Due to the great importance of the fractional kinetic equations, many authors discussed the generalizations of fractional kinetic equation involving various special functions. The purpose of this paper is to obtain the new generalization of fractional kinetic equation pertaining to the incomplete Aleph-function. The solution of the fractional kinetic equations obtained here by using Laplace and Sumudu transforms method. The Riemann-Liouville fractional integral operator is used to obtain the required results. The Solution of the generalized fractional kinetic equation are obtained by using the definition of incomplete Aleph function. The result discussed here can be used for the study of the chemical composition change in stars like the Sun. The solution rendered here are in compact forms suitable for numerical computation. Some special cases involving incomplete I –functions and incomplete H –functions are also considered.
{"title":"Generalized fractional kinetic equations involving incomplete Aleph - function","authors":"J. C. Arya","doi":"10.18488/24.v12i1.3316","DOIUrl":"https://doi.org/10.18488/24.v12i1.3316","url":null,"abstract":"Due to the great importance of the fractional kinetic equations, many authors discussed the generalizations of fractional kinetic equation involving various special functions. The purpose of this paper is to obtain the new generalization of fractional kinetic equation pertaining to the incomplete Aleph-function. The solution of the fractional kinetic equations obtained here by using Laplace and Sumudu transforms method. The Riemann-Liouville fractional integral operator is used to obtain the required results. The Solution of the generalized fractional kinetic equation are obtained by using the definition of incomplete Aleph function. The result discussed here can be used for the study of the chemical composition change in stars like the Sun. The solution rendered here are in compact forms suitable for numerical computation. Some special cases involving incomplete I –functions and incomplete H –functions are also considered.","PeriodicalId":355380,"journal":{"name":"International Journal of Mathematical Research","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121792044","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}
The medium of heat conduction is seemingly important in the world today and needs to be well understood. This paper looks at the steady state heat conduction in a rectangular plate characterized by Dirichlet boundary conditions. The steady state heat model is formulated based on some assumptions governing this phenomenon. The model which is an elliptic partial differential equation is solved using both analytic and numerical methods. The separable variable method which is an analytic method gives rise to a closed form solution. A comparative study was made by comparing the accuracy of the Finite Difference Method (FDM) and the separable variable method and the relative errors determined. The results obtained from the separable variable method were close to the numerical method. The FDM gives approximate solution with less time and fitting resilience. It is thus concluded that the FDM method allows control over mensurable error.
{"title":"Analytical Solution of Steady State Heat Conduction in a Rectangular Plate and Comparison with the Numerical Finite Difference Method","authors":"O. N.","doi":"10.18488/24.v11i1.3035","DOIUrl":"https://doi.org/10.18488/24.v11i1.3035","url":null,"abstract":"The medium of heat conduction is seemingly important in the world today and needs to be well understood. This paper looks at the steady state heat conduction in a rectangular plate characterized by Dirichlet boundary conditions. The steady state heat model is formulated based on some assumptions governing this phenomenon. The model which is an elliptic partial differential equation is solved using both analytic and numerical methods. The separable variable method which is an analytic method gives rise to a closed form solution. A comparative study was made by comparing the accuracy of the Finite Difference Method (FDM) and the separable variable method and the relative errors determined. The results obtained from the separable variable method were close to the numerical method. The FDM gives approximate solution with less time and fitting resilience. It is thus concluded that the FDM method allows control over mensurable error.","PeriodicalId":355380,"journal":{"name":"International Journal of Mathematical Research","volume":"51 Pt 1-2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127523981","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}
Survival analysis deals with failure time data. The presence of censoring makes the application of the classical parametric and nonparametric methods of survival analysis inadequate and as such need’s modifications. Parametric mixture models are applied where a single classical model may not suffice. The parametric mixture needs to be made more robust to address the heterogeneity of survival data. This paper proposed a mixture of two distributions for the analysis of survival data, the models consist of Gamma-Gamma, and Loglogistic-Gamma distributions. Data was simulated to investigate the performance of the models, and used to estimate the maximum likelihood parameters of the models by employing Expectation Maximization (EM). Parameters of the models were estimated and were all close the postulated values. Simulations were repeated to test the consistency and stability of the models through mean square error (MSE) and root mean square error (RMSE), and were all found to be stable and consistent. Real data was applied to determine the best fit among the mixture models and classical distributions using information criteria. Mixture models were found to model the data and the mixture of two different distributions gives the best fit.
