In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.
{"title":"An Analytical Method for Solving General Riccati Equation","authors":"Y. Pala, Mutlu Ozgur Ertas","doi":"10.5281/ZENODO.1129613","DOIUrl":"https://doi.org/10.5281/ZENODO.1129613","url":null,"abstract":"In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.","PeriodicalId":225385,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical and Computational Sciences","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117238439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we have analyzed the transport of analytes under a two dimensional steady incompressible flow of power-law fluids through rectangular nanochannel. A mathematical model based on the Cauchy momentum-Nernst-Planck-Poisson equations is considered to study the combined effect of mixed electroosmotic (EO) and pressure driven (PD) flow. The coupled governing equations are solved numerically by finite volume method. We have studied extensively the effect of key parameters, e.g., flow behavior index, concentration of the electrolyte, surface potential, imposed pressure gradient and imposed electric field strength on the net average flow across the channel. In addition to study the effect of mixed EOF and PD on the analyte distribution across the channel, we consider a nonlinear model based on general convective-diffusion-electromigration equation. We have also presented the retention factor for various values of electrolyte concentration and flow behavior index.
{"title":"Transport of Analytes under Mixed Electroosmotic and Pressure Driven Flow of Power Law Fluid","authors":"Naren Bag, S. Bhattacharyya, Partha P. Gopmandal","doi":"10.5281/ZENODO.1129122","DOIUrl":"https://doi.org/10.5281/ZENODO.1129122","url":null,"abstract":"In this study, we have analyzed the transport of analytes \u0000under a two dimensional steady incompressible flow of power-law \u0000fluids through rectangular nanochannel. A mathematical model \u0000based on the Cauchy momentum-Nernst-Planck-Poisson equations is \u0000considered to study the combined effect of mixed electroosmotic \u0000(EO) and pressure driven (PD) flow. The coupled governing \u0000equations are solved numerically by finite volume method. We \u0000have studied extensively the effect of key parameters, e.g., flow \u0000behavior index, concentration of the electrolyte, surface potential, \u0000imposed pressure gradient and imposed electric field strength on \u0000the net average flow across the channel. In addition to study \u0000the effect of mixed EOF and PD on the analyte distribution \u0000across the channel, we consider a nonlinear model based on \u0000general convective-diffusion-electromigration equation. We have also \u0000presented the retention factor for various values of electrolyte \u0000concentration and flow behavior index.","PeriodicalId":225385,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical and Computational Sciences","volume":"14 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120924392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Migration of a core-shell soft particle under the influence of an external electric field in an electrolyte solution is studied numerically. The soft particle is coated with a positively charged polyelectrolyte layer (PEL) and the rigid core is having a uniform surface charge density. The Darcy-Brinkman extended Navier-Stokes equations are solved for the motion of the ionized fluid, the non-linear Nernst-Planck equations for the ion transport and the Poisson equation for the electric potential. A pressure correction based iterative algorithm is adopted for numerical computations. The effects of convection on double layer polarization (DLP) and diffusion dominated counter ions penetration are investigated for a wide range of Debye layer thickness, PEL fixed surface charge density, and permeability of the PEL. Our results show that when the Debye layer is in order of the particle size, the DLP effect is significant and produces a reduction in electrophoretic mobility. However, the double layer polarization effect is negligible for a thin Debye layer or low permeable cases. The point of zero mobility and the existence of mobility reversal depending on the electrolyte concentration are also presented.
{"title":"A Numerical Study on Electrophoresis of a Soft Particle with Charged Core Coated with Polyelectrolyte Layer","authors":"Partha Sarathi Majee, S. Bhattacharyya","doi":"10.5281/zenodo.1129101","DOIUrl":"https://doi.org/10.5281/zenodo.1129101","url":null,"abstract":"Migration of a core-shell soft particle under the \u0000influence of an external electric field in an electrolyte solution is \u0000studied numerically. The soft particle is coated with a positively \u0000charged polyelectrolyte layer (PEL) and the rigid core is having \u0000a uniform surface charge density. The Darcy-Brinkman extended \u0000Navier-Stokes equations are solved for the motion of the ionized \u0000fluid, the non-linear Nernst-Planck equations for the ion transport and \u0000the Poisson equation for the electric potential. A pressure correction \u0000based iterative algorithm is adopted for numerical computations. The \u0000effects of convection on double layer polarization (DLP) and diffusion \u0000dominated counter ions penetration are investigated for a wide range \u0000of Debye layer thickness, PEL fixed surface charge density, and \u0000permeability of the PEL. Our results show that when the Debye \u0000layer is in order of the particle size, the DLP effect is significant \u0000and produces a reduction in electrophoretic mobility. However, the \u0000double layer polarization effect is negligible for a thin Debye layer \u0000or low permeable cases. The point of zero mobility and the existence \u0000of mobility reversal depending on the electrolyte concentration are \u0000also presented.","PeriodicalId":225385,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical and Computational Sciences","volume":"18 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121642262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Storm Event Analysis (SEA) provides a method to define rainfalls events as storms where each storm has its own amount and duration. By modelling daily probability of different types of storms, the onset, offset and cycle of rainfall seasons can be determined and investigated. Furthermore, researchers from the field of meteorology will be able to study the dynamical characteristics of rainfalls and make predictions for future reference. In this study, four categories of storms; short, intermediate, long and very long storms; are introduced based on the length of storm duration. Daily probability models of storms are built for these four categories of storms in Peninsular Malaysia. The models are constructed by using Bernoulli distribution and by applying linear regression on the first Fourier harmonic equation. From the models obtained, it is found that daily probability of storms at the Eastern part of Peninsular Malaysia shows a unimodal pattern with high probability of rain beginning at the end of the year and lasting until early the next year. This is very likely due to the Northeast monsoon season which occurs from November to March every year. Meanwhile, short and intermediate storms at other regions of Peninsular Malaysia experience a bimodal cycle due to the two inter-monsoon seasons. Overall, these models indicate that Peninsular Malaysia can be divided into four distinct regions based on the daily pattern for the probability of various storm events.
