Search results for: Backward USSOR iterative matrix

Authors: Shazia Javed, Noor Atinah Ahmad

Abstract:

The householder RLS (HRLS) algorithm is an O(N2) algorithm which recursively updates an arbitrary square-root of the input data correlation matrix and naturally provides the LS weight vector. A data dependent householder matrix is applied for such an update. In this paper a recursive estimate of the eigenvalue spread and misalignment of the algorithm is presented at a very low computational cost. Misalignment is found to be highly sensitive to the eigenvalue spread of input signals, output noise of the system and exponential window. Simulation results show noticeable degradation in the misalignment by increase in eigenvalue spread as well as system-s output noise, while exponential window was kept constant.

Keywords: HRLS algorithm, eigenvalue spread, misalignment.

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Authors: Bia Kim, Sewon Lee, Jaesik Lee

Abstract:

This study aims to investigate the gender differences in spatial navigation using the tasks of 2-D matrix navigation and recognition of real driving scene. The results can be summarized as followings. First, female subjects responded faster in 2-D matrix navigation task than male subjects when landmark instructions were provided. Second, in recognition task, male subjects recognized the key elements involved in the past driving scene more accurately than female subjects. In particular, female subjects tended to miss peripheral information. These results suggest the possibility of gender differences in spatial navigation.

Keywords: Gender differences, Spatial navigation, 2-D matrixnavigation, Recognition of driving scene.

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Authors: M. Pourgholi, V.J.Majd

Abstract:

This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.

Keywords: Adaptive observer, linear matrix inequality, nonlinear systems, nonlinear observer, resilient observer, robust estimation.

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Authors: Satyanarayana, K.N. Prabhu

Abstract:

Microstructure, wetting behavior and interfacial reactions between Sn–0.7Cu and Sn–0.3Ag–0.7Cu (SAC0307) solders solidified on Ni coated Al substrates were compared and investigated. Microstructure of Sn–0.7Cu alloy exhibited a eutectic matrix composed of primary β-Sn dendrites with a fine dispersion of Cu6Sn5 intermetallics whereas microstructure of SAC0307 alloy exhibited coarser Cu6Sn5 and finer Ag3Sn precipitates of IMCs with decreased tin dendrites. Contact angles ranging from 22° to 26° were obtained for Sn–0.7Cu solder solidified on substrate surface whereas for SAC0307 solder alloy contact angles were found to be in the range of 20° to 22°. Sn–0.7Cu solder/substrate interfacial region exhibited faceted (Cu, Ni)6Sn5 IMCs protruding into the solder matrix and a small amount of (Cu, Ni)3Sn4 intermetallics at the interface. SAC0307 solder/substrate interfacial region showed mainly (Cu, Ni)3Sn4 intermetallics adjacent to the coating layer and (Cu, Ni)6Sn5 IMCs in the solder matrix. The improvement in the wettability of SAC0307 solder alloy on substrate surface is attributed to the formation of cylindrical shape (Cu,Ni)6Sn5 and a layer of (Cu, Ni)3Sn4 IMCs at the interface.

Keywords: Lead-free solder, wetting, contact angle, intermetallics.

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Authors: Z. Salleh, M. N. Berhan, Koay Mei Hyie, D. H. Isaac

Abstract:

Natural fibres have emerged as the potential reinforcement material for composites and thus gain attraction by many researchers. This is mainly due to their applicable benefits as they offer low density, low cost, renewable, biodegradability and environmentally harmless and also comparable mechanical properties with synthetic fibre composites. The properties of hybrid composites highly depends on several factors, including the interaction of fillers with the polymeric matrix, shape and size (aspect ratio), and orientation of fillers [1]. In this study, natural fibre kenaf composites and kenaf/fibreglass hybrid composites were fabricated by a combination of hand lay-up method and cold-press method. The effect of different fibre types (powder, short and long) on the tensile properties of composites is investigated. The kenaf composites with and without the addition of fibreglass were then characterized by tensile testing and scanning electron microscopy. A significant improvement in tensile strength and modulus were indicated by the introduction of long kenaf/woven fibreglass hybrid composite. However, the opposite trends are observed in kenaf powder composite. Fractographic observation shows that fibre/matrix debonding causes the fibres pull out. This phenomenon results in the fibre and matrix fracture.

