Abstract The Lonely Runner Conjecture is a known open problem that was defined by Wills in 1967 and in 1973 also by Cusick independently of Wills. If we suppose n runners having distinct constant speeds start at a common point and run laps on a circular track with a unit length, then for any given runner, there is a time at which the distance of that runner is at least 1/n from every other runner. There exist several hypothesis verifications for different n mostly based on principles of approximation using number theory. However, the general solution of the conjecture for any n is still an open problem. In our work we will use a unique approach to verify the Lonely Runner Conjecture by the methods of differential geometry, which presents a non-standard solution, but demonstrates to be a suitable method for solving this type of problems. In the paper we will show also the procedure to build an algorithm that shows the possible existence of a solution for any number of runners.
{"title":"Solving Lonely Runner Conjecture through differential geometry","authors":"V. Ďuriš, T. Šumný, D. Gonda, T. Lengyelfalusy","doi":"10.2478/jamsi-2022-0002","DOIUrl":"https://doi.org/10.2478/jamsi-2022-0002","url":null,"abstract":"Abstract The Lonely Runner Conjecture is a known open problem that was defined by Wills in 1967 and in 1973 also by Cusick independently of Wills. If we suppose n runners having distinct constant speeds start at a common point and run laps on a circular track with a unit length, then for any given runner, there is a time at which the distance of that runner is at least 1/n from every other runner. There exist several hypothesis verifications for different n mostly based on principles of approximation using number theory. However, the general solution of the conjecture for any n is still an open problem. In our work we will use a unique approach to verify the Lonely Runner Conjecture by the methods of differential geometry, which presents a non-standard solution, but demonstrates to be a suitable method for solving this type of problems. In the paper we will show also the procedure to build an algorithm that shows the possible existence of a solution for any number of runners.","PeriodicalId":43016,"journal":{"name":"Journal of Applied Mathematics Statistics and Informatics","volume":"18 1","pages":"21 - 28"},"PeriodicalIF":0.3,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47631803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper is concerned with certain generalized subclasses of multivalent quasi-convex functions defined with subordination. Various properties of these classes in regard to the coefficient estimates, distortion theorems, growth theorems, argument theorems and inclusion relations are discussed. Also, the relations with the earlier known results are established.
{"title":"A note on generalized subclasses of multivalent quasi-convex functions","authors":"G. Singh, G. Singh","doi":"10.2478/jamsi-2022-0007","DOIUrl":"https://doi.org/10.2478/jamsi-2022-0007","url":null,"abstract":"Abstract This paper is concerned with certain generalized subclasses of multivalent quasi-convex functions defined with subordination. Various properties of these classes in regard to the coefficient estimates, distortion theorems, growth theorems, argument theorems and inclusion relations are discussed. Also, the relations with the earlier known results are established.","PeriodicalId":43016,"journal":{"name":"Journal of Applied Mathematics Statistics and Informatics","volume":"18 1","pages":"93 - 107"},"PeriodicalIF":0.3,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49342828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, based on new identity we establish some new Simpson like type inequalities for functions whose first derivatives are s-convex via Riemann-Liouville fractional integrals. The case where the derivatives are bounded as well as the case where the derivatives satisfy the Hölder condition are also discussed. The obtained results extend some known results and refine another one. Applications of the results are given at the end.
{"title":"Fractional Simpson like type inequalities for differentiable s-convex functions","authors":"N. Kamouche, S. Ghomrani, B. Meftah","doi":"10.2478/jamsi-2022-0006","DOIUrl":"https://doi.org/10.2478/jamsi-2022-0006","url":null,"abstract":"Abstract In this paper, based on new identity we establish some new Simpson like type inequalities for functions whose first derivatives are s-convex via Riemann-Liouville fractional integrals. The case where the derivatives are bounded as well as the case where the derivatives satisfy the Hölder condition are also discussed. The obtained results extend some known results and refine another one. Applications of the results are given at the end.","PeriodicalId":43016,"journal":{"name":"Journal of Applied Mathematics Statistics and Informatics","volume":"18 1","pages":"73 - 91"},"PeriodicalIF":0.3,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44818302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The multinomial logit model and the cumulative logit model represent two important tools for regression modeling with a categorical response with numerous applications in various fields. First, this paper presents a systematic review of these two models including available tools for model choice (model selection). Then, numerical experiments are presented for two real datasets with an ordinal categorical response. These experiments reveal that a backward model choice procedure by means of hypothesis testing is more effective compared to a procedure based on Akaike information criterion. While the tendency of the backward selection to be superior to Akaike information criterion has recently been justified in linear regression, such a result seems not to have been presented for models with a categorical response. In addition, we report a mistake in VGAM package of R software, which has however no influence on the process of model choice.
