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Towards Locating the Brightest Microlensing Events on the SkyJul 09 1998It is estimated that a star brighter than visual magnitude 17 is undergoing a detectable gravitational microlensing event, somewhere on the sky, at any given time. It is assumed that both lenses and sources are normal stars drawn from a standard Bahcall-Soneira ... More

A Century of Gamma Ray Burst ModelsFeb 04 1994More than 100 gamma-ray burst progenitor models have now been published in refereed journals. A list of the models published before the end of 1992 is presented and briefly discussed. The consensus of the present astronomical community remains that no ... More

Visual Distortions Near a Neutron Star and Black HoleDec 02 1993The visual distortion effects visible to an observer traveling around and descending to the surface of an extremely compact star are described. Specifically, trips to a ``normal" neutron star, a black hole, and an ultracompact neutron star with extremely ... More

The Opposite of Dark Energy: Limits on $w = 2/3$ Ultralight Energy in the Early UniverseMar 28 2007Might stable energy species "lighter" than radiation, with $w > 1/3$, exist? A dimensional expansion of the cosmological Friedmann Equation of energy has a clear place for them. Such energies would affect the universe much differently than dark energies, ... More

Tile or Stare? Cadence and Sky Monitoring Observing Strategies that Maximize the Number of Discovered TransientsJan 29 2003To maximize the number of transients discovered on the sky, should sky-monitoring projects stare at one location or continually jump from location to location, tiling the sky? If tiling is preferred, what cadence maximizes the discovery rate? As sky monitoring ... More

Can a Gravitational Lens Magnify Gravity? A Possible Solar System TestFeb 17 2005Can a gravitational lens magnify gravity? Leading theories of gravity likely indicate "no", but the possibility might be testable by using our Sun as a gravitational lens and carefully aligning a satellite past the minimum transparent focal distance of ... More

Bright Lenses and Optical DepthApr 12 1997In gravitational lensing, the concept of optical depth assumes the lens is dark. Several microlensing detections have now been made where the lens may be bright. Relations are developed between apparent and absolute optical depth in the regime of the ... More

Superluminal Spot Pair Events in Astronomical Settings: Sweeping BeamsDec 24 2014Sweeping beams of light can cast spots moving with superluminal speeds across scattering surfaces. Such faster-than-light speeds are well-known phenomena that do not violate special relativity. It is shown here that under certain circumstances, superluminal ... More

Attributes of Gravitational Lensing ParallaxMay 31 1998The density of stars and MACHOs in the universe could theoretically be determined or limited by simultaneous measurements of compact sources by well separated observers. A gravitational lens effect would be expected to create a slight differential amplification ... More

Magnification Bias in Galactic Microlensing SearchesMar 07 1994It is shown that a significant amount of detectable gravitational microlensing events that could potentially be found by MAssively Parallel Photometry (MAPP) projects (such as the MACHO, EROS and OGLE collaborations) will occur for stars too dim to be ... More

Extension of an Exponential Light Curve GRB Pulse Model Across Energy BandsSep 15 2011A simple mathematical model of GRB pulses in time, suggested in Norris et al. (2005), is extended across energy. For a class of isolated pulses, two of those parameters appear effectively independent of energy. Specifically, statistical fits indicate ... More

A Simple Energy-Dependent Model for GRB Pulses with Interesting Physical ImplicationsSep 19 2011A simple mathematical model for GRB pulses is postulated in both time and energy. The model breaks GRB pulses up into component functions, one general light curve function exclusively in the time dimension and four component functions exclusively in the ... More

The Pulse Scale Conjecture and the Case of BATSE Trigger 2193Jan 19 2000Jul 14 2000The pulses that compose gamma-ray bursts (GRBs) are hypothesized to have the same shape at all energies, differing only by scale factors in time and amplitude. This "Pulse Scale Conjecture" is confirmed here between energy channels of the dominant pulse ... More

Adventures in Friedmann Cosmology: An Educationally Detailed Expansion of the Cosmological Friedmann EquationsMar 28 2007Dec 14 2007The general relativistic cosmological Friedmann equations which describe how the scale factor of the universe evolves are expanded explicitly to include energy forms not usually seen. The evolution of the universe as predicted by the Friedmann equations ... More

Decaying Higgs Fields and Cosmological Dark EnergySep 27 2004The observed dark energy in the universe might give particles inertial mass. We investigate one realization of this idea, that the dark energy field might be a decayed scalar component of a supermultiplet field in the early universe that creates inertial ... More

