Pub Date : 2020-08-01DOI: 10.4172/2168-9679.1000406
G. Yu
Because Newton's third law and Newton's second law proved to be wrong, then according to the new second law of motion and the new third law of motion, the new mechanics principle is produced, the most important and remarkable is, that the momentum is not conserved and the principle of energy is not conserved, it be found.
{"title":"Energy is Not Conserved","authors":"G. Yu","doi":"10.4172/2168-9679.1000406","DOIUrl":"https://doi.org/10.4172/2168-9679.1000406","url":null,"abstract":"Because Newton's third law and Newton's second law proved to be wrong, then according to the new second law of motion and the new third law of motion, the new mechanics principle is produced, the most important and remarkable is, that the momentum is not conserved and the principle of energy is not conserved, it be found.","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"26 1","pages":"1-4"},"PeriodicalIF":0.0,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82479624","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 : 2020-01-01DOI: 10.37421/2168-9679.2020.9.448
Mohamed Moktar Chaffar
In the present paper we define an oriented Star with ??α coefficient α 1 and we further develop the procedure for finding eigenvalues and eigenvectors for an (5 × 5) Starmatrix directly or (5 × 5) Star-matrix indirectly. we give an overview of the methods to compute matrix-multiplication of a Star ??α (generally square 5 × 5) with particular emphasis on the oriented matrix
{"title":"Matrix Representation of a Star","authors":"Mohamed Moktar Chaffar","doi":"10.37421/2168-9679.2020.9.448","DOIUrl":"https://doi.org/10.37421/2168-9679.2020.9.448","url":null,"abstract":"In the present paper we define an oriented Star with ??α coefficient α 1 and we further develop the procedure for finding eigenvalues and eigenvectors for an (5 × 5) Starmatrix directly or (5 × 5) Star-matrix indirectly. we give an overview of the methods to compute matrix-multiplication of a Star ??α (generally square 5 × 5) with particular emphasis on the oriented matrix","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"190 7 1","pages":"1-7"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80165677","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 : 2020-01-01DOI: 10.37421/2168-9679.2020.9.E103
Guillermo Fern, ez Anaya
The journal has been started in the year 2012 and it released its first volume in the same year. Till now, the journal has released 8 volumes by the end of 2019 and is successfully running its 9th Volume. The Journal is an open access publication that features scientific works of considerable significance and impact in all branches of mathematics that concerns with mathematical methods that are typically used in science, engineering, business, and industry. Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role in emphasizing algorithms, numerical methods and symbolic methods with the concept of ubiquitous computing. The journal provides an Open Access platform to analyse new computational and applied techniques for solving the scientific or engineering problems.
{"title":"Editors Note on Applied and Computational Mathematics","authors":"Guillermo Fern, ez Anaya","doi":"10.37421/2168-9679.2020.9.E103","DOIUrl":"https://doi.org/10.37421/2168-9679.2020.9.E103","url":null,"abstract":"The journal has been started in the year 2012 and it released its first volume in the same year. Till now, the journal has released 8 volumes by the end of 2019 and is successfully running its 9th Volume. The Journal is an open access publication that features scientific works of considerable significance and impact in all branches of mathematics that concerns with mathematical methods that are typically used in science, engineering, business, and industry. Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role in emphasizing algorithms, numerical methods and symbolic methods with the concept of ubiquitous computing. The journal provides an Open Access platform to analyse new computational and applied techniques for solving the scientific or engineering problems.","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"7 1","pages":"1-2"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87386727","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 : 2020-01-01DOI: 10.37421/2168-9679.2020.9.451
Joseph Gordon, F. Nyabadza
Formation and the change of individual preferences from one political party to the other has now become a common trend in most democratic countries. Many party members change their preferences over political parties due to the fact that most people are not much satisfied with the trends occurring in their party’s internal democratic principles and as a result change their respective parties. This project work developed and analyzed the use of non-linear mathematical model for the spread of two political parties, the ruling party and the opposition. We used principles borrowed from infectious diseases modeling to track the changes of the membership of each political party taking into consideration preferences. The whole population was assumed to be constant and homogeneously mixed. Steady states were analytically obtained and their stability nature discussed. Conditions for the existence of single parties and the existence of both parties were obtained. Numerical simulations were also performed to support the analytical results. This study has a potential to enrich political dynamics as nations embrace democratic principles.
