83,406 research outputs found
Characterization of Spherical and Plane Curves Using Rotation Minimizing Frames
In this work, we study plane and spherical curves in Euclidean and
Lorentz-Minkowski 3-spaces by employing rotation minimizing (RM) frames. By
conveniently writing the curvature and torsion for a curve on a sphere, we show
how to find the angle between the principal normal and an RM vector field for
spherical curves. Later, we characterize plane and spherical curves as curves
whose position vector lies, up to a translation, on a moving plane spanned by
their unit tangent and an RM vector field. Finally, as an application, we
characterize Bertrand curves as curves whose so-called natural mates are
spherical.Comment: 8 pages. This version is an improvement of the previous one. In
addition to a study of some properties of plane and spherical curves, it
contains a characterization of Bertrand curves in terms of the so-called
natural mate
Effective Sublattice Magnetization and Neel Temperature in Quantum Antiferromagnets
We present an analytic expression for the finite temperature effective
sublattice magnetization which would be detected by inelastic neutron
scattering experiments performed on a two-dimensional square-lattice quantum
Heisenberg antiferromagnets with short range N\'eel order. Our expression,
which has no adjustable parameters, is able to reproduce both the qualitative
behaviour of the phase diagram and the experimental values of the
N\'eel temperature for either doped YBaCuO and
stoichiometric LaCuO compounds. Finally, we remark that by
incorporating frustration and 3D effects as perturbations is sufficient to
explain the deviation of the experimental data from our theoretical curves.Comment: 4 pages, RevTex, 3 figure
Deterministic Seasonality in Dickey-Fuller Tests: Should We Care?
This paper investigates the properties of Dickey-Fuller tests for seasonally unadjusted quarterly data when deterministic seasonality is present but it is neglected in the test regression. While for the random walk case the answer is straightforward, an extensive Monte Carlo study has to be performed for more realistic processes and testing strategies. The most important conclusion is that the common perception that deterministic seasonality has nothing to do with the long-run properties of the data is incorrect. Further numerical evidence on the shortcomings of the general-to-specific t-sig lag selection method is also presented.unit root; Dickey-Fuller tests; similar tests; seasonality; Monte Carlo
The Order of Integration for Quarterly Macroeconomic Time series: a Simple Testing Strategy
Besides introducing a simple and intuitive definition for the order of integration of quarterly time series, this paper also presents a simple testing strategy to determine that order for the case of macroeconomic data. A simulation study shows that much more attention should be devoted to the practical issue of selecting the maximum admissible order of integration. In fact, it is shown that when that order is too high, one may get (spurious) evidence for an excessive number of unit roots, resulting in an overdifferenced series.
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