Pub Date : 2019-04-03DOI: 10.1080/23799927.2019.1625948
Xiao Wang, Yufu Ning
ABSTRACT Backward uncertain differential equation is a class of uncertain differential equations with a terminal value. This paper focuses on its stability analysis. At first, this paper gives the concepts of stability in measure, stability in mean and stability in pth moment for backward uncertain differential equations. In addition, some sufficient conditions in the form of theorem for backward uncertain differential equations being stable in measure, in mean and in pth moment are derived. Meanwhile, this paper further discusses the relationship between these three types of stability.
{"title":"Stability analysis of backward uncertain differential equations","authors":"Xiao Wang, Yufu Ning","doi":"10.1080/23799927.2019.1625948","DOIUrl":"https://doi.org/10.1080/23799927.2019.1625948","url":null,"abstract":"ABSTRACT Backward uncertain differential equation is a class of uncertain differential equations with a terminal value. This paper focuses on its stability analysis. At first, this paper gives the concepts of stability in measure, stability in mean and stability in pth moment for backward uncertain differential equations. In addition, some sufficient conditions in the form of theorem for backward uncertain differential equations being stable in measure, in mean and in pth moment are derived. Meanwhile, this paper further discusses the relationship between these three types of stability.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"51 1","pages":"110 - 95"},"PeriodicalIF":0.8,"publicationDate":"2019-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88082415","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 : 2019-04-03DOI: 10.1080/23799927.2019.1614673
S. Minkevičius
ABSTRACT The modern queueing theory is one of the powerful tools for a quantitative and qualitative analysis of communication systems, computer networks, transportation systems, and many other technical systems. The paper is designated to the analysis of queueing systems, arising in the network theory and communications theory (called open queueing network). We have proved here the theorem on the law of the iterated logarithm (LIL) for the virtual waiting time of a job in an open queueing network under heavy and light traffic conditions. Also, the work presents a survey of papers for the virtual waiting time of a job in heavy traffic. Finally, we present an application of the proved theorems to the technical model from computer network practice.
{"title":"On the analysis of the law of the iterated logarithm in open queueing networks","authors":"S. Minkevičius","doi":"10.1080/23799927.2019.1614673","DOIUrl":"https://doi.org/10.1080/23799927.2019.1614673","url":null,"abstract":"ABSTRACT The modern queueing theory is one of the powerful tools for a quantitative and qualitative analysis of communication systems, computer networks, transportation systems, and many other technical systems. The paper is designated to the analysis of queueing systems, arising in the network theory and communications theory (called open queueing network). We have proved here the theorem on the law of the iterated logarithm (LIL) for the virtual waiting time of a job in an open queueing network under heavy and light traffic conditions. Also, the work presents a survey of papers for the virtual waiting time of a job in heavy traffic. Finally, we present an application of the proved theorems to the technical model from computer network practice.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"35 1","pages":"76 - 94"},"PeriodicalIF":0.8,"publicationDate":"2019-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80929986","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: 10.1080/23799927.2019.1566275
Zhimin Sun, Arne Winterhof
ABSTRACT Automatic sequences such as the Thue–Morse sequence and the Rudin–Shapiro sequence are highly predictable and thus not suitable in cryptography. In particular, they have small expansion complexity. However, they still have a large maximum order complexity. Certain subsequences of automatic sequences are not automatic anymore and may be attractive candidates for applications in cryptography. In this paper we show that subsequences along the squares of certain pattern sequences including the Thue–Morse sequence and the Rudin–Shapiro sequence have also large maximum order complexity but do not suffer a small expansion complexity anymore.
{"title":"On the maximum order complexity of subsequences of the Thue–Morse and Rudin–Shapiro sequence along squares","authors":"Zhimin Sun, Arne Winterhof","doi":"10.1080/23799927.2019.1566275","DOIUrl":"https://doi.org/10.1080/23799927.2019.1566275","url":null,"abstract":"ABSTRACT Automatic sequences such as the Thue–Morse sequence and the Rudin–Shapiro sequence are highly predictable and thus not suitable in cryptography. In particular, they have small expansion complexity. However, they still have a large maximum order complexity. Certain subsequences of automatic sequences are not automatic anymore and may be attractive candidates for applications in cryptography. In this paper we show that subsequences along the squares of certain pattern sequences including the Thue–Morse sequence and the Rudin–Shapiro sequence have also large maximum order complexity but do not suffer a small expansion complexity anymore.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"52 1","pages":"30 - 36"},"PeriodicalIF":0.8,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81877165","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: 10.1080/23799927.2019.1567593
Dongqin Cheng
ABSTRACT In a simple graph , let be the minimum cardinality of the neighbourhoods of any two adjacent vertices, i.e. . Let be the connectivity of G. In this paper, we prove that the pessimistic diagnosability of G, denoted by , is equal to if the following two conditions hold: (1) for any subset with , ; (2) . As examples of its applications, we prove that the pessimistic diagnosabilities of n-dimensional hypercube-like network , dual-cube , pancake network , and burnt pancake graph are (), (), () and (), respectively.
