Search results for: Split Step Method.

Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying Runge- Kutta method.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, order, local error, global error.

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Authors: F. Sokhanvar, A. B. Khoshnevis

Abstract:

In the present work steady inviscid hypersonic flows are calculated by approximate Method. Maslens' inverse method is the chosen approximate method. For the inverse problem, parabolic shock shape is chosen for the two-dimensional flow, and the body shape and flow field are calculated using Maslen's method. For the axisymmetric inverse problem paraboloidal shock is chosen and the surface distribution of pressure is obtained.

Keywords: Hypersonic flow, Inverse problem method

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Authors: G. Candel, D. Naccache

Abstract:

t-SNE is an embedding method that the data science community has widely used. It helps two main tasks: to display results by coloring items according to the item class or feature value; and for forensic, giving a first overview of the dataset distribution. Two interesting characteristics of t-SNE are the structure preservation property and the answer to the crowding problem, where all neighbors in high dimensional space cannot be represented correctly in low dimensional space. t-SNE preserves the local neighborhood, and similar items are nicely spaced by adjusting to the local density. These two characteristics produce a meaningful representation, where the cluster area is proportional to its size in number, and relationships between clusters are materialized by closeness on the embedding. This algorithm is non-parametric. The transformation from a high to low dimensional space is described but not learned. Two initializations of the algorithm would lead to two different embedding. In a forensic approach, analysts would like to compare two or more datasets using their embedding. A naive approach would be to embed all datasets together. However, this process is costly as the complexity of t-SNE is quadratic, and would be infeasible for too many datasets. Another approach would be to learn a parametric model over an embedding built with a subset of data. While this approach is highly scalable, points could be mapped at the same exact position, making them indistinguishable. This type of model would be unable to adapt to new outliers nor concept drift. This paper presents a methodology to reuse an embedding to create a new one, where cluster positions are preserved. The optimization process minimizes two costs, one relative to the embedding shape and the second relative to the support embedding’ match. The embedding with the support process can be repeated more than once, with the newly obtained embedding. The successive embedding can be used to study the impact of one variable over the dataset distribution or monitor changes over time. This method has the same complexity as t-SNE per embedding, and memory requirements are only doubled. For a dataset of n elements sorted and split into k subsets, the total embedding complexity would be reduced from O(n2) to O(n2/k), and the memory requirement from n2 to 2(n/k)2 which enables computation on recent laptops. The method showed promising results on a real-world dataset, allowing to observe the birth, evolution and death of clusters. The proposed approach facilitates identifying significant trends and changes, which empowers the monitoring high dimensional datasets’ dynamics.

Keywords: Concept drift, data visualization, dimension reduction, embedding, monitoring, reusability, t-SNE, unsupervised learning.

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Authors: Guangbin Wang, Liangliang Li, Fuping Tan

Abstract:

In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.

Keywords: Generalized alternating two-stage method, linear system, convergence.

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Authors: H. Naghawi, M. Abu Shattal, W. Idewu

Abstract:

Side friction factors can be defined as all activities taking place at the side of the road and within the traffic stream, which would negatively affect the traffic stream performance. If the effect of these factors is adequately addressed and managed, traffic stream performance and capacity could be improved. The main objective of this paper is to identify and assess the impact of different side friction factors on traffic stream performance of a hypothesized urban arterial road. Hypothetical data were assumed mainly because there is no road operating under ideal conditions, with zero side friction, in the developing countries. This is important for the creation of the base model which is important for comparison purposes. For this purpose, three essential steps were employed. Step one, a hypothetical base model was developed under ideal traffic and geometric conditions. Step two, 18 hypothetical alternative scenarios were developed including side friction factors such as on-road parking, pedestrian movement, and the presence of trucks in the traffic stream. These scenarios were evaluated for one, two, and three lane configurations and under different traffic volumes ranging from low to high. Step three, the impact of side friction, of each scenario, on speed-flow models was evaluated using AIMSUN microscopic traffic simulation software. Generally, it was found that, a noticeable negative shift in the speed flow curves from the base conditions was observed for all scenarios. This indicates negative impact of the side friction factors on free flow speed and traffic stream average speed as well as on capacity.

