Pub Date : 2024-05-24DOI: 10.9734/arjom/2024/v20i5798
Darwin P. Mangubat, Greig Bates C. Flores
Let X be an arbitrary Banach space. The establishment of the Henstock-Kurzweil-Dunford-Stieltjes (HKDS) Integral and Henstock-Kurzweil-Pettis-Stieltjes (HKPS) Integral of an X-valued function over (mathbb{R}) shows a viable and more generalized integration process utilizing the notion of dual spaces and weakly measurable functions. In this manuscript, the authors have discussed about some convergence theorems of Henstock- Kurzweil-Dunford-Stieltjes Integral and Henstock-Kurzweil-Pettis-Stieltjes Integral of X-valued functions on (mathbb{R}) via uniform convergence with respect to the integrand and integrator.
设 X 为任意巴拿赫空间。在 (mathbb{R}) 上建立 X 值函数的 Henstock-Kurzweil-Dunford-Stieltjes (HKDS) 积分和 Henstock-Kurzweil-Pettis-Stieltjes (HKPS) 积分显示了利用对偶空间和弱可测函数概念的可行的、更广义的积分过程。在本手稿中，作者讨论了 Henstock- Kurzweil-Dunford-Stieltjes Integral 和 Henstock-Kurzweil-Pettis-Stieltjes Integral 的一些收敛定理。
{"title":"Some Convergence Theorems of Henstock-Kurzweil-Dunford-Stieltjes Integral and Henstock-Kurzweil- Pettis-Stieltjes Integral of Banach-Valued Functions on (mathbb{R})","authors":"Darwin P. Mangubat, Greig Bates C. Flores","doi":"10.9734/arjom/2024/v20i5798","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i5798","url":null,"abstract":"Let X be an arbitrary Banach space. The establishment of the Henstock-Kurzweil-Dunford-Stieltjes (HKDS) Integral and Henstock-Kurzweil-Pettis-Stieltjes (HKPS) Integral of an X-valued function over (mathbb{R}) shows a viable and more generalized integration process utilizing the notion of dual spaces and weakly measurable functions. In this manuscript, the authors have discussed about some convergence theorems of Henstock- Kurzweil-Dunford-Stieltjes Integral and Henstock-Kurzweil-Pettis-Stieltjes Integral of X-valued functions on (mathbb{R}) via uniform convergence with respect to the integrand and integrator.","PeriodicalId":479543,"journal":{"name":"Asian research journal of mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141100524","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 : 2024-02-13DOI: 10.9734/arjom/2024/v20i1779
E. E. Joshua, E. T. Akpan, Udoinyang Godwin Inyang
Determining the impact of a local control strategy, implemented to curtail the spread of COVID-19 has become obligatory to enable policy makers to combat the so-called long covid. This research used a deterministic SEIAHR-model, incorporating a logistic function to investigate the effect of quasi-lockdown policy during reemergence of corona virus pandemic. The notion of uniform convergence and fixed point theory were used to establish positive invariant region, ultimate boundedness, and existence of unique solution of the model. Nonlinear dynamical behaviours of the model such as stability and oscillating flows occurred at the disease free, and endemic equilibrium points. Using centre manifold theory, a trans-critical bifurcation with hysteresis effect were established, when quasi-lockdown policy was used as a control parameter in the model. A forward sensitivity analysis was conducted to unfold parameters that contributed significantly towards the spread and control of the infection. These parameters were estimated and fitted using least square technique, comparative to the observed real datasets adapted from the Nigeria Centre for Disease Control (NCDC). The polynomial regression model fitted the observed datasets with an average coefficient of determination given as R2 = 0.94. Simulations in form of phase space diagrams were used to validate the theoretic results. Epidemiologically, the model demonstrated that quasi-lockdown policy was necessarily a strategic policy to curb the spread of the infection, but not sufficient to eradicate the disease as the disease persisted endemically. It was shown that the basic reproduction number of the infection was within the critical threshold (R0 (le) 1), when the lockdown policy was enforced strictly, but otherwise on relaxation of the lockdown policy (R0 (ge) 1) Thus a relaxation of the quasi-lockdown policy leads to increase in susceptibility of the populace as the infection risk ratio increases in the model. Similarly, the model predicted that a pre-mature lifting of the lockdown policy could have led to high infectivity on the susceptible class and disastrous to healthy living of the citizens.
