Search results for: precedence diagram method

Authors: Maryam Goodarzi, Mahdieh Sheikhi, Mehdi Goodarzi

Abstract:

This study intends to offer an appropriate strategy development framework for a telecommunication firm (as a case study) which works on Information and Communication Technology (ICT) projects, development of telecommunication networks, and maintenance of local networks, according to its dominant condition. In this approach, first, the objectives were set and the mission was defined. Then, the capability was assessed by SWOT matrix. Using SPACE matrix, the strategy of the company was determined. The strategic direction is set and an appropriate and superior strategy was developed and offered employing QSPM matrix. The theoretical framework or conceptual model of the present study first involves 4 stages of framework development and then from stage 3 (assessing capability) onward, a strategic management model by Fred R. David. In this respect, the tools and methods offered in the framework are appropriate for all kinds of organizations, particularly small firms, and help strategists identify, evaluate, and select strategies.

Keywords: strategy formulation, firm mission, strategic direction, space diagram, quantitative strategic planning matrix, SWOT matrix

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Tohru Kawabe

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In this paper, a new SMC (Sliding Mode Control) method with MP (Model Predictive Control) integral action for the slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method introduce the integral term with standard SMC gain , where the integral gain is optimized for each control period by the MPC algorithms. The aim of this method is to improve the safety and the stability of EVs under braking by controlling the wheel slip ratio. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: sliding mode control, model predictive control, integral action, electric vehicle, slip suppression

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Authors: Cuitao Zhang, Xiongwen He

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According to the new requirements of the future spacecraft, such as networking, modularization and non-cable, this paper studies the CCSDS wireless communications standards, and focuses on the low data-rate wireless communications for spacecraft monitoring and control. The application fields and advantages of wireless communications are analyzed. Wireless communications technology has significant advantages in reducing the weight of the spacecraft, saving time in spacecraft integration, etc. Based on this technology, a scheme for spacecraft data system is put forward. The corresponding block diagram and key wireless interface design of the spacecraft data system are given. The design proposal of the wireless node and information flow of the spacecraft are also analyzed. The results show that the wireless communications scheme is reasonable and feasible. The wireless communications technology can meet the future spacecraft demands in networking, modularization and non-cable.

Keywords: Consultative Committee for Space Data Systems (CCSDS) standards, information flow, non-cable, spacecraft, wireless communications

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Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

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Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: evapotranspiration, hargreaves, equation, FAO-Penman method

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Authors: F. Boufera, F. Debbat

Abstract:

This paper deals with an approach based on limit-cycles method for the problem of obstacle avoidance of mobile robots in unknown environments for any form of obstacles. The purpose of this approach is the improvement of limit-cycles method in order to obtain safe and flexible navigation. The proposed algorithm has been successfully tested in different configuration on simulation.

Keywords: mobile robot, navigation, avoidance of obstacles, limit-cycles method

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Authors: P. C. Tewari, Rajiv Kumar, Dinesh Khanduja

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This paper discusses the performance modeling and availability analysis of Yarn Dyeing System of a Textile Industry. The Textile Industry is a complex and repairable engineering system. Yarn Dyeing System of Textile Industry consists of five subsystems arranged in series configuration. For performance modeling and analysis of availability, a performance evaluating model has been developed with the help of mathematical formulation based on Markov-Birth-Death Process. The differential equations have been developed on the basis of Probabilistic Approach using a Transition Diagram. These equations have further been solved using normalizing condition in order to develop the steady state availability, a performance measure of the system concerned. The system performance has been further analyzed with the help of decision matrices. These matrices provide various availability levels for different combinations of failure and repair rates for various subsystems. The findings of this paper are, therefore, considered to be useful for the analysis of availability and determination of the best possible maintenance strategies which can be implemented in future to enhance the system performance.

Keywords: performance modeling, markov process, steady state availability, availability analysis

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Authors: A. H. Choudhury

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In this paper, a highly accurate numerical method for the solution of one-dimensional fourth-order wave equation is derived. This hyperbolic problem is solved by using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method, and the time variable is discretized by using Newmark schemes.

