Search results for: differential invariant signature curves

Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: Han Xue, Zhang Lanyue

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In order to seek more effective feature extraction technology, feature extraction method based on MFCC combined with vector hydrophone is exposed in the paper. The sound pressure signal and particle velocity signal of two kinds of ships are extracted by using MFCC and its evolution form, and the extracted features are fused by using fisher-ratio and correlated distance criterion. The features are then identified by BP neural network. The results showed that MFCC, First-Order Differential MFCC and Second-Order Differential MFCC features can be used as effective features for recognition of underwater targets, and the fusion feature can improve the recognition rate. Moreover, the results also showed that the recognition rate of the particle velocity signal is higher than that of the sound pressure signal, and it reflects the superiority of vector signal processing.

Keywords: vector information, MFCC, differential MFCC, fusion feature, BP neural network

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Authors: Johnson Oladele Fatokun, I. P. Akpan

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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator

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

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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: Alaa Sheta

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Economic Load Dispatch (ELD) is one of the vital optimization problems in power system planning. Solving the ELD problems mean finding the best mixture of power unit outputs of all members of the power system network such that the total fuel cost is minimized while sustaining operation requirements limits satisfied across the entire dispatch phases. Many optimization techniques were proposed to solve this problem. A famous one is the Quadratic Programming (QP). QP is a very simple and fast method but it still suffer many problem as gradient methods that might trapped at local minimum solutions and cannot handle complex nonlinear functions. Numbers of metaheuristic algorithms were used to solve this problem such as Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO). In this paper, another meta-heuristic search algorithm named Differential Evolution (DE) is used to solve the ELD problem in power systems planning. The practicality of the proposed DE based algorithm is verified for three and six power generator system test cases. The gained results are compared to existing results based on QP, GAs and PSO. The developed results show that differential evolution is superior in obtaining a combination of power loads that fulfill the problem constraints and minimize the total fuel cost. DE found to be fast in converging to the optimal power generation loads and capable of handling the non-linearity of ELD problem. The proposed DE solution is able to minimize the cost of generated power, minimize the total power loss in the transmission and maximize the reliability of the power provided to the customers.

Keywords: economic load dispatch, power systems, optimization, differential evolution

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Authors: Romaric Desbrousses, Lan Lin

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The objective of this study is to determine how Canadian seismic design provisions affect the column axial load resistance of moment-resisting frame reinforced concrete buildings subjected to the differential settlement of their foundation. To do so, two four-storey buildings are designed in accordance with the seismic design provisions of the Canadian Concrete Design Standards. One building is located in Toronto, which is situated in a moderate seismic hazard zone in Canada, and the other in Vancouver, which is in Canada’s highest seismic hazard zone. A finite element model of each building is developed using SAP 2000. A 100 mm settlement is assigned to the base of the building’s center column. The axial load resistance of the column is represented by the demand capacity ratio. The analysis results show that settlement-induced tensile axial forces have a particularly detrimental effect on the conventional settling columns of the Toronto buildings which fail at a much smaller settlement that those in the Vancouver buildings. The results also demonstrate that particular care should be taken in the design of columns in short-span buildings.

Keywords: Columns, Demand, Foundation differential settlement, Seismic design, Non-linear analysis

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In this study, a vibrational differential equation governing on swinging single-degree-of-freedom pendulum in a viscous fluid has been investigated. The damping process is characterized according to two different regimes: at first, damping in stationary viscous fluid, in the second, damping in flowing viscous fluid with constant velocity. Our purpose is to enhance the ability of solving the mentioned nonlinear differential equation with a simple and innovative approach. Comparisons are made between new method and Numerical Method (rkf45). The results show that this method is very effective and simple and can be applied for other nonlinear problems.

Keywords: oscillating systems, angular frequency and damping ratio, pendulum at fluid, locus of maximum

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Authors: Emanuel Guariglia

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In this paper we deal with Chebyshev wavelets. We analyze their properties computing their Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets due the connection coefficients. The differential properties of Chebyshev wavelets, expressed by the connection coefficients (also called refinable integrals), are given by finite series in terms of the Kronecker delta. Moreover, we treat the p-order derivative of Chebyshev wavelets and compute its Fourier transform. Finally, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry.

