Pub Date : 2018-12-24DOI: 10.11648/J.PAMJ.20180705.12
Olinto de Oliveira Santos
The objective of this article is to demonstrate the Collatz Conjecture through the Sets and Binary Numbers Theory, in this manner: 2n + 2n-1+...1. This study shows that there are subsequences of odd numbers within the Collatz sequences, and that by proving the proposition is true for these subsequences, it is subsequently proven that the entire proposition is correct. It is also proven that a sequence which begins with a natural number is generated by a set of operations: Multiplication by 3, addition of 1 and division by 2n. This set of operations shall be called “Movement” in this study, and may be increasing when n=1, and decreasing for n ≥ 2. The numbers in 2n form generate decreasing sequences in which the 3n+1 operation does not occur. One of the important discoveries is how to generate numbers in which the 3n+1 operation only occurs once and how to generate numbers with a minimum quantity of increasing movements that are the numbers of greater “orbits” (Longer sequences that take longer to reach the number one). The conclusion is that, as the decreasing numbers dominate as compared to the increasing ones, the statement that the sequence is always going to reach the number 1 is true.
{"title":"Proving the Collatz Conjecture with Binaries Numbers","authors":"Olinto de Oliveira Santos","doi":"10.11648/J.PAMJ.20180705.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20180705.12","url":null,"abstract":"The objective of this article is to demonstrate the Collatz Conjecture through the Sets and Binary Numbers Theory, in this manner: 2n + 2n-1+...1. This study shows that there are subsequences of odd numbers within the Collatz sequences, and that by proving the proposition is true for these subsequences, it is subsequently proven that the entire proposition is correct. It is also proven that a sequence which begins with a natural number is generated by a set of operations: Multiplication by 3, addition of 1 and division by 2n. This set of operations shall be called “Movement” in this study, and may be increasing when n=1, and decreasing for n ≥ 2. The numbers in 2n form generate decreasing sequences in which the 3n+1 operation does not occur. One of the important discoveries is how to generate numbers in which the 3n+1 operation only occurs once and how to generate numbers with a minimum quantity of increasing movements that are the numbers of greater “orbits” (Longer sequences that take longer to reach the number one). The conclusion is that, as the decreasing numbers dominate as compared to the increasing ones, the statement that the sequence is always going to reach the number 1 is true.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"6 1","pages":"68"},"PeriodicalIF":0.2,"publicationDate":"2018-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81183127","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 : 2018-11-30DOI: 10.11648/J.PAMJ.20180705.11
Renz Chester Rosales Gumaru, Leonida Solivas Casuco, H. Bernal
A perfect number is a positive integer that is equals to the sum of its proper divisors. No one has ever found an odd perfect number in the field of Number Theory. This paper review discussed the history and the origin of Odd Perfect Numbers. The theorems and proofs are given and stated. This paper states the necessary conditions for the existence of odd perfect numbers. In addition, several related studies such as “Odd Near-Perfect Numbers” and “Deficient-Perfect Numbers”. Formulating odd perfect numbers will have a significant contribution to other Mathematics conjectures. This paper compiles all the known information about the existence of an odd perfect number It also lists and explains the necessary theorems and lemmas needed for the study. The results and conclusions shows the ff: Odd Perfect Numbers has a lower bound of 101500, The total number of prime factors/divisors of an odd perfect number is at least 101, and 108 is an appropriate lower bound for the largest prime factor of an odd perfect number and the second large stand third largest prime divisors must exceed 10000 and100 respectively. In summary, it found out that there is a chance for an odd perfect number to exist even if there is a very small possibility.
