Pub Date : 2021-06-30DOI: 10.37622/adsa/16.1.2021.5-15
K. Khan
In this paper, we find survival rate estimates, parameter estimates, variance covariance for some probability distribution models like, Exponential, Inverse Gaussian, Gompertz, Gumbels and Weibull distributions using least-squares estimation method. We found these estimates for the case when partial derivatives were not available and for the case when partial derivatives were available. The first case when partial derivatives were not available, we used the simplex optimization (Nelder and Meads ([6],[7]) and Hooke and Jeeves ([4],[5])) methods and the case when first partial derivatives were available we applied the Quasi – Newton optimization (Davidon-Fletcher-Powel (DFP) and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) methods. The medical data sets of 21 Leukemia cancer patients with time span of 35 weeks ([3]) were used.
本文用最小二乘估计方法对指数分布、逆高斯分布、Gompertz分布、gumbel分布和Weibull分布等概率分布模型进行了存活率估计、参数估计和方差协方差估计。我们发现这些估计值适用于不存在偏导数的情况以及存在偏导数的情况。在第一种情况下，当偏导数不可用时，我们使用单纯形优化(Nelder and Meads([6]，[7])和Hooke and Jeeves([4]，[5]))方法;在第一种情况下，当偏导数可用时，我们应用拟牛顿优化(davidon - fletcher - powell (DFP)和Broyden-Fletcher-Goldfarb-Shanno (BFGS)方法。采用时间跨度为35周的21例白血病患者的医疗数据集[3]。
{"title":"A Comparison of Survivor Rate Estimates for Some Probability Distribution Models Using Least-Squares Method in Conjunction with Simplex and Quasi-Newton Optimization Methods","authors":"K. Khan","doi":"10.37622/adsa/16.1.2021.5-15","DOIUrl":"https://doi.org/10.37622/adsa/16.1.2021.5-15","url":null,"abstract":"In this paper, we find survival rate estimates, parameter estimates, variance covariance for some probability distribution models like, Exponential, Inverse Gaussian, Gompertz, Gumbels and Weibull distributions using least-squares estimation method. We found these estimates for the case when partial derivatives were not available and for the case when partial derivatives were available. The first case when partial derivatives were not available, we used the simplex optimization (Nelder and Meads ([6],[7]) and Hooke and Jeeves ([4],[5])) methods and the case when first partial derivatives were available we applied the Quasi – Newton optimization (Davidon-Fletcher-Powel (DFP) and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) methods. The medical data sets of 21 Leukemia cancer patients with time span of 35 weeks ([3]) were used.","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"130 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87674762","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 : 2021-06-30DOI: 10.37622/adsa/16.1.2021.75-89
A. El-Sayed, Sahar Y. Issa, M. Elmiari
{"title":"Ulam-type Stability for a Boundary Value Problem of Implicit Fractional-orders Differential Equation","authors":"A. El-Sayed, Sahar Y. Issa, M. Elmiari","doi":"10.37622/adsa/16.1.2021.75-89","DOIUrl":"https://doi.org/10.37622/adsa/16.1.2021.75-89","url":null,"abstract":"","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86624360","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 : 2021-06-30DOI: 10.37622/adsa/16.1.2021.201-215
Polshchykov K. A., Lazarev S. A., K. O. R., V. G. S.
{"title":"An algorithm determining the optimal length of the queue of requests for data transmission over the channels of a wireless ad-hoc network","authors":"Polshchykov K. A., Lazarev S. A., K. O. R., V. G. S.","doi":"10.37622/adsa/16.1.2021.201-215","DOIUrl":"https://doi.org/10.37622/adsa/16.1.2021.201-215","url":null,"abstract":"","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83557270","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 : 2021-06-30DOI: 10.37622/adsa/16.1.2021.257-297
Nabila Al Balushi
This paper is a review of the literature related to reliability analysis of complex industrial systems. Many industrial systems have been analysed over the last 3 decades under different operational conditions and assumptions. Mostly, the systems were analysed for estimating the reliability indices such as mean time to systems failure, availability analysis, failure frequency, mean down time, expected busy periods of the repairmen, and their respective cost-benefit analysis. The main objective all over these years was to focus on the system performance over a long period of time; it’s basically case studies on system performance of industrial system. An attempt has been made in this paper to collect the sufficient literature and recommend some useful tips to diversify the discipline for more fruitful results on the system performance.