Keywords: Chebyshev wavelets, Fourier transform, connection coefficients, Taylor series, local fractional derivative, Cantor set

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Authors: Hassan Manouzi

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We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: least squares, wick product, SPDEs, finite element, wiener chaos expansion, gradient method

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Authors: Merve Sagiroglu

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The earthquake-resistant steel structure design is required taking into account the behavior of beam-column connections besides the basic properties of the structure such as material and geometry. Beam-column connections play an important role in the behavior of frame systems. Taking into account the behaviour of connection in analysis and design of steel frames is important due to presenting the actual behavior of frames. So, the behavior of the connections should be well known. The most important force which transmitted by connections in the structural system is the moment. The rotational deformation is customarily expressed as a function of the moment in the connection. So, the moment-rotation curves are the best expression of behaviour of the beam-to-column connections. The designed connections form various moment-rotation curves according to the elements of connection and the shape of placement. The only way to achieve this curve is with real-scale experiments. The experiments of some connections have been carried out partially and are formed in the databank. It has been formed the models using this databank to express the behavior of connection. In this study, theoretical studies have been carried out to model a real behavior of the top and seat angles connections with angles. Two stiffeners in the top and seat angle to increase the stiffness of the connection, and two stiffeners in the beam web to prevent local buckling are used in this beam-to-column connection. Mathematical models have been performed using the database of the beam-to-column connection experiments previously by authors. Using the data of the tests, it has been aimed that analytical expressions have been developed to obtain the moment-rotation curve for the connection details whose test data are not available. The connection has been dimensioned in various shapes and the effect of the dimensions of the connection elements on the behavior has been examined.

Keywords: top and seat angle connection, stiffener, moment-rotation curves, analytical study

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Authors: Xuezhang Hou

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In the present paper, a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions is considered. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a sliding model control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by an ideal sliding mode under control in any accuracy is derived and examined.

Keywords: hyperbolic dynamic system, sliding model control, semigroup of linear operators, partial differential equations

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Authors: Tudor Barbu

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We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: anisotropic diffusion, finite differences, image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation schemes

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Authors: Abdel-Maksoud Abdel-Kader Soliman

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The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

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Authors: S. Njoumi, L. Ben Haj Said, M. J. Amiot, S. Bellagha

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The main objective of this research was to establish the kinetics of variation of total polyphenol content (TPC) and total flavonoid content (TFC) in Tunisian Corchorus olitorius powder and in a traditional home cooked-meal (Molokheiya) when using stewing and stir-frying as cooking methods, but also to compare the effect of these two common cooking practices on water content, TPC, TFC and color. The L*, a* and b* coordinates values of the Molokheiya varied from 24.955±0.039 to 21.301±0.036, from -1.556±0.048 to 0.23±0.026 and from 5.675±0.052 to 6.313±0.103 when using stewing and from 21.328±0.025 to 20.56±0.021, from -1.093± 0.011to 0.121±0.007 and from 5.708±0.020 to 6.263±0.007 when using stir-frying, respectively. TPC and TFC increased during cooking. TPC of Molokheiya varied from 29.852±0.866 mg GAE/100 g to 220.416±0.519 mg GAE/100 g after 150 min of stewing and from 25.257±0.259 mg GAE/100 g to 208.897 ±0.173 mg GAE/100 g using stir-frying method during 150 min. TFC of Molokheiya varied from 48.229±1.47 mg QE/100 g to 843.802±1.841 mg QE/100 g when using stewing and from 37.031± 0.368 mg QE/100 g to 775.312±0.736 mg QE/100 g when using stir-frying. Kinetics followed similar curves in all cases but resulted in different final TPC and TFC. The shape of the kinetics curves suggests zero-order kinetics. The mathematical relations and the numerical approach used to model the kinetics of polyphenol and flavonoid contents in Molokheiya are described.

Keywords: Corchorus olitorius, Molokheiya, phenolic compounds, kinetic

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Authors: H. Ozbasaran

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IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: cantilever, IPN, IPE, lateral torsional buckling

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Authors: Ana Clara Santos, Maria Manuela Portela, Bettina Schaefli

