Search results for: method of similarity

Authors: Vishal Raj, Noorhan Abbas

Abstract:

Ambiguity in NLP (Natural language processing) refers to the ability of a word, phrase, sentence, or text to have multiple meanings. This results in various kinds of ambiguities such as lexical, syntactic, semantic, anaphoric and referential am-biguities. This study is focused mainly on solving the issue of Lexical ambiguity. Word Sense Disambiguation (WSD) is an NLP technique that aims to resolve lexical ambiguity by determining the correct meaning of a word within a given context. Most WSD solutions rely on words for training and testing, but we have used lemma and Part of Speech (POS) tokens of words for training and testing. Lemma adds generality and POS adds properties of word into token. We have designed a novel method to create an affinity matrix to calculate the affinity be-tween any pair of lemma_POS (a token where lemma and POS of word are joined by underscore) of given training set. Additionally, we have devised an al-gorithm to create the sense clusters of tokens using affinity matrix under hierar-chy of POS of lemma. Furthermore, three different mechanisms to predict the sense of target word using the affinity/similarity value are devised. Each contex-tual token contributes to the sense of target word with some value and whichever sense gets higher value becomes the sense of target word. So, contextual tokens play a key role in creating sense clusters and predicting the sense of target word, hence, the model is named Contextual SenSe Model (CSM). CSM exhibits a noteworthy simplicity and explication lucidity in contrast to contemporary deep learning models characterized by intricacy, time-intensive processes, and chal-lenging explication. CSM is trained on SemCor training data and evaluated on SemEval test dataset. The results indicate that despite the naivety of the method, it achieves promising results when compared to the Most Frequent Sense (MFS) model.

Keywords: word sense disambiguation (wsd), contextual sense model (csm), most frequent sense (mfs), part of speech (pos), natural language processing (nlp), oov (out of vocabulary), lemma_pos (a token where lemma and pos of word are joined by underscore), information retrieval (ir), machine translation (mt)

Procedia PDF Downloads 107

Authors: Ali Isapour, Ramin Nateghi

Abstract:

— Markov parameters are unique parameters of the system and remain unchanged under similarity transformations. Markov parameters from a power series that is convergent only if the system matrix’s eigenvalues are inside the unity circle. Therefore, Markov parameters of a stable discrete-time system are convergent. In this study, we aim to realize the system based on Markov parameters by using Artificial Neural Networks (ANN), and this end, we use Flexible Neural Networks. Realization means determining the elements of matrices A, B, C, and D.

Keywords: Markov parameters, realization, activation function, flexible neural network

Procedia PDF Downloads 194

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

Procedia PDF Downloads 411

Authors: Juan Francisco Reinoso Gordo, Francisco Javier Ariza-López, José Rodríguez Avi, Domingo Barrera Rosillo

Abstract:

The evaluation of the quality of a data product is based on the comparison of the product with a reference of greater accuracy. In the case of MDE data products, quality assessment usually focuses on positional accuracy and few studies consider other terrain characteristics, such as slope and orientation. The proposal that is made consists of evaluating the similarity of two DEMs (a product and a reference), through the joint analysis of the distribution functions of the variables of interest, for example, elevations, slopes and orientations. This is a multivariable approach that focuses on distribution functions, not on single parameters such as mean values or dispersions (e.g. root mean squared error or variance). This is considered to be a more holistic approach. The use of the Kolmogorov-Smirnov test is proposed due to its non-parametric nature, since the distributions of the variables of interest cannot always be adequately modeled by parametric models (e.g. the Normal distribution model). In addition, its application to the multivariate case is carried out jointly by means of a single test on the convolution of the distribution functions of the variables considered, which avoids the use of corrections such as Bonferroni when several statistics hypothesis tests are carried out together. In this work, two DEM products have been considered, DEM02 with a resolution of 2x2 meters and DEM05 with a resolution of 5x5 meters, both generated by the National Geographic Institute of Spain. DEM02 is considered as the reference and DEM05 as the product to be evaluated. In addition, the slope and aspect derived models have been calculated by GIS operations on the two DEM datasets. Through sample simulation processes, the adequate behavior of the Kolmogorov-Smirnov statistical test has been verified when the null hypothesis is true, which allows calibrating the value of the statistic for the desired significance value (e.g. 5%). Once the process has been calibrated, the same process can be applied to compare the similarity of different DEM data sets (e.g. the DEM05 versus the DEM02). In summary, an innovative alternative for the comparison of DEM data sets based on a multinomial non-parametric perspective has been proposed by means of a single Kolmogorov-Smirnov test. This new approach could be extended to other DEM features of interest (e.g. curvature, etc.) and to more than three variables