{"title":"A Review of the Reliability Analysis of the Complex Industrial Systems","authors":"Nabila Al Balushi","doi":"10.37622/adsa/16.1.2021.257-297","DOIUrl":"https://doi.org/10.37622/adsa/16.1.2021.257-297","url":null,"abstract":"This paper is a review of the literature related to reliability analysis of complex industrial systems. Many industrial systems have been analysed over the last 3 decades under different operational conditions and assumptions. Mostly, the systems were analysed for estimating the reliability indices such as mean time to systems failure, availability analysis, failure frequency, mean down time, expected busy periods of the repairmen, and their respective cost-benefit analysis. The main objective all over these years was to focus on the system performance over a long period of time; it’s basically case studies on system performance of industrial system. An attempt has been made in this paper to collect the sufficient literature and recommend some useful tips to diversify the discipline for more fruitful results on the system performance.","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83464973","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 : 2021-06-30DOI: 10.37622/adsa/16.1.2021.91-112
A. El-Sayed, Sahar Y. Issa, N. M. Mawed
In this paper, we discuss sufficient conditions for the existence of solutions for a coupled system of hybrid fractional-order differential equation. The continuous dependence of the unique solution on the delay functions will be studied.
本文讨论了一类混合分数阶微分方程耦合系统解存在的充分条件。研究了唯一解对时滞函数的连续依赖。
{"title":"On A Coupled System of Hybrid Fractional-order Differential Equations in Banach Algebras","authors":"A. El-Sayed, Sahar Y. Issa, N. M. Mawed","doi":"10.37622/adsa/16.1.2021.91-112","DOIUrl":"https://doi.org/10.37622/adsa/16.1.2021.91-112","url":null,"abstract":"In this paper, we discuss sufficient conditions for the existence of solutions for a coupled system of hybrid fractional-order differential equation. The continuous dependence of the unique solution on the delay functions will be studied.","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76738542","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 : 2021-06-30DOI: 10.37622/adsa/16.1.2021.133-157
J. Aramaki
In this paper, we derive necessary and sufficient conditions for the existence of a weak solution to the Maxwell-Stokes type equation associated with slip-Navier boundary condition. Our equation is nonlinear and contains, so called, p-curlcurl system. Moreover, we give a result on the continuous dependence of the weak solution on the data. 2010 Mathematics Subject Classification: 35A05, 35H30, 35A15, 35D05
{"title":"Necessary and Sufficient Conditions for the Existence of aWeak Solution to the Maxwell-Stokes Type Equation","authors":"J. Aramaki","doi":"10.37622/adsa/16.1.2021.133-157","DOIUrl":"https://doi.org/10.37622/adsa/16.1.2021.133-157","url":null,"abstract":"In this paper, we derive necessary and sufficient conditions for the existence of a weak solution to the Maxwell-Stokes type equation associated with slip-Navier boundary condition. Our equation is nonlinear and contains, so called, p-curlcurl system. Moreover, we give a result on the continuous dependence of the weak solution on the data. 2010 Mathematics Subject Classification: 35A05, 35H30, 35A15, 35D05","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"71 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82287507","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 : 2021-06-30DOI: 10.37622/adsa/16.1.2021.355-368
A. El-Sayed, S. Salman, S. Ramadan
In this paper, we consider the singularly perturbation of the Riccati difference equation with two different delays. At first, we study the local stability of the fixed points and its corresponding characteristic equation of the linearized system. At second, we show that there is Hopf bifurcation with restricted condition for occurrence. Then we get out the discretized system by applying the method of steps. Local stability and bifurcation analysis of the discretized system. We compare the results with the results of the Riccati differential equation with two different delays. Finally, numerical simulations including bifurcation diagram, Lyapunov exponent and phase portraits are carried out to confirm the analytical findings .
{"title":"On the dynamics of the singularly perturbed Riccati differential equation with two different delays","authors":"A. El-Sayed, S. Salman, S. Ramadan","doi":"10.37622/adsa/16.1.2021.355-368","DOIUrl":"https://doi.org/10.37622/adsa/16.1.2021.355-368","url":null,"abstract":"In this paper, we consider the singularly perturbation of the Riccati difference equation with two different delays. At first, we study the local stability of the fixed points and its corresponding characteristic equation of the linearized system. At second, we show that there is Hopf bifurcation with restricted condition for occurrence. Then we get out the discretized system by applying the method of steps. Local stability and bifurcation analysis of the discretized system. We compare the results with the results of the Riccati differential equation with two different delays. Finally, numerical simulations including bifurcation diagram, Lyapunov exponent and phase portraits are carried out to confirm the analytical findings .","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"286 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80277443","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 : 2021-06-30DOI: 10.37622/adsa/16.1.2021.237-255
M. Torvattanabun, Theeranon Thawila
In this paper,we introduce a new the (4+1)-dimensional fractional Boiti-Leon-Manna-Pempinelli equation. The fractional ( m+ G ′ G ) extension method is successfully applied to establish the exact solutions for the the (4+1)-dimensional fractional Boiti-Leon-Manna-Pempinelli equation. The fractional derivative version of Yang modified, linked with fractional complex transform is employed to reduce fractional differential equations into the corresponding ordinary differential equations. The results show that the new exact solution are precisely obtained and the efficiency of the methods is demonstrated.
