Search results for: consistent and concentrated mass matrices

Authors: Xiuyong Ding, Lan Shu, Xiu Liu

Abstract:

This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.

Keywords: Linear co-positive Lyapunov functions, positive systems, switched systems.

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Authors: Moses C. Siame, Kazutoshi Haga, Atsushi Shibayama

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This study investigates the removal of silica, alumina and phosphorus as impurities from Sanje iron ore using wet high-intensity magnetic separation (WHIMS). Sanje iron ore contains low-grade hematite ore found in Nampundwe area of Zambia from which iron is to be used as the feed in the steelmaking process. The chemical composition analysis using X-ray Florence spectrometer showed that Sanje low-grade ore contains 48.90 mass% of hematite (Fe₂O₃) with 34.18 mass% as an iron grade. The ore also contains silica (SiO₂) and alumina (Al₂O₃) of 31.10 mass% and 7.65 mass% respectively. The mineralogical analysis using X-ray diffraction spectrometer showed hematite and silica as the major mineral components of the ore while magnetite and alumina exist as minor mineral components. Mineral particle distribution analysis was done using scanning electron microscope with an X-ray energy dispersion spectrometry (SEM-EDS) and images showed that the average mineral size distribution of alumina-silicate gangue particles is in order of 100 μm and exists as iron-bearing interlocked particles. Magnetic separation was done using series L model 4 Magnetic Separator. The effect of various magnetic separation parameters such as magnetic flux density, particle size, and pulp density of the feed was studied during magnetic separation experiments. The ore with average particle size of 25 µm and pulp density of 2.5% was concentrated using pulp flow of 7 L/min. The results showed that 10 T was optimal magnetic flux density which enhanced the recovery of 93.08% of iron with 53.22 mass% grade. The gangue mineral particles containing 12 mass% silica and 3.94 mass% alumna remained in the concentrate, therefore the concentrate was further treated in the second stage WHIMS using the same parameters from the first stage. The second stage process recovered 83.41% of iron with 67.07 mass% grade. Silica was reduced to 2.14 mass% and alumina to 1.30 mass%. Accordingly, phosphorus was also reduced to 0.02 mass%. Therefore, the two stage magnetic separation process was established using these results.

Keywords: Sanje iron ore, magnetic separation, silica, alumina, recovery.

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Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding

Abstract:

This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.

Keywords: Common linear co-positive Lyapunov functions, positive systems, switched systems, delays.

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Authors: Geng Yuan, Yiwan Guo, Fahui Zhai, Shuhua Zhang

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In this paper, we discuss some properties of left spectrum and give the representation of linear preserver map the left spectrum of diagonal quaternionic matrices.

Keywords: Quaternionic matrix, left spectrum, linear preserver map.

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Authors: Khosrow Maleknejad, Yaser Rostami

Abstract:

In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions

Keywords: Integro-differential equations, Quartic B-spline wavelet, Operational matrices.

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Authors: Ali N. Suri, Ahmad A. Al-Makhlufi

Abstract:

In this paper the problem of buckling of plates on foundation of finite length and with different side support is studied.

The Finite Strip Method is used as tool for the analysis. This method uses finite strip elastic, foundation, and geometric matrices to build the assembly matrices for the whole structure, then after introducing boundary conditions at supports, the resulting reduced matrices is transformed into a standard Eigenvalue-Eigenvector problem. The solution of this problem will enable the determination of the buckling load, the associated buckling modes and the buckling wave length.

To carry out the buckling analysis starting from the elastic, foundation, and geometric stiffness matrices for each strip a computer program FORTRAN list is developed.

Since stiffness matrices are function of wave length of buckling, the computer program used an iteration procedure to find the critical buckling stress for each value of foundation modulus and for each boundary condition.

The results showed the use of elastic medium to support plates subject to axial load increase a great deal the buckling load, the results found are very close with those obtained by other analytical methods and experimental work.

The results also showed that foundation compensates the effect of the weakness of some types of constraint of side support and maximum benefit found for plate with one side simply supported the other free.

Keywords: Buckling, Finite Strip, Different Sides Support, Plates on Foundation.

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Authors: N.Subramanian, C.Murugesan

Abstract:

This paper is devoted to the study of the general properties of Orlicz space of entire sequence of fuzzy numbers by using infinite matrices.

Keywords: Fuzzy numbers, infinite matrix, Orlicz space, entiresequence.