OT 060420: A Seemingly Optical Transient Recorded by All-Sky CamerasJul 03 2006We report on a ~5th magnitude flash detected for approximately 10 minutes by two CONCAM all-sky cameras located in Cerro Pachon - Chile and La Palma - Spain. A third all-sky camera, located in Cerro Paranal - Chile did not detect the flash, and therefore ... More

Light Echoes from Linear FilamentsMar 16 2017When a flash of light from a star overtakes a straight linear filament of gas or dust and is seen later by an observer, a pattern of perceived illumination occurs that encodes information about the distance to the flash, the distance to illumination fronts ... More

Hardness as a Spectral Peak Estimator for Gamma-Ray BurstsDec 11 2009Feb 04 2010Simple hardness ratios are found to be a good estimator for the spectral peak energy in Gamma-Ray Bursts (GRBs). Specifically, a high correlation strength is found between the $\nu F_{\nu}$ peak in the spectrum of BATSE GRBs, $\epo$, and the hardness ... More

Using Fuzzy Logic for Automatic Analysis of Astronomical PipelinesJun 27 2005Fundamental astronomical questions on the composition of the universe, the abundance of Earth-like planets, and the cause of the brightest explosions in the universe are being attacked by robotic telescopes costing billions of dollars and returning vast ... More

Searching the Internet for evidence of time travelersDec 26 2013Time travel has captured the public imagination for much of the past century, but little has been done to actually search for time travelers. Here, three implementations of Internet searches for time travelers are described, all seeking a prescient mention ... More

Frequency Limits on Naked-Eye Optical Transients Lasting from Minutes to YearsAug 21 2009How often do bright optical transients occur on the sky but go unreported? To constrain the bright end of the astronomical transient function, a systematic search for transients that become bright enough to be noticed by the unaided eye was conducted ... More

Probing For Machos of Mass $10^{-15}M_\odot$-$10^{-7}M_\odot$ with Gamma-Ray Burst Parallax SpacecraftMay 04 1995Two spacecraft separated by $\sim 1\,\au$ and equipped with gamma-ray burst (GRB) detectors could detect or rule out a cosmological density of Massive Compact Halo Objects (MACHOs) in the mass range $10^{-15} M_{\odot}\lsim M \lsim 10^{-7} M_{\odot}$ ... More

Short vs. Long Gamma-Ray Bursts: A Comprehensive Study of Energetics and Prompt Gamma-Ray CorrelationsDec 17 2014Mar 30 2015We present the results of a comprehensive study of the luminosity function, energetics, prompt gamma-ray correlations, and classification methodology of short-hard and long-soft GRBs (SGRBs and LGRBs), based on observational data in the largest catalog ... More

Testing the Gamma-Ray Burst Pulse Start ConjectureSep 03 2009We test the hypothesis that prompt gamma-ray burst pulse emission starts simultaneously at all energies (the Pulse Start Conjecture). Our analysis, using a sample of BATSE bursts observed with four channel, 64-ms data and performed using a pulse fit model, ... More

Testing the Weak Equivalence Principle with Cosmological Gamma Ray BurstsMar 13 2019Gamma Ray Bursts (GRBs) with rapid variations at cosmological distances are used to place new limits on violations of the gravitational weak equivalence principle (WEP). These limits track intrinsic timing deviations between GRB photons of different energies ... More

Gravitational Lensing Characteristics of the Transparent SunNov 29 2007Dec 12 2011The transparent Sun is modeled as a spherically symmetric and centrally condensed gravitational lens using recent Standard Solar Model (SSM) data. The Sun's minimum focal length is computed to a refined accuracy of 23.5 +/- 0.1 AU, just beyond the orbit ... More

A Fuzzy Logic Based Algorithm for Finding Astronomical Objects in Wide-Angle FramesFeb 25 2005Accurate automatic identification of astronomical objects in an imperfect world of non-linear wide-angle optics, imperfect optics, inaccurately pointed telescopes, and defect-ridden cameras is not always a trivial first step. In the past few years, this ... More

PHOTZIP: A Lossy FITS Image Compression Algorithm that Protects User-Defined Levels of Photometric IntegrityOct 07 2004A lossy compression algorithm is presented for astronomical images that protects photometric integrity for detected point sources at a user-defined level of statistical tolerance. PHOTZIP works by modeling, smoothing, and then compressing the astronomical ... More

