Search results for: matrix technology

Authors: Wang Xingbo

Abstract:

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

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

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

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

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

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Authors: Minghui Wang

Abstract:

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

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

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

Abstract:

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

Keywords: Biocomposite, Biomimetic , Nano Hydroxyapatite , Template.

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Authors: Li Jiang, Baoguang Tian

Abstract:

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

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

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

Abstract:

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

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

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

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

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

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

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

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

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Authors: Yanping Liao, Zenan Wu, Ruigang Zhao

Abstract:

Frequency diverse array (FDA) beamforming is a technology developed in recent years, and its antenna pattern has a unique angle-distance-dependent characteristic. However, the beam is always required to have strong concentration, high resolution and low sidelobe level to form the point-to-point interference in the concentrated set. In order to eliminate the angle-distance coupling of the traditional FDA and to make the beam energy more concentrated, this paper adopts a multi-carrier FDA structure based on proposed power exponential frequency offset to improve the array structure and frequency offset of the traditional FDA. The simulation results show that the beam pattern of the array can form a dot-shape beam with more concentrated energy, and its resolution and sidelobe level performance are improved. However, the covariance matrix of the signal in the traditional adaptive beamforming algorithm is estimated by the finite-time snapshot data. When the number of snapshots is limited, the algorithm has an underestimation problem, which leads to the estimation error of the covariance matrix to cause beam distortion, so that the output pattern cannot form a dot-shape beam. And it also has main lobe deviation and high sidelobe level problems in the case of limited snapshot. Aiming at these problems, an adaptive beamforming technique based on exponential correction for multi-carrier FDA is proposed to improve beamforming robustness. The steps are as follows: first, the beamforming of the multi-carrier FDA is formed under linear constrained minimum variance (LCMV) criteria. Then the eigenvalue decomposition of the covariance matrix is ​​performed to obtain the diagonal matrix composed of the interference subspace, the noise subspace and the corresponding eigenvalues. Finally, the correction index is introduced to exponentially correct the small eigenvalues ​​of the noise subspace, improve the divergence of small eigenvalues ​​in the noise subspace, and improve the performance of beamforming. The theoretical analysis and simulation results show that the proposed algorithm can make the multi-carrier FDA form a dot-shape beam at limited snapshots, reduce the sidelobe level, improve the robustness of beamforming, and have better performance.

Keywords: Multi-carrier frequency diverse array, adaptive beamforming, correction index, limited snapshot, robust.

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Authors: Rihab Gam, Anis Sakly, Faouzi M'sahli

Abstract:

A new strategy of control is formulated for chaos synchronization of non-identical chaotic systems with different orders using the Borne and Gentina practical criterion associated with the Benrejeb canonical arrow form matrix, to drift the stability property of dynamic complex systems. The designed controller ensures that the state variables of controlled chaotic slave systems globally synchronize with the state variables of the master systems, respectively. Numerical simulations are performed to illustrate the efficiency of the proposed method.

Keywords: Synchronization, Non-identical chaotic systems, Different orders, Arrow form matrix.

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Authors: Tim Dunne, Weicheng Li, Chris Cheng, Qi Peng

Abstract:

Deeper petroleum reservoirs are more challenging to exploit due to the high hardness and abrasive characteristics of the formations. A cutting structure that consists of particulate diamond impregnated in a supporting matrix is found to be effective. Diamond impregnated bits are favored in these applications due to the higher thermal stability of the matrix material. The diamond particles scour or abrade away concentric grooves while the rock formation adjacent to the grooves is fractured and removed. The matrix material supporting the diamond will wear away, leaving the superficial dull diamonds to fall out. The matrix material wear will expose other embedded intact sharp diamonds to continue the operation. Minimizing the erosion effect on the matrix is an important design consideration, as the life of the bit can be extended by preventing early diamond pull-out. A careful balancing of the key parameters, such as diamond concentration, tungsten carbide and metal binder must be considered during development. Described herein is the design of experiment for developing and lab testing 8 unique samples. ASTM B611 wear testing was performed to benchmark the material performance against baseline products, with further scanning electron microscopy and microhardness evaluations. The recipe S5 with diamond 25/35 mesh size, narrow size distribution, high concentration blended with fine tungsten carbide and Co-Cu-Fe-P metal binder has the best performance, which shows 19% improvement in the ASTM B611 wear test compared with the reference material. In the field trial, the rate of penetration (ROP) is measured as 15 m/h, compared to 9.5, 7.8, and 6.8 m/h of other commercial impregnated bits in the same formation. A second round of optimizing recipe S5 for a higher wear resistance is further reported.