{"title":"Formulating an Odd Perfect Number: An in Depth Case Study","authors":"Renz Chester Rosales Gumaru, Leonida Solivas Casuco, H. Bernal","doi":"10.11648/J.PAMJ.20180705.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20180705.11","url":null,"abstract":"A perfect number is a positive integer that is equals to the sum of its proper divisors. No one has ever found an odd perfect number in the field of Number Theory. This paper review discussed the history and the origin of Odd Perfect Numbers. The theorems and proofs are given and stated. This paper states the necessary conditions for the existence of odd perfect numbers. In addition, several related studies such as “Odd Near-Perfect Numbers” and “Deficient-Perfect Numbers”. Formulating odd perfect numbers will have a significant contribution to other Mathematics conjectures. This paper compiles all the known information about the existence of an odd perfect number It also lists and explains the necessary theorems and lemmas needed for the study. The results and conclusions shows the ff: Odd Perfect Numbers has a lower bound of 101500, The total number of prime factors/divisors of an odd perfect number is at least 101, and 108 is an appropriate lower bound for the largest prime factor of an odd perfect number and the second large stand third largest prime divisors must exceed 10000 and100 respectively. In summary, it found out that there is a chance for an odd perfect number to exist even if there is a very small possibility.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"132 1","pages":"63"},"PeriodicalIF":0.2,"publicationDate":"2018-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85128569","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 : 2018-11-06DOI: 10.11648/J.PAMJ.20180704.11
Ozokeraha Christiana Funmilayo
In recent times, the study of analytic functions has been useful in solving many problems in mechanics, Laplace equation, electrostatics, etc. An analytic function is said to be univalent in a domain if it does not take the same value twice in that domain while an analytic function is said to be p-valent in a domain if it does not take the same value more than p times in that domain. Many researches on properties of p-valent functions using Salagean, Al Oboudi and Opoola differential operators have been reviewed. The aim of this research is to obtain the properties of new subclasses of p-valent functions defined by Salagean differential operator and its objectives are to obtain new subclasses of p-valent functions and the necessary properties for the new subclasses. This research will be a contribution to knowledge in geometric function theory and provide new tools of applications in fluid dynamics and differential equations. This paper introduces new subclasses of p – valent functions defined by Al –Oboudi differential operator. Finally, the paper studies some interesting results including subordination, coefficient inequalities, starlikeness and convexity conditions, Hadamard product and certain properties of neighbourhoods of the new subclasses of p-valent functions. Theorems were used to establish certain conditions of the new subclasses of p-valent functions.
{"title":"On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator","authors":"Ozokeraha Christiana Funmilayo","doi":"10.11648/J.PAMJ.20180704.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20180704.11","url":null,"abstract":"In recent times, the study of analytic functions has been useful in solving many problems in mechanics, Laplace equation, electrostatics, etc. An analytic function is said to be univalent in a domain if it does not take the same value twice in that domain while an analytic function is said to be p-valent in a domain if it does not take the same value more than p times in that domain. Many researches on properties of p-valent functions using Salagean, Al Oboudi and Opoola differential operators have been reviewed. The aim of this research is to obtain the properties of new subclasses of p-valent functions defined by Salagean differential operator and its objectives are to obtain new subclasses of p-valent functions and the necessary properties for the new subclasses. This research will be a contribution to knowledge in geometric function theory and provide new tools of applications in fluid dynamics and differential equations. This paper introduces new subclasses of p – valent functions defined by Al –Oboudi differential operator. Finally, the paper studies some interesting results including subordination, coefficient inequalities, starlikeness and convexity conditions, Hadamard product and certain properties of neighbourhoods of the new subclasses of p-valent functions. Theorems were used to establish certain conditions of the new subclasses of p-valent functions.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"5 1","pages":"45"},"PeriodicalIF":0.2,"publicationDate":"2018-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78750094","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 : 2018-09-28DOI: 10.11648/j.pamj.20180703.12
R. Shuler
The problem of how many colors are required for a planar map has been used as a focal point for discussions of the limits of human direct understanding vs. automated methods. It is important to continue to investigate until it is convincingly proved map coloration is an exemplary irreducible problem or until it is reduced. Meanwhile a new way of thinking about surfaces which hide N-dimensional volumes has arisen in physics employing entropy and the holographic principle. In this paper we define coloration entropy or flexibility as a count of the possible distinct colorations of a map (planar graph), and show how a guaranteed minimum coloration flexibility changes based on additions at a boundary of the map. The map is 4-colorable as long as the flexibility is positive, even though the proof method does not construct a coloration. This demonstration is successful, resulting in a compact and easily comprehended proof of the four color theorem. The use of an entropy-like method suggests comparisons and applications to issues in physics such as black holes. Therefore in conclusion some comments are offered on the relation to physics and the relation of plane-section color-ability to higher dimensional spaces. Future directions of research are suggested which may connect the concepts to not only time and distance and thus entropic gravity but also momentum.
