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A Functional (Monadic) Second-Order Theory of Infinite TreesMar 14 2019This paper presents a complete axiomatization of Monadic Second-Order Logic (MSO) over infinite trees. MSO on infinite trees is a rich system, and its decidability ("Rabin's Tree Theorem") is one of the most powerful known results concerning the decidability ... More

A Curry-Howard Approach to Church's SynthesisMar 23 2018Feb 13 2019Church's synthesis problem asks whether there exists a finite-state stream transducer satisfying a given input-output specification. For specifications written in Monadic Second-Order Logic over infinite words, Church's synthesis can theoretically be ... More

On the confluence of lambda-calculus with conditional rewritingSep 20 2011The confluence of untyped \lambda-calculus with unconditional rewriting is now well un- derstood. In this paper, we investigate the confluence of \lambda-calculus with conditional rewriting and provide general results in two directions. First, when conditional ... More

On the confluence of lambda-calculus with conditional rewritingSep 01 2006Sep 11 2006The confluence of untyped lambda-calculus with unconditional rewriting has already been studied in various directions. In this paper, we investigate the confluence of lambda-calculus with conditional rewriting and provide general results in two directions. ... More

Binaries as Astrophysical Laboratories: Open QuestionsNov 15 2005Binary systems have long been recognized as the source of powerful astrophysical diagnostics. Among the many applications of binary stars, they have been used as probes of stellar structure and evolution (both of single and binary stars) in a broad range ... More

Permutations from an arithmetic settingApr 29 2019Let $m,n$ be positive integers such that $\gcd(n,m^2) = m > 1$. In this paper, we introduce a special class of piecewise-affine permutations of the finite set $[1,n] := \{1,\dots,n\}$ with the property that the reduction $\pmod n$ of $m$ consecutive elements ... More

Unitary Cayley Graphs of Dedekind Domain QuotientsDec 09 2014If $X$ is a commutative ring with unity, then the unitary Cayley graph of $X$, denoted $G_X$, is defined to be the graph whose vertex set is $X$ and whose edge set is $\{\{a,b\}\colon a-b\in U(X)\}$, where $U(X)$ denotes the group of units of $X$. When ... More

The inhabitance paradox: how habitability and inhabitancy are inseparableMar 03 2016The dominant paradigm in assigning "habitability"' to terrestrial planets is to define a circumstellar habitable zone: the locus of orbital radii in which the planet is neither too hot nor too cold for life as we know it. One dimensional climate models ... More

Subgroups of finite index and the just infinite propertyMay 11 2009A residually finite (profinite) group $G$ is just infinite if every non-trivial (closed) normal subgroup of $G$ is of finite index. This paper considers the problem of determining whether a (closed) subgroup $H$ of a just infinite group is itself just ... More

Near-Threshold Production of $η$-MesonsJan 11 1993It is shown that the striking energy variation in the $p\, d \rightarrow \mbox{$^{\, 3}{\rm He}$}\, \eta$ cross section near threshold is probably due to a final state interaction associated with a large (complex) $\eta -\mbox{$^{3}{\rm He}$}$ scattering ... More

The Continuing Outburst of V1647~Orionis: Winter/Spring 2011 ObservationsAug 06 2011Aug 10 2011We present optical and near-IR observations of the young eruptive variable star V1647 Orionis which illuminates McNeil's Nebula. In late 2003, V1647 Ori was observed to brightened by around 5 mag to r'=17.7. In early 2006 the star faded back to its quiescent ... More

V2492 Cygni: The Early Evolution of the 2010 OutburstMay 04 2011We present Gemini-North optical and near-IR observations of a young eruptive star in Cygnus, designated as V2492 Cyg in the General Catalog of Variable Stars. This object is one of two young stars, located within 2 degrees of each other, that recently ... More

Forms and Rotational States of the Nuclei of Ecliptic CometsJan 12 2007In this thesis I present measurements of the physical properties of the nuclei of Jupiter Family comets (JFCs), based on time-series observations. From the time-series photometry rotation rates and elongations were measured, and from these constraints ... More