{"title":"Mathematical Modelling and Computational Dynamics of the impact of Quasi-Lockdown Policy in Control of COVID-19 in Akwa Ibom State, Nigeria","authors":"E. E. Joshua, E. T. Akpan, Udoinyang Godwin Inyang","doi":"10.9734/arjom/2024/v20i1779","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i1779","url":null,"abstract":"Determining the impact of a local control strategy, implemented to curtail the spread of COVID-19 has become obligatory to enable policy makers to combat the so-called long covid. This research used a deterministic SEIAHR-model, incorporating a logistic function to investigate the effect of quasi-lockdown policy during reemergence of corona virus pandemic. The notion of uniform convergence and fixed point theory were used to establish positive invariant region, ultimate boundedness, and existence of unique solution of the model. Nonlinear dynamical behaviours of the model such as stability and oscillating flows occurred at the disease free, and endemic equilibrium points. Using centre manifold theory, a trans-critical bifurcation with hysteresis effect were established, when quasi-lockdown policy was used as a control parameter in the model. A forward sensitivity analysis was conducted to unfold parameters that contributed significantly towards the spread and control of the infection. These parameters were estimated and fitted using least square technique, comparative to the observed real datasets adapted from the Nigeria Centre for Disease Control (NCDC). The polynomial regression model fitted the observed datasets with an average coefficient of determination given as R2 = 0.94. Simulations in form of phase space diagrams were used to validate the theoretic results. Epidemiologically, the model demonstrated that quasi-lockdown policy was necessarily a strategic policy to curb the spread of the infection, but not sufficient to eradicate the disease as the disease persisted endemically. It was shown that the basic reproduction number of the infection was within the critical threshold (R0 (le) 1), when the lockdown policy was enforced strictly, but otherwise on relaxation of the lockdown policy (R0 (ge) 1) Thus a relaxation of the quasi-lockdown policy leads to increase in susceptibility of the populace as the infection risk ratio increases in the model. Similarly, the model predicted that a pre-mature lifting of the lockdown policy could have led to high infectivity on the susceptible class and disastrous to healthy living of the citizens.","PeriodicalId":479543,"journal":{"name":"Asian research journal of mathematics","volume":"54 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139839817","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 : 2024-02-13DOI: 10.9734/arjom/2024/v20i1779
E. E. Joshua, E. T. Akpan, Udoinyang Godwin Inyang
Determining the impact of a local control strategy, implemented to curtail the spread of COVID-19 has become obligatory to enable policy makers to combat the so-called long covid. This research used a deterministic SEIAHR-model, incorporating a logistic function to investigate the effect of quasi-lockdown policy during reemergence of corona virus pandemic. The notion of uniform convergence and fixed point theory were used to establish positive invariant region, ultimate boundedness, and existence of unique solution of the model. Nonlinear dynamical behaviours of the model such as stability and oscillating flows occurred at the disease free, and endemic equilibrium points. Using centre manifold theory, a trans-critical bifurcation with hysteresis effect were established, when quasi-lockdown policy was used as a control parameter in the model. A forward sensitivity analysis was conducted to unfold parameters that contributed significantly towards the spread and control of the infection. These parameters were estimated and fitted using least square technique, comparative to the observed real datasets adapted from the Nigeria Centre for Disease Control (NCDC). The polynomial regression model fitted the observed datasets with an average coefficient of determination given as R2 = 0.94. Simulations in form of phase space diagrams were used to validate the theoretic results. Epidemiologically, the model demonstrated that quasi-lockdown policy was necessarily a strategic policy to curb the spread of the infection, but not sufficient to eradicate the disease as the disease persisted endemically. It was shown that the basic reproduction number of the infection was within the critical threshold (R0 (le) 1), when the lockdown policy was enforced strictly, but otherwise on relaxation of the lockdown policy (R0 (ge) 1) Thus a relaxation of the quasi-lockdown policy leads to increase in susceptibility of the populace as the infection risk ratio increases in the model. Similarly, the model predicted that a pre-mature lifting of the lockdown policy could have led to high infectivity on the susceptible class and disastrous to healthy living of the citizens.
