Search results for: Thrustone's paired comparison method

Authors: G.Hariharan, K.Kannan

Abstract:

In this paper, we develop an accurate and efficient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.

Keywords: FitzHugh-Nagumo equation, Haar wavelet method, adomain decomposition method, computationally attractive.

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Authors: Muhammad Mujtaba Asad, Razali Bin Hassan, Fahad Sherwani

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This paper explains about the voltage output for DC to DC boost converter between open loop, PID controller and fuzzy logic controller through Matlab Simulink. Simulink input voltage was set at 12V and the voltage reference was set at 24V. The analysis on the deviation of voltage resulted that the difference between reference voltage setting and the output voltage is always lower. Comparison between open loop, PID and FLC shows that, the open loop circuit having a bit higher on the deviation of voltage. The PID circuit boosts for FLC has a lesser deviation of voltage and proved that it is such a better performance on control the deviation of voltage during the boost mode.

Keywords: Boost Convertors, Power Electronics, PID, Fuzzy logic, Open loop.

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Authors: Zhaojun Wang, Zongdi Sun, Qinqin Cui, Xingwan Ren

Abstract:

Based on multivariate statistical analysis theory, this paper uses the principal component analysis method, Mahalanobis distance analysis method and fitting method to establish the photovoltaic health model to evaluate the health of photovoltaic panels. First of all, according to weather conditions, the photovoltaic panel variable data are classified into five categories: sunny, cloudy, rainy, foggy, overcast. The health of photovoltaic panels in these five types of weather is studied. Secondly, a scatterplot of the relationship between the amount of electricity produced by each kind of weather and other variables was plotted. It was found that the amount of electricity generated by photovoltaic panels has a significant nonlinear relationship with time. The fitting method was used to fit the relationship between the amount of weather generated and the time, and the nonlinear equation was obtained. Then, using the principal component analysis method to analyze the independent variables under five kinds of weather conditions, according to the Kaiser-Meyer-Olkin test, it was found that three types of weather such as overcast, foggy, and sunny meet the conditions for factor analysis, while cloudy and rainy weather do not satisfy the conditions for factor analysis. Therefore, through the principal component analysis method, the main components of overcast weather are temperature, AQI, and pm2.5. The main component of foggy weather is temperature, and the main components of sunny weather are temperature, AQI, and pm2.5. Cloudy and rainy weather require analysis of all of their variables, namely temperature, AQI, pm2.5, solar radiation intensity and time. Finally, taking the variable values in sunny weather as observed values, taking the main components of cloudy, foggy, overcast and rainy weather as sample data, the Mahalanobis distances between observed value and these sample values are obtained. A comparative analysis was carried out to compare the degree of deviation of the Mahalanobis distance to determine the health of the photovoltaic panels under different weather conditions. It was found that the weather conditions in which the Mahalanobis distance fluctuations ranged from small to large were: foggy, cloudy, overcast and rainy.

Keywords: Fitting, principal component analysis, Mahalanobis distance, SPSS, MATLAB.

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Authors: Nicolas Delcey, Philippe Baucour, Didier Chamagne, Geneviève Wimmer, Auditeau Gérard, Bausseron Thomas, Bouger Odile, Blanvillain Gérard

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This paper proposes a thermal study of the catenary/pantograph interface for a train in motion. A 2.5D complex model of the pantograph strip has been defined and created by a coupling between a 1D and a 2D model. Experimental and simulation results are presented and with a comparison allow validating the 2.5D model. Some physical phenomena are described and presented with the help of the model such as the stagger motion thermal effect, particular heats and the effect of the material characteristics. Finally it is possible to predict the critical thermal configuration during a train trip.

Keywords: 2.5D modelling, pantograph/catenary liaison, sliding contact, Joule effect, moving heat source.

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Authors: S. Cagin, X. Fischer, E. Delacourt, N. Bourabaa, C. Morin, D. Coutellier, B. Carré, S. Loumé

Abstract:

The complexity of scavenging by ports and its impact on engine efficiency create the need to understand and to model it as realistically as possible. However, there are few empirical scavenging models and these are highly specialized. In a design optimization process, they appear very restricted and their field of use is limited. This paper presents a comparison of two methods to establish and reduce a model of the scavenging process in 2-stroke diesel engines. To solve the lack of scavenging models, a CFD model has been developed and is used as the referent case. However, its large size requires a reduction. Two techniques have been tested depending on their fields of application: The NTF method and neural networks. They both appear highly appropriate drastically reducing the model’s size (over 90% reduction) with a low relative error rate (under 10%). Furthermore, each method produces a reduced model which can be used in distinct specialized fields of application: the distribution of a quantity (mass fraction for example) in the cylinder at each time step (pseudo-dynamic model) or the qualification of scavenging at the end of the process (pseudo-static model).

