1,297 research outputs found
The bicomplex quantum Coulomb potential problem
Generalizations of the complex number system underlying the mathematical
formulation of quantum mechanics have been known for some time, but the use of
the commutative ring of bicomplex numbers for that purpose is relatively new.
This paper provides an analytical solution of the quantum Coulomb potential
problem formulated in terms of bicomplex numbers. We define the problem by
introducing a bicomplex hamiltonian operator and extending the canonical
commutation relations to the form [X_i,P_k] = i_1 hbar xi delta_{ik}, where xi
is a bicomplex number. Following Pauli's algebraic method, we find the
eigenvalues of the bicomplex hamiltonian. These eigenvalues are also obtained,
along with appropriate eigenfunctions, by solving the extension of
Schrodinger's time-independent differential equation. Examples of solutions are
displayed. There is an orthonormal system of solutions that belongs to a
bicomplex Hilbert space.Comment: Clarifications; some figures removed; version to appear in Can. J.
Phy
Warped quasi-asymptotically conical Calabi-Yau metrics
We construct many new examples of complete Calabi-Yau metrics of maximal
volume growth on certain smoothings of Cartesian products of Calabi-Yau cones
with smooth cross-sections. A detailed description of the geometry at infinity
of these metrics is given in terms of a compactification by a manifold with
corners obtained through the notion of weighted blow-up for manifolds with
corners. A key analytical step in the construction of these Calabi-Yau metrics
is to derive good mapping properties of the Laplacian on some suitable weighted
H\"older spaces. Our methods also produce singular Calabi-Yau metrics with an
isolated conical singularity modelled on a Calabi-Yau cone distinct from the
tangent cone at infinity, in particular yielding a transition behavior between
different Calabi-Yau cones as conjectured by Yang Li. This is used to exhibit
many examples where the tangent cone at infinity does not uniquely specify a
complete Calabi-Yau metric with exact K\"ahler form.Comment: 64 pages, added the construction of singular Calabi-Yau metrics with
an isolated conical singularity modelled on a Calabi-Yau cone distinct from
the tangent cone at infinity, thus interpolating between two different
Calabi-Yau cone
Compilation of a Database of Research Information on Legume Based Grazing Systems; a Part of the Leggraze Research Project
The establishment of a publicly accessible web-resident database of published and current European research on agronomy, animal production and environmental impact of legume based grazing systems is reported. This database facilitates the sharing of information among the partners of the Low input animal production based on forage legumes for grazing systems (Leggraze), a research project funded by the UE (QL K5 CT-2001-02328). It also forms an important tool for transferring the results of the project to the wider research community and to end users in the agricultural sector and to policy makers at national and community level
Doppler temperatures from O(<sup>1</sup>D) airglow in the daytime thermosphere as observed by the Wind Imaging Interferometer (WINDII) on the UARS satellite
International audienceFrom 1992 to 1997, the WINDII interferometer on board the UARS satellite acquired a large set of thermospheric data from the O(1D) and O(1S) airglows. We report here for the first time on daytime O(1D) Doppler temperatures obtained with version 5.11 of the WINDII data processing software. Using a statistical analysis of the temperatures independently measured by the two WINDII fields of view, we estimate that the temperature variations larger than 40 K can be considered as geophysical. Comparisons of WINDII temperatures measured during magnetically quiet days with temperatures obtained by the MSIS-90 and DTM-94 thermospheric models show a 100 K bias. We demonstrate, however, that the modeled temperature variations represent very well the mean temperature variation observed by WINDII over 4 years. We also show that the observed latitudinal/local time variation is in very good agreement with the two empirical models. Finally, the temperature variations during a magnetically disturbed day are found to be qualitatively well represented in form by the models, but largely underestimated. The presence of non-thermal atoms and instrument related issues are discussed as possible explanations for the 100 K bias between the WINDII Doppler temperatures and the empirical models
One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula
In \cite{Mul} one-parameter planar motion was first introduced and the
relations between absolute, relative, sliding velocities (and accelerations) in
the Euclidean plane were obtained. Moreover, the relations
between the Complex velocities one-parameter motion in the Complex plane were
provided by \cite{Mul}. One-parameter planar homothetic motion was defined in
the Complex plane, \cite{Kur}. In this paper, analogous to homothetic motion in
the Complex plane given by \cite{Kur}, one-parameter planar homothetic motion
is defined in the Hyperbolic plane. Some characteristic properties about the
velocity vectors, the acceleration vectors and the pole curves are given.
Moreover, in the case of homothetic scale identically equal to 1, the
results given in \cite{Yuc} are obtained as a special case. In addition, three
hyperbolic planes, of which two are moving and the other one is fixed, are
taken into consideration and a canonical relative system for one-parameter
planar hyperbolic homothetic motion is defined. Euler-Savary formula, which
gives the relationship between the curvatures of trajectory curves, is obtained
with the help of this relative system
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