Keywords: Diamond containing material, grit hot press insert, impregnated diamond, insert, rate of penetration, ultrahard formation.

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Authors: Manouchehre Ansari, Mahmoud Dehghan Nayeri, Reza Yousefi Zenouz

Abstract:

In order to develop any strategy, it is essential to first identify opportunities, threats, weak and strong points. Assessment of technology level provides the possibility of concentrating on weak and strong points. The results of technology assessment have a direct effect on decision making process in the field of technology transfer or expansion of internal research capabilities so it has a critical role in technology management. This paper presents a conceptual model to analyze the technology capability of a company as a whole and in four main aspects of technology. This model was tested on 10 automotive parts manufacturers in IRAN. Using this model, capability level of manufacturers was investigated in four fields of managing aspects, hard aspects, human aspects, and information and knowledge aspects. Results show that these firms concentrate on hard aspect of technology while others aspects are poor and need to be supported more. So this industry should develop other aspects of technology as well as hard aspect to have effective and efficient use of its technology. These paper findings are useful for the technology planning and management in automotive part manufactures in IRAN and other Industries which are technology followers and transport their needed technologies.

Keywords: Technology, Technological evaluation, TechnologyMaturity

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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: H. D. Ibrahim, H. C. Chinwenyi, H. N. Ude

Abstract:

In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, Gauss-Seidel, Jacobi, algorithm

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Authors: Nishiyama Toshiaki, Tadayuki Kyountani, Nguyen Huu Phuc, Shigeyuki Haruyama, Oke Oktavianty

Abstract:

It is important to clarify the company’s core technology in product development process to strengthen their power in providing technology that meets the customer requirement. QFD method is adopted to clarify the core technology through identifying the high element technologies that are related to the voice of customer, and offer the most delightful features for customer. AHP is used to determine the importance of evaluating factors. A case study was conducted by using this approach in Japan’s Monozukuri Company (so called manufacturing company) to clarify their core technology based on customer requirements.

Keywords: QFD, product development process, core technology, AHP.

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Authors: Osagiede Mercy Afe

Abstract:

After the internet explosion in the 90’s, technology was immediately integrated into the school system. Technology which symbolizes advancement in human knowledge was seen as a setback by many educators. Efforts have been made to help stem this erroneous believes and help educators realize the benefits of technology and ways of implementing it in the classrooms especially in the sciences. This advancement created a constantly expanding gap between the pupil’s perception on the use of technology within the learning atmosphere and the teacher’s perception and limitations hence, the focus of this paper is on the need to refocus on the use of Science and Technology in enhancing children’s potentials in learning at school especially in Science for sustainable development in Nigeria. The paper recommended measures for facilitating the sustenance of science and technology in Nigerian schools so as to enhance the potentials of our children in Science and Technology for a better tomorrow.

Keywords: Children’s potential, Educational system, ICT, Sustainable development.

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Authors: Jeffrey L. Duffany

Abstract:

An optimal solution for a large number of constraint satisfaction problems can be found using the technique of substitution and elimination of variables analogous to the technique that is used to solve systems of equations. A decision function f(A)=max(A2) is used to determine which variables to eliminate. The algorithm can be expressed in six lines and is remarkable in both its simplicity and its ability to find an optimal solution. However it is inefficient in that it needs to square the updated A matrix after each variable elimination. To overcome this inefficiency the algorithm is analyzed and it is shown that the A matrix only needs to be squared once at the first step of the algorithm and then incrementally updated for subsequent steps, resulting in significant improvement and an algorithm complexity of O(n3).

Keywords: Algorithm, complexity, constraint, np-complete.

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Authors: R. Eslami-Farsani, S. M. S. Mousavi Bafrouyi

Abstract:

During past decades, increasing demand of modified Fiber Metal Laminates (FMLs) has stimulated a strong trend towards the development of these structures. FMLs contain several thin layers of metal bonded with composite materials. Characteristics of FMLs such as low specific mass, high bearing strength, impact resistance, corrosion resistance and high fatigue life are attractive. Nowadays, increasing development can be observed to promote the properties of polymer-based composites by nanofillers. By dispersing strong, nanofillers in polymer matrix, modified composites can be developed and tailored to individual applications. On the other hand, the synergic effects of nanoparticles such as graphene and carbon nanotube can significantly improve the mechanical, electrical and thermal properties of nanocomposites. In present paper, the modifying of FMLs by nanofillers and the dispersing of nanoparticles in the polymers matrix are discussed. The evaluations have revealed that this approach is acceptable. Finally, a prospect is presented. This paper will lead to further work on these modified FML species.

