Pub Date : 2021-05-08DOI: 10.11648/J.PAMJ.20211002.12
Peter Jean‐Paul, S. Wahid
Most mathematician, have accepted that a constant divided by zero is undefined. However, accepting this situation is an unsatisfactory solution to the problem as division by zero has arisen frequently enough in mathematics and science to warrant some serious consideration. The aim of this paper was to propose and prove the existence of a new number set in which division by zero is well defined. To do this, the paper first uses set theory to develop the idea of unstructured numbers and uses this new number to create a new number set called “Semi-structured Complex Number set” (Ś). It was then shown that a semi-structured complex number is a three-dimensional number which can be represented in the xyz-space with the x-axis being the real axis, the y-axis the imaginary axis and the z-axis the unstructured axis. A unit of rotation p was defined that enabled rotation of a point along the xy-, xz- and yz- planes. The field axioms were then used to show that the set is a “complete ordered field” and hence prove its existence. Examples of how these semi-structured complex numbers are used algebraically are provided. The successful development of this proposed number set has implications not just in the field of mathematics but in other areas of science where division by zero is essential.
{"title":"Unstructured and Semi-structured Complex Numbers: A Solution to Division by Zero","authors":"Peter Jean‐Paul, S. Wahid","doi":"10.11648/J.PAMJ.20211002.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20211002.12","url":null,"abstract":"Most mathematician, have accepted that a constant divided by zero is undefined. However, accepting this situation is an unsatisfactory solution to the problem as division by zero has arisen frequently enough in mathematics and science to warrant some serious consideration. The aim of this paper was to propose and prove the existence of a new number set in which division by zero is well defined. To do this, the paper first uses set theory to develop the idea of unstructured numbers and uses this new number to create a new number set called “Semi-structured Complex Number set” (Ś). It was then shown that a semi-structured complex number is a three-dimensional number which can be represented in the xyz-space with the x-axis being the real axis, the y-axis the imaginary axis and the z-axis the unstructured axis. A unit of rotation p was defined that enabled rotation of a point along the xy-, xz- and yz- planes. The field axioms were then used to show that the set is a “complete ordered field” and hence prove its existence. Examples of how these semi-structured complex numbers are used algebraically are provided. The successful development of this proposed number set has implications not just in the field of mathematics but in other areas of science where division by zero is essential.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"647 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76833376","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 : 2021-03-26DOI: 10.11648/J.PAMJ.20211002.11
J. A. Nanware
In this paper, qualitative properties such as existence-uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative with initial conditions have been studied. Lower and upper solutions are defined for the problem under investigation. Comparison results are used to develop monotone technique for finite system of differential equations involving R-L sequential fractional derivative with initial conditions when the functions on the right hand side are mixed quasi-monotone. Two convergent monotone sequences are obtained by introducing monotone operator. Lipschitz condition is the key part of the study. Minimal and maximal solutions are obtained by using developed technique. Existence and uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative is also proved as an application of the technique.
{"title":"Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative","authors":"J. A. Nanware","doi":"10.11648/J.PAMJ.20211002.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20211002.11","url":null,"abstract":"In this paper, qualitative properties such as existence-uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative with initial conditions have been studied. Lower and upper solutions are defined for the problem under investigation. Comparison results are used to develop monotone technique for finite system of differential equations involving R-L sequential fractional derivative with initial conditions when the functions on the right hand side are mixed quasi-monotone. Two convergent monotone sequences are obtained by introducing monotone operator. Lipschitz condition is the key part of the study. Minimal and maximal solutions are obtained by using developed technique. Existence and uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative is also proved as an application of the technique.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"13 1","pages":"38"},"PeriodicalIF":0.2,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87015961","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 : 2021-03-04DOI: 10.11648/J.PAMJ.20211001.12
B. Bassey, A. O. Henry
