Pub Date : 2020-09-15DOI: 10.11648/J.PAMJ.20200905.12
S. Andargie, Assaye Belay Gelaw
Currently, because of the wide availability and free service of HAART, HIV/AIDS related morbidity and mortality has decreased significantly. However, patients accessing antiretroviral treatment (ART) programmes in sub-Saharan Africa frequently have very advanced immunodeficiency and various reserches suggest that such patients may have diminished capacity for CD4 cell count recovery. The objective of this study was to investigate the long-term effect of highly active antiretroviral therapy on the CD4 lymphocyte count of HIV-infected Patients. Subjects from the multicenter HAART Program cohort (from Mizan-Tepi University Teaching Hospital and Tepi General Hospital), aged 18 years or older and had an ART treatment start date in between February 1, 2017 to January 31, 2019 were enrolled in the present study and followed for a maximum of 3 years. Liner mixed model with nested random effect were used to model the longitudianl CD4 count over time. The data reveal robust CD4 responses to ART that are continual over several years. Being under HAART for long period and having baseline CD4 count greater than 150 were positively associated with CD4 increment over time while starting ART at late stage (Stage 3 or 4) and being male are negatively assocted with CD4 increment over time. These study show strong and repetitive CD4 response to ART among patients remaining on therapy. Earlier HIV diagnosis and initiation of ART could significantly progress patient outcomes in the study area.
{"title":"Exploration of Long-term CD4 Profile in HIV Patients Under HAART at Mizan-Tepi University Teaching Hospital and Tepi General Hospital, South Western Ethiopia","authors":"S. Andargie, Assaye Belay Gelaw","doi":"10.11648/J.PAMJ.20200905.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20200905.12","url":null,"abstract":"Currently, because of the wide availability and free service of HAART, HIV/AIDS related morbidity and mortality has decreased significantly. However, patients accessing antiretroviral treatment (ART) programmes in sub-Saharan Africa frequently have very advanced immunodeficiency and various reserches suggest that such patients may have diminished capacity for CD4 cell count recovery. The objective of this study was to investigate the long-term effect of highly active antiretroviral therapy on the CD4 lymphocyte count of HIV-infected Patients. Subjects from the multicenter HAART Program cohort (from Mizan-Tepi University Teaching Hospital and Tepi General Hospital), aged 18 years or older and had an ART treatment start date in between February 1, 2017 to January 31, 2019 were enrolled in the present study and followed for a maximum of 3 years. Liner mixed model with nested random effect were used to model the longitudianl CD4 count over time. The data reveal robust CD4 responses to ART that are continual over several years. Being under HAART for long period and having baseline CD4 count greater than 150 were positively associated with CD4 increment over time while starting ART at late stage (Stage 3 or 4) and being male are negatively assocted with CD4 increment over time. These study show strong and repetitive CD4 response to ART among patients remaining on therapy. Earlier HIV diagnosis and initiation of ART could significantly progress patient outcomes in the study area.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"65 2","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72452092","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 : 2020-09-09DOI: 10.11648/j.pamj.20200905.11
A. S. Olaniyan, Omolara Fatimah Bakre, M. A. Akanbi
In recent times, the use of different types of mean in the derivation of explicit Runge-Kutta methods had been on increase. Researchers have explored explicit Runge-Kutta methods derivation by using different types of mean such as geometric mean, harmonic mean, contra-harmonic mean, heronian mean to name but a few; as against the conventional explicit Runge-Kutta methods which was viewed as arithmetic mean. However, despite efforts to improve the derivation of explicit Runge-Kutta methods with use of other types of mean, none has deemed it fit to extend this notion to implicit Runge-Kutta methods. In this article, we present the use of heronian mean as a basis for the construction of implicit Runge-Kutta method in a way of improving the conventional method which is arithmetic mean based. Numerical results was conducted on ordinary differential equations which was compared with the conventional two-stage fourth order implicit Runge-Kutta (IRK4) method and two-stage third order diagonally implicit Runge-Kutta (DIRK3) method. The results presented confirmed that the new scheme performs better than these numerical methods. A better Qualitative properties using Dalquist test equation were established.
