Search results for: metal matrix composites

Authors: M. Shirinbayan, J. Fitoussi, N. Abbasnezhad, A. Lucas, A. Tcharkhtchi

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Sheet Molding Compounds (SMCs) with special microstructures are very attractive to use in automobile structures especially when they are accidentally subjected to collision type accidents because of their high energy absorption capacity. These are materials designated as standard SMC, Advanced Sheet Molding Compounds (A-SMC), Low-Density SMC (LD-SMC) and etc. In this study, testing methods have been performed to compare the mechanical responses and damage phenomena of SMC, LD-SMC, and A-SMC under quasi-static and high strain rate tensile tests. The paper also aims at investigating the effect of an initial pre-damage induced by fatigue on the tensile dynamic behavior of A-SMC. In the case of SMCs and A-SMCs, whatever the fibers orientation and applied strain rate are, the first observed phenomenon of damage corresponds to decohesion of the fiber-matrix interface which is followed by coalescence and multiplication of these micro-cracks and their propagations. For LD-SMCs, damage mechanisms depend on the presence of Hollow Glass Microspheres (HGM) and fibers orientation.

Keywords: SMC, LD-SMC, A-SMC, HGM, damage.

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Authors: Taweechai Nuntawisuttiwong, Natasha Dejdumrong

Abstract:

Geometric modeling plays an important role in the constructions and manufacturing of curve, surface and solid modeling. Their algorithms are critically important not only in the automobile, ship and aircraft manufacturing business, but are also absolutely necessary in a wide variety of modern applications, e.g., robotics, optimization, computer vision, data analytics and visualization. The calculation and display of geometric objects can be accomplished by these six techniques: Polynomial basis, Recursive, Iterative, Coefficient matrix, Polar form approach and Pyramidal algorithms. In this research, the coefficient matrix (simply called monomial form approach) will be used to model polynomial rectangular patches, i.e., Said-Ball, Wang-Ball, DP, Dejdumrong and NB1 surfaces. Some examples of the monomial forms for these surface modeling are illustrated in many aspects, e.g., construction, derivatives, model transformation, degree elevation and degress reduction.

Keywords: Monomial form, rectangular surfaces, CAGD curves, monomial matrix applications.

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Authors: S. Madhu, V. V. Subba Rao

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In the implementation of Carbon Nanotube Reinforced Polymer matrix Composites in structural applications, deflection and stress analysis are important considerations. In the present study, a multi scale analysis of deflection and stress analysis of carbon nanotube (CNT) reinforced polymer composite plates is presented. A micromechanics model based on the Mori-Tanaka method is developed by introducing straight CNTs aligned in one direction. The effect of volume fraction and diameter of CNTs on plate deflection and the stresses are investigated using classical laminate plate theory (CLPT). The study is primarily conducted with the intention of observing the suitability of CNT reinforced polymer composite plates under static loading for structural applications.

Keywords: Carbon Nanotube, Micromechanics, Composite plate, Multi-scale analysis, Classical Laminate Plate Theory.

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Authors: M. T. Sichani, B. J. Pedersen, S. R. K. Nielsen

Abstract:

Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper an empirical cross spectral density function for the along-wind turbulence component over the wind field area is taken as the starting point. The spectrum is spatially discretized in terms of a Hermitian cross-spectral density matrix for the turbulence state vector which turns out not to be positive definite. Since the succeeding state space and ARMA modelling of the turbulence rely on the positive definiteness of the cross-spectral density matrix, the problem with the non-positive definiteness of such matrices is at first addressed and suitable treatments regarding it are proposed. From the adjusted positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modelling method is proposed which allows selection of an appropriate model order, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modelling method.

Keywords: Turbulence, wind turbine, complex coherence, state space modelling, ARMA modelling.