A Catalog of Redshift Estimates for 1366 BATSE Long-Duration Gamma-Ray Bursts: Evidence for Strong Selection Effects on the Phenomenological Prompt Gamma-Ray CorrelationsMar 16 2019We present a catalog of the redshift estimates and probability distributions for 1366 individual Long-duration Gamma-Ray Bursts (LGRBs) detected by the Burst And Transient Source Experiment (BATSE). This result is based on a careful classification and ... More

Dreidel Fairness StudyNov 28 2016Dec 14 2016Are dreidels fair? In other words, does the average dreidel have an equal chance of turning up any one of its four sides? To explore this hypothesis, three different dreidels were each spun hundreds of times with the number of occurrences of each side ... More

Towards a Continuous Record of the SkySep 30 1998May 14 1999It is currently feasible to start a continuous digital record of the entire sky sensitive to any visual magnitude brighter than 15 each night. Such a record could be created with a modest array of small telescopes, which collectively generate no more ... More

How superluminal motion can lead to backward time travelMay 27 2015Sep 08 2015It is commonly asserted that superluminal particle motion can enable backward time travel, but little has been written providing details. It is shown here that the simplest example of a "closed loop" event -- a twin paradox scenario where a single spaceship ... More

Lights Illuminate Surfaces SuperluminallyJun 08 2015When a light bulb is turned on, light moves away from it at speed $c$, by definition. When light from this bulb illuminates a surface, however, this illumination front is not constrained to move at speed $c$. A simple proof is given that this illumination ... More

Finite Source Sizes and the Information Content of MACHO-Type Lens Search Light CurvesJan 05 1994If the dark halo matter is primarily composed of MACHOs toward the lower end of the possible detection range ($ < 10^{-3}$ $M_{\odot}$) a fraction of the lens detection events should involve the lens crossing directly in front of the disk of the background ... More

Practices in Code DiscoverabilityFeb 06 2012Much of scientific progress now hinges on the reliability, falsifiability and reproducibility of computer source codes. Astrophysics in particular is a discipline that today leads other sciences in making useful scientific components freely available ... More

An exposition on Friedmann Cosmology with Negative Energy DensitiesFeb 18 2014Mar 11 2015How would negative energy density affect a classic Friedmann cosmology? Although never measured and possibly unphysical, certain realizations of quantum field theories leaves the door open for such a possibility. In this paper we analyze the evolution ... More

Practices in Code Discoverability: Astrophysics Source Code LibraryFeb 06 2012Here we describe the Astrophysics Source Code Library (ASCL), which takes an active approach to sharing astrophysical source code. ASCL's editor seeks out both new and old peer-reviewed papers that describe methods or experiments that involve the development ... More

Bounds on Spectral Dispersion from Fermi-detected Gamma Ray BurstsSep 23 2011Apr 18 2012Data from four Fermi-detected gamma-ray bursts (GRBs) is used to set limits on spectral dispersion of electromagnetic radiation across the universe. The analysis focuses on photons recorded above 1 GeV for Fermi detected GRB 080916C, GRB 090510A, GRB ... More

Software design for panoramic astronomical pipeline processingNov 23 2005We describe the software requirement and design specifications for all-sky panoramic astronomical pipelines. The described software aims to meet the specific needs of super-wide angle optics, and includes cosmic-ray hit rejection, image compression, star ... More

Limits on the cosmological abundance of supermassive compact objects from a millilensing search in gamma-ray burst dataJan 26 2001A new search for the gravitational lens effects of a significant cosmological density of supermassive compact objects (SCOs) on gamma-ray bursts has yielded a null result. We inspected the timing data of 774 BATSE-triggered GRBs for evidence of millilensing: ... More

GRB Spikes Could Resolve StarsDec 12 1997GRBs vary more rapidly than any other known cosmological phenomena. The lower limits of this variability have not yet been explored. Improvements in detectors would reveal or limit the actual rate of short GRBs. Were microsecond "spike" GRBs to exist ... More

Flux Enhancement of Slow-moving Particles by Sun or Jupiter: Can they be Detected on Earth?May 10 2013Slow-moving particles capable of interacting solely with gravity might be detected on Earth as a result of the gravitational lensing induced focusing action of the Sun. The deflection experienced by these particles are inversely proportional to the square ... More