{"title":"A 2-Stage Implicit Runge-Kutta Method Based on Heronian Mean for Solving Ordinary Differential Equations","authors":"A. S. Olaniyan, Omolara Fatimah Bakre, M. A. Akanbi","doi":"10.11648/j.pamj.20200905.11","DOIUrl":"https://doi.org/10.11648/j.pamj.20200905.11","url":null,"abstract":"In recent times, the use of different types of mean in the derivation of explicit Runge-Kutta methods had been on increase. Researchers have explored explicit Runge-Kutta methods derivation by using different types of mean such as geometric mean, harmonic mean, contra-harmonic mean, heronian mean to name but a few; as against the conventional explicit Runge-Kutta methods which was viewed as arithmetic mean. However, despite efforts to improve the derivation of explicit Runge-Kutta methods with use of other types of mean, none has deemed it fit to extend this notion to implicit Runge-Kutta methods. In this article, we present the use of heronian mean as a basis for the construction of implicit Runge-Kutta method in a way of improving the conventional method which is arithmetic mean based. Numerical results was conducted on ordinary differential equations which was compared with the conventional two-stage fourth order implicit Runge-Kutta (IRK4) method and two-stage third order diagonally implicit Runge-Kutta (DIRK3) method. The results presented confirmed that the new scheme performs better than these numerical methods. A better Qualitative properties using Dalquist test equation were established.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"98 1","pages":"84"},"PeriodicalIF":0.2,"publicationDate":"2020-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79212745","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 : 2020-08-10DOI: 10.11648/j.pamj.20200904.12
N. Faried, H. A. Ghaffar, S. Hamdy
In 2010, Chistyakov, V. V., defined the theory of modular metric spaces. After that, in 2011, Mongkolkeha, C. et. al. studied and proved the new existence theorems of a fixed point for contraction mapping in modular metric spaces for one single-valued map in modular metric space. Also, in 2012, Chaipunya, P. introduced some fixed point theorems for multivalued mapping under the setting of contraction type in modular metric space. In 2014, Abdou, A. A. N., Khamsi, M. A. studied the existence of fixed points for contractive-type multivalued maps in the setting of modular metric space. In 2016, Dilip Jain et. al. presented a multivalued F-contraction and F-contraction of Hardy-Rogers-type in the case of modular metric space with specific assumptions. In this work, we extended these results into the case of a pair of multivalued mappings on proximinal sets in a regular modular metric space. This was done by introducing the notions of best approximation, proximinal set in modular metric space, conjoint F-proximinal contraction, and conjoint F-proximinal contraction of Hardy-Rogers-type for two multivalued mappings. Furthermore, we give an example showing the conditions of the theory which found a common fixed point of a pair of multivalued mappings on proximinal sets in a regular modular metric space. Also, the applications of the obtained results can be used in multiple fields of science like Electrorheological fluids and FORTRAN computer programming as shown in this communication.
