4,379 research outputs found
On Muckenhoupt-Wheeden Conjecture
Let M denote the dyadic Maximal Function. We show that there is a weight w,
and Haar multiplier T for which the following weak-type inequality fails: (With T replaced by M, this is a well-known fact.) This shows
that a dyadic version of the so-called Muckenhoupt-Wheeden Conjecture is false.
This accomplished by using current techniques in weighted inequalities to show
that a particular consequence of the inequality above does not hold.Comment: 14 pages, 2 figures, corrected typo
Nonequilibrium thermodynamics versus model grain growth: derivation and some physical implications
Nonequilibrium thermodynamics formalism is proposed to derive the flux of
grainy (bubbles-containing) matter, emerging in a nucleation growth process.
Some power and non-power limits, due to the applied potential as well as owing
to basic correlations in such systems, have been discussed. Some encouragement
for such a discussion comes from the fact that the nucleation and growth
processes studied, and their kinetics, are frequently reported in literature as
self-similar (characteristic of algebraic correlations and laws) both in basic
entity (grain; bubble) size as well as time scales.Comment: 8 pages, 1 figur
Sharp Bekolle estimates for the Bergman projection
We prove sharp estimates for the Bergman projection in weighted Bergman
spaces in terms of the Bekolle constant. Our main tools are a dyadic model
dominating the operator and an adaptation of a method of Cruz-Uribe, Martell
and Perez.Comment: 12 pages, 1 figur
Mechanical properties of viral capsids
Viruses are known to tolerate wide ranges of pH and salt conditions and to withstand internal pressures as high as 100 atmospheres. In this paper we investigate the mechanical properties of viral capsids, calling explicit attention to the inhomogeneity of the shells that is inherent to their discrete and polyhedral nature. We calculate the distribution of stress in these capsids and analyze their response to isotropic internal pressure (arising, for instance, from genome confinement and/or osmotic activity). We compare our results with appropriate generalizations of classical (i.e., continuum) elasticity theory. We also examine competing mechanisms for viral shell failure, e.g., in-plane crack formation vs radial bursting. The biological consequences of the special stabilities and stress distributions of viral capsids are also discussed
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