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Authors: Justina I. R. Udotong

Abstract:

Diagnostic enzymes like aspartate aminotransferase (AST), alanine aminotransferase (ALT) and alkaline phosphatase (ALP) were determined as indices of heavy metal pollution in Tilapia guinensis. Three different sets of fishes treated with lead (Pb), iron (Fe) and copper (Cu) were used for the study while a fourth group with no heavy metal served as a control. Fishes in each of the groups were exposed to 2.65mg/l of Pb, 0.85mg/l of Fe and 0.35 mg/l of Cu in aerated aquaria for 96 hours. Tissue fractionation of the liver tissues was carried out and the three diagnostic enzymes (AST, ALT, and ALP) were estimated. Serum levels of the same diagnostic enzymes were also measured. The mean values of the serum enzyme activity for ALP in each experimental group were 19.5±1.62, 29.67±2.17 and 1.15±0.27 IU/L for Pb, Fe and Cu groups compared with 9.99±1.34 IU/L enzyme activity in the control. This result showed that Pb and Fe caused increased release of the enzyme into the blood circulation indicating increased tissue damage while Cu caused a reduction in the serum level as compared with the level in the control group. The mean values of enzyme activity obtained in the liver were 102.14±6.12, 140.17±2.06 and 168.23±3.52 IU/L for Pb, Fe and Cu groups, respectively compared to 91.20±9.42 IU/L enzyme activity for the control group. The serum and liver AST and ALT activities obtained in Pb, Fe, Cu and control groups are reported. It was generally noted that the presence of the heavy metal caused liver tissues damage and consequent increased level of the diagnostic enzymes in the serum.

Keywords: Diagnostic enzymes, enzyme activity, heavy metals, tissues investigations.

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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.

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Authors: Tadeusz Pieczonka, Jan Kazior

Abstract:

The influence of SiC powder addition on densification of Al-SiC compacts during sintering in different atmospheres was investigated. It was performed in a dilatometer in flowing nitrogen, nitrogen/hydrogen (95/5 by volume) and argon. Fine, F500 grade of SiC powder was used. Mixtures containing 10 and 30 vol.% of SiC reinforcement were prepared in a Turbula mixer. Green compacts of about 82% of theoretical density were made of each mixture. For comparison, compacts made of pure aluminum powder were also investigated. It was shown that nitrogen is the best sintering atmosphere because only in this atmosphere did shrinkage take place. Its amount is lowered by ceramic powder addition, i.e. the more SiC the less densification occurs. Additionally, the formation of clusters, enhanced in compacts containing 30 vol.% SiC, is also responsible for limiting the shrinkage. Microstructural examinations of sintered composites revealed that sintering of compacts occurs in the presence of the liquid phase exclusively in nitrogen.

Keywords: Al-SiC composites, densification, sintering atmosphere.

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Authors: Arti Vaish, Harish Parthasarathy

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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.

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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.

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Authors: Ramesh S., Sasiraaju A. S., Sidhaarth K., Sudhan Rajkumar N., Manivel Muralidaran V.

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This work presents the result of investigations aimed at determining the hardness of the welded Chromoly (A 4130) steel plate of 2” thickness. Multi pass welding for the thick sections was carried out and analyzed for the Chromoly alloy steel plates. The study of hardness at the weld metal reveals that there is the presence of different micro structure products which yields diverse properties. The welding carried out using GMAW with ER70s-2 electrode. Single V groove design was selected for the butt joint configuration. The presence of hydrogen has been suppressed by selecting low hydrogen electrode. Preheating of the plate prior to welding reduces the cooling rate which also affects the weld metal microstructure. The shielding gas composition used in this analysis is 80% Ar-20% CO2. The experimental analysis gives the detailed study of the hardness of the material.

Keywords: Chromoly, Gas Metal Arc Weld (GMAW), Hardness, Multi pass weld, Shielding gas composition.

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Authors: Michal Polanský, C. Ardil

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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

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Authors: Shaher Bano, Samia Fida, Asif Israr

Abstract:

The synergistic effect of properties of metals and fibers reinforced laminates has diverted attention of the world towards use of robust composite materials known as fiber-metal laminates in many high performance applications. In this study, modification of an adhesively bonded joint as a single lap joint of carbon fibers based CARALL FML has done to increase interlaminar shear strength of the joint. The effect of different configurations of joint designs such as spews, stepped and modification in adhesive by addition of nano-fillers was studied. Both experimental and simulation results showed that modified joint design have superior properties as maximum force experienced stepped joint was 1.5 times more than the simple lap joint. Addition of carbon nano-tubes as nano-fillers in the adhesive joint increased the maximum force due to crack deflection mechanism.

Keywords: Adhesive joint, carbon reinforced aluminium laminate, CARALL, fiber metal laminates, spews.

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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.

