Pub Date : 2017-10-30DOI: 10.11648/J.PAMJ.20170605.13
Nedal Hassan Elbadowi Eljaneid
In the present paper using precise results on the solutions of linear elliptic differential operators with Holder continuous coefficient as well as a variant of the Lery - Schauder method and the gal of this paper to find an adequate degree theory for the infinite dimensional setting and to extend the theory of homotopy classes of maps form to to homotopy classes of maps on infinite dimensional spaces.
{"title":"The Leray-Schauder Degree as Topological Method Solution of Nonlinear Elliptic Equations","authors":"Nedal Hassan Elbadowi Eljaneid","doi":"10.11648/J.PAMJ.20170605.13","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20170605.13","url":null,"abstract":"In the present paper using precise results on the solutions of linear elliptic differential operators with Holder continuous coefficient as well as a variant of the Lery - Schauder method and the gal of this paper to find an adequate degree theory for the infinite dimensional setting and to extend the theory of homotopy classes of maps form to to homotopy classes of maps on infinite dimensional spaces.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"71 1","pages":"148"},"PeriodicalIF":0.2,"publicationDate":"2017-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73370308","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 : 2017-10-26DOI: 10.11648/j.pamj.20170605.12
Xu Hong
Model-based approaches have many applications in bioinformatics studies. Fermat’s last theorem is a theorem in number theory. This paper presented a model-based approach for the demonstration of Fermat’s Last Theorem (FLT). Through the establishment of mathematical model, Fermat’s Last Theorem (FLT) is converted into a problem for feasible solutions in linear programming. By prompting assumptions, and refuting the assumptions, it is demonstrated that Fermat’s Last Theorem is right. The model-based approach for the demonstration of Fermat's Last Theorem (FLT) can assist scientific researchers in biological researches.
{"title":"A Model-Based Approach for The Demonstration of Fermat’s Last Theorem","authors":"Xu Hong","doi":"10.11648/j.pamj.20170605.12","DOIUrl":"https://doi.org/10.11648/j.pamj.20170605.12","url":null,"abstract":"Model-based approaches have many applications in bioinformatics studies. Fermat’s last theorem is a theorem in number theory. This paper presented a model-based approach for the demonstration of Fermat’s Last Theorem (FLT). Through the establishment of mathematical model, Fermat’s Last Theorem (FLT) is converted into a problem for feasible solutions in linear programming. By prompting assumptions, and refuting the assumptions, it is demonstrated that Fermat’s Last Theorem is right. The model-based approach for the demonstration of Fermat's Last Theorem (FLT) can assist scientific researchers in biological researches.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"43 1","pages":"144"},"PeriodicalIF":0.2,"publicationDate":"2017-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80882359","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 is aimed at discussing and comparing the performance of standard method with its hybrid method of the same step number for the solution of first order initial value problems of ordinary differential equations. The continuous formulation for both methods was obtained via interpolation and collocation with the application of the shifted Legendre polynomials as approximate solution which was evaluated at some selected grid points to generate the discrete block methods. The order, consistency, zero stability, convergent and stability regions for both methods were investigated. The methods were then applied in block form as simultaneous numerical integrators over non-overlapping intervals. The results revealed that the hybrid method converges faster than the standard method and has minimum absolute error values.
{"title":"On One Justification on the Use of Hybrids for the Solution of First Order Initial Value Problems of Ordinary Differential Equations","authors":"Kamoh Nathaniel Mahwash, Gyemang Dauda Gyang, Soomiyol Mrumun Comfort","doi":"10.11648/j.pamj.20170605.11","DOIUrl":"https://doi.org/10.11648/j.pamj.20170605.11","url":null,"abstract":"This paper is aimed at discussing and comparing the performance of standard method with its hybrid method of the same step number for the solution of first order initial value problems of ordinary differential equations. The continuous formulation for both methods was obtained via interpolation and collocation with the application of the shifted Legendre polynomials as approximate solution which was evaluated at some selected grid points to generate the discrete block methods. The order, consistency, zero stability, convergent and stability regions for both methods were investigated. The methods were then applied in block form as simultaneous numerical integrators over non-overlapping intervals. The results revealed that the hybrid method converges faster than the standard method and has minimum absolute error values.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"29 1","pages":"137"},"PeriodicalIF":0.2,"publicationDate":"2017-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84825597","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 : 2017-08-06DOI: 10.11648/j.pamj.20170604.14
Geomira George Sanga, O. Makinde, E. Massawe, L. Namkinga
The deterministic model for co-infection of cervical cancer and HIV (Human Immunodeficiency Virus) diseases is formulated and rigorously analyzed. The optimal control theory is employed to the model to study the level of effort is needed to control the transmission of co-infection of cervical cancer and HIV diseases using three controls; prevention, screening and treatment control strategies. Numerical solutions show a remarkable decrease of infected individuals with HPV (Human Papilloma Virus) infection, cervical cancer, cervical cancer and HIV, cervical cancer and AIDS (Acquire Immunodeficiency Syndrome), HIV infection and AIDS after applying the combination of the optimal prevention, screening and treatment control strategies. However, Incremental Cost-Effective Ratio (ICER) shows that the best control strategy of minimizing cervical cancer among HIV-infected individuals with low cost is to use the combination of prevention and treatment control strategies.