All-sky Relative Opacity Mapping Using Night Time Panoramic ImagesJun 15 2005An all-sky cloud monitoring system that generates relative opacity maps over many of the world's premier astronomical observatories is described. Photometric measurements of numerous background stars are combined with simultaneous sky brightness measurements ... More

The Possible Impact of GRB Detector Thresholds on Cosmological Standard CandlesApr 09 2009Nov 03 2011GRB satellites are relatively inefficient detectors of dim hard bursts because they trigger on photon counts, which are number-biased against hard photons. Therefore, for example, given two bursts of identical peak luminosity near the detection threshold, ... More

Astrophysics Source Code Library EnhancementsNov 07 2014The Astrophysics Source Code Library (ASCL; ascl.net) is a free online registry of codes used in astronomy research; it currently contains over 900 codes and is indexed by ADS. The ASCL has recently moved a new infrastructure into production. The new ... More

On Source Density Evolution of Gamma-ray BurstsOct 14 1998Recent optical afterglow observations of gamma-ray bursts indicate a setting and distance scale that many relate to star-formation regions. In this paper, we use $<V/V_{max}>$ and a set of artificial trigger thresholds to probe several potential GRB source ... More

Astrophysics Source Code Library: Incite to Cite!Dec 23 2013The Astrophysics Source Code Library (ASCL, http://ascl.net/) is an online registry of over 700 source codes that are of interest to astrophysicists, with more being added regularly. The ASCL actively seeks out codes as well as accepting submissions from ... More

Practices in source code sharing in astrophysicsApr 25 2013While software and algorithms have become increasingly important in astronomy, the majority of authors who publish computational astronomy research do not share the source code they develop, making it difficult to replicate and reuse the work. In this ... More

Ideas for Advancing Code Sharing (A Different Kind of Hack Day)Dec 27 2013How do we as a community encourage the reuse of software for telescope operations, data processing, and calibration? How can we support making codes used in research available for others to examine? Continuing the discussion from last year Bring out your ... More

The Astrophysics Source Code Library: Where do we go from here?Dec 18 2013The Astrophysics Source Code Library, started in 1999, has in the past three years grown from a repository for 40 codes to a registry of over 700 codes that are now indexed by ADS. What comes next? We examine the future of the ASCL, the challenges facing ... More

Best Practices for a Future Open Code Policy: Experiences and Vision of the Astrophysics Source Code LibraryFeb 02 2018We are members of the Astrophysics Source Code Library's Advisory Committee and its editor-in-chief. The Astrophysics Source Code Library (ASCL, ascl.net) is a successful initiative that advocates for open research software and provides an infrastructure ... More

Continuous Monitoring of Comet Holmes from Before the 2007 OutburstAug 11 2009Sep 01 2010The outburst and subsequent brightness evolution of Comet 17P/Holmes has been observed using the MMT Observatory's All-Sky Camera (Pickering 2006) on Mt. Hopkins near Tucson, Arizona, USA. The comet was picked up at the limiting visual magnitude of 5.5 ... More

Time-Dilation, Log N - Log P, and CosmologyFeb 01 1996We investigate whether a simple cosmology can fit GRB results in both time dilation and Log N - Log P simultaneously. Simplifying assumptions include: all GRBs are spectrally identical to BATSE trigger 143, $\Omega=1$ universe, and no luminosity and number ... More

Test for Time Dilation of Intervals Between Pulse Structures in GRBsJan 30 1996If $\gamma$-ray bursts are at cosmological distances, then not only their constituent pulses but also the intervals between pulses should be time-dilated. Unlike time-dilation measures of pulse emission, intervals would appear to require negligible correction ... More

Calibration of Tests for Time Dilation in GRB Pulse StructuresJan 30 1996Two tests for cosmological time dilation in $\gamma$-ray bursts -- the peak alignment and auto-correlation statistics -- involve averaging information near the times of peak intensity. Both tests require width corrections, assuming cosmological origin ... More

Gravitationally Lensed Gamma-Ray Bursts as Probes of Dark Compact ObjectsOct 23 1998Dec 29 1998If dark matter in the form of compact objects comprises a large fraction of the mass of the universe, then gravitational lensing effects on gamma-ray bursts are expected. We utilize BATSE and Ulysses data to search for lenses of different mass ranges, ... More

