Search results for: ϵ - constraint method

Authors: Mohammad Ghandehari Motlagh

Abstract:

Purpose: Comparing anterior chamber depth (ACD) measured with Orbscan II and Pentacam HR compared with the Smith method results. Methods: Smith method (1979) is a reliable method of measuring ACD only with help of slit lamp. In this study 102 phakic eyes as PRK candidates were imaged with both OrbScan and Pentacam and finally ACD was measured thru Smith method with slit lamp. ACD measured with Smith method was presumed as the gold standard and was compared with ACD of the 2 imaging devices. Contraindication cases for PRK and pseudophakic eyes have been excluded from the study. Results: Mean age of the patients was 35.2 ±14.8 yrs/old including 56 M(54.9%)and 46 F(45.09%).Acceptable correlation of ACD measured thru Smith method with Orbscan and Pentacam are R=0.958 and R=0.942 respectively and so Orbscan results can be used in procedures relying on ACD. Conclusion: ACDs measured with OrbScan is more precise than Pentacam and so can be more useful in some surgery procedures relying ACD results such as phakic IOLs and in cycloplegia contraindications.

Keywords: orbscan, pentacam, anterior chamber depth, slit lamp

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Authors: Ali Heydarimoghim

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In this paper, the optimal placement of charging and discharging stations is done to determine the location and capacity of the stations, reducing the cost of electric vehicle owners' losses, reducing the cost of distribution system losses, and reducing the costs associated with the stations. Also, observing the permissible limits of the bus voltage and the capacity of the stations and their distance are considered as constraints of the problem. Given the traffic situation in different areas of a city, we estimate the amount of energy required to charge and the amount of energy provided to discharge electric vehicles in each area. We then introduce the electricity distribution system of the city in question. Following are the scenarios for introducing the problem and introducing the objective and constraint functions. Finally, the simulation results for different scenarios are compared.

Keywords: charging & discharging stations, hybrid vehicles, optimization, replacement

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Authors: Nada Jasim Habeeb, Rana Saad Mohammed, Muntaha Khudair Abbass

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For more efficient and fast video summarization, this paper presents a surveillance video summarization method. The presented method works to improve video summarization technique. This method depends on temporal differencing to extract most important data from large video stream. This method uses histogram differencing and Sum Conditional Variance which is robust against to illumination variations in order to extract motion objects. The experimental results showed that the presented method gives better output compared with temporal differencing based summarization techniques.

Keywords: temporal differencing, video summarization, histogram differencing, sum conditional variance

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Authors: Shashi Kant Mishra

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In this paper, we consider semi-infinite mathematical programming problems with equilibrium constraints (SIMPEC). We establish necessary and sufficient optimality conditions for the SIMPEC, using convexificators. We study the Wolfe type dual problem for the SIMPEC under the ∂∗convexity assumptions. A Mond-Weir type dual problem is also formulated and studied for the SIMPEC under the ∂∗-convexity, ∂∗-pseudoconvexity and ∂∗quasiconvexity assumptions. Weak duality theorems are established to relate the SIMPEC and two dual programs in the framework of convexificators. Further, strong duality theorems are obtained under generalized standard Abadie constraint qualification (GS-ACQ).

Keywords: mathematical programming problems with equilibrium constraints, optimality conditions, semi-infinite programming, convexificators

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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: Aboussalih Amira, Zarza Tahar, Fedaoui Kamel, Baroura Lazhar, Hammoudi Salah

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316 L steel is a stainless steel frequently used in orthopedic surgery; in the design of implants (hip, knee, shoulder, ankle, etc.), in dental surgery, cardiology, ophthalmology. Before any use, it is essential to predict the macroscopic phenomenological behavior of the material, and to analyze its response. The behavior of 316 L steel in low cycle fatigue, under uniaxial cyclic loading of tension/compression, producing significant plastic deformations leading to material damage. This investigation allowed us to characterize the behavior of the 316L steel employed in the locking of the compression plates (LCP), of which they are generally used in orthopedics to stabilize the fractured bone parts. And to perceive the phenomenon of Ratcheting leading to the damage of LCP by an excess of plastic deformation under nonsymmetrical alternated imposed constraint in low cycle fatigue.