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Authors: M.B.S. Alferjani, A.A. Abdul Samad, N. Mohamad, M. Hilton, N. Ali

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This paper presents the Literature Review of carbon fiber reinforced polymer (CFRP) strips to reinforced concrete (RC) as a strengthening solution for T-beams. Although a great deal of research has been carried out on Rectangular beams strengthened with Fibre-Reinforced Polymer composites (FRP), Fiber reinforced polymer (FRP) composites have been increasingly studied for their application in the flexural or shear strengthening of reinforced concrete (RC) members. A detailed discussion of the shearstrengthening repair with FRP is undertaken. This paper will be limited to research of CFRP material externally bonded to the tensile face of concrete beams. In particular, research studying the effect of externally applied CFRP materials on the shear performance of reinforced concrete beams will be reported.

Keywords: CFRP, Concrete, Flexural, FRP, Shear, Strengthening.

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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.

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Authors: Tao Liu, Qingliang Yu, H. J. H. Brouwers

Abstract:

Among the reaction products in the alkali activated ground granulated blast furnace slag (AAS), the layered double hydroxides (LDHs) have a remarkable capacity of chloride and heavy metal ions absorption. The promotion of LDH phases in the AAS matrix can increase chloride resistance. The objective of this study is that using the different dosages of sodium aluminate to activate slag, consequently, promoting the formation of in-situ LDH. The hydration kinetics of the sodium aluminate activated slag (SAAS) was tested by the isothermal calorimetry. Meanwhile, the reaction products were determined by X-ray diffraction (XRD), thermogravimetric analysis (TGA), and Fourier-transform infrared spectroscopy (FTIR). The sodium hydroxide activated slag is selected as the reference. The results of XRD, TGA, and FTIR showed that the formation of LDH in SAAS is governed by the aluminate dosages.

Keywords: ground granulated blast furnace slag, sodium aluminate activated slag, in-situ LDH formation, chloride absorption

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

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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.

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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.

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Authors: L. Khalfa, M. Bagane, M. L. Cervera, S. Najjar

Abstract:

The aim of this work is to present a low cost adsorbent for removing toxic heavy metals from aqueous solutions. Therefore, we are interested to investigate the efficiency of natural clay minerals collected from south Tunisia and their modified form using sulfuric acid in the removal of toxic metal ions: Zn(II) and Pb(II) from synthetic waste water solutions. The obtained results indicate that metal uptake is pH-dependent and maximum removal was detected to occur at pH 6. Adsorption equilibrium is very rapid and it was achieved after 90 min for both metal ions studied. The kinetics results show that the pseudo-second-order model describes the adsorption and the intraparticle diffusion models are the limiting step. The treatment of natural clay with sulfuric acid creates more active sites and increases the surface area, so it showed an increase of the adsorbed quantities of lead and zinc in single and binary systems. The competitive adsorption study showed that the uptake of lead was inhibited in the presence of 10 mg/L of zinc. An antagonistic binary adsorption mechanism was observed. These results revealed that clay is an effective natural material for removing lead and zinc in single and binary systems from aqueous solution.

Keywords: Lead, zinc heavy metal, activated clay, kinetic study, competitive adsorption, modeling.

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Authors: A.S. Kipcak, N. Baran Acarali, S. Kolemen, N. Tugrul, E. Moroydor Derun, S. Piskin

Abstract:

Fly ash is one of the residues generated in combustion, and comprises the fine particles that rise with the flue gases. Ash which does not rise is termed bottom ash [1]. In our country, it is expected that will be occurred 50 million tons of waste ash per year until 2020. Released waste from the thermal power plants is caused very significant problems as known. The fly ashes can be evaluated by using as adsorbent material. The purpose of this study is to investigate the possibility of use of Tuncbilek fly ash like low-cost adsorbents for heavy metal adsorption. First of all, Tuncbilek fly ash was characterized. For this purpose; analysis such as sieve analysis, XRD, XRF, SEM and FT-IR were performed.