On Suggestive Correlations Between GRBs and Clusters of GalaxiesJul 29 1996Aug 01 1996Recent claims of angular correlations between gamma-ray bursts (GRBs) and clusters of galaxies are evaluated in light of existing but previously uncorrelated GRB positional data. Additional GRB data sets we use include sub-samples of soft BATSE 3B bursts, ... More

Gamma-Ray Burst Peak Duration as a Function of EnergyApr 21 1995Gamma-ray burst time histories often consist of many peaks. These peaks tend to be narrower at higher energy. If gamma-ray bursts are cosmological, the energy dependence of gamma-ray burst time scales must be understood in order to correct the time scale ... More

Gamma-Ray Bursts are Time-AsymmetricNov 18 1993A simple test for time-asymmetry is devised and carried out on the brightest gamma-ray bursts detected by the Burst and Transient Source Experiment (BATSE) on board the {\it Compton} Gamma Ray Observatory. We show evidence that individual bursts are time-asymmetric ... More

Astrophysics Source Code Library: Here we grow again!Nov 18 2016The Astrophysics Source Code Library (ASCL) is a free online registry of research codes; it is indexed by ADS and Web of Science and has over 1300 code entries. Its entries are increasingly used to cite software; citations have been doubling each year ... More

Improving Software Citation and CreditDec 24 2015The past year has seen movement on several fronts for improving software citation, including the Center for Open Science's Transparency and Openness Promotion (TOP) Guidelines, the Software Publishing Special Interest Group that was started at January's ... More

Detection of Signature Consistent with Cosmological Time Dilation in Gamma-Ray BurstsDec 21 1993If gamma-ray bursters are at cosmological distances - as suggested by their isotropic distribution on the sky and by their number-intensity relation - then the burst profiles will be stretched in time, by an amount proportional to the redshift, 1 + $z$. ... More

Duration Distributions of Bright and Dim BATSE Gamma-Ray BurstsAug 17 1994We have measured the T90 and T50 durations of bright and dim gamma-ray bursts (GRBs) detected by the Compton Gamma Ray Observatory's Burst and Transient Source Experiment (BATSE). The T90 (T50) duration is defined as the interval over which 5\% (25\%) ... More

Gross Spectral Differences between Bright and Dim Gamma-Ray BurstsAug 15 1994We find that dim gamma-ray bursts (GRBs) are softer than bright GRBs, as indicated on average by data from the Burst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory. We show that this correlation is statistically significant ... More

Null Result in Gamma-Ray Burst Lensed Echo SearchMar 22 1994We have searched for gravitational-lens induced echoes between gamma-ray bursts (GRBs) in NASA's orbiting {\it Compton} Gamma Ray Observatory's Burst and Transient Source Experiment (BATSE) data. The search was conducted in two phases. In the first phase ... More

The Astrophysics Source Code Library: What's new, what's comingDec 08 2017The Astrophysics Source Code Library (ASCL, ascl.net), established in 1999, is a citable online registry of source codes used in research that are available for download; the ASCL's main purpose is to improve the transparency, reproducibility, and falsifiability ... More

Beat Cepheids as Probes of Stellar and Galactic MetallicityNov 27 2006Jan 12 2007The mere location of a Beat Cepheid model in a Period Ratio vs. Period diagram (Petersen diagram) puts very tight constraints on its metallicity Z. The Beat Cepheid Peterson diagrams are revisited with linear nonadiabatic turbulent convective models, ... More

Modify the Improved Euler scheme to integrate stochastic differential equationsOct 02 2012A practical and new Runge--Kutta numerical scheme for stochastic differential equations is explored. Numerical examples demonstrate the strong convergence of the method. The first order strong convergence is then proved using Ito integrals for both Ito ... More

Shear dispersion along circular pipes is affected by bends, but the torsion of the pipe is negligibleSep 10 2003The flow of a viscous fluid along a curving pipe of fixed radius is driven by a pressure gradient. For a generally curving pipe it is the fluid flux which is constant along the pipe and so I correct fluid flow solutions of Dean (1928) and Topakoglu (1967) ... More

Model dynamics on a multigrid across multiple length and time scalesFeb 08 2008Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time scales. I ... More

The Swift-Hohenberg Equation Requires Non-Local Modifications to Model Spatial Pattern Evolution of Physical ProblemsDec 09 1994I argue that ``good'' mathematical models of spatio-temporal dynamics in two-dimensions require non-local operators in the nonlinear terms. Consequently, the often used Swift-Hohenberg equation requires modification as it is purely local. My aim here ... More

