Pub Date : 2020-02-13DOI: 10.11648/J.PAMJ.20200901.14
F. Obarhua, S. J. Kayode
This paper presents an explicit hybrid method for direct approximation of second order ordinary differential equations. The approach adopted in this work is by interpolation and collocation of a basis function and its corresponding differential system respectively. Interpolation of the basis function was done at both grid and off-grid points while the differential systems are collocated at selected points. Substitution of the unknown parameters into the basis function and simplification of the resulting equation produced the required continuous, consistent and symmetric explicit hybrid method. Attempts were made to derive starting values of the same order with the methods using Taylor’s series expansion to circumvent the inherent disadvantage of starting values of lower order. The methods were applied to solve linear, non-linear, Duffing equation and a system of equation second-order initial value problems directly. Errors in the results obtained were compared with those of the existing implicit methods of the same and even of higher order. The comparison shows that the accuracy of the new method is better than the existing methods.
{"title":"Continuous Explicit Hybrid Method for Solving Second Order Ordinary Differential Equations","authors":"F. Obarhua, S. J. Kayode","doi":"10.11648/J.PAMJ.20200901.14","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20200901.14","url":null,"abstract":"This paper presents an explicit hybrid method for direct approximation of second order ordinary differential equations. The approach adopted in this work is by interpolation and collocation of a basis function and its corresponding differential system respectively. Interpolation of the basis function was done at both grid and off-grid points while the differential systems are collocated at selected points. Substitution of the unknown parameters into the basis function and simplification of the resulting equation produced the required continuous, consistent and symmetric explicit hybrid method. Attempts were made to derive starting values of the same order with the methods using Taylor’s series expansion to circumvent the inherent disadvantage of starting values of lower order. The methods were applied to solve linear, non-linear, Duffing equation and a system of equation second-order initial value problems directly. Errors in the results obtained were compared with those of the existing implicit methods of the same and even of higher order. The comparison shows that the accuracy of the new method is better than the existing methods.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"41 1","pages":"26"},"PeriodicalIF":0.2,"publicationDate":"2020-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86509246","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 : 2020-01-22DOI: 10.11648/J.PAMJ.20200901.13
M. A. Ashebo, V. N. S. R. Repalle
In fuzzy graph theory, strong arcs have separate importance. Assign different colors to the end nodes of strong arcs in the fuzzy graph is strong coloring. Strong coloring plays an important role in solving real-life problems that involve networks. In this work, we introduce the new concept, called strong fuzzy chromatic polynomial (SFCP) of a fuzzy graph based on strong coloring. The SFCP of a fuzzy graph counts the number of k-strong colorings of a fuzzy graph with k colors. The existing methods for determining the chromatic polynomial of the crisp graph are used to obtain SFCP of a fuzzy graph. We establish the necessary and sufficient condition for SFCP of a fuzzy graph to be the chromatic polynomial of its underlying crisp graph. Further, we study SFCP of some fuzzy graph structures, namely strong fuzzy graphs, complete fuzzy graphs, fuzzy cycles, and fuzzy trees. Besides, we obtain relations between SFCP and fuzzy chromatic polynomial of strong fuzzy graphs, complete fuzzy graphs, and fuzzy cycles. Finally, we present dual applications of the proposed work in the traffic flow problem. Once SFCP of a fuzzy graph is obtained, the proposed approach is simple enough and shortcut technique to solve strong coloring problems without using coloring algorithms.
