Search results for: Hadamard matrix

Authors: Zhouji Chen

Abstract:

In this paper, the modified Gauss-Seidel method with the new preconditioner for solving the linear system Ax = b, where A is a nonsingular M-matrix with unit diagonal, is considered. The convergence property and the comparison theorems of the proposed method are established. Two examples are given to show the efficiency and effectiveness of the modified Gauss-Seidel method with the presented new preconditioner.

Keywords: Preconditioned linear system, M-matrix, Convergence, Comparison theorem.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1507

Authors: Arti Vaish, Harish Parthasarathy

Abstract:

In this paper, a novel wave equation for electromagnetic waves in a medium having anisotropic permittivity has been derived with the help of Maxwell-s curl equations. The x and y components of the Maxwell-s equations are written with the permittivity () being a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey, Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z components of the Maxwell-s curl are then used to arrive to the generalized Helmholtz equations for Ez and Hz.

Keywords: Electromagnetism, Maxwell's Equations, Anisotropic permittivity, Wave equation, Matrix Equation, Permittivity tensor.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1706

Authors: Qinyi Mei, Li-Ping Wang

Abstract:

MDS matrices are of great significance in the design of block ciphers and hash functions. In the present paper, we investigate the problem of constructing MDS matrices which are both lightweight and low-latency. We propose a new method of constructing lightweight MDS matrices using circulant matrices which can be implemented efficiently in hardware. Furthermore, we provide circulant MDS matrices with as few bit XOR operations as possible for the classical dimensions 4 × 4, 8 × 8 over the space of linear transformations over finite field F42 . In contrast to previous constructions of MDS matrices, our constructions have achieved fewer XORs.

Keywords: Linear diffusion layer, circulant matrix, lightweight, MDS matrix.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 855

Authors: Michal Polanský, C. Ardil

Abstract:

This paper shows a new method for design of fuzzy observers for Takagi-Sugeno systems. The method is based on Linear matrix inequalities (LMIs) and it allows to insert H constraint into the design procedure. The speed of estimation can tuned be specification of a decay rate of the observer closed loop system. We discuss here also the influence of parametric uncertainties at the output control system stability.

Keywords: H norm, Linear Matrix Inequalities, Observers, Takagi-Sugeno Systems, Parallel Distributed Compensation

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2543

Authors: S.K.Ayyaswamy, S.Balachandran

Abstract:

The Detour matrix (DD) of a graph has for its ( i , j) entry the length of the longest path between vertices i and j. The DD-eigenvalues of a connected graph G are the eigenvalues for its detour matrix, and they form the DD-spectrum of G. The DD-energy EDD of the graph G is the sum of the absolute values of its DDeigenvalues. Two connected graphs are said to be DD- equienergetic if they have equal DD-energies. In this paper, the DD- spectra of a variety of graphs and their DD-energies are calculated.

Keywords: Detour eigenvalue (of a graph), detour spectrum(of a graph), detour energy(of a graph), detour - equienergetic graphs.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1519

Authors: Nang Thwe Thwe Oo

Abstract:

Traditional object segmentation methods are time consuming and computationally difficult. In this paper, onedimensional object detection along the secant lines is applied. Statistical features of texture images are computed for the recognition process. Example matrices of these features and formulae for calculation of similarities between two feature patterns are expressed. And experiments are also carried out using these features.

Keywords: 1-D object segmentation, secant lines, objectoccurrence(frequency) matrix, contiguity matrix, statistical features.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1503

Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper examines the problem of designing a robust H∞ filter for a class of uncertain fuzzy descriptor systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor systems to have an H∞ performance are derived. To alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard uncertain nonlinear descriptor systems. A numerical example is provided to illustrate the design developed in this paper.

Keywords: H∞ control, Takagi-Sugeno (TS) fuzzy model, Linear Matrix Inequalities (LMIs), Descriptor systems.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1406

Authors: Chao Wang, Ting-Zhu Huang Chen Jia

Abstract:

In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.

Keywords: Bi-linear complementarity problem, Linear complementarity problem, Extended linear complementarity problem, Error estimation, P-matrix, M-matrix.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1730

Authors: Balwinder Singh

Abstract:

The present research is a paper on the characterization of aluminum alloy-6063 hybrid metal matrix composites using three different reinforcement materials (SiC, red mud, and fly ash) through stir casting method. The red mud was used in solid form, and particle size range varies between 103-150 µm. During this investigation, fly ash is received from Guru Nanak Dev Thermal Plant (GNDTP), Bathinda. The study has been done by using Taguchi’s L9 orthogonal array by taking fraction wt.% (SiC 5%, 7.5%, and 10% and Red Mud and Fly Ash 2%, 4%, and 6%) as input parameters with their respective levels. The study of the mechanical properties (tensile strength, impact strength, and microhardness) has been done by using Analysis of Variance (ANOVA) with the help of MINITAB 17 software. It is revealed that silicon carbide is the most significant parameter followed by red mud and fly ash affecting the mechanical properties, respectively. The fractured surface morphology of the composites using Field Emission Scanning Electron Microscope (FESEM) shows that there is a good mixing of reinforcement particles in the matrix. Energy-dispersive X-ray spectroscopy (EDS) was performed to know the presence of the phases of the reinforced material.

