Lower Andupper Research Articles

WELL ORDERED MONOTONE ITERATIVE TECHNIQUE FOR NONLINEAR SECOND ORDER FOUR POINT DIRICHLET BVPS

In this article, we develop a monotone iterative technique (MI-technique) with lower and upper (L-U) solutions for a class of four-point Dirichlet nonlinear boundary value problems (NLBVPs), defined as, ... where ..., ... the non linear term ...is continuous function in x, one sided Lipschitz in ψ and Lipschitz in . To show the existence result, we construct Green’s function and iterative sequences for the corresponding linear problem. We use quasilinearization to construct these iterative schemes. We prove maximum principle and establish monotonicity of sequences of lower solution and upper solution such that... Then under certain sufficient conditions we prove that these sequences converge uniformly to the solution ψ(x) in a specific region where

A color image watermarking framework for copyright protection of stereo images based on binocular just noticeable difference and LU decomposition

The copyright protection of three-dimensional (3D) content is a matter of interest in artistic and creative works due to the rights of the holder for the distribution of the material. However, although stereo images are widely used for the generation of 3D content, there is a little amount of research focused on copyright protection for this type of image. In this study, a novel invisible and blind color image watermarking framework for protecting the copyright of the stereo images based on Binocular Just Noticeable Difference (BJND) and lower-and-upper (LU) decomposition is proposed. In this framework, a color watermark is encoded to reduce the information. Then, the BJND model is calculated in the R channel of a stereo image, and finally, LU decomposition is applied into the G and B channels to embed and extract a color watermark. The BJND model has demonstrated a remarkable sensitivity comparable with the Human Visual System (HVS) in luminance changes such as the ones presented in stereo images, guaranteeing a good protection performance and a high imperceptibility. The proposed framework was compared with other state-of-the-art techniques, and it has demonstrated better performance and high resistance to attacks of JPEG compression or impulsive and Gaussian noise. Additionally, this novel framework does not affect the generation of the disparity map or the 3D content when the watermarked stereo images are used for their creation.

ADD, TDA, Cıvıltı-z ve AÜ Ayrıştırma kullanarak Sağlam Görüntü Filigranı Oluşturma

The exponential increase of multimedia technologies usage has made connectivity simpler, more convenient and quicker, but has also contributed to a number of infringements of digital content. Digital watermarking has been known to offer a solution to compliance issues related to copyright infringements in multimedia technology. This paper proposes a robust approach to image watermarking by integrating the benefits of all four algorithms. The proposed method is based on discrete wavelet transform (DWT), chirp z-transform (CZT), lower and upper (LU) decomposition and singular decomposition value (SVD). In this method, using 1-level DWT, the image is broken down into its frequency sub-bands. The LL sub-band is then converted into a z domain using CZT. LU decomposition was then used to further decompose the image into two matrixes, each of which was used to insert the watermark. SVD has been applied to each of the matrixes and the unique value of the watermark is inserted to the matrixes of the decomposed image. The robustness and imperceptibility of the proposed solution was tested by checking the watermarked image for various image processing operations. Experimental findings show that the proposed technique has high imperceptibility capability and it shows a reasonable level of robustness against signal processing operations such as filtering, scaling, JPEG, rotating, gamma correction, blurring, cropping, gaussian noise, contrast enhancement, histogram equalization, and salt & pepper noise.

Direct Solution of Finite Element-Boundary Integral System for Electromagnetic Analysis in Half-Space

An efficient direct solution scheme is presented to solve the finite element-boundary integral (FEBI) system for the analysis of open-region electromagnetic problems in half-space. Data-sparse representation based on hierarichal (H-) matrix is employed to construct the direct solution framework. The FEBI system matrix is first represented to be an H-matrix form, in which the FE submatrices are accurately represented by H-matrices, while the H-matrix approximations of the BI submatrices are constructed by the adaptive cross approximation algorithm combined with singular value decomposition recompression (ACA-SVD). Based on the data-sparse formatted algorithm, the lower and upper (LU) triangular factors of the FEBI system matrix can be computed and stores as H-matrix forms with low computational costs. The resulting method, refered to as the direct FEBI method (D-FEBI), is free of convergence problem and well-suited for multiple right-hand side (RHS) computations. The performance of the D-FEBI is examined by two examples of monostatic electromagnetic scattering above a lossy half-space.

