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

Fate of the runner in hit-and-run collisionsMar 11 2019In similar-sized planetary collisions, a significant part of the impactor often misses the target and continues downrange. We follow the dynamical evolution of "runners" from giant impacts to determine their ultimate fate. Surprisingly, runners re-impact ... More

Graze-and-Merge Collisions under External PerturbersAug 20 2019Graze-and-merge collisions (GMCs) are common multi-step mergers occurring in low-velocity off-axis impacts between similar sized planetary bodies. The first impact happens at somewhat faster than the mutual escape velocity; for typical impact angles this ... More

Constraining the Thermal Properties of Planetary Surfaces using Machine Learning: Application to Airless BodiesFeb 22 2019We present a new method for the determination of the surface properties of airless bodies from measurements of the emitted infrared flux. Our approach uses machine learning techniques to train, validate, and test a neural network representation of the ... More

An Autonomous Passive Navigation Method for Nanosatellite Exploration of the Asteroid BeltFeb 08 2019There are more than 750,000 asteroids identified in the main belt. These asteroids are diverse in composition and size. Some of these asteroids can be traced back to the early solar system and can provide insight into the origins of the so-lar system, ... More

Evaluation of Mother-Daughter Architectures for Asteroid Belt ExplorationDec 28 2018This paper examines the effectiveness of an asteroid exploration architecture comprised of multiple nanosatellite sized spacecraft deployed from a single mother ship into a heliocentric orbit in the main asteroid belt where the mothership is ideally located ... More

Global Scale ImpactsApr 09 2015Global scale impacts modify the physical or thermal state of a substantial fraction of a target asteroid. Specific effects include accretion, family formation, reshaping, mixing and layering, shock and frictional heating, fragmentation, material compaction, ... More

Numerical modeling of the disruption of Comet D/1993 F2 Shoemaker-Levy 9 representing the progenitor by a gravitationally bound assemblage of randomly shaped polyhedraJul 14 2012Aug 29 2012We advance the modeling of rubble-pile solid bodies by re-examining the tidal breakup of comet Shoemaker-Levy 9, an event that occurred during a 1.33 Jupiter radii encounter with that planet in July 1992. Tidal disruption of the comet nucleus led to a ... More

Control of a Bucket-Wheel for Surface Mining of Asteroids and Small-BodiesFeb 01 2017Feb 21 2017Near Earth Asteroids (NEAs) are thought to contain a wealth of resources, including water, iron, titanium, nickel, platinum and silicates. Future space missions that can exploit these resources by performing In-Situ Resource Utilization (ISRU) gain substantial ... More

A Milli-Newton Propulsion System for the Asteroid Mobile Imager and Geologic Observer (AMIGO)Dec 31 2018Exploration of small bodies, namely comets and asteroids remain a challenging endeavor due to their low gravity. The risk is so high that missions such as Hayabusa II and OSIRIS-REx will be performing touch and go missions to obtain samples. The next ... More

An On-Orbit CubeSat Centrifuge for Asteroid Science and ExplorationDec 31 2018There are thousands of asteroids in near-Earth space and millions expected in the Main Belt. They are diverse in their physical properties and compositions. They are also time capsules of the early Solar System making them valuable for planetary science, ... More

Network of Nano-Landers for In-Situ Characterization of Asteroid Impact StudiesSep 09 2017Exploration of asteroids and comets can give insight into the origins of the solar system and can be instrumental in planetary defence and in-situ resource utilization (ISRU). Asteroids, due to their low gravity are a challenging target for surface exploration. ... More

Attitude Control of the Asteroid Origins Satellite 1 (AOSAT 1)Jan 26 2017Exploration of asteroids and small-bodies can provide valuable insight into the origins of the solar system, into the origins of Earth and the origins of the building blocks of life. However, the low-gravity and unknown surface conditions of asteroids ... More

The spherical Brazil Nut Effect and its significance to asteroidsAug 18 2016Many asteroids are likely rubble-piles that are a collection of smaller objects held together by gravity and possibly cohesion. These asteroids are seismically shaken by impacts, which leads to excitation of their constituent particles. As a result it ... More

Constraints on the pre-impact orbits of Solar System giant impactorsNov 14 2017We provide a fast method for computing constraints on impactor pre-impact orbits, applying this to the late giant impacts in the Solar System. These constraints can be used to make quick, broad comparisons of different collision scenarios, identifying ... More

Hektor - an exceptional D-type family among Jovian TrojansJul 15 2016In this work, we analyze Jovian Trojans in the space of suitable resonant elements and we identify clusters of possible collisional origin by two independent methods: the hierarchical clustering and a so-called "randombox". Compared to our previous work ... More

