Pub Date : 2019-08-30DOI: 10.11648/J.PAMJ.20190803.12
Xiaolan Qin, Ricai Luo
The Drazin inverse has applications in a number of areas such as control theory, Markov chains, singular differential and difference equations, and iterative methods in numerical linear algebra. The study on representations for the Drazin inverse of block matrices stems essentially from finding the general expressions for the solutions to singular systems of differential equations, and then stimulated by a problem formulated by Campbell. In 1983, Campbell (Campbell et al. (1976)) established an explicit representation for the Drazin inverse of a 2 × 2 block matrix M in terms of the blocks of the partition, where the blocks A and D are assumed to be square matrices. Special cases of the problems have been studied. In 2009, Chunyuan Deng and Yimin Wei found an explicit representation for the Drazin inverse of an anti-triangular matrix M, where A and BC are generalized Drazin invertible, if AπAB=0 and BC (I–Aπ) =0. Afterwards, several authors have investigated this problem under some limited conditions on the blocks of M. In particular, a representation of the Drazin inverse of M, denoted by Md. In this paper, we consider the Drazin inverse of a sum of two matrices and we derive additive formulas under the conditions of ABAπ=0 and BAπ=0 respectively. Precisely, for a block matrix M, we give a new representation of Md under some conditions that AB=0 and DCAπ=0. Moreover, some particular cases of this result related to the Drazin inverse of block matrices are also considered.
Drazin逆在控制理论、马尔可夫链、奇异微分方程和差分方程以及数值线性代数中的迭代方法等许多领域都有应用。块阵的Drazin逆表示的研究，本质上是从寻找微分方程奇异系统解的一般表达式开始的，然后受到Campbell提出的一个问题的启发。1983年，Campbell (Campbell et al.(1976))建立了2 × 2块矩阵M的Drazin逆的显式表示，表示为分区的块，其中假设块a和D为方阵。并对问题的特殊情况进行了研究。2009年，邓春元和魏益民发现了反三角矩阵M的Drazin逆的显式表示，其中，当π ab =0, BC (I-Aπ) =0时，A和BC是广义Drazin可逆的。随后，一些作者在M块上的一些有限条件下研究了这个问题，特别是M的Drazin逆的表示，用Md表示。本文考虑两个矩阵和的Drazin逆，并分别在ABAπ=0和baa π=0的条件下推导了可加性公式。精确地说，对于分块矩阵M，我们给出了在AB=0和DCAπ=0的条件下Md的新表示。此外，还考虑了与分块矩阵的Drazin逆有关的一些特殊情况。
{"title":"A Note on the Formulas for the Drazin Inverse of the Sum of Two Matrices and Its Applications","authors":"Xiaolan Qin, Ricai Luo","doi":"10.11648/J.PAMJ.20190803.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20190803.12","url":null,"abstract":"The Drazin inverse has applications in a number of areas such as control theory, Markov chains, singular differential and difference equations, and iterative methods in numerical linear algebra. The study on representations for the Drazin inverse of block matrices stems essentially from finding the general expressions for the solutions to singular systems of differential equations, and then stimulated by a problem formulated by Campbell. In 1983, Campbell (Campbell et al. (1976)) established an explicit representation for the Drazin inverse of a 2 × 2 block matrix M in terms of the blocks of the partition, where the blocks A and D are assumed to be square matrices. Special cases of the problems have been studied. In 2009, Chunyuan Deng and Yimin Wei found an explicit representation for the Drazin inverse of an anti-triangular matrix M, where A and BC are generalized Drazin invertible, if AπAB=0 and BC (I–Aπ) =0. Afterwards, several authors have investigated this problem under some limited conditions on the blocks of M. In particular, a representation of the Drazin inverse of M, denoted by Md. In this paper, we consider the Drazin inverse of a sum of two matrices and we derive additive formulas under the conditions of ABAπ=0 and BAπ=0 respectively. Precisely, for a block matrix M, we give a new representation of Md under some conditions that AB=0 and DCAπ=0. Moreover, some particular cases of this result related to the Drazin inverse of block matrices are also considered.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"99 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76735475","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 : 2019-08-06DOI: 10.11648/J.PAMJ.20190803.11
Hu Yunpeng, C. Yonghui
For the last twenty years, there has been a great deal of interest in the theory of two weight. In the present paper, we investigate the two weight norm inequalities for fractional new maximal operator on the Lebesgue space. More specifically, we obtain that the sufficient and necessary conditions for strong and weak type two weight norm inequalities for a new fractional maximal operators by introducing a class of new two weight functions. In the discussion of strong type two weight norm inequalities, we make full use of the properties of dyadic cubes and truncation operators, and utilize the space decomposition technique which space is decomposed into disjoint unions. In contrast, weak type two weight norm inequalities are more complex. We have the aid of some good properties of Ap weight functions and ingeniously use the characteristic function. What should be stressed is that the new two weight functions we introduced contains the classical two weights and our results generalize known results before. In this paper, it is worth noting that w(x)dx may not be a doubling measure if our new weight functions ω∈Ap (φ). Since φ(|Q|)≥1, our new weight functions are including the classical Muckenhoupt weights.