Keywords: Kenaf, Fibreglass, Hybrid Composite, Tensile Strength, Tensile Modulus.

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Authors: T. Kuchukhidze, N. Jalagonia, T. Korkia, V. Gabunia, N. Jalabadze, R. Chedia

Abstract:

In this work, obtaining methods of ultrafine alumina powdery composites and high temperature pressing technology of matrix ceramic composites with different compositions have been discussed. Alumina was obtained by solution combustion synthesis and sol-gel methods. Metal carbides containing powdery composites were obtained by homogenization of finishing powders in nanomills, as well as by their single-step high temperature synthesis .Different types of matrix ceramics composites (α-Al2O3-ZrO2-Y2O3, α-Al2O3- Y2O3-MgO, α-Al2O3-SiC-Y2O3, α-Al2O3-WC-Co-Y2O3, α-Al2O3- B4C-Y2O3, α-Al2O3- B4C-TiB2 etc.) were obtained by using OXYGON furnace. Consolidation of powders were carried out at 1550- 1750°C (hold time - 1 h, pressure - 50 MPa). Corundum ceramics samples have been obtained and characterized by high hardness and fracture toughness, absence of open porosity, high corrosion resistance. Their density reaches 99.5-99.6% TD. During the work, the following devices have been used: High temperature vacuum furnace OXY-GON Industries Inc (USA), Electronic Scanning Microscopes Nikon Eclipse LV 150, Optical Microscope NMM- 800TRF, Planetary mill Pulverisette 7 premium line, Shimadzu Dynamic Ultra Micro Hardness Tester DUH-211S, Analysette 12 Dynasizer.

Keywords: α-Alumina, Consolidation, Matrix Ceramics, Powdery composites.

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Authors: Sukrit Shankar, Pardha Saradhi K., Chetana Shanta Patsa, Jaydev Sharma

Abstract:

Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fractional Fourier Transform and show that the eigenvectors of the proposed matrix has a higher degree of correlation with the Hermite Gaussian functions. Also, the proposed matrix is shown to give better Fractional Fourier responses with various transform orders for different signals.

Keywords: Fractional Fourier Transform, Hamiltonian, Eigen Vectors, Discrete Hermite Gaussians.

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Authors: G.H. Montazeri, Z. Dastkhan, H. Aliabadi

Abstract:

Gas condensate Reservoirs show complicated thermodynamic behavior when their pressure reduces to under dew point pressure. Condensate blockage around the producing well cause significant reduction of production rate as well bottom-hole pressure drops below saturation pressure. The main objective of this work was to examine the well test analysis of naturally fractured lean gas condensate reservoir and investigate the effect of condensate formed around the well-bore on behavior of single phase pseudo pressure and its derivative curves. In this work a naturally fractured lean gas condensate reservoir is simulated with compositional simulator. Different sensitivity analysis done on Corry parameters and result of simulator is feed to analytical well testing software. For consideration of these phenomena eighteen compositional models with Capillary number effect are constructed. Matrix relative permeability obeys Corry relative permeability and relative permeability in fracture is linear. Well testing behavior of these models are studied and interpreted. Results show different sensitivity analysis on relative permeability of matrix does not have strong effect on well testing behavior even most part of the matrix around the well is occupied with condensate.

Keywords: Lean gas, fractured condensate reservoir, capillary number, well testing analysis, relative permeability.

