Non-Abelian Cohomology of Groups

Following Guin's approach to non-abelian cohomology [4] and, using the notion of a crossed bimodule, a second pointed set of cohomology is defined with coefficients in a crossed module, and Guin's six-term exact cohomology sequence is extended to a nine-term exact sequence of cohomology up to dimension 2     

A Novel Fabrication Technique of Long Period Fiber Gratings

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On Blocks with Nilpotent Coefficient Extensions

For modular group algebras over an arbitrary field we define new type of blocks: blocks with nilpotent extensions, and describe their source algebras. To do it, a general pattern is proposed for relations between the source algebra of a block and the source algebra of a block appearing in its decomposition in a suitable extension of the field of coefficients.     

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.

     

High frequency microwave signal generation using dual-wavelength emission of cascaded DFB fiber lasers with wavelength spacing tunability

A dual-wavelength fiber laser source based on two cascaded phase-shifted fiber Bragg gratings is presented. The gratings are written in an erbium-doped fiber, each configuring the cavity of a distributed feedback fiber laser. The spacing between lasing modes is controlled dynamically by the use of piezoelectric actuators. A continuous tuning range of 5-724 pm of the wavelength difference, which is equivalent to a photodetected 0.72-92 GHz range, is obtained. Efficient generation from the L to the W microwave and millimeter bands has been achieved by heterodyne photodetection of the dual-wavelength optical signal.     

Exact stationary-wave solutions in the standard model of the Kerr-Nonlinear optical fiber with the Bragg grating

By using dynamical system method to the standard model of the Kerr-Nonlinear optical fiber with the Bragg grating, under fixed parameter conditions, all possible exact parametric representations of the bounded stationary wave solutions are obtained from the double sine-Gordon equation.     

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.     

Simultaneous Measurement of Refractive Index and Temperature Using a Hybrid Fiber Bragg Grating/Long-Period Fiber Grating Configuration

Abstract

A fiber optic sensing system for simultaneous measurement of refractive index and temperature, based on a hybrid fiber Bragg grating/long-period grating arrangement is described. The experimental results show that this setup has a good performance in terms of linearity and sensitivity, the ratiometric output changes 4%/0.001 RIU and 3.6%/°C, respectively. The sensor resolution for the refractive index is ≈2 × 10^?5 RIU. The simultaneous measurement of the refractive index and temperature was demonstrated. The sensing configuration has the ability to be read-out in reflection and works in the telecommunications window.