Sarason’s interpolation theorem for analytic crossed products

Saito (Math. Proc. Camb. Phil. Soc., 117, 11–20, 1995) proved Sarason’s interpolation theorem for an analytic crossed product determined by a finite von Neumann algebra. We extend this result without the assumption that the von Neumann algebra is finite.     

The real rank zero property of crossed product

Let be a unital -algebra, and let be a -dynamical system with abelian and discrete. In this paper, we introduce the continuous affine map from the trace state space of the crossed product to the -invariant trace state space of . If is of real rank zero and is connected, we have proved that is homeomorphic. Conversely, if is homeomorphic, we also get some properties and real rank zero characterization of . In particular, in that case, is of real rank zero if and only if each unitary element in with the form can be approximated by the unitary elements in with finite spectrum, where , , and if moreover is a unital inductive limit of the direct sums of non-elementary simple -algebras of real rank zero, then the above can be cancelled.

     

Cyclic Cohomology of étale Groupoids: The General Case

We give a general method for computing the cyclic cohomology of crossed products by étale groupoids, extending the Feigin–Tsygan–Nistor spectral sequences. In particular we extend the computations performed by Brylinski, Burghelea, Connes, Feigin, Karoubi, Nistor, and Tsygan for the convolution algebra C _c (G) of an étale groupoid, removing the Hausdorffness condition and including the computation of hyperbolic components. Examples like group actions on manifolds and foliations are considered.     

The study of wave motion in the Talbot interferometer with a lens

We present the study of the wave motion in the Talbot interferometer with an additional element such as a lens for all related audiences. Our solutions are in the analytic form. A general principle of the Talbot effect, which is the optical near-field effect, is the Fresnel diffraction. The Fresnel integral is rather complicated. We therefore introduce an alternative method which is based on the wave propagation through the transmission functions of the grating and the lens. Our method has been proved by a simple experimental setup.     

偶交叉双积Hopf代数B RH的构造

本文给出了Doi Y.构造的偶交叉积B H的代数结构与Reshetikhim～N.构造的双代数BRH的余代数结构在张量空间B H上构成双代数(记为BRH)的充要条件,利用此结论具体构造了一个有趣的例子H4 KZ2,证明了当B,H均为Hopf.代数时BRH也为Hopf代数,最后给出这类双代数的映射刻划.     

Constructing the Co cyclic Structures for Crossed Copro duct Coalgebras

In this paper, we construct a cocylindrical object associated to two coal-gebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduct c...     

Invariant properties of representations under cleft extensions

The main aim of this paper is to give the invariant properties of representations of algebras under cleft extensions over a semisimple Hopf algebra. Firstly, we explain the concept of the cleft extension and give a relation between the cleft extension and the crossed product which is the approach we depend upon. Then, by making use of them, we prove that over an algebraically closed field k, for a finite dimensional Hopf algebra H which is semisimple as well as its dual H*, the representation type of an algebra is an invariant property under a finite dimensional H-cleft extension . In the other part, we still show that over an arbitrary field k, the Nakayama property of a k-algebra is also an invariant property under an H -cleft extension when the radical of the algebra is H-stable.     

Tunable All-Optical Microwave Filters Based on Fiber Loop and Chirped Fiber Bragg Gratings

All-optical microwave filters are important parts of fiber-optic microwave/millimeter wave processing systems. In this paper, two novel passive tunable all-optical microwave filters based on fiber loop and chirped fiber Bragg gratings (CFBGs) are demonstrated, where the frequency response of the both filters can be continuously tuned by adjusting the wavelength of the input light. The required free spectral range (FSR) of the filters can be obtained by carefully controlling the length of fiber loop and the positions of the CFBGs in the fiber loop. Experimental results prove the feasibility of the proposed filtering structures.     

Processes limiting the rate of response in photorefractive composites

The processes limiting the rate of response of highly diffractive, reorientationally enhanced photorefractive polymer composite materials are identified from a series of degenerate four wave mixing and Mach–Zehnder interferometric measurements. In the regime of low intensity writing beams charge generation limits the rate of holographic grating formation, but at higher intensities charge transport or reorientation of dye molecules can restrict the rate of grating formation more strongly. A grating risetime of 540 ms is observed in a composite of high dye content with high reorientational mobility of the dye molecules. In this case it is proposed that the charge carrier mobility of the doped poly(N-vinylcarbazole):2,4,7-trinitro-9-fluorenone (PVK:TNF) matrix is the principal limiting factor in grating response rates.