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This work assesses the performance of an analytical model framework to generate daily flow duration curves, FDCs, based on climatic characteristics of the catchments and on their streamflow recession coefficients. According to the analytical model framework, precipitation is considered to be a stochastic process, modeled as a marked Poisson process, and recession is considered to be deterministic, with parameters that can be computed based on different models. The analytical model framework was tested for three case studies with different hydrological regimes located in Switzerland: pluvial, snow-dominated and glacier. For that purpose, five time intervals were analyzed (the four meteorological seasons and the civil year) and two developments of the model were tested: one considering a linear recession model and the other adopting a nonlinear recession model. Those developments were combined with recession coefficients obtained from two different approaches: forward and inverse estimation. The performance of the analytical framework when considering forward parameter estimation is poor in comparison with the inverse estimation for both, linear and nonlinear models. For the pluvial catchment, the inverse estimation shows exceptional good results, especially for the nonlinear model, clearing suggesting that the model has the ability to describe FDCs. For the snow-dominated and glacier catchments the seasonal results are better than the annual ones suggesting that the model can describe streamflows in those conditions and that future efforts should focus on improving and combining seasonal curves instead of considering single annual ones.

Keywords: analytical streamflow distribution, stochastic process, linear and non-linear recession, hydrological modelling, daily discharges

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Authors: Olawale Babatunde Olatinsu, Deborah Oluwaseun Olorode

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Industrial rocks were collected from a quarry site at Ewekoro in south-western Nigeria and analysed using Nuclear Magnetic Resonance (NMR) technique. NMR measurement was conducted on the samples in partial water-saturated and full brine-saturated conditions. Raw NMR data were analysed with the aid of T2 curves and T2 spectra generated by inversion of raw NMR data using conventional regularized least-squares inversion routine. Results show that NMR transverse relaxation (T2) signatures fairly adequately distinguish between the rock types. Similar T2 curve trend and rates at partial saturation suggests that the relaxation is mainly due to adsorption of water on micropores of similar sizes while T2 curves at full saturation depict relaxation decay rate as: 1/T2(shale)>1/ T2(glauconite)>1/ T2(limestone) and 1/T2(sandstone). NMR T2 distributions at full brine-saturation show: unimodal distribution in shale; bimodal distribution in sandstone and glauconite; and trimodal distribution in limestone. Full saturation T2 distributions revealed the presence of well-developed and more abundant micropores in all the samples with T2 in the range, 402-504 μs. Mesopores with amplitudes much lower than those of micropores are present in limestone, sandstone and glauconite with T2 range: 8.45-26.10 ms, 6.02-10.55 ms, and 9.45-13.26 ms respectively. Very low amplitude macropores of T2 values, 90.26-312.16 ms, are only recognizable in limestone samples. Samples with multiple peaks showed well-connected pore systems with sandstone having the highest degree of connectivity. The difference in T2 curves and distributions for the rocks at full saturation can be utilised as a potent diagnostic tool for discrimination of these rock types found at Ewekoro.

Keywords: Ewekoro, NMR techniques, industrial rocks, characterization, relaxation

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Authors: Daniel Llanes, Alfredo Reyes, Sonia E. Ruiz, Federico Valenzuela Beltran

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Steel frames have been used in building construction for more than one hundred years. Beam-column may be connected to columns using either stiffened or unstiffened angles at the top and bottom beam flanges. Designers often assume that these assemblies acted as “pinned” connections for gravity loads and that the stiffened connections would act as “fixed” connections for lateral loads. Observation of damages sustained by buildings during the 1994 Northridge earthquake indicated that, contrary to the intended behavior, in many cases, brittle fractures initiated within the connections at very low levels of plastic demand, and in some cases, while the structures remained essentially elastic. Due to the damage presented in these buildings other type of alternative connections have been proposed. According to a research funded by the Federal Emergency Management Agency (FEMA), the screwed connections have better performance when they are subjected to cyclic loads, but at the same time, these connections have some degree of flexibility. Due to this situation, some researchers ventured into the study of semi-rigid connections. In the present study three steel buildings, constituted by regular frames are analyzed. Two types of connections are considered: pinned and semi-rigid connections. With the aim to estimate their structural capacity, a number of incremental dynamic analyzes are performed. 3D structural models are used for the analyses. The seismic ground motions were recorded on sites near Los Angeles, California, where the structures are supposed to be located. The vulnerability curves of the building are obtained in terms of maximum inter-story drifts. The vulnerability curves (which correspond to the models with two different types of connections) are compared, and its implications on its structural design and performance is discussed.