Keywords: AIMSUN, parked vehicles, pedestrians, side friction, traffic performance, trucks.

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Authors: Morteza Abbaszadeh, Parvin Nikpoorparizi, Mina Shahrooz

Abstract:

For the first time since 1940 and presentation of theodorson-s theory, distribution of thrust, torque and efficiency along the blade of a counter rotating propeller axial fan was studied with a novel method in this research. A constant chord, constant pitch symmetric fan was investigated with Reynolds Stress Turbulence method in this project and H.E.S. method was utilized to obtain distribution profiles from C.F.D. tests outcome. C.F.D. test results were validated by estimation from Playlic-s analytical method. Final results proved ability of H.E.S. method to obtain distribution profiles from C.F.D test results and demonstrated interesting facts about effects of solidity and differences between distributions in front and rear section.

Keywords: C.F.D Test, Counter Rotating Propeller, H.E.S. Method, R.S.M. Method

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Authors: Wararat Rungworawut, Twittie Senivongse

Abstract:

Business process model describes process flow of a business and can be seen as the requirement for developing a software application. This paper discusses a BPM2CD guideline which complements the Model Driven Architecture concept by suggesting how to create a platform-independent software model in the form of a UML class diagram from a business process model. An important step is the identification of UML classes from the business process model. A technique for object-oriented analysis called domain analysis is borrowed and key concepts in the business process model will be discovered and proposed as candidate classes for the class diagram. The paper enhances this step by using ontology search to help identify important classes for the business domain. As ontology is a source of knowledge for a particular domain which itself can link to ontologies of related domains, the search can give a refined set of candidate classes for the resulting class diagram.

Keywords: Business Process Model, Model DrivenArchitecture, Ontology, UML Class Diagram.

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Authors: R. Mafi Gholami, S. M. Borghei, S. M. Mousavi

Abstract:

In this study, the ability of Aspergillus niger and Penicillium simplicissimum to extract heavy metals from a spent refinery catalyst was investigated. For the first step, a spent processing catalyst from one of the oil refineries in Iran was physically and chemically characterized. Aspergillus niger and Penicillium simplicissimum were used to mobilize Al/Co/Mo/Ni from hazardous spent catalysts. The fungi were adapted to the mixture of metals at 100-800 mg L-1 with increments in concentration of 100 mg L-1. Bioleaching experiments were carried out in batch cultures. To investigate the production of organic acids in sucrose medium, analyses of the culture medium by HPLC were performed at specific time intervals after inoculation. The results obtained from Inductive coupled plasma-optical emission spectrometry (ICP-OES) showed that after the one-step bioleaching process using Aspergillus niger, maximum removal efficiencies of 27%, 66%, 62% and 38% were achieved for Al, Co, Mo and Ni, respectively. However, the highest removal efficiencies using Penicillium simplicissimum were of 32%, 67%, 65% and 38% for Al, Co, Mo and Ni, respectively

Keywords: Aspergillus niger, Bioleaching, Heavy metals, Penicillium simplicissimum, Spent catalyst

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Authors: Néjib Hassen, Thouraya Ettaghzouti, Kamel Besbes

Abstract:

In this paper, a modified CCCII is presented. We have used a current mirror with low supply voltage. This circuit is operated at low supply voltage of ±1V. Tspice simulations for TSMC 0.18μm CMOS Technology has shown that the current and voltage bandwidth are respectively 3.34GHz and 4.37GHz, and parasitic resistance at port X has a value of 169.320 for a control current of 120μA. In order to realize this circuit, we have implemented in this first step a universal current mode filter where the frequency can reach the 134.58MHz. In the second step, we have implemented two simulated inductors: one floating and the other grounded. These two inductors are operated in high frequency and variable depending on bias current I0. Finally, we have used the two last inductors respectively to implement two sinusoidal oscillators domains of frequencies respectively: [470MHz, 692MHz], and [358MHz, 572MHz] for bias currents I0 [80μA, 350μA].

