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Analytical results for a Bessel function times Legendre polynomials class integrals
When treating problems of vector diffraction in electromagnetic theory, the
evaluation of the integral involving Bessel and associated Legendre functions
is necessary. Here we present the analytical result for this integral that will
make unnecessary numerical quadrature techniques or localized approximations.
The solution is presented using the properties of the Bessel and associated
Legendre functions.Comment: 4 page
Ordenha higiênica de leite de cabra.
Passos para ordenha higiênica; Limpeza da sala de ordenha e dos vasilhames.bitstream/item/132809/1/ID-38686.pd
A 3-form Gauge Potential in 5D in connection with a Possible Dark Sector of 4D-Electrodynamics
We here propose a 5-dimensional {\bf Abelian gauge} model based on the mixing
between a potential and an Abelian 3-form field by means of a
topological mass term. An extended covariant derivative is introduced to
minimally couple a Dirac field to the potential, while this same
covariant derivative non-minimally couples the 3-form field to the charged
fermion. A number of properties are discussed in 5D; in particular, the
appearance of a topological fermionic current. A 4-dimensional reduced version
of the model is investigated and, { \bf in addition to the electric- and
magnetic-sort of fields,} there emerges an extra set of electric- and
magnetic-like fields which contribute a negative pressure and may be identified
as a possible fraction of dark energy. The role of the topological fermionic
current is also contemplated upon dimensional reduction from 5D to 4D. Other
issues we present in 4 space-time dimensions are the emergence {\bf of a
pseudo-scalar massive particle,} an extra massive neutral gauge boson,{\bf
which we interpret as a kind of paraphoton}, and the calculation of spin- and
velocity-dependent interparticle potentials associated to the exchange of the
intermediate bosonic fields of the model.Comment: -- 30 pages -- L. P. R. Ospedal appears as a new co-author;
modifications by inclusion of the gravitational sector and the attainment of
a spin- and velocity-dependent potential as an application have been worked
out in this Revised Versio
Metabolic diversity of diazotrophic bacteria isolates from Brazilian maize and sorghum cultivars by the biolog system.
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