{"title":"Strong Fuzzy Chromatic Polynomial (SFCP) of Fuzzy Graphs and Some Fuzzy Graph Structures with Applications","authors":"M. A. Ashebo, V. N. S. R. Repalle","doi":"10.11648/J.PAMJ.20200901.13","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20200901.13","url":null,"abstract":"In fuzzy graph theory, strong arcs have separate importance. Assign different colors to the end nodes of strong arcs in the fuzzy graph is strong coloring. Strong coloring plays an important role in solving real-life problems that involve networks. In this work, we introduce the new concept, called strong fuzzy chromatic polynomial (SFCP) of a fuzzy graph based on strong coloring. The SFCP of a fuzzy graph counts the number of k-strong colorings of a fuzzy graph with k colors. The existing methods for determining the chromatic polynomial of the crisp graph are used to obtain SFCP of a fuzzy graph. We establish the necessary and sufficient condition for SFCP of a fuzzy graph to be the chromatic polynomial of its underlying crisp graph. Further, we study SFCP of some fuzzy graph structures, namely strong fuzzy graphs, complete fuzzy graphs, fuzzy cycles, and fuzzy trees. Besides, we obtain relations between SFCP and fuzzy chromatic polynomial of strong fuzzy graphs, complete fuzzy graphs, and fuzzy cycles. Finally, we present dual applications of the proposed work in the traffic flow problem. Once SFCP of a fuzzy graph is obtained, the proposed approach is simple enough and shortcut technique to solve strong coloring problems without using coloring algorithms.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"16 1","pages":"16"},"PeriodicalIF":0.2,"publicationDate":"2020-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74282462","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 : 2020-01-18DOI: 10.11648/J.PAMJ.20200901.12
Fekadu Tesgera Agama, V. N. S. R. Repalle
The fuzzy graph theory, its properties, total coloring and applications are currently climbing up. With this concept of fuzzy graph, total fuzzy graph is defined and its properties as well as fuzzy total colorings have been well discussed and studied. Similarly the theory of crisp graph, its properties, applications and colorings are well considered. Moreover, 1-quasi total graphs for crisp graphs, their properties and colorings were discussed by some researchers and the bounds for its total coloring have been established. In this manuscript, from the concept of fuzzy graph we introduced the definition of 1-quasi total graph for fuzzy graphs. To elaborate the definition we provide practical example of fuzzy graph and from this graph we construct the 1-quasi total fuzzy graph of the given fuzzy graph, so that the definition to be meaning full and their relationships can be easily observed from the sketched graphs. In addition some theorems related to the properties of 1-quasi total fuzzy graphs are stated and proved. The results of these theorems are compared with the results obtained from total fuzzy graphs, so that the differences and similarities that 1-quasi total fuzzy graph can have with that of total fuzzy graphs are revealed. Moreover, we define 1-quasi total coloring of fuzzy total graphs and give an example of total coloring of 1-quasi total graphs.
{"title":"1-Quasi Total Fuzzy Graph and Its Total Coloring","authors":"Fekadu Tesgera Agama, V. N. S. R. Repalle","doi":"10.11648/J.PAMJ.20200901.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20200901.12","url":null,"abstract":"The fuzzy graph theory, its properties, total coloring and applications are currently climbing up. With this concept of fuzzy graph, total fuzzy graph is defined and its properties as well as fuzzy total colorings have been well discussed and studied. Similarly the theory of crisp graph, its properties, applications and colorings are well considered. Moreover, 1-quasi total graphs for crisp graphs, their properties and colorings were discussed by some researchers and the bounds for its total coloring have been established. In this manuscript, from the concept of fuzzy graph we introduced the definition of 1-quasi total graph for fuzzy graphs. To elaborate the definition we provide practical example of fuzzy graph and from this graph we construct the 1-quasi total fuzzy graph of the given fuzzy graph, so that the definition to be meaning full and their relationships can be easily observed from the sketched graphs. In addition some theorems related to the properties of 1-quasi total fuzzy graphs are stated and proved. The results of these theorems are compared with the results obtained from total fuzzy graphs, so that the differences and similarities that 1-quasi total fuzzy graph can have with that of total fuzzy graphs are revealed. Moreover, we define 1-quasi total coloring of fuzzy total graphs and give an example of total coloring of 1-quasi total graphs.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"75 1","pages":"9"},"PeriodicalIF":0.2,"publicationDate":"2020-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78582489","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 : 2020-01-04DOI: 10.11648/J.PAMJ.20200901.11
Uchechukwu Opara
The calculus of variations applied in multivariate problems can give rise to several classical Partial Differential Equations (PDE’s) of interest. To this end, it is acknowledged that a vast range of classical PDE’s were formulated initially from variational problems. In this paper, we aim to formulate such equations arising from the viewpoint of optimization of energy functionals on smooth Riemannian manifolds. These energy functionals are given as sufficiently regular integrals of other functionals defined on the manifolds. Relevant Banach domains which contain the optimal functional solutions are identified by preliminary analysis, and then necessary optimality conditions are discovered by differentiation in these Banach spaces. To determine specific optimal functionals in simple settings, smaller target domains are taken as appropriate subsets of the Banach (Sobolev) spaces. Briefings on analytical implications and approaches proffered are included for the aforementioned simple settings as well as more general case scenarios.