Keywords: Reinforcement, silicon carbide, fly ash, red mud.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 733

Authors: Hilal Adnan Fadhil, Syed Alwei, R. Badlishah Ahmad

Abstract:

A new code for spectral-amplitude coding optical code-division multiple-access system is proposed called Random diagonal (RD) code. This code is constructed using code segment and data segment. One of the important properties of this code is that the cross correlation at data segment is always zero, which means that Phase Intensity Induced Noise (PIIN) is reduced. For the performance analysis, the effects of phase-induced intensity noise, shot noise, and thermal noise are considered simultaneously. Bit-error rate (BER) performance is compared with Hadamard and Modified Frequency Hopping (MFH) codes. It is shown that the system using this new code matrices not only suppress PIIN, but also allows larger number of active users compare with other codes. Simulation results shown that using point to point transmission with three encoded channels, RD code has better BER performance than other codes, also its found that at 0 dbm PIIN noise are 10-10 and 10-11 for RD and MFH respectively.

Keywords: OCDMA, MFH, PIIN, and BER.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1790

Authors: H. Afer, N. Rouag, R. Penelle

Abstract:

In the Fe-3%Si sheets, grade Hi-B, with AlN and MnS as inhibitors, the Goss grains which abnormally grow do not have a size greater than the average size of the primary matrix. In this heterogeneous microstructure, the size factor is not a required condition for the secondary recrystallization. The onset of the small Goss grain abnormal growth appears to be related to a particular behavior of their grain boundaries, to the local texture and to the distribution of the inhibitors. The presence and the evolution of oriented clusters ensure to the small Goss grains a favorable neighborhood to grow. The modified Monte-Carlo approach, which is applied, considers the local environment of each grain. The grain growth is dependent of its real spatial position; the matrix heterogeneity is then taken into account. The grain growth conditions are considered in the global matrix and in different matrixes corresponding to A component clusters. The grain growth behaviour is considered with introduction of energy only, energy and mobility, energy and mobility and precipitates.

Keywords: Abnormal grain growth, grain boundary energy andmobility, neighbourhood, oriented clusters.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1374

Authors: M. Ghorbany

Abstract:

A square matrix over the complex field with non- negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful representation of G by quasi-permutation matrices over the rationals and the complex numbers are denoted by q(G) and c(G) respectively. Finally r (G) denotes the minimal degree of a faithful rational valued complex character of C. The purpose of this paper is to calculate q(G), c(G) and r(G) for the group S L(2, q) when extended by a certain group of order two.

Keywords: General linear group, Quasi-permutation

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1080

Authors: Baoguang Tian, Nan Chen

Abstract:

A new relative efficiency in linear model in reference is instructed into the linear weighted regression, and its upper and lower bound are proposed. In the linear weighted regression model, for the best linear unbiased estimation of mean matrix respect to the least-squares estimation, two new relative efficiencies are given, and their upper and lower bounds are also studied.

Keywords: Linear weighted regression, Relative efficiency, Mean matrix, Trace.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2477

Authors: Milan Hladik

Abstract:

The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.

Keywords: Linear interval systems, solution set, interval matrix, symmetric matrix.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1288

Authors: Mohamed Ali AlShaari, Khalid M. ElFitori

Abstract:

In the field of Quran Studies known as GHAREEB AL QURAN (The study of the meanings of strange words and structures in Holy Quran), it is difficult to distinguish some pragmatic meanings from conceptual meanings. One who wants to study this subject may need to look for a common usage between any two words or more; to understand general meaning, and sometimes may need to look for common differences between them, even if there are synonyms (word sisters).

Some of the distinguished scholars of Arabic linguistics believe that there are no synonym words, they believe in varieties of meaning and multi-context usage. Based on this viewpoint, our method was designedto look for synonyms of a word, then the differences that distinct the word and their synonyms.

There are many available books that use such a method e.g. synonyms books, dictionaries, glossaries, and some books on the interpretations of strange vocabulary of the Holy Quran, but it is difficult to look up words in these written works.