Devastatingly, in spite of the long standing research works on HIV/AIDS infection and treatment dynamics, reviews of existing models clearly shown that the behavioral attitude to treatment consistency by those screened to become aware and those receiving treatment have not been given the desired attention. Moreso, the inconsistency following avoidable treatment truncation and later resumption of treatment by these classes of infectives, which could lead to colossal drug abuse is also not accorded the much expected consideration. Therefore, in this present study, we sought and formulated a nonlinear 6-Dimensional deterministic mathematical HIV/AIDS dynamic model that accounted for the global stability analysis of the role of antiretroviral therapy abuse for the treatment of HIV/AIDS epidemic. The model is structured upon dynamical interactions between 6-subpopulations and HI-virus under bilinear control functions with constant screening of the susceptible. It is assumed that the rate of resumption of ART upon truncation is less than initial ART truncation following the incorporation of HIV aware infectives not ready to receive ART treatment and HIV aware infectives with truncated treatment protocol The system mathematical well-posedness was investigated and model reproduction number determined for both off- treatment (with value ) and for onset-treatment (with value ). We considered the model for off-treatment and thereafter by incorporating LaSalle’s invariant principle into classical Lyapunov function method, we presented an approach for the global stability analysis of the role of ART abuse in HIV/AIDS treatment. Furthermore, the analysis and results of this paper presented a dynamic methodological application of bilinear control functions and an impeccable understanding of the fundamental mechanism in HIV/AIDS treatment in the presence of ART abuse. Using in-built Runge-Kutta of order of precision 4 in a Mathcad surface, numerical validity of model is conducted to investigate the study theoretical and analytical predictions. Results shows that application of onset-treatment functions with trend of ART abuse yield tremendous reduction in HIV/AIDS infection epidemic following the recovery rate of the susceptible population with value increasing from 0.5 cells/mm3 to 1.203 cells/mm3 within the first months and attained stability of 0.62 cells/mm3 through the time interval of 20- 30 months.
{"title":"Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics","authors":"B. Bassey, A. O. Henry","doi":"10.11648/J.PAMJ.20211001.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20211001.12","url":null,"abstract":"Devastatingly, in spite of the long standing research works on HIV/AIDS infection and treatment dynamics, reviews of existing models clearly shown that the behavioral attitude to treatment consistency by those screened to become aware and those receiving treatment have not been given the desired attention. Moreso, the inconsistency following avoidable treatment truncation and later resumption of treatment by these classes of infectives, which could lead to colossal drug abuse is also not accorded the much expected consideration. Therefore, in this present study, we sought and formulated a nonlinear 6-Dimensional deterministic mathematical HIV/AIDS dynamic model that accounted for the global stability analysis of the role of antiretroviral therapy abuse for the treatment of HIV/AIDS epidemic. The model is structured upon dynamical interactions between 6-subpopulations and HI-virus under bilinear control functions with constant screening of the susceptible. It is assumed that the rate of resumption of ART upon truncation is less than initial ART truncation following the incorporation of HIV aware infectives not ready to receive ART treatment and HIV aware infectives with truncated treatment protocol The system mathematical well-posedness was investigated and model reproduction number determined for both off- treatment (with value ) and for onset-treatment (with value ). We considered the model for off-treatment and thereafter by incorporating LaSalle’s invariant principle into classical Lyapunov function method, we presented an approach for the global stability analysis of the role of ART abuse in HIV/AIDS treatment. Furthermore, the analysis and results of this paper presented a dynamic methodological application of bilinear control functions and an impeccable understanding of the fundamental mechanism in HIV/AIDS treatment in the presence of ART abuse. Using in-built Runge-Kutta of order of precision 4 in a Mathcad surface, numerical validity of model is conducted to investigate the study theoretical and analytical predictions. Results shows that application of onset-treatment functions with trend of ART abuse yield tremendous reduction in HIV/AIDS infection epidemic following the recovery rate of the susceptible population with value increasing from 0.5 cells/mm3 to 1.203 cells/mm3 within the first months and attained stability of 0.62 cells/mm3 through the time interval of 20- 30 months.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"46 1","pages":"9"},"PeriodicalIF":0.2,"publicationDate":"2021-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91291310","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}
This paper describes a method for the numerical solution of linear system of equations. The main interest of refinement of accelerated over relaxation (RAOR) method is to minimize the spectral radius of the iteration matrix in order to increase the rate of convergence of the method comparing to the accelerated over relaxation (AOR) method. That is minimizing the spectral radius means increasing the rate of convergence of the method. This motivates us to refine the refinement of accelerated over relaxation method called second refinement of accelerated over relaxation method (SRAOR). In this paper, we proposed a second refinement of accelerated over relaxation method, which decreases the spectral radius of the iteration matrix significantly comparing to that of the refinement of accelerated over relaxation (RAOR) method. The method is a two-parameter generalization of the refinement of accelerated over relaxation methods and the optimal value of each parameter is derived. The third, fourth and in general the kth refinement of accelerated methods are also derived. The spectral radius of the iteration matrix and convergence criteria of the second refinement of accelerated over relaxation (SRAOR) are discussed. Finally a numerical example is given in order to see the efficiency of the proposed method comparing with that of the existing methods.