2010年，Chistyakov, V. V.定义了模度量空间理论。之后，2011年Mongkolkeha, C.等研究并证明了模度量空间中一个单值映射在模度量空间中收缩映射不动点的存在性新定理。Chaipunya, P.(2012)也引入了模度量空间中缩型集合下的多值映射的不动点定理。2014年，Abdou, A. A. N.， Khamsi, M. A.研究了模度量空间下缩型多值映射不动点的存在性。2016年，Dilip Jain等人提出了模度量空间中具有特定假设的多值f -收缩和hardy - rogers型f -收缩。在这项工作中，我们将这些结果推广到正则模度量空间中近端集合上的一对多值映射。通过引入两个多值映射的最佳逼近、模度量空间中的近端集、联合f -近端收缩和hardy - rogers型的联合f -近端收缩的概念来实现。在此基础上，给出了正则模度量空间中近集上的一对多值映射存在公共不动点的条件。此外，所获得的结果可以应用于多个科学领域，如电流变流体和FORTRAN计算机编程，如本通信所示。
{"title":"Common Fixed Point for Two Multivalued Mappings on Proximinal Sets in Regular Modular Space","authors":"N. Faried, H. A. Ghaffar, S. Hamdy","doi":"10.11648/j.pamj.20200904.12","DOIUrl":"https://doi.org/10.11648/j.pamj.20200904.12","url":null,"abstract":"In 2010, Chistyakov, V. V., defined the theory of modular metric spaces. After that, in 2011, Mongkolkeha, C. et. al. studied and proved the new existence theorems of a fixed point for contraction mapping in modular metric spaces for one single-valued map in modular metric space. Also, in 2012, Chaipunya, P. introduced some fixed point theorems for multivalued mapping under the setting of contraction type in modular metric space. In 2014, Abdou, A. A. N., Khamsi, M. A. studied the existence of fixed points for contractive-type multivalued maps in the setting of modular metric space. In 2016, Dilip Jain et. al. presented a multivalued F-contraction and F-contraction of Hardy-Rogers-type in the case of modular metric space with specific assumptions. In this work, we extended these results into the case of a pair of multivalued mappings on proximinal sets in a regular modular metric space. This was done by introducing the notions of best approximation, proximinal set in modular metric space, conjoint F-proximinal contraction, and conjoint F-proximinal contraction of Hardy-Rogers-type for two multivalued mappings. Furthermore, we give an example showing the conditions of the theory which found a common fixed point of a pair of multivalued mappings on proximinal sets in a regular modular metric space. Also, the applications of the obtained results can be used in multiple fields of science like Electrorheological fluids and FORTRAN computer programming as shown in this communication.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"103 1","pages":"74"},"PeriodicalIF":0.2,"publicationDate":"2020-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80742142","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 : 2020-07-28DOI: 10.11648/j.pamj.20200904.11
Joseph Roger Arhin, Francis Sam, K. Coker, Toufic Seini
Big data has in recent years gained ground in many scientific and engineering problems. It seems to some extent prohibitive for traditional matrix decomposition methods (i.e. QR, SVD, EVD, etc.) to handle such large-scale problems involving data matrix. Many researchers have developed several algorithms to decompose such big data matrices. An accuracy-enhanced randomized singular value decomposition method (referred to as AE-RSVDM) with orthonormalization recently becomes the state-of-the-art to factorize large data matrices with satisfactory speed and accuracy. In our paper, low-rank matrix approximations based on randomization are studied, with emphasis on accelerating the computational efficiency on large data matrices. By this, we accelerate the AE-RSVDM with modified normalized power iteration to result in an accelerated version. The accelerated version is grounded on a two-stage scheme. The first stage seeks to find the range of a sketch matrix which involves a Gaussian random matrix. A low-dimensional space is then created from the high-dimensional data matrix via power iteration. Numerical experiments on matrices of different sizes demonstrate that our accelerated variant achieves speedups while attaining the same reconstruction error as the AE-RSVDM with orthonormalization. And with data from Google art project, we have made known the computational speed-up of the accelerated variant over the AE-RSVDM algorithm for decomposing large data matrices with low-rank form.
