Search results for: LP-Sasakian manifolds

Authors: Erhan Ata, H. Hilmi Hacisalihoğlu, Yusuf Yayli

Abstract:

In this work some characterizations of semi Riemannian curvature tensor on almost split quaternion Kaehler manifolds and some characterizations of Ricci tensor on almost split quaternion Kaehler manifolds are given.

Keywords: Almost split quaternion Kaehler manifold, Riemann curvature, Ricci curvature.

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Authors: Jay Prakash Singh

Abstract:

The aim of the present paper is to study properties of Quasi conformally flat LP-Sasakian manifolds with a coefficient α. In this paper, we prove that a Quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α is an η−Einstein and in a quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α if the scalar curvature tensor is constant then M is of constant curvature.

Keywords: LP-Sasakian manifolds, coefficient α, quasi conformal curvature tensor, concircular vector field, torse forming vector field, η-Einstein manifold.

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Authors: Lina Wu, Ye Li, Jia Liu

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We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in L^q space to infinite in non-L^q space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.

Keywords: Differential Forms, Hölder Inequality, Liouville-type problems, p-balanced growth, p-harmonic maps, q-energy growth, tests for series.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

In this paper presents a technique for developing the computational efficiency in simulating double output induction generators (DOIG) with two rotor circuits where stator transients are to be included. Iterative decomposition is used to separate the flux– Linkage equations into decoupled fast and slow subsystems, after which the model order of the fast subsystems is reduced by neglecting the heavily damped fast transients caused by the second rotor circuit using integral manifolds theory. The two decoupled subsystems along with the equation for the very slowly changing slip constitute a three time-scale model for the machine which resulted in increasing computational speed. Finally, the proposed method of reduced order in this paper is compared with the other conventional methods in linear and nonlinear modes and it is shown that this method is better than the other methods regarding simulation accuracy and speed.

Keywords: DOIG, Iterative separation, Integral manifolds, Reduced order.

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Authors: M. Zamurad Shah, M. Kemal Özgören, Raza Samar

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This paper presents a 3D guidance scheme for Unmanned Aerial Vehicles (UAVs). The proposed guidance scheme is based on the sliding mode approach using nonlinear sliding manifolds. Generalized 3D kinematic equations are considered here during the design process to cater for the coupling between longitudinal and lateral motions. Sliding mode based guidance scheme is then derived for the multiple-input multiple-output (MIMO) system using the proposed nonlinear manifolds. Instead of traditional sliding surfaces, nonlinear sliding surfaces are proposed here for performance and stability in all flight conditions. In the reaching phase control inputs, the bang-bang terms with signum functions are accompanied with proportional terms in order to reduce the chattering amplitudes. The Proposed 3D guidance scheme is implemented on a 6-degrees-of-freedom (6-dof) simulation of a UAV and simulation results are presented here for different 3D trajectories with and without disturbances.

Keywords: Unmanned Aerial Vehicles, Sliding mode control, 3D Guidance, Path following, trajectory tracking, nonlinear sliding manifolds.

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Authors: Mohamed Gouskir, Belaid Bouikhalene, Hicham Aissaoui, Benachir Elhadadi

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In this paper, we present an application of Riemannian geometry for processing non-Euclidean image data. We consider the image as residing in a Riemannian manifold, for developing a new method to brain edge detection and brain extraction. Automating this process is a challenge due to the high diversity in appearance brain tissue, among different patients and sequences. The main contribution, in this paper, is the use of an edge-based anisotropic diffusion tensor for the segmentation task by integrating both image edge geometry and Riemannian manifold (geodesic, metric tensor) to regularize the convergence contour and extract complex anatomical structures. We check the accuracy of the segmentation results on simulated brain MRI scans of single T1-weighted, T2-weighted and Proton Density sequences. We validate our approach using two different databases: BrainWeb database, and MRI Multiple sclerosis Database (MRI MS DB). We have compared, qualitatively and quantitatively, our approach with the well-known brain extraction algorithms. We show that using a Riemannian manifolds to medical image analysis improves the efficient results to brain extraction, in real time, outperforming the results of the standard techniques.

