Search results for: singular values

Authors: Mabel A. Leva

Abstract:

This study defines a methodology to compute unitary costs for freight transportation modes. The main objective was to gather relevant costs data to support the formulation and evaluation of railway, road, pipelines and port projects. This article will concentrate on the following steps: Compilation and analysis of relevant modal cost studies, Methodological adjustments to make cost figures comparable between studies, Definition of typology and scope of transportation modes, Analysis and validation of cost values for relevant freight transportation modes in Chile. In order to define the comparison methodology for the costs between the different transportation modes, it was necessary to consider that the relevant cost depends on who performs the comparison. Thus, for the transportation user (e.g. exporter) the pertinent costs are the mode tariffs, whereas from the operators perspective (e.g. rail manager), the pertinent costs are the operating costs of each mode.

Keywords: Intermodal costs, Logistics, Transportation costs.

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Authors: Keunhong Chae, Seokho Yoon

Abstract:

In this paper, frequency offset (FO) estimation schemes robust to the non-Gaussian noise environments are proposed for orthogonal frequency division multiplexing (OFDM) systems. First, a maximum-likelihood (ML) estimation scheme in non-Gaussian noise environments is proposed, and then, the complexity of the ML estimation scheme is reduced by employing a reduced set of candidate values. In numerical results, it is demonstrated that the proposed schemes provide a significant performance improvement over the conventional estimation scheme in non-Gaussian noise environments while maintaining the performance similar to the estimation performance in Gaussian noise environments.

Keywords: Frequency offset estimation, maximum-likelihood, non-Gaussian noise environment, OFDM, training symbol.

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Authors: S. Farzi

Abstract:

Recently, a lot of attention has been devoted to advanced techniques of system modeling. PNN(polynomial neural network) is a GMDH-type algorithm (Group Method of Data Handling) which is one of the useful method for modeling nonlinear systems but PNN performance depends strongly on the number of input variables and the order of polynomial which are determined by trial and error. In this paper, we introduce GPNN (genetic polynomial neural network) to improve the performance of PNN. GPNN determines the number of input variables and the order of all neurons with GA (genetic algorithm). We use GA to search between all possible values for the number of input variables and the order of polynomial. GPNN performance is obtained by two nonlinear systems. the quadratic equation and the time series Dow Jones stock index are two case studies for obtaining the GPNN performance.

Keywords: GMDH, GPNN, GA, PNN.

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Authors: T. G. Emam

Abstract:

The effect of variable chemical reaction on heat and mass transfer characteristics over unsteady stretching surface embedded in a porus medium is studied. The governing time dependent boundary layer equations are transformed into ordinary differential equations containing chemical reaction parameter, unsteadiness parameter, Prandtl number and Schmidt number. These equations have been transformed into a system of first order differential equations. MATHEMATICA has been used to solve this system after obtaining the missed initial conditions. The velocity gradient, temperature, and concentration profiles are computed and discussed in details for various values of the different parameters.

Keywords: Heat and mass transfer, stretching surface, chemical reaction, porus medium.

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Authors: Thi Nguyen, Lee Gordon-Brown, Jim Peterson, Peter Wheeler

Abstract:

An additive fuzzy system comprising m rules with n inputs and p outputs in each rule has at least t m(2n + 2 p + 1) parameters needing to be tuned. The system consists of a large number of if-then fuzzy rules and takes a long time to tune its parameters especially in the case of a large amount of training data samples. In this paper, a new learning strategy is investigated to cope with this obstacle. Parameters that tend toward constant values at the learning process are initially fixed and they are not tuned till the end of the learning time. Experiments based on applications of the additive fuzzy system in function approximation demonstrate that the proposed approach reduces the learning time and hence improves convergence speed considerably.

Keywords: Additive fuzzy system, improving convergence, parameter learning process, unsupervised learning.

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Authors: Y. Lasbet, A. L. Boukhalkhal, K. Loubar

Abstract:

The study of mixed convection is, usually, focused on the straight channels in which the onset of the mixed convection is well defined as function of the ratio between Grashof number and Reynolds number, Gr/Re. This is not the case for a complex channel wherein the mixed convection is not sufficiently examined in the literature. Our paper focuses on the study of the mixed convection in a complex geometry in which our main contribution reveals that the critical value of the ratio Gr/Re for the onset of the mixed convection increases highly in the type of geometry contrary to the straight channel. Furthermore, the accentuated secondary flow in this geometry prevents the thermal stratification in the flow and consequently the buoyancy driven becomes negligible. To perform these objectives, a numerical study in complex geometry for several values of the ratio Gr/Re with prescribed wall heat flux (H2), was realized by using the CFD code.