{"title":"Partial Differential Equation Formulations from Variational Problems","authors":"Uchechukwu Opara","doi":"10.11648/J.PAMJ.20200901.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20200901.11","url":null,"abstract":"The calculus of variations applied in multivariate problems can give rise to several classical Partial Differential Equations (PDE’s) of interest. To this end, it is acknowledged that a vast range of classical PDE’s were formulated initially from variational problems. In this paper, we aim to formulate such equations arising from the viewpoint of optimization of energy functionals on smooth Riemannian manifolds. These energy functionals are given as sufficiently regular integrals of other functionals defined on the manifolds. Relevant Banach domains which contain the optimal functional solutions are identified by preliminary analysis, and then necessary optimality conditions are discovered by differentiation in these Banach spaces. To determine specific optimal functionals in simple settings, smaller target domains are taken as appropriate subsets of the Banach (Sobolev) spaces. Briefings on analytical implications and approaches proffered are included for the aforementioned simple settings as well as more general case scenarios.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"38 1","pages":"1"},"PeriodicalIF":0.2,"publicationDate":"2020-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90637276","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 : 2019-12-31DOI: 10.11648/J.PAMJ.20190806.12
Fuxian Chen, Qiuhui Chen, Weibin Wu, Xiaoming Wang
Wavelet transform is an important quadratic representation in time-frequency domain of signals. The main advantage of wavelet transform is the time frequency localization as compared with the fourier transform. Due to the reason of dilation and translation operation acting the basic time-frequency atoms. Therefore a multi-resoloution analysis strategy is devoted to the construction of wavelet basis of L2(R), which also establishes a bridge between engineer and mathematics. The construction of wavelets is equivalent to the design of filter banks with complete reconstruction. In this note we investigate filter banks from the Fibonacci sequence. The draw back is that, the convergence z-transform is less than 1, hence it can not be used as filter. By adopting the Hadamard product of the Fibonacci sequence and a geometric sequence, a type of Fibonacci-based bi-orthogonal filter banks are constructed. This kind of filter banks are based two bricks: Bezout polynomials and the mask of the cardinal B-splines. These filters are essentially rational functions, which have potential applications in system identification and signal processing.
{"title":"Filter Banks from the Fibonacci Sequence","authors":"Fuxian Chen, Qiuhui Chen, Weibin Wu, Xiaoming Wang","doi":"10.11648/J.PAMJ.20190806.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20190806.12","url":null,"abstract":"Wavelet transform is an important quadratic representation in time-frequency domain of signals. The main advantage of wavelet transform is the time frequency localization as compared with the fourier transform. Due to the reason of dilation and translation operation acting the basic time-frequency atoms. Therefore a multi-resoloution analysis strategy is devoted to the construction of wavelet basis of L2(R), which also establishes a bridge between engineer and mathematics. The construction of wavelets is equivalent to the design of filter banks with complete reconstruction. In this note we investigate filter banks from the Fibonacci sequence. The draw back is that, the convergence z-transform is less than 1, hence it can not be used as filter. By adopting the Hadamard product of the Fibonacci sequence and a geometric sequence, a type of Fibonacci-based bi-orthogonal filter banks are constructed. This kind of filter banks are based two bricks: Bezout polynomials and the mask of the cardinal B-splines. These filters are essentially rational functions, which have potential applications in system identification and signal processing.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89687918","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 : 2019-12-24DOI: 10.11648/J.PAMJ.20190806.11
Mohit Kumar, R. Arora, Ajay Kumar
The evolution of fuzzy mathematics commenced with the introduction of the notion of fuzzy set by Zadeh, where the concept of uncertainty has been introduced in the theory of sets in a non probabilistic manner. The several researchers were conducting the generalization of the concept of fuzzy sets. The present research paper focuses on the existence of fixed points in fuzzy metric space. Hardy-Rogers is to establish a fixed point theorem for three maps of a complete metric space. The contractive condition is generalized and the commuting condition of Jungck is replaced by the concept of weakly commuting. The three Hardy-Rogers type mappings are extended in fuzzy metric space and also extend to generalize non-expansive mapping define over a compact fuzzy metric space. The contractive condition is generalization of Hardy-Rogers and the commuting condition of Jungck is replace by the concept of weakly commuting. Our results deals with mappings satisfying a condition weaker than commutativity in complete fuzzy metric space and is the generalization in complete fuzzy metric space of Hardy-Rogers type mappings in complete metric space. We also provide some illustrative example to support our result. We apply also our main results to derive unique and common fixed point for contractive mappings.