Collisional Formation and Modeling of Asteroid FamiliesFeb 13 2015In the last decade, thanks to the development of sophisticated numerical codes, major breakthroughs have been achieved in our understanding of the formation of asteroid families by catastrophic disruption of large parent bodies. In this review, we describe ... More

Coupling SPH and thermochemical models of planets: Methodology and example of a Mars-sized bodyOct 09 2017Giant impacts have been suggested to explain various characteristics of terrestrial planets and their moons. However, so far in most models only the immediate effects of the collisions have been considered, while the long-term interior evolution of the ... More

Realistic On-The-Fly Outcomes of Planetary Collisions: Machine Learning Applied to Simulations of Giant ImpactsMar 11 2019Planet formation simulations are capable of directly integrating the evolution of hundreds to thousands of planetary embryos and planetesimals, as they accrete pairwise to become planets. In principle such investigations allow us to better understand ... More

Giant Impact: An Efficient Mechanism for the Devolatilization of Super-EarthsSep 18 2015Oct 16 2015Mini-Neptunes and volatile-poor super-Earths coexist on adjacent orbits in proximity to host stars such as Kepler-36 and Kepler-11. Several post-formation processes have been proposed for explaining the origin of the compositional diversity: the mass ... More

Optimized Bucket Wheel Design for Asteroid ExcavationJan 26 2017Current spacecraft need to launch with all of their required fuel for travel. This limits the system performance, payload capacity, and mission flexibility. One compelling alternative is to perform In-Situ Resource Utilization (ISRU) by extracting fuel ... More

Effect of Re-impacting Debris on the Solidification of the Lunar Magma OceanApr 13 2018Anorthosites that comprise the bulk of the lunar crust are believed to have formed during solidification of a Lunar Magma Ocean (LMO) in which these rocks would have floated to the surface. This early flotation crust would have formed a thermal blanket ... More

Guidance, Navigation and Control of Asteroid Mobile Imager and Geologic Observer (AMIGO)Feb 06 2019The science and origins of asteroids is deemed high priority in the Planetary Science Decadal Survey. Major scientific goals for the study of planetesimals are to decipher geological processes in SSSBs not determinable from investigation via in-situ experimentation, ... More

A Cubesat Centrifuge for Long Duration Milligravity ResearchMay 22 2017May 23 2017We advocate a low-cost strategy for long-duration research into the 'milligravity' environment of asteroids, comets and small moons, where surface gravity is a vector field typically less than 1/1000 the gravity of Earth. Unlike the microgravity environment ... More

Boulder Stranding in Ejecta Launched by an Impact Generated Seismic PulseDec 04 2018We consider how an impact generated seismic pulse affects the surface of an asteroid distant from the impact site. With laboratory experiments on dry polydisperse gravel mixtures, we track the trajectories of particles ejected from the surface by a single ... More

On-Orbit Smart Camera System to Observe Illuminated and Unilluminated Space ObjectsSep 06 2018The wide availability of Commercial Off-The-Shelf (COTS) electronics that can withstand Low Earth Orbit conditions has opened avenue for wide deployment of CubeSats and small-satellites. CubeSats thanks to their low developmental and launch costs offer ... More

GNC Challenges and Opportunities of CubeSat Science Missions Deployed from the Lunar GatewayMar 31 2019The Lunar Gateway is expected to be positioned on-orbit around the Moon or in a Halo orbit at the L2 Lagrange point. The proposed Lunar Gateway is a game-changer for enabling new, high-priority lunar science utilizing Cu-beSats and presents a refreshing ... More

Exoplanet Science Priorities from the Perspective of Internal and Surface Processes for Silicate and Ice Dominated WorldsApr 13 2018The geophysics of extrasolar planets is a scientific topic often regarded as standing largely beyond the reach of near-term observations. This reality in no way diminishes the central role of geophysical phenomena in shaping planetary outcomes, from formation, ... More

Catastrophic disruptions revisitedJul 09 1999We use a smooth particle hydrodynamics method (SPH) to simulate colliding rocky and icy bodies from cm-scale to hundreds of km in diameter, in an effort to define self-consistently the threshold for catastrophic disruption. Unlike previous efforts, this ... More

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

A global view of quantum computation with noisy componentsJun 30 2016The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over the histories ... More

On RG-flow and the Cosmological ConstantDec 07 1999Dec 13 1999The AdS/CFT correspondence implies that the effective action of certain strongly coupled large $N$ gauge theories satisfy the Hamilton-Jacobi equation of 5d gravity. Using an analogy with the relativistic point particle, I construct a low energy effective ... More

Global Aspects of Electric-Magnetic DualityJun 01 1995Jun 06 1995We show that the partition function of free Maxwell theory on a generic Euclidean four-manifold transforms in a non-trivial way under electric-magnetic duality. The classical part of the partition sum can be mapped onto the genus-one partition function ... More

Ordinary differential equations with only entire solutionsJun 06 1997We prove necessary and sufficient conditions for a system $\dot z_i=z_ip_i(z)$ ($p_i$ a polynomial) to have only entire analytic functions as solutions.