{"title":"Cervical Cancer and HIV Diseases Co-dynamics with Optimal Control and Cost Effectiveness","authors":"Geomira George Sanga, O. Makinde, E. Massawe, L. Namkinga","doi":"10.11648/j.pamj.20170604.14","DOIUrl":"https://doi.org/10.11648/j.pamj.20170604.14","url":null,"abstract":"The deterministic model for co-infection of cervical cancer and HIV (Human Immunodeficiency Virus) diseases is formulated and rigorously analyzed. The optimal control theory is employed to the model to study the level of effort is needed to control the transmission of co-infection of cervical cancer and HIV diseases using three controls; prevention, screening and treatment control strategies. Numerical solutions show a remarkable decrease of infected individuals with HPV (Human Papilloma Virus) infection, cervical cancer, cervical cancer and HIV, cervical cancer and AIDS (Acquire Immunodeficiency Syndrome), HIV infection and AIDS after applying the combination of the optimal prevention, screening and treatment control strategies. However, Incremental Cost-Effective Ratio (ICER) shows that the best control strategy of minimizing cervical cancer among HIV-infected individuals with low cost is to use the combination of prevention and treatment control strategies.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"40 1","pages":"124"},"PeriodicalIF":0.2,"publicationDate":"2017-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78815944","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 : 2017-07-31DOI: 10.11648/J.PAMJ.20170604.13
Jiangping Xiao
Congruence is a special type of equivalence relation which plays a vital role in the study of quotient structures of different algebraic structures. The purpose of this paper is to study the quotient structure of ( n, m )-semigroup by using the notion of congruence in ( n, m )-semigroup. Firstly, the concept of homomorphism on ( n, m )-semigroup is introduced. Then, the concept of congruence on ( n, m )-semigroup is defined, and some basic properties are studied. Finally, it is proved that the set of congruences on an ( n, m )-semigroup is a complete lattice. All these generalize the corresponding notions and results for usual binary and ternary semigroups.
{"title":"A Study of Congruence on ( n, m )-semigroup","authors":"Jiangping Xiao","doi":"10.11648/J.PAMJ.20170604.13","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20170604.13","url":null,"abstract":"Congruence is a special type of equivalence relation which plays a vital role in the study of quotient structures of different algebraic structures. The purpose of this paper is to study the quotient structure of ( n, m )-semigroup by using the notion of congruence in ( n, m )-semigroup. Firstly, the concept of homomorphism on ( n, m )-semigroup is introduced. Then, the concept of congruence on ( n, m )-semigroup is defined, and some basic properties are studied. Finally, it is proved that the set of congruences on an ( n, m )-semigroup is a complete lattice. All these generalize the corresponding notions and results for usual binary and ternary semigroups.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"56 1","pages":"120"},"PeriodicalIF":0.2,"publicationDate":"2017-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88221627","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 : 2017-07-20DOI: 10.11648/J.PAMJ.20170604.12
M. Malkov
The Galois algebra and the universal Post algebra of compositions are constructed. The universe of the Galois algebra contains relations, both discrete and continuous. The found proofs of Galois connections are shorter and simpler. It is noted that anti-isomorphism of the two algebras of functions and of relations allows to transfer the results of the modern algebra of functions to the algebra of relations, and vice versa, to transfer the results of the modern algebra of relations to the algebra of functions. A new Post algebra is constructed by using pre-iterative algebra and by adding relations as one more universe of the algebra. The universes of relations and functions are discrete or continuous. It is proved that the Post algebra of relations and the Galois algebra are equal. This allows to replace the operation of conjunction by the operation of substitution and to exclude the operation of exist quantifier.