{"title":"Mathematical Modelling and Computational Dynamics of the impact of Quasi-Lockdown Policy in Control of COVID-19 in Akwa Ibom State, Nigeria","authors":"E. E. Joshua, E. T. Akpan, Udoinyang Godwin Inyang","doi":"10.9734/arjom/2024/v20i1779","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i1779","url":null,"abstract":"Determining the impact of a local control strategy, implemented to curtail the spread of COVID-19 has become obligatory to enable policy makers to combat the so-called long covid. This research used a deterministic SEIAHR-model, incorporating a logistic function to investigate the effect of quasi-lockdown policy during reemergence of corona virus pandemic. The notion of uniform convergence and fixed point theory were used to establish positive invariant region, ultimate boundedness, and existence of unique solution of the model. Nonlinear dynamical behaviours of the model such as stability and oscillating flows occurred at the disease free, and endemic equilibrium points. Using centre manifold theory, a trans-critical bifurcation with hysteresis effect were established, when quasi-lockdown policy was used as a control parameter in the model. A forward sensitivity analysis was conducted to unfold parameters that contributed significantly towards the spread and control of the infection. These parameters were estimated and fitted using least square technique, comparative to the observed real datasets adapted from the Nigeria Centre for Disease Control (NCDC). The polynomial regression model fitted the observed datasets with an average coefficient of determination given as R2 = 0.94. Simulations in form of phase space diagrams were used to validate the theoretic results. Epidemiologically, the model demonstrated that quasi-lockdown policy was necessarily a strategic policy to curb the spread of the infection, but not sufficient to eradicate the disease as the disease persisted endemically. It was shown that the basic reproduction number of the infection was within the critical threshold (R0 (le) 1), when the lockdown policy was enforced strictly, but otherwise on relaxation of the lockdown policy (R0 (ge) 1) Thus a relaxation of the quasi-lockdown policy leads to increase in susceptibility of the populace as the infection risk ratio increases in the model. Similarly, the model predicted that a pre-mature lifting of the lockdown policy could have led to high infectivity on the susceptible class and disastrous to healthy living of the citizens.","PeriodicalId":479543,"journal":{"name":"Asian research journal of mathematics","volume":"6 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139779720","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 : 2024-02-13DOI: 10.9734/arjom/2024/v20i1778
Adeniran A. T., Faweya O.
This paper develops a New Bivariate-Gamma Distribution (NBGD) and explores its mathematical and statistical properties such as marginal probability distributions, moments, product moment, covariance and correlation. The study further investigates the various special cases of the NBGD. The new distribution is more robust with additional parameters and flexible for modelling real datasets.
{"title":"A New Type of Bivariate-Gamma Probability Function","authors":"Adeniran A. T., Faweya O.","doi":"10.9734/arjom/2024/v20i1778","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i1778","url":null,"abstract":"This paper develops a New Bivariate-Gamma Distribution (NBGD) and explores its mathematical and statistical properties such as marginal probability distributions, moments, product moment, covariance and correlation. The study further investigates the various special cases of the NBGD. The new distribution is more robust with additional parameters and flexible for modelling real datasets.","PeriodicalId":479543,"journal":{"name":"Asian research journal of mathematics","volume":"85 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139840780","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 : 2024-02-13DOI: 10.9734/arjom/2024/v20i1778
Adeniran A. T., Faweya O.
This paper develops a New Bivariate-Gamma Distribution (NBGD) and explores its mathematical and statistical properties such as marginal probability distributions, moments, product moment, covariance and correlation. The study further investigates the various special cases of the NBGD. The new distribution is more robust with additional parameters and flexible for modelling real datasets.
{"title":"A New Type of Bivariate-Gamma Probability Function","authors":"Adeniran A. T., Faweya O.","doi":"10.9734/arjom/2024/v20i1778","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i1778","url":null,"abstract":"This paper develops a New Bivariate-Gamma Distribution (NBGD) and explores its mathematical and statistical properties such as marginal probability distributions, moments, product moment, covariance and correlation. The study further investigates the various special cases of the NBGD. The new distribution is more robust with additional parameters and flexible for modelling real datasets.","PeriodicalId":479543,"journal":{"name":"Asian research journal of mathematics","volume":"122 43","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139780900","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 : 2023-12-18DOI: 10.9734/arjom/2023/v19i12768
S. O. Juma, J. K. Sigey, J. Abonyo, S. K. Maritim
The study of the effect of hall and ion slip on an inclined conductor on MHD natural and forced convection in a heated wavy chamber with a constant transversal magnetic field applied. The governing momentum and energy equation were solved by applying finite central scheme approximation and the resulting partial difference equations were solved by MATLAB software. The study showed that an increase heat absorption coefficient lowers the surface heat transfer thus lowering flow rate. An increase in Rayleigh number increases the flow rate while an increase in the angle of inclination of the conductor increases the buoyancy force component thereby increasing the flow rate. The results further showed that flow rate became higher at an inclination angle of 90º. In addition, the results also showed that an increase in Hartmann increases the flow rate. The Hartmann number, Rayleigh number and Absorption coefficient are analytically discussed and represented in tables and graphical profiles with respect to flow velocity and temperature profile due to engineering demand. This current study a direct application in the development of MHD propelled vessels in the marine and space-craft department.
