20,081 research outputs found
Picard-Fuchs Ordinary Differential Systems in N=2 Supersymmetric Yang-Mills Theories
In general, Picard-Fuchs systems in N=2 supersymmetric Yang-Mills theories
are realized as a set of simultaneous partial differential equations. However,
if the QCD scale parameter is used as unique independent variable instead of
moduli, the resulting Picard-Fuchs systems are represented by a single ordinary
differential equation (ODE) whose order coincides with the total number of
independent periods. This paper discusses some properties of these Picard-Fuchs
ODEs. In contrast with the usual Picard-Fuchs systems written in terms of
moduli derivatives, there exists a Wronskian for this ordinary differential
system and this Wronskian produces a new relation among periods, moduli and QCD
scale parameter, which in the case of SU(2) is reminiscent of scaling relation
of prepotential. On the other hand, in the case of the SU(3) theory, there are
two kinds of ordinary differential equations, one of which is the equation
directly constructed from periods and the other is derived from the SU(3)
Picard-Fuchs equations in moduli derivatives identified with Appell's
hypergeometric system, i.e., Burchnall's fifth order ordinary differential
equation published in 1942. It is shown that four of the five independent
solutions to the latter equation actually correspond to the four periods in the
SU(3) gauge theory and the closed form of the remaining one is established by
the SU(3) Picard-Fuchs ODE. The formula for this fifth solution is a new one.Comment: \documentstyle[12pt,preprint,aps,prb]{revtex}, to be published in J.
Math. Phy
Mineralogical Mapping in the Cuprite Mining District, Nevada
The airborne imaging spectrometer (AIS) has provided for the first time, the possibility to map mineralogical constituents in the Earth's surface and thus has enormously increased the value of remote-sensing data as a tool in the solution of geologic problems. The question addressed with AIS at Cuprite was how well could the mineral components at the surface of a hydrothermal alteration zone be detected, identified and mapped? The question was answered positively and is discussed. A relatively rare mineral, buddingtonie, that could not have been detected by conventional means, was discovered and mapped by the use of AIS
Third order differential subordination and superordination results for analytic functions involving the Srivastava-Attiya operator
In this article, by making use of the linear operator introduced and studied
by Srivastava and Attiya \cite{srivastava1}, suitable classes of admissible
functions are investigated and the dual properties of the third-order
differential subordinations are presented. As a consequence, various
sandwich-type theorems are established for a class of univalent analytic
functions involving the celebrated Srivastava-Attiya transform. Relevant
connections of the new results are pointed out.Comment: 16. arXiv admin note: substantial text overlap with arXiv:1809.0651
The wavelength of neutrino and neutral kaon oscillations
Neutral kaons, and probably also neutrinos, exhibit oscillations between
flavor eigenstates, as a result of being produced in a superposition of mass
eigenstates. Several recent papers have addressed the question of the energies
and momenta of the components of these states, and their effect on the
coherence of the states and on the wavelength of the oscillations. We point out
that the mass eigenstates need have neither equal momentum nor equal energy,
but can nevertheless be coherent, and that a correct treatment of the
kinematics recovers the usual result for the wavelength of the flavor
oscillations.Comment: 7 pages, Latex, no figures. Added references. Formatted for Phys.
Lett. B (needs elsart.cls
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