{"title":"Hardy-Rogers Type Mappings for Fuzzy Metric Space","authors":"Mohit Kumar, R. Arora, Ajay Kumar","doi":"10.11648/J.PAMJ.20190806.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20190806.11","url":null,"abstract":"The evolution of fuzzy mathematics commenced with the introduction of the notion of fuzzy set by Zadeh, where the concept of uncertainty has been introduced in the theory of sets in a non probabilistic manner. The several researchers were conducting the generalization of the concept of fuzzy sets. The present research paper focuses on the existence of fixed points in fuzzy metric space. Hardy-Rogers is to establish a fixed point theorem for three maps of a complete metric space. The contractive condition is generalized and the commuting condition of Jungck is replaced by the concept of weakly commuting. The three Hardy-Rogers type mappings are extended in fuzzy metric space and also extend to generalize non-expansive mapping define over a compact fuzzy metric space. The contractive condition is generalization of Hardy-Rogers and the commuting condition of Jungck is replace by the concept of weakly commuting. Our results deals with mappings satisfying a condition weaker than commutativity in complete fuzzy metric space and is the generalization in complete fuzzy metric space of Hardy-Rogers type mappings in complete metric space. We also provide some illustrative example to support our result. We apply also our main results to derive unique and common fixed point for contractive mappings.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"63 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90473336","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 : 2019-10-24DOI: 10.11648/J.PAMJ.20190805.12
S. Abdul-Kareem, A. A. Abdulkareem
The aim of introducing and studying the notion of closed quasi injective S-act is to create a basis facilitate for the exchange ideas between module theory and act theory. As well as it represents a generalization of the quasi-injective act. The quasi-injective act was first introduced and studied by A. M. Lopez, Jr. and J. K. Luedeman, 1979. Then the author was one of the researchers which introduced several generalizations for this notion from several aspects because of its importance. More accurately, the contribution of this paper to the field of competence can be summarized into three points as follows: First: The possibilities for applying the topic of this article helps researchers about how can connect class of injectivity with its generalizations. Second: Study the topic of this article contributes to the improvement of the vision for finding the corresponding between acts theory and module theory. Third: This article has dealt with the important subject in the field of science and knowledge especially in algebra and can take it as a basis for future work for the researchers who work on algebra. Now, in this paper, the concept of closed quasi injective acts over monoids is introduced which represents a generalization of quasi injective. Several characterizations of this concept are given to show the behavior of the property of closed quasi injective. Relationship of the concept of closed quasi injective acts over monoids with Hopfian, co-Hopfian and directly finite property are considered. This work gives the answer to the question of what are the conditions to be met in the subacts in order to inherit the property of closed quasi injectivity. We obtained the main result in this direction in proposition (2.5) and proposition (2.6). A part of this paper was devoted to studying the relationship among the class of closed quasi injective acts with some generalizations of injectivity.