Keywords: Diesel engine, Design optimization, Model reduction, Neural network, NTF algorithm, Scavenging.

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Authors: Anurag Sharma, Christian W. Omlin

Abstract:

Self-organizing map (SOM) is a well known data reduction technique used in data mining. It can reveal structure in data sets through data visualization that is otherwise hard to detect from raw data alone. However, interpretation through visual inspection is prone to errors and can be very tedious. There are several techniques for the automatic detection of clusters of code vectors found by SOM, but they generally do not take into account the distribution of code vectors; this may lead to unsatisfactory clustering and poor definition of cluster boundaries, particularly where the density of data points is low. In this paper, we propose the use of an adaptive heuristic particle swarm optimization (PSO) algorithm for finding cluster boundaries directly from the code vectors obtained from SOM. The application of our method to several standard data sets demonstrates its feasibility. PSO algorithm utilizes a so-called U-matrix of SOM to determine cluster boundaries; the results of this novel automatic method compare very favorably to boundary detection through traditional algorithms namely k-means and hierarchical based approach which are normally used to interpret the output of SOM.

Keywords: cluster boundaries, clustering, code vectors, data mining, particle swarm optimization, self-organizing maps, U-matrix.

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Authors: Chanon Aphirukmatakun, Natasha Dejdumrong

Abstract:

In image processing and visualization, comparing two bitmapped images needs to be compared from their pixels by matching pixel-by-pixel. Consequently, it takes a lot of computational time while the comparison of two vector-based images is significantly faster. Sometimes these raster graphics images can be approximately converted into the vector-based images by various techniques. After conversion, the problem of comparing two raster graphics images can be reduced to the problem of comparing vector graphics images. Hence, the problem of comparing pixel-by-pixel can be reduced to the problem of polynomial comparisons. In computer aided geometric design (CAGD), the vector graphics images are the composition of curves and surfaces. Curves are defined by a sequence of control points and their polynomials. In this paper, the control points will be considerably used to compare curves. The same curves after relocated or rotated are treated to be equivalent while two curves after different scaled are considered to be similar curves. This paper proposed an algorithm for comparing the polynomial curves by using the control points for equivalence and similarity. In addition, the geometric object-oriented database used to keep the curve information has also been defined in XML format for further used in curve comparisons.

Keywords: Bezier curve, Said-Ball curve, Wang-Ball curve, DP curve, CAGD, comparison, geometric object database.

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Authors: L. Fridrichova, R. Knížek, V. Bajzík

Abstract:

Drape is one of the important visual characteristics of the fabric. This paper is introducing an innovative method of measurement and evaluation of the drape shape of the fabric. The measuring principle is based on the possibility of multiple vertical strain of the fabric. This method more accurately simulates the real behavior of the fabric in the process of draping. The method is fully automated, so the sample can be measured by using any number of cycles in any time horizon. Using the present method of measurement, we are able to describe the viscoelastic behavior of the fabric.

Keywords: Drape, drape shape, automated drape meter.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

Batteries and fuel cells contain a great potential to back up severe photovoltaic power fluctuations under inclement weather conditions. In this paper comparison between batteries and fuel cells is carried out in detail only for their PV power backup options, so their common attributes and different attributes is discussed. Then, the common and different attributes are compared; accordingly, the fuel cell is selected as the backup of Photovoltaic system. Finally, environmental evaluation of the selected hybrid plant was made in terms of plant-s land requirement and lifetime CO2 emissions, and then compared with that of the conventional fossilfuel power generating forms.

Keywords: Fuel cell, PV cell, hybrid power plant.

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Authors: Mohammed Salem Alzahrani

Abstract:

In this paper, student admission process is studied to optimize the assignment of vacant seats with three main objectives. Utilizing all vacant seats, satisfying all programs of study admission requirements and maintaining fairness among all candidates are the three main objectives of the optimization model. Seat Assignment Method (SAM) is used to build the model and solve the optimization problem with help of Northwest Coroner Method and Least Cost Method. A closed formula is derived for applying the priority of assigning seat to candidate based on SAM.

Keywords: Admission Process Model, Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM).