A quantum cloning bound and application to quantum key distributionMar 20 2013Aug 14 2013We introduce a quantum cloning bound which we apply to a straightforward and relatively direct security proof of the prepare-and-measure Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol against collective attacks. The approach we propose ... More

On geometric phases for quantum trajectoriesAug 30 2006A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by using Uhlmann's ... More

Experimentally testable geometric phase of sequences of Everett's relative quantum statesMar 09 2009May 25 2009Everett's concept of relative state is used to introduce a geometric phase that depends nontrivially on entanglement in a pure quantum state. We show that this phase can be measured in multiparticle interferometry. A correlation-dependent generalization ... More

Geometric phase in weak measurementsApr 06 2006Sep 27 2006Pancharatnam's geometric phase is associated with the phase of a complex-valued weak value arising in a certain type of weak measurement in pre- and post-selected quantum ensembles. This makes it possible to test the nontransitive nature of the relative ... More

Geometric phases in quantum informationMar 16 2015Oct 07 2015The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by focusing on three ... More

Nonadiabatic holonomic single-qubit gates in off-resonant $Λ$ systemsNov 03 2015We generalize nonadiabatic holonomic quantum computation in a resonant $\Lambda$ configuration proposed in [New J. Phys. 14 (2012) 103035] to the case of off-resonant driving lasers. We show that any single-qubit holonomic gate can be realized by separately ... More

Stabilised finite element methods for ill-posed problems with conditional stabilityDec 09 2015In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific Computing, and ... More

The Baltic Meetings 1957 to 1967Dec 07 2015The Baltic meetings of astronomers from Northern Germany and Scandinavia began in 1957 and gathered up to 70 participants. Reports of the presentations are available from all meetings, providing an overview of the interests of astronomers in this part ... More

Young astronomer in Denmark 1946 to 1958Dec 07 2015This is a personal account of how I became an astronomer. Fascinated by the stars and planets in the dark sky over Lolland, an island 100 km south of Copenhagen, the interest in astronomy was growing. Encouraged by my teachers, I polished mirrors and ... More

Asymptotic degree distribution of a duplication-deletion random graph modelAug 19 2014We study a discrete-time duplication-deletion random graph model and analyse its asymptotic degree distribution. The random graphs consists of disjoint cliques. In each time step either a new vertex is brought in with probability $0<p<1$ and attached ... More

Classical Black Holes Are HotAug 16 2014Nov 09 2014In the early 1970s it is was realized that there is a striking formal analogy between the Laws of black-hole mechanics and the Laws of classical thermodynamics. Before the discovery of Hawking radiation, however, it was generally thought that the analogy ... More

Tight asymptotic key rate for the BB84 protocol with local randomisation and device imprecisionsMay 22 2014Aug 04 2014Local randomisation is a preprocessing procedure in which one of the legitimate parties of a quantum key distribution (QKD) scheme adds noise to their version of the key and was found by Kraus et al. [Phys. Rev. Lett. 95, 080501 (2005)] to improve the ... More

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

Categories with families, FOLDS and logic enriched type theoryMay 05 2016Categories with families (cwfs) is an established semantical structure for dependent type theories, such as Martin-L\"of type theory. Makkai's first-order logic with dependent sorts (FOLDS) is an example of a so-called logic enriched type theory. We introduce ... More

Two-point functions of SU(2)-subsector and length-two operators in dCFTMay 24 2017Jun 01 2017We consider a particular set of two-point functions in the setting of N = 4 SYM with a defect, dual to the fuzzy-funnel solution for the probe D5-D3-brane system. The two-point functions in focus involve a single trace operator in the SU(2)-subsector ... More

On the 3n+l Quantum Number in the Cluster ProblemJun 08 1996It has recently been suggested that an exactly solvable problem characterized by a new quantum number may underlie the electronic shell structure observed in the mass spectra of medium-sized sodium clusters. We investigate whether the conjectured quantum ... More

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

Supershells in Metal Clusters: Self-Consistent Calculations and their Semiclassical InterpretationJun 05 1996To understand the electronic shell- and supershell-structure in large metal clusters we have performed self-consistent calculations in the homogeneous, spherical jellium model for a variety of different materials. A scaling analysis of the results reveals ... More

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

Grand Unification with Higher Rank Product GroupsJan 27 2005Various ideas support the notion that the GUT gauge group might be a semi-simple direct-product group such as $SU(5) \times SU(5)$. The doublet-triplet splitting problem can be solved with a direct product group. String theory suggests that the GUT scale ... More