FER Performance Analysis and Optimization of Diagonal Structure Based QC-LDPC Codes with Girth 12 Using LU Decomposition

The manuscript presents the construction of a diagonally structured Parity check matrix using lower and upper (LU) decomposition for regular Quasi Cyclic-Low Density Parity Check Codes (QC-LDPC) with girth 12. This diagonally structured parity check matrix reduces the sparsity characteristics of QC-LDPC codes. The regular Quasi Cyclic-LDPC code has been constructed using circulant shifting and randomization method in which uniform distribution of non-zero elements, XOR operation, and pairing of row and column has been done. A Simplified Log Domain Sum-Product Algorithm (SLDSPA) is used for the decoding of the constructed code. To reduce the CPU run time of the constructed code, a column-wise loop optimization technique is applied. The frame error rate and CPU run time is calculated for different code lengths such as code1 (816, 408), code2 (1008, 504), code3 (1032, 516), code4 (1944, 972), code5 (672, 336) and code6 (504, 252). The construction of regular QC-LDPC codes on half code rate is obtained for the weight of each row is 6 and each column is given by 3. The results showing that the constructed code is better performing in terms of Low FER (10−1 to 10−7), Low SNR (0 to 3.5 dB) and Less CPU run time in milliseconds.

Pumping optimization of coastal aquifers using probabilistic search – case study: Quaternary aquifer of El-Arish Rafah, Egypt

Abstract The increased pumping of freshwater from coastal aquifers, to meet growing demands, causes an environmental problem called saltwater intrusion. Consequently, proper management schemes are necessary to tackle such a situation and permit the optimal development of coastal groundwater basins. In this research, a probabilistic search algorithm, namely Probabilistic Global Search Lausanne (PGSL), is used to calculate optimal pumping rates of unconfined coastal aquifer. The results of using PGSL are compared with a stochastic search optimization technique, Shuffled Frog Leaping Algorithm (SFLA). The finite element method is applied to simulate the hydraulic response of the steady state homogenous aquifer. The lower and upper (LU) decomposition method is adapted to invert the conductance matrix, which noticeably decreases the computation time. The results of both the PGSL and the SFLA are verified through the application on the aquifer system underlying the City of Miami Beach in the north of Spain. Multiple independent optimization runs are carried out to provide more insightful comparison outcomes. Consequently, a statistical analysis is performed to assess the performance of each algorithm. The two optimization algorithms are then applied on the Quaternary aquifer of El-Arish Rafah area, Egypt. The results show that both algorithms can effectively be used to obtain nearly global solutions compared with other previous published results.

Topological structures of a type of granule based covering rough sets

Rough set theory is one of important models of granular computing. Lower and upper approximation operators are two important basic concepts in rough set theory. The classical Pawlak approximation operators are based on partition and have been extended to covering approximation operators. Covering is one of the fundamental concepts in the topological theory, then topological methods are useful for studying the properties of covering approximation operators. This paper presents topological properties of a type of granular based covering approximation operators, which contains seven pairs of approximation operators. Then, topologies are induced naturally by the seven pairs of covering approximation operators, and the topologies are just the families of all definable subsets about the covering approximation operators. Binary relations are defined from the covering to present topological properties of the topological spaces, which are proved to be equivalence relations. Moreover, connectedness, countability, separation property and Lindel?f property of the topological spaces are discussed. The results are not only beneficial to obtain more properties of the pairs of covering approximation operators, but also have theoretical and actual significance to general topology.

A new approach of nonblind watermarking methods based on DWT and SVD via LU decomposition

Multimedia security has been the focal point of considerable research activity in the last decade, mainly because of its wide application area. Watermarking, in particular, is identified as a major technology to achieve copyright protection and multimedia security. Therefore, recent studies in the literature include some evident approaches for embedding data into a multimedia element. Because of its useful frequency component separation, the discrete wavelet transform (DWT) is commonly used in watermarking schemes. Moreover, singular value decomposition (SVD) and lower-and-upper (LU) decomposition have little effect on the perception of the watermark. Therefore, in this study, a combination of DWT and SVD via LU decomposition is proposed as a new nonblind watermarking algorithm that requires cover work to detect the watermark. Experimental results show that the proposed algorithm is considerably robust and reliable against certain attacks without degrading the input image, by embedding a binary watermark on the low-low band. Moreover, the threshold values are data-dependent for watermarks after attacks; that is, the threshold value is always different from another for certain attacks so that similarity ratios in this algorithm, as a quality metric, are much more than those of the other algorithms consisting of DWT and/or SVD despite strong attacks causing lower peak signal-to-noise ratio values. Apart from robustness, reliability, and data-dependence, the other novel aspect of this study is to expand the application areas of watermarking with a new algorithm consisting of DWT, LU, and SVD, and this study will contribute to the literature for certain cases.

