In this paper we study some comparative growth properties of composite entire functions in terms of their maximum terms on the basis of their relative orders (relative lower orders) with respect to another entire function.
{"title":"Some Growth Properties of Entire Functions Depending on Their Relative Orders","authors":"S. Datta, T. Biswas, D. C. Pramanik","doi":"10.12816/0017355","DOIUrl":"https://doi.org/10.12816/0017355","url":null,"abstract":"In this paper we study some comparative growth properties of composite entire functions in terms of their maximum terms on the basis of their relative orders (relative lower orders) with respect to another entire function.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127010032","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, a new fractional spline function of polynomial form with the idea of the lacunary interpolation is considered to find approximate solution for fractional differential equations (FDEs). The proposed method is applicable for α ∈ (0, 1], where α denotes the order of the fractional derivative in the Caputo sense. Convergence analysis of the method is considered. Some illustrative examples are presented and the obtained results reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems. The study is conducted through illustrative examples and error analysis. keywords: Fractional integral and derivative, Caputo Derivative, Taylor’s expansion, Error bound, Spline functions. 68 Faraidun K. Hamasalh and Pshtiwan O. Muhammad
本文考虑了一种新的多项式形式的分数阶样条函数，利用缺插值的思想求分数阶微分方程的近似解。该方法适用于α∈(0,1)，其中α表示分数阶导数在Caputo意义上的阶数。对该方法进行了收敛性分析。算例表明，该方法对此类问题的求解是非常有效、方便和准确的。通过举例和误差分析进行了研究。关键词:分数积分与导数，卡普托导数，泰勒展开，误差界，样条函数[68] Faraidun K. Hamasalh和Pshtiwan O. Muhammad
{"title":"Generalized Quartic Fractional Spline Interpolation with Applications","authors":"F. Hamasalh, Pshtiwan O. Muhammad","doi":"10.12816/0010710","DOIUrl":"https://doi.org/10.12816/0010710","url":null,"abstract":"In this paper, a new fractional spline function of polynomial form with the idea of the lacunary interpolation is considered to find approximate solution for fractional differential equations (FDEs). The proposed method is applicable for α ∈ (0, 1], where α denotes the order of the fractional derivative in the Caputo sense. Convergence analysis of the method is considered. Some illustrative examples are presented and the obtained results reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems. The study is conducted through illustrative examples and error analysis. keywords: Fractional integral and derivative, Caputo Derivative, Taylor’s expansion, Error bound, Spline functions. 68 Faraidun K. Hamasalh and Pshtiwan O. Muhammad","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":"442 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125761294","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}
The object of this paper is to introduce a new class of ideal convergent (briefly I -convergent) sequence spaces using an infinite matrix, sequence of modulus functions and difference operator defined on n -normed spaces. We study these spaces for some linear topological structures and algebraic properties.
{"title":"New A-Generalized Sequence Spaces Defined by Ideal Convergence and a Sequence of Modulus Functions on Multiple Normed Spaces","authors":"T. Jalal","doi":"10.12816/0010708","DOIUrl":"https://doi.org/10.12816/0010708","url":null,"abstract":"The object of this paper is to introduce a new class of ideal convergent (briefly I -convergent) sequence spaces using an infinite matrix, sequence of modulus functions and difference operator defined on n -normed spaces. We study these spaces for some linear topological structures and algebraic properties.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129205546","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 deals with the study of a class of nonlinear evolution systems with parameter t which may interpreted as the time or the absolute temperature. Such type of problems arise in the study of quasistatic problem in viscoplasticity. The existence and uniqueness of the solution is obtained using standard arguments for elliptic equations followed by a xed point technique. The continuous dependence of the solution with respect to the data is also given. Finally, a mechanical example is presented in order to illustrate this result.