Sub-Compton quantum non-equilibrium and Majorana systemsJun 05 2013We study the Majorana equation from the point of view of the de Broglie-Bohm pilot-wave theory (according to which a quantum ensemble of fermions is not only described by a spinor but also by a distribution of position configurations). Although the Majorana ... More

Lipschitz-free spaces and Schur propertiesMar 04 2016Apr 11 2017In this paper we study $\ell_1$-like properties for some Lipschitz-free spaces. The main result states that, under some natural conditions, the Lipschitz-free space over a proper metric space linearly embeds into an $\ell_1$-sum of finite dimensional ... More

A Note about Iterated Arithmetic FunctionsJan 24 2015Let $f\colon\mathbb{N}\rightarrow\mathbb{N}_0$ be a multiplicative arithmetic function such that for all primes $p$ and positive integers $\alpha$, $f(p^{\alpha})<p^{\alpha}$ and $f(p)\vert f(p^{\alpha})$. Suppose also that any prime that divides $f(p^{\alpha})$ ... More

Counting 3-Stack-Sortable PermutationsMar 21 2019We prove a "Decomposition Lemma" that allows us to count preimages of certain sets of permutations under West's stack-sorting map $s$. As a first application, we give a new proof of Zeilberger's formula for the number of 2-stack-sortable permutations ... More

An Arithmetic Function Arising from the Dedekind $ψ$ FunctionJan 05 2015Jan 07 2015We define $\overline{\psi}$ to be the multiplicative arithemtic function that satisfies \[\overline{\psi}(p^{\alpha})=\begin{cases} p^{\alpha-1}(p+1), & \mbox{if } p\neq 2; \\ p^{\alpha-1}, & \mbox{if } p=2 \end{cases}\] for all primes $p$ and positive ... More

Polyurethane TogglesApr 09 2019We consider the involutions known as "toggles," which have been used to give simplified proofs of the fundamental properties of the promotion and evacuation maps. We transfer these involutions so that they generate a group $\mathscr P_n$ that acts on ... More

Motzkin Intervals and Valid Hook ConfigurationsApr 23 2019We define a new natural partial order on Motzkin paths that serves as an intermediate step between two previously-studied partial orders. We provide a bijection between valid hook configurations of $312$-avoiding permutations and intervals in these new ... More

Absence of resonance near the critical line on asymptotically hyperbolic spacesJun 24 2004Sep 02 2005As a consequence of a result of Cardoso and Vodev, we show that the resolvent of the Laplacian on asymptotically hyperbolic manifolds is analytic in an exponential neighbourhood of the critical line. The case of non-trapping metrics with constant curvature ... More

Cabling Conjecture for Small Bridge NumberJul 06 2015Let $k\subset S^3$ be a nontrivial knot. The Cabling Conjecture of Francisco Gonz\'alez-Acu\~na and Hamish Short posits that $\pi$-Dehn surgery on $k$ produces a reducible manifold if and only if $k$ is a $(p,q)$-cable knot and the surgery slope $\pi$ ... More

Triple Crossing Number of Knots and LinksJul 31 2012Sep 04 2012A triple crossing is a crossing in a projection of a knot or link that has three strands of the knot passing straight through it. A triple crossing projection is a projection such that all of the crossings are triple crossings. We prove that every knot ... More

A new paradigm for the universeNov 03 2003Jan 25 2012A new paradigm for the universe is presented in which the universe is far older than current estimates and there is no big bang.