{"title":"The pessimistic diagnosability of graphs and its applications to four kinds of interconnection networks","authors":"Dongqin Cheng","doi":"10.1080/23799927.2019.1567593","DOIUrl":"https://doi.org/10.1080/23799927.2019.1567593","url":null,"abstract":"ABSTRACT In a simple graph , let be the minimum cardinality of the neighbourhoods of any two adjacent vertices, i.e. . Let be the connectivity of G. In this paper, we prove that the pessimistic diagnosability of G, denoted by , is equal to if the following two conditions hold: (1) for any subset with , ; (2) . As examples of its applications, we prove that the pessimistic diagnosabilities of n-dimensional hypercube-like network , dual-cube , pancake network , and burnt pancake graph are (), (), () and (), respectively.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"34 1","pages":"37 - 47"},"PeriodicalIF":0.8,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82732261","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: 10.1080/23799927.2019.1570974
Xiaoyuan Wang, W. Chu
ABSTRACT By means of partial fraction decomposition, derivative operator and inverse series relations, some algebraic identities involving symmetric functions are established. As applications, they are specialized to several summation formulae containing harmonic numbers and q-harmonic numbers.
{"title":"Harmonic number sums and q-analogues","authors":"Xiaoyuan Wang, W. Chu","doi":"10.1080/23799927.2019.1570974","DOIUrl":"https://doi.org/10.1080/23799927.2019.1570974","url":null,"abstract":"ABSTRACT By means of partial fraction decomposition, derivative operator and inverse series relations, some algebraic identities involving symmetric functions are established. As applications, they are specialized to several summation formulae containing harmonic numbers and q-harmonic numbers.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"22 2","pages":"48 - 56"},"PeriodicalIF":0.8,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72548211","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: 10.1080/23799927.2019.1587516
Chunhua Cao, Ling Li, Di Yang
ABSTRACT Let , where , be the set of ith powers of primitive words. A language is called strongly bi-singular if the minimal-length words in it are neither prefixes nor suffixes of any other word in the language. Strongly bi-singular languages forms a free monoid with respect to the concatenation of languages. The main result of this paper is that if we start with the basis of this free monoid together with the languages for all , then the resulting family of languages is a code. So we find a free monoid which properly contains the free monoid of all strongly bi-singular languages.
{"title":"A free monoid containing all strongly Bi-singular languages and non-primitive words","authors":"Chunhua Cao, Ling Li, Di Yang","doi":"10.1080/23799927.2019.1587516","DOIUrl":"https://doi.org/10.1080/23799927.2019.1587516","url":null,"abstract":"ABSTRACT Let , where , be the set of ith powers of primitive words. A language is called strongly bi-singular if the minimal-length words in it are neither prefixes nor suffixes of any other word in the language. Strongly bi-singular languages forms a free monoid with respect to the concatenation of languages. The main result of this paper is that if we start with the basis of this free monoid together with the languages for all , then the resulting family of languages is a code. So we find a free monoid which properly contains the free monoid of all strongly bi-singular languages.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"141 1","pages":"57 - 66"},"PeriodicalIF":0.8,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74866690","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: 10.1080/23799927.2023.2173656
Moritz Beck, K. Lam, J. Ng, Sabine Storandt, Chun Jiang Zhu
Given a graph , a k-Path Cover is defined as a subset C of the nodes V such that every simple path in G consisting of k nodes contains at least one node from C. Similarly, a k-Shortest Path Cover has to contain at least one node of every shortest path in G that consists of k nodes. In this paper, we extend the notion of k-(Shortest) Path Covers such that the objects to be covered don't have to be single paths but can be concatenations of up to p simple (or shortest) paths. For the generalized problem of computing concatenated -Shortest Path Covers, we present theoretical results regarding the VC-dimension of the concatenated path set in dependency of p in undirected as well as directed graphs. By proving a low VC-dimension in both settings, we enable the design of efficient approximation algorithms. Furthermore, we discuss how a pruning algorithm originally developed for k-Path Cover computation can be abstracted and modified in order to also solve concatenated -Path Cover problems. A crucial ingredient for the pruning algorithm to work efficiently is a path concatenation recognition algorithm. We describe general recognition algorithms for simple path concatenations as well as shortest path concatenations. Subsequently, we present more refined results for interesting special cases as piecewise shortest paths, hyperpaths, round tours, and trees. An extensive experimental study on different graph types proves the applicability and efficiency of our approaches.