Keywords: Complex geometry, heat transfer, laminar flow, mixed convection, Nusselt number.

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Authors: Pranav Ravikumar, Arunabha Bera, Vijay K. Mehra, Anand Kumar

Abstract:

This paper solves the Non Linear Schrodinger Equation using the Split Step Fourier method for modeling an optical fiber. The model generates a complex wave of optical pulses and using the results obtained two graphs namely Loss versus Wavelength and Dispersion versus Wavelength are generated. Taking Chromatic Dispersion and Polarization Mode Dispersion losses into account, the graphs generated are compared with the graphs formulated by JDS Uniphase Corporation which uses standard values of dispersion for optical fibers. The graphs generated when compared with the JDS Uniphase Corporation plots were found to be more or less similar thus verifying that the model proposed is right. MATLAB software was used for doing the modeling.

Keywords: Modulation, Non Linear Schrodinger Equation, Optical fiber, Split Step Fourier Method.

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Authors: Mohd Sazli Saad, Hishamuddin Jamaluddin, Intan Zaurah Mat Darus

Abstract:

This paper presents the development of an active vibration control using direct adaptive controller to suppress the vibration of a flexible beam system. The controller is realized based on linear parametric form. Differential evolution optimisation algorithm is used to optimize the controller using single objective function by minimizing the mean square error of the observed vibration signal. Furthermore, an alternative approach is developed to systematically search for the best controller model structure together with it parameter values. The performance of the control scheme is presented and analysed in both time and frequency domain. Simulation results demonstrate that the proposed scheme is able to suppress the unwanted vibration effectively.

Keywords: flexible beam, finite difference method, active vibration control, differential evolution, direct adaptive controller

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Authors: Arun Jacob, Leena R., Krishnakumar T.S., Jose Prakash M.

Abstract:

Effective cooling of electronic equipment has emerged as a challenging and constraining problem of the new century. In the present work the feasibility and effectiveness of jet impingement cooling on electronics were investigated numerically and experimentally. Studies have been conducted to see the effect of the geometrical parameters such as jet diameter (D), jet to target spacing (Z) and ratio of jet spacing to jet diameter (Z/D) on the heat transfer characteristics. The values of Reynolds numbers considered are in the range 7000 to 42000. The results obtained from the numerical studies are validated by conducting experiments. From the studies it is found that the optimum value of Z/D ratio is 5. For a given Reynolds number, the Nusselt number increases by about 28% if the diameter of the nozzle is increased from 1mm to 2mm. Correlations are proposed for Nusselt number in terms of Reynolds number and these are valid for air as the cooling medium.

Keywords: CFD, heat transfer coefficient, Nusselt number, ratio of jet diameter to jet spacing (Z/D), Reynolds number, turbulence model.

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Authors: Supatchalee Sirichokworrakit

Abstract:

Fishbone of Nile Tilapia (Tilapia nilotica), waste from the frozen Nile Tilapia fillet factory, is one of calcium sources. In order to increase fish bone powder value, this study aimed to investigate the effect of Tilapia bone flour (TBF) addition (5, 10, 15% by flour weight) on cooking quality, texture and sensory attributes of noodles. The results indicated that tensile strength, color value (a*) and water absorption of noodles significantly decreased (p£0.05) as the levels of TBF increased from 0-15%. While cooking loss, cooking time and color values (L* and b*) of noodles significantly increased (p£0.05). Sensory evaluation indicated that noodles with 5% TBF received the highest overall acceptability score.

Keywords: Tilapia bone flour, Noodles, Cooking quality, Calcium.

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Authors: Ekta Singh, M. P. Singh

Abstract:

The habitat where the present study has been carried out is productive in relation to nutrient quality and they may perform several useful functions, but are also threatened for their existence. Hence, the proposed work, will add much new information about biodiversity of macrophytes in drains and their embankment. All the species were identified with their different stages of growth which encountered on the three selected sites (I, II and III). The number of species occurring at each site is grouped seasonally, i.e. summer, rainy and winter season and the species were further recorded for the study of phytosociology. Phytosociological characters such as frequency, density and abundance were influenced by the climatic, anthropogenic and biotic stresses prevailing at the three study sites. All the species present at the study sites have shown maximum values of frequency, density and abundance in rainy season in comparison to that of summer and winter seasons.