Keywords: Current controlled current conveyor CCCII, floating inductor, grounded inductor, oscillator, universal filter.

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Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

Keywords: Exact solution, The (3+1)-dimensional breaking soliton equation, ( G G )-expansion method, Riccati equation, Modified Fexpansion method.

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Authors: Thomas Kampke

Abstract:

Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.

Keywords: Euler method, fixed points, golden section, multi-step procedures, Runge Kutta methods.

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Authors: Sathans, A. Swarup

Abstract:

This paper presents the development and application of an adaptive neuro fuzzy inference system (ANFIS) based intelligent hybrid neuro fuzzy controller for automatic generation control (AGC) of two-area interconnected thermal power system with reheat non linearity. The dynamic response of the system has been studied for 1% step load perturbation in area-1. The performance of the proposed neuro fuzzy controller is compared against conventional proportional-integral (PI) controller, state feedback linear quadratic regulator (LQR) controller and fuzzy gain scheduled proportionalintegral (FGSPI) controller. Comparative analysis demonstrates that the proposed intelligent neuro fuzzy controller is the most effective of all in improving the transients of frequency and tie-line power deviations against small step load disturbances. Simulations have been performed using Matlab®.

Keywords: Automatic generation control, ANFIS, LQR, Hybrid neuro fuzzy controller

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Authors: Rony Reátegui, Cesar Chácara, Benjamin Castañeda, Rafael Aguilar

Abstract:

Nowadays, Heritage Building Information Modeling (HBIM) is considered an efficient tool to represent and manage information of Cultural Heritage (CH). The basis of this tool relies on a 3D model generally obtained from a Cloud-to-BIM procedure. There are different methods to create an HBIM model that goes from manual modeling based on the point cloud to the automatic detection of shapes and the creation of objects. The selection of these methods depends on the desired Level of Development (LOD), Level of Information (LOI), Grade of Generation (GOG) as well as on the availability of commercial software. This paper presents the 3D modeling of a stone masonry chapel using Recap Pro, Revit and Dynamo interface following a three-step methodology. The first step consists of the manual modeling of simple structural (e.g., regular walls, columns, floors, wall openings, etc.) and architectural (e.g., cornices, moldings and other minor details) elements using the point cloud as reference. Then, Dynamo is used for generative modeling of complex structural elements such as vaults, infills and domes. Finally, semantic information (e.g., materials, typology, state of conservation, etc.) and pathologies are added within the HBIM model as text parameters and generic models’ families respectively. The application of this methodology allows the documentation of CH following a relatively simple to apply process that ensures adequate LOD, LOI and GOG levels. In addition, the easy implementation of the method as well as the fact of using only one BIM software with its respective plugin for the scan-to-BIM modeling process means that this methodology can be adopted by a larger number of users with intermediate knowledge and limited resources, since the BIM software used has a free student license.

Keywords: Cloud-to-BIM, cultural heritage, generative modeling, HBIM, parametric modeling, Revit.

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Authors: Hossain Aziz, Rinku Mukherjee

Abstract:

A potential flow model is used to study the unsteady flow past two airfoils in configuration, each of which is suddenly set into motion. The airfoil bound vortices are modeled using lumped vortex elements and the wake behind the airfoil is modeled by discrete vortices. This consists of solving a steady state flow problem at each time-step where unsteadiness is incorporated through the “zero normal flow on a solid surface" boundary condition at every time instant. Additionally, along with the “zero normal flow on a solid surface" boundary condition Kelvin-s condition is used to compute the strength of the latest wake vortex shed from the trailing edge of the airfoil. Location of the wake vortices is updated at each time-step to get the wake shape at each time instant. Results are presented to show the effect of airfoil-airfoil interaction and airfoil-wake interaction on the aerodynamic characteristics of each airfoil.