Observation of M87 with VERITASSep 23 2007The giant radio galaxy M87 is the only extragalactic non-blazar object which has been detected as a source of very high energy gamma-rays. It represents a unique opportunity to study the phenomena of gamma-ray emission from a nearby AGN. In this paper ... More

An introduction to mesic nucleiJan 14 2016There is much speculation and a modest amount of evidence that certain mesons might form quasi-bound states with nuclei to produce really exotic states of matter. For this to be a practical possibility, the interaction between the meson and nucleons at ... More

COSY-11 : How will we remember it ?Sep 03 2007A personal selection is made of the highlights of the COSY-11 physics program undertaken at the COoler SYnchrotron of the Forschungszentrum Juelich. This has been particularly rich in the field of strange and non-strange meson production in proton-proton ... More

On the structure of just infinite profinite groupsJun 09 2009Jun 26 2009A profinite group $G$ is just infinite if every closed normal subgroup of $G$ is of finite index. We prove that an infinite profinite group is just infinite if and only if, for every open subgroup $H$ of $G$, there are only finitely many open normal subgroups ... More

Mony a Mickle Maks a Muckle: Minor Body Observations with Optical Telescopes of All SizesMar 17 2009I review the current capabilities of small, medium and large telescopes in the study of minor bodies of the Solar System (MBOSS), with the goal of identifying those areas where the next generation of Extremely Large Telescopes (ELTs) are required to progress. ... More

Some Poset Pattern-Avoidance Problems Posed by YakoubovAug 13 2016Extending the work of Yakoubov, we enumerate the linear extensions of comb posets that avoid certain length-$3$ patterns. We resolve many of Yakoubov's open problems and prove both of the conjectures from her paper.

Some Poset Pattern-Avoidance Problems Posed by YakoubovAug 13 2016Nov 24 2016Extending the work of Yakoubov, we enumerate the linear extensions of comb posets that avoid certain length-$3$ patterns. We resolve many of Yakoubov's open problems and prove both of the conjectures from her paper.

Enumerating Periodic Points of Certain Sequential Dynamical SystemsNov 22 2015A sequential dynamical system (SDS) consists of an undirected simple graph $Y$ with vertices $v_1,v_2,\ldots,v_n$, a collection of vertex functions $\{f_{v_i}\}_{i=1}^n$, a permutation $\pi\in S_n$, and a collection of states $A$. In this system, vertices ... More

Preimages under the Stack-Sorting AlgorithmNov 18 2015Apr 06 2016We use a method for determining the number of preimages of any permutation under the stack-sorting map in order to obtain recursive upper bounds for the numbers $W_t(n)$ and $W_t(n,k)$ of $t$-stack sortable permutations of length $n$ and $t$-stack sortable ... More

Improved gluonic actions on anisotropic latticesAug 05 1996The use of novel perturbatively-improved gluonic actions on anisotropic lattices in which the temporal spacing is much smaller than that in the spatial directions is discussed. Such actions permit more efficient measurements of noisy correlation functions, ... More

Postorder PreimagesApr 06 2016Jun 02 2018Given a set $Y$ of decreasing plane trees and a permutation $\pi$, how many trees in $Y$ have $\pi$ as their postorder? Using combinatorial and geometric constructions, we provide a method for answering this question for certain sets $Y$ and all permutations ... More

On 2-powerfully Perfect Numbers in Three Quadratic RingsDec 09 2014Dec 11 2014Using an extension of the abundancy index to imaginary quadratic rings with unique factorization, we define what we call $n$-powerfully perfect numbers in these rings. This definition serves to extend the concept of perfect numbers that have been defined ... More

An Extension of the Abundancy Index to Certain Quadratic RingsJun 17 2015We begin by introducing an extension of the traditional abundancy index to imaginary quadratic rings with unique factorization. After showing that many of the properties of the traditional abundancy index continue to hold in our extended form, we investigate ... More

Unitary Multiperfect Numbers in Certain Quadratic RingsDec 09 2014A unitary divisor $c$ of a positive integer $n$ is a positive divisor of $n$ that is relatively prime to $\displaystyle{\frac{n}{c}}$. For any integer $k$, the function $\sigma_k^*$ is a multiplicative arithmetic function defined so that $\sigma_k^*(n)$ ... More