{"title":"Model choice for regression models with a categorical response","authors":"J. Kalina","doi":"10.2478/jamsi-2022-0005","DOIUrl":"https://doi.org/10.2478/jamsi-2022-0005","url":null,"abstract":"Abstract The multinomial logit model and the cumulative logit model represent two important tools for regression modeling with a categorical response with numerous applications in various fields. First, this paper presents a systematic review of these two models including available tools for model choice (model selection). Then, numerical experiments are presented for two real datasets with an ordinal categorical response. These experiments reveal that a backward model choice procedure by means of hypothesis testing is more effective compared to a procedure based on Akaike information criterion. While the tendency of the backward selection to be superior to Akaike information criterion has recently been justified in linear regression, such a result seems not to have been presented for models with a categorical response. In addition, we report a mistake in VGAM package of R software, which has however no influence on the process of model choice.","PeriodicalId":43016,"journal":{"name":"Journal of Applied Mathematics Statistics and Informatics","volume":"18 1","pages":"59 - 71"},"PeriodicalIF":0.3,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45276453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the numerical solution of the boundary value problem for second order fuzzy linear differential equations is discussed. We consider the fuzzy difference equation to replace the fuzzy differential equation. The numerical solution of the boundary value problem is obtained by calculating the fuzzy difference equation. Finally, an example is given, to verify the effectiveness of this method.
{"title":"Numerical Solution of Boundary Value Problems for Second Order Fuzzy Linear Differential Equations","authors":"Haixia Wang","doi":"10.22457/jmi.v22a06207","DOIUrl":"https://doi.org/10.22457/jmi.v22a06207","url":null,"abstract":"In this paper, the numerical solution of the boundary value problem for second order fuzzy linear differential equations is discussed. We consider the fuzzy difference equation to replace the fuzzy differential equation. The numerical solution of the boundary value problem is obtained by calculating the fuzzy difference equation. Finally, an example is given, to verify the effectiveness of this method.","PeriodicalId":43016,"journal":{"name":"Journal of Applied Mathematics Statistics and Informatics","volume":"43 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74313152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates the approximate analytical solutions of third-order timefractional dispersive partial differential equations in one-and higher-dimensional spaces by employing a newly developed analytical method, the Sumudu transform iterative method. To express fractional derivatives, the Caputo operator is used. Furthermore, the results of this investigation are graphically represented, and the solution graphs reveal that the approximate solutions are closely connected to the exact solutions.
{"title":"Analytical Investigation of Third-Order Time-Fractional Dispersive Partial Differential Equations Using Sumudu Transform Iterative Method","authors":"R. K. Bairwa","doi":"10.22457/jmi.v23a02210","DOIUrl":"https://doi.org/10.22457/jmi.v23a02210","url":null,"abstract":"This paper investigates the approximate analytical solutions of third-order timefractional dispersive partial differential equations in one-and higher-dimensional spaces by employing a newly developed analytical method, the Sumudu transform iterative method. To express fractional derivatives, the Caputo operator is used. Furthermore, the results of this investigation are graphically represented, and the solution graphs reveal that the approximate solutions are closely connected to the exact solutions.","PeriodicalId":43016,"journal":{"name":"Journal of Applied Mathematics Statistics and Informatics","volume":"46 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87216914","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}
To define a new basis function to obtain a basis that can inherit the excellent properties of the traditional B-spline method and Bézier method, global and locality of shape adjustment, and can accurately represent the elliptical arc and circle. Firstly, an optimal standard full positive base, the cut angle algorithm, the 1 C and 2 C continuous proof of the base under the quasi-extended Chebyshev space in this paper. Secondly, the base on the rectangular field to the triangular field to obtain the quasi-cubic triangular Bernstein-Bézier base on the triangular field. Thirdly, this base can accurately represent the elliptic arc and circle, and then gives the base cutting algorithm on the triangular domain, and reverse introduce two conditions under which the quasi-cubic triangular Bernstein-Bézier surfaces are 1 G continuous in surface splicing. After a lot of analysis and examples, the new basis function has excellent properties of traditional methods, and can also flexibly adjust the shape parameters to obtain the required curve surface, which meets the actual industrial design requirements.