Keywords: Abundance, Biodiversity, Density, Frequency, Macrophytes, Phytosociology.

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Authors: M. Wannaborworn, B. Jongsomjit, T. Shiono

Abstract:

Copolymerization of ethylene with 1-hexene was carried out using two ansa-fluorenyl titanium derivative complexes. The substituent effect on the catalytic activity, monomer reactivity ratio and polymer property was investigated. It was found that the presence of t-Bu groups on fluorenyl ring exhibited remarkable catalytic activity and produced polymer with high molecular weight. However, these catalysts produce polymer with narrow molecular weight distribution, indicating the characteristic of single-site metallocene catalyst. Based on 13C NMR, we can observe that monomer reactivity ratio was affected by catalyst structure. The rH values of complex 2 were lower than that of complex 1 which might be result from the higher steric hindrance leading to a reduction of 1- hexene insertion step.

Keywords: Constrained geometry catalyst, linear low density polyethylene, copolymerization, reactivity ratio

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Authors: S. M. Ali, N. R. Dhar

Abstract:

Tool wear and surface roughness prediction plays a significant role in machining industry for proper planning and control of machining parameters and optimization of cutting conditions. This paper deals with developing an artificial neural network (ANN) model as a function of cutting parameters in turning steel under minimum quantity lubrication (MQL). A feed-forward backpropagation network with twenty five hidden neurons has been selected as the optimum network. The co-efficient of determination (R2) between model predictions and experimental values are 0.9915, 0.9906, 0.9761 and 0.9627 in terms of VB, VM, VS and Ra respectively. The results imply that the model can be used easily to forecast tool wear and surface roughness in response to cutting parameters.

Keywords: ANN, MQL, Surface Roughness, Tool Wear.

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Authors: L. A. S. Dionel, B. A. P. Santos, V. C. P. Lopes, L. G. Vasconcelos, M. A. Soares, E. B. Morais

Abstract:

This study investigated the biosorption of the azo dye reactive Black B (RBB) from aqueous solution using the nonviable biomass of Cladosporium cladosporioides LM1. The biosorption systems were carried out in batch mode considering different conditions of initial pH, contact time, temperature, initial dye concentration and biosorbent dosage. Higher removal rate of RBB was obtained at pH 2. Biosorption data were successfully described by pseudo-second-order kinetic model and Langmuir isotherm model with the maximum monolayer biosorption capacity estimated at 71.43 mg/g. The values of thermodynamic parameters such as ∆G°, ∆H° and ∆S° indicated that the biosorption of RBB onto fungal biomass was spontaneous and exothermic in nature. It can be concluded that nonviable biomass of Cladosporium cladosporioides LM1 may be an attractive low-cost biosorbent for the removal of azo dye RBB from aqueous solution.

Keywords: Color removal, isotherms and kinetics models, thermodynamic studies, fungus.

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Authors: Sedrak Vardanyan

Abstract:

The investigation of the vibrational character of magnetic cylindrical shells placed in an axial magnetic field has important practical applications. In this work, we study the vibrational behaviour of such a cylindrical shell by making use of the so-called exact space treatment, which does not assume any hypothesis. We discuss the effects of several practically important boundary conditions on the vibrations of the described setup. We find that, for some cases of boundary conditions, e.g. clamped, simply supported or peripherally earthed, as well as for some values of the wave numbers, the vibrational frequencies of the shell are approximately zero. The theoretical and numerical exploration of this fact confirms that the vibrations are absent or attenuate very rapidly. For all the considered cases, the imaginary part of the frequencies is negative, which implies stability for the vibrational process.

Keywords: Free vibrations, magnetic cylindrical shells, exact space treatment, bending vibrational frequencies.

