We have two concepts of Douglas spaces and Landsberg spaces as generalizations of Berwald spaces. S. Bacso  gave the definition of a weakly-Berwald space as another generalization of Berwald spaces. In 1972, M. Matsumoto has introduced the concept of (α, β)-metric, which is a Finsler meric, contstructed from a Riemannian metric and a differential 1-form. In this paper, we study an important class of (α, β)-metrics in the form L = , known as second approximate Matsumoto metric on an n-dimensional manifold and get the conditions for such metrics to be weakly-Berwald metrics, where α = is a Riemannian metric and β = biyi is a 1-form. A Finsler space with an (α,β)-metric is a weakly-Berwald space, if and only if is a 1-form. We show that it becomes a weakly Berwald space under some geometric and algebraic conditions.
In this paper a Volterra – Hammerstein integral equation (V-HIE), with two continuous kernels of position k (x, y) and of time F(t,T) , is considered in the Banach space C ([0,1] x [0,T]), T < 1. The existence of a unique solution of the V-HIE, is discussed and proved. A quadratic numerical method is used to obtain a system of Hammerstein integral equations (SHIEs) in position and the existence of a unique solution of the SHIEs, under certain conditions, is proved. Moreover, we use two different methods, quadratic method (QM) and Simpson's rule (SR), to transform, in each method, the SHIEs into a nonlinear algebraic system (NAS). In addition, the existence of a unique solution of each algebraic system is guaranteed and proved. The Adomian decomposition method (ADM) is used to solve SHIEs without having to convert the system to a linearity. Finally, some applications contain numerical results, in some different time, are calculated and the error estimate, in each case, is computed.
In this paper we discuss all the CBIR technique and analysis the methods. We also compare all the feature extraction techniques in the tabular form. Color features are extracted with the help of color moments, color histogram, invariant color histogram, and dominant color. Color based CBIR technique there are limitations in the mention method in the table. So we decide to enhance the color based method in the content based image retrieval method. We analysis the all color based method which is used in the proposed method by authors. But color classification methods are not discussed in the above methods. So in the CBIR system if we used the color classification method based on the red, green and blue channel. We easily get the object as well as color. And we also studied various texture and shape based technique that is used by many authors in our research. Texture based various techniques are Gray Level Co-occurrence matrix (GLCM), Gabor Transform and Tamura Features. Texture descriptor provides a measure of properties such as smoothness, roughness, and regularity. The texture of the region is structural, statistical and spectral are three principal approaches used in image processing. Shape features are extracted using many approaches like as Histogram of Edge Directions, Region Moments, invariant Moments, Zernike moments, Legendre Moments.
Feature extraction and feature selection place an important role in online character recognition and as procedure in choosing the relevant feature that yields minimum classification error. Character recognition has been a good research area for many years because of its potential applications in all the fields. However, most existing classifiers used in recognizing online handwritten characters suffer from poor selection of features and slow convergence which affect recognition accuracy. A genetic algorithm was modified through its fitness function and genetic operators to minimize the character recognition errors. In this paper Modified Genetic Algorithm (MGA) was used to select optimized feature subset of the character to extract discriminant features for classification task. Some of research works have tried to improve online character recognition and their works were based on learning rate and error adjustment which slow down the training process. Thus, to alleviate this problems, a genetic based neural network model was developed using MGA to optimize an existing Modified Optical Backpropagation (MOBP) neural network. Two classifiers (C1 and C2) were formulated from MGA-MOBP such that C1 classified using MGA at classification level while C2 employed MGA at both feature selection level and classification level. The experiment results showed that the developed C2 achieved a better performance with no recognition failure and 99.44 recognition accuracy.
Oscillatory blood flow in convergent and divergent channels is investigated. The problem which involves a set of non-linear differential equations is handled analytically using the method of regular perturbation series solutions. Solutions are obtained for the velocities, pressure and wall shear stress, and are analyzed graphically. It is found that the variations in the pulse amplitude and height of constriction reduce the axial velocity and pressure but increase the radial velocity and wall shear stress. More so, it is observed that flow separation occurs in the radial velocity and pressure structures in the convergent and divergent regions respectively, when the height of the constriction are varied.
In this paper, the Vaisman-Gray manifolds with flat projective curvature tensor are investigated. It is shown that which conditions are necessary for a Vaisman-Gray manifold with flat projective curvature tensor is a nearly Kaehler (NK) manifold, a locally conformal Kahler (LCK) manifold and an Einstein manifold. Finally, The relation between certain two special classes of almost Hermitian manifold with respect to the projective tensor has been studied.