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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Using Monte Carlo to optimize variable cutsDec 20 2007Dec 20 2007A Monte Carlo method to optimize cuts on variables is presented and evaluated. The method gives a much higher signal to noise ratio than does a manual choice of cuts.

Low Threshold Bootstrap Percolation on the Hamming TorusJul 09 2014Jun 09 2015This paper analyzes various questions pertaining to bootstrap percolation on the $d$-dimensional Hamming torus where each node is open with probability $p$ and the percolation threshold is 2. For each $d'<d$ we find the critical exponent for the event ... More

SIR dynamics in random networks with heterogeneous connectivityMay 15 2007Random networks with specified degree distributions have been proposed as realistic models of population structure, yet the problem of dynamically modeling SIR-type epidemics in random networks remains complex. I resolve this dilemma by showing how the ... More

SIR dynamics in structured populations with heterogeneous connectivityAug 22 2005Dec 20 2005Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by describing the ... More

On the analytic computation of massless propagators in dimensional regularizationMay 09 2013Mar 20 2014We comment on the algorithm to compute periods using hyperlogarithms, applied to massless Feynman integrals in the parametric representation. Explicitly, we give results for all three-loop propagators with arbitrary insertions including order $\varepsilon^4$ ... More

Necessary and sufficient conditions for differentiating under the integral signJan 02 2001We give necessary and sufficient conditions for differentiating under the integral sign an integral that depends on a parameter. The conditions require the equality of two iterated integrals and depend on being able to integrate every derivative. The ... More

The regulated primitive integralNov 15 2009A function on the real line is called regulated if it has a left limit and a right limit at each point. If $f$ is a Schwartz distribution on the real line such that $f=F'$ (distributional or weak derivative) for a regulated function $F$ then the regulated ... More

Recursive prescription for logarithmic jet rate coefficientsMay 27 2013Feb 11 2014We derive a recursion relation for the analytic leading logarithmic coefficients of a final state gluon cascade. We demonstrate the potential of our method by analytically computing the rate coefficients for the emission of up to 80 gluons in both the ... More

Test of renormalization predictions for universal finite-size scaling functionsNov 02 1999We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular epsilon-expansion, where ... More

Black Hole Evaporation and ComplementarityMar 17 1995About twenty years ago Hawking made the remarkable suggestion that the black hole evaporation process will inevitably lead to a fundamental loss of quantum coherence. The mechanism by which the quantum radiation is emitted appears to be insensitive to ... More

Finite von Neumann algebra factors with property GammaOct 13 2000Oct 14 2000Techniques introduced by G. Pisier in his proof that finite von Neumann factors with property gamma have length at most 5 are modified to prove that the length is 3. It is proved that if such a factor is a complemented subspace of some larger C*-algebra ... More

On invertibility preserving linear maps, simultaneous triangularization and Property LFeb 18 1997Let F be a linear unital map of a unital matrix algebra A over the complex numbers into the complex n by n matrices. Then F induces a linear unital map Fk of the k by k matrices over A into the complex nk by nk matrices by the action of F on each entry ... More

Torsion and electron motion in Quantum Dots with crystal lattice dislocationsNov 25 1997The motion of a conducting electron in a quantum dot with one or several dislocations in the underlying crystal lattice is considered in the continuum picture, where dislocations are represented by torsion of space. The possible effects of torsion are ... More

Endomorphisms of quantized Weyl algebrasJul 15 2010Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic. We discuss how this conjecture can be approached by means of (second) quantized ... More

Comment on "Geometric phases for mixed states during cyclic evolutions"Apr 30 2004Jul 08 2004It is shown that a recently suggested concept of mixed state geometric phase in cyclic evolutions [2004 {\it J. Phys. A} {\bf 37} 3699] is gauge dependent.

Isometric Embeddability of SnowflakesSep 21 2015We show that a snowflake of a metric space with positive Hausdorff dimension does not admit an isometric embedding into euclidean space.