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Authors: Marque Adrien, Delahaye Daniel, Marechal Pierre, Berry Isabelle

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Wind direction and uncertainty are crucial in aircraft or unmanned aerial vehicle trajectories. By computing wind covariance matrices on each spatial grid point, these spatial grids can be defined as images with symmetric positive definite matrix elements. A data pre-processing step, a specific convolution, a specific max-pooling, and specific flatten layers are implemented to process such images. Then, the neural network is applied to spatial grids, whose elements are wind covariance matrices, to solve classification problems related to the feasibility of unmanned aerial vehicles based on wind direction and wind uncertainty.

Keywords: Wind direction, uncertainty level, Unmanned Aerial Vehicle, convolution neural network, SPD matrices.

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Authors: Aki Happonen, Adrian Burian, Erwin Hemming

Abstract:

Fixed-point simulation results are used for the performance measure of inverting matrices by Cholesky decomposition. The fixed-point Cholesky decomposition algorithm is implemented using a fixed-point reconfigurable processing element. The reconfigurable processing element provides all mathematical operations required by Cholesky decomposition. The fixed-point word length analysis is based on simulations using different condition numbers and different matrix sizes. Simulation results show that 16 bits word length gives sufficient performance for small matrices with low condition number. Larger matrices and higher condition numbers require more dynamic range for a fixedpoint implementation.

Keywords: Cholesky Decomposition, Fixed-point, Matrix inversion, Reconfigurable processing.

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Authors: Ahmed Noor Al-Qayyim, Barlas Ozden Caglayan

Abstract:

Structural failure is caused mainly by damage that often occurs on structures. Many researchers focus on to obtain very efficient tools to detect the damage in structures in the early state. In the past decades, a subject that has received considerable attention in literature is the damage detection as determined by variations in the dynamic characteristics or response of structures. The study presents a new damage identification technique. The technique detects the damage location for the incomplete structure system using output data only. The method indicates the damage based on the free vibration test data by using ‘Two Points Condensation (TPC) technique’. This method creates a set of matrices by reducing the structural system to two degrees of freedom systems. The current stiffness matrices obtain from optimization the equation of motion using the measured test data. The current stiffness matrices compare with original (undamaged) stiffness matrices. The large percentage changes in matrices’ coefficients lead to the location of the damage. TPC technique is applied to the experimental data of a simply supported steel beam model structure after inducing thickness change in one element, where two cases consider. The method detects the damage and determines its location accurately in both cases. In addition, the results illustrate these changes in stiffness matrix can be a useful tool for continuous monitoring of structural safety using ambient vibration data. Furthermore, its efficiency proves that this technique can be used also for big structures.

Keywords: Damage detection, two points–condensation, structural health monitoring, signals processing, optimization.

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Authors: Guangbin Wang, Xue Li, Fuping Tan

Abstract:

In this paper, we present some new upper bounds for the spectral radius of iterative matrices based on the concept of doubly α diagonally dominant matrix. And subsequently, we give two examples to show that our results are better than the earlier ones.

Keywords: doubly α diagonally dominant matrix, eigenvalue, iterative matrix, spectral radius, upper bound.

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Authors: Zhong-xi Gao, Hou-biao Li

Abstract:

Recently, some convergent results of the generalized AOR iterative (GAOR) method for solving linear systems with strictly diagonally dominant matrices are presented in [Darvishi, M.T., Hessari, P.: On convergence of the generalized AOR method for linear systems with diagonally dominant cofficient matrices. Appl. Math. Comput. 176, 128-133 (2006)] and [Tian, G.X., Huang, T.Z., Cui, S.Y.: Convergence of generalized AOR iterative method for linear systems with strictly diagonally dominant cofficient matrices. J. Comp. Appl. Math. 213, 240-247 (2008)]. In this paper, we give the convergence of the GAOR method for linear systems with strictly doubly diagonally dominant matrix, which improves these corresponding results.

Keywords: Diagonally dominant matrix, GAOR method, Linear system, Convergence

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Authors: J. J. Peña, J. Morales, J. García-Ravelo, L. Arcos-Díaz

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The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.

Keywords: Free particle, point canonical transformation method, position-dependent mass, staggered mass distribution.

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Authors: O. Punjarat, S. Chucheepsakul, T. Phanyasahachart

Abstract:

This paper focuses on a variational formulation of large amplitude free vibration behavior of a very sag marine cable. In the static equilibrium state, the marine cable has a very large sag configuration. In the motion state, the marine cable is assumed to vibrate in in-plane motion with large amplitude from the static equilibrium position. The total virtual work-energy of the marine cable at the dynamic state is formulated which involves the virtual strain energy due to axial deformation, the virtual work done by effective weight, and the inertia forces. The equations of motion for the large amplitude free vibration of marine cable are obtained by taking into account the difference between the Euler’s equation in the static state and the displaced state. Based on the Galerkin finite element procedure, the linear and nonlinear stiffness matrices, and mass matrices of the marine cable are obtained and the eigenvalue problem is solved. The natural frequency spectrum and the large amplitude free vibration behavior of marine cable are presented.