Connected Components of Complex Divisor FunctionsNov 12 2017May 04 2018For any complex number $c$, define the divisor function $\sigma_c\colon\mathbb N\to\mathbb C$ by $\displaystyle\sigma_c(n)=\sum_{d\mid n}d^c$. Let $\overline{\sigma_c(\mathbb N)}$ denote the topological closure of the range of $\sigma_c$. Extending previous ... More

On Ranges of Variants of the Divisor Functions that are DenseJul 04 2015For a real number $t$, let $s_t$ be the multiplicative arithmetic function defined by $\displaystyle{s_t(p^{\alpha})=\sum_{j=0}^{\alpha}(-p^t)^j}$ for all primes $p$ and positive integers $\alpha$. We show that the range of a function $s_{-r}$ is dense ... More

A new paradigm for the universeNov 03 2003Dec 21 2017This book provides a completely new approach to understanding the universe. The main idea is that the principal objects in the universe form a spectrum unified by the presence of a massive or hypermassive black hole. These objects are variously called ... More

Lens rigidity for manifolds with hyperbolic trapped setDec 04 2014Dec 21 2015For a Riemannian manifold $(M,g)$ with strictly convex boundary $\partial M$, the lens data consists in the set of lengths of geodesics $\gamma$ with endpoints on $\partial M$, together with their endpoints $(x_-,x_+)\in \partial M\times \partial M$ and ... More

The Harish-Chandra integralJun 28 2018This paper introduces Harish-Chandra's integral formula for compact, connected, semisimple Lie groups. It is intended for mathematicians and physicists who are familiar with the basics of Lie groups and Lie algebras but who may not be specialists in representation ... More

Preimages under the Stack-Sorting AlgorithmNov 18 2015Jun 02 2018We use a method for determining the number of preimages of any permutation under the stack-sorting map in order to obtain recursive upper bounds for the numbers $W_t(n)$ and $W_t(n,k)$ of $t$-stack sortable permutations of length $n$ and $t$-stack sortable ... More

Anti-Power Prefixes of the Thue-Morse WordJul 20 2016Oct 08 2016Recently, Fici, Restivo, Silva, and Zamboni defined a $k$-anti-power to be a word of the form $w_1w_2\cdots w_k$, where $w_1,w_2,\ldots,w_k$ are distinct words of the same length. They defined $AP(x,k)$ to be the set of all positive integers $m$ such ... More

Stack-Sorting Preimages of Permutation ClassesSep 10 2018Feb 11 2019We extend and generalize many of the enumerative results concerning West's stack-sorting map $s$. First, we prove a useful theorem that allows one to efficiently compute $|s^{-1}(\pi)|$ for any permutation $\pi$, answering a question of Bousquet-M\'elou. ... More

Connectivity for bridge-alterable graph classesNov 13 2013Mar 01 2016A collection of graphs is called bridge-alterable if, for each graph G with a bridge e, G is in the class if and only if G-e is. For example the class of forests is bridge-alterable. For a random forest $F_n$ sampled uniformly from the set of forests ... More

On the contribution of fluorescence to Ly$α$ halos (LAHs) around star forming galaxiesMar 15 2016Apr 12 2016We quantify the contribution of Ly$\alpha$ fluorescence to observed spatially extended Ly$\alpha$ halos around Ly$\alpha$ emitters (LAE) at redshift ${\rm z=3.1}$. The key physical quantities that describe the fluorescent signal include (${\it i}$) the ... More

Tutorial models of the climate and habitability of Proxima Centauri b: a thin atmosphere is sufficient to distribute heat given low stellar fluxAug 25 2016Proxima Centauri b, an Earth-size planet in the habitable zone of our nearest stellar neighbour, has just been discovered. A theoretical framework of synchronously rotating planets, in which the risk of a runaway greenhouse on the sunlight side and atmospheric ... More

Number and Luminosity Evolution of Interacting Galaxies as a Natural explanation for the Galaxy CountsMay 23 1995A newly developed isochrone synthesis algorithm for the photometric evolution of galaxies is described. Two initial mass functions, IMFs, in particular, the recent IMF determined by Kroupa, Tout, and Gilmore, three photometric transformations, and a 1-Gyr-burst ... More

SaturnaliaJun 24 1998A personal choice is made of the highlights of the physics programme carried out at the Saturne-2 facility over the last twenty years.