Keywords: Fiber metal laminate, nanofiller, polymer matrix, property modification.

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Authors: Mnisi Blessing, Christopher Amoah

Abstract:

The usage of modern technology is widespread in industrialised nations. The issue still pertains to developing countries since they struggle to use technology in the building sector. The study aims to identify the barriers to technology usage in quantity surveying firms. Quantity Surveyors were interviewed via Microsoft teams due to the dispersed nature of the participants. However, where the interview was not possible, the interview guide was emailed to the participants to fill in. In all, 12 participants were interviewed out of the 25 participants contacted. The data received were analysed using the content analysis process. The study's findings demonstrate that quantity surveyors have access to a wide range of technology that significantly enhances their project activities. However, quantity surveying companies are hesitant to use technology for several reasons, including the cost and maintenance associated with it. Other obstacles include a lack of knowledge, poor market acceptance, legal obstacles, and budgetary constraints. Despite the advantages associated with modern technology applications, quantity surveying firms are not using them, which may ultimately affect their work output. Therefore, firms need to re-examine these obstacles, inhibiting their adoption of technology in the work process to enhance their production. The study reveals the main hindrances to technology usage, which may help firms institute measures to address them.

Keywords: Technology usage barriers, technology implementation, technology acceptance, quantity surveying.

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Authors: S. P. Jordan, G. Christian, S. P. Jeffs

Abstract:

Modern composite materials are increasingly being chosen in replacement of heavier metallic material systems within many engineering fields including aerospace and automotive industries. The increasing push towards satisfying environmental targets are fuelling new material technologies and manufacturing processes. This paper will introduce materials and manufacturing processes using metal matrix composites along with manufacturing processes optimized at Alvant Ltd., based in Basingstoke in the UK which offers modern, cost effective, selectively reinforced composites for light-weighting applications within engineering. An overview and introduction into modern optimized manufacturing methods capable of producing viable replacements for heavier metallic and lower temperature capable polymer composites are offered. A review of the capabilities and future applications of this viable material is discussed to highlight the potential involved in further optimization of old manufacturing techniques, to fully realize the potential to lightweight material using cost-effective methods.

Keywords: Aluminum matrix composites, light-weighting, hybrid squeeze casting, strategically placed reinforcements.

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Authors: Chiung-Hui Chen

Abstract:

With advancements in science and technology, the concept of the Internet of Things (IoT) has gradually developed. The development of the intelligent environment adds intelligence to objects in the living space by using the IoT. In the smart environment, when multiple users share the living space, if different service requirements from different users arise, then the context-aware system will have conflicting situations for making decisions about providing services. Therefore, the purpose of establishing a communication and negotiation mechanism among objects in the intelligent environment is to resolve those service conflicts among users. This study proposes developing a decision-making methodology that uses “Event Agents” as its core. When the sensor system receives information, it evaluates a user’s current events and conditions; analyses object, location, time, and environmental information; calculates the priority of the object; and provides the user services based on the event. Moreover, when the event is not single but overlaps with another, conflicts arise. This study adopts the “Multiple Events Correlation Matrix” in order to calculate the degree values of incidents and support values for each object. The matrix uses these values as the basis for making inferences for system service, and to further determine appropriate services when there is a conflict.

Keywords: Internet of things, intelligent object, event agents, negotiation mechanism, degree of similarity.

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

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In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: Linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control.

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Authors: M. M. Doroodmand, Z.Tahvildar, M. H.Sheikhi

Abstract:

novel and simple method is introduced for rapid and highly efficient water treatment by reverse osmosis (RO) method using multi-walled carbon nanotubes (MWCNTs) / polyacrylonitrile (PAN) polymer as a flexible, highly efficient, reusable and semi-permeable mixed matrix membrane (MMM). For this purpose, MWCNTs were directly synthesized and on-line purified by chemical vapor deposition (CVD) process, followed by directing the MWCNT bundles towards an ultrasonic bath, in which PAN polymer was simultaneously suspended inside a solid porous silica support in water at temperature to ~70 οC. Fabrication process of MMM was finally completed by hot isostatic pressing (HIP) process. In accordance with the analytical figures of merit, the efficiency of fabricated MMM was ~97%. The rate of water treatment process was also evaluated to 6.35 L min-1. The results reveal that, the CNT-based MMM is suitable for rapid treatment of different forms of industrial, sea, drinking and well water samples.