Keywords: data quality, DEM, kolmogorov-smirnov test, multivariate DEM comparison

Procedia PDF Downloads 115

Authors: Chui Ka Shing

Abstract:

This case study research attempts to examine the use of the Bar Model Method approach in learning and teaching mathematics in a primary school in Hong Kong. The objectives of the study are to find out to what extent (a) the Bar Model Method approach enhances the construction of students’ mathematics concepts, and (b) the school-based mathematics curriculum development with adopting the Bar Model Method approach. This case study illuminates the effectiveness of using the Bar Model Method to solve mathematics problems from Primary 1 to Primary 6. Some effective pedagogies and assessments were developed to strengthen the use of the Bar Model Method across year levels. Suggestions including school-based curriculum development for using Bar Model Method and further study were discussed.

Keywords: bar model method, curriculum development, mathematics education, problem solving

Procedia PDF Downloads 219

Authors: Yang Zhong, Heng Liu

Abstract:

The decoupling method and the modified Naiver method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. The basic governing equations for Mindlin plates are first decoupled into independent partial differential equations which can be solved separately. Using modified Navier method, the analytic solution of rectangular thick plate with all edges clamped supported is then derived. The solution method used in this paper leave out the complicated derivation for calculating coefficients and obtain the solution to problems directly. Numerical comparisons show the correctness and accuracy of the results at last.

Keywords: Mindlin plates, decoupling method, modified Navier method, bending rectangular plates

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Authors: Azizakhanim Maharramli

Abstract:

The gradual transition from entrenched traditional technology and organization of construction production to innovative additive construction technology inevitably meets technological, technical, organizational, labour, and, finally, social difficulties. Therefore, the chosen nodal method will lead to the elimination of the above difficulties, combining some of the usual methods of construction and the myth in world practice that the labour force is subjected to a strong stream of reduction. The nodal method of additive technology will create favourable conditions for the optimal degree of distribution of labour across facilities due to the consistent performance of homogeneous work and the introduction of additive technology and traditional technology into construction production.

Keywords: parallel method, sequential method, stream method, combined method, nodal method

Procedia PDF Downloads 94

Authors: Mahacine Amrani

Abstract:

A simple and rapid method for the determination of alcohol in gasoline-alcohol mixtures using density measurements is described. The method can determine a minimum of 1% of alcohol by volume. The precision of the method is ± 3%.The method is more useful for field test in the quality assessment of alcohol blended fuels.

Keywords: gasoline-alcohol, mixture, alcohol determination, density, measurement, Morocco

Procedia PDF Downloads 322

Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

Procedia PDF Downloads 375

Authors: Jiankang Wang, Hongyang Yu

Abstract:

This paper proposes a portable online 3D modeling method. The method first utilizes a depth camera to collect data and compresses the depth data using a frame-by-frame lossless data compression method. The color image is encoded using the H.264 encoding format. After the cloud obtains the color image and depth image, a 3D modeling method based on bundlefusion is used to complete the 3D modeling. The results of this study indicate that this method has the characteristics of portability, online, and high efficiency and has a wide range of application prospects.

Keywords: 3D reconstruction, bundlefusion, lossless compression, depth image

Procedia PDF Downloads 82

Authors: Haijie Li, Xuping Zhang

Abstract:

This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method

Procedia PDF Downloads 428

Authors: Lila Boulekbache-Makhlouf, Kahina Djaoud, Myriam Tazarourte, Samir Hadjal, Khodir Madani

