{"title":"COMPARISON ON THE ROBUSTNESS AGAINST ERASURE RATES OF NUMERICALLY ERASURE-ROBUST FRAMES","authors":"Y. Liu","doi":"10.12732/ijam.v33i4.3","DOIUrl":"https://doi.org/10.12732/ijam.v33i4.3","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"37 1","pages":"585"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80599207","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}
{"title":"SECOND HANKEL DETERMINANT FOR A CLASS OF ANALYTIC FUNCTIONS DEFINED BY RUSCHEWEYH DERIVATIVE","authors":"J. Choi","doi":"10.12732/ijam.v33i4.6","DOIUrl":"https://doi.org/10.12732/ijam.v33i4.6","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"64 1","pages":"609"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75894077","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}
In this paper, the residual power series method is developed to solve a class of coupled partial differential equations. This approach improves solutions by reducing the residual error functions to create a rapidly convergent series. The description of the proposed method is presented to approximate the solution by highlighting all the steps necessary to implement the algorithm. Meanwhile, the scheme is tested on several cases of examples arising in the field of finance. Numerical results obtained justify that the proposed method is effective, accurate and simple in application. AMS Subject Classification: 35A25, 35C10, 65D99
{"title":"NUMERICAL MODELING OF COUPLED PARTIAL DIFFERENTIAL EQUATIONS USING RESIDUAL ERROR FUNCTIONS","authors":"I. Komashynska","doi":"10.12732/ijam.v33i4.9","DOIUrl":"https://doi.org/10.12732/ijam.v33i4.9","url":null,"abstract":"In this paper, the residual power series method is developed to solve a class of coupled partial differential equations. This approach improves solutions by reducing the residual error functions to create a rapidly convergent series. The description of the proposed method is presented to approximate the solution by highlighting all the steps necessary to implement the algorithm. Meanwhile, the scheme is tested on several cases of examples arising in the field of finance. Numerical results obtained justify that the proposed method is effective, accurate and simple in application. AMS Subject Classification: 35A25, 35C10, 65D99","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"28 1","pages":"649"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84068187","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}
Abstract: In the case of the Burges equation, this work proves the following conjecture: impulses, delays, and nonlocal conditions, under some assumptions, do not destroy some posed system qualitative properties since they are themselves intrinsic to it. we verified that the property of controllability is robust under this type of disturbances. Specifically, we prove that the interior approximate controllability of the linear heat equation is not destroyed if we add impulses, nonlocal conditions, and a nonlinear perturbation with delay in the state. This is done by using new techniques avoiding fixed point theorems employed by A.E. Bashirov et al. In this case the delay helps us to prove the approximate controllability of this system by pulling back the control solution to a fixed curve in a short time interval, and from this position, we are able to reach a neighborhood of the final state in time τ by using the fact that the corresponding linear heat equation is approximately controllable on any interval [t0, τ ], 0 < t0 < τ .
{"title":"CONTROLLABILITY OF THE BURGERS EQUATION UNDER THE INFLUENCE OF IMPULSES, DELAY AND NONLOCAL CONDITIONS","authors":"C. Duque, J. Uzcátegui, Hugo Leiva, Oscar Camacho","doi":"10.12732/ijam.v33i4.2","DOIUrl":"https://doi.org/10.12732/ijam.v33i4.2","url":null,"abstract":"Abstract: In the case of the Burges equation, this work proves the following conjecture: impulses, delays, and nonlocal conditions, under some assumptions, do not destroy some posed system qualitative properties since they are themselves intrinsic to it. we verified that the property of controllability is robust under this type of disturbances. Specifically, we prove that the interior approximate controllability of the linear heat equation is not destroyed if we add impulses, nonlocal conditions, and a nonlinear perturbation with delay in the state. This is done by using new techniques avoiding fixed point theorems employed by A.E. Bashirov et al. In this case the delay helps us to prove the approximate controllability of this system by pulling back the control solution to a fixed curve in a short time interval, and from this position, we are able to reach a neighborhood of the final state in time τ by using the fact that the corresponding linear heat equation is approximately controllable on any interval [t0, τ ], 0 < t0 < τ .","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"86 1","pages":"573"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78157485","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}
Abstract: A study for the problem of unsteady convection flow of a viscous incompressible electrically conducting micro-polar fluid in a porous medium past an inclined moving porous plate in the presence of a transverse magnetic field, heat generation, radiation absorption, chemical reaction and suction is presented. The porous plate moves with a constant velocity and the stream velocity is assumed to follow an exponentially increasing perturbation law. The porous plate absorbs the polar fluid with a suction velocity which varies with time. The dimensionless governing equations are solved analytically by perturbation technique. The numerical results are also compared with corresponding Newtonian fluid flow problems. The effects of various parameters on the velocity, micro-rotation, temperature, concentration fields, skin friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are presented in graphical and tabular form.