生存分析处理的是失效时间数据。审查的存在使得经典的参数和非参数生存分析方法的应用不足，因此需要进行修改。参数混合模型应用于单一经典模型可能不满足的地方。参数混合需要更加稳健，以解决生存数据的异质性。本文提出了一种混合分布来分析生存数据，该模型由Gamma-Gamma和logistic- gamma分布组成。通过模拟数据来考察模型的性能，并利用期望最大化(EM)来估计模型的最大似然参数。对模型的参数进行了估计，均接近假设值。通过均方误差(mean square error, MSE)和均方根误差(root mean square error, RMSE)对模型的一致性和稳定性进行了反复模拟，均得到稳定一致的结果。利用真实数据，利用信息准则确定混合模型与经典分布的最佳拟合。发现了混合模型来模拟数据，两种不同分布的混合给出了最佳拟合。
{"title":"A Mixture of Gamma-Gamma, Loglogistic-Gamma Distributions for the Analysis of Heterogenous Survival Data","authors":"Othman Musa Yakubu, Y. Mohammed, A. Imam","doi":"10.18488/24.v11i1.2924","DOIUrl":"https://doi.org/10.18488/24.v11i1.2924","url":null,"abstract":"Survival analysis deals with failure time data. The presence of censoring makes the application of the classical parametric and nonparametric methods of survival analysis inadequate and as such need’s modifications. Parametric mixture models are applied where a single classical model may not suffice. The parametric mixture needs to be made more robust to address the heterogeneity of survival data. This paper proposed a mixture of two distributions for the analysis of survival data, the models consist of Gamma-Gamma, and Loglogistic-Gamma distributions. Data was simulated to investigate the performance of the models, and used to estimate the maximum likelihood parameters of the models by employing Expectation Maximization (EM). Parameters of the models were estimated and were all close the postulated values. Simulations were repeated to test the consistency and stability of the models through mean square error (MSE) and root mean square error (RMSE), and were all found to be stable and consistent. Real data was applied to determine the best fit among the mixture models and classical distributions using information criteria. Mixture models were found to model the data and the mixture of two different distributions gives the best fit.","PeriodicalId":355380,"journal":{"name":"International Journal of Mathematical Research","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116917966","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}
{"title":"Application of Interval Valued Fuzzy Soft Max-Min Decision Making Method","authors":"R. M. Zulqarnain, M. Saeed, Bagh Ali, N. Ahmad, Liaqat Ali, Sohaib Abdal","doi":"10.18488/journal.24.2020.91.11.19","DOIUrl":"https://doi.org/10.18488/journal.24.2020.91.11.19","url":null,"abstract":"Article History Received: 10 January 2020 Revised: 13 February 2020 Accepted: 17 March 2020 Published: 8 April 2020","PeriodicalId":355380,"journal":{"name":"International Journal of Mathematical Research","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133045061","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 : 2019-04-25DOI: 10.18488/JOURNAL.24.2019.81.1.20
D. Lu, Shenghui Ye
{"title":"Optical Solitary Wave Solutions of the Space-Time Fractional Modified Equal-Width Equation and their Applications","authors":"D. Lu, Shenghui Ye","doi":"10.18488/JOURNAL.24.2019.81.1.20","DOIUrl":"https://doi.org/10.18488/JOURNAL.24.2019.81.1.20","url":null,"abstract":"","PeriodicalId":355380,"journal":{"name":"International Journal of Mathematical Research","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115202205","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 : 2016-02-25DOI: 10.18488/journal.24/2016.5.2/24.2.75.102
G. Farok, M. Wahab
Supply Chain Management (SCM) demands management of complex dependencies for sensitivity and sustainability on contest of teams, departments, drivers and matrices. It requires risk analysis of global partnerships, win-win contracts and sharing agreements with relevant companies. Supply Chain flexibility, drivers and metrics may include measurements for procurement, production, transportation, inventory, warehousing, material handling, packaging and customer service. There are hundreds of sensitivity that can be used to score Supply Chain Management performance. These results would lead to support and accommodate the sustainability which can be influenced by supply strategies and decisions on supply chain flexibility.