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Authors: A. Ashjaran, R. Ghazi-saeidi, E. Yazdanshenas, A. Rashidi

Abstract:

In this research, the main aim is to investigate the antimicrobial effectiveness of ammonyx solutions finishing on Sweatshirt Sport with immersion method. 60 Male healthy subjects (football player) participated in this study. They were dressed in a Sweatshirt for 14 days and some microbes found on them were investigated. The antimicrobial effect of different ammonyx solutions(1/100, 1/500, 1/1000, 1/2000 v/v solutions of Ammonyx) on the identified microbes was studied by the zone inhabitation method in vitro. In the next step the Sweatshirt Sports were treated with the same different solutions of ammonyx and the antimicrobial effectiveness was assessed by colony count method in different times and the results were compared whit untreated ones. Some mechanical properties of treated cotton/polyester yarn that used in Sweatshirt Sport were measured after 30 days and were compared with untreated one. Finally after finishing, scanning electron microscopy (SEM) was used to compare the surfaces of the finished and unfinished specimens. The results showed the presence of five pathogenic microbes on Sweatshirt Sports such as Escherichia coli, Staphylococcus aureus, Aspergillus, Mucor and Candida. The inhalation time for treated on Sweatshirt Sports improved. The amount of colony growth on treated clothes reduced considerably and moreover the mechanical tests results showed no significant deterioration effect of studies properties in comparison to the untreated yarn. The visual examination of the SEM indicated that the antimicrobial treatments were applied usefully to fabrics.

Keywords: Pathogenic microbes, Sweatshirt Sports, Ammonyx, antimicrobial treatment

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Authors: M Nayeripour, H. Khorsand, A. Roosta, T. Niknam, E. Azad

Abstract:

Series compensators have been used for many years, to increase the stability and load ability of transmission line. They compensate retarded or advanced volt drop of transmission lines by placing advanced or retarded voltage in series with them to compensate the effective reactance, which cause to increase load ability of transmission lines. In this paper, two method of fuzzy controller, based on power reference tracking and impedance reference tracking have been developed on TCSC controller in order to increase load ability and improving power oscillation damping of system. In these methods, fire angle of thyristors are determined directly through the special Rule-bases with the error and change of error as the inputs. The simulation results of two area four- machines power system show the good performance of power oscillation damping in system. Comparison of this method with classical PI controller shows the increasing speed of system response in power oscillation damping.

Keywords: TCSC, Two area network, Fuzzy controller, Power oscillation damping.

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Authors: Kai Wang, Yanling Zu

Abstract:

By utilizing the comparison theorem and Lyapunov second method, some sufficient conditions for the permanence and global attractivity of positive periodic solution for a predator-prey model with mutual interference m ∈ (0, 1) and delays τi are obtained. It is the first time that such a model is considered with delays. The significant is that the results presented are related to the delays and the mutual interference constant m. Several examples are illustrated to verify the feasibility of the results by simulation in the last part.

Keywords: Predator-prey model, Mutual interference, Delays, Permanence, Global attractivity

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Authors: Belkacem Brahmi, Mohand Ouamer Bibi

Abstract:

In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.

Keywords: Convex quadratic programming, dual support methods, active set methods.

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

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Authors: Sarra Ben Hariz, Zied Elouedi, Khaled Mellouli

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The belief K-modes method (BKM) approach is a new clustering technique handling uncertainty in the attribute values of objects in both the cluster construction task and the classification one. Like the standard version of this method, the BKM results depend on the chosen initial modes. So, one selection method of initial modes is developed, in this paper, aiming at improving the performances of the BKM approach. Experiments with several sets of real data show that by considered the developed selection initial modes method, the clustering algorithm produces more accurate results.

Keywords: Clustering, Uncertainty, Belief function theory, Belief K-modes Method, Initial modes selection.

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Authors: Sara Barati, Karim Ivaz

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In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.

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Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

Abstract:

As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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Authors: A.Memari

Abstract:

In this article, a simulation method called the Homotopy Perturbation Method (HPM) is employed in the steady flow of a Walter's B' fluid in a vertical channel with porous wall. We employed Homotopy Perturbation Method to derive solution of a nonlinear form of equation obtained from exerting similarity transforming to the ordinary differential equation gained from continuity and momentum equations of this kind of flow. The results obtained from the Homotopy Perturbation Method are then compared with those from the Runge–Kutta method in order to verify the accuracy of the proposed method. The results show that the Homotopy Perturbation Method can achieve good results in predicting the solution of such problems. Ultimately we use this solution to obtain the other terms of velocities and physical discussion about it.

Keywords: Steady flow; Walter's B' Fluid;, vertical channel;porous media, Homotopy Perturbation Method (HPM), Numerical Solution (NS).