Keywords: 316L SS, locking compression plate, low cycle fatigue, ratcheting

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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: Nikhat Nawaz, S. Srinivasulu, P. Kesava Rao

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Feature extraction plays an important role in many remote sensing applications. Automatic extraction of water bodies is of great significance in many remote sensing applications like change detection, image retrieval etc. This paper presents a procedure for automatic extraction of water information from remote sensing images. The algorithm uses the relative location of R-colour component of the chromaticity diagram. This method is then integrated with the effectiveness of the spatial scale transformation of whole method. The whole method is based on water index fitted from spectral library. Experimental results demonstrate the improved accuracy and effectiveness of the integrated method for automatic extraction of water bodies.

Keywords: feature extraction, remote sensing, image retrieval, chromaticity, water index, spectral library, integrated method

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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

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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: M. H. Hussain, I. Musirin, A. F. Abidin, S. R. A. Rahim

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This paper presents the implementation of Artificial Bees Colony (ABC) algorithm in solving Directional OverCurrent Relays (DOCRs) coordination problem for near-end faults occurring in fixed network topology. The coordination optimization of DOCRs is formulated as linear programming (LP) problem. The objective function is introduced to minimize the operating time of the associated relay which depends on the time multiplier setting. The proposed technique is to taken as a technique for comparison purpose in order to highlight its superiority. The proposed algorithms have been tested successfully on 8 bus test system. The simulation results demonstrated that the ABC algorithm which has been proved to have good search ability is capable in dealing with constraint optimization problems.

Keywords: artificial bees colony, directional overcurrent relay coordination problem, relay settings, time multiplier setting

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Authors: Matloub Hussaina

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This paper investigates the impact of information sharing and capacity constraints on backlog bullwhip effect of Automatic Pipe Line Inventory and Order Based Production Control System (APIOBPCS). System dynamic simulation using iThink Software has been applied. It has been found that smooth ordering by Tier 1 can be achieved when Tier 1 has medium capacity constraints. Simulation experiments also show that information sharing helps to reduce 50% of backlog bullwhip effect in capacitated supply chains. This knowledge is of value per se, giving supply chain operations managers and designers a practical way in to controlling the backlog bullwhip effect. Future work should investigate the total cost implications of capacity constraints and safety stocks in multi-echelon supply chain.

Keywords: supply chain dynamics, information sharing, capacity constraints, simulation, APIOBPCS

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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: Avinash Nayak, Debopam Das

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The current work implements the variational principle to find the optimum initial perturbation that provides maximum growth in an impulsively blocked channel flow. The conventional method for studying temporal stability has always been through modal analysis. In most of the transient flows, this modal analysis is still followed with the quasi-steady assumption, i.e. change in base flow is much slower compared to perturbation growth rate. There are other studies where transient analysis on time dependent flows is done by formulating the growth of perturbation as an initial value problem. But the perturbation growth is sensitive to the initial condition. This study intends to find the initial perturbation that provides the maximum growth at a later time. Here, the expression of base flow for blocked channel is derived and the formulation is based on the two dimensional perturbation with stream function representing the perturbation quantity. Hence, the governing equation becomes the Orr-Sommerfeld equation. In the current context, the cost functional is defined as the ratio of disturbance energy at a terminal time 'T' to the initial energy, i.e. G(T) = ||q(T)||2/||q(0)||2 where q is the perturbation and ||.|| defines the norm chosen. The above cost functional needs to be maximized against the initial perturbation distribution. It is achieved with the constraint that perturbation follows the basic governing equation, i.e. Orr-Sommerfeld equation. The corresponding adjoint equation is derived and is solved along with the basic governing equation in an iterative manner to provide the initial spatial shape of the perturbation that provides the maximum growth G (T). The growth rate is plotted against time showing the development of perturbation which achieves an asymptotic shape. The effects of various parameters, e.g. Reynolds number, are studied in the process. Thus, the study emphasizes on the usage of optimal perturbation and its growth to understand the stability characteristics of time dependent flows. The assumption of quasi-steady analysis can be verified against these results for the transient flows like impulsive blocked channel flow.