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Authors: Muhammad Tahir, Muhammad H. Sayyad, Dil N. Khan, Fazal Wahab

Abstract:

Herein, the organic semiconductor methyl orange (MO), is investigated for the first time for its electronic applications. For this purpose, Al/MO/n-Si heterojunction is fabricated through economical cheap and simple “drop casting” technique. The currentvoltage (I-V) measurements of the device are made at room temperature under dark conditions. The I-V characteristics of Al/MO/n-Si junction exhibits asymmetrical and rectifying behavior that confirms the formation of diode. The diode parameters such as rectification ratio (RR), turn on voltage (Vturn on), reverse saturation current (I0), ideality factor (n), barrier height ( b f ), series resistance (Rs) and shunt resistance (Rsh) are determined from I-V curves using Schottky equations. These values of these parameters are also extracted and verified by applying Cheung’s functions. The conduction mechanisms are explained from the forward bias I-V characteristics using the power law.

Keywords: Electrical properties, Organic/inorganic heterojunction diode, Methyl Orange, Cheungs Functions

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Authors: M. G. C. A. Cimino, G. Frosini, B. Lazzerini, F. Marcelloni

Abstract:

In the last decades, a number of robust fuzzy clustering algorithms have been proposed to partition data sets affected by noise and outliers. Robust fuzzy C-means (robust-FCM) is certainly one of the most known among these algorithms. In robust-FCM, noise is modeled as a separate cluster and is characterized by a prototype that has a constant distance δ from all data points. Distance δ determines the boundary of the noise cluster and therefore is a critical parameter of the algorithm. Though some approaches have been proposed to automatically determine the most suitable δ for the specific application, up to today an efficient and fully satisfactory solution does not exist. The aim of this paper is to propose a novel method to compute the optimal δ based on the analysis of the distribution of the percentage of objects assigned to the noise cluster in repeated executions of the robust-FCM with decreasing values of δ . The extremely encouraging results obtained on some data sets found in the literature are shown and discussed.

Keywords: noise prototype, robust fuzzy clustering, robustfuzzy C-means

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Authors: Jolanta Tamošaitienė

Abstract:

The article focuses on a developed comprehensive model to be used in an agile environment for the risk assessment and selection based on multi-attribute methods. The model is based on a multi-attribute evaluation of risk in construction, and the determination of their optimality criterion values are calculated using complex Multiple Criteria Decision-Making methods. The model may be further applied to risk assessment in an agile construction environment. The attributes of risk in a construction project are selected by applying the risk assessment condition to the construction sector, and the construction process efficiency in the construction industry accounts for the agile environment. The paper presents the comprehensive risk assessment model in an agile construction environment. It provides a background and a description of the proposed model and the developed analysis of the comprehensive risk assessment model in an agile construction environment with the criteria.

Keywords: Assessment, environment, agile, model, risk.

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Authors: K. Khanafer

Abstract:

The aim of this investigation was to validate the fluid-structure interaction (FSI) model of type B aortic dissection with our experimental results from a bench-top-model. Another objective was to study the relationship between the size of a septectomy that increases the outflow of the false lumen and its effect on the values of the differential of pressure between true lumen and false lumen. FSI analysis based on Galerkin’s formulation was used in this investigation to study flow pattern and hemodynamics within a flexible type B aortic dissection model using boundary conditions from our experimental data. The numerical results of our model were verified against the experimental data for various tear size and location. Thus, CFD tools have a potential role in evaluating different scenarios and aortic dissection configurations.

Keywords: Aortic dissection, fluid-structure interaction, in vitro model, numerical.

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Authors: J. Lonska, V. Boronenko

Abstract:

The result of process of territory-s development is the territory-s state of development (TSoD), which is pointed towards the provision and improvement of people-s life conditions. The authors offer to measure the TSoD according to their own developed model. Using the available statistical data regarding the values of model-s elements, the authors empirically show which element mainly determines the TSoD. The findings of the research showed that the key elements of the TSoD are the “Material welfare of people" and “People-s health". Performing a deeper statistical analysis of correlation between these elements, it turned out that it is not so necessary for a country to be bent on trying to increase the material growth of a territory, because a relatively high index of life expectancy at birth could be ensured also by much more modest material resources. On the other hand, the economical feedback of longer lifespan within countries with lower material performance is also relatively low.

Keywords: Development indices, health, territory's state of development, wealth.