An Examination of Possible Gravitational Perturbations in the Transit Timing Variations of Exoplanet WASP-3bJun 21 2011Maciejewski et al. (2010) claim to have detected a possible sinusoidal variation in the transit timing variations of exoplanet WASP-3b, which is currently the only known planet orbiting the star WASP-3. According to Maciejewski's analysis, this signal ... More

On the Density of Ranges of Generalized Unitary Divisor FunctionsJul 09 2015For any integer $t$, the unitary divisor function $\sigma_t^*$ is the multiplicative arithmetic function defined by $\sigma_t^*(p^{\alpha})=1+p^{\alpha t}$ for all primes $p$ and positive integers $\alpha$. The range of the unitary divisor function $\sigma_{-1}^*$ ... More

Quadruple crossing number of knots and linksNov 12 2012Jan 28 2013A quadruple crossing is a crossing in a projection of a knot or link that has four strands of the knot passing straight through it. A quadruple crossing projection is a projection such that all of the crossings are quadruple crossings. In a previous paper, ... More

Resonances and scattering poles on asymptotically hyperbolic manifoldsMar 31 2004On an asymptotically hyperbolic manifold (X,g), we show that the resolvent resonances coincide, with multiplicities, with the poles of the renormalized scattering operator, except for the special points n/2-k (with k>0 integer) where an additional term ... More

Sinkhorn Divergence of Topological Signature Estimates for Time Series ClassificationFeb 14 2019Distinguishing between classes of time series sampled from dynamic systems is a common challenge in systems and control engineering, for example in the context of health monitoring, fault detection, and quality control. The challenge is increased when ... More

Generalized Krein formula and determinants for even dimensional Poincare-Einstein manifoldsDec 08 2005Aug 02 2007For a class of even dimensional conformally compact manifolds (X,g), we define a generalized Krein spectral function by applying a renormalized trace functional to the spectral measure of the Laplacian. We then show that this is the phase of the Kontsevich-Vishik ... More

Spiders and Generalized ConfluenceSep 27 2018Sep 28 2018Given a semisimple Lie algebra $\mathfrak{g}$, we can represent invariants of tensor products of fundamental representations of the quantum enveloping algebra $U_q(\mathfrak{g})$ using particular directed graphs called webs. In particular webs are trivalent ... More

Improved effective estimates of Pólya's Theorem for quadratic formsApr 08 2018Apr 14 2018Following de Loera and Santos, the P\'olya exponent of a $n$-ary real form (i.e. a homogeneous polynomial in $n$ variables with real coefficients) $f$ is the infimum of the upward closed set of nonnegative integers $m$ such that $(x_1 + \cdots + x_n)^m ... More

Upper Bounds for Stern's Diatomic Sequence and Related SequencesJun 25 2015Let $(s_2(n))_{n=0}^\infty$ denote Stern's diatomic sequence. For $n\geq 2$, we may view $s_2(n)$ as the number of partitions of $n-1$ into powers of $2$ with each part occurring at most twice. More generally, for integers $b,n\geq 2$, let $s_b(n)$ denote ... More

Generalized augmented alternating links and hyperbolic volumeJun 09 2015Augmented alternating links are links obtained by adding trivial components that bound twice-punctured disks to non-split reduced non-2-braid prime alternating projections. These links are known to be hyperbolic. Here, we extend to show that generalized ... More

Eventual positivity of Hermitian polynomials and integral operatorsDec 04 2014Quillen proved that, if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Hermitian squares. Catlin-D'Angelo and ... More

