Mahler Measure of "Almost" Reciprocal Polynomials

Here we give a lower bound of the Mahler measure on a set of polynomials that are "almost" reciprocal. Here "almost" reciprocal means that the outermost coefficients of each polynomial mirror each other in proportion, while this pattern breaks down for the innermost coefficients

The number of k-tons in the coupon collector problem

Consider the coupon collector problem where each box of a brand of cereal contains a coupon and there are n different types of coupons. Suppose that the probability of a box containing a coupon of a specific type is $1/n$ and that we keep buying boxes until we collect at least $m$ coupons of each type. For $k\geq m$ call a certain coupon a $k$-ton if we see it $k$ times by the time we have seen $m$ copies of all of the coupons. Here we determine the asymptotic distribution of the number of $k$-tons after we have collected $m$ copies of each coupon for any $k$ in a restricted range, given any fixed $m$. We also determine the asymptotic joint probability distribution over such values of $k$ and the total number of coupons collected

On Maximum Margin Hierarchical Classification

We present work in progress towards maximum margin hierarchical classification where the objects are allowed to belong to more than one category at a time. The classification hierarchy is represented as a Markov network equipped with an exponential family defined on the edges. We present a variation of the maximum margin multilabel learning framework, suited to the hierarchical classification task and allows efficient implementation via gradient-based methods. We compare the behaviour of the proposed method to the recently introduced hierarchical regularized least squares classifier as well as two SVM variants in Reuter's news article classification

Ground-state properties and superfluidity of two- and quasi two-dimensional solid 4He

In a recent study we have reported a new type of trial wave function symmetric under the exchange of particles and which is able to describe a supersolid phase. In this work, we use the diffusion Monte Carlo method and this model wave function to study the properties of solid 4He in two- and quasi two-dimensional geometries. In the purely two-dimensional case, we obtain results for the total ground-state energy and freezing and melting densities which are in good agreement with previous exact Monte Carlo calculations performed with a slightly different interatomic potential model. We calculate the value of the zero-temperature superfluid fraction \rho_{s} / \rho of 2D solid 4He and find that it is negligible in all the considered cases, similarly to what is obtained in the perfect (free of defects) three-dimensional crystal using the same computational approach. Interestingly, by allowing the atoms to move locally in the perpendicular direction to the plane where they are confined to zero-point oscillations (quasi two-dimensional crystal) we observe the emergence of a finite superfluid density that coexists with the periodicity of the system.Comment: 16 pages, 8 figure

Connecting music and mathematics: Exploring the professional development of primary school teachers in the English context

Building upon previous research, a small-scale qualitative study was established to work with generalist class teachers in primary schools in London, UK. The research explored how music and mathematics may be co-taught so as to support ongoing professional development. Early findings suggest that the co-teaching of music and mathematics supported: i) a meaningful context for exploration and mastery within both subject domains; ii) extended dialogues within both subject domains; iii) collaborative dialogues between teachers focused on problem solving and learning in preference to previous foci around content and repetition; and iv) a need for the further examination of the impact of teacher identity on issues including planning, craft and professional knowledge and the notion of an ‘expert’

System optimization of gasdynamic lasers, computer program user's manual

The user's manual for a computer program that performs system optimization of gasdynamic lasers is provided. Detailed input/output formats are CDC 7600/6600 computers using a dialect of FORTRAN. Sample input/output data are provided to verify correct program operation along with a program listing

The average magnetic field draping and consistent plasma properties of the Venus magnetotail

A new technique has been developed to determine the average structure of the Venus magnetotail (in the range from −8 Rv to −12 Rv) from the Pioneer Venus magnetometer observations. The spacecraft position with respect to the cross-tail current sheet is determined from an observed relationship between the field-draping angle and the magnitude of the field referenced to its value in the nearby magnetosheath. This allows us statistically to remove the effects of tail flapping and variability of draping for the first time and thus to map the average field configuration in the Venus tail. From this average configuration we calculate the cross-tail current density distribution and J × B forces. Continuity of the tangential electric field is utilized to determine the average variations of the X-directed velocity which is shown to vary from −250 km/s at −8 Rv to −470 km/s at −12 Rv. From the calculated J × B forces, plasma velocity, and MHD momentum equation the approximate plasma acceleration, density, and temperature in the Venus tail are determined. The derived ion density is approximately ∼0.07 p+/cm³ (0.005 O+/cm³) in the lobes and ∼0.9 p+/cm³ (0.06 O+/cm³) in the current sheet, while the derived approximate average plasma temperature for the tail is ∼6×106 K for a hydrogen plasma or ∼9×107 K for an oxygen plasma

Nanometer-scale GaAs clusters from organometallic precursors

We report the synthesis of crystalline nanometer-scale GaAs clusters by homogeneous vapor-phase nucleation from organometallic precursors. Cluster synthesis is performed in a hot wall organometallic vapor-phase epitaxy reactor at atmospheric pressure. High resolution transmission electron microscopy studies reveal that the aerosol produced is composed of highly faceted single crystal GaAs particles in the 10–20 nm range. The influence of growth temperature and reactant concentration on cluster morphology is discussed