{"title":"Two Weight Characterization of New Maximal Operators","authors":"Hu Yunpeng, C. Yonghui","doi":"10.11648/J.PAMJ.20190803.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20190803.11","url":null,"abstract":"For the last twenty years, there has been a great deal of interest in the theory of two weight. In the present paper, we investigate the two weight norm inequalities for fractional new maximal operator on the Lebesgue space. More specifically, we obtain that the sufficient and necessary conditions for strong and weak type two weight norm inequalities for a new fractional maximal operators by introducing a class of new two weight functions. In the discussion of strong type two weight norm inequalities, we make full use of the properties of dyadic cubes and truncation operators, and utilize the space decomposition technique which space is decomposed into disjoint unions. In contrast, weak type two weight norm inequalities are more complex. We have the aid of some good properties of Ap weight functions and ingeniously use the characteristic function. What should be stressed is that the new two weight functions we introduced contains the classical two weights and our results generalize known results before. In this paper, it is worth noting that w(x)dx may not be a doubling measure if our new weight functions ω∈Ap (φ). Since φ(|Q|)≥1, our new weight functions are including the classical Muckenhoupt weights.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"45 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79518342","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 : 2019-07-10DOI: 10.11648/J.PAMJ.20190802.12
Abdellah Menasri
Most physical phenomena are modeled as continuous or discrete dynamic systems of a second dimension or more, but because of the multiplicity of bifurcation parameters and the large dimension, researchers have big problems for the study of this type of systems. For this reason, this article proposes a new method that facilitates the qualitative study of continuous dynamic systems of three dimensions in general and chaotic systems in particular, which contains many parameters of bifurcations. This method is based on projection on the plane and on an appropriate bifurcation parameter.
{"title":"Dynamic Analysis of a Three-dimensional Non-linear Continuous System","authors":"Abdellah Menasri","doi":"10.11648/J.PAMJ.20190802.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20190802.12","url":null,"abstract":"Most physical phenomena are modeled as continuous or discrete dynamic systems of a second dimension or more, but because of the multiplicity of bifurcation parameters and the large dimension, researchers have big problems for the study of this type of systems. For this reason, this article proposes a new method that facilitates the qualitative study of continuous dynamic systems of three dimensions in general and chaotic systems in particular, which contains many parameters of bifurcations. This method is based on projection on the plane and on an appropriate bifurcation parameter.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"38 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88824137","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 : 2019-06-26DOI: 10.11648/J.PAMJ.20190802.11
M. Malkov
The classification of subalgebras of every algebra of finite-valued functions is constructed. Classes of this classifications do not intersect. Each class contains subalgebras with the same number of functions in minimal basis. Class with ordinal number 0 contains subalgebras that have no basis. The class with finite ordinal number n contains subalgebras whose minimal basis has n functions. The set of subalgebras of this class are countable. There is a class with infinite ordinal number. Subalgebras of this class have a minimal basis with infinite number of functions. The set of these subalgebras is continual. Only the class with ordinal number 1 is essential, all other classes are fictitious, since they are useless to classify functions. But classification of functions is the main problem of the algebra of finite-valued functions. A class of this classification is a set of functions extracted from one-member bases of a subalgebra. Each function generates by superpositions some subalgebra, and only this subalgebra. So, this function belongs to only one class. All these classes of functions belong to the class 1 of subalgebras. All subalgebras from classes with the other ordinal numbers are useless to classify functions. The set of these fictitious subalgebras is continual, the set of essential subalgebras are countable. The top level of the classification of functions contains the algebra of finite-valued functions. Next level contains maximal subalgebras. According to I.G. Rosenberg, there are 6 sets of maximal subalgebras. I.G. Rosenberg was wrong to state the set of his quasilinear functions be maximal. Only Yablonsky’s set of quasilinear functions is maximal. The sixth Rosenberg’s set also turns to be wrong. This right set was built by A.I. Maltsev. But from 6 sets only 3 sets contain essential subalgebras. And all maximal essential subalgebras containing 3-valued 2-place functions are built.