{"title":"Second Refinement of Accelerated over Relaxation Method for the Solution of Linear System","authors":"Wondosen Lisanu Assefa, Ashenafi Woldeselassie Teklehaymanot","doi":"10.11648/J.PAMJ.20211001.13","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20211001.13","url":null,"abstract":"This paper describes a method for the numerical solution of linear system of equations. The main interest of refinement of accelerated over relaxation (RAOR) method is to minimize the spectral radius of the iteration matrix in order to increase the rate of convergence of the method comparing to the accelerated over relaxation (AOR) method. That is minimizing the spectral radius means increasing the rate of convergence of the method. This motivates us to refine the refinement of accelerated over relaxation method called second refinement of accelerated over relaxation method (SRAOR). In this paper, we proposed a second refinement of accelerated over relaxation method, which decreases the spectral radius of the iteration matrix significantly comparing to that of the refinement of accelerated over relaxation (RAOR) method. The method is a two-parameter generalization of the refinement of accelerated over relaxation methods and the optimal value of each parameter is derived. The third, fourth and in general the kth refinement of accelerated methods are also derived. The spectral radius of the iteration matrix and convergence criteria of the second refinement of accelerated over relaxation (SRAOR) are discussed. Finally a numerical example is given in order to see the efficiency of the proposed method comparing with that of the existing methods.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"57 2 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83396844","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 : 2021-02-10DOI: 10.11648/J.PAMJ.20211001.11
David Muriuki Gikunju, P. Kamaku, Augustus Wali Nzomo
Error correcting coding is an effective technique of detecting and correcting errors which may occur due to environmental interference or physical defects such as human errors in the communication channels. The International Standard Serial Number code is internationally used for identifying the title of serial publications. This paper analyzes the efficiency of the international standard serial number code as an error correcting scheme. Moreover, the paper explores on the factors which affect the efficiency of any error correcting scheme. The study utilizes weight checksum technique to detect and correct error(s) in a code word. It is clear that ISSN code is not an efficient error coding scheme. ISSN code is only reliable in error detection. ISSN code can detect any error in the code iff the weight checksum equation does not hold. However, the code does not detect silent errors. The study develops a new efficient and robust modified ISSN code that is efficient in error detection and correction capabilities. The code has dual mechanism for error detection and correction in a code word. If the weight checksum equation does not hold and secondly, if the conditions for the generating equation do not hold. Modified ISSN code can detect and correct silent errors in a code word. Modified ISSN code is an efficient error coding scheme for it is efficient in error detection and correction capabilities.
