Search results for: Derived graph

Authors: C. C. Lv, Y. L. Sun, D. W. Zuo

Abstract:

Cemented carbide balls are usually implemented in industry under the environment of high speed, high temperature, corrosiveness and strong collisions. However, its application is limited due to high fabrication cost, processing efficiency and quality. A novel eccentric lapping method with two rotatable lapping plates was proposed in this paper. A mathematical model was constructed to analyze the influence of each design parameter on this lapping method. To validate this new lapping method, an orthogonal experiment was conducted with cemented carbide balls (YG6). The simulation model was verified and the optimal lapping parameters were derived. The results show that the surface roundness of the balls reaches to 0.65um from 2um in 1 hour using this lapping method. So, using this novel lapping method, it can effectively improve the machining precision and efficiency of cemented carbide balls.

Keywords: Cemented carbide balls, eccentric lapping, high precision, lapping tracks, V-groove.

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Authors: Yongkun Li, Meng Hu

Abstract:

A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results. Based on the global Hopf bifurcation theorem for general functional differential equations, the global existence of periodic solutions is established.

Keywords: Predator-prey system, stage structure, time delay, HOPF bifurcation, periodic solution, stability.

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Authors: Abhijit Mitra, Pranab Kumar Banerjee, C. Ardil

Abstract:

We introduce an effective approach for automatic offline au- thentication of handwritten samples where the forgeries are skillfully done, i.e., the true and forgery sample appearances are almost alike. Subtle details of temporal information used in online verification are not available offline and are also hard to recover robustly. Thus the spatial dynamic information like the pen-tip pressure characteristics are considered, emphasizing on the extraction of low density pixels. The points result from the ballistic rhythm of a genuine signature which a forgery, however skillful that may be, always lacks. Ten effective features, including these low density points and den- sity ratio, are proposed to make the distinction between a true and a forgery sample. An adaptive decision criteria is also derived for better verification judgements.

Keywords: Handwritten document verification, Skilled forgeries, Low density pixels, Adaptive decision boundary.

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Authors: Sinchul Back, Sun Ho Kim, Jennifer LaPrade, Ilju Seong

Abstract:

Due to the advantage of using the Internet, cybercriminals can reach target(s) without border controls. Prior research on criminology and crime science has largely been void of empirical studies on journey-to-cybercrime and crime opportunity. Thus, the purpose of this study is to understand more about cyber offender spatial decision making associated with crime opportunity factors (i.e., co-offending, offender-stranger). Data utilized in this study were derived from 306 U.S. Federal court cases of cybercrime. The findings of this study indicated that there was a positive relationship between co-offending and journey-to-cybercrime, whereas there was no link between offender-stranger and journey-to-cybercrime. Also, the results showed that there was no relationship between cybercriminal sex, age, and journey-to-cybercrime. The policy implications and limitations of this study are discussed.

Keywords: Co-offending, crime opportunity, journey-to-cybercrime, offender-stranger.

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Authors: David W.S. Tai, Ren-Cheng Zhang, Sheng-Hung Chang, Chin-Pin Chen, Jia-Ling Chen

Abstract:

This study reports results of a meta-analytic path analysis e-learning Acceptance Model with k = 27 studies, Databases searched included Information Sciences Institute (ISI) website. Variables recorded included perceived usefulness, perceived ease of use, attitude toward behavior, and behavioral intention to use e-learning. A correlation matrix of these variables was derived from meta-analytic data and then analyzed by using structural path analysis to test the fitness of the e-learning acceptance model to the observed aggregated data. Results showed the revised hypothesized model to be a reasonable, good fit to aggregated data. Furthermore, discussions and implications are given in this article.