{"title":"Algebra of Finite-Valued Functions: Classification of Functions and Subalgebras, Essential and Fictitious Subalgebras","authors":"M. Malkov","doi":"10.11648/J.PAMJ.20190802.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20190802.11","url":null,"abstract":"The classification of subalgebras of every algebra of finite-valued functions is constructed. Classes of this classifications do not intersect. Each class contains subalgebras with the same number of functions in minimal basis. Class with ordinal number 0 contains subalgebras that have no basis. The class with finite ordinal number n contains subalgebras whose minimal basis has n functions. The set of subalgebras of this class are countable. There is a class with infinite ordinal number. Subalgebras of this class have a minimal basis with infinite number of functions. The set of these subalgebras is continual. Only the class with ordinal number 1 is essential, all other classes are fictitious, since they are useless to classify functions. But classification of functions is the main problem of the algebra of finite-valued functions. A class of this classification is a set of functions extracted from one-member bases of a subalgebra. Each function generates by superpositions some subalgebra, and only this subalgebra. So, this function belongs to only one class. All these classes of functions belong to the class 1 of subalgebras. All subalgebras from classes with the other ordinal numbers are useless to classify functions. The set of these fictitious subalgebras is continual, the set of essential subalgebras are countable. The top level of the classification of functions contains the algebra of finite-valued functions. Next level contains maximal subalgebras. According to I.G. Rosenberg, there are 6 sets of maximal subalgebras. I.G. Rosenberg was wrong to state the set of his quasilinear functions be maximal. Only Yablonsky’s set of quasilinear functions is maximal. The sixth Rosenberg’s set also turns to be wrong. This right set was built by A.I. Maltsev. But from 6 sets only 3 sets contain essential subalgebras. And all maximal essential subalgebras containing 3-valued 2-place functions are built.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"66 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85799580","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 : 2019-05-09DOI: 10.11648/J.PAMJ.20190801.13
Junmei Wang
In this paper, we study the boundedness of some sublinear operators with rough kernels, satisfied by most of the operators in classical harmonic analysis, on the generalized weighted grand Morrey spaces. More specifically, we show that the sublinear operators with rough kernels are bounded on these spaces under the conditions that the operators and the kernel functions satisfy some size conditions, and the operators are bounded on Lebesgue spaces. This is done by exploiting the well-known boundedness of sublinear operators with rough kernels on Lebesgue spaces, a more explicit decomposition of the generalized weighted grand Morrey spaces and the good properties of the weight functions and the kernel functions. Through combining some properties of Ap weight with the relevant lemmas of operators with rough kernel, we obtain the boundedness for sublinear operators with rough kernels on weighted grand morrey spaces. Furthermore, using the equivalent norm and the properties of BMO functions, an application of the boundedness of the sublinear operators with rough kernels to the corresponding commutators formed by certain operators and BMO functions are also considered. And the boundedness of commutator is obtained by the lemma of function BMO.
{"title":"Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces","authors":"Junmei Wang","doi":"10.11648/J.PAMJ.20190801.13","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20190801.13","url":null,"abstract":"In this paper, we study the boundedness of some sublinear operators with rough kernels, satisfied by most of the operators in classical harmonic analysis, on the generalized weighted grand Morrey spaces. More specifically, we show that the sublinear operators with rough kernels are bounded on these spaces under the conditions that the operators and the kernel functions satisfy some size conditions, and the operators are bounded on Lebesgue spaces. This is done by exploiting the well-known boundedness of sublinear operators with rough kernels on Lebesgue spaces, a more explicit decomposition of the generalized weighted grand Morrey spaces and the good properties of the weight functions and the kernel functions. Through combining some properties of Ap weight with the relevant lemmas of operators with rough kernel, we obtain the boundedness for sublinear operators with rough kernels on weighted grand morrey spaces. Furthermore, using the equivalent norm and the properties of BMO functions, an application of the boundedness of the sublinear operators with rough kernels to the corresponding commutators formed by certain operators and BMO functions are also considered. And the boundedness of commutator is obtained by the lemma of function BMO.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"33 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81915131","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 : 2019-04-09DOI: 10.11648/J.PAMJ.20190801.11
M. Malkov
An algebraic approach to the theory of countable functions is given. Compositions (superpositions) of functions are used instead of recursions. Arithmetic and analytic algorithms are defined. All closed sets are founded. Mathematically precise definitions of logic algorithms with quantifiers of existence and universality are given. Logic algorithm for fast-growing function is built as example. Classification of functions is given. There are non-computable functions. These functions are fictitious (useless) and their set is continual. The set of computable functions is countable. Incompleteness of disjunction and negation, conjunction and negation, of Pierce, Sheffer and diagonal Webb functions is proved. The completeness of the set of one-place functions and any all-valued essential function (Slupecki theorem) is proved for computable functions. Existence of generators of all computable functions is proved too.
