446 research outputs found
Low regularity solutions of two fifth-order KdV type equations
The Kawahara and modified Kawahara equations are fifth-order KdV type
equations and have been derived to model many physical phenomena such as
gravity-capillary waves and magneto-sound propagation in plasmas. This paper
establishes the local well-posedness of the initial-value problem for Kawahara
equation in with and the local well-posedness
for the modified Kawahara equation in with .
To prove these results, we derive a fundamental estimate on dyadic blocks for
the Kawahara equation through the multiplier norm method of Tao
\cite{Tao2001} and use this to obtain new bilinear and trilinear estimates in
suitable Bourgain spaces.Comment: 17page
Weighted maximal regularity estimates and solvability of non-smooth elliptic systems II
We continue the development, by reduction to a first order system for the
conormal gradient, of \textit{a priori} estimates and solvability for
boundary value problems of Dirichlet, regularity, Neumann type for divergence
form second order, complex, elliptic systems. We work here on the unit ball and
more generally its bi-Lipschitz images, assuming a Carleson condition as
introduced by Dahlberg which measures the discrepancy of the coefficients to
their boundary trace near the boundary. We sharpen our estimates by proving a
general result concerning \textit{a priori} almost everywhere non-tangential
convergence at the boundary. Also, compactness of the boundary yields more
solvability results using Fredholm theory. Comparison between classes of
solutions and uniqueness issues are discussed. As a consequence, we are able to
solve a long standing regularity problem for real equations, which may not be
true on the upper half-space, justifying \textit{a posteriori} a separate work
on bounded domains.Comment: 76 pages, new abstract and few typos corrected. The second author has
changed nam
Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited
We show the David-Jerison construction of big pieces of Lipschitz graphs
inside a corkscrew domain does not require its surface measure be upper Ahlfors
regular. Thus we can study absolute continuity of harmonic measure and surface
measure on NTA domains of locally finite perimeter using Lipschitz
approximations. A partial analogue of the F. and M. Riesz Theorem for simply
connected planar domains is obtained for NTA domains in space. As a consequence
every Wolff snowflake has infinite surface measure.Comment: 22 pages, 6 figure
Convergence Rates in L^2 for Elliptic Homogenization Problems
We study rates of convergence of solutions in L^2 and H^{1/2} for a family of
elliptic systems {L_\epsilon} with rapidly oscillating oscillating coefficients
in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a
consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov
eigenvalues of {L_\epsilon}. Most of our results, which rely on the recently
established uniform estimates for the L^2 Dirichlet and Neumann problems in
\cite{12,13}, are new even for smooth domains.Comment: 25 page
A Nanoscale Parametric Feedback Oscillator
We describe and demonstrate a new oscillator topology, the parametric feedback oscillator (PFO). The PFO paradigm is applicable to a wide variety of nanoscale devices and opens the possibility of new classes of oscillators employing innovative frequency-determining elements, such as nanoelectromechanical systems (NEMS), facilitating integration with circuitry and system-size reduction. We show that the PFO topology can also improve nanoscale oscillator performance by circumventing detrimental effects that are otherwise imposed by the strong device nonlinearity in this size regime
Inversion polymorphism in populations of Drosophila subobscura from urban and non-urban environments
Populations of Drosophila subobscura from the urban area of Belgrade and from the locality, Deliblato, which is not under strong anthropogenic influence, were studied with the aim to characterize and compare their genetic structure by examining chromosomal inversion polymorphism. Additional analysis and comparison of this type of polymorphism with several other populations from different habitats in the central Balkans, was done. The obtained results indicate higher heterozygosity in the population from Belgrade. Despite being ecologically marginal and under strong and complex influences, this population did not show a decline in the number of inversions and it is not highly differentiated compared to the referent populations.
The effect of lead on the developmental stability of Drosophila subobscura through selection in laboratory conditions
Fluctuating asymmetry (FA), the increased variation of bilateral symmetry in a sample of individuals, can indicate disturbance in developmental stability caused by environmental and/or genomic stress. This developmental instability was analyzed in Drosophila subobscura maintained for seven generations on two different concentrations of lead in laboratory conditions. The FA4 index showed that the genotypes reared on the higher lead concentration were in developmental homeostasis, except for males in the F7 generation, for both wing size parameters. The results show that different degrees of lead pollution cause different responses to selection of the exposed population in laboratory conditions
Synthetic sequence generator for recommender systems - memory biased random walk on sequence multilayer network
Personalized recommender systems rely on each user's personal usage data in
the system, in order to assist in decision making. However, privacy policies
protecting users' rights prevent these highly personal data from being publicly
available to a wider researcher audience. In this work, we propose a memory
biased random walk model on multilayer sequence network, as a generator of
synthetic sequential data for recommender systems. We demonstrate the
applicability of the synthetic data in training recommender system models for
cases when privacy policies restrict clickstream publishing.Comment: The new updated version of the pape
A Passive Phase Noise Cancellation Element
We introduce a new method for reducing phase noise in oscillators, thereby
improving their frequency precision. The noise reduction device consists of a
pair of coupled nonlinear resonating elements that are driven parametrically by
the output of a conventional oscillator at a frequency close to the sum of the
linear mode frequencies. Above the threshold for parametric response, the
coupled resonators exhibit self-oscillation at an inherent frequency. We find
operating points of the device for which this periodic signal is immune to
frequency noise in the driving oscillator, providing a way to clean its phase
noise. We present results for the effect of thermal noise to advance a broader
understanding of the overall noise sensitivity and the fundamental operating
limits
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