{"title":"A Fixed Point Method for a Class of Nonlinear Evolution Systems Modeling a Mechanical Phenomenon","authors":"A. Merouani, Abdelmoumene Djabi","doi":"10.12816/0010705","DOIUrl":"https://doi.org/10.12816/0010705","url":null,"abstract":"This paper deals with the study of a class of nonlinear evolution systems with parameter t which may interpreted as the time or the absolute temperature. Such type of problems arise in the study of quasistatic problem in viscoplasticity. The existence and uniqueness of the solution is obtained using standard arguments for elliptic equations followed by a xed point technique. The continuous dependence of the solution with respect to the data is also given. Finally, a mechanical example is presented in order to illustrate this result.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124964473","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}
Mohammad Hamdan, Hisham A. Shehadeh, Qusai Y. Obeidat
The most challenges of Wireless Body Area Network (WBAN) are energy consumption because its works using limited resource like battery and end-to-end delay because it is used to transmit real time parameters of patients' health status like Electrocardiogram (ECG). In this paper we present and discuss the modeling of a multi objective problem. The first objective is the minimization of the end to end delay; the second objective is maximization of the energy efficiency of the network depending on packets payload size. We use jMetal to test the problem using three genetic algorithms (NSGA-II, SPEA-II and OMOPSO) and we compare between them.
无线体域网络(Wireless Body Area Network, WBAN)面临的最大挑战是能量消耗，因为它使用有限的电池等资源来工作，而且由于它用于传输心电图(ECG)等患者健康状态的实时参数，因此端到端延迟。本文提出并讨论了多目标问题的建模方法。第一个目标是最小化端到端延迟;第二个目标是根据数据包的有效负载大小最大化网络的能源效率。我们使用jMetal使用三种遗传算法(NSGA-II, SPEA-II和OMOPSO)来测试问题，并在它们之间进行比较。
{"title":"Multi - Objective Optimization of Electrocardiogram Monitoring Network for Elderly Patient in Home","authors":"Mohammad Hamdan, Hisham A. Shehadeh, Qusai Y. Obeidat","doi":"10.12816/0010711","DOIUrl":"https://doi.org/10.12816/0010711","url":null,"abstract":"The most challenges of Wireless Body Area Network (WBAN) are energy consumption because its works using limited resource like battery and end-to-end delay because it is used to transmit real time parameters of patients' health status like Electrocardiogram (ECG). In this paper we present and discuss the modeling of a multi objective problem. The first objective is the minimization of the end to end delay; the second objective is maximization of the energy efficiency of the network depending on packets payload size. We use jMetal to test the problem using three genetic algorithms (NSGA-II, SPEA-II and OMOPSO) and we compare between them.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115742605","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}
A third order non-linear boundary value problem that arises from the problem of boundary-layer flows of an incompressible non-Newtonian fluid modelled by a power-law rheology is considered. The shear stress parameter (curvature at the origin) is computed for different values of the power-law index n and different values of (the initial rates of change at the origin). The interrelationships between these parameters are examined and regions of linear/non-linear interaction/dependence are revealed.
{"title":"Parameter Variation in a Third Order Singular Boundary Value Problem","authors":"S. Al-Ashhab","doi":"10.12816/0010709","DOIUrl":"https://doi.org/10.12816/0010709","url":null,"abstract":"A third order non-linear boundary value problem that arises from the problem of boundary-layer flows of an incompressible non-Newtonian fluid modelled by a power-law rheology is considered. The shear stress parameter (curvature at the origin) is computed for different values of the power-law index n and different values of (the initial rates of change at the origin). The interrelationships between these parameters are examined and regions of linear/non-linear interaction/dependence are revealed.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128152331","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}
An unsteady, two dimensional, hydro magnetic, laminar mixed convective boundary layer flow of an incompressible and electrically conducting fluid along an infinite vertical plate embedded in the porous medium with heat and mass transfer is analyzed, by taking into account the effects of viscous dissipation and heat absorption. The dimensionless governing equations for this investigation are solved analytically using Galerkin finite element method. Numerical evaluation of the numerical results is performed and the results for velocity, temperature and concentration profiles within the boundary layer are discussed and shown through graphically.
{"title":"Heat and Mass Transfer Effects on an Unsteady Hydromagnetic Free Convective Flow over an Infinite Vertical Plate Embedded in a Porous Medium with Heat Absorption","authors":"G. Murali, Ajit Paul, N. Babu","doi":"10.12816/0010706","DOIUrl":"https://doi.org/10.12816/0010706","url":null,"abstract":"An unsteady, two dimensional, hydro magnetic, laminar mixed convective boundary layer flow of an incompressible and electrically conducting fluid along an infinite vertical plate embedded in the porous medium with heat and mass transfer is analyzed, by taking into account the effects of viscous dissipation and heat absorption. The dimensionless governing equations for this investigation are solved analytically using Galerkin finite element method. Numerical evaluation of the numerical results is performed and the results for velocity, temperature and concentration profiles within the boundary layer are discussed and shown through graphically.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124623055","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 the middle of 17th century, Pierre de Fermat mentioned that no value of n > 2 could satisfy the equation x n + y n = z n , where n, x, y and z are all positive integers. The statement is popularly known as Fermat’s last theorem. An acceptable mathematical proof of this theorem is being explored still today. When searched online treasures of resources, one may find various proofs of this theorem. In this paper I am not discussing any historical attempts that failed or partially succeeded. I am going to discuss the approach which I have adopted to proof this theorem. The approach is based on odd-even classification of positive integers. Assumption that the equation x n + y n = z n , where n, x, y and z are all positive integers, has a solution for n > 2 leads to some contradiction.