{"title":"Algebra of Countably Functions and Theorems of Completeness","authors":"M. Malkov","doi":"10.11648/J.PAMJ.20190801.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20190801.11","url":null,"abstract":"An algebraic approach to the theory of countable functions is given. Compositions (superpositions) of functions are used instead of recursions. Arithmetic and analytic algorithms are defined. All closed sets are founded. Mathematically precise definitions of logic algorithms with quantifiers of existence and universality are given. Logic algorithm for fast-growing function is built as example. Classification of functions is given. There are non-computable functions. These functions are fictitious (useless) and their set is continual. The set of computable functions is countable. Incompleteness of disjunction and negation, conjunction and negation, of Pierce, Sheffer and diagonal Webb functions is proved. The completeness of the set of one-place functions and any all-valued essential function (Slupecki theorem) is proved for computable functions. Existence of generators of all computable functions is proved too.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"30 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82600508","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 : 2019-01-11DOI: 10.11648/j.pamj.20180706.13
M. Malkov
There are two algebras of compositions, Post and Jablonsky algebras. Definitions of these algebras was very simple. The article gives mathematically precise definition of these algebras by using Mal’cev’s definitions of the algebras. A. I. Mal’cev defined pre-iterative and iterative algebras of compositions. The significant extension of pre-iterative algebra is given in the article. Iterative algebra is incorrect. E. L. Post used implicitly pre-iterative algebra. S. V. Jablonsky used implicitly iterative algebra. The Jablonsky algebra has the operation of adding fictitious variables. But this operation is not primitive, since the addition of fictitious variables is possible at absence of this operation. If fictitious functions are deleted in the Jablonsky algebra then this algebra becomes correct. A natural classification of closed sets is given and fictitious closed sets are exposed. The number of fictitious closed sets is continual, the number of essential closed sets is countable.
有两种复合代数:Post代数和Jablonsky代数。这些代数的定义非常简单。本文利用马尔切夫的代数定义，给出了这些代数在数学上的精确定义。A. I. Mal 'cev定义了组合的预迭代代数和迭代代数。本文给出了预迭代代数的重要推广。迭代代数是错误的。E. L. Post使用隐式预迭代代数。S. V. Jablonsky使用隐式迭代代数。雅布隆斯基代数具有添加虚变量的运算。但是这个操作不是原始的，因为在没有这个操作的情况下也可以添加虚构的变量。如果在雅布隆斯基代数中删除虚函数，则该代数是正确的。给出了闭集的自然分类，并给出了虚拟的闭集。虚闭集的个数是连续的，本质闭集的个数是可数的。
{"title":"Post and Jablonsky Algebras of Compositions (Superpositions)","authors":"M. Malkov","doi":"10.11648/j.pamj.20180706.13","DOIUrl":"https://doi.org/10.11648/j.pamj.20180706.13","url":null,"abstract":"There are two algebras of compositions, Post and Jablonsky algebras. Definitions of these algebras was very simple. The article gives mathematically precise definition of these algebras by using Mal’cev’s definitions of the algebras. A. I. Mal’cev defined pre-iterative and iterative algebras of compositions. The significant extension of pre-iterative algebra is given in the article. Iterative algebra is incorrect. E. L. Post used implicitly pre-iterative algebra. S. V. Jablonsky used implicitly iterative algebra. The Jablonsky algebra has the operation of adding fictitious variables. But this operation is not primitive, since the addition of fictitious variables is possible at absence of this operation. If fictitious functions are deleted in the Jablonsky algebra then this algebra becomes correct. A natural classification of closed sets is given and fictitious closed sets are exposed. The number of fictitious closed sets is continual, the number of essential closed sets is countable.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"9 1","pages":"95"},"PeriodicalIF":0.2,"publicationDate":"2019-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87658698","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 : 2019-01-02DOI: 10.11648/J.PAMJ.20180706.12
L. Jingli
In order to explore mathematics learning methods suitable for liberal arts students specially and the educational value of mathematics application cases developed by liberal arts students, an experiment of mathematics application case study was carried out in the first grade liberal arts undergraduate students. 205 mathematics application cases have been obtained, and case studies were used with the statistical summarization and analytical generalization methods. From 2009 to 2013, about 531 liberal arts freshmen in statistical course completed a total of 90 mathematics survey reports containing the university campus life (58 cases), professional related research (21 cases), social issues (11 cases) and so on. From 2014 to 2018, liberal arts students completed 115 mathematics application cases in Applied Probability and Statistics class which can be divided into 3 categories according to the degree of innovation: using mathematical knowledge to solve problems (79 cases), empirical survey (14 cases) and literature analysis (22 cases). The case topics selected by liberal arts students are all related to their own interests, and the innovative uses are for the vast majority. Conclusion: (i) writing a mathematics survey report is an appropriate way for students to apply mathematics; (ii) mathematics application is the fusion of interest and knowledge in probability and statistical area for liberal arts undergraduate students; (iii) the development process of mathematics application cases can demonstrate innovative thinking and application ability for liberal arts undergraduate students.
