerspectiveNov 06 2002The general form of soft supersymmetry breaking terms at one loop for effective supergravity models based on the weakly-coupled heterotic string are presented, with special emphasis on those terms arising from the superconformal anomaly. The standard ... More

An application of free transport to mixed $q$-Gaussian algebrasJul 17 2015Nov 04 2015We consider the mixed $q$-Gaussian algebras introduced by Speicher which are generated by the variables $X_i=l_i+l_i^*,i=1,\ldots,N$, where $l_i^* l_j-q_{ij}l_j l_i^*=\delta_{i,j}$ and $-1<q_{ij}=q_{ji}<1$. Using the free monotone transport theorem of ... More

Some integer factorization algorithms using elliptic curvesApr 20 2010Lenstra's integer factorization algorithm is asymptotically one of the fastest known algorithms, and is ideally suited for parallel computation. We suggest a way in which the algorithm can be speeded up by the addition of a second phase. Under some plausible ... More

Projective linear configurations via non-reductive actionsJan 03 2014We study the iterated blow-up X of projective space along an arbitrary collection of linear subspaces. By replacing the universal torsor with an $\mathbb{A}^1$-homotopy equivalent model, built from $\mathbb{A}^1$-fiber bundles not just algebraic line ... More

On asymptotic approximations to the log-Gamma and Riemann-Siegel theta functionsSep 13 2016Oct 06 2016We give bounds on the error in the asymptotic approximation of the log-Gamma function $\ln\Gamma(z)$ for complex $z$ in the right half-plane. These improve on earlier bounds by Behnke and Sommer (1962), Spira (1971), and Hare (1997). We show that $|R_{k+1}(z)/T_k(z)| ... More

Old and new algorithms for piMar 12 2013This is a letter to the editor concerning Semjon Adlaj's article "An eloquent formula for the perimeter of an ellipse", AMS Notices 59, 8 (2012), 1094-1099.

Regularity of Schramm-Loewner Evolutions, annular crossings, and rough path theoryJul 18 2011Oct 18 2011When studying stochastic processes, it is often fruitful to have an understanding of several different notions of regularity. One such notion is the optimal H\"older exponent obtainable under reparametrization. In this paper, we show that the chordal ... More

Bundles of coloured posets and a Leray-Serre spectral sequence for Khovanov homologyAug 12 2008Aug 26 2010The decorated hypercube found in the construction of Khovanov homology for links is an example of a Boolean lattice equipped with a presheaf of modules. One can place this in a wider setting as an example of a coloured poset, that is to say a poset with ... More

Some long-period random number generators using shifts and xorsApr 19 2010Marsaglia recently introduced a class of xorshift random number generators (RNGs) with periods 2n-1 for n = 32, 64, etc. Here we give a generalisation of Marsaglia's xorshift generators in order to obtain fast and high-quality RNGs with extremely long ... More

George Forsythe's last paperMay 06 2010May 07 2010We describe von Neumann's elegant idea for sampling from the exponential distribution, Forsythe's generalization for sampling from a probability distribution whose density has the form exp(-G(x)), where G(x) is easy to compute (e.g. a polynomial), and ... More

The Local Velocity AnomalyAug 17 2007There is a velocity discontinuity at about 7 Mpc between the galaxies of the Local Sheet that are moving together with low internal velocity dispersion and the adjacent structures. The Local Sheet bounds the Local Void. The Local Sheet is determined to ... More

Moduli Space of Cubic Surfaces as Ball Quotient via Hypergeometric FunctionsApr 04 2004We describe hypergeometric functions of Deligne-Mostow type for open subsets of the configuration space of six points on P^2, induced from those for seven points on P^1. The seven point ball quotient example DM(2^5,1^2) does not appear on Mostow's original ... More

A Survey of the Hodge Conjecture for Abelian VarietiesSep 26 1997We review what is known about the Hodge conjecture for abelian varieties, with some emphasis on how Mumford-Tate groups have been applied to this problem.

Stability of fast algorithms for structured linear systemsMay 05 2010We survey the numerical stability of some fast algorithms for solving systems of linear equations and linear least squares problems with a low displacement-rank structure. For example, the matrices involved may be Toeplitz or Hankel. We consider algorithms ... More

On supercompactness and the continuum functionJun 03 2013Sep 11 2013Given a cardinal $\kappa$ that is $\lambda$-supercompact for some regular cardinal $\lambda\geq\kappa$ and assuming $\GCH$, we show that one can force the continuum function to agree with any function $F:[\kappa,\lambda]\cap\REG\to\CARD$ satisfying $\forall\alpha,\beta\in\dom(F)$ ... More

Structural properties of acyclic heaps of pieces with Kazhdan--Lusztig theoryOct 05 2008We introduce the notions of boundary vertex, linear equivalence and effective boundary vertex in the context of Viennot's heaps of pieces. We prove that in the heap of a fully commutative element in a star reducible Coxeter group, every boundary vertex ... More

A^1-homotopy groups, excision, and solvable quotientsFeb 10 2009Mar 09 2009We study some properties of A^1-homotopy groups: geometric interpretations of connectivity, excision results, and a re-interpretation of quotients by free actions of connected solvable groups in terms of covering spaces in the sense of A^1-homotopy theory. ... More

Genericity of Filling ElementsJul 22 2010An element of a finitely generated non-Abelian free group F(X) is said to be filling if that element has positive translation length in every very small action of F(X) on an $\mathbb{R}$-tree. We give a proof that the set of filling elements of F(X) is ... More

Asymptotic approximation of central binomial coefficients with rigorous error boundsAug 17 2016Sep 15 2016We show that a well-known asymptotic series for the logarithm of the central binomial coefficient is strictly enveloping, so the error incurred in truncating the series is of the same sign as the next term, and is bounded in magnitude by that term. We ... More