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Authors: Adil Al-Rammahi

Abstract:

Image or document encryption is needed through egovernment data base. Really in this paper we introduce two matrices images, one is the public, and the second is the secret (original). The analyses of each matrix is achieved using the transformation of singular values decomposition. So each matrix is transformed or analyzed to three matrices say row orthogonal basis, column orthogonal basis, and spectral diagonal basis. Product of the two row basis is calculated. Similarly the product of the two column basis is achieved. Finally we transform or save the files of public, row product and column product. In decryption stage, the original image is deduced by mutual method of the three public files.

Keywords: Image cryptography, Singular values decomposition.

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Authors: Khaled N. El-Hashmi, Omar K.Gnieber

Abstract:

The clinical laboratory has received considerable recognition globally due to the rapid development of advanced technology, economic demands and its role in a patient’s treatment cycle. Although various cross-domain experiments and practices with respect to clinical laboratory projects are ready for the full swing, the customer needs are still ambiguous and debatable. The purpose of this study is to apply Kano’s model and customer satisfaction matrix to categorize service quality attributes in order to see how well these attributes are able to satisfy customer needs. The result reveals that ten of the 26 service quality attributes have greater impacts on highly increasing customer’s satisfaction and should be taken in consideration firstly.

Keywords: Clinical laboratory, Customer satisfaction matrix, Kano’s Model, Quality Attributes, Voice of Customer.

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Authors: Shengbiao Wu, Weihua Cao, Min Wu, Can Liu

Abstract:

This paper presents an intelligent tuning method of microwave filter based on complex neural network and improved space mapping. The tuning process consists of two stages: the initial tuning and the fine tuning. At the beginning of the tuning, the return loss of the filter is transferred to the passband via the error of phase. During the fine tuning, the phase shift caused by the transmission line and the higher order mode is removed by the curve fitting. Then, an Cauchy method based on the admittance parameter (Y-parameter) is used to extract the coupling matrix. The influence of the resonant cavity loss is eliminated during the parameter extraction process. By using processed data pairs (the amount of screw variation and the variation of the coupling matrix), a tuning model is established by the complex neural network. In view of the improved space mapping algorithm, the mapping relationship between the actual model and the ideal model is established, and the amplitude and direction of the tuning is constantly updated. Finally, the tuning experiment of the eight order coaxial cavity filter shows that the proposed method has a good effect in tuning time and tuning precision.

Keywords: Microwave filter, scattering parameter (s-parameter), coupling matrix, intelligent tuning.

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Authors: J. Hajri, H. Hrizi, N. Sboui, H. Baudrand

Abstract:

This paper presents a study of SIW circuits (Substrate Integrated Waveguide) with a rigorous and fast original approach based on Iterative process (WCIP). The theoretical suggested study is validated by the simulation of two different examples of SIW circuits. The obtained results are in good agreement with those of measurement and with software HFSS.

Keywords: Convergence study, HFSS, Modal decomposition, SIW Circuits, WCIP Method.

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Authors: Akrem Sellami, Imed Riadh Farah, Basel Solaiman

Abstract:

With the development of HyperSpectral Imagery (HSI) technology, the spectral resolution of HSI became denser, which resulted in large number of spectral bands, high correlation between neighboring, and high data redundancy. However, the semantic interpretation is a challenging task for HSI analysis due to the high dimensionality and the high correlation of the different spectral bands. In fact, this work presents a dimensionality reduction approach that allows to overcome the different issues improving the semantic interpretation of HSI. Therefore, in order to preserve the spatial information, the Tensor Locality Preserving Projection (TLPP) has been applied to transform the original HSI. In the second step, knowledge has been extracted based on the adjacency graph to describe the different pixels. Based on the transformation matrix using TLPP, a weighted matrix has been constructed to rank the different spectral bands based on their contribution score. Thus, the relevant bands have been adaptively selected based on the weighted matrix. The performance of the presented approach has been validated by implementing several experiments, and the obtained results demonstrate the efficiency of this approach compared to various existing dimensionality reduction techniques. Also, according to the experimental results, we can conclude that this approach can adaptively select the relevant spectral improving the semantic interpretation of HSI.