{"title":"Bézier Curves and Surfaces with three Parameters and Extensions in the Triangular Domain","authors":"Wang Lu, Zhang Guicang","doi":"10.22457/jmi.v22a04204","DOIUrl":"https://doi.org/10.22457/jmi.v22a04204","url":null,"abstract":"To define a new basis function to obtain a basis that can inherit the excellent properties of the traditional B-spline method and Bézier method, global and locality of shape adjustment, and can accurately represent the elliptical arc and circle. Firstly, an optimal standard full positive base, the cut angle algorithm, the 1 C and 2 C continuous proof of the base under the quasi-extended Chebyshev space in this paper. Secondly, the base on the rectangular field to the triangular field to obtain the quasi-cubic triangular Bernstein-Bézier base on the triangular field. Thirdly, this base can accurately represent the elliptic arc and circle, and then gives the base cutting algorithm on the triangular domain, and reverse introduce two conditions under which the quasi-cubic triangular Bernstein-Bézier surfaces are 1 G continuous in surface splicing. After a lot of analysis and examples, the new basis function has excellent properties of traditional methods, and can also flexibly adjust the shape parameters to obtain the required curve surface, which meets the actual industrial design requirements.","PeriodicalId":43016,"journal":{"name":"Journal of Applied Mathematics Statistics and Informatics","volume":"2015 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83163537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper shows that the Diophantine equation (p+6)x - p y = z2 where p is a prime number with p ≡ 1 (mod 28), has a unique non-negative integer solution. The solution is ( , , ) (0,0,0) x y z = .
本文证明了丢芬图方程(p+6)x - p y = z2，其中p是素数，且p≡1 (mod 28)，具有唯一的非负整数解。解是(，，)(0,0,0)x y z =。
{"title":"On the Diophantine Equation (p+6)x - p y = z2 where p is a Prime Number with p ≡ 1 (mod 28)","authors":"S. Tadee","doi":"10.22457/jmi.v23a05213","DOIUrl":"https://doi.org/10.22457/jmi.v23a05213","url":null,"abstract":"This paper shows that the Diophantine equation (p+6)x - p y = z2 where p is a prime number with p ≡ 1 (mod 28), has a unique non-negative integer solution. The solution is ( , , ) (0,0,0) x y z = .","PeriodicalId":43016,"journal":{"name":"Journal of Applied Mathematics Statistics and Informatics","volume":"47 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81275629","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}
For L L = ∗ → ( , , ) a complete residuated lattice, a type of L -fuzzy covering rough sets was defined by Li [8] in 2017. In this paper, a further study on rough sets was given. Precisely, a single axiomatic characterization of the L -fuzzy covering rough sets was presented, and the relationships between the -fuzzy covering rough sets and L -fuzzy relation rough sets were established.
对于L L =∗→(，，)完全剩馀格，Li[8]在2017年定义了一类L -模糊覆盖粗糙集。本文对粗糙集进行了进一步的研究。准确地说，给出了L -模糊覆盖粗糙集的单一公理化表征，并建立了-模糊覆盖粗糙集与L -模糊关系粗糙集之间的关系。
{"title":"A Further Study on L-Fuzzy Covering Rough Sets","authors":"Yao-liang Xu, Dan-dan Zou, LingYue Li","doi":"10.22457/jmi.v22a05208","DOIUrl":"https://doi.org/10.22457/jmi.v22a05208","url":null,"abstract":"For L L = ∗ → ( , , ) a complete residuated lattice, a type of L -fuzzy covering rough sets was defined by Li [8] in 2017. In this paper, a further study on rough sets was given. Precisely, a single axiomatic characterization of the L -fuzzy covering rough sets was presented, and the relationships between the -fuzzy covering rough sets and L -fuzzy relation rough sets were established.","PeriodicalId":43016,"journal":{"name":"Journal of Applied Mathematics Statistics and Informatics","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84141066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The theory of three-way decision provides an effective tool for decision-making under uncertainty and incomplete information when a two-way decision is difficult to make. In this paper, we try to transform an intuitionistic fuzzy set into a pessimistic shadowed set or an optimistic shadowed set by using two intuitionistic fuzzy parameters and the classical shadowed set. Accordingly, the pessimistic three-way decision or the optimistic three-way decision of intuitionistic fuzzy set are investigated by means of the proposed shadowed sets. In addition, a method to calculate the thresholds by the minimum cost principle is proposed and some examples are given for illustrating the validity of the method.
{"title":"The Shadowed Set, Intuitionistic Fuzzy Set and their Three-way Decision","authors":"Guangpeng Ta, Z. Gong","doi":"10.22457/jmi.v22a02206","DOIUrl":"https://doi.org/10.22457/jmi.v22a02206","url":null,"abstract":"The theory of three-way decision provides an effective tool for decision-making under uncertainty and incomplete information when a two-way decision is difficult to make. In this paper, we try to transform an intuitionistic fuzzy set into a pessimistic shadowed set or an optimistic shadowed set by using two intuitionistic fuzzy parameters and the classical shadowed set. Accordingly, the pessimistic three-way decision or the optimistic three-way decision of intuitionistic fuzzy set are investigated by means of the proposed shadowed sets. In addition, a method to calculate the thresholds by the minimum cost principle is proposed and some examples are given for illustrating the validity of the method.","PeriodicalId":43016,"journal":{"name":"Journal of Applied Mathematics Statistics and Informatics","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76039540","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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