Unrestricted algorithms for elementary and special functionsApr 21 2010We describe some "unrestricted" algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by examples. ... More

The complexity of multiple-precision arithmeticApr 21 2010In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision required increases ... More

Resolved optical-infrared SEDs of galaxies: universal relations and their break-down on local scalesJun 10 2011A large body of evidence has demonstrated that the global rest-frame optical and IR colours of galaxies correlate well with each other, as well as with other galactic properties such as surface brightness and morphology. However the processes that lead ... More

Faint End of the Galaxy Luminosity Function: A Chronometer for Structure Formation?Apr 03 2001There is accumulating evidence that the faint end of the galaxy luminosity function might be very different in different locations. The luminosity function might be sharply rising in rich clusters and flat or declining in regions of low density. If galaxies ... More

The Cosmological Parameters H_0 and Omega_0Feb 03 1998The first section discusses a recalibration of the luminosity-linewidth technique and its use in a determination of H_0. The recalibration introduces (i) new cluster calibration data, (ii) new corrections for reddening as a function of inclination, and ... More

Algebraic vector bundles on punctured affine spaces and smooth quadricsMar 03 2013We construct examples of non-isomorphic algebraic vector bundles on the punctured affine space with isomorphic pullbacks to the smooth quadric.

On unipotent quotients and some A^1-contractible smooth schemesMar 05 2007Oct 18 2007We study quotients of quasi-affine schemes by unipotent groups over fields of characteristic 0. To do this, we introduce a notion of stability which allows us to characterize exactly when a principal bundle quotient exists and, together with a cohomological ... More

Multiple-precision zero-finding methods and the complexity of elementary function evaluationApr 20 2010May 30 2010We consider methods for finding high-precision approximations to simple zeros of smooth functions. As an application, we give fast methods for evaluating the elementary functions log(x), exp(x), sin(x) etc. to high precision. For example, if x is a positive ... More

Note on Computing Ratings from EigenvectorsMay 05 2010We consider the problem of computing ratings using the results of games played between a set of n players, and show how this problem can be reduced to computing the positive eigenvectors corresponding to the dominant eigenvalues of certain n by n matrices. ... More

Rigid idealsMay 31 2016An ideal $I$ on a cardinal $\kappa$ is called \emph{rigid} if all automorphisms of $P(\kappa)/I$ are trivial. An ideal is called \emph{$\mu$-minimal} if whenever $G\subseteq P(\kappa)/I$ is generic and $X\in P(\mu)^{V[G]}\setminus V$, it follows that ... More

Easton's Theorem for Ramsey and Strongly Ramsey cardinalsSep 05 2012We show that, assuming GCH, if $\kappa$ is a Ramsey or a strongly Ramsey cardinal and $F$ is a class function on the regular cardinals having a closure point at $\kappa$ and obeying the constraints of Easton's theorem, namely, $F(\alpha)\leq F(\beta)$ ... More

A Simple Approach to Error Reconciliation in Quantum Key DistributionMay 07 2010We discuss the error reconciliation phase in quantum key distribution (QKD) and analyse a simple scheme in which blocks with bad parity (that is, blocks containing an odd number of errors) are discarded. We predict the performance of this scheme and show, ... More

Indestructibility of generically strong cardinalsMar 25 2014Aug 03 2015Foreman proved the Duality Theorem, which gives an algebraic characterization of certain ideal quotients in generic extensions. As an application he proved that generic supercompactness of $\omega_1$ is preserved by any proper forcing. We generalize portions ... More

Constructing Hyperbolic ManifoldsJul 22 1999In this paper we show how to obtain representations of Coxeter groups acting on H^n to certain classical groups. We determine when the kernel of such a representation is torsion-free and thus the quotient a hyperbolic n-manifold.

Free monotone transport for infinite variablesNov 19 2015We extend the free monotone transport theorem of Guionnet and Shlyakhtenko to the case of infinite variables. As a first application, we provide a criterion for when mixed $q$-Gaussian algebras are isomorphic to $L(\mathbb{F}_\infty)$; namely, when the ... More

Hidden Sector Gaugino Condensation and the Observable WorldSep 22 2000We study the phenomenology of a class of models describing modular invariant gaugino condensation in the hidden sector of a low-energy effective theory derived from the heterotic string. Placing simple demands on the resulting observable sector - such ... More

Generalising Tuenter's binomial sumsJul 14 2014Jan 19 2015Tuenter [Fibonacci Quarterly 40 (2002), 175-180] and other authors have considered centred binomial sums of the form \[S_r(n) = \sum_k \binom{2n}{k}|n-k|^r,\] where $r$ and $n$ are non-negative integers. We consider sums of the form \[U_r(n) = \sum_k ... More

On the periods of generalized Fibonacci recurrencesApr 30 2010We give a simple condition for a linear recurrence (mod 2^w) of degree r to have the maximal possible period 2^(w-1).(2^r-1). It follows that the period is maximal in the cases of interest for pseudo-random number generation, i.e. for 3-term linear recurrences ... More

Uses of randomness in computationApr 19 2010Apr 20 2010Random number generators are widely used in practical algorithms. Examples include simulation, number theory (primality testing and integer factorization), fault tolerance, routing, cryptography, optimization by simulated annealing, and perfect hashing. ... More

On asymptotic approximations to the log-Gamma and Riemann-Siegel theta functionsSep 13 2016We give new bounds on the error in the asymptotic approximation of the log-Gamma function $\ln\Gamma(z)$ (also $\ln\Gamma(z+\frac{1}{2}))$ for complex $z$ in the right half-plane. These improve on bounds by Hare (1997) and Spira (1971). We show that $|R_{k+1}(z)| ... More