{"title":"Galois and Post Algebras of Compositions (Superpositions)","authors":"M. Malkov","doi":"10.11648/J.PAMJ.20170604.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20170604.12","url":null,"abstract":"The Galois algebra and the universal Post algebra of compositions are constructed. The universe of the Galois algebra contains relations, both discrete and continuous. The found proofs of Galois connections are shorter and simpler. It is noted that anti-isomorphism of the two algebras of functions and of relations allows to transfer the results of the modern algebra of functions to the algebra of relations, and vice versa, to transfer the results of the modern algebra of relations to the algebra of functions. A new Post algebra is constructed by using pre-iterative algebra and by adding relations as one more universe of the algebra. The universes of relations and functions are discrete or continuous. It is proved that the Post algebra of relations and the Galois algebra are equal. This allows to replace the operation of conjunction by the operation of substitution and to exclude the operation of exist quantifier.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"36 1","pages":"114"},"PeriodicalIF":0.2,"publicationDate":"2017-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90200775","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 : 2017-07-18DOI: 10.11648/j.pamj.20170604.11
Mashadi, Chitra Valentika, S. Gemawati, Hasriati
In this article we discuss Napoleon’s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. The proof of Napoleon’s theorem is carried out using a congruence approach. In the last section we discuss the development of Napoleon’s theorem on a quadrilateral by drawing a square from the midpoint of a line connecting each of the angle points of each square, where each of the squares is constructed on any quadrilateral and forming a square by using the row line concept.
{"title":"The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction","authors":"Mashadi, Chitra Valentika, S. Gemawati, Hasriati","doi":"10.11648/j.pamj.20170604.11","DOIUrl":"https://doi.org/10.11648/j.pamj.20170604.11","url":null,"abstract":"In this article we discuss Napoleon’s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. The proof of Napoleon’s theorem is carried out using a congruence approach. In the last section we discuss the development of Napoleon’s theorem on a quadrilateral by drawing a square from the midpoint of a line connecting each of the angle points of each square, where each of the squares is constructed on any quadrilateral and forming a square by using the row line concept.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"04 1","pages":"108"},"PeriodicalIF":0.2,"publicationDate":"2017-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85963453","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 : 2017-06-29DOI: 10.11648/J.PAMJ.20170603.12
I. N. Sitati, B. Nzimbi, S. Luketero, J. M. Khalagai
In this paper, notions of A-almost similarity and the Lie algebra of A-skew-adjoint operators in Hilbert space are introduced. In this context, A is a self-adjoint and an invertible operator. It is shown that A-almost similarity is an equivalence relation. Conditions under which A-almost similarity implies similarity are outlined and in which case their spectra is located. Conditions under which an A-skew adjoint operator reduces to a skew adjoint operator are also given. By relaxing some conditions on normal and unitary operators, new results on A -normal, binormal and A-binormal operators are proved. Finally A-skew adjoint operators are characterized and the relationship between A-self- adjoint and A-skew adjoint operators is given.
{"title":"Remarks on A -skew-adjoint, A -almost Similarity Equivalence and Other Operators in Hilbert Space","authors":"I. N. Sitati, B. Nzimbi, S. Luketero, J. M. Khalagai","doi":"10.11648/J.PAMJ.20170603.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20170603.12","url":null,"abstract":"In this paper, notions of A-almost similarity and the Lie algebra of A-skew-adjoint operators in Hilbert space are introduced. In this context, A is a self-adjoint and an invertible operator. It is shown that A-almost similarity is an equivalence relation. Conditions under which A-almost similarity implies similarity are outlined and in which case their spectra is located. Conditions under which an A-skew adjoint operator reduces to a skew adjoint operator are also given. By relaxing some conditions on normal and unitary operators, new results on A -normal, binormal and A-binormal operators are proved. Finally A-skew adjoint operators are characterized and the relationship between A-self- adjoint and A-skew adjoint operators is given.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"56 1","pages":"101"},"PeriodicalIF":0.2,"publicationDate":"2017-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72795252","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 : 2017-05-27DOI: 10.11648/j.pamj.20170603.11
Nirina Gilbert Rasolofoson, R. Andriambololona
Arithmetic Logic Unit (ALU) is a fundamental building block of a central processing unit (CPU) in any computing system. The ALU is the hardware that performs logical (and, or, xor) and basic arithmetic (addition, subtraction, multiplication, division) operations. Thus, its construction requires techniques in which the treatment of operands should be consistent with operations rules. In this paper, ALU based on matrix calculation introduced and developed by Raoelina Andriambololona is proposed. These techniques aim to remove illogic and inconsistent appearing in the international writing numeration with the usual rules in arithmetic. We also propose the design of code converters which convert Binary to BCD (Binary Coded Decimal) code and vice versa using matrix calculation.