{"title":"Entropy-Like State Counting Leads to Human Readable Four Color Map Theorem Proof","authors":"R. Shuler","doi":"10.11648/j.pamj.20180703.12","DOIUrl":"https://doi.org/10.11648/j.pamj.20180703.12","url":null,"abstract":"The problem of how many colors are required for a planar map has been used as a focal point for discussions of the limits of human direct understanding vs. automated methods. It is important to continue to investigate until it is convincingly proved map coloration is an exemplary irreducible problem or until it is reduced. Meanwhile a new way of thinking about surfaces which hide N-dimensional volumes has arisen in physics employing entropy and the holographic principle. In this paper we define coloration entropy or flexibility as a count of the possible distinct colorations of a map (planar graph), and show how a guaranteed minimum coloration flexibility changes based on additions at a boundary of the map. The map is 4-colorable as long as the flexibility is positive, even though the proof method does not construct a coloration. This demonstration is successful, resulting in a compact and easily comprehended proof of the four color theorem. The use of an entropy-like method suggests comparisons and applications to issues in physics such as black holes. Therefore in conclusion some comments are offered on the relation to physics and the relation of plane-section color-ability to higher dimensional spaces. Future directions of research are suggested which may connect the concepts to not only time and distance and thus entropic gravity but also momentum.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"55 1","pages":"37"},"PeriodicalIF":0.2,"publicationDate":"2018-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91333958","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 : 2018-08-08DOI: 10.11648/J.PAMJ.20180703.11
W. Mwangi
The division by zero has been a challenge over years, which is in two forms: one involves a non-zero numerator while the other involves a zero numerator. This work deals with the second form of division, with the aim of finding a solution to the equation obtained when the expression is equated to, say x, where x is not a quantity but the ‘number of times of one whole’. In this work, zero divided by itself has been exhausted using different approaches and methods to come to a conclusion; that this division has a unique solution, 1. Some of the methods employed include geometric series, logarithm, indices, reciprocals, factorials, self-operations, Euler’s number, binomial expansions, graphical method among others. The conclusion has been made that zero divided by zero is 1. The reverse of division by multiplication is not applicable because zero has been associated with two ‘abnormal’ properties or behaviour that’s not with other numbers.
{"title":"Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution","authors":"W. Mwangi","doi":"10.11648/J.PAMJ.20180703.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20180703.11","url":null,"abstract":"The division by zero has been a challenge over years, which is in two forms: one involves a non-zero numerator while the other involves a zero numerator. This work deals with the second form of division, with the aim of finding a solution to the equation obtained when the expression is equated to, say x, where x is not a quantity but the ‘number of times of one whole’. In this work, zero divided by itself has been exhausted using different approaches and methods to come to a conclusion; that this division has a unique solution, 1. Some of the methods employed include geometric series, logarithm, indices, reciprocals, factorials, self-operations, Euler’s number, binomial expansions, graphical method among others. The conclusion has been made that zero divided by zero is 1. The reverse of division by multiplication is not applicable because zero has been associated with two ‘abnormal’ properties or behaviour that’s not with other numbers.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"6 1","pages":"20"},"PeriodicalIF":0.2,"publicationDate":"2018-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87377669","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 : 2018-07-17DOI: 10.11648/J.PAMJ.20180702.11
Joseph Gogodze
This study proposes a game-theoretic approach to solve a multiobjective decision-making problem. The essence of the method is that a normalized decision matrix can be considered as a payoff matrix for some zero-sum matrix game, in which the first player chooses an alternative and the second player chooses a criterion. Herein, the solution in mixed strategies of this game is used to construct a weighted sum of the primary criteria that leads to a solution of the primary multiobjective decision-making problem. The proposed method leads to a notionally objective weighting method for multiobjective decision-making and provides “true weights” even in the absence of preliminary subjective evaluations. The proposed new method has a simple application. It can be applied to decision-making problems with any number of alternatives/criteria, and its practical realization is limited only by the capabilities of the solver of the linear programming problem formulated to solve the corresponding zero-sum game. Moreover, as observed from the solutions of the illustrative examples, the results obtained with the proposed method are quite appropriate and competitive.
