This paper studies the traveling wave solutions of a susceptible and infectious (SI) mathematical model with and without recruitment rates. Our research provides numerical solutions for the proposed models, confirming the existence of traveling wave solutions. We meticulously calculate the minimal traveling wave speeds and analytically determine the spreading speed without turnover for the susceptible population. The paper also investigates the relationship between the spreading speeds and the model parameters. Additionally, we identify the threshold density of susceptible individuals, a crucial point below which the disease cannot persist. Our findings also confirm that the disease ceases to exist if the death rates surpass the rate of new cases of infections.
{"title":"Traveling wave solutions of a susceptible-infectious model","authors":"Khalaf Alanazi","doi":"10.56947/amcs.v24.354","DOIUrl":"https://doi.org/10.56947/amcs.v24.354","url":null,"abstract":"This paper studies the traveling wave solutions of a susceptible and infectious (SI) mathematical model with and without recruitment rates. Our research provides numerical solutions for the proposed models, confirming the existence of traveling wave solutions. We meticulously calculate the minimal traveling wave speeds and analytically determine the spreading speed without turnover for the susceptible population. The paper also investigates the relationship between the spreading speeds and the model parameters. Additionally, we identify the threshold density of susceptible individuals, a crucial point below which the disease cannot persist. Our findings also confirm that the disease ceases to exist if the death rates surpass the rate of new cases of infections.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"43 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141648799","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 paper we have considered two higher order difference operators generated by two higher order difference functions on the Hilbert space of square summable functions. By allowing the leading coefficients to be unbounded and the other coefficients as constant functions, we have shown that the composites of two symmetric difference operators are symmetric if the leading coefficients are scalar multiple of each other and the common divisor of their orders is 1. Using examples, we have shown that these conditions of symmetry cannot be weakened. Furthermore, We have shown that the deficiency indices of the composites is equal to the sum of the deficiency indices of the individual operators and that the spectra of the self-adjoint operator extensions is the whole of the real line.
{"title":"Symmetric operator extensions of composites of higher order difference operators","authors":"B. Okello, F. Nyamwala, D. Ambogo","doi":"10.56947/amcs.v24.352","DOIUrl":"https://doi.org/10.56947/amcs.v24.352","url":null,"abstract":"In this paper we have considered two higher order difference operators generated by two higher order difference functions on the Hilbert space of square summable functions. By allowing the leading coefficients to be unbounded and the other coefficients as constant functions, we have shown that the composites of two symmetric difference operators are symmetric if the leading coefficients are scalar multiple of each other and the common divisor of their orders is 1. Using examples, we have shown that these conditions of symmetry cannot be weakened. Furthermore, We have shown that the deficiency indices of the composites is equal to the sum of the deficiency indices of the individual operators and that the spectra of the self-adjoint operator extensions is the whole of the real line.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"123 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141665636","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 main objective of this research is to examine the radiation effects of an unsteady MHD Williamson biofluid (Blood) over a wedge that interacts with thermophoresis diffusion and Brownian motion. The necessary prerequisites of partial differential equations (PDEs) ensure the development of suitable mathematical frameworks for momentum, energy, and concentration. These appropriate nonlinear PDEs are frequently transmuted into ordinary differential equations (ODEs) by implemented similarity transformation. The results of these ODEs have a significant impact on the BVP4C approach from the MATLAB package computational structures. The graphs and tabular data provided the various values for pertinent parameters on the non-dimensional velocity temperature, concentration profiles, and the numerical values of skin friction, Nusselt number, and Sherwood number were found and discussed in detail. A novel aspect of the research effort was the effective incorporation of multiple linear regression (MLR) employing machine learning (ML), a statistical technique to forecast the physical quantities for present numerical results with an accuracy of 95%. Finally, the response and predicted variables were verified using linear regression. The potential benefit of these outcomes is to develop novel therapeutic and diagnostic strategies for cancer treatment, as well as for a better understanding of medical problems and designing more effective drug delivery systems. In particular, for significant developments in computer technology and resources, the enormous computational cost of these simulations still keeps them from becoming a clinical tool. An additional benefit is that the outcomes showed acceptable congruence with the tangible findings of recent research and enlargements for future investigators.
