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Academic Journal of Applied Mathematical Sciences最新文献

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On the Positive Pell Equation 关于正Pell方程
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-07-02 DOI: 10.32861/ajams.67.85.92
N. Thiruniraiselvi, M. Gopalan
{"title":"On the Positive Pell Equation","authors":"N. Thiruniraiselvi, M. Gopalan","doi":"10.32861/ajams.67.85.92","DOIUrl":"https://doi.org/10.32861/ajams.67.85.92","url":null,"abstract":"The binary quadratic equation () representing the hyperbola is studied for its non-zero distinct integer solutions. A few interesting properties among the solutions are presented. Employing the integer solutions of the equation under consideration, integer solutions for special straight lines, hyperbolas and parabolas are exhibited.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"208 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116515396","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}
引用次数: 0
Computatıonal Algorıthm for the Numerıcal Solutıon of Systems of Volterra Integro-Dıfferentıal Equatıons
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-06-05 DOI: 10.32861/ajams.66.66.76
F. Iyanda, Tiamiyu Abdgafar Tunde
{"title":"Computatıonal Algorıthm for the Numerıcal Solutıon of Systems of Volterra Integro-Dıfferentıal Equatıons","authors":"F. Iyanda, Tiamiyu Abdgafar Tunde","doi":"10.32861/ajams.66.66.76","DOIUrl":"https://doi.org/10.32861/ajams.66.66.76","url":null,"abstract":"In this paper, we employ variational iterative method (VIM) to develop a suitable Algorithm for the numerical solution of systems of Volterra integro-differential equations. The formulated algorithm is used to solve first and second order linear and nonlinear system of Volterra integrodifferential equations which demonstrated a good numerical approach to overcome lengthen computational and integral simplification involves. Moreover, the comparison of the exact solution with the approximated solutions are made and approximate solutions p(x) q(t) proved to converge to the exact solutions p(x) q(t) respectively. The results reveal that the formulated algorithm are simple, effective and faster than analytical approach of solving Volterra integro-differential equations.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125431437","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}
引用次数: 0
Spectral Features of Systems With Chaotic Dynamics 混沌动力学系统的谱特征
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-06-05 DOI: 10.32861/ajams.66.58.65
Perevoznikov E. N.
{"title":"Spectral Features of Systems With Chaotic Dynamics","authors":"Perevoznikov E. N.","doi":"10.32861/ajams.66.58.65","DOIUrl":"https://doi.org/10.32861/ajams.66.58.65","url":null,"abstract":"Using the Lorentz model and Hamiltonian systems without dissipation as an example, spectral methods for analyzing the dynamics of systems with chaotic behavior are considered. The insufficiency of the traditional approach to the study of perturbation dynamics based on an analysis of the roots of the classical spectral equation is discussed. It is proposed to study nonlinear systems using the method of constructing spectral equations with different eigenvalues, which allows one to take into account the randomness and multiplicity of states. The spectral features of instability and chaos for systems without dissipation are shown by the example of short-wave perturbations of a flow of a weakly ionized plasma gas.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121885495","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}
引用次数: 0
On Properties of Derivations in Normed Spaces 赋范空间中导数的性质
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-06-05 DOI: 10.32861/ajams.66.77.79
Benard Okelo
{"title":"On Properties of Derivations in Normed Spaces","authors":"Benard Okelo","doi":"10.32861/ajams.66.77.79","DOIUrl":"https://doi.org/10.32861/ajams.66.77.79","url":null,"abstract":"Let δ: Cp→Cp be normal, then the linear map ( ) attains a local minimum at Cp if and only if z Cp such that ( )( ( )≥0. Also let Cp, and let ( ) have the polar decomposition ( ) ( ) then the map attains local minimum on Cp at T if and only if ( ) . Regarding orthogonality, let S Cp and let N(S) have the polar decomposition N(S) = U|N(S)|, then ( ) ( ) for X Cp if ( ) . Moreover, the map has a local minimum at if and only if ( )( ( )) for y . In this paper, we give some results on local minimum and orthogonality of normal derivations in Cp-Classes. We employ some techniques for normal derivations due to Mecheri, Hacene, Bounkhel and Anderson.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114018950","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}
引用次数: 0
Three-Step Two-Hybrid Block Method for the Direct Solution of Second-Order Ordinary Differential Equations 二阶常微分方程直接解的三步双混合块法
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-03-25 DOI: 10.32861/ajams.63.15.23
Raymond Dominic, T. K. Yusuf
{"title":"Three-Step Two-Hybrid Block Method for the Direct Solution of Second-Order Ordinary Differential Equations","authors":"Raymond Dominic, T. K. Yusuf","doi":"10.32861/ajams.63.15.23","DOIUrl":"https://doi.org/10.32861/ajams.63.15.23","url":null,"abstract":"In this paper a three-step two hybrid block method with two offgrid hybrid points chosen within interval [Xn,Xn+1] and [Xn+1,Xn+2] was developed to solve second Order Ordinary Differential Equations directly, using the power series as the basic function to approximate and generate some continuous schemes. The basic properties of the method was investigated and was found to converge. Numerical Solution of our method was tested on some stiff equations and was found to give better approximation than the existing method.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132110592","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}
引用次数: 0
M2D-QPCA: An Improved Quaternion Principal Component Analysis Method for Color Face Recognition M2D-QPCA:改进的四元数主成分分析方法用于彩色人脸识别
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-02-25 DOI: 10.32861/ajams.62.5.14
Song Song, Kaisong Sun, Minghui Wang