Equity Allocation and Portfolio Selection in InsuranceJul 24 1999A discrete time probabilistic model, for optimal equity allocation and portfolio selection, is formulated so as to apply to (at least) reinsurance. In the context of a company with several portfolios (or subsidiaries), representing both liabilities and ... More

A penalty free non-symmetric Nitsche type method for the weak imposition of boundary conditionsJun 28 2011Nov 04 2011In this note we show that the non-symmetric version of the classical Nitsche's method for the weak imposition of boundary conditions is stable without penalty term. We prove optimal $H^1$-error estimates and $L^2$-estimates that are suboptimal with half ... More

The continuous primitive integral in the planeJun 27 2019An integral is defined on the plane that includes the Henstock--Kurzweil and Lebesgue integrals (with respect to Lebesgue measure). A space of primitives is taken as the set of continuous real-valued functions $F(x,y)$ defined on the extended real plane ... More

The dominating colour of an infinite Pólya urn modelJun 19 2015Jun 29 2015We study a P\'olya-type urn model defined as follows. Start at time 0 with a single ball of some colour. Then, at each time n>0, choose a ball from the urn uniformly at random. With probability 1/2<p<1, return the ball to the urn along with another ball ... More

Integrals and Banach spaces for finite order distributionsOct 17 2011Let $\Bc$ denote the real-valued functions continuous on the extended real line and vanishing at $-\infty$. Let $\Br$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\infty$. Define $\acn$ to be the space ... More

Henstock--Kurzweil Fourier transformsDec 07 2002The Fourier transform is considered as a Henstock--Kurzweil integral. Sufficient conditions are given for the existence of the Fourier transform and necessary and sufficient conditions are given for it to be continuous. The Riemann--Lebesgue lemma fails: ... More

Convolutions with the continuous primitive integralSep 23 2009If $F$ is a continuous function on the real line and $f=F'$ is its distributional derivative then the continuous primitive integral of distribution $f$ is $\int_a^bf=F(b)-F(a)$. This integral contains the Lebesgue, Henstock--Kurzweil and wide Denjoy integrals. ... More

Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problem. Part II: hyperbolic equationsAug 02 2013May 02 2014In this paper we consider stabilised finite element methods for hyperbolic transport equations without coercivity. Abstract conditions for the convergence of the methods are introduced and these conditions are shown to hold for three different stabilised ... More

Robust error estimates in weak norms for advection dominated transport problems with rough dataMar 08 2013May 02 2014We consider mixing problems in the form of transient convection--diffusion equations with a velocity vector field with multiscale character and rough data. We assume that the velocity field has two scales, a coarse scale with slow spatial variation, which ... More

Projection stabilisation of Lagrange multipliers for the imposition of constraints on interfaces and boundariesMar 19 2012Aug 02 2013Projection stabilisation applied to general Lagrange multiplier finite element methods is introduced and analysed in an abstract framework. We then consider some applications of the stabilised methods: (i) the weak imposition of boundary conditions, (ii) ... More

The $L^p$ primitive integralAug 17 2012For each $1\leq p<\infty$ a space of integrable Schwartz distributions, $L^'^{\,p}$, is defined by taking the distributional derivative of all functions in $L^p$. Here, $L^p$ is with respect to Lebesgue measure on the real line. If $f\in L^'^{\,p}$ such ... More

Commutator inequalities via Schur productsDec 15 2015For a self-adjoint unbounded operator D on a Hilbert space H, a bounded operator y on H and some complex Borel functions g(t) we establish inequalities of the type ||[g(D),y]|| \leq A|||y|| + B||[D,y]|| + ...+ X|[D, [D,...[D, y]...]]||. The proofs take ... More

Stabilised finite element methods for non-symmetric, non-coercive and ill-posed problems. Part I: elliptic equationsApr 08 2013Aug 02 2013In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element residual and ... More

Vertex Operators, Grassmannians, and Hilbert SchemesOct 29 2009May 21 2010We describe a well-known collection of vertex operators on the infinite wedge representation as a limit of geometric correspondences on the equivariant cohomology groups of a finite-dimensional approximation of the Sato grassmannian, by cutoffs in high ... More

Vertex Operators and Moduli Spaces of SheavesJun 09 2009The Nekrasov partition function in supersymmetric quantum gauge theory is mathematically formulated as an equivariant integral over certain moduli spaces of sheaves on a complex surface. In ``Seiberg-Witten Theory and Random Partitions'', Nekrasov and ... More

Localization of directed polymers with general reference walkAug 11 2017Jun 18 2019Directed polymers in random environment have usually been constructed with a simple random walk on the integer lattice. It has been observed before that several standard results for this model continue to hold for a more general reference walk. Some finer ... More

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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