Keywords: steel frame Buildings, vulnerability curves, semi-rigid connections, pinned connections

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Authors: J. J. Cetina-Denis, R. M. López-Gutiérrez, R. Ramírez-Ramírez, C. Cruz-Hernández

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This work addresses the problem of designing an algorithm capable of generating chaotic trajectories for mobile robots. Particularly, the chaotic behavior is induced in the linear and angular velocities of a Khepera III differential mobile robot by infusing them with the states of the H´enon chaotic map. A possible application, using the properties of chaotic systems, is patrolling a work area. In this work, numerical and experimental results are reported and analyzed. In addition, two quantitative numerical tests are applied in order to measure how chaotic the generated trajectories really are.

Keywords: chaos, chaotic trajectories, differential mobile robot, Henon map, Khepera III robot, patrolling applications

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Authors: Deva Kanta Phukan

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An attempt is made where an electrically conducting fluid is injected from a fixed outer cylindrical casing onto an inner moving cylindrical rod. A magnetic field is applied parallel to the axis of the cylindrical rod. The basic governing set of partial differential equations for conservation of mass and momentum are reduced to a set of non-linear ordinary differential equation by introducing similarity transformation, which are integrated numerically. A perturbation solution for the case of large magnetic parameter is derived for constant Reynolds number.

Keywords: annular axi-symmetric stagnation flow, conducting fluid, magnetic field, moving cylinder

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Authors: Andrea J. Alarcón, Maxime Daulat, Raydel Lorenzo, Renato P. Da Cunha, Pierre Breul

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Brazil has increased the use of renewable energy during the last years. Due to its sunshine and large surface area, photovoltaic panels founded in helical piles have been used to produce solar energy. Since Brazilian territory is mainly cover by highly porous structured tropical soils, when the helical piles are installed this structure is broken and its soil properties are modified. Considering the special characteristics of these soils, helical foundations behavior must be extensively studied. The first objective of this work is to determine the most suitable method to estimate the tensile capacity of helical piles in tropical soils. The second objective is to simulate the behavior of these piles in tropical soil. To obtain the rupture to assess load-displacement curves and the ultimate load, also a numerical modelling using Plaxis software was conducted. Lastly, the ultimate load and the load-displacements curves are compared with experimental values to validate the implemented model.

Keywords: finite element, helical piles, modelling, tropical soil, uplift capacity

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Authors: Yao Jiajia, Wu Guanlin, LIU Fang, Xue Junshuai, Zhang Jincheng, Hao Yue

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Resonant tunneling diodes (RTDs) based on GaN have been extensively studied. However, no results of multiple logic states achieved by RTDs were reported by the methods of epitaxy in the GaN materials. In this paper, the multiple negative-differential resistance regions by combining two discrete double-barrier RTDs in series have been first demonstrated. Plasma-assisted molecular beam epitaxy (PA-MBE) was used to grow structures consisting of two vertical RTDs. The substrate was a GaN-on-sapphire template. Each resonant tunneling structure was composed of a double barrier of AlN and a single well of GaN with undoped 4-nm space layers of GaN on each side. The AlN barriers were 1.5 nm thick, and the GaN well was 2 nm thick. The resonant tunneling structures were separated from each other by 30-nm thick n+ GaN layers. The bottom and top layers of the structures, grown neighboring to the spacer layers that consist of 200-nm-thick n+ GaN. These devices with two tunneling structures exhibited uniform peaks and valleys current and also had two negative differential resistance NDR regions equally spaced in bias voltage. The current-voltage (I-V) characteristics of resonant tunneling structures with diameters of 1 and 2 μm were analyzed in this study. These structures exhibit three stable operating points, which are investigated in detail. This research demonstrates that using molecular beam epitaxy MBE to vertically grow multiple resonant tunneling structures is a promising method for achieving multiple negative differential resistance regions and stable logic states. These findings have significant implications for the development of digital circuits capable of multi-value logic, which can be achieved with a small number of devices.

Keywords: GaN, AlN, RTDs, MBE, logic state

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Authors: Razi Khalafi

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Brain is the information processing center of the human body. Stimuli in form of information are transferred to the brain and then brain makes the decision on how to respond to them. In this research we propose a new partial differential equation which analyses the EEG signals and make a relationship between the incoming stimuli and the brain response to them. In order to test the proposed model, a set of external stimuli applied to the model and the model’s outputs were checked versus the real EEG data. The results show that this model can model the EEG signal well. The proposed model is useful not only for modeling of the EEG signal in case external stimuli but it can be used for the modeling of brain response in case of internal stimuli.