Keywords: Mixed Matrix Membrane, Carbon Nanostructures, Chemical Vapour Deposition, Hot Isostatic Pressing

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Authors: Jiashang Jiang, Yongxin Yuan

Abstract:

In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping matrix and skew-symmetric gyroscopic matrix complied with the required eigenvalue equation are found under a weighted Frobenius norm sense.

Keywords: Model updating, damped gyroscopic system, partially prescribed spectral information.

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Authors: Jayshree Patnaik, Bhaskar Bhowmick

Abstract:

The economic growth of any nation is steered and dependent on innovation in technology. It can be preferably argued that technology has enhanced the quality of life. Technology is linked both with an economic and a social structure. But there are some parts of the world or communities which are yet to reap the benefits of technological innovation. Business and organizations are now well equipped with cutting-edge innovations that improve the firm performance and provide them with a competitive edge, but rarely does it have a positive impact on any community which is weak and marginalized. In recent times, it is observed that communities are actively handling social or ecological issues with the help of indigenous technologies. Thus, "Appropriate Technology" comes into the discussion, which is quite prevalent in the rural third world. Appropriate technology grew as a movement in the mid-1970s during the energy crisis, but it lost its stance in the following years when people started it to describe it as an inferior technology or dead technology. Basically, there is no such technology which is inferior or sophisticated for a particular region. The relevance of appropriate technology lies in penetrating technology into a larger and weaker section of community where the “Bottom of the pyramid” can pay for technology if they find the price is affordable. This is a theoretical paper which primarily revolves around how appropriate technology has faded and again evolved in both developed and developing countries. The paper will try to focus on the various concepts, history and challenges faced by the appropriate technology over the years. Appropriate technology follows a documented approach but lags in overall design and diffusion. Diffusion of technology into the poorer sections of community remains unanswered until the present time. Appropriate technology is multi-disciplinary in nature; therefore, this openness allows having a varied working model for different problems. Appropriate technology is a friendly technology that seeks to improve the lives of people in a constraint environment by providing an affordable and sustainable solution. Appropriate technology needs to be defined in the era of modern technological advancement for sustainability.

Keywords: Appropriate technology, community, developing country, sustainability.

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Authors: Vitalice K. Oduol, C. Ardil

Abstract:

A method is presented for obtaining the error probability for block codes. The method is based on the eigenvalueeigenvector properties of the code correlation matrix. It is found that under a unary transformation and for an additive white Gaussian noise environment, the performance evaluation of a block code becomes a one-dimensional problem in which only one eigenvalue and its corresponding eigenvector are needed in the computation. The obtained error rate results show remarkable agreement between simulations and analysis.

Keywords: bit error rate, block codes, code correlation matrix, eigenstructure, soft-decision decoding, weight vector.

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Authors: Seongmin Yim

Abstract:

The Korean government has applied preliminary feasibility study for new and huge R&D programs since 2008.The study is carried out from the viewpoints of technology, policy, and Economics. Then integrate the separate analysis and finally arrive at a definite result; whether a program is feasible or unfeasible, This paper describes the concept and method of the feasibility analysis focused on technological viability assessment for technical analysis. It consists of technology trend assessment and technology level assessment. Through the analysis, we can determine the chance of schedule delay or cost overrun occurring in the proposed plan.

Keywords: Preliminary Feasibility Study, Technological viability, Technology Trend Assessment, Technology Level Assessment

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Authors: Elragig Aiman, Dreiwi Hanan, Townley Stuart, Elmabrook Idriss

Abstract:

In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.

Keywords: Diffusion driven instability, common Lyapunov function (CLF), turing pattern, positive-definite matrix.

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method.

Keywords: Neural networks, Globally asymptotic stability, LMI approach, Additive time-varying delays.

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Authors: Xia Zhou, Shouming Zhong

Abstract:

The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, Itˆo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.

Keywords: Synchronization, delay-range-dependent, Markov chain, generalized Itō's formula, brownian motion, M-matrix.

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