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In Algeria, important quantities of secondary date variety (Phoenix dactylifera L.) are generated in each campaign; their chemical composition is similar to that of commercial dates. The present work aims to valorize this common date variety (Degla-Beida) which is often poorly exploited. In this context, we tried to prepare syrup from the secondary date variety and to evaluate the effect of conventional extraction (CE) or water bath extraction (WBE) and alternative extraction (microwaves assisted extraction (MAE), and ultrasounds assisted extraction (UAE)) on its total sugar content (TSC), using response surface methodology (RSM). Then, the analysis of individual sugars was performed by high-performance liquid chromatography (HPLC). Maximum predicted TSC recoveries under the optimized conditions for MAE, UAE and CE were 233.248 ± 3.594 g/l, 202.889 ± 5.797 g/l, and 233.535 ± 5.412 g/l, respectively, which were close to the experimental values: 233.796 ± 1.898 g/l; 202.037 ± 3.401 g/l and 234.380 ± 2.425 g/l. HPLC analysis revealed high similarity in the sugar composition of date juices obtained by MAE (60.11% sucrose, 16.64% glucose and 23.25% fructose) and CE (50.78% sucrose, 20.67% glucose and 28.55% fructose), although a large difference was detected for that obtained by UAE (0.00% sucrose, 46.94% glucose and 53.06% fructose). Microwave-assisted extraction was the best method for the preparation of date syrup with an optimal recovery of total sugar content. However, ultrasound-assisted extraction was the best one for the preparation of date syrup with high content of reducing sugars.

Keywords: dates, extraction, RSM, sugars, syrup

Procedia PDF Downloads 157

Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire

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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.

Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters

Procedia PDF Downloads 190

Authors: Somaya Adwan, Rasha Majed, Lamya'a Majed, Hamzah Arof

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In order to produce images with whole body parts, X-ray of different portions of the body parts is assembled using image stitching methods. A new method for image stitching that exploits mutually feature based method and direct based method to identify and merge pairs of X-ray medical images is presented in this paper. The performance of the proposed method based on this hybrid approach is investigated in this paper. The ability of the proposed method to stitch and merge the overlapping pairs of images is demonstrated. Our proposed method display comparable if not superior performance to other feature based methods that are mentioned in the literature on the standard databases. These results are promising and demonstrate the potential of the proposed method for further development to tackle more advanced stitching problems.

Keywords: image stitching, direct based method, panoramic image, X-ray

Procedia PDF Downloads 541

Authors: M. O. Olayiwola

Abstract:

Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

Procedia PDF Downloads 429

Authors: Salah Ghamari

Abstract:

In this study, the ability of self organizing map artificial (SOM) neural networks in clustering the wheat seeds varieties according to morphological properties of them was considered. The SOM is one type of unsupervised competitive learning. Experimentally, five morphological features of 300 seeds (including three varieties: gaskozhen, Md and sardari) were obtained using image processing technique. The results show that the artificial neural network has a good performance (90.33% accuracy) in classification of the wheat varieties despite of high similarity in them. The highest classification accuracy (100%) was achieved for sardari.

Keywords: artificial neural networks, clustering, self organizing map, wheat variety

Procedia PDF Downloads 656

Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: Alkaben Patel

Abstract:

The proposed RP-HPLC method is easy, rapid, economical, precise and accurate stability indicating RP-HPLC method for simultaneous estimation of Astorvastatin and Methylcobalamine in their combined dosage form has been developed.The separation was achieved by LC-20 AT C18(250mm*4.6mm*2.6mm)Colum and water (pH 3.5): methanol 70:30 as mobile phase, at a flow rate of 1ml/min. wavelength of this dosage form is 215nm.The drug is related to stress condition of hydrolysis, oxidation, photolysis and thermal degradation.

Keywords: RP- HPLC, atorvastatin, methylcobalamine, method, development, validation

Procedia PDF Downloads 335

Authors: Akshay Agrawal, Anand K. Srivastava

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The increasing amount of XML datasets available to casual users increases the necessity of investigating techniques to extract knowledge from these data. Data mining is widely applied in the database research area in order to extract frequent correlations of values from both structured and semi-structured datasets. The increasing availability of heterogeneous XML sources has raised a number of issues concerning how to represent and manage these semi structured data. In recent years due to the importance of managing these resources and extracting knowledge from them, lots of methods have been proposed in order to represent and cluster them in different ways.