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Authors: Hamed Vahdat Nejad, Hameed Reza Pourreza, Hasan Ebrahimi

Abstract:

A new fuzzy filter is presented for noise reduction of images corrupted with additive noise. The filter consists of two stages. In the first stage, all the pixels of image are processed for determining noisy pixels. For this, a fuzzy rule based system associates a degree to each pixel. The degree of a pixel is a real number in the range [0,1], which denotes a probability that the pixel is not considered as a noisy pixel. In the second stage, another fuzzy rule based system is employed. It uses the output of the previous fuzzy system to perform fuzzy smoothing by weighting the contributions of neighboring pixel values. Experimental results are obtained to show the feasibility of the proposed filter. These results are also compared to other filters by numerical measure and visual inspection.

Keywords: Additive noise, Fuzzy logic, Image processing, Noise reduction.

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Authors: Mohammad Sadeghi, Behrouz Heidari, Korush Montazeri

Abstract:

In this article, we synthesize a novel chitosan -based superabsorbent hydrogel via graft copolymerization of mixtures acrylic acid (AA) and N-vinyl pyrollidon onto chitosan backbones. The polymerization reaction was carried out in an aqueous medium and in the presence of ammonium persulfate (APS) as an initiator and N,N'-methylene bisacrylamide (MBA) as a crosslinker.The hydrogel structures were confirmed by FTIR spectroscopy. The swelling behavior of these absorbent polymers was also investigated in various salt solutions. Results indicated that the swelling capacity decreased with an increase in the ionic strength of the swelling medium. Furthermore, the swelling of superabsorbing hydrogels was examined in solutions with pH values ranging between 1.0 and 13.0. It showed a reversible pH-responsive behavior at pHs 2.0 and 8.0. This on-off switching behavior makes the synthesized hydrogels as an excellent candidate for controlled delivery of bioactive agents.

Keywords: chitosan, acrylic acid, N-vinyl pyrollidon, hydrogel, Ibuprofen's drug delivery

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Authors: Quy Dang Nguyen, Reza Nakhaie Jazar

Abstract:

The paper investigates vibration dynamics of tire-road separation for a quarter-car model; this separation model is developed to be close to the real situation considering the tire is able to separate from the ground plane. A set of piecewise linear mathematical models is developed and matches the in-contact and no-contact states to be considered as mother models for further investigations. The bound dynamics are numerically simulated in the time response and phase portraits. The separation analysis may determine which values of suspension parameters can delay and avoid the no-contact phenomenon, which results in improving ride comfort and eliminating the potentially dangerous oscillation. Finally, model verification is carried out in the MSC-ADAMS environment.

Keywords: Quarter-car vibrations, tire-road separation, separation analysis, separation dynamics, ride comfort, ADAMS validation.

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Authors: Ghulam Nabi Naz

Abstract:

After independence, the popular belief that Gandhian will not indulge in corruption got a setback, post-independence setup paved the way for heavy corruption. The menace which would have dealt with strong legal provisions has become a way of life of Indian society. Corruption is recognized as the single biggest problem facing the country today. It undermines democracy and rule of law, violates human rights, distorts market and corrodes the moral fibre of people. The paper discusses the causes and possible remedial measures of corruption and response of people in Indian society. It emphasizes the factors which provide fertile ground for growth of corruption like, degradation of moral values, absence of a strong anti-corruption law and its effective enforcement, accountability, consistency and a defective system of fighting elections. The paper also highlights the reforms necessary for fighting corruption in India.

Keywords: Embezzlement, colonial, licence Raj, good governance, misappropriation, Sangh ideologue, Anna movement.

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Authors: H. Fazlinejad, A. Halvaee

Abstract:

In this study, characteristics of ATIG welds using ZnO flux on aluminum was investigated and compared with TIG welds. Autogenously AC-ATIG bead on plate welding was applied on Al1050 plate with a coating of ZnO as the flux. Different levels of welding current and flux layer thickness was considered to study the effect of heat input and flux quantity on ATIG welds and was compared with those of TIG welds. Geometrical investigation of the weld cross sections revealed that penetration depth of the ATIG welds with ZnO flux, was increased up to 2 times in some samples compared to the TIG welds. Optical metallographic and Scanning Electron Microscopy (SEM) observations revealed similar microstructures in TIG and ATIG welds. Composition of the ATIG welds slag was also analyzed using X-ray diffraction. In both TIG and ATIG samples, the lowest values of microhardness were observed in the HAZ.

Keywords: ATIG, active flux, weld penetration, Al 1050, ZnO.

