1,394 research outputs found
Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces
In this paper we study the Pettis integral of fuzzy mappings in arbitrary
Banach spaces. We present some properties of the Pettis integral of fuzzy
mappings and we give conditions under which a scalarly integrable fuzzy mapping
is Pettis integrable
Lineability of non-differentiable Pettis primitives
Let X be an infinite-dimensional Banach space. In 1995, settling a long
outstanding problem of Pettis, Dilworth and Girardi constructed an X-valued
Pettis integrable function on [0; 1] whose primitive is nowhere weakly
differentiable. Using their technique and some new ideas we show that ND, the
set of strongly measurable Pettis integrable functions with nowhere weakly
differentiable primitives, is lineable, i.e., there is an infinite dimensional
vector space whose nonzero vectors belong to ND
Multifunctions determined by integrable functions
Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in the sense of Bochner, McShane or Birkhoff can be transferred to the generated multifunction while Henstock integrability does not guarantee i
Determining the carrier-envelope phase of intense few-cycle laser pulses
The electromagnetic radiation emitted by an ultra-relativistic accelerated
electron is extremely sensitive to the precise shape of the field driving the
electron. We show that the angular distribution of the photons emitted by an
electron via multiphoton Compton scattering off an intense
(I>10^{20}\;\text{W/cm^2}), few-cycle laser pulse provides a direct way of
determining the carrier-envelope phase of the driving laser field. Our
calculations take into account exactly the laser field, include relativistic
and quantum effects and are in principle applicable to presently available and
future foreseen ultra-strong laser facilities.Comment: 4 pages, 2 figure
A GENERAL COMPUTATIONAL APPROACH FOR MAGNETOHYDRODYNAMIC FLOWS USING THE CFX CODE: BUOYANT FLOW THROUGH A VERTICAL SQUARE CHANNEL
The buoyancy-driven magnetoconvection in the cross
section of an infinitely long vertical square duct is investigated
numerically using the CFX code package. The
implementation of a magnetohydrodynamic (MHD) problem
in CFX is discussed, with particular reference to the
Lorentz forces and the electric potential boundary conditions
for arbitrary electrical conductivity of the walls.
The method proposed is general and applies to arbitrary
geometries with an arbitrary orientation of the magnetic
field. Results for fully developed flow under various thermal
boundary conditions are compared with asymptotic
analytical solutions. The comparison shows that the asymptotic
analysis is confirmed for highly conducting walls
as high velocity jets occur at the side walls. For weakly
conducting walls, the side layers become more conducting
than the side walls, and strong electric currents flow
within these layers parallel to the magnetic field. As a
consequence, the velocity jets are suppressed, and the core
solution is only corrected by the viscous forces near the
wall. The implementation of MHD in CFX is achieved
Pair production in a strong slowly varying magnetic field: the effect of a background gravitational field
The production probability of an pair in the presence of a strong,
uniform and slowly varying magnetic field is calculated by taking into account
the presence of a background gravitational field. The curvature of the
spacetime metric induced by the gravitational field not only changes the
transition probabilities calculated in the Minkowski spacetime but also primes
transitions that are strictly forbidden in absence of the gravitational field.Comment: 56 pages, no figure
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