{"title":"Using a Two-Person Zero-Sum Game to Solve a Decision-Making Problem","authors":"Joseph Gogodze","doi":"10.11648/J.PAMJ.20180702.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20180702.11","url":null,"abstract":"This study proposes a game-theoretic approach to solve a multiobjective decision-making problem. The essence of the method is that a normalized decision matrix can be considered as a payoff matrix for some zero-sum matrix game, in which the first player chooses an alternative and the second player chooses a criterion. Herein, the solution in mixed strategies of this game is used to construct a weighted sum of the primary criteria that leads to a solution of the primary multiobjective decision-making problem. The proposed method leads to a notionally objective weighting method for multiobjective decision-making and provides “true weights” even in the absence of preliminary subjective evaluations. The proposed new method has a simple application. It can be applied to decision-making problems with any number of alternatives/criteria, and its practical realization is limited only by the capabilities of the solver of the linear programming problem formulated to solve the corresponding zero-sum game. Moreover, as observed from the solutions of the illustrative examples, the results obtained with the proposed method are quite appropriate and competitive.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"55 1","pages":"11"},"PeriodicalIF":0.2,"publicationDate":"2018-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84662914","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 : 2018-03-27DOI: 10.11648/J.PAMJ.20180701.12
D. N. Kingangi
Many researchers in operator theory have attempted to determine the relationship between the norm of an elementary operator of finite length and the norms of its coefficient operators. Various results have been obtained using varied approaches. In this paper, we attempt this problem by the use of the Stampfli’s maximal numerical range.
{"title":"On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range","authors":"D. N. Kingangi","doi":"10.11648/J.PAMJ.20180701.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20180701.12","url":null,"abstract":"Many researchers in operator theory have attempted to determine the relationship between the norm of an elementary operator of finite length and the norms of its coefficient operators. Various results have been obtained using varied approaches. In this paper, we attempt this problem by the use of the Stampfli’s maximal numerical range.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"1 1","pages":"6"},"PeriodicalIF":0.2,"publicationDate":"2018-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88809953","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 : 2018-02-02DOI: 10.11648/J.PAMJ.20180701.11
I. Bassi, Yakubu Gabriel, O. O. Galadima
The aim of this research is to extend the new type of compact spaces called Q* compact spaces, study its properties and generate new results of the space. It investigate the Q*-compactness of topological spaces with separable, Q*-metrizable, Q*-Hausdorff, homeomorphic, connected and finite intersection properties. The closed interval [0, 1] is Q* compact. So, it is deduced that the closed interval [0, 1] is Q*-compact. For example, if ( X, τ ) = ℝ and A = (0, ∞) then A is not Q*-compact. A subset S of ℝ is Q*-compact. Also, if ( X , τ ) is a Q*-compact metrizable space. Then ( X , τ ) is separable. ( Y , τ 1 ) is Q*-compact and metrizable if f is a continuous mapping of a Q*-compact metric space (X, d) onto a Q*-Hausdorff space ( Y , τ 1 ). An infinite subset of a Q*-compact space must have a limit point. The continuous mapping of a Q*-compact space has a greatest element and a least element. Eleven theorems were considered and their results were presented accordingly.