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Authors: Ho Young Son, Bu Seog Ju, Woo Young Jung

Abstract:

This study presents the seismic safety evaluation of weir structure subjected to strong earthquake ground motions, as a flood defense structure in civil engineering structures. The seismic safety analysis procedure was illustrated through development of Finite Element (FE) and InFinite Element (IFE) method in ABAQUS platform. The IFE model was generated by CINPS4, 4-node linear one-way infinite model as a sold continuum infinite element in foundation areas of the weir structure and then nonlinear FE model using friction model for soil-structure interactions was applied in this study. In order to understand the complex behavior of weir structures, nonlinear time history analysis was carried out. Consequently, it was interesting to note that the compressive stress gave more vulnerability to the weir structure, in comparison to the tensile stress, during an earthquake. The stress concentration of the weir structure was shown at the connection area between the weir body and stilling basin area. The stress both tension and compression was reduced in IFE model rather than FE model of weir structures.

Keywords: Weir, Finite Element, Infinite Element, Nonlinear, Earthquake.

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Authors: Bharathi P. T, P. Subashini

Abstract:

Ice cover County has a significant impact on rivers as it affects with the ice melting capacity which results in flooding, restrict navigation, modify the ecosystem and microclimate. River ices are made up of different ice types with varying ice thickness, so surveillance of river ice plays an important role. River ice types are captured using infrared imaging camera which captures the images even during the night times. In this paper the river ice infrared texture images are analysed using first-order statistical methods and secondorder statistical methods. The second order statistical methods considered are spatial gray level dependence method, gray level run length method and gray level difference method. The performance of the feature extraction methods are evaluated by using Probabilistic Neural Network classifier and it is found that the first-order statistical method and second-order statistical method yields low accuracy. So the features extracted from the first-order statistical method and second-order statistical method are combined and it is observed that the result of these combined features (First order statistical method + gray level run length method) provides higher accuracy when compared with the features from the first-order statistical method and second-order statistical method alone.

Keywords: Gray Level Difference Method, Gray Level Run Length Method, Kurtosis, Probabilistic Neural Network, Skewness, Spatial Gray Level Dependence Method.

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Authors: Jahangir Jafari, Nematollah Khorasani, Afshin Danehkar

Abstract:

Having a very many number of pipelines all over the country, Iran is one of the countries consists of various ecosystems with variable degrees of fragility and robusticity as well as geographical conditions. This study presents a state-of-the-art method to estimate environmental risks of pipelines by recommending rational equations including FES, URAS, SRS, RRS, DRS, LURS and IRS as well as FRS to calculate the risks. This study was carried out by a relative semi-quantitative approach based on land uses and HVAs (High-Value Areas). GIS as a tool was used to create proper maps regarding the environmental risks, land uses and distances. The main logic for using the formulas was the distance-based approaches and ESI as well as intersections. Summarizing the results of the study, a risk geographical map based on the ESIs and final risk score (FRS) was created. The study results showed that the most sensitive and so of high risk area would be an area comprising of mangrove forests located in the pipeline neighborhood. Also, salty lands were the most robust land use units in the case of pipeline failure circumstances. Besides, using a state-of-the-art method, it showed that mapping the risks of pipelines out with the applied method is of more reliability and convenience as well as relative comprehensiveness in comparison to present non-holistic methods for assessing the environmental risks of pipelines. The focus of the present study is “assessment" than that of “management". It is suggested that new policies are to be implemented to reduce the negative effects of the pipeline that has not yet been constructed completely

Keywords: ERM, ESI, ERA, Pipeline, Assalouyeh

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

Abstract:

In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: Embedded Runge-Kutta-Fehlberg method, Initial value problem.

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Authors: Ihor Trots, Yuriy Tasinkevych, Andrzej Nowicki, Marcin Lewandowski

Abstract:

The paper presents the study of synthetic transmit aperture method applying the Golay coded transmission for medical ultrasound imaging. Longer coded excitation allows to increase the total energy of the transmitted signal without increasing the peak pressure. Signal-to-noise ratio and penetration depth are improved maintaining high ultrasound image resolution. In the work the 128-element linear transducer array with 0.3 mm inter-element spacing excited by one cycle and the 8 and 16-bit Golay coded sequences at nominal frequencies 4 MHz was used. Single element transmission aperture was used to generate a spherical wave covering the full image region and all the elements received the echo signals. The comparison of 2D ultrasound images of the wire phantom as well as of the tissue mimicking phantom is presented to demonstrate the benefits of the coded transmission. The results were obtained using the synthetic aperture algorithm with transmit and receive signals correction based on a single element directivity function.