Keywords: Band selection, dimensionality reduction, feature extraction, hyperspectral imagery, semantic interpretation.

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

Abstract:

In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial-type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: Difference Equations, Jost Functions, Asymptotics, Eigenvalues, Continuous Spectrum, Spectral Singularities.

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Authors: Thuraya M. Qaradaghi, Newroz N. Abdulrazaq

Abstract:

The McEliece cryptosystem is an asymmetric type of cryptography based on error correction code. The classical McEliece used irreducible binary Goppa code which considered unbreakable until now especially with parameter [1024, 524, and 101], but it is suffering from large public key matrix which leads to be difficult to be used practically. In this work Irreducible and Separable Goppa codes have been introduced. The Irreducible and Separable Goppa codes used are with flexible parameters and dynamic error vectors. A Comparison between Separable and Irreducible Goppa code in McEliece Cryptosystem has been done. For encryption stage, to get better result for comparison, two types of testing have been chosen; in the first one the random message is constant while the parameters of Goppa code have been changed. But for the second test, the parameters of Goppa code are constant (m=8 and t=10) while the random message have been changed. The results show that the time needed to calculate parity check matrix in separable are higher than the one for irreducible McEliece cryptosystem, which is considered expected results due to calculate extra parity check matrix in decryption process for g2(z) in separable type, and the time needed to execute error locator in decryption stage in separable type is better than the time needed to calculate it in irreducible type. The proposed implementation has been done by Visual studio C#.

Keywords: McEliece cryptosystem, Goppa code, separable, irreducible.

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Authors: Xianbiao Jia, Hong Li, Yang Liu, Zhichao Fang

Abstract:

In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.

Keywords: The coupled Burgers equation, H1-Galerkin mixed finite element method, Backward Euler's method, Optimal error estimates.

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Authors: Jaromír Marek, Jakub Wiener, Yan Wang

Abstract:

The main goal of this study was to find simple and industrially applicable production of ion exchangers based on nanofibrous polystyrene matrix and characterization of prepared material. Starting polystyrene nanofibers were sulfonated and crosslinked under appropriate conditions at the same time by sulfuric acid. Strongly acidic cation exchanger was obtained in such a way. The polymer matrix was made from polystyrene nanofibers prepared by Nanospider^TM technology.

Various types postpolymerization reactions and other methods of crosslinking were studied. Greatly different behavior between nano- and microsize materials was observed. The final nanofibrous material was characterized and compared to common granular ion exchangers and available microfibrous ion exchangers. The sorption properties of nanofibrous ion exchangers were compared with the granular ion exchangers. For nanofibrous ion exchangers of comparable ion exchange capacity was observed considerably faster adsorption kinetics.

Keywords: Electrospinning, ion exchangers, nanofibers, polystyrene.

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Authors: Allouche Moez, Souissi Mansour, Chaabane Mohamed, Mehdi Driss

Abstract:

This paper deals with the synthesis of fuzzy state feedback controller of induction motor with optimal performance. First, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate a non linear system in the synchronous d-q frame rotating with electromagnetic field-oriented. Next, a fuzzy controller is designed to stabilise the induction motor and guaranteed a minimum disturbance attenuation level for the closed-loop system. The gains of fuzzy control are obtained by solving a set of Linear Matrix Inequality (LMI). Finally, simulation results are given to demonstrate the controller-s effectiveness.