Counting 3-Stack-Sortable PermutationsMar 21 2019May 07 2019We prove a "Decomposition Lemma" that allows us to count preimages of certain sets of permutations under West's stack-sorting map $s$. As a first application, we give a new proof of Zeilberger's formula for the number of 2-stack-sortable permutations ... More

The generalised Fitting subgroup of a profinite groupApr 02 2009The generalised Fitting subgroup of a finite group is the group generated by all subnormal subgroups that are either nilpotent or quasisimple. The importance of this subgroup in finite group theory stems from the fact that it always contains its own centraliser, ... More

Hyperbolic KnotsSep 29 2003In 1978, W. Thurston revolutionized low diemsional topology with his work on hyperbolic 3-manifolds. In this paper, we discuss what is currently known about knots in the 3-sphere with hyperbolic complements. Then focus is on geometric invariants coming ... More

350 micron observations of local IRAS galaxies using SHARC-IIDec 12 2003The cosmologically significant population of dusty galaxies detected at sub-mm and mm wavelengths by SCUBA and MAMBO have played a central part in many of the discussions at this workshop. Obtaining their redshifts is critical in understanding their role ... More

Linear structure of Lipschitz-free spaces over countable compact metric spacesMar 04 2016Jun 01 2016In this paper we show that the Lipschitz-free space over some compact metric spaces linearly embed into a l1-sum of finite dimensional subspaces of itself. We also prove that under natural conditions, the Lipschitz-free space over a compact metric space ... More

Approaches to threshold meson productionOct 15 1998Near-threshold data on meson production in nucleon-nucleon scattering are analysed in the short-range limit which permits a quantitative comparison of the production in two and three-body final states. The relative strengths of different meson productions ... More

eta meson production in nucleon-nucleon collisionsAug 03 2010New experimental data are presented on the energy dependence of the total cross sections for the np -> d eta and quasi-two-body pp -> pp eta reactions, where the final diproton is detected at very low excitation energy. Differential cross sections of ... More

SaturnalesJun 24 1998Un choix personnel a ete fait d'evenements memorables du programme de physique realise a Saturne-2 pendant les derniers 20 ans.

On the Density of Ranges of Generalized Divisor Functions with Restricted DomainsJul 09 2015We begin by defining functions $\sigma_{t,k}$, which are generalized divisor functions with restricted domains. For each positive integer $k$, we show that, for $r>1$, the range of $\sigma_{-r,k}$ is a subset of the interval $\displaystyle{\left[1,\frac{\zeta(r)}{\zeta((k+1)r)}\right)}$. ... More

Nondegenerate $2 \times k \times (k+1)$ HypermatricesJun 14 2016Jun 17 2016We construct an extension of Gaussian elimination to show that if $\mathbb{F}$ is a topological field, then there is a transitive, free, and continuous action of a natural quotient of $GL_k(\mathbb{F}) \times GL_{k+1}(\mathbb{F})$ on the set $M_k(\mathbb{F})$ ... More

Exploring the spectrum of QCD using a space-time latticeSep 21 2005Some past and ongoing explorations of the spectrum of QCD using Monte Carlo simulations on a space-time lattice are described. Glueball masses in the pure-gauge theory are reviewed, and the energies of gluonic excitations in the presence of a static quark-antiquark ... More

Venus: Key to understanding the evolution of terrestrial planetsMar 31 2017Why are the terrestrial planets so different? Venus should be the most Earth-like of all our planetary neighbours. Its size, bulk composition and distance from the Sun are very similar to those of the Earth. Its original atmosphere was probably similar ... More

On Sparsely Schemmel Totient NumbersDec 09 2014For each positive integer $r$, let $S_r$ denote the $r^{th}$ Schemmel totient function, a multiplicative arithmetic function defined by \[S_r(p^{\alpha})=\begin{cases} 0, & \mbox{if } p\leq r; \\ p^{\alpha-1}(p-r), & \mbox{if } p>r \end{cases}\] for all ... More