Keywords: E-learning, Meta Analytic Path Analysis, Technology Acceptance Model

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Authors: Othmane Fahim, Naoual Belouaggadia. Charifa David, Mohamed Ezzine

Abstract:

To make better use of cooling resources, systems have been derived on the basis of the use of night radiator systems for heat pumping. Using the TRNSYS tool we determined the influence of the climatic characteristics of the two zones in Morocco on the temperature of the outer surface of a Photovoltaic Thermal Panel “PVT” made of aluminum. The proposal to improve the performance of the panel allowed us to have little heat absorption during the day and give the same performance of a panel made of aluminum at night. The variation in the granite-based panel temperature recorded a deviation from the other materials of 0.5 °C, 2.5 °C on the first day respectively in Marrakech and Casablanca, and 0.2 °C and 3.2 °C on the second night. Power varied between 110.16 and 32.01 W/m² marked in Marrakech, to be the most suitable area to practice night cooling by night radiation.

Keywords: Morocco, TRANSYS, radiative cooling.

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

Abstract:

In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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Authors: Sanchita Chauhan, V.K. Srivastava

Abstract:

Catalytic converters are used for minimizing the release of pollutants to the atmosphere. It is during the warm-up period that hydrocarbons are seen to be released in appreciable quantities from these converters. In this paper the conversion of a fast oxidizing hydrocarbon propylene is analysed using two numerical methods. The quasi steady state method assumes the accumulation terms to be negligible in the gas phase mass and energy balance equations, however this term is present in the solid phase energy balance. The unsteady state model accounts for the accumulation term to be present in the gas phase mass and energy balance and in the solid phase energy balance. The results derived from the two models for gas concentration, gas temperature and solid temperature are compared.

Keywords: Propylene, catalyst, quasi steady state, unsteady state.

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Authors: M. Behbahani-Nejad, Y. Shekari

Abstract:

A reduced order modeling approach for natural gas transient flow in pipelines is presented. The Euler equations are considered as the governing equations and solved numerically using the implicit Steger-Warming flux vector splitting method. Next, the linearized form of the equations is derived and the corresponding eigensystem is obtained. Then, a few dominant flow eigenmodes are used to construct an efficient reduced-order model. A well-known test case is presented to demonstrate the accuracy and the computational efficiency of the proposed method. The results obtained are in good agreement with those of the direct numerical method and field data. Moreover, it is shown that the present reduced-order model is more efficient than the conventional numerical techniques for transient flow analysis of natural gas in pipelines.

Keywords: Eigenmode, Natural Gas, Reduced Order Modeling, Transient Flow.

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Authors: Yun Jong Choi, Nam Woong, PooGyeon Park

Abstract:

Variable Structure Control (VSC) is one of the most useful tools handling the practical system with uncertainties and disturbances. Up to now, unfortunately, not enough studies on the input-saturated system with linear-growth-bound disturbances via VSC have been presented. Therefore, this paper proposes an asymp¬totic stability condition for the system via VSC. The designed VSC controller consists of two control parts. The linear control part plays a role in stabilizing the system, and simultaneously, the nonlinear control part in rejecting the linear-growth-bound disturbances perfectly. All conditions derived in this paper are expressed with Linear Matrices Inequalities (LMIs), which can be easily solved with an LMI toolbox in MATLAB.

Keywords: Input saturation, linear-growth bounded disturbances, linear matrix inequality (LMI), variable structure control

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Authors: L. Parisi

Abstract:

Kinematic data wisely correlate vector quantities in space to scalar parameters in time to assess the degree of symmetry between the intact limb and the amputated limb with respect to a normal model derived from the gait of control group participants. Furthermore, these particular data allow a doctor to preliminarily evaluate the usefulness of a certain rehabilitation therapy. Kinetic curves allow the analysis of ground reaction forces (GRFs) to assess the appropriateness of human motion. Electromyography (EMG) allows the analysis of the fundamental lower limb force contributions to quantify the level of gait asymmetry. However, the use of this technological tool is expensive and requires patient’s hospitalization. This research work suggests overcoming the above limitations by applying artificial neural networks.

Keywords: Kinetics, kinematics, cyclograms, neural networks.