{"title":"Retracted: Applications of Mathematical Modeling for Sensitivity and Sustainability in Supply Chain Flexibility","authors":"G. Farok, M. Wahab","doi":"10.18488/journal.24/2016.5.2/24.2.75.102","DOIUrl":"https://doi.org/10.18488/journal.24/2016.5.2/24.2.75.102","url":null,"abstract":"Supply Chain Management (SCM) demands management of complex dependencies for sensitivity and sustainability on contest of teams, departments, drivers and matrices. It requires risk analysis of global partnerships, win-win contracts and sharing agreements with relevant companies. Supply Chain flexibility, drivers and metrics may include measurements for procurement, production, transportation, inventory, warehousing, material handling, packaging and customer service. There are hundreds of sensitivity that can be used to score Supply Chain Management performance. These results would lead to support and accommodate the sustainability which can be influenced by supply strategies and decisions on supply chain flexibility.","PeriodicalId":355380,"journal":{"name":"International Journal of Mathematical Research","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126640498","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 : 2014-09-24DOI: 10.18488/journal.24/2014.3.6/24.6.63.81
R. Titus, Lagat Cheruiyot Robert
The current use of Highly Active Anti-Retroviral Therapy (HAART) strategy to control Human Immunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS) is inefficient in eradicating HIV/AIDS due to inadequate understanding of the dynamics relating to interaction between the immune system components and HIV. As a result, a pool of potential transmitters is continuously created and thus HIV has remained a pandemic. In this paper, we formulate a mathematical model using differential equations to study the effects of time lag τ>0 due to cellular latency and pharmacological delays and chemotherapy on the control strategy of AIDS epidemic. Equilibrium points of the model are computed and used to determine the reproductive ratio〖 R〗_0. This important threshold parameter is then used to determine the critical bounds of time lag τ∈[τ_min,τ_min] and therapeutic window C_p∈[MEC,MTC] that is, the bounds; above Minimum Effect Concentration (MEC) and below Minimum Toxic Concentration (MTC), where drug plasma concentration C_p should lie for effective maintenance of low levels of viral load and reduction of drug toxicity. The mathematical model gives qualitative understanding of HIV prognostic information which is a means of rejuvenating the existing Antiretroviral drugs (ARV’s). Numerical simulations show that a stable and persistent endemic equilibrium state of low viral load is achieved when these thresholds τ∈[0,25] and C_p∈[0.79,0.91] are satisfied. This persistent equilibrium state will lead to eventual eradication of HIV/AIDS.
{"title":"The Bounds of Time Lag and Chemotherapeutic Efficacy in the Control of HIV/AIDS","authors":"R. Titus, Lagat Cheruiyot Robert","doi":"10.18488/journal.24/2014.3.6/24.6.63.81","DOIUrl":"https://doi.org/10.18488/journal.24/2014.3.6/24.6.63.81","url":null,"abstract":"The current use of Highly Active Anti-Retroviral Therapy (HAART) strategy to control Human Immunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS) is inefficient in eradicating HIV/AIDS due to inadequate understanding of the dynamics relating to interaction between the immune system components and HIV. As a result, a pool of potential transmitters is continuously created and thus HIV has remained a pandemic. In this paper, we formulate a mathematical model using differential equations to study the effects of time lag τ>0 due to cellular latency and pharmacological delays and chemotherapy on the control strategy of AIDS epidemic. Equilibrium points of the model are computed and used to determine the reproductive ratio〖 R〗_0. This important threshold parameter is then used to determine the critical bounds of time lag τ∈[τ_min,τ_min] and therapeutic window C_p∈[MEC,MTC] that is, the bounds; above Minimum Effect Concentration (MEC) and below Minimum Toxic Concentration (MTC), where drug plasma concentration C_p should lie for effective maintenance of low levels of viral load and reduction of drug toxicity. The mathematical model gives qualitative understanding of HIV prognostic information which is a means of rejuvenating the existing Antiretroviral drugs (ARV’s). Numerical simulations show that a stable and persistent endemic equilibrium state of low viral load is achieved when these thresholds τ∈[0,25] and C_p∈[0.79,0.91] are satisfied. This persistent equilibrium state will lead to eventual eradication of HIV/AIDS.","PeriodicalId":355380,"journal":{"name":"International Journal of Mathematical Research","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133377931","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 : 2014-09-06DOI: 10.18488/journal.24/2014.3.5/24.5.49.62
R. Wesonga, F. Nabugoomu, Abraham Owino, L. Atuhaire, A. Ssekiboobo, Xavier Mugisha, J. Ntozi, T. Makumbi, Peter Jehopio, B. Ocaya
The coining of the expression free and fair was a good way towards evaluating elections, but fell short of qualifying its real quantification to guide an informed judgment; this paper provides guidance for such a definition. Data from the Uganda National Baseline Survey were used to assess the dynamics of the determinants for a free and fair election. All determinants were statistically significant (p<0.01) for the two multinomial models (free and fair election models). The predicted probabilities for free and fair were each used as inputs to form probability distribution function could jointly define the expression free and fair using a bivariate normal distribution. A strong positive correlation was identified between an election being free and fair (ρ=0.9693,p<0.01) implying the reliability of the statistical models in jointly considering free and fair. The study recommends development of central statistical computational system to inform electoral bodies and judges in passing scientifically backed ruling on whether an election is free and fair. A threshold percentage for any election to be referred to as free and fair could be developed either deterministically or stochastically and provisions of which passed under electoral law.