{"title":"Effects of an Inclined Cente red Conductor on MHD Natural and Forced Convection Within a Heated Wavy Chamber","authors":"S. O. Juma, J. K. Sigey, J. Abonyo, S. K. Maritim","doi":"10.9734/arjom/2023/v19i12768","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i12768","url":null,"abstract":"The study of the effect of hall and ion slip on an inclined conductor on MHD natural and forced convection in a heated wavy chamber with a constant transversal magnetic field applied. The governing momentum and energy equation were solved by applying finite central scheme approximation and the resulting partial difference equations were solved by MATLAB software. The study showed that an increase heat absorption coefficient lowers the surface heat transfer thus lowering flow rate. An increase in Rayleigh number increases the flow rate while an increase in the angle of inclination of the conductor increases the buoyancy force component thereby increasing the flow rate. The results further showed that flow rate became higher at an inclination angle of 90º. In addition, the results also showed that an increase in Hartmann increases the flow rate. The Hartmann number, Rayleigh number and Absorption coefficient are analytically discussed and represented in tables and graphical profiles with respect to flow velocity and temperature profile due to engineering demand. This current study a direct application in the development of MHD propelled vessels in the marine and space-craft department.","PeriodicalId":479543,"journal":{"name":"Asian research journal of mathematics","volume":" 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138994766","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 : 2023-12-16DOI: 10.9734/arjom/2023/v19i12767
Yuan Anisa, Muhammad Hafiz, Fadhillah Azmi
The rapid progress in technology and information has facilitated the integration of computer-based technology into the realm of education. Utilizing computer technology as a learning medium or learning resource is something that must be done. Indeed, a plethora of educational resources are readily available on the internet in the form of electronic learning (e-learning). The predominant format of content in e-learning platforms is textual, which poses challenges for students in comprehending mathematical concepts due to the nature of mathematical material that often involves detailed explanations of problem-solving procedures. Due to this rationale, instructional materials presented in the format of videos serve as a viable substitute for textual media. The educational videos that have been produced can be published on online platforms dedicated to video sharing, such as YouTube. The objective of this study is to assess the viability of YouTube as an educational resource for mathematical education. The present study employs a qualitative descriptive methodology, wherein the researcher assumes the role of the primary instrument. The study involved an examination of mathematics learning materials that were released by various channels on the YouTube platform. Additionally, interviews were performed with mathematics educators and high school students to gather their perspectives on the use of YouTube as a resource for studying mathematics. The findings of the study indicate the existence of YouTube channels that offer mathematics educational content suitable for student learning purposes. In the study, it was found that 30% of the participating students utilised YouTube as a means of acquiring knowledge in the field of mathematics. However, it is worth noting that participants inadvertently stumbled into mathematics learning videos on YouTube while utilising the platform as a source for learning mathematics. Students utilise the Google search engine to seek for relevant material, subsequently employing YouTube as a platform to locate videos that align with their specific preferences. Based on interviews conducted with mathematics educators and students, it is evident that YouTube has the potential to serve as a viable platform for mathematical education. However, it is crucial to acknowledge and evaluate the various advantages and disadvantages associated with its use in this context.