{"title":"Design of ALU and Code Converter Using Matrix Calculation","authors":"Nirina Gilbert Rasolofoson, R. Andriambololona","doi":"10.11648/j.pamj.20170603.11","DOIUrl":"https://doi.org/10.11648/j.pamj.20170603.11","url":null,"abstract":"Arithmetic Logic Unit (ALU) is a fundamental building block of a central processing unit (CPU) in any computing system. The ALU is the hardware that performs logical (and, or, xor) and basic arithmetic (addition, subtraction, multiplication, division) operations. Thus, its construction requires techniques in which the treatment of operands should be consistent with operations rules. In this paper, ALU based on matrix calculation introduced and developed by Raoelina Andriambololona is proposed. These techniques aim to remove illogic and inconsistent appearing in the international writing numeration with the usual rules in arithmetic. We also propose the design of code converters which convert Binary to BCD (Binary Coded Decimal) code and vice versa using matrix calculation.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"26 1","pages":"89"},"PeriodicalIF":0.2,"publicationDate":"2017-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78593934","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 : 2017-05-13DOI: 10.11648/j.pamj.s.2017060301.12
Kande Dickson Kinyua, Kuria Joseph Gikonyo
From a mathematical perspective, a surface is a generalization of a plane which does not necessarily require being flat, that is, the curvature is not necessarily zero. Often, a surface is defined by equations that are satisfied by some coordinates of its points. A surface may also be defined as the image, in some space of dimensions at least three, of a continuous function of two variables (some further conditions are required to insure that the image is not a curve). In this case, one says that one has a parametric surface, which is parametrized by these two variables, called parameters. Parametric equations of surfaces are often irregular at some points. This is formalized by the concept of manifold: in the context of manifolds, typically in topology and differential geometry, a surface is a manifold of dimension two; this means that a surface is a topological space such that every point has a neighborhood which is homeomorphic to an open subset of the Euclidean plane. A parametric surface is the image of an open subset of the Euclidean plane by a continuous function, in a topological space, generally a Euclidean space of dimension at least three. The paper aims at giving an introduction to the theory of surfaces from differential geometry perspective.
{"title":"An Introduction to Differential Geometry: The Theory of Surfaces","authors":"Kande Dickson Kinyua, Kuria Joseph Gikonyo","doi":"10.11648/j.pamj.s.2017060301.12","DOIUrl":"https://doi.org/10.11648/j.pamj.s.2017060301.12","url":null,"abstract":"From a mathematical perspective, a surface is a generalization of a plane which does not necessarily require being flat, that is, the curvature is not necessarily zero. Often, a surface is defined by equations that are satisfied by some coordinates of its points. A surface may also be defined as the image, in some space of dimensions at least three, of a continuous function of two variables (some further conditions are required to insure that the image is not a curve). In this case, one says that one has a parametric surface, which is parametrized by these two variables, called parameters. Parametric equations of surfaces are often irregular at some points. This is formalized by the concept of manifold: in the context of manifolds, typically in topology and differential geometry, a surface is a manifold of dimension two; this means that a surface is a topological space such that every point has a neighborhood which is homeomorphic to an open subset of the Euclidean plane. A parametric surface is the image of an open subset of the Euclidean plane by a continuous function, in a topological space, generally a Euclidean space of dimension at least three. The paper aims at giving an introduction to the theory of surfaces from differential geometry perspective.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"12 1","pages":"6"},"PeriodicalIF":0.2,"publicationDate":"2017-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88563478","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：