Keywords: Rejection disturbance, fuzzy modelling, open-loop control, Fuzzy feedback controller, fuzzy observer, Linear Matrix Inequality (LMI)

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Authors: Dipti Patra, Mridula J

Abstract:

In this paper, we propose a new image segmentation approach for colour textured images. The proposed method for image segmentation consists of two stages. In the first stage, textural features using gray level co-occurrence matrix(GLCM) are computed for regions of interest (ROI) considered for each class. ROI acts as ground truth for the classes. Ohta model (I1, I2, I3) is the colour model used for segmentation. Statistical mean feature at certain inter pixel distance (IPD) of I2 component was considered to be the optimized textural feature for further segmentation. In the second stage, the feature matrix obtained is assumed to be the degraded version of the image labels and modeled as Markov Random Field (MRF) model to model the unknown image labels. The labels are estimated through maximum a posteriori (MAP) estimation criterion using ICM algorithm. The performance of the proposed approach is compared with that of the existing schemes, JSEG and another scheme which uses GLCM and MRF in RGB colour space. The proposed method is found to be outperforming the existing ones in terms of segmentation accuracy with acceptable rate of convergence. The results are validated with synthetic and real textured images.

Keywords: Texture Image Segmentation, Gray Level Cooccurrence Matrix, Markov Random Field Model, Ohta colour space, ICM algorithm.

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Authors: António L. Topa

Abstract:

A complete spectral representation for the electromagnetic field of planar multilayered waveguides inhomogeneously filled with omega media is presented. The problem of guided electromagnetic propagation is reduced to an eigenvalue equation related to a 2 ´ 2 matrix differential operator. Using the concept of adjoint waveguide, general bi-orthogonality relations for the hybrid modes (either from the discrete or from the continuous spectrum) are derived. For the special case of homogeneous layers the linear operator formalism is reduced to a simple 2 ´ 2 coupling matrix eigenvalue problem. Finally, as an example of application, the surface and the radiation modes of a grounded omega slab waveguide are analyzed.

Keywords: Metamaterials, linear operators, omega media, layered waveguide, orthogonality relations

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Authors: Hans H. Diel

Abstract:

This paper describes a computer model of Quantum Field Theory (QFT), referred to in this paper as QTModel. After specifying the initial configuration for a QFT process (e.g. scattering) the model generates the possible applicable processes in terms of Feynman diagrams, the equations for the scattering matrix, and evaluates probability amplitudes for the scattering matrix and cross sections. The computations of probability amplitudes are performed numerically. The equations generated by QTModel are provided for demonstration purposes only. They are not directly used as the base for the computations of probability amplitudes. The computer model supports two modes for the computation of the probability amplitudes: (1) computation according to standard QFT, and (2) computation according to a proposed functional interpretation of quantum theory.

Keywords: Computational Modeling, Simulation of Quantum Theory, Quantum Field Theory, Quantum Electrodynamics

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Authors: Chia-Hsin Wu, Chen-Hao Wuang, Yu-Hung Chou, Chia-Chih Chen, Pei-Ju Chen, Hsiao-Chen You, Yi-Shin Deng

Abstract:

Food mileage is one of the important issues concerning environmental sustainability. In this research we have utilized a prototype platform with iterative user-centered testing. With these findings we successfully demonstrate the use of the context of persuasive methods to influence users- attitudes towards the sustainable concept.

Keywords: Behavior change, food mileage, persuasive technology, sustainability.

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Authors: Mengzhuo Luo, Shouming Zhong

Abstract:

This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived.

Keywords: Delay-dependent stability, Neural networks, Time varying delay, Linear matrix inequality (LMI).

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Authors: Meng Hu, Lili Wang

Abstract:

In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. Finally, an example is given to illustrate our results by using MATLAB LMI toolbox.

Keywords: Hopfield neural network, linear matrix inequality, exponential stability, time delay, T-S fuzzy model.

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Authors: Sh. Hamada, N. Burtebayev, N. Amangeldi, A. Amar

Abstract:

The aim of this work is to study the elastic transfer phenomenon which takes place in the elastic scattering of 16O on 12C at energies near the Coulomb barrier. Where, the angular distribution decrease steadily with increasing the scattering angle, then the cross section will increase at backward angles due to the α-transfer process. This reaction was also studied at different energies for tracking the nuclear rainbow phenomenon. The experimental data of the angular distribution at these energies were compared to the calculation predictions. The optical potential codes such as SPIVAL and Distorted Wave Born Approximation (DWUCK5) were used in analysis.

