Abstract: One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.
Abstract: Face recognition is the problem of identifying or recognizing individuals in an image. This paper investigates a possible method to bring a solution to this problem. The method proposes an amalgamation of Principal Component Analysis (PCA), K-Means clustering, and Convolutional Neural Network (CNN) for a face recognition system. It is trained and evaluated using the ORL dataset. This dataset consists of 400 different faces with 40 classes of 10 face images per class. Firstly, PCA enabled the usage of a smaller network. This reduces the training time of the CNN. Thus, we get rid of the redundancy and preserve the variance with a smaller number of coefficients. Secondly, the K-Means clustering model is trained using the compressed PCA obtained data which select the K-Means clustering centers with better characteristics. Lastly, the K-Means characteristics or features are an initial value of the CNN and act as input data. The accuracy and the performance of the proposed method were tested in comparison to other Face Recognition (FR) techniques namely PCA, Support Vector Machine (SVM), as well as K-Nearest Neighbour (kNN). During experimentation, the accuracy and the performance of our suggested method after 90 epochs achieved the highest performance: 99% accuracy F1-Score, 99% precision, and 99% recall in 463.934 seconds. It outperformed the PCA that obtained 97% and KNN with 84% during the conducted experiments. Therefore, this method proved to be efficient in identifying faces in the images.
Abstract: In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.
Abstract: Moringa oleifera is a plant containing many nutrients that are mostly concentrated within the leaves. Commonly, the separation process of these nutrients involves solid-liquid extraction followed by evaporation and drying to obtain a concentrated extract, which is rich in proteins, vitamins, carbohydrates, and other essential nutrients that can be used in the food industry. In this work, three drying methods were used, which involved very different temperature and pressure conditions, to evaluate the effect of each method on the vitamin C content and the antioxidant efficiency of the extracts. Solid-liquid extractions of Moringa leaf (LE) were carried out by employing an ethanol solution (35% v/v) at 50 °C for 2 hours. The resulting extracts were then dried i) in a convective oven (CO) at 100 °C and at an atmospheric pressure of 750 mbar for 8 hours, ii) in a vacuum evaporator (VE) at 50 °C and at 300 mbar for 2 hours, and iii) in a freeze-drier (FD) at -40 °C and at 0.050 mbar for 36 hours. The antioxidant capacity (EC50, mg solids/g DPPH) of the dry solids was calculated by the free radical inhibition method employing DPPH˙ at 517 nm, resulting in a value of 2902.5 ± 14.8 for LE, 3433.1 ± 85.2 for FD, 3980.1 ± 37.2 for VE, and 8123.5 ± 263.3 for CO. The calculated antioxidant efficiency (AE, g DPPH/(mg solids·min)) was 2.920 × 10-5 for LE, 2.884 × 10-5 for FD, 2.512 × 10-5 for VE, and 1.009 × 10-5 for CO. Further, the content of vitamin C (mg/L) determined by HPLC was 59.0 ± 0.3 for LE, 49.7 ± 0.6 for FD, 45.0 ± 0.4 for VE, and 23.6 ± 0.7 for CO. The results indicate that the convective drying preserves vitamin C and antioxidant efficiency to 40% and 34% of the initial value, respectively, while vacuum drying to 76% and 86%, and freeze-drying to 84% and 98%, respectively.
Abstract: It is known that the mean investment evolves from a very low initial value to some high level in the Continuous Prisoner's Dilemma. We examine how the cooperation level evolves from a low initial level to a high level in our Demographic Multi-level Donor-Recipient situation. In the Multi-level Donor-Recipient game, one player is selected as a Donor and the other as a Recipient randomly. The Donor has multiple cooperative moves and one defective move. A cooperative move means the Donor pays some cost for the Recipient to receive some benefit. The more cooperative move the Donor takes, the higher cost the Donor pays and the higher benefit the Recipient receives. The defective move has no effect on them. Two consecutive Multi-level Donor-Recipient games, one as a Donor and the other as a Recipient, can be viewed as a discrete version of the Continuous Prisoner's Dilemma. In the Demographic Multi-level Donor-Recipient game, players are initially distributed spatially. In each period, players play multiple Multi-level Donor-Recipient games against other players. He leaves offspring if possible and dies because of negative accumulated payoff of him or his lifespan. Cooperative moves are necessary for the survival of the whole population. There is only a low level of cooperative move besides the defective move initially available in strategies of players. A player may modify and expand his strategy by his recent experiences or practices. We distinguish several types of a player about modification and expansion. We show, by Agent-Based Simulation, that introducing only the modification increases the emergence rate of cooperation and introducing both the modification and the expansion further increases it and a high level of cooperation does emerge in our Demographic Multi-level Donor-Recipient Game.