Keywords: Aerodynamics, Airfoils, Configuration, Unsteady.

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Authors: Diako Azizi, Ahmad Gholami, Vahid Abbasi

Abstract:

Optimal selection of electrical insulations in electrical machinery insures reliability during operation. From the insulation studies of view for electrical machines, stator is the most important part. This fact reveals the requirement for inspection of the electrical machine insulation along with the electro-thermal stresses. In the first step of the study, a part of the whole structure of machine in which covers the general characteristics of the machine is chosen, then based on the electromagnetic analysis (finite element method), the machine operation is simulated. In the simulation results, the temperature distribution of the total structure is presented simultaneously by using electro-thermal analysis. The results of electro-thermal analysis can be used for designing an optimal cooling system. In order to design, review and comparing the cooling systems, four wiring structures in the slots of Stator are presented. The structures are compared to each other in terms of electrical, thermal distribution and remaining life of insulation by using Finite Element analysis. According to the steps of the study, an optimization algorithm has been presented for selection of appropriate structure.

Keywords: Electrical field, field distribution, insulation, winding, finite element method, electro thermal

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Authors: M. Amiri

Abstract:

In this work, functionally graded materials (FGMs), subjected to loading, which varies with time has been studied. The material properties of FGM are changing through the thickness of material as power law distribution. The conical shells have been chosen for this study so in the first step capability equations for FGM have been obtained. With Galerkin method, these equations have been replaced with time dependant differential equations with variable coefficient. These equations have solved for different initial conditions with variation methods. Important parameters in loading conditions are semi-vertex angle, external pressure and material properties. Results validation has been done by comparison between with those in previous studies of other researchers.

Keywords: Impulsive semi-vertex angle, loading, functionally graded materials, composite material.

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Authors: Hassan Saberi-Nik, Mahin Golchaman

Abstract:

This paper applies the homotopy analysis method method to a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. Comparison of the approximate solution with the exact one reveals that the method is very effective.

Keywords: Homotopy analysis method, differential-difference, nanotechnology.

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Authors: Lei Wang, Sizong Guo

Abstract:

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.

Keywords: Fuzzy-valued function, fuzzy initial value problem, strongly generalized differentiability, adomian decomposition method.

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Authors: Yiqin Lin, Liang Bao

Abstract:

This paper is devoted to the numerical solution of large-scale linear ill-posed systems. A multilevel regularization method is proposed. This method is based on a synthesis of the Arnoldi-Tikhonov regularization technique and the multilevel technique. We show that if the Arnoldi-Tikhonov method is a regularization method, then the multilevel method is also a regularization one. Numerical experiments presented in this paper illustrate the effectiveness of the proposed method.

Keywords: Discrete ill-posed problem, Tikhonov regularization, discrepancy principle, Arnoldi process, multilevel method.

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Authors: M.Radmehr, S.M.Anisheh, I.Yousefian

Abstract:

In this work a new offline signature recognition system based on Radon Transform, Fractal Dimension (FD) and Support Vector Machine (SVM) is presented. In the first step, projections of original signatures along four specified directions have been performed using radon transform. Then, FDs of four obtained vectors are calculated to construct a feature vector for each signature. These vectors are then fed into SVM classifier for recognition of signatures. In order to evaluate the effectiveness of the system several experiments are carried out. Offline signature database from signature verification competition (SVC) 2004 is used during all of the tests. Experimental result indicates that the proposed method achieved high accuracy rate in signature recognition.

