Variable mesh finite difference method of fifth Order have been derived for solution of Singular two point boundary Value problem, which reduces to the method of Order six, for uniform mesh case. These methods are self starting and are exact for u=r-1. The convergence of the sixth Order method is discussed. The absolute error, for solution of four problems, two linear and two nonlinear are listed to show the accurate and effectiveness of the present method.

In this paper, a steganography technique for JPEG 2000 compressed images using Singular Value Decomposition (SVD) in wavelet transform domain is proposed. In this technique, discrete wavelet transform (DWT) is applied on the cover image to get wavelet coefficients and Singular Value Decomposition is applied on these wavelet coefficients to get their Singular Values. Secret data bits are embedded into these Singular Values using scaling factor. Different compression rates are also considered for JPEG 2000 images after embedding the secret images. Genetic algorithm (GA) is used to optimize the Value of scaling factor (SF). Maximum capacity of the proposed technique is 25% of cover image size and maximum peak signal to noise ratio (PSNR) Values between cover and its stego image is more than the PSNR of existing techniques. Embedding capacity of proposed technique is also Higher than the embedding capacity of existing techniques. Also, PSNR between secret image and extracted image is High and hence the visual quality of the extracted secret image is good enough to the human visual system. Steg analysis tests are performed on the stego images to show imperceptibility of proposed technique.

Different methods are used for the formation of the null basis matrix of a structure followed by calculating the element forces when the force method of structural analysis is utilized. Singular Value Decomposition (SVD) method is one of the algebraic methods in force method that uses equilibrium matrix in its computation of finding element forces. By increasing the dimensions of the equilibrium matrix in large scale structures, the time needed for making orthogonal matrices grows. In recent decades many researchers have worked on block-diagonalization of structural matrices such as stiffness matrix in symmetric structures to reduce the computational time and simplify the equations. Block-diagonalization of equilibrium matrix can also reduce the computational time in algebraic force methods. In this paper block-diagonalization of equilibrium matrices of circulant structure is performed using Kronocker product and SVD method is utilized to calculate the block-diagonalization null basis matrix. Finally the results are compared to those of the method without block-diagonalization and other algebraic methods.

Disguised face recognition is a major challenge in the field of face recognition which has been taken less attention. Therefore, in this paper a disguised face recognition algorithm based on Local Phase Quantization (LPQ) method and Singular Value Decomposition (SVD) is presented which deals with two main challenges. The first challenge is when an individual intentionally alters the appearance by using disguise accessories, and the second one is when gallery images are limited for recognition. LPQ has been used for extraction of the statistical feature of the phase in windows with different sizes for each pixel of the image. SVD is used to cope with the challenge of the gallery images limitation and also with the help of original images extracted from that, every single image turns to three renovated images. In this study, disguise is intended as a blur in the image and Local phase quantization method is robust against the disguised mode, due to the use of the statistical feature of the Fourier transform phase. Also the use of different-sized window instead of fixed window in feature extraction stage, the performance of the proposed method has increased. The distance of images from each other is computed by using Manhattan and Euclidean distance for recognition in the proposed method. The Performance of the proposed algorithm has been evaluated by using three series of experiments on two real and synthesized databases. The first test has been performed by evaluating all the possible combinations of the different sized windows created in the feature extraction stage, and the second experiment has been done by reducing the number of gallery images and then the third one has been carried out in different disguise. In all cases, the proposed method is competitive with to several existing well-known algorithms and when there is only an image of the person it even outperforms them.

In this paper we characterize di erent classes of matrices in Minkowski space M by generalizing the Singular Value Decomposition in terms of m-projectors. Furthermore, we establish results on the relation between the range spaces and rank of the range disjoint matrices by utilizing the Singular Value Decomposition obtained in terms of m-projectors. Since there is no result on the formulation of Minkowski inverse of the sum of two matrices, we have established an expression for the Minkowski inverse of the sum of a range disjoint matrix with its Minkowski adjoint, which will ease to formulate an expression for the Minkowski inverse of the sum of two matrices in general case.

Introduction: Brain visual evoked potential (VEP) signals are commonly known to be accompanied by High levels of background noise typically from the spontaneous background brain activity of electroencephalography (EEG) signals. Material and Methods: A model based on dyadic filter bank, discrete wavelet transform (DWT), and Singular Value Decomposition (SVD) was developed to analyze the raw data of visual evoked potentials and extract time-locked signals with external visual stimulation. A bio-amplifier (iERG 100P) and data acquisition system (OMB-DAQ-3000) were utilized to record EEG raw data from the human scalp. MATLAB Data Acquisition Toolbox, Wavelet Toolbox, and Simulink model were employed to analyze EEG signals and extract VEP responses. Results: Results were verified in Simulink environment for the real recorded EEG data. The proposed model allowed precise Decomposition and classification of VEP signals through the combined operation of DWT and SVD. DWT was successfully used for the Decomposition of VEP signals to different frequencies followed by SVD for feature extraction and classification. Conclusion: The visual and quantitative results indicated that the impact of the proposed technique of combining DWT and SVD was promising. Combining the two techniques led to a two-fold increase in the impact of peak signal to noise ratio of all the tested signals compared to using each technique individually.