Keywords: Axial deformation, free vibration, Galerkin Finite Element Method, large amplitude, variational method.

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Authors: Adil AL-Rammahi

Abstract:

In this short paper, new properties of transition matrix were introduced. Eigen values for small order transition matrices are calculated in flexible method. For benefit of these properties applications of these properties were studied in the solution of Markov's chain via steady state vector, and information theory via channel entropy. The implemented test examples were promised for usages.

Keywords: Eigen value problem, transition matrix, state vector, information theory.

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Authors: Wolfram Irsa, Lorenz Boruch

Abstract:

Innovative solutions in additive manufacturing applying material extrusion for functional parts necessitates innovative filaments with persistent quality. Uniform homogeneity and consistent dispersion of particles embedded in filaments generally require multiple cycles of extrusion or well-prepared primal matter by injection molding, kneader machines, or mixing equipment. These technologies commit to dedicated equipment that are rarely at disposal in production laboratories unfamiliar with research in polymer materials. This stands in contrast to laboratories which investigate on complex material topics and technology science to leverage on the potential of 3-D printing. Consequently, scientific studies in labs are often constrained to compositions and concentrations of fillers offered from the market. Therefore, we present a prototypal laboratory methodology scalable to tailored primal matter for extruding ceramic composite filaments with fused filament fabrication (FFF) technology. A desktop single-screw extruder serves as core device for the experiments. Custom-made filament encapsulates the ceramic fillers and serves with polylactide (PLA), which is a thermoplastic polyester, as primal matter and is processed in the melting area of the extruder preserving the defined concentration of the fillers. Validated results demonstrate that this approach enables continuously produced and uniform composite filaments with consistent homogeneity. It is 3-D printable with controllable dimensions, which is a prerequisite for any scalable application. Additionally, digital microscopy confirms steady dispersion of the ceramic particles in the composite filament. This permits a 2D reconstruction of the planar distribution of the embedded ceramic particles in the PLA matrices. The innovation of the introduced method lies in the smart simplicity of preparing the composite primal matter. It circumvents the inconvenience of numerous extrusion operations and expensive laboratory equipment. Nevertheless, it delivers consistent filaments of controlled, predictable, and reproducible filler concentration, which is the prerequisite for any industrial application. The introduced prototypal laboratory methodology seems capable for other polymer matrices and suitable to further utilitarian particle types, beyond and above of ceramic fillers. This inaugurates a roadmap for supplementary laboratory development of peculiar composite filaments, providing value for industries and societies. This low-threshold entry of sophisticated preparation of composite filaments - enabling businesses creating their own dedicated filaments - will support the mutual efforts for establishing 3D printing to new functional devices.

Keywords: Additive manufacturing, ceramic composites, complex filament, industrial application.

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Authors: Guangbin Wang, Fuping Tan

Abstract:

In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

Keywords: Singular H-matrix, linear systems, extrapolated iterative method, GMAOR method, convergence.

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Authors: Aki Happonen, Adrian Burian, Erwin Hemming

Abstract:

Fixed-point simulation results are used for the performance measure of inverting matrices using a reconfigurable processing element. Matrices are inverted using the Cholesky decomposition algorithm. The reconfigurable processing element is capable of all required mathematical operations. The fixed-point word length analysis is based on simulations of different condition numbers and different matrix sizes.

Keywords: Cholesky Decomposition, Fixed-point, Matrixinversion, Reconfigurable processing.

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Authors: Yongxin Yuan, Jiashang Jiang

Abstract:

In this paper the gradient based iterative algorithm is presented to solve the linear matrix equation AXB +CXTD = E, where X is unknown matrix, A,B,C,D,E are the given constant matrices. It is proved that if the equation has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. Two numerical examples show that the introduced iterative algorithm is quite efficient.

Keywords: matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: Zhengsheng Wang, Jing Qi, Chuntao Liu, Yuanjun Li

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The harmonic Arnoldi method can be used to find interior eigenpairs of large matrices. However, it has been shown that this method may converge erratically and even may fail to do so. In this paper, we present a new method for computing interior eigenpairs of large nonsymmetric matrices, which is called weighted harmonic Arnoldi method. The implementation of the method has been tested by numerical examples, the results show that the method converges fast and works with high accuracy.