{"title":"The Potential of YouTube as a Source of Mathematics Learning Education","authors":"Yuan Anisa, Muhammad Hafiz, Fadhillah Azmi","doi":"10.9734/arjom/2023/v19i12767","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i12767","url":null,"abstract":"The rapid progress in technology and information has facilitated the integration of computer-based technology into the realm of education. Utilizing computer technology as a learning medium or learning resource is something that must be done. Indeed, a plethora of educational resources are readily available on the internet in the form of electronic learning (e-learning). The predominant format of content in e-learning platforms is textual, which poses challenges for students in comprehending mathematical concepts due to the nature of mathematical material that often involves detailed explanations of problem-solving procedures. Due to this rationale, instructional materials presented in the format of videos serve as a viable substitute for textual media. The educational videos that have been produced can be published on online platforms dedicated to video sharing, such as YouTube. The objective of this study is to assess the viability of YouTube as an educational resource for mathematical education. The present study employs a qualitative descriptive methodology, wherein the researcher assumes the role of the primary instrument. The study involved an examination of mathematics learning materials that were released by various channels on the YouTube platform. Additionally, interviews were performed with mathematics educators and high school students to gather their perspectives on the use of YouTube as a resource for studying mathematics. The findings of the study indicate the existence of YouTube channels that offer mathematics educational content suitable for student learning purposes. In the study, it was found that 30% of the participating students utilised YouTube as a means of acquiring knowledge in the field of mathematics. However, it is worth noting that participants inadvertently stumbled into mathematics learning videos on YouTube while utilising the platform as a source for learning mathematics. Students utilise the Google search engine to seek for relevant material, subsequently employing YouTube as a platform to locate videos that align with their specific preferences. Based on interviews conducted with mathematics educators and students, it is evident that YouTube has the potential to serve as a viable platform for mathematical education. However, it is crucial to acknowledge and evaluate the various advantages and disadvantages associated with its use in this context.","PeriodicalId":479543,"journal":{"name":"Asian research journal of mathematics","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138966994","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 : 2023-12-14DOI: 10.9734/arjom/2023/v19i11766
Wensheng Yang, Miqin Chen
In this paper, we propose a new Leslie-Gower predator-prey model with predator-dependent prey refuge. Firstly, we obtain the positivity and boundedness of the system solution. Secondly, we prove that the origin is unstable using blow-up method, analyze the existence and local stability of the boundary equilibrium point and positive equilibrium point, and prove that the unique positive equilibrium point of the system is globally asymptotically stable by constructing a suitable Dulac function. Finally, mathematic analysis and numerical simulation show that: (1) when the strength of the predator-dependent prey refuge k = 0 , the dynamics of the predator-prey system without predator-dependent prey refuge are consistent with the results obtained from the traditional Leslie-Gower predator-prey system; (2) when k tends to positive infinity, the predator-dependent refuge lead to prey population densities fall somewhere between without prey refuge and with proportional refuge. However, the predator densities within this new form of the predator-dependent prey refuge is greater than the densities of predators without prey refuge and with proportional refuge; (3) increasing the strength k of the predator-dependent prey refuge can increase the densities of predator and prey populations respectively.
本文提出了一种新的莱斯利-高尔捕食者-猎物模型，该模型具有捕食者依赖性的猎物避难所。首先，我们得到了系统解的实在性和有界性。其次，利用炸毁法证明了原点不稳定，分析了边界平衡点和正平衡点的存在性和局部稳定性，并通过构造合适的杜拉克函数证明了系统的唯一正平衡点是全局渐近稳定的。最后，数学分析和数值模拟表明(1) 当依赖捕食者的猎物庇护强度 k = 0 时，无依赖捕食者的猎物庇护的捕食者-猎物系统的动力学与传统的 Leslie-Gower 捕食者-猎物系统的结果一致；(2) 当 k 趋于正无穷大时，依赖捕食者的庇护导致猎物种群密度介于无猎物庇护和有比例庇护之间。然而，这种新形式的捕食者依赖猎物庇护所内的捕食者密度大于无猎物庇护所和有比例庇护所的捕食者密度；（3）增加捕食者依赖猎物庇护所的强度 k 可以分别增加捕食者和猎物种群的密度。
{"title":"The Impact of Predator-dependent Prey Refuge on the Dynamics of a Leslie-Gower Predator-prey Model","authors":"Wensheng Yang, Miqin Chen","doi":"10.9734/arjom/2023/v19i11766","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11766","url":null,"abstract":"In this paper, we propose a new Leslie-Gower predator-prey model with predator-dependent prey refuge. Firstly, we obtain the positivity and boundedness of the system solution. Secondly, we prove that the origin is unstable using blow-up method, analyze the existence and local stability of the boundary equilibrium point and positive equilibrium point, and prove that the unique positive equilibrium point of the system is globally asymptotically stable by constructing a suitable Dulac function. Finally, mathematic analysis and numerical simulation show that: (1) when the strength of the predator-dependent prey refuge k = 0 , the dynamics of the predator-prey system without predator-dependent prey refuge are consistent with the results obtained from the traditional Leslie-Gower predator-prey system; (2) when k tends to positive infinity, the predator-dependent refuge lead to prey population densities fall somewhere between without prey refuge and with proportional refuge. However, the predator densities within this new form of the predator-dependent prey refuge is greater than the densities of predators without prey refuge and with proportional refuge; (3) increasing the strength k of the predator-dependent prey refuge can increase the densities of predator and prey populations respectively.","PeriodicalId":479543,"journal":{"name":"Asian research journal of mathematics","volume":"8 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138970978","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 : 2023-12-09DOI: 10.9734/arjom/2023/v19i11765