Dimension estimates in non-conformal setting

Given an arbitrary subset of a non-conformal repeller of a $C^1$ map. Using directly the definitions of Hausdorff dimension and Box dimension and of pressure, this paper first proves that the zeros of the topological pressure on this set give its dimension estimates. And without using the estimate of pointwise dimension of an ergodic measure on a non-conformal repeller, it is showed that the zeros of non-additive measure-theoretic pressure give the lower and upper bound of dimension estimate for it. Some results from [22,41] are extended for $C^1$ maps or arbitrary subsets of a non-conformal repeller. And a remark on Rugh's result [34] is also given in this paper.

Forced Consensus of Multi-Agent Systems with Directed Communication Topology and Interval Time-Varying Delay

This paper is concernedwith forced consensus problem for directed multi-agent systems with intervaltime-varying delay, whereall agents approach a constant reference trajectory under the condition thatonly a subset of the agents can receive information from the reference state. Thetime-varying delay is assumed to belong to an interval with known lower andupper bounds, but its lower bound may be greater than zero. We first propose a consensusalgorithm that extends the existing results in the literature to account forinterval time-varying delay. Then, the consensus stability analysis isconducted by introducing an appropriate Lyapunov-Krasovskii functional and using Jensen inequalitytechnique. A delay-range-dependentstability criterion is derived in terms of linear matrixinequalities, which can be efficiently solved by the interior-point algorithm.Finally, simulation examples indicatethe capabilities of the proposed algorithm.

Introducing Doolittle multivariate calibration algorithm for infrared spectrometric determination of STTP, SS, and SC in Iranian washing powder

The basic principle of Doolittle multivariate calibration algorithm (DMCA) was investigated and used for simultaneous quantitative determination of sodium tripolyphosphate (STPP), sodium sulfate (SS), and sodium carbonate (SC) in commercial washing powders with serious overlapping. The process of the Doolittle decomposition algorithm (DDA) is implemented by lower and upper (LU) triangular matrix decomposition which is robust and convenient. Then it was applied to overcome the problem of overlapping spectra of different components in the detergent washing powder. The root mean square error of prediction (RMSEP) for DMCA is 0.084 which confirms the improvement in accuracy, in comparison with K-Matrix (KM) (RMSEP=0.118). It was demonstrated that DDA can avoid matrix inverting, reduce the orders of matrices, and needs a little time for analysis. Therefore, it has bright prospects in chemometrics and it is feasible that the Doolittle algorithm could be applied to the practical determinations in real samples with spectral overlapping.

Pivoting Strategies in the Solution of the Saint-Venant Equations

Pivoting was incorporated in the process of solving the linear system of equations that results after discretizing the Saint- Venant equations using the four-point implicit scheme, and applying the Newton–Raphson algorithm to the resulting set of nonlinear equations. Both exchange of rows only (partial pivoting) and exchange of rows and columns (full pivoting) were investigated using the CanalMan hydraulic model. Partial pivoting was used with the LU (lower and upper) decomposition linear equation solver, whereas full pivoting was used with the Gauss–Jordan elimination algorithm. It was demonstrated that the application of partial and full pivoting to the solution of the linear set of equations during Newton–Raphson iterations can make the difference between convergence and divergence of the solution, and should be applied as needed. However, full pivoting should be used only when needed because it slows the simulation considerably.

An algorithm for decomposing a class of matrices into lower and upper triangular matrices

A fast and computationally effecient algorithm for decomposing a class of matrices into a product of lower and upper (LU) triangular matrices is introduced. The class of matrices considered is almost tridiagonal with the exception being that the upper rightmost element and lower leftmost element are nonzero.