{"title":"Machine learning impact of radiative blood flow over a wedge in a time-dependent MHD Williamson fluid","authors":"Priyadharshini P, Karpagam V","doi":"10.56947/amcs.v22.275","DOIUrl":"https://doi.org/10.56947/amcs.v22.275","url":null,"abstract":"The main objective of this research is to examine the radiation effects of an unsteady MHD Williamson biofluid (Blood) over a wedge that interacts with thermophoresis diffusion and Brownian motion. The necessary prerequisites of partial differential equations (PDEs) ensure the development of suitable mathematical frameworks for momentum, energy, and concentration. These appropriate nonlinear PDEs are frequently transmuted into ordinary differential equations (ODEs) by implemented similarity transformation. The results of these ODEs have a significant impact on the BVP4C approach from the MATLAB package computational structures. The graphs and tabular data provided the various values for pertinent parameters on the non-dimensional velocity temperature, concentration profiles, and the numerical values of skin friction, Nusselt number, and Sherwood number were found and discussed in detail. A novel aspect of the research effort was the effective incorporation of multiple linear regression (MLR) employing machine learning (ML), a statistical technique to forecast the physical quantities for present numerical results with an accuracy of 95%. Finally, the response and predicted variables were verified using linear regression. The potential benefit of these outcomes is to develop novel therapeutic and diagnostic strategies for cancer treatment, as well as for a better understanding of medical problems and designing more effective drug delivery systems. In particular, for significant developments in computer technology and resources, the enormous computational cost of these simulations still keeps them from becoming a clinical tool. An additional benefit is that the outcomes showed acceptable congruence with the tangible findings of recent research and enlargements for future investigators.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"137 32","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140369633","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 paper, we present some fundamental results for the Parseval continuous K- frames in Hilbert space and we study some properties of an equal-norm of vectors. Furthermore, we show that a set of K-norm vectors can be extended to become a K-norm of K-frame.
{"title":"Equal-norm Parseval continuous K-frames in Hilbert spaces","authors":"M. Rossafi, Hafida Massit","doi":"10.56947/amcs.v22.281","DOIUrl":"https://doi.org/10.56947/amcs.v22.281","url":null,"abstract":"In this paper, we present some fundamental results for the Parseval continuous K- frames in Hilbert space and we study some properties of an equal-norm of vectors. Furthermore, we show that a set of K-norm vectors can be extended to become a K-norm of K-frame.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"129 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140369766","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 theory of Γ-semigroups is an extension of the semigroup theory. In this paper, we examine the left operator semigroup L and the right operator semigroup R via modified definition of Γ-semigroup and deduce some results of operator semigroups acting on a Γ-semigroup. Further, we study some relationships between Green’s equivalence relations of a Γ-semigroup and its left (right) operator semigroup. In particular, we show that if two elements of a Γ-semigroup S are L(R)-related, then the two elements of L(R) resulting from S for every α ∈ Γ are also L(R)-related. Also, we describe that if two elements of S are α and β-idempotent such that the two elements are R-related in L, then their R-relation holds in S for some α, β ∈ Γ.
Γ-半群理论是半群理论的延伸。在本文中，我们通过修改Γ-半群的定义来研究左算子半群 L 和右算子半群 R，并推导出作用于Γ-半群的算子半群的一些结果。此外，我们还研究了 Γ-半群的格林等价关系与其左（右）算子半群之间的一些关系。特别是，我们证明了如果 Γ半群 S 的两个元素是 L(R) 相关的，那么对于每个 α∈ Γ 而言，由 S 产生的 L(R) 的两个元素也是 L(R) 相关的。此外，我们还描述了如果 S 的两个元素是 α 和 β-幂等元素，并且这两个元素在 L 中是 R 相关的，那么对于某个 α, β∈ Γ，它们的 R 相关性在 S 中成立。
{"title":"Connections of Green's relations of a Γ-semigroup with operator semigroups","authors":"J. Awolola, Musa Ibrahim","doi":"10.56947/amcs.v22.285","DOIUrl":"https://doi.org/10.56947/amcs.v22.285","url":null,"abstract":"The theory of Γ-semigroups is an extension of the semigroup theory. In this paper, we examine the left operator semigroup L and the right operator semigroup R via modified definition of Γ-semigroup and deduce some results of operator semigroups acting on a Γ-semigroup. Further, we study some relationships between Green’s equivalence relations of a Γ-semigroup and its left (right) operator semigroup. In particular, we show that if two elements of a Γ-semigroup S are L(R)-related, then the two elements of L(R) resulting from S for every α ∈ Γ are also L(R)-related. Also, we describe that if two elements of S are α and β-idempotent such that the two elements are R-related in L, then their R-relation holds in S for some α, β ∈ Γ.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"70 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140371473","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 paper, we investigate the existence and uniqueness of a fixed point of almost Z-contractions via simulation function in complete partial b-metric spaces using (α, β)-admissibility. Also, some illustrative examples are given to validate the results. Furthermore, an application to the BVP is given. Our results extend and generalize several previous works from the existing literature.
{"title":"Fixed point results for almost Z-contractions in partial b-metric spaces via simulation function","authors":"G. Saluja","doi":"10.56947/amcs.v22.279","DOIUrl":"https://doi.org/10.56947/amcs.v22.279","url":null,"abstract":"In this paper, we investigate the existence and uniqueness of a fixed point of almost Z-contractions via simulation function in complete partial b-metric spaces using (α, β)-admissibility. Also, some illustrative examples are given to validate the results. Furthermore, an application to the BVP is given. Our results extend and generalize several previous works from the existing literature.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"120 34","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140370154","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 paper, we have proved some common fixed point results using generalized contraction mapping in G-cone metric spaces over Banach algebras. Our results are a generalization and extension of several well-known results related to fixed point theory.