Keywords: blocked channel flow, calculus of variation, hydrodynamic stability, optimal perturbation

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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: 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: 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: Gloria Patricia Manurung

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Jakarta Bus Rapid Transit (BRT) system which was established in 2009 to reduce private vehicle usage and ease the rush hour gridlock throughout the Jakarta Greater area, has failed to achieve its purpose. With gradually increasing the number of private vehicles ownership and reduced road space by the BRT lane construction, private vehicle users intuitively invade the exclusive lane of BRT, creating local traffic along the BRT network. Invaded BRT lanes costs become the same with the road network, making BRT which is supposed to be the main public transportation in the city becoming unreliable. Efforts to guard critical lanes with preventing the invasion by allocating traffic agents at several intersections have been expended, lead to the improving congestion level along the lane. Given a set of number of traffic agents, this study uses an analytical approach to finding the best deployment strategy of traffic agent on a simplified Jakarta road network in minimizing the BRT link cost which is expected to lead to the improvement of BRT system time reliability. User-equilibrium model of traffic assignment is used to reproduce the origin-destination demand flow on the network and the optimum solution conventionally can be obtained with brute force algorithm. This method’s main constraint is that traffic assignment simulation time escalates exponentially with the increase of set of agent’s number and network size. Our proposed metaheuristic and heuristic algorithms perform linear simulation time increase and result in minimized BRT cost approaching to brute force algorithm optimization. Further analysis of the overall network link cost should be performed to see the impact of traffic agent deployment to the network system.

Keywords: traffic assignment, user equilibrium, greedy algorithm, optimization

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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: Srishti Bhatt, Vaibhav Bhavsar, Adil Hussain, Aashay Mhaske, S. C. Bali, T. S. Srikanth

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Shape Memory Alloys (SMA) are widely known for their unique shape recovery properties. SMA based actuation systems have high-force to weight ratio, light weight and also bio-compatible material. Which is why they are being used in different fields of aerospace, robotics, automotive and biomedical industries. However, in the automotive industry plenty of patents are available but commercially viable products are very few in market. This could be due to SMA material limitations like small stroke, direct dependability of lifecycle on stroke, pull load of the wire and high cycle time. In automotive sector, SMA being considered as an actuator which is required to have high stroke and constraint arises to accommodate a long length of wire (to compensate maximum 4 % strain as per better fatigue life cycle) not only increases complexity but also adds on the cost. More than 200 different types of actuators are used in an automobile, few of them whose efficiency can highly increase by replacing them with SMA based actuators which include latch lock mechanism, glove box, Head lamp leveling, side mirror and rear mirror leveling, tailgate opener and fuel lid cap actuator. To overcome the limitation of available space for required stroke of an actuator which leads to study the effect of different loading positions on SMA wires, different orientations of SMA wire by using pulleys and lever based systems to achieve maximum stroke. This investigation summarizes the loading under the V shape orientation the required stroke and carrying load capacity in more compact in comparison with straight orientation of wire. Similarly, the U shape orientation its showing higher load carrying capacity but reduced stroke which is aligned with concept of bundled wire method. Life-cycle of these orientations were also evaluated.

Keywords: actuators, automotive, nitinol, shape memory alloy, SMA wire orientations

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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: 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: Muhammad Saqib Manzoor, Camille Dickson-Deane, Prashan Karunaratne

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Cobb-Douglas production (utility) function is a fundamental function widely used in economics teaching and research. The key reason is the function's characteristics to describe the actual production using inputs like labour and capital. The characteristics of the function like returns to scale, marginal, and diminishing marginal productivities are covered in the introductory units in both microeconomics and macroeconomics with a 2-dimensional static visualisation of the function. However, less insight is provided regarding three-dimensional surface, changes in the curvature properties due to returns to scale, the linkage of the short-run production function with its long-run counterpart and marginal productivities, the level curves, and the constraint optimisation. Since (freshman) learners have diverse prior knowledge and cognitive skills, the existing “one size fits all” approach is not very helpful. The aim of this study is to bridge this gap by introducing technological intervention with interactive animations of the three-dimensional surface and sequential unveiling of the characteristics mentioned above using Python software. A small classroom intervention has helped students enhance their analytical and visualisation skills towards active and authentic learning of this topic. However, to authenticate the strength of our approach, a quasi-Delphi study will be conducted to ask domain-specific experts, “What value to the learning process in economics is there using a 2-dimensional static visualisation compared to using a 3-dimensional dynamic visualisation?’ Here three perspectives of the intervention were reviewed by a panel comprising of novice students, experienced students, novice instructors, and experienced instructors in an effort to determine the learnings from each type of visualisations within a specific domain of knowledge. The value of this approach is key to suggesting different pedagogical methods which can enhance learning outcomes.

Keywords: cobb-douglas production function, quasi-Delphi method, effective teaching and learning, 3D-visualisations

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