Keywords: XML, similarity measure, clustering, cluster quality, semantic clustering

Procedia PDF Downloads 379

Authors: Guilherme Giacomini, Ana Luiza Menegatti Pavan, Allan Felipe Fattori Alves, Marcela de Oliveira, Fernando Antonio Bacchim Neto, José Ricardo de Arruda Miranda, Seizo Yamashita, Diana Rodrigues de Pina

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The maxillary sinus (MS), part of the paranasal sinus complex, is one of the most enigmatic structures in modern humans. The literature has suggested that MSs function as olfaction accessories, to heat or humidify inspired air, for thermoregulation, to impart resonance to the voice and others. Thus, the real function of the MS is still uncertain. Furthermore, the MS anatomy is complex and varies from person to person. Many diseases may affect the development process of sinuses. The incidence of rhinosinusitis and other pathoses in the MS is comparatively high, so, volume analysis has clinical value. Providing volume values for MS could be helpful in evaluating the presence of any abnormality and could be used for treatment planning and evaluation of the outcome. The computed tomography (CT) has allowed a more exact assessment of this structure, which enables a quantitative analysis. However, this is not always possible in the clinical routine, and if possible, it involves much effort and/or time. Therefore, it is necessary to have a convenient, robust, and practical tool correlated with the MS volume, allowing clinical applicability. Nowadays, the available methods for MS segmentation are manual or semi-automatic. Additionally, manual methods present inter and intraindividual variability. Thus, the aim of this study was to develop an automatic tool to quantity the MS volume in CT scans of paranasal sinuses. This study was developed with ethical approval from the authors’ institutions and national review panels. The research involved 30 retrospective exams of University Hospital, Botucatu Medical School, São Paulo State University, Brazil. The tool for automatic MS quantification, developed in Matlab®, uses a hybrid method, combining different image processing techniques. For MS detection, the algorithm uses a Support Vector Machine (SVM), by features such as pixel value, spatial distribution, shape and others. The detected pixels are used as seed point for a region growing (RG) segmentation. Then, morphological operators are applied to reduce false-positive pixels, improving the segmentation accuracy. These steps are applied in all slices of CT exam, obtaining the MS volume. To evaluate the accuracy of the developed tool, the automatic method was compared with manual segmentation realized by an experienced radiologist. For comparison, we used Bland-Altman statistics, linear regression, and Jaccard similarity coefficient. From the statistical analyses for the comparison between both methods, the linear regression showed a strong association and low dispersion between variables. The Bland–Altman analyses showed no significant differences between the analyzed methods. The Jaccard similarity coefficient was > 0.90 in all exams. In conclusion, the developed tool to quantify MS volume proved to be robust, fast, and efficient, when compared with manual segmentation. Furthermore, it avoids the intra and inter-observer variations caused by manual and semi-automatic methods. As future work, the tool will be applied in clinical practice. Thus, it may be useful in the diagnosis and treatment determination of MS diseases. Providing volume values for MS could be helpful in evaluating the presence of any abnormality and could be used for treatment planning and evaluation of the outcome. The computed tomography (CT) has allowed a more exact assessment of this structure which enables a quantitative analysis. However, this is not always possible in the clinical routine, and if possible, it involves much effort and/or time. Therefore, it is necessary to have a convenient, robust and practical tool correlated with the MS volume, allowing clinical applicability. Nowadays, the available methods for MS segmentation are manual or semi-automatic. Additionally, manual methods present inter and intraindividual variability. Thus, the aim of this study was to develop an automatic tool to quantity the MS volume in CT scans of paranasal sinuses. This study was developed with ethical approval from the authors’ institutions and national review panels. The research involved 30 retrospective exams of University Hospital, Botucatu Medical School, São Paulo State University, Brazil. The tool for automatic MS quantification, developed in Matlab®, uses a hybrid method, combining different image processing techniques. For MS detection, the algorithm uses a Support Vector Machine (SVM), by features such as pixel value, spatial distribution, shape and others. The detected pixels are used as seed point for a region growing (RG) segmentation. Then, morphological operators are applied to reduce false-positive pixels, improving the segmentation accuracy. These steps are applied in all slices of CT exam, obtaining the MS volume. To evaluate the accuracy of the developed tool, the automatic method was compared with manual segmentation realized by an experienced radiologist. For comparison, we used Bland-Altman statistics, linear regression and Jaccard similarity coefficient. From the statistical analyses for the comparison between both methods, the linear regression showed a strong association and low dispersion between variables. The Bland–Altman analyses showed no significant differences between the analyzed methods. The Jaccard similarity coefficient was > 0.90 in all exams. In conclusion, the developed tool to automatically quantify MS volume proved to be robust, fast and efficient, when compared with manual segmentation. Furthermore, it avoids the intra and inter-observer variations caused by manual and semi-automatic methods. As future work, the tool will be applied in clinical practice. Thus, it may be useful in the diagnosis and treatment determination of MS diseases.