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Authors: Rajeev Ranjan Sahay

Abstract:

Transient storage zones along the flow paths of rivers have great influence on the dispersion of pollutants that are either accidentally or otherwise led into them. The speed with which these pollution clouds get transported and dispersed downstream is, to a large extent, explained by the longitudinal dispersion coefficients in the free-flowing zones of rivers (Kf). In the present work, a new empirical expression for Kf has been derived employing genetic programming (GP) on published dispersion data. The proposed expression uses few hydraulic and geometric characteristics of a river that are readily available to field engineers. Based on various performance indices, the proposed expression is found superior to other existing expression for Kf.

Keywords: Dispersion, parameter estimation, rivers, transient pollutant.

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Authors: S. Bangphan, P. Bangphan, T.Boonkang

Abstract:

Implementation of response surface methodology (RSM) was employed to study the effects of two factor (rubber clearance and round per minute) in brown rice peeling machine of The optimal BROKENS yield (19.02, average of three repeats),.The optimized composition derived from RSM regression was analyzed using Regression analysis and Analysis of Variance (ANOVA). At a significant level α = 0.05, the values of Regression coefficient, R 2 (adj)were 97.35 % and standard deviation were 1.09513. The independent variables are initial rubber clearance, and round per minute parameters namely. The investigating responses are final rubber clearance, and round per minute (RPM). The restriction of the optimization is the designated.

Keywords: Brown rice, Response surface methodology(RSM), Rubber clearance, Round per minute (RPM), Peeling machine.

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Authors: Kaan T. Oner, Ertugrul Cetinsoy, Efe Sirimoglu, Cevdet Hancer, Taylan Ayken, Mustafa Unel

Abstract:

We present our ongoing work on the development of a new quadrotor aerial vehicle which has a tilt-wing mechanism. The vehicle is capable of take-off/landing in vertical flight mode (VTOL) and flying over long distances in horizontal flight mode. Full dynamic model of the vehicle is derived using Newton-Euler formulation. Linear and nonlinear controllers for the stabilization of attitude of the vehicle and control of its altitude have been designed and implemented via simulations. In particular, an LQR controller has been shown to be quite effective in the vertical flight mode for all possible yaw angles. A sliding mode controller (SMC) with recursive nature has also been proposed to stabilize the vehicle-s attitude and altitude. Simulation results show that proposed controllers provide satisfactory performance in achieving desired maneuvers.

Keywords: UAV, VTOL, dynamic model, stabilization, LQR, SMC

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Authors: S. S. Salehi, A. Shamloo

Abstract:

Poor ability of cartilage tissue when experiencing a damage leads scientists to use tissue engineering as a reliable and effective method for regenerating or replacing damaged tissues. An artificial tissue should have some features such as biocompatibility, biodegradation and, enough mechanical properties like the original tissue. In this work, a composite hydrogel is prepared by using natural and synthetic materials that has high porosity. Mechanical properties of different combinations of polymers such as modulus of elasticity were tested, and a hydrogel with good mechanical properties was selected. Bone marrow derived mesenchymal stem cells were also seeded into the pores of the sponge, and the results showed the adhesion and proliferation of cells within the hydrogel after one month. In comparison with previous works, this study offers a new and efficient procedure for the fabrication of cartilage like tissue and further cartilage repair.

Keywords: Cartilage tissue engineering, hydrogel, mechanical strength, mesenchymal stem cell.

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Authors: Al-Salamin Hussain, Elias O. Tembe

Abstract:

Supply chain (SC) is an operational research (OR) approach and technique which acts as catalyst within central nervous system of business today. Without SC, any type of business is at doldrums, hence entropy. SC is the lifeblood of business today because it is the pivotal hub which provides imperative competitive advantage. The paper present a conceptual framework dubbed as Homomorphic Conceptual Framework for Effective Supply Chain Strategy (HCEFSC).The term Homomorphic is derived from abstract algebraic mathematical term homomorphism (same shape) which also embeds the following mathematical application sets: monomorphisms, isomorphism, automorphisms, and endomorphism. The HCFESC is intertwined and integrated with wide and broad sets of elements.

Keywords: Automorphisms, Homomorphism, Monomorphisms, Supply Chain.