Keywords: Golay coded sequences, radiation pattern, synthetic aperture, ultrasound imaging.

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Authors: Saheed A. Gbadegeshin

Abstract:

Commercialization method is a means to make inventions available at the market for final consumption. It is described as an important tool for keeping business enterprises sustainable and improving national economic growth. Thus, there are several scholarly publications on it, either presenting or testing different methods for commercialization. However, young entrepreneurs, technologists and scientists would like to know the best method to commercialize their innovations. Then, this question arises: What is the best commercialization method? To answer the question, a systematic literature review was conducted, and practitioners were interviewed. The literary results revealed that there are many methods but new methods are needed to improve commercialization especially during these times of economic crisis and political uncertainty. Similarly, the empirical results showed there are several methods, but the best method is the one that reduces costs, reduces the risks associated with uncertainty, and improves customer participation and acceptability. Therefore, it was concluded that new commercialization method is essential for today's high technologies and a method was presented.

Keywords: Commercialization method, high technology, lean start-up methodology, technology, knowledge.

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Authors: Li Hao, Yan Zhang, Jingan Cui

Abstract:

The Eulerian numerical method is proposed to analyze the explosion in tunnel. Based on this method, an original software M-MMIC2D is developed by Cµ program language. With this software, the explosion problem in the tunnel with three expansion-chambers is numerically simulated, and the results are found to be in full agreement with the observed experimental data.

Keywords: Eulerian method, numerical simulation, shock wave, tunnel

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Authors: K. Benamrane, T. Abdelkrim, T. Benslimane, Aeh. Benkhelifa, B. Bezza

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This paper presents a comparison between two Pulse Width Modulation (PWM) algorithms applied to a three-level Neutral Point Clamped (NPC) Voltage Source Inverter (VSI). The first algorithm applied is the triangular-sinusoidal strategy; the second is the Space Vector Pulse Width Modulation (SVPWM) strategy. In the first part, we present a topology of three-level NCP VSI. After that, we develop the two PWM strategies to control this converter. At the end the experimental results are presented.

Keywords: Multilevel inverter, Space vector pulse width modulation (SVPWM), triangular-sinusoidal strategy.

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Authors: Jindřiška Šedová, Miloš Šeda

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This paper summarizes and compares approaches to solving the knapsack problem and its known application in capital budgeting. The first approach uses deterministic methods and can be applied to small-size tasks with a single constraint. We can also apply commercial software systems such as the GAMS modelling system. However, because of NP-completeness of the problem, more complex problem instances must be solved by means of heuristic techniques to achieve an approximation of the exact solution in a reasonable amount of time. We show the problem representation and parameter settings for a genetic algorithm framework.

Keywords: Capital budgeting, knapsack problem, GAMS, heuristic method, genetic algorithm.

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Authors: Chaitanya Vyas

Abstract:

This paper identifies limitations of existing two e- Governance services viz. railway ticket booking and passport service in India. The comparison has been made as to how in the past these two citizen services were operating manually and how these services are taken online via e-Governance. Different e-Governance projects, investment aspects, and role of corporate are discussed. For Indian Railway online ticketing a comparison has been made between state run booking website and popular private firm run booking websites. For passport service, observations through personal visit to passport center is described. Suggestions are made to improve these services further to improve citizen service experiences.

Keywords: e-Governance, citizen services, Indian Railways, passport.

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Authors: Thuraya M. Qaradaghi, Newroz N. Abdulrazaq

Abstract:

The McEliece cryptosystem is an asymmetric type of cryptography based on error correction code. The classical McEliece used irreducible binary Goppa code which considered unbreakable until now especially with parameter [1024, 524, and 101], but it is suffering from large public key matrix which leads to be difficult to be used practically. In this work Irreducible and Separable Goppa codes have been introduced. The Irreducible and Separable Goppa codes used are with flexible parameters and dynamic error vectors. A Comparison between Separable and Irreducible Goppa code in McEliece Cryptosystem has been done. For encryption stage, to get better result for comparison, two types of testing have been chosen; in the first one the random message is constant while the parameters of Goppa code have been changed. But for the second test, the parameters of Goppa code are constant (m=8 and t=10) while the random message have been changed. The results show that the time needed to calculate parity check matrix in separable are higher than the one for irreducible McEliece cryptosystem, which is considered expected results due to calculate extra parity check matrix in decryption process for g2(z) in separable type, and the time needed to execute error locator in decryption stage in separable type is better than the time needed to calculate it in irreducible type. The proposed implementation has been done by Visual studio C#.

Keywords: McEliece cryptosystem, Goppa code, separable, irreducible.

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