{"title":"An Empirical Research on Mathematical Case Development in Mathematical Teaching in Liberal Arts College","authors":"L. Jingli","doi":"10.11648/J.PAMJ.20180706.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20180706.12","url":null,"abstract":"In order to explore mathematics learning methods suitable for liberal arts students specially and the educational value of mathematics application cases developed by liberal arts students, an experiment of mathematics application case study was carried out in the first grade liberal arts undergraduate students. 205 mathematics application cases have been obtained, and case studies were used with the statistical summarization and analytical generalization methods. From 2009 to 2013, about 531 liberal arts freshmen in statistical course completed a total of 90 mathematics survey reports containing the university campus life (58 cases), professional related research (21 cases), social issues (11 cases) and so on. From 2014 to 2018, liberal arts students completed 115 mathematics application cases in Applied Probability and Statistics class which can be divided into 3 categories according to the degree of innovation: using mathematical knowledge to solve problems (79 cases), empirical survey (14 cases) and literature analysis (22 cases). The case topics selected by liberal arts students are all related to their own interests, and the innovative uses are for the vast majority. Conclusion: (i) writing a mathematics survey report is an appropriate way for students to apply mathematics; (ii) mathematics application is the fusion of interest and knowledge in probability and statistical area for liberal arts undergraduate students; (iii) the development process of mathematics application cases can demonstrate innovative thinking and application ability for liberal arts undergraduate students.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"30 1","pages":"88"},"PeriodicalIF":0.2,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75765645","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 : 2019-01-02DOI: 10.11648/j.pamj.20180706.11
Bazuaye Frank Etin-Osa
Recently, there has been a great deal of interest in the formulation of Runge-Kutta methods based on averages other than the conventional Arithmetic Mean for the numerical solution of Ordinary differential equations. In this paper, a new 4th Order Hybrid Runge-Kutta method based on linear combination of Arithmetic mean, Geometric mean and the Harmonic mean to solve first order initial value problems (IVPs) in ordinary differential equations (ODEs) is presented. Also the stability region for the method is shown. Moreover, the new method is compared with Runge-Kutta method based on arithmetic mean, geometric mean and harmonic mean. The numerical results indicate that the performance of the new method show superiority in terms of accuracy to some of other well known methods in literature and the stability investigation is in agreement with the known fourth order Runge-Kutta methods but with excellent stability region.
{"title":"A New 4 th Order Hybrid Runge-Kutta Methods for Solving Initial Value Problems (IVPs)","authors":"Bazuaye Frank Etin-Osa","doi":"10.11648/j.pamj.20180706.11","DOIUrl":"https://doi.org/10.11648/j.pamj.20180706.11","url":null,"abstract":"Recently, there has been a great deal of interest in the formulation of Runge-Kutta methods based on averages other than the conventional Arithmetic Mean for the numerical solution of Ordinary differential equations. In this paper, a new 4th Order Hybrid Runge-Kutta method based on linear combination of Arithmetic mean, Geometric mean and the Harmonic mean to solve first order initial value problems (IVPs) in ordinary differential equations (ODEs) is presented. Also the stability region for the method is shown. Moreover, the new method is compared with Runge-Kutta method based on arithmetic mean, geometric mean and harmonic mean. The numerical results indicate that the performance of the new method show superiority in terms of accuracy to some of other well known methods in literature and the stability investigation is in agreement with the known fourth order Runge-Kutta methods but with excellent stability region.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"7 1","pages":"78"},"PeriodicalIF":0.2,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91337721","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 : 2019-01-01DOI: 10.11648/j.pamj.20190801.12
Abdel Radi Abdel Rahman Abdel Gadi
{"title":"Comparison Between the Production of Hibiscus in Kordofan States Using Matlab","authors":"Abdel Radi Abdel Rahman Abdel Gadi","doi":"10.11648/j.pamj.20190801.12","DOIUrl":"https://doi.org/10.11648/j.pamj.20190801.12","url":null,"abstract":"","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"14 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78763849","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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