{"title":"THE STUDY OF MAGNETO HYDRODYNAMIC FREE CONVECTIVE FLOW AND HEAT TRANSFER IN A POROUS MEDIUM WITH HEAT GENERATION, RADIATION ABSORPTION AND CHEMICAL REACTION","authors":"George Buzuzi","doi":"10.12732/ijam.v33i4.15","DOIUrl":"https://doi.org/10.12732/ijam.v33i4.15","url":null,"abstract":"Abstract: A study for the problem of unsteady convection flow of a viscous incompressible electrically conducting micro-polar fluid in a porous medium past an inclined moving porous plate in the presence of a transverse magnetic field, heat generation, radiation absorption, chemical reaction and suction is presented. The porous plate moves with a constant velocity and the stream velocity is assumed to follow an exponentially increasing perturbation law. The porous plate absorbs the polar fluid with a suction velocity which varies with time. The dimensionless governing equations are solved analytically by perturbation technique. The numerical results are also compared with corresponding Newtonian fluid flow problems. The effects of various parameters on the velocity, micro-rotation, temperature, concentration fields, skin friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are presented in graphical and tabular form.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"3 1","pages":"733"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76334140","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 article is devoted to investigate the singular values as well as the real fixed points of one-parameter families of transcendental meromorphic functions which are associated with fundamental trigonometric functions sin z, cos z and tan z. For this purpose, we consider the functions fμ(z) = sin z z+μ , gη(z) = cos z z+η and hκ(z) = tan z z2 + κ for μ > 0, η > 0 and κ > 0 respectively, and z ∈ C. It is found that the functions fμ(z) and gη(z) have infinite number of bounded singular values while the function hκ(z) has infinite number of unbounded singular values. Moreover, the real fixed points of fμ(z), gη(z) and hκ(z) are described. AMS Subject Classification: 30D05; 37C25; 58K05
本文研究了与基本三角函数sinz、cos z和tanz有关的超越亚纯函数单参数族的奇异值和实不动点。为此，我们分别考虑了μ > 0、η > 0和κ > 0时的函数fμ(z) = sin z z+μ、gη(z) = cos z z+η和hκ(z) = tan z z2 + κ。发现函数fμ(z)和gη(z)有无限个有界奇异值，函数hκ(z)有无限个无界奇异值。并给出了fμ(z)、gη(z)和hκ(z)的实不动点。AMS学科分类:30D05;这件37;58 k05
{"title":"SINGULAR VALUES AND REAL FIXED POINTS OF ONE-PARAMETER FAMILIES ASSOCIATED WITH FUNDAMENTAL TRIGONOMETRIC FUNCTIONS[4pt] $sin z$, $cos z$ and $tan z$","authors":"Mohammad Sajid","doi":"10.12732/ijam.v33i4.8","DOIUrl":"https://doi.org/10.12732/ijam.v33i4.8","url":null,"abstract":"This article is devoted to investigate the singular values as well as the real fixed points of one-parameter families of transcendental meromorphic functions which are associated with fundamental trigonometric functions sin z, cos z and tan z. For this purpose, we consider the functions fμ(z) = sin z z+μ , gη(z) = cos z z+η and hκ(z) = tan z z2 + κ for μ > 0, η > 0 and κ > 0 respectively, and z ∈ C. It is found that the functions fμ(z) and gη(z) have infinite number of bounded singular values while the function hκ(z) has infinite number of unbounded singular values. Moreover, the real fixed points of fμ(z), gη(z) and hκ(z) are described. AMS Subject Classification: 30D05; 37C25; 58K05","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"8 1","pages":"635"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90042564","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}
We use the mean-variance model to study a portfolio problem characterized by an investment in two different types of asset. We consider m logically independent risky assets and a risk-free asset. We analyze m risky assets coinciding with m distributions of probability inside of a linear space. They generate a distribution of probability of a multivariate risky asset of order m. We show that an m-dimensional linear manifold is generated by m basic risky assets. They identify m finite partitions, where each of them is characterized by n incompatible and exhaustive elementary events. We suppose that it turns out to be n > m without loss of generality. Given m risky assets, we prove that all risky assets contained in an m-dimensional linear manifold are related. We prove that two any risky assets of them are conversely α-orthogonal, so their covariance is equal to 0. We reinterpret principal component analysis by showing that the principal components are basic risky assets of an m-dimensional linear manifold. We consider a Bayesian adjustment of differences between prior distributions to posterior distributions existing with respect to a probabilistic and economic hypothesis. AMS Subject Classification: 51F99, 60B05, 91B06, 91B30, 91B82