Anees Al-Harbi, Waleed M. Al-Hamdan, L. Wazzan
In this research, we will develop a numerical scheme for solving the nonlinear logarithmic Schrödinger’s equation using the Linearized implicit scheme, that has second-order accuracy in space and time, with significant savings in computational time. We then compare the results to those obtained previously using the Crank-Nicolson scheme of the finite difference method. The stability and precision of this method will be evaluated before it is implemented. Precise solution and conserved quantities will be used to prove the efficiency as well as reliability of the method that has been proposed. Additionally, tests are conducted to explore the interactions that take place between two and three solitons. The numerical findings of our investigation demonstrated that the behavior of interactions is elastic.
{"title":"A Linearized Implicit Scheme for Solving Logarithmic Nonlinear Schrödinger’s Equation","authors":"Anees Al-Harbi, Waleed M. Al-Hamdan, L. Wazzan","doi":"10.9734/arjom/2023/v19i11765","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11765","url":null,"abstract":"In this research, we will develop a numerical scheme for solving the nonlinear logarithmic Schrödinger’s equation using the Linearized implicit scheme, that has second-order accuracy in space and time, with significant savings in computational time. We then compare the results to those obtained previously using the Crank-Nicolson scheme of the finite difference method. The stability and precision of this method will be evaluated before it is implemented. Precise solution and conserved quantities will be used to prove the efficiency as well as reliability of the method that has been proposed. Additionally, tests are conducted to explore the interactions that take place between two and three solitons. The numerical findings of our investigation demonstrated that the behavior of interactions is elastic.","PeriodicalId":479543,"journal":{"name":"Asian research journal of mathematics","volume":"3 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138585588","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 : 2023-12-04DOI: 10.9734/arjom/2023/v19i11764
Duromola M. K., Kayode S. J., Lawal R. S.
In this article, we focus on linear hybrid multistep method for direct solution of initial value problems of third order ordinary differential equations without reduction to system of first-order ordinary differential equations. The derivation of the method involved using collocation and interpolation techniques with power series as basis function to produce a system of linear equations. The unknown parameters in the system of equations were obtained through the Gaussian elimination technique. The values of the determined parameters were then substituted and evaluated at different grid and off-grid points to produce the required continuous block method. The discrete scheme obtained from the method is self-starting with improved accuracy and a larger interval of absolute stability. Basic properties of the method were investigated. The results showed that the method is zero stable, consistent , convergent and of order seven. The performance of the method was tested by solving linear and nonlinear problems of general third order ordinary differential equations. The result were found to compare favourably with some existing methods in literature.
{"title":"Linear Hybrid Multistep Block Method for Direct Solution of Initial Value Problems of Third Order Ordinary Differential Equations","authors":"Duromola M. K., Kayode S. J., Lawal R. S.","doi":"10.9734/arjom/2023/v19i11764","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11764","url":null,"abstract":"In this article, we focus on linear hybrid multistep method for direct solution of initial value problems of third order ordinary differential equations without reduction to system of first-order ordinary differential equations. The derivation of the method involved using collocation and interpolation techniques with power series as basis function to produce a system of linear equations. The unknown parameters in the system of equations were obtained through the Gaussian elimination technique. The values of the determined parameters were then substituted and evaluated at different grid and off-grid points to produce the required continuous block method. The discrete scheme obtained from the method is self-starting with improved accuracy and a larger interval of absolute stability. Basic properties of the method were investigated. The results showed that the method is zero stable, consistent , convergent and of order seven. The performance of the method was tested by solving linear and nonlinear problems of general third order ordinary differential equations. The result were found to compare favourably with some existing methods in literature.","PeriodicalId":479543,"journal":{"name":"Asian research journal of mathematics","volume":"39 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138603827","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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