本文引入和研究闭拟内射s -行为的概念，目的是为模块理论与行为理论的思想交流创造一个基础。同时它也代表了拟单射行为的一种推广。拟内射行为最早是由A. M. Lopez, Jr.和J. K. Luedeman(1979)提出并研究的。由于这一概念的重要性，笔者从几个方面对其进行了一些概括。更准确地说，本文对能力领域的贡献可以概括为以下三点:第一:应用本文主题的可能性有助于研究人员如何将注入性类别与其概括联系起来。第二:研究本文的课题有助于提高视野，找到行为理论与模块理论之间的对应关系。第三，本文论述了科学和知识领域特别是代数领域的重要课题，可以作为今后代数研究者工作的基础。本文引入了模群上闭拟内射的概念，它是拟内射的推广。给出了这一概念的几个刻画，以证明闭拟内射性质的行为。考虑了具有Hopfian、协Hopfian和直接有限性质的模群上闭拟内射行为的概念之间的关系。这一工作给出了为了继承闭拟注入的性质，在主体中需要满足什么条件的问题的答案。我们在命题(2.5)和命题(2.6)中得到了这个方向的主要结果。本文用一些关于内射的推广研究了一类闭拟内射行为之间的关系。
{"title":"About the Closed Quasi Injective S-Acts Over Monoids","authors":"S. Abdul-Kareem, A. A. Abdulkareem","doi":"10.11648/J.PAMJ.20190805.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20190805.12","url":null,"abstract":"The aim of introducing and studying the notion of closed quasi injective S-act is to create a basis facilitate for the exchange ideas between module theory and act theory. As well as it represents a generalization of the quasi-injective act. The quasi-injective act was first introduced and studied by A. M. Lopez, Jr. and J. K. Luedeman, 1979. Then the author was one of the researchers which introduced several generalizations for this notion from several aspects because of its importance. More accurately, the contribution of this paper to the field of competence can be summarized into three points as follows: First: The possibilities for applying the topic of this article helps researchers about how can connect class of injectivity with its generalizations. Second: Study the topic of this article contributes to the improvement of the vision for finding the corresponding between acts theory and module theory. Third: This article has dealt with the important subject in the field of science and knowledge especially in algebra and can take it as a basis for future work for the researchers who work on algebra. Now, in this paper, the concept of closed quasi injective acts over monoids is introduced which represents a generalization of quasi injective. Several characterizations of this concept are given to show the behavior of the property of closed quasi injective. Relationship of the concept of closed quasi injective acts over monoids with Hopfian, co-Hopfian and directly finite property are considered. This work gives the answer to the question of what are the conditions to be met in the subacts in order to inherit the property of closed quasi injectivity. We obtained the main result in this direction in proposition (2.5) and proposition (2.6). A part of this paper was devoted to studying the relationship among the class of closed quasi injective acts with some generalizations of injectivity.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"16 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87281412","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 : 2019-10-24DOI: 10.11648/J.PAMJ.20190805.11
M Musraini, R. Efendi, Endang Lily, Ponco Hidayah
Recently, a definition of fractional which refers to classical calculus form called conformable fractional calculus has been introduced. The main idea of the concept of conformable fractional calculus is how to determine the derivative and integral with fractional order either rational numbers or real numbers. One of the most popular definitions of conformable fractional calculus is defined by Katugampola which is used in this study. This definition satisfies in some respects of classical calculus involved conformable fractional derivative and conformable fractional integral. In the branch of conformable fractional derivatives, some of the additional results such as analysis of fractional derivative in quotient property, product property and Rolle theorem are given. An application on classical calculus such as determining monotonicity of function is also given. Then, in the case of fractional integral, this definition showed that the fractional derivative and the fractional integral are inverses of each other. Some of the classical integral properties are also satisfied on conformable fractional integral. Additionally, this study also has shown that fractional integral acts as a limit of a sum. After that, comparison properties on fractional integral are provided. Finally, the mean value theorem and the second mean value theorem are also applicable for fractional integral.