Keywords: hyperbolic problem, semidiscrete approximations, stability, Wavelet-Galerkin Method

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Authors: Abdul Qader Melhm, Hussein Elrafidi

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This paper is dealing with studying the structural behavior of a steel-composite hollow reinforced concrete (RC) column model under combined eccentric loading. The composite model consists of an inner steel tube surrounded via a concrete core with longitudinal and circular transverse reinforcement. The radius of gyration according to American and Euro specifications be calculated, in order to calculate the thinnest ratio for this type of composite column model, in addition to the flexural rigidity. Formulas for interaction diagram is given for this type of model, which is a general loading conditions in which an element is exposed to an axial load with bending at the same time. The structural capacity of this model, elastic, plastic loads and strains will be computed and compared with experimental results. The total eccentric axial load of the column model is calculated based on the effective length KL available from several relationships provided in the paper. Furthermore, the inner tube experiences buckling failure after reaching its maximum strength will be investigated.

Keywords: column, composite, eccentric, inner tube, interaction, reinforcement

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Authors: Rahman Dashti, Ehsan Gord

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In this paper, an improved impedance based fault location method is proposed. In this method, online fault locating is performed using voltage and current information at the beginning of the feeder. Determining precise fault location in a short time increases reliability and efficiency of the system. The proposed method utilizes information about main component of voltage and current at the beginning of the feeder and distributed generation unit (DGU) in order to precisely locate different faults in acceptable time. To evaluate precision and accuracy of the proposed method, a 13-node is simulated and tested using MATLAB.

Keywords: distribution network, fault section determination, distributed generation units, distribution protection equipment

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Authors: Luguang Qi, Chuang Xie

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In recent years, there has been an increase in the number of reports on cocrystal polymorphism and stoichiomorphism. However, the research on the factors that influence these phenomena is limited. Herein, picolinamide (PAM), nicotinamide (NAM), and isonicotinamide (INA) were selected as co-formers to form multicomponent solids with 4-chloro-3-sulfamoylbenzoic acid (CSBA). Six new cocrystal forms of CSBA were discovered, and their crystal structures were determined. It was found that PAM and NAM can only form one cocrystal with CSBA, while INA can form up to four cocrystals, including both cocrystal polymorphism and stoichiomorphism. Molecular electrostatic potential analysis and crystal structure analysis showed that the functional group position of PAM limited the diversity of cocrystal synthons, while the lattice energy limited the diversity of cocrystal synthons when NAM acted as a co-former. Only INA was not subject to these restrictions when forming cocrystals. Finally, the influence of solvents on cocrystals was illustrated by determining the ternary phase diagrams. The mechanism of two similar solvents, ethyl acetate, and acetone, controlling the crystallization of cocrystal polymorphism was analyzed by molecular simulations.

Keywords: cocrystal polymorphism, cocrystal stoichiomorphism, phase diagram, molecular simulation

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Authors: W. S. Lawal, T. Akande

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Abstract— Four (4) difference methods were employed to detoxify Jatropha carcas, they were physical method (it include soaking and sun drying) Chemical (the use of methylated sprit, hexane and methane). Biological (the use of Aspergillus niger and then sundry for 7days and then Bacillus lichiformis) and Combined method (the combination of chemical and biological methods). Phobol esther analysis was carried out after the detoxification methods and it was found that the combined method is better off (P<0.05). Detoxified Jatropha from each of this methods was sundry and grinded for easy inclusion into poultry feed, detoxified jatropha was included at 0%, 0.5%, 1%, 2%, 3%, 4%, and 5% but the combined method was increased up to 7% because the birds were able to tolerate it, the 0% was the control experiment. 405 day old broiler chicks was used to test the effect of detoxified Jatropha carcas on their performance, there are 5birds per treatment and there are 3 replicates, the experiment lasted for 8weeks,highest number of mortality was obtained in physical method, birds in chemical method tolerated up to 3% Jatropha carcas, biological method is better, as birds there were comfortable at 5% but the best of them is combined method the birds did very well at 7% as there were less mortality and highest weight gain was achieved here (P<0.05) and it was recommended.