Abstract: The aim of this work is the parallel implementation
of k-means in MATLAB, in order to reduce the execution time.
Specifically, a new function in MATLAB for serial k-means algorithm
is developed, which meets all the requirements for the conversion to a
function in MATLAB with parallel computations. Additionally, two
different variants for the definition of initial values are presented.
In the sequel, the parallel approach is presented. Finally, the
performance tests for the computation times respect to the numbers
of features and classes are illustrated.
Abstract: Soil contamination phenomena are a wide world issue that has received the important attention in the last decades. The main pollutants that have affected soils are especially those resulted from the oil extraction, transport and processing. This paper presents results obtained in the framework of a research project focused on the management of contaminated sites with petroleum products/ REMPET. One of the specific objectives of the REMPET project was to assess the electrochemical treatment (improved with polarity change respect to the typical approach) as a treatment option for the remediation of total petroleum hydrocarbons (TPHs) from contaminated soils. Petroleum hydrocarbon compounds attach to soil components and are difficult to remove and degrade. Electrochemical treatment is a physicochemical treatment that has gained acceptance as an alternative method, for the remediation of organic contaminated soils comparing with the traditional methods as bioremediation and chemical oxidation. This type of treatment need short time and have high removal efficiency, being usually applied in heterogeneous soils with low permeability. During the experimental tests, the following parameters were monitored: pH, redox potential, humidity, current intensity, energy consumption. The electrochemical method was applied in an experimental setup with the next dimensions: 450 mm x 150 mm x 150 mm (L x l x h). The setup length was devised in three electrochemical cells that were connected at two power supplies. The power supplies configuration was provided in such manner that each cell has a cathode and an anode without overlapping. The initial value of TPH concentration in soil was of 1420.28 mg/kgdw. The remediation method has been applied for only 21 days, when it was already noticed an average removal efficiency of 31 %, with better results in the anode area respect to the cathode one (33% respect to 27%). The energy consumption registered after the development of the experiment was 10.6 kWh for exterior power supply and 16.1 kWh for the interior one. Taking into account that at national level, the most used methods for soil remediation are bioremediation (which needs too much time to be implemented and depends on many factors) and thermal desorption (which involves high costs in order to be implemented), the study of electrochemical treatment will give an alternative to these two methods (and their limitations).
Abstract: A numerical technique in a boundary-fitted curvilinear grid model is developed to simulate the extent of inland inundation along the coastal belts of Peninsular Malaysia and Southern Thailand due to 2004 Indian ocean tsunami. Tsunami propagation and run-up are also studied in this paper. The vertically integrated shallow water equations are solved by using the method of lines (MOL). For this purpose the boundary-fitted grids are generated along the coastal and island boundaries and the other open boundaries of the model domain. A transformation is used to the governing equations so that the transformed physical domain is converted into a rectangular one. The MOL technique is applied to the transformed shallow water equations and the boundary conditions so that the equations are converted into ordinary differential equations initial value problem. Finally the 4th order Runge-Kutta method is used to solve these ordinary differential equations. The moving boundary technique is applied instead of fixed sea side wall or fixed coastal boundary to ensure the movement of the coastal boundary. The extent of intrusion of water and associated tsunami propagation are simulated for the 2004 Indian Ocean tsunami along the west coast of Peninsular Malaysia and southern Thailand. The simulated results are compared with the results obtained from a finite difference model and the data available in the USGS website. All simulations show better approximation than earlier research and also show excellent agreement with the observed data.
Abstract: Clustering is an intensive research for some years
because of its multifaceted applications, such as biology, information
retrieval, medicine, business and so on. The expectation maximization
(EM) is a kind of algorithm framework in clustering methods, one
of the ten algorithms of machine learning. Traditionally, optimization
of objective function has been the standard approach in EM. Hence,
research has investigated the utility of evolutionary computing and
related techniques in the regard. Chemical Reaction Optimization
(CRO) is a recently established method. So the property embedded
in CRO is used to solve optimization problems. This paper presents
an algorithm framework (EM-CRO) with modified CRO operators
based on EM cluster problems. The hybrid algorithm is mainly
to solve the problem of initial value sensitivity of the objective
function optimization clustering algorithm. Our experiments mainly
take the EM classic algorithm:k-means and fuzzy k-means as an
example, through the CRO algorithm to optimize its initial value, get
K-means-CRO and FKM-CRO algorithm. The experimental results
of them show that there is improved efficiency for solving objective
function optimization clustering problems.