{"title":"Individual Preferences and the Growth Dynamics of Two Political Parties: Insights through a Simple Mathematical Model","authors":"Joseph Gordon, F. Nyabadza","doi":"10.37421/2168-9679.2020.9.451","DOIUrl":"https://doi.org/10.37421/2168-9679.2020.9.451","url":null,"abstract":"Formation and the change of individual preferences from one political party to the other has now become a common trend in most democratic countries. Many party members change their preferences over political parties due to the fact that most people are not much satisfied with the trends occurring in their party’s internal democratic principles and as a result change their respective parties. This project work developed and analyzed the use of non-linear mathematical model for the spread of two political parties, the ruling party and the opposition. We used principles borrowed from infectious diseases modeling to track the changes of the membership of each political party taking into consideration preferences. The whole population was assumed to be constant and homogeneously mixed. Steady states were analytically obtained and their stability nature discussed. Conditions for the existence of single parties and the existence of both parties were obtained. Numerical simulations were also performed to support the analytical results. This study has a potential to enrich political dynamics as nations embrace democratic principles.","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"5 1","pages":"1-7"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89922435","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 : 2020-01-01DOI: 10.37421/2168-9679.2020.9.450
Mohamed Moktar Chaffar
This paper gives two definitions: Star with coefficient a real and Star System with coefficient α in five unknowns. Examples of Star-System and Star-set are given, a relationship between two star-Systems is noted, and some general theorems are proven.
{"title":"Star with Coefficient a in the set of Real Numbers","authors":"Mohamed Moktar Chaffar","doi":"10.37421/2168-9679.2020.9.450","DOIUrl":"https://doi.org/10.37421/2168-9679.2020.9.450","url":null,"abstract":"This paper gives two definitions: Star with coefficient a real and Star System with coefficient α in five unknowns. Examples of Star-System and Star-set are given, a relationship between two star-Systems is noted, and some general theorems are proven.","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"40 1","pages":"1-8"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89566064","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 : 2020-01-01DOI: 10.4172/2168-9679.1000455
S. Kwao, Francis T. Batsa, Samuel Na, Gaston M. Kuzamunu
Vaccination has been the only preventive mechanism of tuberculosis (TB) yet due to inconsistencies in the efficacy of the mostly used vaccine, Baccille Calmette-Guerin (BCG), re-vaccination has been deemed to be ineffective. In this work, we sought to assess the impact of age-vaccination and re-vaccination on the transmission dynamics of TB. We developed an age-vaccination re- vaccination model to explore the disease transmission dynamics and the impact of re-vaccination on the disease transmission. By applying the vaccine within ten year intervals, we noticed that, there is no significant difference when the vaccine is administered once or many times for people less than 45 years of age. However, re-vaccination can prove to be effective when it is applied either before or immediately after the waning of the first vaccine.
{"title":"Assessing the Impact of Age andndash;Vaccination Structure Models on the Dynamics of Tuberculosis Transmission","authors":"S. Kwao, Francis T. Batsa, Samuel Na, Gaston M. Kuzamunu","doi":"10.4172/2168-9679.1000455","DOIUrl":"https://doi.org/10.4172/2168-9679.1000455","url":null,"abstract":"Vaccination has been the only preventive mechanism of tuberculosis (TB) yet due to inconsistencies in the efficacy of the mostly used vaccine, Baccille Calmette-Guerin (BCG), re-vaccination has been deemed to be ineffective. In this work, we sought to assess the impact of age-vaccination and re-vaccination on the transmission dynamics of TB. We developed an age-vaccination re- vaccination model to explore the disease transmission dynamics and the impact of re-vaccination on the disease transmission. By applying the vaccine within ten year intervals, we noticed that, there is no significant difference when the vaccine is administered once or many times for people less than 45 years of age. However, re-vaccination can prove to be effective when it is applied either before or immediately after the waning of the first vaccine.","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"18 1","pages":"1-6"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77608291","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 : 2020-01-01DOI: 10.4172/2168-9679.1000457
Abidha Monica Gwecho, Wang Shu, Onyango Thomas Mboya
Flow through biological ion channel is understandably complex to support numerous and vital processes that promote life. To account for the biological evolution, mathematical modelling that incorporates electrostatic interaction of ions and effects due to size exclusion has been studied, conceivably with element of difficulty and inaccuracy. In this paper the Nernst-Planck(NP) equation for ion fluxes that uses Lennard Jonnes(LJ) potential to incorporate finite size effects in terms of hard sphere repulsion is examined. To minimize emerging numerical intricacy, the LJ potential is modified by a band limit function with a cut-off length to eliminate troublesome high frequencies in the integral function. This process is achieved through Fourier transform to simplify and hence render the mPNP equation solvable with precision. The resultant modified NP and Poisson equation representing electrostatic potential are then coupled to form system of equation which describes a realistic transport phenomena in ion channel. Consequently, to discretize the 2D steady system of equations, mixed finite element approach based on Taylor hood eight node square referenced elements is adopted. In the method, Galerkin weighted residual approach help obtain sparse matrix and finally Picard Method applied to the nonlinear terms in the algebraic equations to linearize them and improve rate of convergence. Iterative solution for the system of equations then obtained and concentration profiles of ion species under varied steric effects for mPNP are computed and analysed