Long-wave models of thin film fluid dynamicsNov 04 1994Centre manifold techniques are used to derive rationally a description of the dynamics of thin films of fluid. The derived model is based on the free-surface $\eta(x,t)$ and the vertically averaged horizontal velocity $\avu(x,t)$. The approach appears ... More

A thermodynamical formalism for Monge-Ampere equations, Moser-Trudinger inequalities and Kahler-Einstein metricsNov 17 2010Nov 13 2012We develop a variational calculus for a certain free energy functional on the space of all probability measures on a Kahler manifold X. This functional can be seen as a generalization of Mabuchi's K-energy functional and its twisted versions to more singular ... More

Kahler-Einstein metrics emerging from free fermions and statistical mechanicsSep 15 2010Jun 25 2011We propose a statistical mechanical derivation of Kahler-Einstein metrics, i.e. solutions to Einstein's vacuum field equations in Euclidean signature (with a cosmological constant) on a compact Kahler manifold X. The microscopic theory is given by a canonical ... More

Sharp inequalities for determinants of Toeplitz operators and dbar-Laplacians on line bundlesMay 26 2009We prove sharp inequalities for determinants of Toeplitz operators and twisted Laplace operators on the two-sphere, generalizing the Moser-Trudinger-Onofri inequality. In particular a sharp version of conjectures of Gillet-Soule and Fang motivated by ... More

On the optimal regularity of weak geodesics in the space of metrics on a polarized manifoldMay 26 2014Let (X,L) be a polarized compact manifold, i.e. L is an ample line bundle over X and denote by H the infinite dimensional space of all positively curved Hermitian metrics on L equipped with the Mabuchi metric. In this short note we show, using Bedford-Taylor ... More

Holistically discretise the Swift-Hohenberg equation on a scale larger than its spatial patternOct 15 2001I introduce an innovative methodology for deriving numerical models of systems of partial differential equations which exhibit the evolution of spatial patterns. The new approach directly produces a discretisation for the evolution of the pattern amplitude, ... More

Comparative Study of the Hadronic Production of $B_c$ MesonsAug 22 1996The full order $\alpha_s^4$ perturbative QCD calculation of the production of $B_c$ mesons at the Tevatron is compared with the fragmentation approximation. The non-fragmentation diagrams, in which two or more quarks and/or gluons can simultaneously be ... More

H-alpha features with hot onsets III. Fibrils in Lyman-alpha and with ALMASep 05 2016Nov 24 2016In H-alpha most of the solar surface is covered by dense canopies of long opaque fibrils, but predictions for quiet-Sun observations with ALMA have ignored this fact. Comparison with Ly-alpha suggests that the large opacity of H-alpha fibrils is caused ... More

Constructing Strong Markov ProcessesMar 11 2013The construction presented in this paper can be briefly described as follows: starting from any "finite-dimensional" Markov transition function p_t, on a measurable state space (E,B), we construct a strong Markov process on a certain "intrinsic" state ... More

A Radix Representation for each van der Waerden number $W(r, k)$ with $r$ colors: Why $\log_{r}W(r, k) < k^{2}$ is true whenever $k$ is the number of terms in the arithmetic progressionApr 24 2016May 07 2016Here we show that by expressing a van der Waerden number $W(r, k)$ by its radix polynomial representation, it not only is possible to locate each proper subset on $\mathbb{R}$ in which the van der Waerden number lies, but also to show that conditions ... More

How to find the least upper bound on the van der Waerden Number $W(r, k)$ that is some integer Power of the coloring Integer $r$Dec 11 2015Jan 26 2016What is a least integer upper bound on van der Waerden number $W(r, k)$ among the powers of the integer $r$? We show how this can be found by expanding the integer $W(r, k)$ into powers of $r$. Doing this enables us to find both a least upper bound and ... More

Local WarmingSep 04 2012Using 55 years of daily average temperatures from a local weather station, I made a least-absolute-deviations (LAD) regression model that accounts for three effects: seasonal variations, the 11-year solar cycle, and a linear trend. The model was formulated ... More

Remarks on tree-level topological string theoriesNov 13 1995A few observations concerning topological string theories at the string-tree level are presented: (1) The tree-level, large phase space solution of an arbitrary model is expressed in terms of a variational problem, with an ``action'' equal, at the solution, ... More