{"title":"Daily Probability Model of Storm Events in Peninsular Malaysia","authors":"M. Bakar, N. M. Ariff, A. Jemain","doi":"10.5281/ZENODO.1123892","DOIUrl":"https://doi.org/10.5281/ZENODO.1123892","url":null,"abstract":"Storm Event Analysis (SEA) provides a method to define rainfalls events as storms where each storm has its own amount and duration. By modelling daily probability of different types of storms, the onset, offset and cycle of rainfall seasons can be determined and investigated. Furthermore, researchers from the field of meteorology will be able to study the dynamical characteristics of rainfalls and make predictions for future reference. In this study, four categories of storms; short, intermediate, long and very long storms; are introduced based on the length of storm duration. Daily probability models of storms are built for these four categories of storms in Peninsular Malaysia. The models are constructed by using Bernoulli distribution and by applying linear regression on the first Fourier harmonic equation. From the models obtained, it is found that daily probability of storms at the Eastern part of Peninsular Malaysia shows a unimodal pattern with high probability of rain beginning at the end of the year and lasting until early the next year. This is very likely due to the Northeast monsoon season which occurs from November to March every year. Meanwhile, short and intermediate storms at other regions of Peninsular Malaysia experience a bimodal cycle due to the two inter-monsoon seasons. Overall, these models indicate that Peninsular Malaysia can be divided into four distinct regions based on the daily pattern for the probability of various storm events.","PeriodicalId":225385,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical and Computational Sciences","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128852864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-17DOI: 10.24200/SQUJS.VOL20ISS2PP19-30
Kamel Al-khaled
In this paper, numerical solutions for nonlinear coupled Korteweg-de Vries(abbreviated as KdV) equations are calculated by the Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. The first step is to discretize time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.
{"title":"Numerical Wave Solutions for Nonlinear Coupled Equations Using Sinc-Collocation Method","authors":"Kamel Al-khaled","doi":"10.24200/SQUJS.VOL20ISS2PP19-30","DOIUrl":"https://doi.org/10.24200/SQUJS.VOL20ISS2PP19-30","url":null,"abstract":"In this paper, numerical solutions for nonlinear coupled Korteweg-de Vries(abbreviated as KdV) equations are calculated by the Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. The first step is to discretize time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.","PeriodicalId":225385,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical and Computational Sciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131586893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-28DOI: 10.22237/JMASM/1478003040
C. Udomboso, A. Chukwu, I. Dontwi
In this paper, we derived and investigated the Adjusted Network Information Criterion (ANIC) criterion, based on Kullback's symmetric divergence, which has been designed to be an asymptotically unbiased estimator of the expected Kullback-Leibler information of a fitted model. The ANIC improves model selection in more sample sizes than does the NIC.
本文推导并研究了基于Kullback对称散度的调整网络信息准则(Adjusted Network Information Criterion, ANIC)准则，该准则被设计为拟合模型的期望Kullback- leibler信息的渐近无偏估计。与NIC相比，ANIC在更多的样本量上改进了模型选择。
{"title":"An Adjusted Network Information Criterion for Model Selection in Statistical Neural Network Models","authors":"C. Udomboso, A. Chukwu, I. Dontwi","doi":"10.22237/JMASM/1478003040","DOIUrl":"https://doi.org/10.22237/JMASM/1478003040","url":null,"abstract":"In this paper, we derived and investigated the Adjusted Network Information Criterion (ANIC) criterion, based on Kullback's symmetric divergence, which has been designed to be an asymptotically unbiased estimator of the expected Kullback-Leibler information of a fitted model. The ANIC improves model selection in more sample sizes than does the NIC.","PeriodicalId":225385,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical and Computational Sciences","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127698068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-04-02DOI: 10.1007/978-3-319-46310-0_13
Linda Smail, Zineb Azouz
{"title":"Factorization of Computations in Bayesian Networks: Interpretation of Factors","authors":"Linda Smail, Zineb Azouz","doi":"10.1007/978-3-319-46310-0_13","DOIUrl":"https://doi.org/10.1007/978-3-319-46310-0_13","url":null,"abstract":"","PeriodicalId":225385,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical and Computational Sciences","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130586979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. D. Wiraningsih, F. Agusto, L. Aryati, S. Toaha, S. Lenhart, Widodo, W. Govaerts
This paper considers a deterministic model for the transmission dynamics of rabies virus in the wild dogs - domestic dogs - human zoonotic cycle. The effect of vaccination and culling in dogs is considered on the model, then the stability was analysed to get basic reproduction number. We use the next generation matrix method and Routh Hurwitz test to analyze the stability of the Disease Free Equilibrium and Endemic Equilibrium of this model.
{"title":"Stability Analysis of Rabies Model with Vaccination Effect and Culling in Dogs","authors":"E. D. Wiraningsih, F. Agusto, L. Aryati, S. Toaha, S. Lenhart, Widodo, W. Govaerts","doi":"10.12988/AMS.2015.53197","DOIUrl":"https://doi.org/10.12988/AMS.2015.53197","url":null,"abstract":"This paper considers a deterministic model for the transmission dynamics of rabies virus in the wild dogs - domestic dogs - human zoonotic cycle. The effect of vaccination and culling in dogs is considered on the model, then the stability was analysed to get basic reproduction number. We use the next generation matrix method and Routh Hurwitz test to analyze the stability of the Disease Free Equilibrium and Endemic Equilibrium of this model.","PeriodicalId":225385,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical and Computational Sciences","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130515088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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