{"title":"Efficiency of International Standard Serial Number Code as an Error Correcting Scheme","authors":"David Muriuki Gikunju, P. Kamaku, Augustus Wali Nzomo","doi":"10.11648/J.PAMJ.20211001.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20211001.11","url":null,"abstract":"Error correcting coding is an effective technique of detecting and correcting errors which may occur due to environmental interference or physical defects such as human errors in the communication channels. The International Standard Serial Number code is internationally used for identifying the title of serial publications. This paper analyzes the efficiency of the international standard serial number code as an error correcting scheme. Moreover, the paper explores on the factors which affect the efficiency of any error correcting scheme. The study utilizes weight checksum technique to detect and correct error(s) in a code word. It is clear that ISSN code is not an efficient error coding scheme. ISSN code is only reliable in error detection. ISSN code can detect any error in the code iff the weight checksum equation does not hold. However, the code does not detect silent errors. The study develops a new efficient and robust modified ISSN code that is efficient in error detection and correction capabilities. The code has dual mechanism for error detection and correction in a code word. If the weight checksum equation does not hold and secondly, if the conditions for the generating equation do not hold. Modified ISSN code can detect and correct silent errors in a code word. Modified ISSN code is an efficient error coding scheme for it is efficient in error detection and correction capabilities.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"20 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84458245","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 : 2021-01-01DOI: 10.11648/j.pamj.20211005.12
Magdy Salah El-Azab, M. Shokry, Reham Emad Aly
{"title":"Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System","authors":"Magdy Salah El-Azab, M. Shokry, Reham Emad Aly","doi":"10.11648/j.pamj.20211005.12","DOIUrl":"https://doi.org/10.11648/j.pamj.20211005.12","url":null,"abstract":"","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"54 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81111534","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 : 2021-01-01DOI: 10.11648/j.pamj.20211006.11
Zoïnabo Savadogo, Sougoursi Jean Yves Zaré, Wambié Zongo, Somdouda Sawadogo, B. Somé
: Social choice theory includes the study of voting methods. In the literature on social choice theory many methods exist, the main objective of all these methods is the determination of a good method. However, many of these methods give controversial results which often lead to disputes. It should also be noted that sometimes, regardless of the method used, there are people who are not ready to accept the results given by the ballot box. The ideal would be to find a method with good properties, because it seems that there are no completely satisfactory methods. Since the goal of a voting method is to reconcile several points of view into a general interest, one should focus on the properties. The geometric mean does not lead to a compensation of weak criteria by stronger ones as it is the case with the arithmetic mean. Indeed, by using the geometric mean, even if only one criterion is very weak and the others are very strong, a candidate may not be well ranked; moreover, assent voting is very well appreciated in the literature by many authors and also generates huge opportunities. This justifies our choice in this work to combine geometric mean and assent voting to develop a method with good properties.
{"title":"New Innovative Method in the Field of Social Choice Theory","authors":"Zoïnabo Savadogo, Sougoursi Jean Yves Zaré, Wambié Zongo, Somdouda Sawadogo, B. Somé","doi":"10.11648/j.pamj.20211006.11","DOIUrl":"https://doi.org/10.11648/j.pamj.20211006.11","url":null,"abstract":": Social choice theory includes the study of voting methods. In the literature on social choice theory many methods exist, the main objective of all these methods is the determination of a good method. However, many of these methods give controversial results which often lead to disputes. It should also be noted that sometimes, regardless of the method used, there are people who are not ready to accept the results given by the ballot box. The ideal would be to find a method with good properties, because it seems that there are no completely satisfactory methods. Since the goal of a voting method is to reconcile several points of view into a general interest, one should focus on the properties. The geometric mean does not lead to a compensation of weak criteria by stronger ones as it is the case with the arithmetic mean. Indeed, by using the geometric mean, even if only one criterion is very weak and the others are very strong, a candidate may not be well ranked; moreover, assent voting is very well appreciated in the literature by many authors and also generates huge opportunities. This justifies our choice in this work to combine geometric mean and assent voting to develop a method with good properties.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"113 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82201888","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 : 2021-01-01DOI: 10.11648/j.pamj.20211004.12
Ezra Precious Ndidiamaka, Okonta Charles Arinze, Okoro Udu Ukpai
{"title":"Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models","authors":"Ezra Precious Ndidiamaka, Okonta Charles Arinze, Okoro Udu Ukpai","doi":"10.11648/j.pamj.20211004.12","DOIUrl":"https://doi.org/10.11648/j.pamj.20211004.12","url":null,"abstract":"","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"708 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74763069","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 : 2020-11-11DOI: 10.11648/j.pamj.20200906.11
Fekadu Tadege Kobe
This paper proposes and analyses a basic deterministic mathematical model to investigate Simulation for controlling the spread of malaria Diseases Transmission dynamics. The model has seven non-linear differential equations which describe the control of malaria with two state variables for mosquito’s populations and five state variables for human’s population. To represent the classification of human population we have included protection and treatment compartments to the basic SIR epidemic model and extended it to SPITR model and to introduce the new SPITR modified model by adding vaccination for the transmission dynamics of malaria with four time dependent control measures in Ethiopia Insecticide treated bed nets (ITNS), Treatments, Indoor Residual Spray (IRs) and Intermittent preventive treatment of malaria in pregnancy (IPTP). The models are analyzed qualitatively to determine criteria for control of a malaria transmission dynamics and are used to calculate the basic reproduction R0. The equilibria of malaria models are determined. In addition to having a disease-free equilibrium, which is globally asymptotically stable when the R0<1, the basic malaria model manifest one's possession of (a quality of) the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists (at the same time) with a stable endemic equilibrium for a certain range of associated reproduction number less than one. The results also designing the effects of some model parameters, the infection rate and biting rate. The numerical analysis and numerical simulation results of the model suggested that the most effective strategies for controlling or eradicating the spread of malaria were suggest using insecticide treated bed nets, indoor residual spraying, prompt effective diagnosis and treatment of infected individuals with vaccination is more effective for children.
