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 $1$ pointwise, so that the associated Fourier multipliers on noncommutative $L_p$-spaces satisfy the pointwise convergence for all $1<p<\infty$. 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 $L_p$-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 $\mathcal{M}$ be a von Neumann algebra equipped with a normal semifinite faithful trace, $(\mathbb{X},\,d,\,\mu)$ be a space of homogeneous type in the sense of Coifman and Weiss, and $\mathcal{N}=L_\infty(\mathbb{X})\overline{\otimes}\mathcal{M}$. In this paper, we introduce and then conduct a systematic study on the operator-valued Hardy space $\mathcal{H}_p(\mathbb{X},\,\mathcal{M})$ for all $1\leq p<\infty$ and operator-valued BMO space $\mathcal{BMO}(\mathbb{X},\,\mathcal{M})$. The main results of this paper include $H_1$--$BMO$ duality theorem, atomic decomposition of $\mathcal{H}_1(\mathbb{X},\,\mathcal{M})$, interpolation between these Hardy spaces and BMO spaces, and equivalence between mixture Hardy spaces and $L_p$-spaces. %Compared with the communcative results, the novelty of this article is that $\mu$ 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 $L_p(\mathcal{N})$-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 $(\rho, x)\in\R\times\R^d$ by using the Littlewood--Paley $g$ and $g^\ast$ functions and the associated heat kernel estimate. The multiplier we have investigated is defined on $\mathbb R \times \mathbb N$.Comment: 14 pages, no figure. All comments are welcom

Maximal ergodic inequalities for some positive operators on noncommutative LpL_p-spaces

In this paper, we establish the one-sided maximal ergodic inequalities for a large subclass of positive operators on noncommutative $L_p$-spaces for a fixed $1<p<\infty$, 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 $L_p([0,1])$. 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