Keywords: Brain, stimuli, partial differential equation, response, eeg signal

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Authors: Y. M. Aiyesimi, S. O. Abah, G. T. Okedayo

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A general analysis has been developed to study the chemical reaction effects on unsteady MHD double-diffusive free convective flow over a vertical stretching plate. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are solved numerically by using Runge-Kutta shooting technique. The effects of the chemical parameters are examined on the velocity, temperature and concentration profiles.

Keywords: chemical reaction, MHD, double-diffusive, stretching plate

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Authors: Shima Soltanzadeh, Mohammad Hosain Fazel Zarandi, Mojtaba Barzegar Astanjin

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Diagnosis of male infertility by the laboratory tests is expensive and, sometimes it is intolerable for patients. Filling out the questionnaire and then using classification method can be the first step in decision-making process, so only in the cases with a high probability of infertility we can use the laboratory tests. In this paper, we evaluated the performance of four classification methods including naive Bayesian, neural network, logistic regression and fuzzy c-means clustering as a classification, in the diagnosis of male infertility due to environmental factors. Since the data are unbalanced, the ROC curves are most suitable method for the comparison. In this paper, we also have selected the more important features using a filtering method and examined the impact of this feature reduction on the performance of each methods; generally, most of the methods had better performance after applying the filter. We have showed that using fuzzy c-means clustering as a classification has a good performance according to the ROC curves and its performance is comparable to other classification methods like logistic regression.

Keywords: classification, fuzzy c-means, logistic regression, Naive Bayesian, neural network, ROC curve

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Authors: Woo-seok Choi, Eun-sup Kim, Nam-Seo Park

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The demand for new technique in soft ground improvement continuously increases as general soft ground methods like PBD and DCM have a application problem in soft grounds with deep depth and wide distribution in Southern coast of Korea and Southeast. In this study, partial cement mixing method utilizing geogrid and fixing unit(CMG) is suggested and Finite element analysis is performed for analyzing the depth of surface soil and deep soil stabilization and comparing with DCM method. In the result of the experiment, the displacement in DCM method were lower than the displacement in CMG, it's because the upper load is transferred to deep part soil not treated by cement in CMG method case. The differential settlement in DCM method was higher than the differential settlement in CMG, because of the effect load transfer effect by surface part soil treated by cement and geogrid. In conclusion, CMG method has the advantage of economics and constructability in embankment road, railway, etc in which differential settlement is the important consideration.

Keywords: soft ground, geogrid, fixing unit, partial cement mixing, finite element analysis

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Authors: Gilbert Makanda, Roelf Sypkens

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A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: differential equations, knowledge acquisition, least squares nonlinear, dynamical systems

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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

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Authors: Kamal, J. P. Narayan

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In the present wok the effects of basin-shape-ratio on the frequency content and spectral amplitudes of the basin-generated surface waves and the associated spatial variation of ground motion amplification and differential ground motion in a 3D semi-spherical basin has been studied. A recently developed 3D fourth-order spatial accurate time-domain finite-difference (FD) algorithm based on the parsimonious staggered-grid approximation of the 3D viscoelastic wave equations was used to estimate seismic responses. The simulated results demonstrated the increase of both the frequency content and the spectral amplitudes of the basin-generated surface waves and the duration of ground motion in the basin with the increase of shape-ratio of semi-spherical basin. An increase of the average spectral amplification (ASA), differential ground motion (DGM) and the average aggravation factor (AAF) towards the centre of the semi-spherical basin was obtained.

Keywords: 3D viscoelastic simulation, basin-generated surface waves, basin-shape-ratio effects, average spectral amplification, aggravation factors and differential ground motion

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Authors: Michael Fundator

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Groundbreaking application of biomathematical and biochemical research in neural networks processes to formation of non-canonical bases, islands, and analog bases in DNA and mRNA at or near the transcription that contradicts the long anticipated statistical assumptions for the distribution of bases and analog bases compounds is implemented through statistical and stochastic methods apparatus with addition of quantum principles, where the usual transience of Poisson spike train becomes very instrumental tool for finding even almost periodical type of solutions to Fokker-Plank stochastic differential equation. Present article develops new multidimensional methods of finding solutions to stochastic differential equations based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem that allows the stochastic processes with jumps under certain conditions to have γ-Holder continuous modification that is used as basis for finding analogous parallels in dynamics of neutral networks and formation of analog bases and transcription in DNA.

Keywords: Fokker-Plank stochastic differential equation, Kolmogorov-Chentsov continuity theorem, neural networks, translation and transcription

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