Keywords: Transfer reaction, DWBA, Elastic Scattering, Optical Potential Codes.

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Authors: Xian Ming Gu, Ting Zhu Huang, Hou Biao Li

Abstract:

In this paper, getting an high-efficiency parallel algorithm to solve sparse block pentadiagonal linear systems suitable for vectors and parallel processors, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are appropriate when the desired target is to maximize parallelism. Moreover, some theoretical results about these preconditioners are presented and how to construct preconditioners effectively for any nonsingular block pentadiagonal H-matrices is also described. In addition, the availability of these preconditioners is illustrated with some numerical experiments arising from two dimensional biharmonic equation.

Keywords: Parallel algorithm, Pentadiagonal matrix, Polynomial approximate inverse, Preconditioners, Stair matrix.

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Authors: Ching-Sheng Wang, Xin-Mao Huang, Ming-Yu Hung

Abstract:

In this paper, we present a method named Signal Level Matrix (SLM) which can improve the accuracy and stability of active RFID indoor positioning system. Considering the accuracy and cost, we use uniform distribution mode to set up and separate the overlapped signal covering areas, in order to achieve preliminary location setting. Then, based on the proposed SLM concept and the characteristic of the signal strength value that attenuates as the distance increases, this system cross-examines the distribution of adjacent signals to locate the users more accurately. The experimental results indicate that the adaptive positioning method proposed in this paper could improve the accuracy and stability of the positioning system effectively and satisfyingly.

Keywords: RFID positioning, localization, indoor, location-aware.

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Authors: Duy Cuong Nguyen, Ali Makke, Guillaume Montay

Abstract:

This work presents an improved single fiber pull-out test for fiber/matrix interface characterization. This test has been used to study the Inter-Facial Shear Strength ‘IFSS’ of hemp fibers reinforced polypropylene (PP). For this aim, the fiber diameter has been carefully measured using a tomography inspired method. The fiber section contour can then be approximated by a circle or a polygon. The results show that the IFSS is overestimated if the circular approximation is used. The Influence of the molding temperature on the IFSS has also been studied. We find that a molding temperature of 183◦C leads to better interfacial properties. Above or below this temperature the interface strength is reduced.

Keywords: Interface, pull-out, processing, temperature, hemp, polypropylene, composite.

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Authors: Norman Wu, Darren Sun

Abstract:

Key performance indicators (KPIs) are used for post result evaluation in the construction industry, and they normally do not have provisions for changes. This paper proposes a set of dynamic key performance indicators (d-KPIs) which predicts the future performance of the activity being measured and presents the opportunity to change practice accordingly. Critical to the predictability of a construction project is the ability to achieve automated data collection. This paper proposes an effective way to collect the process and engineering management data from an integrated construction management system. The d-KPI matrix, consisting of various indicators under seven categories, developed from this study can be applied to close monitoring of the development projects of aged-care facilities. The d-KPI matrix also enables performance measurement and comparison at both project and organization levels.

Keywords: Aged-care project, construction, dynamic KPI, healthcare system.

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Authors: Basheer M. Al-Maqaleh, Kamal K. Bharadwaj

Abstract:

Automated discovery of hierarchical structures in large data sets has been an active research area in the recent past. This paper focuses on the issue of mining generalized rules with crisp hierarchical structure using Genetic Programming (GP) approach to knowledge discovery. The post-processing scheme presented in this work uses flat rules as initial individuals of GP and discovers hierarchical structure. Suitable genetic operators are proposed for the suggested encoding. Based on the Subsumption Matrix(SM), an appropriate fitness function is suggested. Finally, Hierarchical Production Rules (HPRs) are generated from the discovered hierarchy. Experimental results are presented to demonstrate the performance of the proposed algorithm.

Keywords: Genetic Programming, Hierarchy, Knowledge Discovery in Database, Subsumption Matrix.

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