Exo-Jupiters and Saturns from two Gaia-like missionsAug 19 2014Detection and orbit determination for thousands of planets with periods up to about 40 years would be obtained by astrometry from two Gaia-like missions, results which cannot be obtained by any other mission, planned or proposed. A billion stars of all ... More

Astrometry 1960-80: from Hamburg to HipparcosAug 08 2014Astrometry, the most ancient branch of astronomy, was facing extinction during much of the 20th century in the competition with astrophysics. The revival of astrometry came with the European astrometry satellite Hipparcos, approved by ESA in 1980 and ... More

A stabilized nonconforming finite element method for the elliptic Cauchy problemJun 17 2014In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. We prove error estimates using continuous dependence estimates in the $L^2$-norm. The effect of perturbations in data on the estimates ... More

A Primer on Energy ConditionsApr 30 2014An energy condition, in the context of a wide class of spacetime theories (including general relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be ... More

Feynman integrals via hyperlogarithmsJun 30 2014This talk summarizes recent developments in the evaluation of Feynman integrals using hyperlogarithms. We discuss extensions of the original method, new results that were obtained with this approach and point out current problems and future directions. ... More

The Double Eulerian Polynomial and Inversion TablesJan 22 2014We show that the pair (des, ides) of statistics on the set of permu- tations has the same distribution as the pair (asc, row) of statistics on the set of inversion tables, proving a conjecture of Visontai. The common generating function of these pairs ... More

A Simple Proof of the Marker-Steinhorn Theorem for Expansions of Ordered Abelian GroupsSep 23 2013We give a short and self-contained proof of the Marker-Steinhorn Theorem for o-minimal expansions of ordered groups, based on an analysis of linear orders definable in such structures.

Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integralsMar 13 2014We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we discuss various ... More

Performance and Optimization Abstractions for Large Scale Heterogeneous Systems in the Cactus/Chemora FrameworkAug 06 2013We describe a set of lower-level abstractions to improve performance on modern large scale heterogeneous systems. These provide portable access to system- and hardware-dependent features, automatically apply dynamic optimizations at run time, and target ... More

Tournament limits: Degree distributions, score functions and self-conversenessNov 29 2016Motivated by known results for finite tournaments, we define and study the score functions of tournament kernels and the degree distributions of tournament limits. Our main theorem completely characterises those distributions that appear as the degree ... More

Continuity in the Alexiewicz normJun 21 2006If $f$ is a Henstock--Kurzweil integrable function on the real line, the Alexiewicz norm of $f$ is $\|f\|=\sup_I|\int_I f|$ where the supremum is taken over all intervals $I\subset\R$. Define the translation $\tau_x$ by $\tau_xf(y)=f(y-x)$. Then $\|\tau_xf-f\|$ ... More

Some divergent trigonometric integralsJan 02 2001Some divergent trigonometric integrals have appeared in standard tables for many years, listed as converging. We give a simple proof that these integrals diverge and trace their history. The original error was made when a (startlingly) famous mathematician ... More

Classification of pairs of rotations in finite-dimensional Euclidean spaceFeb 20 2008A rotation in a Euclidean space V is an orthogonal map on V which acts locally as a plane rotation with some fixed angle. We give a classification of all pairs of rotations in finite-dimensional Euclidean space, up to simultaneous conjugation with orthogonal ... More

Hall-Littlewood polynomials and vector bundles on the Hilbert schemeDec 28 2012Let $E$ be the bundle defined by applying a polynomial representation of $GL_n$ to the tautological bundle on the Hilbert scheme of $n$ points in the complex plane. By a result of Haiman, the Cech cohomology groups $H^i(E)$ vanish for all $i>0$. It follows ... More

On Young tableau involutions and patterns in permutationsAug 01 2009This thesis deals with three different aspects of the combinatorics of permutations. In the first two papers, two flavours of pattern avoiding permutations are examined; and in the third paper Young tableaux, which are closely related to permutations ... More

Rapidity Dependence of Elliptic Flow at RHICJan 04 2006The measured elliptic flow (v2) of identified particles as a function of pT and centrality at RHIC suggests the created medium in Au+Au collisions achieves early local thermal equilibrium that is followed by hydrodynamic expansion. It is not known if ... More

On weakly D-differentiable operatorsMar 29 2013Mar 11 2015For an unbounded self-adjoint operator D on a Hilbert space H and a bounded operator a on H we say that a is weakly D-differentiable if for any pair of vectors x, y in H the function <exp(itD) a exp(-itD)x, y> is differentiable at t =0. We find several ... More

Generalized integrands and bond portfolios: Pitfalls and counter examplesSep 12 2009Jan 05 2011We construct Zero-Coupon Bond markets driven by a cylindrical Brownian motion in which the notion of generalized portfolio has important flaws: There exist bounded smooth random variables with generalized hedging portfolios for which the price of their ... More