{"title":"Mathematical Model of Controlling the Spread of Malaria Disease Using Intervention Strategies","authors":"Fekadu Tadege Kobe","doi":"10.11648/j.pamj.20200906.11","DOIUrl":"https://doi.org/10.11648/j.pamj.20200906.11","url":null,"abstract":"This paper proposes and analyses a basic deterministic mathematical model to investigate Simulation for controlling the spread of malaria Diseases Transmission dynamics. The model has seven non-linear differential equations which describe the control of malaria with two state variables for mosquito’s populations and five state variables for human’s population. To represent the classification of human population we have included protection and treatment compartments to the basic SIR epidemic model and extended it to SPITR model and to introduce the new SPITR modified model by adding vaccination for the transmission dynamics of malaria with four time dependent control measures in Ethiopia Insecticide treated bed nets (ITNS), Treatments, Indoor Residual Spray (IRs) and Intermittent preventive treatment of malaria in pregnancy (IPTP). The models are analyzed qualitatively to determine criteria for control of a malaria transmission dynamics and are used to calculate the basic reproduction R0. The equilibria of malaria models are determined. In addition to having a disease-free equilibrium, which is globally asymptotically stable when the R0<1, the basic malaria model manifest one's possession of (a quality of) the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists (at the same time) with a stable endemic equilibrium for a certain range of associated reproduction number less than one. The results also designing the effects of some model parameters, the infection rate and biting rate. The numerical analysis and numerical simulation results of the model suggested that the most effective strategies for controlling or eradicating the spread of malaria were suggest using insecticide treated bed nets, indoor residual spraying, prompt effective diagnosis and treatment of infected individuals with vaccination is more effective for children.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"1 1","pages":"101"},"PeriodicalIF":0.2,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83949600","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 : 2020-10-28DOI: 10.11648/J.PAMJ.20200905.13
G. An, Ying Yao
Suppose that is a real or complex unital Banach *-algebra, is a unital Banach -bimodule, and G ∈ is a left separating point of . In this paper, we investigate whether the additive mapping δ: → satisfies the condition A,B ∈ , AB = G ⇒ Aδ(B)+δ(A)B*= δ(G) characterize Jordan *-derivations. Initially, we prove that if is a real unital C*-algebra and G = I is the unit element in , then δ (non-necessarily continuous) is a Jordan *-derivation. In addition, we prove that if is a real unital C*-algebra and δ is continuous, then δ is a Jordan *-derivation. Finally, we show that if is a complex factor von Neumann algebra and δ is linear, then δ (non-necessarily continuous) is equal to zero.
{"title":"Characterizations of Jordan *-derivations on Banach *-algebras","authors":"G. An, Ying Yao","doi":"10.11648/J.PAMJ.20200905.13","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20200905.13","url":null,"abstract":"Suppose that is a real or complex unital Banach *-algebra, is a unital Banach -bimodule, and G ∈ is a left separating point of . In this paper, we investigate whether the additive mapping δ: → satisfies the condition A,B ∈ , AB = G ⇒ Aδ(B)+δ(A)B*= δ(G) characterize Jordan *-derivations. Initially, we prove that if is a real unital C*-algebra and G = I is the unit element in , then δ (non-necessarily continuous) is a Jordan *-derivation. In addition, we prove that if is a real unital C*-algebra and δ is continuous, then δ is a Jordan *-derivation. Finally, we show that if is a complex factor von Neumann algebra and δ is linear, then δ (non-necessarily continuous) is equal to zero.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"31 1","pages":"96"},"PeriodicalIF":0.2,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87244553","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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