4,525 research outputs found
The variance conjecture on projections of the cube
We prove that the uniform probability measure on every
-dimensional projection of the -dimensional unit cube verifies the
variance conjecture with an absolute constant provided that . We also prove that if
, the conjecture is true
for the family of uniform probabilities on its projections on random
-dimensional subspaces
A characterization of dual quermassintegrals and the roots of dual steiner polynomials
For any finite with , we provide a
characterization of those tuples of positive numbers
which are dual querma\ss integrals of two star bodies. It turns out that this
problem is related to the moment problem. Based on this relation we also get
new inequalities for the dual querma\ss integrals. Moreover, the above
characterization will be the key tool in order to investigate structural
properties of the set of roots of dual Steiner polynomials of star bodies
Lorenz-Mie scattering of focused light via complex focus fields: an analytic treatment
The Lorenz-Mie scattering of a wide class of focused electromagnetic fields
off spherical particles is studied. The focused fields in question are
constructed through complex focal displacements, leading to closed-form
expressions that can exhibit several interesting physical properties, such as
orbital and/or spin angular momentum, spatially-varying polarization, and a
controllable degree of focusing. These fields constitute complete bases that
can be considered as nonparaxial extensions of the standard Laguerre-Gauss
beams and the recently proposed polynomials-of-Gaussians beams. Their analytic
form turns out to lead also to closed-form expressions for their multipolar
expansion. Such expansion can be used to compute the field scattered by a
spherical particle and the resulting forces and torques exerted on it, for any
relative position between the field's focus and the particle.Comment: 11 pages, 7 figure
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