305 research outputs found
Representation of uncertain multichannel digital signal spaces and study of pattern recognition based on metrics and difference values on fuzzy n-cell number spaces
In this paper, we discuss the problem of characterization for uncertain multichannel digital signal spaces, propose using fuzzy n-cell number space to represent uncertain n-channel digital signal space, and put forward a method of constructing such fuzzy n-cell numbers. We introduce two new metrics and concepts of certain types of difference values on fuzzy n -cell number space and study their properties. Further, based on the metrics or difference values appropriately defined, we put forward an algorithmic version of pattern recognition in an imprecise or uncertain environment, and we also give practical examples to show the application and rationality of the proposed technique
Bis[1-benzyl-3-(quinolin-8-ylmethyl)-2,3-dihydro-1H-imidazol-2-yl]dibromidopalladium(II) acetonitrile disolvate
In the title compound, [PdBr2(C20H17N3)2]·2CH3CN, the Pd atom, which lies on an inversion center, is four-coordinated in a square-planar geometry. The two imidazole rings are coplanar and nearly perpendicular to the plane formed by Pd, the coordinated imidazole C atom and one of the Br atoms, making a dihedral angle of 75.1 (2)°
Pointwise convergence of noncommutative Fourier series
This paper is devoted to the study of pointwise convergence of Fourier series
for compact groups, group von Neumann algebras and quantum groups. It is
well-known that a number of approximation properties of groups can be
interpreted as some summation methods and mean convergence of the associated
noncommutative Fourier series. Based on this framework, this work studies the
refined counterpart of pointwise convergence of these Fourier series. We
establish a general criterion of maximal inequalities for approximative
identities of noncommutative Fourier multipliers. As a result we prove that for
any countable discrete amenable group, there exists a sequence of finitely
supported positive definite functions tending to pointwise, so that the
associated Fourier multipliers on noncommutative -spaces satisfy the
pointwise convergence for all . In a similar fashion, we also
obtain results for a large subclass of groups (as well as discrete quantum
groups) with the Haagerup property and the weak amenability. We also consider
the analogues of Fej\'{e}r means and Bochner-Riesz means in the noncommutative
setting. Even back to the Fourier series of -functions on Euclidean spaces
and non-abelian compact groups, our results seem novel and yield new problems.
On the other hand, we obtain as a byproduct the dimension free bounds of the
noncommutative Hardy-Littlewood maximal inequalities associated with convex
bodies.Comment: v3: 83 pages; this version contains some corrections. v2: 74 pages;
new results are added in Section 4, Section 5 and Section 6.
Operator-Valued Hardy spaces and BMO Spaces on Spaces of Homogeneous Type
Let be a von Neumann algebra equipped with a normal semifinite
faithful trace, be a space of homogeneous type in the
sense of Coifman and Weiss, and
. In this paper,
we introduce and then conduct a systematic study on the operator-valued Hardy
space for all and
operator-valued BMO space . The main
results of this paper include -- duality theorem, atomic
decomposition of , interpolation
between these Hardy spaces and BMO spaces, and equivalence between mixture
Hardy spaces and -spaces. %Compared with the communcative results, the
novelty of this article is that is not assumed to satisfy the reverse
double condition. %The approaches we develop bypass the use of harmonicity of
infinitesimal generator, which allows us to extend Mei's seminal work
\cite{m07} to a broader setting. %Our results extend Mei's seminal work
\cite{m07} to a broader setting. In particular, without the use of
non-commutative martingale theory as in Mei's seminal work \cite{m07}, we
provide a direct proof for the interpolation theory. Moreover, under our
assumption on Calder\'{o}n representation formula, these results are even new
when going back to the commutative setting for spaces of homogeneous type which
fails to satisfy reverse doubling condition. As an application, we obtain the
-boundedness of operator-valued Calder\'{o}n-Zygmund
operators.Comment: 48page
A Mikhlin--H\"ormander multiplier theorem for the partial harmonic oscillator
We prove a Mikhlin--H\"ormander multiplier theorem for the partial harmonic
oscillator H_{\textup{par}}=-\pa_\rho^2-\Delta_x+|x|^2 for by using the Littlewood--Paley and functions
and the associated heat kernel estimate. The multiplier we have investigated is
defined on .Comment: 14 pages, no figure. All comments are welcom
Maximal ergodic inequalities for some positive operators on noncommutative -spaces
In this paper, we establish the one-sided maximal ergodic inequalities for a
large subclass of positive operators on noncommutative -spaces for a fixed
, which particularly applies to positive isometries and general
positive Lamperti contractions or power bounded doubly Lamperti operators;
moreover, it is known that this subclass recovers all positive contractions on
the classical Lebesgue spaces . Our study falls into neither the
category of positive contractions considered by Junge-Xu \cite{JUX07} nor the
class of power bounded positive invertible operators considered by
Hong-Liao-Wang \cite{HOLW18}. Our strategy essentially relies on various
structural characterizations and dilation properties associated with Lamperti
operators, which are of independent interest. More precisely, we give a
structural description of Lamperti operators in the noncommutative setting, and
obtain a simultaneous dilation theorem for Lamperti contractions. As a
consequence we establish the maximal ergodic theorem for the strong closure of
the convex hull of corresponding family of positive contractions. Moreover, in
conjunction with a newly-built structural theorem, we also obtain the maximal
ergodic inequalities for positive power bounded doubly Lamperti operators.