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Authors: Luiz G. Véras, Felipe L. Medeiros, Lamartine F. Guimarães

Abstract:

This work approaches the automatic planning of paths for Unmanned Aerial Vehicles (UAVs) through the application of the Rapidly Exploring Random Tree Star-Smart (RRT*-Smart) algorithm. RRT*-Smart is a sampling process of positions of a navigation environment through a tree-type graph. The algorithm consists of randomly expanding a tree from an initial position (root node) until one of its branches reaches the final position of the path to be planned. The algorithm ensures the planning of the shortest path, considering the number of iterations tending to infinity. When a new node is inserted into the tree, each neighbor node of the new node is connected to it, if and only if the extension of the path between the root node and that neighbor node, with this new connection, is less than the current extension of the path between those two nodes. RRT*-smart uses an intelligent sampling strategy to plan less extensive routes by spending a smaller number of iterations. This strategy is based on the creation of samples/nodes near to the convex vertices of the navigation environment obstacles. The planned paths are smoothed through the application of the method called quintic pythagorean hodograph curves. The smoothing process converts a route into a dynamically-viable one based on the kinematic constraints of the vehicle. This smoothing method models the hodograph components of a curve with polynomials that obey the Pythagorean Theorem. Its advantage is that the obtained structure allows computation of the curve length in an exact way, without the need for quadratural techniques for the resolution of integrals.

Keywords: Path planning, path smoothing, Pythagorean hodograph curve, RRT*-Smart.

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Authors: Liliana M. Ştefan, Ana M. Pană, Geza Bandur, Marcel Popa, Lucian M. Rusnac

Abstract:

Polymers are one of the most widely used materials in our every day life. The subject of renewable resources has attracted great attention in the last period of time. New polymeric materials derived from renewable resources, like carbohydrates draw attention to public eye especially because of their biocompatibility and biodegradability. The aim of our paper was to obtain environmentally compatible polymers from monosaccharides. Novel glycopolymers based on D-glucose have been obtained from copolymerization of a new monomer carrying carbohydrate moiety with methyl methacrylate (MMA) via free radical bulk polymerization. Differential scanning calorimetry (DSC) was performed in order to study the copolymerization process of the monomer into the chosen co-monomer; the activation energy of this process was evaluated using Ozawa method. The copolymers obtained were characterized using ATR-FTIR spectroscopy. The thermal stability of the obtained products was studied by thermogravimetry (TG).

Keywords: DSC, glycopolymer, monosaccarides, TG.

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Authors: Anamika Gupta, Naveen Kumar, Vasudha Bhatnagar

Abstract:

This paper focuses on analyzing medical diagnostic data using classification rules in data mining and context reduction in formal concept analysis. It helps in finding redundancies among the various medical examination tests used in diagnosis of a disease. Classification rules have been derived from positive and negative association rules using the Concept lattice structure of the Formal Concept Analysis. Context reduction technique given in Formal Concept Analysis along with classification rules has been used to find redundancies among the various medical examination tests. Also it finds out whether expensive medical tests can be replaced by some cheaper tests.

Keywords: Data Mining, Formal Concept Analysis, Medical Data, Negative Classification Rules.

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Authors: S. K. Fasogbon

Abstract:

Chaotic system may lead to instability, extreme sensitivity and performance reduction in control systems. It is therefore important to understand the causes of such undesirable characteristics in control system especially in the automobile fuel gauges. This is because without accurate fuel gauges in automobile systems, it will be difficult if not impossible to embark on a journey whether during odd hours of the day or where fuel is difficult to obtain. To this end, this work studied the impacts of fuel tank rust and faulty component of fuel gauge system (voltage stabilizer) on the chaotic characteristics of fuel gauges. The results obtained were analyzed using Graph iSOFT package. Over the range of experiments conducted, the results obtained showed that rust effect of the fuel tank would alter the flow density, consequently the fluid pressure and ultimately the flow velocity of the fuel. The responses of the fuel gauge pointer to the faulty voltage stabilizer were erratic causing noticeable instability of gauge measurands indicated. The experiment also showed that the fuel gauge performed optimally by indicating the highest degree of accuracy when combined the effect of rust free tank and non-faulty voltage stabilizer conditions (± 6.75% measurand error) as compared to only the rust free tank situation (± 15% measurand error) and only the non-faulty voltage stabilizer condition (± 40% measurand error). The study concludes that both the fuel tank rust and the faulty voltage stabilizer gauge component have a significant effect on the sensitivity of fuel gauge and its accuracy ultimately. Also, by the reason of literature, our findings can also be said to be valid for all other fluid meters and gauges applicable in plant machineries and most hydraulic systems.