{"title":"An Accelerated Accuracy-enhanced Randomized Singular Value Decomposition for Factorizing Matrices with Low-rank Structure","authors":"Joseph Roger Arhin, Francis Sam, K. Coker, Toufic Seini","doi":"10.11648/j.pamj.20200904.11","DOIUrl":"https://doi.org/10.11648/j.pamj.20200904.11","url":null,"abstract":"Big data has in recent years gained ground in many scientific and engineering problems. It seems to some extent prohibitive for traditional matrix decomposition methods (i.e. QR, SVD, EVD, etc.) to handle such large-scale problems involving data matrix. Many researchers have developed several algorithms to decompose such big data matrices. An accuracy-enhanced randomized singular value decomposition method (referred to as AE-RSVDM) with orthonormalization recently becomes the state-of-the-art to factorize large data matrices with satisfactory speed and accuracy. In our paper, low-rank matrix approximations based on randomization are studied, with emphasis on accelerating the computational efficiency on large data matrices. By this, we accelerate the AE-RSVDM with modified normalized power iteration to result in an accelerated version. The accelerated version is grounded on a two-stage scheme. The first stage seeks to find the range of a sketch matrix which involves a Gaussian random matrix. A low-dimensional space is then created from the high-dimensional data matrix via power iteration. Numerical experiments on matrices of different sizes demonstrate that our accelerated variant achieves speedups while attaining the same reconstruction error as the AE-RSVDM with orthonormalization. And with data from Google art project, we have made known the computational speed-up of the accelerated variant over the AE-RSVDM algorithm for decomposing large data matrices with low-rank form.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"15 1","pages":"64"},"PeriodicalIF":0.2,"publicationDate":"2020-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81849923","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 : 2020-07-14DOI: 10.11648/J.PAMJ.20200903.13
N. Stojanović
Quasi-asymptotic behavior of functions as a method has its application in observing many physical phenomena which are expressed by differential equations. The aim of the asymptotic method is to allow one to present the solution of a problem depending on the large (or small) parameter. One application of asymptotic methods in describing physical phenomena is the quasi-asymptotic approximation. The aim of this paper is to look at the quasi-asymptotic properties of multidimensional distributions by extracted variable. Distribution T(x0,x) from S'(Ṝ+1×Rn) has the property of the separability of variables, if it can be represented in form T(x0,x)=∑φi(x0)ψi (x) where distributions, φi(x0) from S'(Ṝ1) and ψi from S(Rn), x0 from Ṝ1+ and x is element Rn different values of do not depend on each other. Distribution T(x0,x) the element S'(Ṝ+1×Rn) is homogeneous and of order α at variable x0 is element Ṝ1+ and x=x1,x2,…,xn from Rn if for k>0 it applies that T(kx0,kx)=kα T(x0,x). The method of separating variables is one of the most widespread methods for solving linear differential equations in mathematical physics. In this paper, the results by V. S Vladimirov are used to present the proof of the basic theorems, regarding the quasi-asymptotic behavior of multidimensional distributions by a singular variable, with the application of quasi-asymptotics to the solution of differential equations.
函数的拟渐近行为作为一种方法，在观察许多用微分方程表示的物理现象时有其应用。渐近方法的目的是允许人们根据大(或小)参数给出问题的解。渐近方法在描述物理现象中的一个应用是拟渐近逼近。本文的目的是通过抽取变量来研究多维分布的拟渐近性质。S'(Ṝ+1×Rn)中的分布T(x0,x)具有变量可分性，如果它可以表示为T(x0,x)=∑φi(x0)ψi (x)其中分布φi(x0)来自S'(Ṝ1)和ψi来自S(Rn)， x0来自Ṝ1+和x是元素Rn的不同值不依赖于彼此。分布T(x0,x)元素S'(Ṝ+1×Rn)是齐次的，在变量x0处的α阶是元素Ṝ1+，x =x1,x2，…，xn，如果k>0，适用于T(kx0,kx)=kα T(x0,x)。分离变量法是数学物理中最常用的求解线性微分方程的方法之一。本文利用V. S . Vladimirov的结果，给出了关于多维分布的奇异变量拟渐近性的基本定理的证明，并将拟渐近性应用于微分方程的解。
{"title":"Some Separate Quasi-Asymptotics Properties of Multidimensional Distributions and Application","authors":"N. Stojanović","doi":"10.11648/J.PAMJ.20200903.13","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20200903.13","url":null,"abstract":"Quasi-asymptotic behavior of functions as a method has its application in observing many physical phenomena which are expressed by differential equations. The aim of the asymptotic method is to allow one to present the solution of a problem depending on the large (or small) parameter. One application of asymptotic methods in describing physical phenomena is the quasi-asymptotic approximation. The aim of this paper is to look at the quasi-asymptotic properties of multidimensional distributions by extracted variable. Distribution T(x0,x) from S'(Ṝ+1×Rn) has the property of the separability of variables, if it can be represented in form T(x0,x)=∑φi(x0)ψi (x) where distributions, φi(x0) from S'(Ṝ1) and ψi from S(Rn), x0 from Ṝ1+ and x is element Rn different values of do not depend on each other. Distribution T(x0,x) the element S'(Ṝ+1×Rn) is homogeneous and of order α at variable x0 is element Ṝ1+ and x=x1,x2,…,xn from Rn if for k>0 it applies that T(kx0,kx)=kα T(x0,x). The method of separating variables is one of the most widespread methods for solving linear differential equations in mathematical physics. In this paper, the results by V. S Vladimirov are used to present the proof of the basic theorems, regarding the quasi-asymptotic behavior of multidimensional distributions by a singular variable, with the application of quasi-asymptotics to the solution of differential equations.