{"title":"M2D-QPCA: An Improved Quaternion Principal Component Analysis Method for Color Face Recognition","authors":"Song Song, Kaisong Sun, Minghui Wang","doi":"10.32861/ajams.62.5.14","DOIUrl":"https://doi.org/10.32861/ajams.62.5.14","url":null,"abstract":"Principal component analysis (PCA) is one of the successful dimensionality reduction approaches for color face recognition. For various PCA methods, the experiments show that the contribution of eigenvectors is different and different weights of eigenvectors can cause different effects. Based on this, a modified and simplified color two-dimensional quaternion principal component analysis (M2D-QPCA) method is proposed along the framework of the color two-dimensional quaternion principal component analysis (2D-QPCA) method and the improved two-dimensional quaternion principal component analysis (2D-GQPCA) method. The shortcomings of 2D-QPCA are corrected and the CPU time of 2D-GQPCA is reduced. The experiments on two real face data sets show that the accuracy of M2D-QPCA is better than that of 2D-QPCA and other PCA-like methods and the CPU time of M2D-QPCA is less than that of 2D-GQPCA.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127504428","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}
引用次数: 1
Method of Averaging for Some Parabolic Partial Differential Equations 一类抛物型偏微分方程的平均方法
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-01-25 DOI: 10.32861/ajams.61.1.4
M. El-Borai, Hamed Kamal Awad, R. H. M. Ali
{"title":"Method of Averaging for Some Parabolic Partial Differential Equations","authors":"M. El-Borai, Hamed Kamal Awad, R. H. M. Ali","doi":"10.32861/ajams.61.1.4","DOIUrl":"https://doi.org/10.32861/ajams.61.1.4","url":null,"abstract":"Quantitative and qualitative analysis of the Averaging methods for the parabolic partial differential equation appears as an exciting field of the investigation. In this paper, we generalize some known results due to Krol on the averaging methods and use them to solve the parabolic partial differential equation.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132752279","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}
引用次数: 2
Existence and Uniqueness for the Controllability of a Dynamical System 动力系统可控性的存在唯一性
Academic Journal of Applied Mathematical Sciences Pub Date : 2019-12-02 DOI: 10.32861/ajams.512.168.173
Eli Innocent Cleopas, G. C. Abanum
{"title":"Existence and Uniqueness for the Controllability of a Dynamical System","authors":"Eli Innocent Cleopas, G. C. Abanum","doi":"10.32861/ajams.512.168.173","DOIUrl":"https://doi.org/10.32861/ajams.512.168.173","url":null,"abstract":"In this paper, we consider the existence and uniqueness for the controllability of a dynamical system. Here, measure of non-compactness of set was employed to examine the conditions for darbo’s fixed point theorem which is used to established the existence and uniqueness solution for nonlinear integro-differential equation with implicit derivatives.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"277 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122953250","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}
引用次数: 0
Handling Critical Multicollinearity Using Parametric Approach 用参数法处理临界多重共线性
Academic Journal of Applied Mathematical Sciences Pub Date : 2019-11-05 DOI: 10.32861/ajams.511.150.163
O. Maxwell, G. A. Osuji, Ibeakuzie Precious Onyedikachi, Chinelo Ijeoma Obi-Okpala, I. U. Chinedu, O. I. Frank
{"title":"Handling Critical Multicollinearity Using Parametric Approach","authors":"O. Maxwell, G. A. Osuji, Ibeakuzie Precious Onyedikachi, Chinelo Ijeoma Obi-Okpala, I. U. Chinedu, O. I. Frank","doi":"10.32861/ajams.511.150.163","DOIUrl":"https://doi.org/10.32861/ajams.511.150.163","url":null,"abstract":"In regression analysis, it is relatively necessary to have a correlation between the response and explanatory variables, but having correlations amongst explanatory variables is something undesired. This paper focuses on five methodologies for handling critical multicollinearity, they include: Partial Least Square Regression (PLSR), Ridge Regression (RR), Ordinary Least Square Regression (OLS), Least Absolute Shrinkage and Selector Operator (LASSO) Regression, and the Principal Component Analysis (PCA). Monte Carlo Simulations comparing the methods was carried out with the sample size greater than or equal to the levels (n>p) considered in most cases, the Average Mean Square Error (AMSE) and Akaike Information Criterion (AIC) values were computed. The result shows that PCR is the most superior and more efficient in handling critical multicollinearity problems, having the lowest AMSE and AIC values for all the sample sizes and different levels considered.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128037966","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}
引用次数: 2
On Two Covariates Cosine and Sine Noisy-Wave Trigonometry Regression of Heartbeats 心跳的两协变量余弦和正弦噪声波三角回归
Academic Journal of Applied Mathematical Sciences Pub Date : 2019-10-25 DOI: 10.32861/ajams.510.140.149
O. Olawale
{"title":"On Two Covariates Cosine and Sine Noisy-Wave Trigonometry Regression of Heartbeats","authors":"O. Olawale","doi":"10.32861/ajams.510.140.149","DOIUrl":"https://doi.org/10.32861/ajams.510.140.149","url":null,"abstract":"This paper proposes and describes the acumen on alternate two covariates linear Cosine and Sine regression functions that possessed a noisy-wave or tone frequencies via wave-trend of actualized observations of regressors and responsive variable needed in fitting a wavy equation of trigonometry regression. The method of maximum likelihood was used in estimating parameters associated to the Cosine and Sine alternate functions via vector coefficients as well as their distributional and residual properties. The estimations obtained via the method were enthralled to the noisy-wave mesokurtic observations of babies’ rate of heartbeats exactly an hour after birth (HR1), two hours after birth (HR2) and three hours after birth (HR3). The implementation and illustrative application was via R using the heartbeat dataset. It was gleaned that the trigonometry equation line .......","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122124844","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}
引用次数: 1
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