Keywords: phobol esther, inclusion level, tolerance level, Jatropha carcas

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Authors: Hadi Farhadian, Homayoon Katibeh

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In this paper, groundwater seepage into Amirkabir tunnel has been estimated using analytical and numerical methods for 14 different sections of the tunnel. Site Groundwater Rating (SGR) method also has been performed for qualitative and quantitative classification of the tunnel sections. The obtained results of above-mentioned methods were compared together. The study shows reasonable accordance with results of the all methods unless for two sections of tunnel. In these two sections there are some significant discrepancies between numerical and analytical results mainly originated from model geometry and high overburden. SGR and the analytical and numerical calculations, confirm the high concentration of seepage inflow in fault zones. Maximum seepage flow into tunnel has been estimated 0.425 lit/sec/m using analytical method and 0.628 lit/sec/m using numerical method occurred in crashed zone. Based on SGR method, six sections of 14 sections in Amirkabir tunnel axis are found to be in "No Risk" class that is supported by the analytical and numerical seepage value of less than 0.04 lit/sec/m.

Keywords: water Seepage, Amirkabir Tunnel, analytical method, DEM, SGR

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Authors: M. Shannag, A. Charif, S. Naser, F. Faisal, A. Karim

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Structural lightweight concrete is used primarily to reduce the dead-load weight in concrete members such as floors in high-rise buildings and bridge decks. With given materials, it is generally desired to have the highest possible strength/unit weight ratio with the lowest cost of concrete. The work presented herein is part of an ongoing research project that investigates the properties of concrete mixes containing locally available Scoria lightweight aggregates and mineral admixtures. Properties considered included: workability, unit weight, compressive strength, and splitting tensile strength. Test results indicated that developing structural lightweight concretes (SLWC) using locally available Scoria lightweight aggregates and specific blends of silica fume and fly ash seems to be feasible. The stress-strain diagrams plotted for the structural LWC mixes developed in this investigation were comparable to a typical stress-strain diagram for normal weight concrete with relatively larger strain capacity at failure in case of LWC.

Keywords: lightweight concrete, scoria, stress, strain, silica fume, fly ash

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Authors: S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, M. Suleiman

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The method of solving second order stiff ordinary differential equation (ODEs) that is based on backward differentiation formula (BDF) is considered in this paper. We derived the method by increasing the order of the existing method using an improved strategy in choosing the step size. Numerical results are presented to compare the efficiency of the proposed method to the MATLAB’s suite of ODEs solvers namely ode15s and ode23s. The method was found to be efficient to solve second order ordinary differential equation.

Keywords: backward differentiation formulae, block backward differentiation formulae, stiff ordinary differential equation, variable step size

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Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: Maysam Shahsavari, Seyed Jamalaldin Haddadi

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There are several methods to localize a mobile robot such as relative, absolute and probabilistic. In this paper, particle filter due to its simple implementation and the fact that it does not need to know to the starting position will be used. This method estimates the position of the mobile robot using a probabilistic distribution, relying on a known map of the environment instead of predicting it. Afterwards, it updates this estimation by reading input sensors and control commands. To receive information from the surrounding world, distance to obstacles, for example, a Kinect is used which is much cheaper than a laser range finder. Finally, after explaining the Adaptive Particle Filter method and its implementation in detail, we will compare this method with the dead reckoning method and show that this method is much more suitable for situations in which we have a map of the environment.