Keywords: Harmonic Arnoldi method, weighted harmonic Arnoldi method, eigenpair, interior eigenproblem, non symmetric matrix.

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Authors: Miklos Palfia

Abstract:

An iterative definition of any n variable mean function is given in this article, which iteratively uses the two-variable form of the corresponding two-variable mean function. This extension method omits recursivity which is an important improvement compared with certain recursive formulas given before by Ando-Li-Mathias, Petz- Temesi. Furthermore it is conjectured here that this iterative algorithm coincides with the solution of the Riemann centroid minimization problem. Certain simulations are given here to compare the convergence rate of the different algorithms given in the literature. These algorithms will be the gradient and the Newton mehod for the Riemann centroid computation.

Keywords: Means, matrix means, operator means, geometric mean, Riemannian center of mass.

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Authors: Xu Jianguo

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In this paper, a generalized self-consistent scheme, or “three phase model", is used to set up a micro-mechanics model for rough surface contact with randomly distributed asperities. The dimensionless average real pressure p is obtained as function of the ratio of the real contact area to the apparent contact area, 0 A / A r . Both elastic and plastic materials are considered, and the influence of the plasticity of material on p is discussed. Both two-dimensional and three-dimensional rough surface contact problems are considered.

Keywords: Contact mechanics, plastic deformation, self-consistent scheme.

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Authors: S. Kopylov, C. Z. Bo

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This study is aimed at exploring the possibility of energy recovery through the suppression of vibrations. The article describes design of electromagnetic dynamic damper. The magnetic part of the device performs the function of a tuned mass damper, thereby providing both energy regeneration and damping properties to the protected mass. According to the theory of tuned mass damper, equations of mathematical models were obtained. Then, under given properties of current system, amplitude frequency response was investigated. Therefore, main ideas and methods for further research were defined.

Keywords: Electromagnetic damper, oscillations with two degrees of freedom, regeneration systems, tuned mass damper.

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Authors: Liu Ping

Abstract:

In this paper, for an arbitrary multiplicative functional f from the set of all upper triangular fuzzy matrices to the fuzzy algebra, we prove that there exist a multiplicative functional F and a functional G from the fuzzy algebra to the fuzzy algebra such that the image of an upper triangular fuzzy matrix under f can be represented as the product of all the images of its main diagonal elements under F and other elements under G.

Keywords: Multiplicative functional, triangular fuzzy matrix, fuzzy addition operation, fuzzy multiplication operation.

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Authors: Shuvro Chowdhury, Esmat Farzana, Rizvi Ahmed, A. T. M. Golam Sarwar, M. Ziaur Rahman Khan

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The threshold voltage and capacitance voltage characteristics of ultra-thin Silicon-on-Insulator MOSFET are greatly influenced by the thickness and doping concentration of the silicon film. In this work, the capacitance voltage characteristics and threshold voltage of the device have been analyzed with quantum mechanical effects using the Self-Consistent model. Reduction of channel thickness and adding doping impurities cause an increase in the threshold voltage. Moreover, the temperature effects cause a significant amount of threshold voltage shift. The temperature dependence of threshold voltage has also been observed with Self- Consistent approach which are well supported from experimental performance of practical devices.

Keywords: C-V characteristics, Self-Consistent Analysis, Siliconon-Insulator, Ultra-thin film.

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Authors: Yiqin Lin, Wenbo Li

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Dimensionality reduction and feature extraction are of crucial importance for achieving high efficiency in manipulating the high dimensional data. Two-dimensional discriminant locality preserving projection (2D-DLPP) and two-dimensional discriminant supervised LPP (2D-DSLPP) are two effective two-dimensional projection methods for dimensionality reduction and feature extraction of face image matrices. Since 2D-DLPP and 2D-DSLPP preserve the local structure information of the original data and exploit the discriminant information, they usually have good recognition performance. However, 2D-DLPP and 2D-DSLPP only employ single-sided projection, and thus the generated low dimensional data matrices have still many features. In this paper, by combining the discriminant supervised LPP with the bidirectional projection, we propose the bidirectional discriminant supervised LPP (BDSLPP). The left and right projection matrices for BDSLPP can be computed iteratively. Experimental results show that the proposed BDSLPP achieves higher recognition accuracy than 2D-DLPP, 2D-DSLPP, and bidirectional discriminant LPP (BDLPP).

Keywords: Face recognition, dimension reduction, locality preserving projection, discriminant information, bidirectional projection.