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"40 1","pages":"64"},"PeriodicalIF":0.2,"publicationDate":"2020-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77306336","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 : 2020-07-04DOI: 10.11648/J.PAMJ.20200903.12
S. Ihedioha, Nanle Tanko Danat, A. Buba
In this work, we studied the optimal investment problem of an investor who had exponential utility preference and traded two assets; (1) a risky asset which price dynamics was governed by the Constant Elasticity of variance (CEV) model and (2) a risk-free asset which price system followed the Ornstein-Uhlenbeck model. We employed the maximum principle of dynamic programming to obtain the Hamilton-Jacobi-Bellman (H-J-B) equation on which the first principle and the elimination of variable dependency were applied to get the closed-form of the investor’s optimal strategies. Two scenarios where the Brownian motions correlated and where they did not correlate were investigated. Also considered were the cases of when transaction cost was involved and when transaction cost was not involved. This lead to six cases that among the results obtained was that the investor has an optimal investment strategy that requires more amount of money for investment when the Brownian motions do not correlate and there is transaction cost than when the Brownian motions correlate and there is no transaction.
{"title":"Investor’s Optimal Strategy with and Without Transaction Cost Under Ornstein-Uhlenbeck and Constant Elasticity of Variance (CEV) Models Via Exponential Utility Maximization","authors":"S. Ihedioha, Nanle Tanko Danat, A. Buba","doi":"10.11648/J.PAMJ.20200903.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20200903.12","url":null,"abstract":"In this work, we studied the optimal investment problem of an investor who had exponential utility preference and traded two assets; (1) a risky asset which price dynamics was governed by the Constant Elasticity of variance (CEV) model and (2) a risk-free asset which price system followed the Ornstein-Uhlenbeck model. We employed the maximum principle of dynamic programming to obtain the Hamilton-Jacobi-Bellman (H-J-B) equation on which the first principle and the elimination of variable dependency were applied to get the closed-form of the investor’s optimal strategies. Two scenarios where the Brownian motions correlated and where they did not correlate were investigated. Also considered were the cases of when transaction cost was involved and when transaction cost was not involved. This lead to six cases that among the results obtained was that the investor has an optimal investment strategy that requires more amount of money for investment when the Brownian motions do not correlate and there is transaction cost than when the Brownian motions correlate and there is no transaction.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"27 1","pages":"55"},"PeriodicalIF":0.2,"publicationDate":"2020-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82542376","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 : 2020-06-20DOI: 10.11648/J.PAMJ.20200903.11
Mir Md. Moheuddin, Muhammad Abdus Sattar Titu, Saddam Hossain
In this paper, we mainly propose the approximate solutions to solve the integration problems numerically using the quadrature method including the Trapezoidal method, Simpson’s 1/3 method, and Simpson’s 3/8 method. The three proposed methods are quite workable and practically well suitable for solving integration problems. Through the MATLAB program, our numerical solutions are determined as well as compared with the exact values to verify the higher accuracy of the proposed methods. Some numerical examples have been utilized to give the accuracy rate and simple implementation of our methods. In this study, we have compared the performance of our solutions and the computational attempt of our proposed methods. Moreover, we explore and calculate the errors of the three proposed methods for the sake of showing our approximate solution’s superiority. Then, among these three methods, we analyzed the approximate errors to prove which method shows more appropriate results. We also demonstrated the approximate results and observed errors to give clear idea graphically. Therefore, from the analysis, we can point out that only the minimum error is in Simpson’s 1/3 method which will beneficial for the readers to understand the effectiveness in solving the several numerical integration problems.