{"title":"Numerical Approach for Determining Impact of Steric Effects in Biological Ion Channel","authors":"Abidha Monica Gwecho, Wang Shu, Onyango Thomas Mboya","doi":"10.4172/2168-9679.1000457","DOIUrl":"https://doi.org/10.4172/2168-9679.1000457","url":null,"abstract":"Flow through biological ion channel is understandably complex to support numerous and vital processes that promote life. To account for the biological evolution, mathematical modelling that incorporates electrostatic interaction of ions and effects due to size exclusion has been studied, conceivably with element of difficulty and inaccuracy. In this paper the Nernst-Planck(NP) equation for ion fluxes that uses Lennard Jonnes(LJ) potential to incorporate finite size effects in terms of hard sphere repulsion is examined. To minimize emerging numerical intricacy, the LJ potential is modified by a band limit function with a cut-off length to eliminate troublesome high frequencies in the integral function. This process is achieved through Fourier transform to simplify and hence render the mPNP equation solvable with precision. The resultant modified NP and Poisson equation representing electrostatic potential are then coupled to form system of equation which describes a realistic transport phenomena in ion channel. Consequently, to discretize the 2D steady system of equations, mixed finite element approach based on Taylor hood eight node square referenced elements is adopted. In the method, Galerkin weighted residual approach help obtain sparse matrix and finally Picard Method applied to the nonlinear terms in the algebraic equations to linearize them and improve rate of convergence. Iterative solution for the system of equations then obtained and concentration profiles of ion species under varied steric effects for mPNP are computed and analysed","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"9 1","pages":"1-4"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75033089","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 : 2020-01-01DOI: 10.4172/2168-9679.1000456
J. Pedro, M. Banda, P. Sibanda
In this paper, a new one-dimensional Finite Volume Method for Hyperbolic Conservation Laws is presented. The method consists in an improved numerical inter-cell flux function at the element interface. To back theoretically the method, necessary components for convergence are presented. Therefore, it is proved that the method is consistent with the P.D.E and that it is monotone with respect its variables. Moreover, to validate the approach and show its efficiency, we compute several one-dimensional test problems with discontinuous solutions and we make comparisons with traditional methods. The results show an improvement on the non-oscillatory shock-capturing properties based on the new approach.
{"title":"A New One-Dimensional Finite Volume Method for Hyperbolic Conservation Laws","authors":"J. Pedro, M. Banda, P. Sibanda","doi":"10.4172/2168-9679.1000456","DOIUrl":"https://doi.org/10.4172/2168-9679.1000456","url":null,"abstract":"In this paper, a new one-dimensional Finite Volume Method for Hyperbolic Conservation Laws is presented. The method consists in an improved numerical inter-cell flux function at the element interface. To back theoretically the method, necessary components for convergence are presented. Therefore, it is proved that the method is consistent with the P.D.E and that it is monotone with respect its variables. Moreover, to validate the approach and show its efficiency, we compute several one-dimensional test problems with discontinuous solutions and we make comparisons with traditional methods. The results show an improvement on the non-oscillatory shock-capturing properties based on the new approach.","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"5 1","pages":"1-9"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79191658","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 : 2020-01-01DOI: 10.37421/2168-9679.2020.9.E102
Kyriaki D. Tsilika
The journal has been started in the year 2012 and it released its first volume in the same year. Till now, the journal has released 8 volumes by the end of 2019 and is successfully running its 9th Volume. The Journal is an open access publication that features scientific works of considerable significance and impact in all branches of mathematics that concerns with mathematical methods that are typically used in science, engineering, business, and industry. Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role in emphasizing algorithms
{"title":"Editor Note on Journal of Applied and Computational Mathematics July","authors":"Kyriaki D. Tsilika","doi":"10.37421/2168-9679.2020.9.E102","DOIUrl":"https://doi.org/10.37421/2168-9679.2020.9.E102","url":null,"abstract":"The journal has been started in the year 2012 and it released its first volume in the same year. Till now, the journal has released 8 volumes by the end of 2019 and is successfully running its 9th Volume. The Journal is an open access publication that features scientific works of considerable significance and impact in all branches of mathematics that concerns with mathematical methods that are typically used in science, engineering, business, and industry. Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role in emphasizing algorithms","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"2 14","pages":"1-2"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91506380","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 : 2020-01-01DOI: 10.4172/2168-9679.1000448
Faragó István
Journal of Applied & Computational Mathematics (JACM) successfully released issues in 2019. It is the most preferred and highly accessed Journal in the field science where computing plays a central and essential role in emphasizing algorithms, numerical methods and symbolic methods with the concept of ubiquitous computing. The journal provides an Open Access platform to analyze new computational and applied techniques for solving the scientific or engineering problems
{"title":"Editor note on Journal of Applied and Computational Mathematics","authors":"Faragó István","doi":"10.4172/2168-9679.1000448","DOIUrl":"https://doi.org/10.4172/2168-9679.1000448","url":null,"abstract":"Journal of Applied & Computational Mathematics (JACM) successfully released issues in 2019. It is the most preferred and highly accessed Journal in the field science where computing plays a central and essential role in emphasizing algorithms, numerical methods and symbolic methods with the concept of ubiquitous computing. The journal provides an Open Access platform to analyze new computational and applied techniques for solving the scientific or engineering problems","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"3 1","pages":"1-1"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82096671","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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