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Authors: S.B. Thakre, L.B. Bhuyar, S.J. Deshmukh

Abstract:

This paper examines the use of mechanical aerator for oxidation-ditch process. The rotor, which controls the aeration, is the main component of the aeration process. Therefore, the objective of this study is to find out the variations in overall oxygen transfer coefficient (KLa) and aeration efficiency (AE) for different configurations of aerator by varying the parameters viz. speed of aerator, depth of immersion, blade tip angles so as to yield higher values of KLa and AE. Six different configurations of aerator were developed and fabricated in the laboratory and were tested for abovementioned parameters. The curved blade rotor (CBR) emerged as a potential aerator with blade tip angle of 47°. The mathematical models are developed for predicting the behaviour of CBR w.r.t kLa and power. In laboratory studies, the optimum value of KLa and AE were observed to be 10.33 h-1 and 2.269 kg O2/ kWh.

Keywords: Aerator, Aeration efficiency, Dissolve Oxygen, Overall oxygen transfer coefficient, Oxidation ditch.

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Authors: Haga Elimam

Abstract:

This paper investigates the connotation, and some of the realistic implications, of the economic reform of health sector in under developed countries. The paper investigates the issues that economic reforms have to address, and the policy targets they are considered to accomplish. The work argues that the development of economic reform is not connected only with understanding the priorities and refining them, furthermore with reformation and restructuring the organizations through which health policies are employed. Considering various organizational values, that are likely to be regular to all economic reform programs, a regulatory approach to institutional reform is unsuitable. The paper further investigates the selection of economic reform that may as well influence via technical suggestions and analysis, but the verdict to continue, and the consequent success of execution, eventually depends on the progressive political sustainability. The paper concludes by giving examples of institutional reforms from various underdeveloped countries and includes recommendation of the responsibility and control of donor organizations.

Keywords: Economic Reform, Health Sector, underdeveloped Countries.

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Authors: S. A. Naeini, M. Ghorbani Tochaee

Abstract:

The aim of this study is to assess the influence of plastic fines content on sand-clay mixtures on maximum shear modulus and liquefaction resistance using a series of resonant column tests. A high plasticity clay called bentonite was added to 161 Firoozkooh sand at the percentages of 10, 15, 20, 25, 30 and 35 by dry weight. The resonant column tests were performed on the remolded specimens at constant confining pressure of 100 KPa and then the values of G_max and liquefaction resistance were investigated. The maximum shear modulus and cyclic resistance ratio (CRR) are examined in terms of fines content. Based on the results, the maximum shear modulus and liquefaction resistance tend to decrease within the increment of fine contents.

Keywords: Gmax, liquefaction, plastic fines, resonant column, sand-clay mixtures, bentonite.

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Authors: Vitalice K. Oduol

Abstract:

The paper considers a single-server queue with fixedsize batch Poisson arrivals and exponential service times, a model that is useful for a buffer that accepts messages arriving as fixed size batches of packets and releases them one packet at time. Transient performance measures for queues have long been recognized as being complementary to the steady-state analysis. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. The paper exploits practical modelling to obtain a solution to the integral equation encountered in the analysis. Results obtained indicate that under heavy load conditions, there is significant disparity in the statistics between the transient and steady state values.

Keywords: batch arrivals, modelling, single-server queue, time-varying probabilities, transient analysis.

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Authors: F. Nkontchou Ngongang, M. Tchawe Tchawe, B. Djeumako, B. Kenmeugne

Abstract:

In this work, the flow structure in the Songloulou dam, is visualized in a time interval to observe the different fluid layers in our structure. Firstly, the three-dimensional modelling of the penstock is carried out in the software Gambit, followed by calculations in Fluent that proceeds introduction of boundary conditions. After calculation, we identified four periods corresponding to four regimes. In the first, spanning from 0.00 to 1.50s, we have the non-developed hydraulically rough turbulent regime, characterized by abrupt variations with modifications of the velocity fields. The second extends from 1.50 to 3.50s, where we have the transition regime characterized by slight variations and modifications of the velocity fields but with a great difference of the values of the current lines. From 3.50 to 5.00s, we encounter the third, which is the fully developed turbulent hydraulically rough regime, characterized by fields that vary no more, but have minute differences in the streamlines. The last period is from 5.00s and more, where we have a flow that is almost stationary, hence there are no changes in the fields.

Keywords: Unsteady flow, penstock, friction coefficient, hydroelectric dam.

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