Keywords: particle filter, localization, methods, odometry, kinect

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Authors: Mohammad Mojtahedpoor

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In this paper, it has been studied the method of optimal design of the supersonic nozzle. It could make viscous axisymmetric nozzles that the quality of their outlet flow is quite desired. In this method, it is optimized the divergent nozzle, at first. The initial divergent nozzle contour is designed through the method of characteristics and adding a suitable boundary layer to the inviscid contour. After that, it is made a proper grid and then simulated flow by the numerical solution and AUSM+ method by using the operation boundary condition. At the end, solution outputs are investigated and optimized. The numerical method has been validated with experimental results. Also, in order to evaluate the effectiveness of the present method, the nozzles compared with the previous studies. The comparisons show that the nozzles obtained through this method are sufficiently better in some conditions, such as the flow uniformity, size of the boundary layer, and obtained an axial length of the nozzle. Designing the convergent nozzle part affects by flow uniformity through changing its axial length and input diameter. The results show that increasing the length of the convergent part improves the output flow uniformity.

Keywords: nozzle, supersonic, optimization, characteristic method, CFD

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Assiya Madenovna Borsynbayeva, Kairat Altynbekovich Turgenbayev, Nikolay Petrovich Ivanov

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In this article presents the results of rapid diagnostics of tuberculosis in comparison with classical bacteriological method. The proposed method of rapid diagnosis of tuberculosis than bacteriological method allows shortening the time of diagnosis to 7 days, to visualize the growth of mycobacteria in the semi-liquid medium and differentiate the type of mycobacterium. Fast definition of Mycobacterium tuberculosis and its derivatives in the culture medium is a new and promising direction in the diagnosis of tuberculosis.

Keywords: animal diagnosis of tuberculosis, bacteriological diagnostics, antigen, specific antibodies, immunological reaction

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Shailendra Kumar Singh

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In the 21st century, we are living through extraordinary times as we are linguistically blessed to live through an era in which the each sociolinguistic example of living appears to be refreshingly new without any precedence of the past. The word `New Linguistic World Order’ is no longer just the intangible fascination but an indication of the emerging reality that we are living through a time in which the word ‘linguistic purism’ no longer invokes the sense of self categorization and self identification. The contemporary world of today is linguistically rewarding. This is a time in which the very existence of global, powerful and local needs to be revisited in the context of power shift, demographic shift, social psychological shift and technological shift. Hence, the old linguistic world view has to be challenged in the midst of 21st century. The first years of the 21st century have thus far been marked by the rise global economy, technological revolution and demographic shift, now we are witnessing linguistic shift which is leading towards forming a new linguistic world order. On the other hand, with rising powers of China and India in Asia in tandem the notion of alternative west is set to become a lot more interesting linguistically. It comes at a point when the world is moving towards inclusive globalization due to vanishing power corridor of the west and ascending geopolitical impact of emerging superpower and superpower in waiting. Now it is a reality that the western world no longer continues to rise – in fact, it will have more pressure to act in situation when the alternative west is looking for balanced globalization. It is more than likely that demographically strong languages of alternative west will be in advantageous position. The paper challenges our preconceptions about the nature of sociolinguistic nature of world in the 21st century. It investigates what a linguistic world is likely to be in the future in contrast to what was a linguistic world before 21st century. In particular, the paper tries to answer the following questions: (a) What will be the common linguistic thread across world? (b) How unprecedented transformations can be mapped linguistically? (c) Do we need alternative linguistics to define inclusive globalization as the linguistic reality of the contemporary world has already been reshaped by increasingly integrated world economy, linguistic revolution and alternative west? (d) In which ways these issues can be addressed holistically? (e) Why linguistic world order is changing dramatically? (f) Is it true that the linguistic world around is changing faster than we can even really cope? (g) Is it true that what is coming next is linguistically greater than ever? (h) Do we need to prepare ourselves with new theoretical strategies to address emerging sociolinguistic reality?

Keywords: alternative linguistics, new linguistic world order, power shift, demographic shift, social psychological shift, technological shift

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Authors: Tejush Badal, Sanaa Alwidian

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Class diagrams are useful tools within the Unified Modelling Language (UML) to model and visualize the relationships between, and properties of objects within a system. As a system evolves over time and space (e.g., products), a series of models with several commonalities and variabilities create what is known as a model family. In circumstances where there are several versions of a model, examining each model individually, becomes expensive in terms of computation resources. To avoid performing redundant operations, this paper proposes an approach for representing a family of class diagrams into Union Models to represent model families using a single generic model. The paper aims to analyze and reason about a family of class diagrams using union models as opposed to individual analysis of each member model in the family. The union algorithm provides a holistic view of the model family, where the latter cannot be otherwise obtained from an individual analysis approach, this in turn, enhances the analysis performed in terms of speeding up the time needed to analyze a family of models together as opposed to analyzing individual models, one model at a time.