{"title":"A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods","authors":"Mir Md. Moheuddin, Muhammad Abdus Sattar Titu, Saddam Hossain","doi":"10.11648/J.PAMJ.20200903.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20200903.11","url":null,"abstract":"In this paper, we mainly propose the approximate solutions to solve the integration problems numerically using the quadrature method including the Trapezoidal method, Simpson’s 1/3 method, and Simpson’s 3/8 method. The three proposed methods are quite workable and practically well suitable for solving integration problems. Through the MATLAB program, our numerical solutions are determined as well as compared with the exact values to verify the higher accuracy of the proposed methods. Some numerical examples have been utilized to give the accuracy rate and simple implementation of our methods. In this study, we have compared the performance of our solutions and the computational attempt of our proposed methods. Moreover, we explore and calculate the errors of the three proposed methods for the sake of showing our approximate solution’s superiority. Then, among these three methods, we analyzed the approximate errors to prove which method shows more appropriate results. We also demonstrated the approximate results and observed errors to give clear idea graphically. Therefore, from the analysis, we can point out that only the minimum error is in Simpson’s 1/3 method which will beneficial for the readers to understand the effectiveness in solving the several numerical integration problems.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"14 1","pages":"46"},"PeriodicalIF":0.2,"publicationDate":"2020-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82393032","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 : 2020-04-23DOI: 10.11648/J.PAMJ.20200902.12
C. Tcheka
Steenrod operations are cohomology operations that are themselves natural transformations between cohomology functors. There are two distinct types of steenrod operations initially constructed by Norman Steenrod and called Steenrod squares and reduced p-th power operations usually denoted Sq and pi respectively. Since their creation, it has been proved that these operations can be constructed in the cohomology of many algebraic structures, for instance in the cohomology of simplicial restricted Lie algebras, the cohomology of cocommutative Hopf algebras and the homology of infinite loop space. Later on J. P. May developped a general algebraic setting in which all the above cases can be studied. In this work we consider a cyclic group π of oder a fixed prime p and combine theπ-strongly homotopy commutative Hopf algebra structure to the May’s approach with the aim to build these natural transformations on the Hochschild cohomology groups. Moreover we give under some conditions a link of these natural transformations with the Gerstenhaber algebra structure.