For that reason, we proposed a logical entity, which we called Differences Matrix (DM).

DM groups the synonyms words to extract the relations between them and to know the general meaning, which defines the skeleton of all word synonyms; this meaning is expressed by a word of its sisters.

In Differences Matrix, we used  the sisters(words) as titles for rows and columns, and in the obtained  cells we tried to define the row title (word) by using column title (her sister), so the relations between sisters appear, the expected result is well defined groups of sisters for each word. We represented the obtained results formally, and used the defined groups as a base for building the ontology of the Holy Quran synonyms.

Keywords: Quran, synonyms, Differences Matrix, ontology

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2116

Authors: Biao Qin, Jin Huang

Abstract:

In this paper, together with some improved Lyapunov-Krasovskii functional and effective mathematical techniques, several sufficient conditions are derived to guarantee the error system is globally asymptotically stable with H∞ performance, in which both the time-delay and its time variation can be fully considered. In order to get less conservative results of the state estimation condition, zero equalities and reciprocally convex approach are employed. The estimator gain matrix can be obtained in terms of the solution to linear matrix inequalities. A numerical example is provided to illustrate the usefulness and effectiveness of the obtained results.

Keywords: H∞ performance, Neural networks, State estimation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1446

Authors: Shazia Javed, Noor Atinah Ahmad

Abstract:

In this paper an efficient incomplete factorization preconditioner is proposed for the Least Mean Squares (LMS) adaptive filter. The proposed preconditioner is approximated from a priori knowledge of the factors of input correlation matrix with an incomplete strategy, motivated by the sparsity patter of the upper triangular factor in the QRD-RLS algorithm. The convergence properties of IPLMS algorithm are comparable with those of transform domain LMS(TDLMS) algorithm. Simulation results show efficiency and robustness of the proposed algorithm with reduced computational complexity.

Keywords: Autocorrelation matrix, Cholesky's factor, eigenvalue spread, Markov input.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1794

Authors: Sahil, Rajeev Saha, Sanjeev Kumar

Abstract:

Material selection is one of the key issues for the production of reliable and quality products in industries. A number of materials are available for a single product due to which material selection become a difficult task. The aim of this paper is to select appropriate material for gear used in fuel pump by using Graph Theory and Matrix Approach (GTMA). GTMA is a logical and systematic approach that can be used to model and analyze various engineering systems. In present work, four alternative material and their seven attributes are used to identify the best material for given product.

Keywords: Material, GTMA, MADM, digraph, decision making.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1030

Authors: C. B. Vishwakarma

Abstract:

The author presented a method for model order reduction of large-scale time-invariant systems in time domain. In this approach, two modified Hankel matrices are suggested for getting reduced order models. The proposed method is simple, efficient and retains stability feature of the original high order system. The viability of the method is illustrated through the examples taken from literature.

Keywords: Model Order Reduction, Stability, Hankel Matrix, Time-Domain, Integral Square Error.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2079

Authors: Lianglin Xiong, Xiuyong Ding, Shouming Zhong

Abstract:

In this paper, the problem of asymptotical stability of neutral systems with nonlinear perturbations is investigated. Based on a class of novel augment Lyapunov functionals which contain freeweighting matrices, some new delay-dependent asymptotical stability criteria are formulated in terms of linear matrix inequalities (LMIs) by using new inequality analysis technique. Numerical examples are given to demonstrate the derived condition are much less conservative than those given in the literature.

Keywords: Asymptotical stability, neutral system, nonlinear perturbation, delay-dependent, linear matrix inequality (LMI).

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1522

Authors: Yue Du, Sahan C. B. Herath, Qing-Guo Wang, Harry Asada, Peter C. Y. Chen

Abstract:

Mechanical interaction between endothelial cells (ECs) and the extracellular matrix (or collagen gel) is known to influence the sprouting response of endothelial cells during angiogenesis. This influence is believed to impact on the capability of endothelial cells to sense soluble chemical cues. Quantitative analysis of endothelial-cell-mediated displacement of the collagen gel provides a means to explore this mechanical interaction. Existing analysis in this context is generally limited to 2D settings. In this paper, we investigate the mechanical interaction between endothelial cells and the extracellular matrix in terms of the endothelial-cellmediated displacement of the collagen gel in both 2D and 3D. Digital image correlation and Digital volume correlation are applied on confocal reflectance image stacks to analyze cell-mediated displacement of the gel. The skeleton of the sprout is extracted from phase contrast images and superimposed on the displacement field to further investigate the link between the development of the sprout and the displacement of the gel.