Random graphs from a weighted minor-closed classOct 09 2012There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable minor-closed class, such as the class of all planar graphs. Here we use combinatorial and probabilistic methods to investigate a more general ... More

On Arithmetic Functions Related to Iterates of the Schemmel Totient FunctionsJun 17 2015We begin by introducing an interesting class of functions, known as the Schemmel totient functions, that generalizes the Euler totient function. For each Schemmel totient function $L_m$, we define two new functions, denoted $R_m$ and $H_m$, that arise ... More

Enumerating Cliques in Direct Product GraphsJul 17 2017Nov 19 2018The unitary Cayley graph of $\mathbb Z/n\mathbb Z$, denoted $G_{\mathbb Z/n\mathbb Z}$, is the graph with vertices $0,1,\ldots,$ $n-1$ in which two vertices are adjacent if and only if their difference is relatively prime to $n$. These graphs are central ... More

A new proof of Harish-Chandra's integral formulaDec 11 2017Jul 02 2018We present a new proof of Harish-Chandra's formula $$\Pi(h_1) \Pi(h_2) \int_G e^{\langle \mathrm{Ad}_g h_1, h_2 \rangle} dg = \frac{ [ \! [ \Pi, \Pi ] \!] }{|W|} \sum_{w \in W} \epsilon(w) e^{\langle w(h_1),h_2 \rangle},$$ where $G$ is a compact, connected, ... More

Meromorphic properties of the resolvent on asymptotically hyperbolic manifoldsNov 24 2003Mar 29 2004We show that the resolvent of the Laplacian on asymptotically hyperbolic spaces extends meromorphically with finite rank poles to the complex plane if and only if the metric is `even' (in a sense). If it is not even, there exist some cases where the resolvent ... More

Lower Bounds in the Preprocessing and Query Phases of Routing AlgorithmsJan 18 2015Sep 07 2015In the last decade, there has been a substantial amount of research in finding routing algorithms designed specifically to run on real-world graphs. In 2010, Abraham et al. showed upper bounds on the query time in terms of a graph's highway dimension ... More

On the Density of Ranges of Generalized Divisor Functions with Restricted DomainsJul 09 2015Apr 09 2017We begin by defining functions $\sigma_{t,k}$, which are generalized divisor functions with restricted domains. For each positive integer $k$, we show that, for $r>1$, the range of $\sigma_{-r,k}$ is a subset of the interval $\displaystyle{\left[1,\frac{\zeta(r)}{\zeta((k+1)r)}\right)}$. ... More

Ranges of Unitary Divisor FunctionsJul 09 2015Jun 18 2018For any real $t$, the unitary divisor function $\sigma_t^*$ is the multiplicative arithmetic function defined by $\sigma_t^*(p^{\alpha})=1+p^{\alpha t}$ for all primes $p$ and positive integers $\alpha$. Let $\overline{\sigma_t^*(\mathbb N)}$ denote the ... More

On the Density of Ranges of Generalized Divisor FunctionsJun 17 2015The range of the divisor function $\sigma_{-1}$ is dense in the interval $[1,\infty)$. However, the range of the function $\sigma_{-2}$ is not dense in the interval $\displaystyle{\left[1,\frac{\pi^2}{6}\right)}$. We begin by generalizing the divisor ... More

Fertility NumbersSep 11 2018A nonnegative integer is called a fertility number if it is equal to the number of preimages of a permutation under West's stack-sorting map. We prove structural results concerning permutations, allowing us to deduce information about the set of fertility ... More

Connectivity for random graphs from a weighted bridge-addable classMar 15 2012Aug 01 2012There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable structured class, such as the class of all planar graphs. Here we consider a general 'bridge-addable' class of graphs - if a graph is in the ... More

Catalan Intervals and Uniquely Sorted PermutationsApr 04 2019For each positive integer $k$, we consider five well-studied posets defined on the set of Dyck paths of semilength $k$. We establish bijections between uniquely sorted permutations that avoid various patterns and intervals in these posets. We end with ... More