Abstract: Laplace transformations have wide applications in
engineering and sciences. All previous studies of modified Laplace
transformations depend on differential equation with initial
conditions. The purpose of our paper is to solve the linear differential
equations (not initial value problem) and then find the general
solution (not particular) via the Laplace transformations without
needed any initial condition. The study involves both types of
differential equations, ordinary and partial.
Abstract: In this paper, we introduce a generalized Chebyshev
collocation method (GCCM) based on the generalized Chebyshev
polynomials for solving stiff systems. For employing a technique
of the embedded Runge-Kutta method used in explicit schemes, the
property of the generalized Chebyshev polynomials is used, in which
the nodes for the higher degree polynomial are overlapped with those
for the lower degree polynomial. The constructed algorithm controls
both the error and the time step size simultaneously and further
the errors at each integration step are embedded in the algorithm
itself, which provides the efficiency of the computational cost. For
the assessment of the effectiveness, numerical results obtained by the
proposed method and the Radau IIA are presented and compared.
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.
Abstract: 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.
Abstract: A novel method based on Genetic Algorithm to solve the boundary value problems (BVPs) of the Falkner–Skan equation over a semi-infinite interval has been presented. In our approach, we use the free boundary formulation to truncate the semi-infinite interval into a finite one. Then we use the shooting method based on Genetic Algorithm to transform the BVP into initial value problems (IVPs). Genetic Algorithm is used to calculate shooting angle. The initial value problems arisen during shooting are computed by Runge-Kutta Fehlberg method. The numerical solutions obtained by the present method are in agreement with those obtained by previous authors.
Abstract: This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.
Abstract: In this paper, by establishing a new comparison result, we investigate the existence of positive solutions for initial value problems of nonlinear systems of second order integro-differential equations in Banach space.We improve and generalize some results (see[5,6]), and the results is new even in finite dimensional spaces.
Abstract: In this paper, a stochastic predator-prey system with Holling II functional response is studied. First, we show that there is a unique positive solution to the system for any given positive initial value. Then, stochastically bounded of the positive solution to the stochastic system is derived. Moreover, sufficient conditions for global asymptotic stability are also established. In the end, some simulation figures are carried out to support the analytical findings.
Abstract: Vortices can develop in intakes of turbojet and turbo
fan aero engines during high power operation in the vicinity of solid
surfaces. These vortices can cause catastrophic damage to the engine.
The factors determining the formation of the vortex include both
geometric dimensions as well as flow parameters. It was shown that
the threshold at which the vortex forms or disappears is also
dependent on the initial flow condition (i.e. whether a vortex forms
after stabilised non vortex flow or vice-versa). A computational fluid
dynamics study was conducted to determine the difference in
thresholds between the two conditions. This is the first reported
numerical investigation of the “memory effect". The numerical
results reproduce the phenomenon reported in previous experimental
studies and additional factors, which had not been previously studied,
were investigated. They are the rate at which ambient velocity
changes and the initial value of ambient velocity. The former was
found to cause a shift in the threshold but not the later. It was also
found that the varying condition thresholds are not symmetrical about
the neutral threshold. The vortex to no vortex threshold lie slightly
further away from the neutral threshold compared to the no vortex to
vortex threshold. The results suggests that experimental investigation
of vortex formation threshold performed either in vortex to no vortex
conditions, or vice versa, solely may introduce mis-predictions
greater than 10%.
Abstract: A block backward differentiation formula of uniform
order eight is proposed for solving first order stiff initial value
problems (IVPs). The conventional 8-step Backward Differentiation
Formula (BDF) and additional methods are obtained from the same
continuous scheme and assembled into a block matrix equation which
is applied to provide the solutions of IVPs on non-overlapping
intervals. The stability analysis of the method indicates that the
method is L0-stable. Numerical results obtained using the proposed
new block form show that it is attractive for solutions of stiff problems
and compares favourably with existing ones.
Abstract: Iron in groundwater is one of the problems that render the water unsuitable for drinking. The concentration above 0.3 mg/L is common in groundwater. The conventional method of removal is by precipitation under oxic condition. In this study, iron removal under anaerobic conditions was examined by batch experiment as a main purpose. The process involved by purging of groundwater samples with H2S to form iron sulfide. Removal up to 83% for 1 mg/L iron solution was achieved. The removal efficiency dropped to 82% and 75% for the higher initial iron concentrations 3.55 and 5.01 mg/L, respectively. The average residual sulfide concentration in water after the process was 25*g/L. The Eh level during the process was -272 mV. The removal process was found to follow the first order reaction with average rate constant of 4.52 x 10-3. The half-life for the concentrations to reduce from initial values was 157 minutes.