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Authors: Juan L. Acero, F. Javier Benitez, Francisco J. Real, Gloria Roldan, Francisco Casas

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The bromination of five selected pharmaceuticals (metoprolol, naproxen, amoxicillin, hydrochlorotiazide and phenacetin) in ultrapure water and in three water matrices (a groundwater, a surface water from a public reservoir and a secondary effluent from a WWTP) was investigated. The apparent rate constants for the bromination reaction were determined as a function of the pH, and the sequence obtained for the reaction rate was amoxicillin > naproxen >> hydrochlorotiazide ≈ phenacetin ≈ metoprolol. The proposal of a kinetic mechanism, which specifies the dissociation of bromine and each pharmaceutical according to their pKa values and the pH allowed the determination of the intrinsic rate constants for every elementary reaction. The influence of the main operating conditions (pH, initial bromine dose, and the water matrix) on the degradation of pharmaceuticals was established. In addition, the presence of bromide in chlorination experiments was investigated. The presence of bromide in wastewaters and drinking waters in the range of 10 to several hundred μg L-1 accelerated slightly the oxidation of the selected pharmaceuticals during chorine disinfection.

Keywords: Pharmaceuticals, bromine, chlorine, apparent andintrinsic rate constants, water matrices, degradation rates

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Authors: Ahmed Abdulghani Taha, Mohammad Abdulghani Taha

Abstract:

This study aims at being acquainted with the using the body fat percentage (%BF) with body Mass Index (BMI) as input parameters in fuzzy logic decision support system to predict properly the lifted weight for students at weightlifting class lift according to his abilities instead of traditional manner. The sample included 53 male students (age = 21.38 ± 0.71 yrs, height (Hgt) = 173.17 ± 5.28 cm, body weight (BW) = 70.34 ± 7.87.6 kg, Body mass index (BMI) 23.42 ± 2.06 kg.m-2, fat mass (FM) = 9.96 ± 3.15 kg and fat percentage (% BF) = 13.98 ± 3.51 %.) experienced the weightlifting class as a credit and has variance at BW, Hgt and BMI and FM. BMI and % BF were taken as input parameters in FUZZY logic whereas the output parameter was the lifted weight (LW). There were statistical differences between LW values before and after using fuzzy logic (Diff 3.55± 2.21, P > 0.001). The percentages of the LW categories proposed by fuzzy logic were 3.77% of students to lift 1.0 fold of their bodies; 50.94% of students to lift 0.95 fold of their bodies; 33.96% of students to lift 0.9 fold of their bodies; 3.77% of students to lift 0.85 fold of their bodies and 7.55% of students to lift 0.8 fold of their bodies. The study concluded that the characteristic changes in body composition experienced by students when undergoing weightlifting could be utilized side by side with the Fuzzy logic decision support system to determine the proper workloads consistent with the abilities of students.

Keywords: Fuzzy logic, body mass index, body fat percentage, weightlifting.

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Authors: I. Norhuda, A. K. Mohd Omar

Abstract:

The purpose of the study was to determine the amount of Palm Kernel Oil (PKO) extracted from a packed bed of palm kernels in a supercritical fluid extractor using supercritical carbon dioxide (SC-CO2) as an environmental friendly solvent. Further, the study sought to ascertain the values of the overall mass transfer coefficient (K) of PKO evaluation through a mass transfer model, at constant temperature of 50 °C, 60 °C, and 70 °C and pressures range from 27.6 MPa, 34.5 MPa, 41.4 MPa and 48.3 MPa respectively. Finally, the study also seeks to demonstrate the application of the overall mass transfer coefficient values in relation to temperature and pressure. The overall mass transfer coefficient was found to be dependent pressure at each constant temperature of 50 °C, 60 °C and 70 °C. The overall mass transfer coefficient for PKO in a packed bed of palm kernels was found to be in the range of 1.21X 10-4 m min-1 to 1.72 X 10-4 m min-1 for a constant temperature of 50 °C and in the range of 2.02 X 10-4 m min-1 to 2.43 X 10-4 m min-1 for a constant temperature of 60 °C. Similar increasing trend of the overall mass transfer coefficient from 1.77 X 10-4 m min-1 to 3.64 X 10-4 m min-1 was also observed at constant temperature of 70 °C within the same pressure range from 27.6 MPa to 48.3 MPa.

Keywords: Overall Mass Transfer Coefficient (D), Supercritical Carbon Dioxide (SC-CO2), Palm Kernel Oil (PKO).

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Authors: Faruk Fırat Çalım, Nurullah Karaca, Hakan Tacettin Türker

Abstract:

In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: Circular rod, Out-of-plane free vibration analysis, Transfer Matrix Method.

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