Keywords: Chaotic system, degree of accuracy, measurand, sensitivity of fuel gauge.

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Authors: D.M. Weeraddana, K.S. Walgama, E.C. Kulasekere

Abstract:

A framework to estimate the state of dynamically varying environment where data are generated from heterogeneous sources possessing partial knowledge about the environment is presented. This is entirely derived within Dempster-Shafer and Evidence Filtering frameworks. The belief about the current state is expressed as belief and plausibility functions. An addition to Single Input Single Output Evidence Filter, Multiple Input Single Output Evidence Filtering approach is introduced. Variety of applications such as situational estimation of an emergency environment can be developed within the framework successfully. Fire propagation scenario is used to justify the proposed framework, simulation results are presented.

Keywords: Dempster-Shafer Belief theory, Evidence Filtering, Evidence Fusion, Sensor Modalities, Wireless Sensor Networks

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Authors: B. Tiseo, V. Quaranta, G. Bruno, R. Gardi, T. Watts, S. Dussy

Abstract:

This paper describes the qualification test campaign performed on the Demise Observation Capsule DOC-EQM as part of the Future Launch Preparatory Program FLPP3. The mechanical environment experienced during launch ascent and separation phase was first identified and then replicated in terms of sine, random and shock vibration. The loads identification is derived by selecting the worst possible case. Vibration and shock qualification test performed at CIRA Space Qualification laboratory is herein described. Mechanical fixtures’ design and validation, carried out by means of FEM, is also addressed due to its fundamental role in the vibrational test campaign. The Demise Observation Capsule (DOC) successfully passed the qualification test campaign. Functional test and resonance search have not been point any fault and damages of the capsule.

Keywords: Capsule, demise, DOC, launch environment, Re-Entry, qualification.

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Authors: Malinda G. Sirisena

Abstract:

The aim of this research is to evaluate the effectiveness of software quality assurance approaches of Sri Lankan offshore software development organizations, and to propose a framework which could be used across all offshore software development organizations.

An empirical study was conducted using derived framework from popular software quality evaluation models. The research instrument employed was a questionnaire survey among thirty seven Sri Lankan registered offshore software development organizations.

The findings demonstrate a positive view of Effectiveness of Software Quality Assurance – the stronger predictors of Stability, Installability, Correctness, Testability and Changeability. The present study’s recommendations indicate a need for much emphasis on software quality assurance for the Sri Lankan offshore software development organizations.

Keywords: Software Quality Assurance (SQA), Offshore Software Development, Quality Assurance Evaluation Models, Effectiveness of Quality Assurance.

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Authors: Jong Woo Kim, Go Bong Choi, Sang Hwan Son, Dae Shik Kim, Jung Chul Suh, Jong Min Lee

Abstract:

The Markov decision process (MDP) based methodology is implemented in order to establish the optimal schedule which minimizes the cost. Formulation of MDP problem is presented using the information about the current state of pipe, improvement cost, failure cost and pipe deterioration model. The objective function and detailed algorithm of dynamic programming (DP) are modified due to the difficulty of implementing the conventional DP approaches. The optimal schedule derived from suggested model is compared to several policies via Monte Carlo simulation. Validity of the solution and improvement in computational time are proved.

Keywords: Markov decision processes, Dynamic Programming, Monte Carlo simulation, Periodic replacement, Weibull distribution.