本文引入了一个新的(4+1)维分数阶boit - leon - manna - pempinelli方程。应用分数阶(m+ G’G)扩展方法，成功地建立了(4+1)维分数阶boit - leon - manna - pempinelli方程的精确解。利用杨氏修正的分数阶导数形式，结合分数阶复变换，将分数阶微分方程化为相应的常微分方程。结果表明，新的精确解得到了精确解，证明了方法的有效性。
{"title":"New Exact Solution of The (4+1)-Dimensional Fractional Boiti-Leon-Manna-Pempinelli Equation by The Expansion Method","authors":"M. Torvattanabun, Theeranon Thawila","doi":"10.37622/adsa/16.1.2021.237-255","DOIUrl":"https://doi.org/10.37622/adsa/16.1.2021.237-255","url":null,"abstract":"In this paper,we introduce a new the (4+1)-dimensional fractional Boiti-Leon-Manna-Pempinelli equation. The fractional ( m+ G ′ G ) extension method is successfully applied to establish the exact solutions for the the (4+1)-dimensional fractional Boiti-Leon-Manna-Pempinelli equation. The fractional derivative version of Yang modified, linked with fractional complex transform is employed to reduce fractional differential equations into the corresponding ordinary differential equations. The results show that the new exact solution are precisely obtained and the efficiency of the methods is demonstrated.","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"117 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91046394","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 : 2020-12-30DOI: 10.37622/ADSA/15.2.2020.217-229
E. Bassiouny, R. Rajagopalan
The present work investigates the thermoelastic behaviour of an elastic material occupying the half space subjected to shock wave in the context of the fractional order generalized thermoelasticity associated with two relaxation times. The Laplace transform together with the Laplace transform of Caputo fractional integral has been applied to solve the closed form of the obtained solutions in the Laplace transform domain. The inversion of the dimensionless physical quantities are obtained numericaly using a complex inversion formula of Laplace transform based on a Fourier expansion. The variation of the heat conduction, the distribution of the stress and the strain with the fractional order parameter, second relaxation time and time are studied and the results presented graphically. Comparison between the effects of different parameters has been illustrated graphically.
{"title":"Hyperbolic Two Temperature Fractional-Order Thermoelastic Model Subjected to Thermal Loading with Two Relaxation Times","authors":"E. Bassiouny, R. Rajagopalan","doi":"10.37622/ADSA/15.2.2020.217-229","DOIUrl":"https://doi.org/10.37622/ADSA/15.2.2020.217-229","url":null,"abstract":"The present work investigates the thermoelastic behaviour of an elastic material occupying the half space subjected to shock wave in the context of the fractional order generalized thermoelasticity associated with two relaxation times. The Laplace transform together with the Laplace transform of Caputo fractional integral has been applied to solve the closed form of the obtained solutions in the Laplace transform domain. The inversion of the dimensionless physical quantities are obtained numericaly using a complex inversion formula of Laplace transform based on a Fourier expansion. The variation of the heat conduction, the distribution of the stress and the strain with the fractional order parameter, second relaxation time and time are studied and the results presented graphically. Comparison between the effects of different parameters has been illustrated graphically.","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74986524","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 : 2020-12-30DOI: 10.37622/ADSA/15.2.2020.271-281
A. Radouane, Fouad Ouziney, D. Mentagui
In this paper, we establish a new type of minimax problem using the results given by [1]. 2010 Mathematics Subject Classification: 47H08;54H25;49J35,46A03
{"title":"A New Version of the Minimax Problem","authors":"A. Radouane, Fouad Ouziney, D. Mentagui","doi":"10.37622/ADSA/15.2.2020.271-281","DOIUrl":"https://doi.org/10.37622/ADSA/15.2.2020.271-281","url":null,"abstract":"In this paper, we establish a new type of minimax problem using the results given by [1]. 2010 Mathematics Subject Classification: 47H08;54H25;49J35,46A03","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86816318","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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