{"title":"Concatenated k-path covers","authors":"Moritz Beck, K. Lam, J. Ng, Sabine Storandt, Chun Jiang Zhu","doi":"10.1080/23799927.2023.2173656","DOIUrl":"https://doi.org/10.1080/23799927.2023.2173656","url":null,"abstract":"Given a graph , a k-Path Cover is defined as a subset C of the nodes V such that every simple path in G consisting of k nodes contains at least one node from C. Similarly, a k-Shortest Path Cover has to contain at least one node of every shortest path in G that consists of k nodes. In this paper, we extend the notion of k-(Shortest) Path Covers such that the objects to be covered don't have to be single paths but can be concatenations of up to p simple (or shortest) paths. For the generalized problem of computing concatenated -Shortest Path Covers, we present theoretical results regarding the VC-dimension of the concatenated path set in dependency of p in undirected as well as directed graphs. By proving a low VC-dimension in both settings, we enable the design of efficient approximation algorithms. Furthermore, we discuss how a pruning algorithm originally developed for k-Path Cover computation can be abstracted and modified in order to also solve concatenated -Path Cover problems. A crucial ingredient for the pruning algorithm to work efficiently is a path concatenation recognition algorithm. We describe general recognition algorithms for simple path concatenations as well as shortest path concatenations. Subsequently, we present more refined results for interesting special cases as piecewise shortest paths, hyperpaths, round tours, and trees. An extensive experimental study on different graph types proves the applicability and efficiency of our approaches.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"46 1","pages":"32 - 56"},"PeriodicalIF":0.8,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84703052","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 : 2018-12-12DOI: 10.1080/23799927.2018.1552991
E. Cheng, Spencer Liu, Christopher Melekian, Karimah Sweet, Chittesh Thavamani, Freddie Zhao
ABSTRACT A strong matching preclusion set in a graph is a set of vertices and edges whose removal leaves the graph with no perfect matchings or almost perfect matchings. The strong matching preclusion number of a graph is the minimum cardinality of a strong matching preclusion set. The notion of strong matching preclusion was introduced by Park and Ihm as an extension of the matching preclusion problem, where only edges may be deleted. The folded Petersen cubes are a class of interconnection networks, formed by iterated Cartesian products of the well-known Petersen graph and the complete graph , which possess many desirable properties. In this paper, we find the strong matching preclusion number of the folded Petersen cubes and categorize all optimal strong matching preclusion sets of these graphs. To do so, we develop and utilize more general results related to strong matching preclusion for graphs formed by Cartesian products of particular graphs.
{"title":"Strong matching preclusion problem of the folded Petersen cube*","authors":"E. Cheng, Spencer Liu, Christopher Melekian, Karimah Sweet, Chittesh Thavamani, Freddie Zhao","doi":"10.1080/23799927.2018.1552991","DOIUrl":"https://doi.org/10.1080/23799927.2018.1552991","url":null,"abstract":"ABSTRACT A strong matching preclusion set in a graph is a set of vertices and edges whose removal leaves the graph with no perfect matchings or almost perfect matchings. The strong matching preclusion number of a graph is the minimum cardinality of a strong matching preclusion set. The notion of strong matching preclusion was introduced by Park and Ihm as an extension of the matching preclusion problem, where only edges may be deleted. The folded Petersen cubes are a class of interconnection networks, formed by iterated Cartesian products of the well-known Petersen graph and the complete graph , which possess many desirable properties. In this paper, we find the strong matching preclusion number of the folded Petersen cubes and categorize all optimal strong matching preclusion sets of these graphs. To do so, we develop and utilize more general results related to strong matching preclusion for graphs formed by Cartesian products of particular graphs.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"14 1","pages":"1 - 15"},"PeriodicalIF":0.8,"publicationDate":"2018-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80595959","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 : 2018-11-12DOI: 10.1080/23799927.2021.1905717
A. Rudi
The goal in the min-# curve simplification problem is to reduce the number of vertices of a polygonal curve without changing its shape significantly. Usually the vertices of the simplified curve are required to be a subset of the vertices of the input curve. We study the case in which new vertices can be placed on the edges of the input curve, and the set of vertices of the simplified curve appear in order along the input curve. If error is defined as the maximum distance between corresponding sub-curves of the input and simplified curves, we present an approximation algorithm for curves in the plane that computes a curve whose number of links is at most twice the minimum possible.
{"title":"Approximate curve-restricted simplification of polygonal curves","authors":"A. Rudi","doi":"10.1080/23799927.2021.1905717","DOIUrl":"https://doi.org/10.1080/23799927.2021.1905717","url":null,"abstract":"The goal in the min-# curve simplification problem is to reduce the number of vertices of a polygonal curve without changing its shape significantly. Usually the vertices of the simplified curve are required to be a subset of the vertices of the input curve. We study the case in which new vertices can be placed on the edges of the input curve, and the set of vertices of the simplified curve appear in order along the input curve. If error is defined as the maximum distance between corresponding sub-curves of the input and simplified curves, we present an approximation algorithm for curves in the plane that computes a curve whose number of links is at most twice the minimum possible.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"20 1","pages":"178 - 187"},"PeriodicalIF":0.8,"publicationDate":"2018-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90231794","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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