20,287 research outputs found
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 and that
we keep buying boxes until we collect at least coupons of each type. For
call a certain coupon a -ton if we see it times by the time we
have seen copies of all of the coupons. Here we determine the asymptotic
distribution of the number of -tons after we have collected copies of
each coupon for any in a restricted range, given any fixed . We also
determine the asymptotic joint probability distribution over such values of
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
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