{"title":"Classical Properties on Conformable Fractional Calculus","authors":"M Musraini, R. Efendi, Endang Lily, Ponco Hidayah","doi":"10.11648/J.PAMJ.20190805.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20190805.11","url":null,"abstract":"Recently, a definition of fractional which refers to classical calculus form called conformable fractional calculus has been introduced. The main idea of the concept of conformable fractional calculus is how to determine the derivative and integral with fractional order either rational numbers or real numbers. One of the most popular definitions of conformable fractional calculus is defined by Katugampola which is used in this study. This definition satisfies in some respects of classical calculus involved conformable fractional derivative and conformable fractional integral. In the branch of conformable fractional derivatives, some of the additional results such as analysis of fractional derivative in quotient property, product property and Rolle theorem are given. An application on classical calculus such as determining monotonicity of function is also given. Then, in the case of fractional integral, this definition showed that the fractional derivative and the fractional integral are inverses of each other. Some of the classical integral properties are also satisfied on conformable fractional integral. Additionally, this study also has shown that fractional integral acts as a limit of a sum. After that, comparison properties on fractional integral are provided. Finally, the mean value theorem and the second mean value theorem are also applicable for fractional integral.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88391425","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 : 2019-10-09DOI: 10.11648/j.pamj.20190804.12
Ihda Hasbiyati, Widiawati Putri, A. Adnan, Ahriyati, Hasriati
Parking lots are one of the most important elements of transportation infrastructure. Parking lots with good design and the selection of suitable parking angles will provide optimal vehicle capacity. In this article, we will discuss the parking lot in the form of a Parallelogram with a broad concept of area, for parking a private car vehicle. In this paper, the land in the form of a jug is formed of two right and rectangular triangles. The method used is a linear program method that is formed from the broad concept of the area with the help of lindo software. The results obtained from this article are the forms of Parallelogram which are formed from two right triangles which are used divided into two parts, namely a right triangle with a base and a height of half a rectangle resulting in a total parking area of 873,600 square meters, with the number of car vehicles that can be parked on the inside of a parking lot with a 90 degree angle is as much as 520 car vehicles. So it can be concluded that the numbers formed from two right triangles and rectangles produce the optimal number of vehicles with a 90 degree parking angle.
{"title":"Parking Lot Optimization in Parallelogram Using the Concept Area of Rectangular and Right Triangle","authors":"Ihda Hasbiyati, Widiawati Putri, A. Adnan, Ahriyati, Hasriati","doi":"10.11648/j.pamj.20190804.12","DOIUrl":"https://doi.org/10.11648/j.pamj.20190804.12","url":null,"abstract":"Parking lots are one of the most important elements of transportation infrastructure. Parking lots with good design and the selection of suitable parking angles will provide optimal vehicle capacity. In this article, we will discuss the parking lot in the form of a Parallelogram with a broad concept of area, for parking a private car vehicle. In this paper, the land in the form of a jug is formed of two right and rectangular triangles. The method used is a linear program method that is formed from the broad concept of the area with the help of lindo software. The results obtained from this article are the forms of Parallelogram which are formed from two right triangles which are used divided into two parts, namely a right triangle with a base and a height of half a rectangle resulting in a total parking area of 873,600 square meters, with the number of car vehicles that can be parked on the inside of a parking lot with a 90 degree angle is as much as 520 car vehicles. So it can be concluded that the numbers formed from two right triangles and rectangles produce the optimal number of vehicles with a 90 degree parking angle.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82534991","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 : 2019-09-03DOI: 10.11648/J.PAMJ.20190804.11
M. Malkov
Real numbers are divided into fictitious (non-computable) and essential (computable). Fictitious numbers do not have numerical values, essential numbers have algorithms for constructing these numbers with any exactness. The set of fictitious numbers is continual, the set of essential numbers is countable. Functions are also divided into fictitious, defined over the set of fictitious numbers, and essential, defined over the set of essential numbers. Essential functions have an algorithm for calculating any value with any exactness. All functions of applied mathematics and some functions of abstract mathematics are essential The set these functions is countable. The four upper levels of classification of real functions are constructed. This classification uses superpositions of functions and diagonal sets borrowed from the algebra of finite-valued functions.
{"title":"Algebra of Real Functions: Classification of Functions, Fictitious and Essential Functions","authors":"M. Malkov","doi":"10.11648/J.PAMJ.20190804.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20190804.11","url":null,"abstract":"Real numbers are divided into fictitious (non-computable) and essential (computable). Fictitious numbers do not have numerical values, essential numbers have algorithms for constructing these numbers with any exactness. The set of fictitious numbers is continual, the set of essential numbers is countable. Functions are also divided into fictitious, defined over the set of fictitious numbers, and essential, defined over the set of essential numbers. Essential functions have an algorithm for calculating any value with any exactness. All functions of applied mathematics and some functions of abstract mathematics are essential The set these functions is countable. The four upper levels of classification of real functions are constructed. This classification uses superpositions of functions and diagonal sets borrowed from the algebra of finite-valued functions.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"2 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81531814","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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