{"title":"On Statistical Definition of Free and Fair Election: Bivariate Normal Distribution Model","authors":"R. Wesonga, F. Nabugoomu, Abraham Owino, L. Atuhaire, A. Ssekiboobo, Xavier Mugisha, J. Ntozi, T. Makumbi, Peter Jehopio, B. Ocaya","doi":"10.18488/journal.24/2014.3.5/24.5.49.62","DOIUrl":"https://doi.org/10.18488/journal.24/2014.3.5/24.5.49.62","url":null,"abstract":"The coining of the expression free and fair was a good way towards evaluating elections, but fell short of qualifying its real quantification to guide an informed judgment; this paper provides guidance for such a definition. Data from the Uganda National Baseline Survey were used to assess the dynamics of the determinants for a free and fair election. All determinants were statistically significant (p<0.01) for the two multinomial models (free and fair election models). The predicted probabilities for free and fair were each used as inputs to form probability distribution function could jointly define the expression free and fair using a bivariate normal distribution. A strong positive correlation was identified between an election being free and fair (ρ=0.9693,p<0.01) implying the reliability of the statistical models in jointly considering free and fair. The study recommends development of central statistical computational system to inform electoral bodies and judges in passing scientifically backed ruling on whether an election is free and fair. A threshold percentage for any election to be referred to as free and fair could be developed either deterministically or stochastically and provisions of which passed under electoral law.","PeriodicalId":355380,"journal":{"name":"International Journal of Mathematical Research","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131268360","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 : 2014-04-19DOI: 10.18488/journal.24/2014.3.3/24.3.25.36
Sunday Emmanuel Fadugba, Joseph Temitayo Okunlola, A. O. Ajayi, O. H. Edogbanya
This paper presents mathematical model for the study of traffic flow on the highways. The effect of the density of cars on the overall interactions of the vehicles along a given distance of the road was investigated. We also observed that the density of cars per mile affects the net rate of interaction between them.
{"title":"On Mathematical Model for the Study of Traffic Flow on the High Ways","authors":"Sunday Emmanuel Fadugba, Joseph Temitayo Okunlola, A. O. Ajayi, O. H. Edogbanya","doi":"10.18488/journal.24/2014.3.3/24.3.25.36","DOIUrl":"https://doi.org/10.18488/journal.24/2014.3.3/24.3.25.36","url":null,"abstract":"This paper presents mathematical model for the study of traffic flow on the highways. The effect of the density of cars on the overall interactions of the vehicles along a given distance of the road was investigated. We also observed that the density of cars per mile affects the net rate of interaction between them.","PeriodicalId":355380,"journal":{"name":"International Journal of Mathematical Research","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123557729","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 : 2014-04-19DOI: 10.18488/journal.24/2014.3.2/24.2.15.24
K. Vanathi, V. Subramanian, K. Arjunan
In this paper, we make an attempt to study the algebraic nature of Q-intuitionistic fuzzy subsemiring of a semiring and some properties of Q-intuitionistic fuzzy subsemiring of a semiring are investigated. AMS Mathematics Subject Classification (2010): 06D72, 08A72, 03F55.
{"title":"Notes on Q-Intuitionistic Fuzzy Subsemiring of a Semiring","authors":"K. Vanathi, V. Subramanian, K. Arjunan","doi":"10.18488/journal.24/2014.3.2/24.2.15.24","DOIUrl":"https://doi.org/10.18488/journal.24/2014.3.2/24.2.15.24","url":null,"abstract":"In this paper, we make an attempt to study the algebraic nature of Q-intuitionistic fuzzy subsemiring of a semiring and some properties of Q-intuitionistic fuzzy subsemiring of a semiring are investigated. AMS Mathematics Subject Classification (2010): 06D72, 08A72, 03F55.","PeriodicalId":355380,"journal":{"name":"International Journal of Mathematical Research","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127113904","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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