{"title":"A REINTERPRETATION OF PRINCIPAL COMPONENT ANALYSIS CONNECTED WITH LINEAR MANIFOLDS IDENTIFYING RISKY ASSETS OF A PORTFOLIO","authors":"P. Angelini","doi":"10.12732/ijam.v33i4.14","DOIUrl":"https://doi.org/10.12732/ijam.v33i4.14","url":null,"abstract":"We use the mean-variance model to study a portfolio problem characterized by an investment in two different types of asset. We consider m logically independent risky assets and a risk-free asset. We analyze m risky assets coinciding with m distributions of probability inside of a linear space. They generate a distribution of probability of a multivariate risky asset of order m. We show that an m-dimensional linear manifold is generated by m basic risky assets. They identify m finite partitions, where each of them is characterized by n incompatible and exhaustive elementary events. We suppose that it turns out to be n > m without loss of generality. Given m risky assets, we prove that all risky assets contained in an m-dimensional linear manifold are related. We prove that two any risky assets of them are conversely α-orthogonal, so their covariance is equal to 0. We reinterpret principal component analysis by showing that the principal components are basic risky assets of an m-dimensional linear manifold. We consider a Bayesian adjustment of differences between prior distributions to posterior distributions existing with respect to a probabilistic and economic hypothesis. AMS Subject Classification: 51F99, 60B05, 91B06, 91B30, 91B82","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"33 1","pages":"709"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76238617","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}
We consider a broad class of linear operator equations that includes systems of ordinary differential equations, difference equations and fractionalorder ordinary differential equations. This class also includes operator exponentials and powers, as well as eigenvalue problems and Fredholm integral equations. Many problems in engineering and the physical and natural sciences can be described by such operator equations. We generalise the fundamental matrix to a fundamental operator and provide a new explicit method for obtaining an exact series solution to these types of operator equations, together with sufficient conditions for convergence and error bounds. Illustrative examples are also given. AMS Subject Classification: 34A30, 15A16, 34A08, 39A05, 47A75
{"title":"ON A GENERALISATION OF THE FUNDAMENTAL MATRIX AND THE SOLUTION OF OPERATOR EQUATIONS","authors":"M. Rodrigo","doi":"10.12732/ijam.v33i3.5","DOIUrl":"https://doi.org/10.12732/ijam.v33i3.5","url":null,"abstract":"We consider a broad class of linear operator equations that includes systems of ordinary differential equations, difference equations and fractionalorder ordinary differential equations. This class also includes operator exponentials and powers, as well as eigenvalue problems and Fredholm integral equations. Many problems in engineering and the physical and natural sciences can be described by such operator equations. We generalise the fundamental matrix to a fundamental operator and provide a new explicit method for obtaining an exact series solution to these types of operator equations, together with sufficient conditions for convergence and error bounds. Illustrative examples are also given. AMS Subject Classification: 34A30, 15A16, 34A08, 39A05, 47A75","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"23 1","pages":"413"},"PeriodicalIF":0.0,"publicationDate":"2020-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78211489","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}
In this paper, we investigate the existence and uniqueness of positive solutions of boundary value problems (BVPs) for fractional differential equations (FDEs) with boundary conditions (BCs) involving the RiemannLiouville (RL) fractional derivative of the form:
{"title":"UPPER AND LOWER SOLUTIONS METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS","authors":"Jayshree Patil","doi":"10.12732/ijam.v33i3.8","DOIUrl":"https://doi.org/10.12732/ijam.v33i3.8","url":null,"abstract":"In this paper, we investigate the existence and uniqueness of positive solutions of boundary value problems (BVPs) for fractional differential equations (FDEs) with boundary conditions (BCs) involving the RiemannLiouville (RL) fractional derivative of the form:","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"10 1","pages":"479"},"PeriodicalIF":0.0,"publicationDate":"2020-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75439601","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}
{"title":"ON MICRO $T_{1over 2}$ SPACE","authors":"H. Ibrahim","doi":"10.12732/ijam.v33i3.1","DOIUrl":"https://doi.org/10.12732/ijam.v33i3.1","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"37 1","pages":"369"},"PeriodicalIF":0.0,"publicationDate":"2020-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72805132","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：