Habitability of waterworlds: runaway greenhouses, atmospheric expansion and multiple climate states of pure water atmospheresMar 16 2015There are four different stable climate states for pure water atmospheres, as might exist on so-called "waterworlds". I map these as a function of solar constant for planets ranging in size from Mars size to 10 Earth-mass. The states are: globally ice ... More

Anti-Power Prefixes of the Thue-Morse WordJul 20 2016Aug 06 2016Recently, Fici, Restivo, Silva, and Zamboni defined a $k$-anti-power to be a word of the form $w_1w_2\cdots w_k$, where $w_1,w_2,\ldots,w_k$ are distinct words of the same length. They defined $AP(x,k)$ to be the set of all positive integers $m$ such ... More

Finiteness properties of profinite groupsFeb 15 2010Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite groups are an important ... More

A problem in the Kourovka notebook concerning the number of conjugacy classes of a finite groupOct 30 2008In this paper, we consider Problem 14.44 in the Kourovka notebook, which is a conjecture about the number of conjugacy classes of a finite group. While elementary, this conjecture is still open and appears to elude any straightforward proof, even in the ... More

Production of $η$ Mesons Near ThresholdMar 11 1993It is argued that the strong energy dependence of the $p\, d \rightarrow \,^{3\!}H\!e\, \eta$ cross section near threshold is due to a final state interaction between the $\eta$ meson and the $^3$He nucleus. The large scattering length that this implies ... More

Meson Production at COSY-TOF and COSY-ANKEAug 03 2010The roles of the COSY-TOF and COSY-ANKE spectrometers in the measurement of strange meson production are briefly reviewed, mainly in connection with new results on the pp -> K^+ p Lambda, pp -> K^+ p Sigma^0 and pp -> K^+ n Sigma^+ reactions.

Coupled-channel effects in kaon pair productionNov 29 2008Two coupled channel effects connected with kaon pair production in proton-proton collisions are discussed. (1) Although there is ample evidence that the antikaon is strongly attracted to the recoil protons in pp -> K+pK-p, residual effects of the K+K- ... More

The legacy of the experimental hadron physics programme at COSYNov 22 2016The experimental hadronic physics programme at the COoler SYnchrotron of the Forschungszentrum Juelich terminated at the end of 2014. After describing the accelerator and the associated facilities, a review is presented of the major achievements in the ... More

Schur properties over some Lipschitz-free spacesMar 04 2016Nov 30 2016In this paper we show that the Lipschitz-free space over some proper metric spaces (every closed ball is compact) linearly embed into a $\ell_1$-sum of finite dimensional subspaces of itself. We also prove that under natural conditions, the Lipschitz-free ... More

Binary Codes and Period-$2$ Orbits of Sequential Dynamical SystemsSep 13 2015A sequential dynamical system (SDS) consists of an undirected simple graph $Y$ with vertices $v_1,v_2,\ldots,v_n$, a collection of vertex functions $\{f_{v_i}\}_{i=1}^n$, a permutation $\pi\in S_n$, and a collection of states $A$. The vertices update ... More

Baryon spectroscopy on the lattice: recent resultsAug 08 2003Progress in determining the baryon spectrum using computer simulations of quarks and gluons in lattice QCD are summarized and some future plans are outlined.

The Monte Carlo method in quantum field theoryFeb 20 2007This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo method with Markov-chain ... More

The finiteness theorem for invariants of a finite group (translation of Emmy Noether's "Der Endlichkeitsatz der Invarianten endlicher Gruppen")Mar 22 2015A translation of Emmy Noether's paper "Der Endlichkeitsatz der Invarianten endlicher Gruppen" (Mathematische Annalen, vol. 77, 1920, pages 89--92). In Noether's words, the paper gives "an entirely elementary finiteness proof---using only the theory of ... More