Keywords: maxillary sinus, support vector machine, region growing, volume quantification

Procedia PDF Downloads 504

Authors: Said Baadel, Fadi Thabtah, Joan Lu

Abstract:

Clustering involves the partitioning of n objects into k clusters. Many clustering algorithms use hard-partitioning techniques where each object is assigned to one cluster. In this paper, we propose an overlapping algorithm MCOKE which allows objects to belong to one or more clusters. The algorithm is different from fuzzy clustering techniques because objects that overlap are assigned a membership value of 1 (one) as opposed to a fuzzy membership degree. The algorithm is also different from other overlapping algorithms that require a similarity threshold to be defined as a priority which can be difficult to determine by novice users.

Keywords: data mining, k-means, MCOKE, overlapping

Procedia PDF Downloads 575

Authors: Deva Kanta Phukan

Abstract:

An investigation is made to carry out to study the thermal-diffusion and diffusion thermo-effects in hydro-magnetic unsteady flow by a mixed convection boundary layer past an impermeable vertical stretching sheet embedded in a conducting fluid-saturated porous medium in the presence of a chemical reaction effect. The velocity of stretching surface, the surface temperature and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed in to self similar unsteady equations using similarity transformations and solved numerically by the Runge kutta fourth order scheme in association with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, temperature, the concentration, the skin friction , and the Nusselt and Sherwood numbers are shown graphically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.

Keywords: heat and mass transfer, boundary layer flow, porous media, magnetic field, Soret number, Dufour’s number

Procedia PDF Downloads 445

Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

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The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: The Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.

Keywords: apportionment, bias, divisor, fair, measurement

Procedia PDF Downloads 366

Authors: Pisit Poolprasert, Auttpol Nakwa, Keerati Tanruean, Ezra Mongkolchaichana, Ezra Mongkolchaichana, Sinlapachai Senarat, Mark Tunmore

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This present preliminary study aimed to observe the butterfly species diversity in two selected subdistricts i.e., Mae Klong and Umphang of Umphang district, Tak province, northern Thailand, during May to September 2018. A survey method using sweep net was employed along line transects between 10.00-12.00 a.m. and 13.00-15.00 p.m. A total of 337 butterflies representing 37 species, 26 genera in five families were encountered. The family Nymphalidae held the highest species richness (15 species), followed by Papilionidae (9 species) and Pieridae (6 speices), respectively. Herein, four uncommon species, namely Junonia iphita iphita, Tanaecia julii odilina, Penthema darlisa melema, and Papilio alcmenor alcmenor, were discovered in this time. The Shannon diversity (H’) for all samples obtained from the pooled data set of this observation valued 2.563 with relatively high values of Evenness (J’= 0.710) and Simpson index and (D = 0.829). For similarity index (Ss), the assemblage recorded of butterfly species between Mae Klang-Umphang shared about 0.629, implying that the environmental conditions in both surveyed zones were alike. Additionally, the accumulation curve in both locations of the butterfly was still increasing gradually when the collection ended, indicating that the lepidopteran species would be raised if we continue to survey more in next month. Nevertheless, to gain more butterfly taxa, observing different plant communities covering every season and using several survey techniques should be considered for further investigation.

Keywords: butterfly, biodiversity, tak province, thailand

Procedia PDF Downloads 114

Authors: Mei-Jie Xu, Yang Zhong

Abstract:

Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

Procedia PDF Downloads 305

Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

Procedia PDF Downloads 205

Authors: Alexander Matrosov, Guriy Shirunov

Abstract:

A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.

Keywords: general solution, method of initial functions, superposition method, thick isotropic plates

Procedia PDF Downloads 597

Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

Procedia PDF Downloads 388

Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

Procedia PDF Downloads 265