Keywords: Fractal Dimension, Offline Signature Recognition, Radon Transform, Support Vector Machine

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Authors: Min Sun, Jing Liu

Abstract:

In this paper, we focus on the alternating direction method, which is one of the most effective methods for solving structured variational inequalities(VI). In fact, we propose a proximal parallel alternating direction method which only needs to solve two strongly monotone sub-VI problems at each iteration. Convergence of the new method is proved under mild assumptions. We also present some preliminary numerical results, which indicate that the new method is quite efficient.

Keywords: structured variational inequalities, proximal point method, global convergence

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Authors: Kero T., Söderberg R., Andersson M., Lindkvist L.

Abstract:

The introduction of mass-customization has enabled new ways to treat patients within medicine. However, the introduction of industrialized treatments has also meant new obstacles. The purpose of this study was to introduce and theoretically test a method for improving dental crown fit. The optimization method allocates support points in order to check the final variation for dental crowns. Three different types of geometries were tested and compared. The three geometries were also divided into three sub-geometries: Current method, Optimized method and Feasible method. The Optimized method, using the whole surface for support points, provided the best results. The results support the objective of the study. It also seems that the support optimization method can dramatically improve the robustness of dental crown treatments.

Keywords: Bio-medicine, Dentistry, Mass-customization, Optimization and Robust design.

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Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin

Abstract:

This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.

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Authors: Sarun Phibanchon

Abstract:

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

Keywords: soliton, iterative method, spectral method, plasma

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Authors: Weijun Bao, Huiquan Li

Abstract:

Using steelmaking slag as a raw material, aragonite superstructure product had been synthesized via an indirect CO2 mineral sequestration rout. It mainly involved two separate steps, in which the element of calcium is first selectively leached from steelmaking slag by a novel leaching media consisting of organic solvent Tributyl phosphate (TBP), acetic acid, and ultra-purity water, followed by enhanced carbonation in a separate step for aragonite superstructure production as well as efficiency recovery of leaching media. Based on the different leaching medium employed in the steelmaking slag leaching process, two typical products were collected from the enhanced carbonation step. The products were characterized by X-ray powder diffraction (XRD) and scanning electron microscopy (SEM), respectively. It reveals that the needle-like aragonite crystals self-organized into aragonite superstructure particles including aragonite microspheres as well as dumbbell-like spherical particles, can be obtained from the steelmaking slag with the purity over 99%.

Keywords: Aragonite superstructure, Steelmaking slag, Indirect CO2 mineral sequestration, Selective leaching, Enhanced carbonation.

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Authors: Hossein Tavallali, Mohammad Ali Karimi, Gohar Deilamy-Rad

Abstract:

The proposed method for speciation, preconcentration and determination of Fe(II) and Fe(III) in pharmaceutical products was developed using of alumina-coated magnetite nanoparticles (Fe₃O₄/Al₂O₃ NPs) as solid phase extraction (SPE) sorbent in magnetic mixed hemimicell solid phase extraction (MMHSPE) technique followed by flame atomic absorption spectrometry analysis. The procedure is based on complexation of Fe(II) with 1, 10-phenanthroline (OP) as complexing reagent for Fe(II) that immobilized on the modified Fe₃O₄/Al₂O₃ NPs. The extraction and concentration process for pharmaceutical sample was carried out in a single step by mixing the extraction solvent, magnetic adsorbents under ultrasonic action. Then, the adsorbents were isolated from the complicated matrix easily with an external magnetic field. Fe(III) ions determined after facility reduced to Fe(II) by added a proper reduction agent to sample solutions. Compared with traditional methods, the MMHSPE method simplified the operation procedure and reduced the analysis time. Various influencing parameters on the speciation and preconcentration of trace iron, such as pH, sample volume, amount of sorbent, type and concentration of eluent, were studied. Under the optimized operating conditions, the preconcentration factor of the modified nano magnetite for Fe(II) 167 sample was obtained. The detection limits and linear range of this method for iron were 1.0 and 9.0 - 175 ng.mL⁻¹, respectively. Also the relative standard deviation for five replicate determinations of 30.00 ng.mL^-1 Fe²⁺ was 2.3%.