在本文中，我们利用巴拿赫代数上的 G 锥度量空间中的广义收缩映射证明了一些常见的定点结果。我们的结果是对定点理论相关的几个著名结果的概括和扩展。
{"title":"Some common fixed point theorems using G-Cone metric spaces with Banach algebra","authors":"Anil Kumar Mishra, Padmavati Sudha","doi":"10.56947/amcs.v22.257","DOIUrl":"https://doi.org/10.56947/amcs.v22.257","url":null,"abstract":"In this paper, we have proved some common fixed point results using generalized contraction mapping in G-cone metric spaces over Banach algebras. Our results are a generalization and extension of several well-known results related to fixed point theory.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"51 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140371422","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}
Adnane Kaddiri, A. Jamea, Mohamed Laghdir, El Mehdi Hassoune
Our aim in this paper is to study the existence result of entropy solution for a specific type of nonlinear degenerate weighted elliptic p(.)-Laplacian problems with Dirichlet-type boundary condition and L1 data. In the framework of the theory of weighted Sobolev spaces with variable exponents, we use the regularization approach combined with a priori estimates.
{"title":"Existence of entropy solutions to nonlinear degenerate weighted elliptic p(.)-Laplacian problem and L1-data","authors":"Adnane Kaddiri, A. Jamea, Mohamed Laghdir, El Mehdi Hassoune","doi":"10.56947/amcs.v22.290","DOIUrl":"https://doi.org/10.56947/amcs.v22.290","url":null,"abstract":"Our aim in this paper is to study the existence result of entropy solution for a specific type of nonlinear degenerate weighted elliptic p(.)-Laplacian problems with Dirichlet-type boundary condition and L1 data. In the framework of the theory of weighted Sobolev spaces with variable exponents, we use the regularization approach combined with a priori estimates. ","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"142 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140369063","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}
João Carlos Ferreira, Maria das Graças Bruno Marietto
In this paper we study the additivity of multiplicative Jordan triple higher semi-derivations on rings and standard operator algebras.
在本文中，我们研究了环和标准算子代数上的乘法约旦三重高次半衍生的可加性。
{"title":"Multiplicative Jordan triple higher semi-derivations on rings and standard operator algebras","authors":"João Carlos Ferreira, Maria das Graças Bruno Marietto","doi":"10.56947/amcs.v22.270","DOIUrl":"https://doi.org/10.56947/amcs.v22.270","url":null,"abstract":"In this paper we study the additivity of multiplicative Jordan triple higher semi-derivations on rings and standard operator algebras.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"62 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140371718","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}
An analytical study of the motion of a steady, homogenous, incompressible, plane electrically conducting micropolar fluid flow through a porous medium subjected to a transverse magnetic field is carried out. The governing non linear partial differential equations describing the continuity, momentum and angular momentum are converted into a system of linear partial differential equations by means of hodograph transformation. Further the flow equations have been obtained in terms of Legendre transform function of the stream function. Results are summarized in the form of a theorem. Lastly two examples have been taken as application to illustrate the developed theory and exact solutions are determined. The expressions for velocity, micro-rotation, streamline and pressure distribution are obtained in each case. The streamline patterns are plotted and also the pressure variation with x and y are studied for varying porous media parameter at constant density of fluid and also for varying density of different fluids at constant porous media parameter value.
本文对稳定、均质、不可压缩、平面导电微极性流体在横向磁场作用下流经多孔介质的运动进行了分析研究。通过霍多图变换，将描述连续性、动量和角动量的非线性偏微分方程转换为线性偏微分方程系统。此外，还通过流函数的 Legendre 变换函数获得了流动方程。结果以定理的形式进行了总结。最后，以两个应用实例来说明所开发的理论，并确定了精确解。在每种情况下都得到了速度、微旋转、流线和压力分布的表达式。绘制了流线模式图，并研究了在流体密度恒定的情况下，多孔介质参数变化以及在多孔介质参数值恒定的情况下，不同流体密度变化时压力随 x 和 y 变化的情况。
{"title":"Flow of MHD micropolar fluid through porous medium: a hodograhic approach for exact solution","authors":"Sayantan Sil","doi":"10.56947/amcs.v22.287","DOIUrl":"https://doi.org/10.56947/amcs.v22.287","url":null,"abstract":"An analytical study of the motion of a steady, homogenous, incompressible, plane electrically conducting micropolar fluid flow through a porous medium subjected to a transverse magnetic field is carried out. The governing non linear partial differential equations describing the continuity, momentum and angular momentum are converted into a system of linear partial differential equations by means of hodograph transformation. Further the flow equations have been obtained in terms of Legendre transform function of the stream function. Results are summarized in the form of a theorem. Lastly two examples have been taken as application to illustrate the developed theory and exact solutions are determined. The expressions for velocity, micro-rotation, streamline and pressure distribution are obtained in each case. The streamline patterns are plotted and also the pressure variation with x and y are studied for varying porous media parameter at constant density of fluid and also for varying density of different fluids at constant porous media parameter value.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"31 33","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140372851","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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