3,705 research outputs found
McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions
Evidence is presented to suggest that, in three dimensions, spherical
6-designs with N points exist for N=24, 26, >= 28; 7-designs for N=24, 30, 32,
34, >= 36; 8-designs for N=36, 40, 42, >= 44; 9-designs for N=48, 50, 52, >=
54; 10-designs for N=60, 62, >= 64; 11-designs for N=70, 72, >= 74; and
12-designs for N=84, >= 86. The existence of some of these designs is
established analytically, while others are given by very accurate numerical
coordinates. The 24-point 7-design was first found by McLaren in 1963, and --
although not identified as such by McLaren -- consists of the vertices of an
"improved" snub cube, obtained from Archimedes' regular snub cube (which is
only a 3-design) by slightly shrinking each square face and expanding each
triangular face. 5-designs with 23 and 25 points are presented which, taken
together with earlier work of Reznick, show that 5-designs exist for N=12, 16,
18, 20, >= 22. It is conjectured, albeit with decreasing confidence for t >= 9,
that these lists of t-designs are complete and that no others exist. One of the
constructions gives a sequence of putative spherical t-designs with N= 12m
points (m >= 2) where N = t^2/2 (1+o(1)) as t -> infinity.Comment: 16 pages, 1 figur
A gauge invariant chiral unitary framework for kaon photo- and electroproduction on the proton
We present a gauge invariant approach to photoproduction of mesons on
nucleons within a chiral unitary framework. The interaction kernel for
meson-baryon scattering is derived from the chiral effective Lagrangian and
iterated in a Bethe-Salpeter equation. Within the leading order approximation
to the interaction kernel, data on kaon photoproduction from SAPHIR, CLAS and
CBELSA/TAPS are analyzed in the threshold region. The importance of gauge
invariance and the precision of various approximations in the interaction
kernel utilized in earlier works are discussed.Comment: 23 pages, 13 figs, EPJ A styl
The support of the logarithmic equilibrium measure on sets of revolution in
For surfaces of revolution in , we investigate the limit
distribution of minimum energy point masses on that interact according to
the logarithmic potential , where is the Euclidean distance
between points. We show that such limit distributions are supported only on the
``out-most'' portion of the surface (e.g., for a torus, only on that portion of
the surface with positive curvature). Our analysis proceeds by reducing the
problem to the complex plane where a non-singular potential kernel arises whose
level lines are ellipses
Solving the difference initial-boundary value problems by the operator exponential method
We suggest a modification of the operator exponential method for the
numerical solving the difference linear initial boundary value problems. The
scheme is based on the representation of the difference operator for given
boundary conditions as the perturbation of the same operator for periodic ones.
We analyze the error, stability and efficiency of the scheme for a model
example of the one-dimensional operator of second difference
Pengaruh Metode Pembelajaran Inquiry Berbasis Visualisasi Materi Larutan Elektrolit dan Nonelektrolit di Kelas X IPA SMA Negeri 1 Kawangkoan
The purpose of this study is to examine the effect of visualization-based inquiry learning methods on student learning outcomes in electrolyte and non-electrolyte solution material. This research was conducted in Kawangkoan 1 Public High School, in the even semester X IPA students, 2018/2019 academic year. Class X IPA students 1 (n = 31) as the experimental class and class X IPA 2 (n = 32) as the control class. The test used in this study statistical t test with significance level α = 0.05 with the testing criteriat> ttable then H0 is rejected and H1 accepted. The results obtained in this test obtained tcount 5.25> ttable 1.670. This test is done not to improve student learning outcomes beyond the minimum standard of completeness criteria in school but this testing is only to see the effect of visualization based inquiry learning methods on student learning outcomes. Based on the results obtained it can be concluded that there are differences in student learning outcomes applied with conventional learning models (control class) and visualization based inquiry learning methods (experimental class
Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary
We investigate the zero temperature structure of a crystalline monolayer
constrained to lie on a two-dimensional Riemannian manifold with variable
Gaussian curvature and boundary. A full analytical treatment is presented for
the case of a paraboloid of revolution. Using the geometrical theory of
topological defects in a continuum elastic background we find that the presence
of a variable Gaussian curvature, combined with the additional constraint of a
boundary, gives rise to a rich variety of phenomena beyond that known for
spherical crystals. We also provide a numerical analysis of a system of
classical particles interacting via a Coulomb potential on the surface of a
paraboloid.Comment: 12 pages, 8 figure
Dark energy constraints and correlations with systematics from CFHTLS weak lensing, SNLS supernovae Ia and WMAP5
We combine measurements of weak gravitational lensing from the CFHTLS-Wide
survey, supernovae Ia from CFHT SNLS and CMB anisotropies from WMAP5 to obtain
joint constraints on cosmological parameters, in particular, the dark energy
equation of state parameter w. We assess the influence of systematics in the
data on the results and look for possible correlations with cosmological
parameters.
We implement an MCMC algorithm to sample the parameter space of a flat CDM
model with a dark-energy component of constant w. Systematics in the data are
parametrised and included in the analysis. We determine the influence of
photometric calibration of SNIa data on cosmological results by calculating the
response of the distance modulus to photometric zero-point variations. The weak
lensing data set is tested for anomalous field-to-field variations and a
systematic shape measurement bias for high-z galaxies.
Ignoring photometric uncertainties for SNLS biases cosmological parameters by
at most 20% of the statistical errors, using supernovae only; the parameter
uncertainties are underestimated by 10%. The weak lensing field-to-field
variance pointings is 5%-15% higher than that predicted from N-body
simulations. We find no bias of the lensing signal at high redshift, within the
framework of a simple model. Assuming a systematic underestimation of the
lensing signal at high redshift, the normalisation sigma_8 increases by up to
8%. Combining all three probes we obtain -0.10<1+w<0.06 at 68% confidence
(-0.18<1+w<0.12 at 95%), including systematic errors. Systematics in the data
increase the error bars by up to 35%; the best-fit values change by less than
0.15sigma. [Abridged]Comment: 14 pages, 10 figures. Revised version, matches the one to be
published in A&A. Modifications have been made corresponding to the referee's
suggestions, including reordering of some section
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