Keywords: Angiogenesis, digital image correlation, digital volume correlation, interaction between ECs and ECM.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1720

Authors: Wang Xingbo

Abstract:

Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Keywords: Algorithm, determinant, computation, eigenvalue, time complexity.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1157

Authors: S. H. Lee, M. J. Park, O. M. Kwon

Abstract:

In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of such system are obtained by solving a set of Linear Matrix Inequalities (LMIs). One numerical example is included to show the effectiveness of the proposed criteria.

Keywords: Multi-agent, Linear Matrix Inequalities (LMIs), Kronecker Product, Sampled-Data, Lyapunov method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1747

Authors: Minghui Wang

Abstract:

Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.

Keywords: Matrix equation, bisymmetric matrix, least squares problem, like-minimum norm, iterative algorithm.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1495

Authors: M.Meskinfam, M. S. Sadjadi, H.Jazdarreh

Abstract:

In this study, we report the synthesis and characterization of nanohydroxyapatite (nHAp) in gelatin-starch matrix via biomimetic method. Characterization of the samples was performed using X-ray diffraction (XRD) and Fourier Transform infrared spectroscopy (FT-IR). The Size and morphology of the nHAp samples were determined using scanning and transmission electron microscopy (SEM and TEM). The results reveal that the shape and morphology of nHAp is influenced by presence of biopolymers as template. Carbonyl and amino groups from gelatin and hydroxyl from starch play crucial roles in HAp formation on the surface of gelatin-starch.

Keywords: Biocomposite, Biomimetic , Nano Hydroxyapatite , Template.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2604

Authors: Li Jiang, Baoguang Tian

Abstract:

In this paper, we present the preconditioned mixed-type splitting iterative method for solving the linear systems, Ax = b, where A is a Z-matrix. And we give some comparison theorems to show that the convergence rate of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give a numerical example to illustrate our results.

Keywords: Z-matrix, mixed-type splitting iterative method, precondition, comparison theorem, linear system.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1207

Authors: Mikko Mäkelä, Risto Pöykiö, Gary Watkins, Hannu Nurmesniemi, Olli Dahl

Abstract:

Trace element speciation of an integrated soil amendment matrix was studied with a modified BCR sequential extraction procedure. The analysis included pseudo-total concentration determinations according to USEPA 3051A and relevant physicochemical properties by standardized methods. Based on the results, the soil amendment matrix possessed neutralization capacity comparable to commercial fertilizers. Additionally, the pseudo-total concentrations of all trace elements included in the Finnish regulation for agricultural fertilizers were lower than the respective statutory limit values. According to chemical speciation, the lability of trace elements increased in the following order: Hg < Cr < Co < Cu < As < Zn < Ni < Pb < Cd < V < Mo < Ba. The validity of the BCR approach as a tool for chemical speciation was confirmed by the additional acid digestion phase. Recovery of trace elements during the procedure assured the validity of the approach and indicated good quality of the analytical work.

Keywords: BCR, bioavailability, trace element, industrialresidue, sequential extraction

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1845

Authors: Hong Li, Shou-ming Zhong, Hou-biao Li

Abstract:

In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.

Keywords: Interval fractional-order systems, linear matrix inequality (LMI), asymptotical stability.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3621

Authors: R. K. Z. Sahbudin, M. K. Abdullah, M. Mokhtar, S. B. A. Anas, S. Hitam

Abstract:

A subcarrier - spectral amplitude coding optical code division multiple access system using the Khazani-Syed code with Complementary subtraction detection technique is proposed. The proposed system has been analyzed by taking into account the effects of phase-induced intensity noise, shot noise, thermal noise and intermodulation distortion noise. The performance of the system has been compared with the spectral amplitude coding optical code division multiple access system using the Hadamard code and the Modified Quadratic Congruence code. The analysis shows that the proposed system can eliminate the multiple access interference using the Complementary subtraction detection technique, and hence improve the overall system performance.

Keywords: Complementary subtraction, Khazani-Syed code, multiple access interference, phase-induced intensity noise

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1744

Authors: Fadl M. Ba-Alwi, Kamal K. Bharadwaj

Abstract:

In this paper a novel algorithm is proposed that integrates the process of fuzzy hierarchy generation and rule discovery for automated discovery of Production Rules with Fuzzy Hierarchy (PRFH) in large databases.A concept of frequency matrix (Freq) introduced to summarize large database that helps in minimizing the number of database accesses, identification and removal of irrelevant attribute values and weak classes during the fuzzy hierarchy generation.Experimental results have established the effectiveness of the proposed algorithm.

Keywords: Data Mining, Degree of subsumption, Freq matrix, Fuzzy hierarchy.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1313