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Authors: A.O. Boudraa, J.C. Cexus, Z. Saidi

Abstract:

This paper introduces a new signal denoising based on the Empirical mode decomposition (EMD) framework. The method is a fully data driven approach. Noisy signal is decomposed adaptively into oscillatory components called Intrinsic mode functions (IMFs) by means of a process called sifting. The EMD denoising involves filtering or thresholding each IMF and reconstructs the estimated signal using the processed IMFs. The EMD can be combined with a filtering approach or with nonlinear transformation. In this work the Savitzky-Golay filter and shoftthresholding are investigated. For thresholding, IMF samples are shrinked or scaled below a threshold value. The standard deviation of the noise is estimated for every IMF. The threshold is derived for the Gaussian white noise. The method is tested on simulated and real data and compared with averaging, median and wavelet approaches.

Keywords: Empirical mode decomposition, Signal denoisingnonstationary process.

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Authors: Ibrahim F. Jasim, Najah F. Jasim

Abstract:

The problem of controlling a two link robotic manipulator, consisting of a rotating and a prismatic links, is addressed. The actuations of both links are assumed to have unknown dead zone nonlinearities and friction torques modeled by LuGre friction model. Because of the existence of the unknown dead zone and friction torque at the actuations, unknown parameters and unmeasured states would appear to be part of the overall system dynamics that need for estimation. Unmeasured states observer, unknown parameters estimators, and robust adaptive control laws have been derived such that closed loop global stability is achieved. Simulation results have been performed to show the efficacy of the suggested approach.

Keywords: Adaptive Robust Control, Dead Zone, Friction Torques, Robotic Manipulators.

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Authors: M. Behbahani-Nejad, A. Bagheri

Abstract:

An efficient transient flow simulation for gas pipelines and networks is presented. The proposed transient flow simulation is based on the transfer function models and MATLABSimulink. The equivalent transfer functions of the nonlinear governing equations are derived for different types of the boundary conditions. Next, a MATLAB-Simulink library is developed and proposed considering any boundary condition type. To verify the accuracy and the computational efficiency of the proposed simulation, the results obtained are compared with those of the conventional finite difference schemes (such as TVD, method of lines, and other finite difference implicit and explicit schemes). The effects of the flow inertia and the pipeline inclination are incorporated in this simulation. It is shown that the proposed simulation has a sufficient accuracy and it is computationally more efficient than the other methods.

Keywords: Gas network, MATLAB-Simulink, transfer functions, transient flow.

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Authors: M. A. Hajeeh

Abstract:

Pumping systems are an integral part of water desalination plants, their effective functioning is vital for the operation of a plant. In this research work, the reliability and availability of pressurized pumps in a reverse osmosis desalination plant are studied with the objective of finding configurations that provides optimal performance. Six configurations of a series system with different number of warm and cold standby components were examined. Closed form expressions for the mean time to failure (MTTF) and the long run availability are derived and compared under the assumption that the time between failures and repair times of the primary and standby components are exponentially distributed. Moreover, a cost/ benefit analysis is conducted in order to identify a configuration with the best performance and least cost. It is concluded that configurations with cold standby components are preferable especially when the pumps are of the size.

Keywords: Availability, Cost/ benefit, Mean time to failure, Pumps.

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Authors: Tan K. B., Norhashidah Hj. M. Ali

Abstract:

In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.

Keywords: Standard point Crank-Nicolson (CN), Rotated point Crank-Nicolson (RCN), Explicit Group (EG), Explicit Decoupled Group (EDG).

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Authors: Feng Cheng Chang

Abstract:

A given polynomial, possibly with multiple roots, is factored into several lower-degree distinct-root polynomials with natural-order-integer powers. All the roots, including multiplicities, of the original polynomial may be obtained by solving these lowerdegree distinct-root polynomials, instead of the original high-degree multiple-root polynomial directly. The approach requires polynomial Greatest Common Divisor (GCD) computation. The very simple and effective process, “Monic polynomial subtractions" converted trickily from “Longhand polynomial divisions" of Euclidean algorithm is employed. It requires only simple elementary arithmetic operations without any advanced mathematics. Amazingly, the derived routine gives the expected results for the test polynomials of very high degree, such as p( x) =(x+1)1000.

Keywords: Polynomial roots, greatest common divisor, Longhand polynomial division, Euclidean GCD Algorithm.

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