Detection of a Hypercharge Axion in ATLASMay 28 2001This Master of Science thesis treats the hypercharge axion, which is a hypothetical pseudo-scalar particle with electroweak interactions. First, the theoretical context and the motivations for this study are discussed. In short, the hypercharge axion ... More

Tomography of random social networksSep 15 2005We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at a distance ... More

Limit points of the iterative scaling procedureJul 23 2012The iterative scaling procedure (ISP) is an algorithm which computes a sequence of matrices, starting from some given matrix. The objective is to find a matrix 'proportional' to the given matrix, having given row and column sums. In many cases, for example ... More

Path correlations in a randomly oriented complete bipartite graphFeb 08 2011In a randomly oriented graph containing vertices $x$ and $y$, denote by $\{x\to y\}$ the event that there is a directed path from $x$ to $y$. We study the correlation between the events $\{x\to y\}$ and $\{y\to z\}$ for a (large) oriented complete bipartite ... More

Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz PotentialSep 27 2010The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or "Hele- Shaw") problem in the plane. The guiding principle in this connection is the fact that "non-physical" ... More

Characterizing the Set of Coherent Lower Previsions with a Finite Number of Constraints or VerticesMar 15 2012The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a reformulation ... More

Outbursts of WZ Sge stars/TOADs: a phenomenological comparison with soft X-ray transientsDec 01 1998The outbursts of WZ Sge stars (or TOADs), are compared to those seen in the (soft) X-ray transients. Both types of outbursts exhibit strong similarities: large amplitudes, long recurrence times, occurrence of superhumps, and of rebrightenings or reflares ... More

Towards 4U 1630-47: a black-hole soft X-ray transient odysseyJul 27 1998Aug 12 19984U 1630-47 is a black-hole X-ray transient with one of the shortest recurrence times. Despite its regular outburst behaviour little is known about this source. Only recently has attention to this system increased. I discuss there the basic known (X-ray) ... More

Estimates of the remainder in Taylor's theorem using the Henstock--Kurzweil integralJun 18 2004When a real-valued function of one variable is approximated by its $n^{th}$ degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue $p$-norms in cases where $f^{(n)}$ or $f^{(n+1)}$ are Henstock--Kurzweil integrable. When ... More

Normal forms for the G_2-action on the real symmetric 7x7-matrices by conjugationMar 12 2007Jun 08 2007The exceptional Lie group G_2 acts on the set of real symmetric 7x7-matrices by conjugation. We solve the normal form problem for this group action. In view of earlier results, this gives rise to a classification of all finite-dimensional real flexible ... More

Askey-Wilson polynomials and the quantum SU(2) group: survey and applicationsJul 25 1994Generalised matrix elements of the irreducible representations of the quantum $SU(2)$ group are defined using certain orthonormal bases of the representation space. The generalised matrix elements are relatively infinitesimal invariant with respect to ... More

One-parameter orthogonality relations for basic hypergeometric seriesMay 27 2003The second order hypergeometric q-difference operator is studied for the value c=-q. For certain parameter regimes the corresponding recurrence relation can be related to a symmetric operator on the Hilbert space l^2(Z). The operator has deficiency indices ... More

Static overscreening and nonlinear response in the Hubbard ModelMay 29 2001We investigate the static charge response for the Hubbard model. Using the Slave-Boson method in the saddle-point approximation we calculate the charge susceptibility. We find that RPA works quite well close to half-filling, breaking, of course, down ... More

Equity Allocation and Portfolio Selection in Insurance: A simplified Portfolio ModelJul 22 1999A quadratic discrete time probabilistic model, for optimal portfolio selection in (re-)insurance is studied. For positive values of underwriting levels, the expected value of the accumulated result is optimized, under constraints on its variance and on ... More

Rapidly growing Fourier integralsJan 02 2001The Riemann-Lebesgue Lemma says that the Fourier transform of an absolutely integrable function on the real line tends to zero as the transform parameter tends to infinity. When the integral is allowed to converge conditionally, the transform can have ... More

Constructivist and Structuralist Foundations: Bishop's and Lawvere's Theories of SetsJan 30 2012Bishop's informal set theory is briefly discussed and compared to Lawvere's Elementary Theory of the Category of Sets (ETCS). We then present a constructive and predicative version of ETCS, whose standard model is based on the constructive type theory ... More