Keywords: analysis, class diagram, model family, unified modeling language, union model

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Authors: F. J. Adeyeye, D. Eni, K. M. Okedoye

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In this paper we present a Hybrid of Adomian decomposition method (ADM). This is the substitution of a One-step method of Taylor’s series approximation of orders I and II, into the nonlinear part of Adomian decomposition method resulting in a convergent series scheme. This scheme is applied to solve some Logistic problems represented as Abelian differential equation and the results are compared with the actual solution and Runge-kutta of order IV in order to ascertain the accuracy and efficiency of the scheme. The findings shows that the scheme is efficient enough to solve logistic problems considered in this paper.

Keywords: Adomian decomposition method, nonlinear part, one-step method, Taylor series approximation, hybrid of Adomian polynomial, logistic problem, Malthusian parameter, Verhulst Model

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Authors: Abid Fida Masih

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Forced degradation study of Rifaximin was conducted to determine the stability indicating potential of HPLC testing method for detection of Rifaximin in formulated tablets to be employed for quality control and stability testing. The questioned method applied with mobile phase methanol: water (70:30), 5µm, 250 x 4.6mm, C18 column, wavelength 293nm and flow rate of 1.0 ml/min. Forced degradation study was performed under oxidative, acidic, basic, thermal and photolytic conditions. The applied method successfully determined the degradation products after acidic and basic degradation without interfering with Rifaximin detection. Therefore, the method was said to be stability indicating and can be applied for quality control and stability testing of Rifaxmin tablets during its shelf life.

Keywords: forced degradation, high-performance liquid chromatography, method validation, rifaximin, stability indicating method

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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Authors: S. Zenhari, M. R. Hematiyan, A. Khosravifard, M. R. Feizi

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The boundary element method (BEM) and the method of fundamental solutions (MFS) are well-known fundamental solution-based methods for solving a variety of problems. Both methods are boundary-type techniques and can provide accurate results. In comparison to the finite element method (FEM), which is a domain-type method, the BEM and the MFS need less manual effort to solve a problem. The aim of this study is to compare the accuracy and reliability of the BEM and the MFS. This comparison is made for 2D potential and elasticity problems with different boundary and loading conditions. In the comparisons, both convex and concave domains are considered. Both linear and quadratic elements are employed for boundary element analysis of the examples. The discretization of the problem domain in the BEM, i.e., converting the boundary of the problem into boundary elements, is relatively simple; however, in the MFS, obtaining appropriate locations of collocation and source points needs more attention to obtain reliable solutions. The results obtained from the presented examples show that both methods lead to accurate solutions for convex domains, whereas the BEM is more suitable than the MFS for concave domains.

Keywords: boundary element method, method of fundamental solutions, elasticity, potential problem, convex domain, concave domain

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Authors: Junyou Shi, Weiwei Cui

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Testability modeling is a commonly used method in testability design and analysis of system. A dependency matrix will be obtained from testability modeling, and we will give a quantitative evaluation about fault detection and isolation. Based on the dependency matrix, we can obtain the diagnosis tree. The tree provides the procedures of the fault detection and isolation. But the dependency matrix usually includes built-in test (BIT) and manual test in fact. BIT runs the test automatically and is not limited by the procedures. The method above cannot give a more efficient diagnosis and use the advantages of the BIT. A Comprehensive method of fault detection and isolation is proposed. This method combines the advantages of the BIT and Manual test by splitting the matrix. The result of the case study shows that the method is effective.

Keywords: fault detection, fault isolation, testability modeling, BIT

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Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

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The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: closed surfaces, high-order approachs, numerical solutions, reaction-diffusion systems

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