An Explanation of Dayton Miller's Anomalous "Ether Drift" ResultAug 24 2006Oct 15 2006In 1933 Dayton Miller published in this journal the results of his voluminous observations using his ether drift interferometer, and proclaimed that he had determined the "absolute motion of the earth". This result is in direct conflict with the prediction ... More

A holistic finite difference approach models linear dynamics consistentlyMar 23 2000I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of finite difference ... More

Stable singularities of wave-fronts in general relativityAug 03 2001A wave-front in a space-time $\cal M$ is a family of null geodesics orthogonal to a smooth spacelike two-surface in $\cal M$; it is of some interest to know how a wave-front can fail to be a smoothly immersed surface in $\cal M$. In this paper we see ... More

Macroscale, slowly varying, models emerge from the microscale dynamics in long thin domainsOct 06 2013Dec 09 2013Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the system to have structures that vary slowly in the long dimension. Extant mathematical ... More

Resolve subgrid microscale interactions to discretise stochastic partial differential equationsJan 29 2006Mar 08 2010Constructing discrete models of stochastic partial differential equations is very delicate. Stochastic centre manifold theory provides novel support for coarse grained, macroscale, spatial discretisations of nonlinear stochastic partial differential or ... More

The Quillen metric, analytic torsion and tunneling for high powers of a holomorphic line bundleJun 15 2011Let L be a line bundle over a compact complex manifold X (possibly non-Kahler) and denote by h_{L} and h_{X} fixed Hermitian metrics on L and TX, respectively. We generalize the asymptotics for the induced Quillen metric on the determinant line associated ... More

Determinantal point processes and fermions on complex manifolds: large deviations and bosonizationDec 22 2008Jun 24 2011We study determinantal random point processes on a compact complex manifold X associated to an Hermitian metric on a line bundle over X and a probability measure on X. Physically, this setup describes a free fermion gas on X subject to a U(1)- gauge field ... More

Solar ALMA predictions: tutorialNov 16 2016I have proposed that long Halpha fibrils are caused by heating events of which the tracks are afterwards outlined by contrails of cooling gas with extraordinary Halpha opacity and yet larger opacity at the ALMA wavelengths. Here I detail the radiative ... More

Strange--Beauty Meson Production by Fragmentation in Proton--Antiproton CollisionsDec 14 1995The cross sections for the production of $B_s$ and $B_s^*$ mesons through the fragmentation process in $\bar{p}p$ collisions were calculated. The input parameters were determined from the measured $B_s$ and $B_s^*$ production rates in $e^+e^-$ annihilation. ... More

A Constituent Picture of Hadrons from Light-Front QCDApr 12 1996It may be possible to derive a constituent approximation for bound states in QCD using hamiltonian light-front field theory. Cutoffs that violate explicit gauge invariance and Lorentz covariance must be employed. A similarity renormalization group and ... More

A Simple Confinement Mechanism for Light-Front Quantum ChromodynamicsNov 04 1994Nov 07 1994Light-front field theory offers a scenario in which a constituent picture of hadrons may arise, but only if cutoffs that violate explicit covariance and gauge invariance are used. The perturbative renormalization group can be used to approximate the cutoff ... More

Universal cycles for permutationsOct 30 2007A universal cycle for permutations is a word of length n! such that each of the n! possible relative orders of n distinct integers occurs as a cyclic interval of the word. We show how to construct such a universal cycle in which only n+1 distinct integers ... More

The Concept of Electric Charge and the Hypothesis of Magnetic PolesSep 05 2018Jan 22 2019We examine a generic field theory in which the field particle has two couplings. It is of particular interest when these are the electroweak, e, and the hypothetical magnetoweak, g. The new field operators are obtained by replacing the field operators ... More

The Asymptotic Behaviors of $\log_{r}W(r, k)$ and $\log_{k}W(r, k)$, when $W(r, k)$ is a van der Waerden NumberJan 16 2016Feb 22 2016We derive the asymptotic behaviors of $\log_{r}W(r, k)$ and $\log_{k}W(r, k)$, when $W(r, k)$ is a van der Waerden Number. We use the approach to consider the subsets on the real line in which $W(2, 7)$ might lie.

Normal form transforms separate slow and fast modes in stochastic dynamical systemsJan 22 2007Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate transforms of stochastic ... More

The Complex Roots of Random SumsAug 21 2015Aug 03 2016This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are assumed to be ... More