Optical time-domain differentiation based on intensive differential group delay

An optical time-domain differentiation scheme is proposed and demonstrated based on the intensive differential group delay in a high birefringence fibre waveguide. Results show that the differentiation waveforms agree well with the mathematically calculated derivatives. Both error and efficiency will increase when the birefringence fibre becomes longer, and the error rises up more quickly while the efficiency approaches to a maximum of ~0.25. By using a 1-m birefringence fibre a lower error of ~0.26% is obtained with an efficiency of 1% for the first-order differentiation of 10-ps Gaussian optical pulses, and the high-order optical differentiation up to 4th order is achieved with an error less than 3%. Due to its compact structure being easy to integrate and cascade into photonic circuits, our scheme has great potential for ultrafast signal processing.

Generalized covariant differentiation and axiom-based tensor analysis

This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.

Feature Selection Using Grey Wolf Optimization with Random Differential Grouping

Big data are regarded as a tremendous technology for processing a huge variety of data in a short time and with a large storage capacity.The user’s access over the internet creates massive data processing over the internet.Big data require an intelligent feature selection model by addressing huge varieties of data.Traditional feature selection techniques are only applicable to simple data mining.Intelligent techniques are needed in big data processing and machine learning for an efficient classification.Major feature selection algorithms read the input features as they are.Then,the features are preprocessed and classified.Here,an algorithm does not consider the relatedness.During feature selection,all features are misread as outputs.Accordingly,a less optimal solution is achieved.In our proposed research,we focus on the feature selection by using supervised learning techniques called grey wolf optimization(GWO)with decomposed random differential grouping(DrnDG-GWO).First,decomposition of features into subsets based on relatedness in variables is performed.Random differential grouping is performed using a fitness value of two variables.Now,every subset is regarded as a population in GWO techniques.The combination of supervised machine learning with swarm intelligence techniques produces best feature optimization results in this research.Once the features are optimized,we classify using advanced kNN process for accurate data classification.The result of DrnDGGWO is compared with those of the standard GWO and GWO with PSO for feature selection to compare the efficiency of the proposed algorithm.The accuracy and time complexity of the proposed algorithm are 98%and 5 s,which are better than the existing techniques.

Novel Tunable PMD Compensation Technology Using Linear Chirped Fiber Bragg Grating

Based on uniform fiber Bragg grating bonded with a magnetostrictive rod in the non-uniform magnetic field,a novel PMD compensation technique is proposed.This all-fiber PMD compensation technology is cost-effective and flexible in designing the differential group delay profile.

Painlevé Property and Integrability of Polynomial Dynamical Systems

The main purpose of this paper is to investigate the connection between the Painlev′e property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has Painlev′e property, then it admits certain class of first integrals. We also present some relationships between the Painlev′e property and the structure of the differential Galois group of the corresponding variational equations along some complex integral curve.

High Differential Group Index of Dispersion Compensating Fibers for OCDMA Encoder/Decoder

We report the LPG pair device that can be used as a pulse duplicator or an OCDMA encoder/decoder. Due to the ring core region of dispersion compensating fiber (DCF), we can shorten the device length by a third and obtain surrounding insensitive LPG devices.

Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application

The Morales-Ramis theory provides an effective and powerful non-integrability criterion for complex analytic Hamiltonian systems via the differential Galoisian obstruction.In this paper,we give a new Morales-Ramis type theorem on the meromorphic Jacobi non-integrability of general analytic dynamical systems.The key point is to show that the existence of Jacobian multipliers of a nonlinear system implies the existence of common Jacobian multipliers of Lie algebra associated with the identity component.In addition,we apply our results to the polynomial integrability of Karabut systems for stationary gravity waves in finite depth.

Generalized Covariant Derivative with Respect to Time in Flat Space(Ⅰ):Eulerian Description

This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included:(a) the restricted covariant derivative with respect to time for Eulerian component is defined;(b) the postulate of the covariant form invariability in time field is set up;(c) the generalized covariant derivative with respect to time for generalized Eulerian component is defined;(d) the algebraic structure of the generalized covariant derivative with respect to time is made clear;(e) the covariant differential transformation group in time filed is derived. These progresses reveal the covariant form invariability of Eulerian space and time.

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Let X denote a complex analytic manifold, and let Aut(X) denote the space of invertible maps of a germ (X, a) to a germ (X, b); this space is obviously a groupoid; roughly speaking, a 'Lie groupoid' is a subgroupoid of Aut(X) defined by a system of partial differential equations.To a foliation with singularities on X one attaches such a groupoid, e.g. the smallest one whose Lie algebra contains the vector fields tangent to the foliation. It is called 'the Galois groupoid of the foliation'. Some examples are considered, for instance foliations of codimension one, and foliations defined by linear differential equations; in this last case one recuperates the usual differential Galois group.

Generalized Covariant Derivative with Respect to Time in Flat Space(Ⅱ):Lagrangian Description

The previous paper reported a new derivative in the Eulerian description in flat space—the generalized covariant derivative of generalized Eulerian component with respect to time. This paper extends the thought from the Eulerian description to the Lagrangian description:on the basis of the postulate of covariant form invariability in time field, we define a new derivative in the Lagrangian description in flat space—the generalized covariant derivative of generalized Lagrangian component with respect to time. Besides, the covariant differential transformation group is set up. The covariant form invariability of Lagrangian space-time is ascertained.