{"title":"The Study of the Concept of Q*Compact Spaces","authors":"I. Bassi, Yakubu Gabriel, O. O. Galadima","doi":"10.11648/J.PAMJ.20180701.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20180701.11","url":null,"abstract":"The aim of this research is to extend the new type of compact spaces called Q* compact spaces, study its properties and generate new results of the space. It investigate the Q*-compactness of topological spaces with separable, Q*-metrizable, Q*-Hausdorff, homeomorphic, connected and finite intersection properties. The closed interval [0, 1] is Q* compact. So, it is deduced that the closed interval [0, 1] is Q*-compact. For example, if ( X, τ ) = ℝ and A = (0, ∞) then A is not Q*-compact. A subset S of ℝ is Q*-compact. Also, if ( X , τ ) is a Q*-compact metrizable space. Then ( X , τ ) is separable. ( Y , τ 1 ) is Q*-compact and metrizable if f is a continuous mapping of a Q*-compact metric space (X, d) onto a Q*-Hausdorff space ( Y , τ 1 ). An infinite subset of a Q*-compact space must have a limit point. The continuous mapping of a Q*-compact space has a greatest element and a least element. Eleven theorems were considered and their results were presented accordingly.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"43 1","pages":"1"},"PeriodicalIF":0.2,"publicationDate":"2018-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89919342","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 : 2017-12-18DOI: 10.11648/j.pamj.20170606.12
Basri Çaliskan
Let be a strong semilattice of semigroups such that is finite and each be a family of disjoint semigroups. In this article some finiteness conditions which are periodicity, local finiteness and locally finite presentability are considered for . It is proven that a strong semilattice of semigroups is periodic, locally finite, locally finitely presented and residually finite, respectively if and only if is finite and each semigroup is periodic, locally finite, locally finitely presented and residually finite, respectively.
{"title":"Some Finiteness Conditions for Strong Semilattice of Semigroups","authors":"Basri Çaliskan","doi":"10.11648/j.pamj.20170606.12","DOIUrl":"https://doi.org/10.11648/j.pamj.20170606.12","url":null,"abstract":"Let be a strong semilattice of semigroups such that is finite and each be a family of disjoint semigroups. In this article some finiteness conditions which are periodicity, local finiteness and locally finite presentability are considered for . It is proven that a strong semilattice of semigroups is periodic, locally finite, locally finitely presented and residually finite, respectively if and only if is finite and each semigroup is periodic, locally finite, locally finitely presented and residually finite, respectively.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"24 1","pages":"160"},"PeriodicalIF":0.2,"publicationDate":"2017-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83240248","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 : 2017-11-14DOI: 10.11648/j.pamj.20170606.11
Mengshan Li, Genqin Sun, Huaijin Zhang, Keming Su, Bingsheng Chen, Yan Wu
Petroleum price are affected by some uncertainties and nonlinear factors, how to predict the price effectively is the focus of the present study. In this paper, a 3 layers back propagation artificial neural network model based on particle swarm optimization algorithm combined with chaos theory and self-adaptive weight strategy is developed, the model structure is 7-13-1, and used to predict the petroleum price. By comparing with the other models, it shows that the model proposed in this paper has good prediction performance, the prediction accuracy and correlations are better.
{"title":"Prediction of Petroleum Price Using Back Propagation Artificial Neural Network Based on Chaotic Self-Adaptive Particle Swarm Algorithm","authors":"Mengshan Li, Genqin Sun, Huaijin Zhang, Keming Su, Bingsheng Chen, Yan Wu","doi":"10.11648/j.pamj.20170606.11","DOIUrl":"https://doi.org/10.11648/j.pamj.20170606.11","url":null,"abstract":"Petroleum price are affected by some uncertainties and nonlinear factors, how to predict the price effectively is the focus of the present study. In this paper, a 3 layers back propagation artificial neural network model based on particle swarm optimization algorithm combined with chaos theory and self-adaptive weight strategy is developed, the model structure is 7-13-1, and used to predict the petroleum price. By comparing with the other models, it shows that the model proposed in this paper has good prediction performance, the prediction accuracy and correlations are better.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"18 1","pages":"154"},"PeriodicalIF":0.2,"publicationDate":"2017-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83206260","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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