{"title":"Cohomology Operations andπ-Strongly Homotopy Commutative Hopf Algebra","authors":"C. Tcheka","doi":"10.11648/J.PAMJ.20200902.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20200902.12","url":null,"abstract":"Steenrod operations are cohomology operations that are themselves natural transformations between cohomology functors. There are two distinct types of steenrod operations initially constructed by Norman Steenrod and called Steenrod squares and reduced p-th power operations usually denoted Sq and pi respectively. Since their creation, it has been proved that these operations can be constructed in the cohomology of many algebraic structures, for instance in the cohomology of simplicial restricted Lie algebras, the cohomology of cocommutative Hopf algebras and the homology of infinite loop space. Later on J. P. May developped a general algebraic setting in which all the above cases can be studied. In this work we consider a cyclic group π of oder a fixed prime p and combine theπ-strongly homotopy commutative Hopf algebra structure to the May’s approach with the aim to build these natural transformations on the Hochschild cohomology groups. Moreover we give under some conditions a link of these natural transformations with the Gerstenhaber algebra structure.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"9 1","pages":"37"},"PeriodicalIF":0.2,"publicationDate":"2020-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78919224","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 : 2020-04-14DOI: 10.11648/J.PAMJ.20200902.11
Jemal Demsie Abraha
In this paper three numerical methods are discussed to find the approximate solutions of a systems of first order ordinary differential equations. Those are Classical Runge-Kutta method, Modified Euler method and Euler method. For each methods formulas are developed for n systems of ordinary differential equations. The formulas explained by these methods are demonstrated by examples to identify the most accurate numerical methods. By comparing the analytical solution of the dependent variables with the approximate solution, absolute errors are calculated. The resulting value indicates that classical fourth order Runge-Kutta method offers most closet values with the computed analytical values. Finally from the results the classical fourth order is more efficient method to find the approximate solutions of the systems of ordinary differential equations.
{"title":"Comparison of Numerical Methods for System of First Order Ordinary Differential Equations","authors":"Jemal Demsie Abraha","doi":"10.11648/J.PAMJ.20200902.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20200902.11","url":null,"abstract":"In this paper three numerical methods are discussed to find the approximate solutions of a systems of first order ordinary differential equations. Those are Classical Runge-Kutta method, Modified Euler method and Euler method. For each methods formulas are developed for n systems of ordinary differential equations. The formulas explained by these methods are demonstrated by examples to identify the most accurate numerical methods. By comparing the analytical solution of the dependent variables with the approximate solution, absolute errors are calculated. The resulting value indicates that classical fourth order Runge-Kutta method offers most closet values with the computed analytical values. Finally from the results the classical fourth order is more efficient method to find the approximate solutions of the systems of ordinary differential equations.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"57 1","pages":"32"},"PeriodicalIF":0.2,"publicationDate":"2020-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86427931","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}
Evon M. O. Abu-Taieh, Issam Alhadid, Ali Zolait, Jeihan M. Abu-Tayeh
UNSTRUCTURED COVID-19 is a highly contagious and lethal virus-based disease. Social distancing is the only way to stop the virus from spreading. In this context, the researchers suggest a social distancing application named SDA-COVID-19. The suggested App (SDA-COVID-19) will help individuals maintain social distancing by the exchange of data among phones about potentially infected and/or contaminated people with COVID-19, with whom an individual socialized or came in contact, whereby, an individual will be alerted if a COVID-19 infected person is in close proximity. Two versions are suggested for SDA-COVID-19 one is Service-Oriented and the other is Bluetooth oriented.
{"title":"SDA-COVID-19: Social Distancing App for COVID-19 Track and Control (Preprint)","authors":"Evon M. O. Abu-Taieh, Issam Alhadid, Ali Zolait, Jeihan M. Abu-Tayeh","doi":"10.2196/preprints.19120","DOIUrl":"https://doi.org/10.2196/preprints.19120","url":null,"abstract":"\u0000 UNSTRUCTURED\u0000 COVID-19 is a highly contagious and lethal virus-based disease. Social distancing is the only way to stop the virus from spreading. In this context, the researchers suggest a social distancing application named SDA-COVID-19. The suggested App (SDA-COVID-19) will help individuals maintain social distancing by the exchange of data among phones about potentially infected and/or contaminated people with COVID-19, with whom an individual socialized or came in contact, whereby, an individual will be alerted if a COVID-19 infected person is in close proximity. Two versions are suggested for SDA-COVID-19 one is Service-Oriented and the other is Bluetooth oriented.\u0000","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"19 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73691895","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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