We also observe that the concrete examples of positive contractions without
Akcoglu's dilation, which were constructed by Junge-Le Merdy \cite{JUL07},
still satisfy the maximal ergodic inequality. We also discuss some other
examples, showing sharp contrast to the classical situation.Comment: v6: minor changes, with more details of proof in Section
Large Eddy Simulation of Unstably Stratified Turbulent Flow over Urban-Like Building Arrays
Thermal instability induced by solar radiation is the most common condition of urban atmosphere in daytime. Compared to researches under neutral conditions, only a few numerical works studied the unstable urban boundary layer and the effect of buoyancy force is unclear. In this paper, unstably stratified turbulent boundary layer flow over three-dimensional urban-like building arrays with ground heating is simulated. Large eddy simulation is applied to capture main turbulence structures and the effect of buoyancy force on turbulence can be investigated. Lagrangian dynamic subgrid scale model is used for complex flow together with a wall function, taking into account the large pressure gradient near buildings. The numerical model and method are verified with the results measured in wind tunnel experiment. The simulated results satisfy well with the experiment in mean velocity and temperature, as well as turbulent intensities. Mean flow structure inside canopy layer varies with thermal instability, while no large secondary vortex is observed. Turbulent intensities are enhanced, as buoyancy force contributes to the production of turbulent kinetic energy
Dendrimer-entrapped gold nanoparticles as potential CT contrast agents for blood pool imaging
The purpose of this study was to evaluate dendrimer-entrapped gold nanoparticles [Au DENPs] as a molecular imaging [MI] probe for computed tomography [CT]. Au DENPs were prepared by complexing AuCl4- ions with amine-terminated generation 5 poly(amidoamine) [G5.NH2] dendrimers. Resulting particles were sized using transmission electron microscopy. Serial dilutions (0.001 to 0.1 M) of either Au DENPs or iohexol were scanned by CT in vitro. Based on these results, Au DENPs were injected into mice, either subcutaneously (10 μL, 0.007 to 0.02 M) or intravenously (300 μL, 0.2 M), after which the mice were imaged by micro-CT or a standard mammography unit. Au DENPs prepared using G5.NH2 dendrimers as templates are quite uniform and have a size range of 2 to 4 nm. At Au concentrations above 0.01 M, the CT value of Au DENPs was higher than that of iohexol. A 10-μL subcutaneous dose of Au DENPs with [Au] ≥ 0.009 M could be detected by micro-CT. The vascular system could be imaged 5 and 20 min after injection of Au DENPs into the tail vein, and the urinary system could be imaged after 60 min. At comparable time points, the vascular system could not be imaged using iohexol, and the urinary system was imaged only indistinctly. Findings from this study suggested that Au DENPs prepared using G5.NH2 dendrimers as templates have good X-ray attenuation and a substantial circulation time. As their abundant surface amine groups have the ability to bind to a range of biological molecules, Au DENPs have the potential to be a useful MI probe for CT
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