17世纪中叶，皮埃尔·德·费马提到，没有一个n > 2的值能满足方程x n + y n = z n，其中n、x、y、z都是正整数。这个命题通常被称为费马大定理。这个定理的一个可接受的数学证明至今仍在探索中。当搜索网上的资源宝藏时，人们可以找到这个定理的各种证明。在本文中，我不讨论任何失败或部分成功的历史尝试。我将讨论我用来证明这个定理的方法。该方法基于正整数的奇偶分类。假设方程x n + y n = z n，其中n、x、y和z都是正整数，当n > 2时有解，会产生一些矛盾。
{"title":"Proof of Fermat Last Theorem Based on Odd Even Classification of Integers","authors":"Vinay Kumar","doi":"10.12816/0010702","DOIUrl":"https://doi.org/10.12816/0010702","url":null,"abstract":"In the middle of 17th century, Pierre de Fermat mentioned that no value of n > 2 could satisfy the equation x n + y n = z n , where n, x, y and z are all positive integers. The statement is popularly known as Fermat’s last theorem. An acceptable mathematical proof of this theorem is being explored still today. When searched online treasures of resources, one may find various proofs of this theorem. In this paper I am not discussing any historical attempts that failed or partially succeeded. I am going to discuss the approach which I have adopted to proof this theorem. The approach is based on odd-even classification of positive integers. Assumption that the equation x n + y n = z n , where n, x, y and z are all positive integers, has a solution for n > 2 leads to some contradiction.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124263983","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}
The paper is devoted to determine the solution of the non-stationary heat equation in a non axial symmetric cylindrical coordinates subject to mixed discontinuous boundary conditions of the second kind and third kinds, with the aid of a finite Fourier transform and dual integral equations method. The solution of the given mixed problem is introduced to a Fredholm integral equation of the second kind.
{"title":"Integral Transforms and Dual Integral Equations to Solve Heat Equation with Mixed Conditions","authors":"N. Hoshan","doi":"10.12816/0010701","DOIUrl":"https://doi.org/10.12816/0010701","url":null,"abstract":"The paper is devoted to determine the solution of the non-stationary heat equation in a non axial symmetric cylindrical coordinates subject to mixed discontinuous boundary conditions of the second kind and third kinds, with the aid of a finite Fourier transform and dual integral equations method. The solution of the given mixed problem is introduced to a Fredholm integral equation of the second kind.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132424322","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}
There are many hot topics related to cloud computing paradigm, and one of these important fields is data security in cloud data storage that aims to make users data more secure and for ensure privacy for users. In this paper we intend to introduced a comprehensive study on security of cloud data store, since there have been little works deals with. The introduced papers here addressed this problem from different views, some deals with encryption algorithm while other researchers made comparisons between different techniques. On the other hand, some papers proposed new technique or made some enhancements on existing ones either depends on statistical or un-statistical encryption algorithms. Till now there are no optimal suggested solutions that solve the security on cloud data store.
{"title":"Comprehensive Study on Data Security in Cloud Data Store","authors":"Hisham A. Shehadeh, Qusai Y. Obeidat, D. Darwish","doi":"10.12816/0010704","DOIUrl":"https://doi.org/10.12816/0010704","url":null,"abstract":"There are many hot topics related to cloud computing paradigm, and one of these important fields is data security in cloud data storage that aims to make users data more secure and for ensure privacy for users. In this paper we intend to introduced a comprehensive study on security of cloud data store, since there have been little works deals with. The introduced papers here addressed this problem from different views, some deals with encryption algorithm while other researchers made comparisons between different techniques. On the other hand, some papers proposed new technique or made some enhancements on existing ones either depends on statistical or un-statistical encryption algorithms. Till now there are no optimal suggested solutions that solve the security on cloud data store.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127646869","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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