Keywords: Fly ash, heavy metal, sieve, adsorbent

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Authors: Aresh Vikram Singh, Sarika Nagar

Abstract:

The tamarind based resin containing hydroxypropane sulphonic acid groups has been synthesized and their adsorption behavior for heavy metal ions has been investigated using batch and column experiments. The hydroxypropane sulphonic acid group has been incorporated onto tamarind by a modified Porath's method of functionalisation of polysaccharides. The tamarind hydroxypropane sulphonic acid (THPSA) resin can selectively remove of heavy metal ions, which are contained in industrial wastewater. The THPSA resin was characterized by FTIR and thermogravimetric analysis. The effects of various adsorption conditions, such as pH, treatment time and adsorbent dose were also investigated. The optimum adsorption condition was found at pH 6, 120 minutes of equilibrium time and 0.1 gram of resin dose. The orders of distribution coefficient values were determined.

Keywords: Distribution coefficient, industrial wastewater, polysaccharides, tamarind hydroxypropane sulphonic acid resin, thermogravimetric analysis.

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Authors: O. I. Rufai, G. I. Lawal, B. O. Bolasodun, S. I. Durowaye, J. O. Etoh

Abstract:

It is an established fact that polymers have several physical limitations such as low stiffness and low resistance to impact on loading. Hence, polymers do not usually have requisite mechanical strength for application in various fields. The reinforcement by high strength fibers provides the polymer substantially enhanced mechanical properties and makes them more suitable for a large number of diverse applications. This research evaluates the effects of particulate Cow bone and Groundnut shell additions on the mechanical properties and microstructure of cow bone and groundnut shell reinforced epoxy composite in order to assess the possibility of using it as a material for engineering applications. Cow bone and groundnut shell particles reinforced with epoxy (CBRPC and GSRPC) was prepared by varying the cow bone and groundnut shell particles from 0-25 wt% with 5 wt% intervals. A Hybrid of the Cow bone and Groundnut shell (HGSCB) reinforce with epoxy was also prepared. The mechanical properties of the developed composites were investigated. Optical microscopy was used to examine the microstructure of the composites. The results revealed that mechanical properties did not increase uniformly with additions in filler but exhibited maximum properties at specific percentages of filler additions. From the Microscopic evaluation, it was discovered that homogeneity decreases with increase in % filler, this could be due to poor interfacial bonding.

Keywords: Groundnut shell reinforced polymer composite (GSRPC), Cow bone reinforced polymer composite (CBRPC), Hybrid of ground nutshell and cowbone (HGSCB).

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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.

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Authors: K. Hiro, Y. Imai, T. Sasayama

Abstract:

Cavitation under static negative pressure is not revealed well. The Berthelot method to generate such negative pressure can be a means to study cavitation inception. In this study, metal Berthelot tubes built in observation windows are newly developed and are checked whether high static negative pressure is generated or not. Negative pressure in the tube with a pair of a corundum plate and an aluminum gasket increased with temperature cycles. The trend was similar to that as reported before.

Keywords: Berthelot method, negative pressure, cavitation.

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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

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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.

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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.

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Authors: Kyongsoo Lee, , Seong-Il Kim, Byeong-Kwon Ju

Abstract:

An aqueous methanol sensor for use in direct methanol fuel cells (DMFCs) applications is demonstrated; the methanol sensor is built using dispersed single-walled carbon nanotubes (SWCNTs) with Nafion117 solution to detect the methanol concentration in water. The study is aimed at the potential use of the carbon nanotubes array as a methanol sensor for direct methanol fuel cells (DMFCs). The concentration of methanol in the fuel circulation loop of a DMFC system is an important operating parameter, because it determines the electrical performance and efficiency of the fuel cell system. The sensor is also operative even at ambient temperatures and responds quickly to changes in the concentration levels of the methanol. Such a sensor can be easily incorporated into the methanol fuel solution flow loop in the DMFC system.

Keywords: methanol concentration, SWCNT, nafion composites

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Authors: J. S. Kim

Abstract:

This paper presents a 0.13-µm Complementary Metal-Oxide Semiconductor (CMOS) vector modulator for beamforming system. The vector modulator features a 360° phase and gain range of -10 dB to 10 dB with a root mean square phase and amplitude error of only 2.2° and 0.45 dB, respectively. These features make it a suitable for wireless backhaul system in the 5 GHz industrial, scientific, and medical (ISM) bands. It draws a current of 20.4 mA from a 1.2 V supply. The total chip size is 1.87x1.34 mm².

Keywords: CMOS, vector modulator, beamforming, wireless backhaul, ISM.

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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

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