Keywords: Alumina-coated magnetite nanoparticles, magnetic mixed hemimicell solid-phase extraction, Fe(ΙΙ) and Fe(ΙΙΙ), pharmaceutical sample.

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Authors: Franklin Nantui Mabe, Samuel A. Donkoh, Seidu Al-Hassan

Abstract:

Rice yields among agro-ecological zones are heterogeneous. Farmers, researchers and policy makers are making frantic efforts to bridge rice yield gaps between agro-ecological zones through the promotion of improved agricultural technologies (IATs). Farmers are also modifying these IATs and blending them with indigenous farming practices (IFPs) to form farmer innovation systems (FISs). Also, different metafrontier models have been used in estimating productivity performances and their drivers. This study used the two-step stochastic metafrontier model to estimate the productivity performances of rice farmers and their determining factors in GSZ, FSTZ and CSZ. The study used both primary and secondary data. Farmers in CSZ are the most technically efficient. Technical inefficiencies of farmers are negatively influenced by age, sex, household size, education years, extension visits, contract farming, access to improved seeds, access to irrigation, high rainfall amount, less lodging of rice, and well-coordinated and synergized adoption of technologies. Albeit farmers in CSZ are doing well in terms of rice yield, they still have the highest potential of increasing rice yield since they had the lowest TGR. It is recommended that government through the ministry of food and agriculture, development partners and individual private companies promote the adoption of IATs as well as educate farmers on how to coordinate and synergize the adoption of the whole package. Contract farming concept and agricultural extension intensification should be vigorously pursued to the latter.

Keywords: Efficiency, farmer innovation systems, improved agricultural technologies, two-step stochastic metafrontier approach.

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Authors: Caihong Su

Abstract:

Transition prediction of boundary layers has always been an important problem in fluid mechanics both theoretically and practically, yet notwithstanding the great effort made by many investigators, there is no satisfactory answer to this problem. The most popular method available is so-called e-N method which is heavily dependent on experiments and experience. The author has proposed improvements to the e-N method, so to reduce its dependence on experiments and experience to a certain extent. One of the key assumptions is that transition would occur whenever the velocity amplitude of disturbance reaches 1-2% of the free stream velocity. However, the reliability of this assumption needs to be verified. In this paper, transition prediction on a flat plate is investigated by using both the improved e-N method and the parabolized stability equations (PSE) methods. The results show that the transition locations predicted by both methods agree reasonably well with each other, under the above assumption. For the supersonic case, the critical velocity amplitude in the improved e-N method should be taken as 0.013, whereas in the subsonic case, it should be 0.018, both are within the range 1-2%.

Keywords: Boundary layer, e-N method, PSE, Transition

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Authors: T. Lantharthong, N. Rugthaicharoencheep, A. Phayomhom

Abstract:

This paper presents the electrical effect of two neighboring distribution substation during the construction phase. The size of auxiliary grounding grid have an effect on entire grounding system. The bigger the size of auxiliary grounding grid, the lower the GPR and maximum touch voltage, with the exception that when the two grids are unconnected, i.e. the bigger the size of auxiliary grounding grid, the higher the maximum step voltage. The results in this paper could be served as design guideline of grounding system, and perhaps remedy of some troublesome grounding grids in power distribution’s system. Modeling and simulation is carried out on the Current Distribution Electromagnetic interference Grounding and Soil structure (CDEGS) program. The simulation results exhibit the design and analysis of power system grounding and perhaps could be set as a standard in grounding system design and modification in distribution substations.

Keywords: Grounding System, Touch Voltage, Step Voltage, Safety Criteria.

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Authors: Olayiwola M.O., Gbolagade A .W., Akinpelu F. O.

Abstract:

In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.

Keywords: Variational iteration method, boundary value problems, convergence, restricted variation.

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