Keywords: Riemannian manifolds, Riemannian Tensor, Brain Segmentation, Non-Euclidean data, Brain Extraction.

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Authors: Sameerah Jamal, Abdul Hamid Kara, Ashfaque H. Bokhari

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Equations on curved manifolds display interesting properties in a number of ways. In particular, the symmetries and, therefore, the conservation laws reduce depending on how curved the manifold is. Of particular interest are the wave and Gordon-type equations; we study the symmetry properties and conservation laws of these equations on the Milne and Bianchi type III metrics. Properties of reduction procedures via symmetries, variational structures and conservation laws are more involved than on the well known flat (Minkowski) manifold.

Keywords: Bianchi metric, conservation laws, Milne metric, symmetries.

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Authors: Guy Rosman, Alexander M. Bronstein, Michael M. Bronstein, Ron Kimmel

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We present a new algorithm for nonlinear dimensionality reduction that consistently uses global information, and that enables understanding the intrinsic geometry of non-convex manifolds. Compared to methods that consider only local information, our method appears to be more robust to noise. Unlike most methods that incorporate global information, the proposed approach automatically handles non-convexity of the data manifold. We demonstrate the performance of our algorithm and compare it to state-of-the-art methods on synthetic as well as real data.

Keywords: Dimensionality reduction, manifold learning, multidimensional scaling, geodesic distance, boundary detection.

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Authors: Erhan Ata, Yusuf Yaylı

Abstract:

Let M be an almost split quaternionic manifold on which its almost split quaternionic structure is defined by a three dimensional subbundle V of ( T M) T (M) * Ôèù and {F,G,H} be a local basis for V . Suppose that the (global) (1, 2) tensor field defined[V ,V ]is defined by [V,V ] = [F,F]+[G,G] + [H,H], where [,] denotes the Nijenhuis bracket. In ref. [7], for the almost split-hypercomplex structureH = J α,α =1,2,3, and the Obata connection ÔêçH vanishes if and only if H is split-hypercomplex. In this study, we give a prof, in particular, prove that if either M is a split quaternionic Kaehler manifold, or if M is a splitcomplex manifold with almost split-complex structure F , then the vanishing [V ,V ] is equivalent to that of all the Nijenhuis brackets of {F,G,H}. It follows that the bundle V is trivial if and only if [V ,V ] = 0 .

Keywords: Almost split - hypercomplex structure, Almost split quaternionic structure, Almost split quaternion Kaehler manifold, Obata connection.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

Due to the increasing penetration of wind energy, it is necessary to possess design tools that are able to simulate the impact of these installations in utility grids. In order to provide a net contribution to this issue a detailed wind park model has been developed and is briefly presented. However, the computational costs associated with the performance of such a detailed model in describing the behavior of a wind park composed by a considerable number of units may render its practical application very difficult. To overcome this problem integral manifolds theory has been applied to reduce the order of the detailed wind park model, and therefore create the conditions for the development of a dynamic equivalent which is able to retain the relevant dynamics with respect to the existing a.c. system. In this paper integral manifold method has been introduced for order reduction. Simulation results of the proposed method represents that integral manifold method results fit the detailed model results with a higher precision than singular perturbation method.

Keywords: Wind, Reduced Order, Integral Manifold.

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Authors: Gabriel I. Loaiza O., Carlos A. Cadavid M., Juan C. Arango P.

Abstract:

It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ = −1/2 , as does the family of usual Gaussian distributions. In the present paper, firstly we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ1, θ2; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the Inverse q−Gaussian distribution family (q < 3), as the family obtained by replacing the usual exponential function by the Tsallis q−exponential function in the expression for the Inverse Gaussian distribution, and observe that it supports two possible geometries, the Fisher and the q−Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q−Fisher geometry of the Inverse q−Gaussian distribution family, similar to the ones obtained in the case of the Inverse Gaussian distribution family.

Keywords: Base of Changes, Information Geometry, Inverse Gaussian distribution, Inverse q-Gaussian distribution, Statistical Manifolds.

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