In this paper, we analyze properties of prime number sequences produced by the alternating sum of higher-order subsequences of the primes. We also introduce a new sieve which will generate these prime number sequences via the systematic selection and elimination of prime number indexes on the real number line.
{"title":"Properties of Higher-Order Prime Number Sequences","authors":"Michael P. May","doi":"10.35834/2020/3202158","DOIUrl":"https://doi.org/10.35834/2020/3202158","url":null,"abstract":"In this paper, we analyze properties of prime number sequences produced by the alternating sum of higher-order subsequences of the primes. We also introduce a new sieve which will generate these prime number sequences via the systematic selection and elimination of prime number indexes on the real number line.","PeriodicalId":42784,"journal":{"name":"Missouri Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49218086","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}
. Theoretical concepts of crisp graphs are highly utilized in computer science and applications. They are especially important in many research areas in computer science like image segmentation, data mining, clustering, network routing, and image capturing. If the role of vertices and edges are uncertain, having two opposite ef-fects, positive and negative, then bipolar fuzzy graphs always play an important factor. In this paper, some important results on different types of operations of bipolar fuzzy graphs are improved. First, we explain some important theorems about the degree of composition, tensor product, and normal product of two bipolar fuzzy graphs using examples.
{"title":"Empirical Results on Operations of Bipolar Fuzzy Graphs with Their Degree","authors":"Soumitra Poulik, G. Ghorai","doi":"10.35834/2020/3202211","DOIUrl":"https://doi.org/10.35834/2020/3202211","url":null,"abstract":". Theoretical concepts of crisp graphs are highly utilized in computer science and applications. They are especially important in many research areas in computer science like image segmentation, data mining, clustering, network routing, and image capturing. If the role of vertices and edges are uncertain, having two opposite ef-fects, positive and negative, then bipolar fuzzy graphs always play an important factor. In this paper, some important results on different types of operations of bipolar fuzzy graphs are improved. First, we explain some important theorems about the degree of composition, tensor product, and normal product of two bipolar fuzzy graphs using examples.","PeriodicalId":42784,"journal":{"name":"Missouri Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49389095","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}
{"title":"Four New Concepts of Extensions of KU/UP-Algebras","authors":"A. Satirad, R. Chinram, Aiyared Iampan","doi":"10.35834/2020/3202138","DOIUrl":"https://doi.org/10.35834/2020/3202138","url":null,"abstract":"","PeriodicalId":42784,"journal":{"name":"Missouri Journal of Mathematical Sciences","volume":"32 1","pages":"138-157"},"PeriodicalIF":0.4,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46655067","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}
{"title":"A Hypergroup Dual Space Can be Unbounded","authors":"Adam Parr","doi":"10.35834/2020/3201071","DOIUrl":"https://doi.org/10.35834/2020/3201071","url":null,"abstract":"","PeriodicalId":42784,"journal":{"name":"Missouri Journal of Mathematical Sciences","volume":"32 1","pages":"71-79"},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45094175","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}
{"title":"Finitely Generated Submoduloids and Prime Submoduloids on a Nexus","authors":"R. Kamrani, A. Hasankhani, M. Bolourian","doi":"10.35834/2020/3201088","DOIUrl":"https://doi.org/10.35834/2020/3201088","url":null,"abstract":"","PeriodicalId":42784,"journal":{"name":"Missouri Journal of Mathematical Sciences","volume":"32 1","pages":"88-109"},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41712499","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 short paper, we examine a curious feature of the Collatz function. When the sequences generated by the Collatz function on consecutive integer initial points are arranged into an array, certain arithmetic sequences show up with common differences given by products of twos and threes. The common differences themselves are further related by a formula that depends on even versus odd input. While we do not solve the Collatz Conjecture by this observation, we present our findings as interesting mathematical results in their own rights.
{"title":"Arithmetic Sequences and Blocks of Powers of Two in the Collatz Array","authors":"S. Ault, Matthew Cliatt","doi":"10.35834/2020/3201032","DOIUrl":"https://doi.org/10.35834/2020/3201032","url":null,"abstract":"In this short paper, we examine a curious feature of the Collatz function. When the sequences generated by the Collatz function on consecutive integer initial points are arranged into an array, certain arithmetic sequences show up with common differences given by products of twos and threes. The common differences themselves are further related by a formula that depends on even versus odd input. While we do not solve the Collatz Conjecture by this observation, we present our findings as interesting mathematical results in their own rights.","PeriodicalId":42784,"journal":{"name":"Missouri Journal of Mathematical Sciences","volume":"32 1","pages":"32-38"},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46891689","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}
{"title":"On the Log-Concavity Density Function: A Case of Exponential Power Distribution and its Application","authors":"A. Olosunde","doi":"10.35834/2020/3201039","DOIUrl":"https://doi.org/10.35834/2020/3201039","url":null,"abstract":"","PeriodicalId":42784,"journal":{"name":"Missouri Journal of Mathematical Sciences","volume":"32 1","pages":"39-48"},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49030645","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 purpose of this article is to introduce three types of supra compactness and three types of supra Lindelofness via supra topological spaces based on the supra pre-open sets. With the help of examples, we illustrate the relationships among them and show their relationships with some kinds of supra compactness and supra Lindelofness given in [3]. We characterize each type of space and investigate the image of them under pre-irresolute mappings. Also, we prove that these spaces are preserved under the finite product spaces, and give a sufficient condition for the equivalence among supra compact, almost supra compact and supra pre-compact spaces. At the end of each section, we provide some examples to demonstrate that the spaces studied and their counterparts, introduced in [9], are independent of each other.
{"title":"Various Types of Supra Pre-compact and Supra Pre-Lindelöf Spaces","authors":"T. Al-shami, Baravan A. Asaad, M. El-Gayar","doi":"10.35834/2020/3201001","DOIUrl":"https://doi.org/10.35834/2020/3201001","url":null,"abstract":"The purpose of this article is to introduce three types of supra compactness and three types of supra Lindelofness via supra topological spaces based on the supra pre-open sets. With the help of examples, we illustrate the relationships among them and show their relationships with some kinds of supra compactness and supra Lindelofness given in [3]. We characterize each type of space and investigate the image of them under pre-irresolute mappings. Also, we prove that these spaces are preserved under the finite product spaces, and give a sufficient condition for the equivalence among supra compact, almost supra compact and supra pre-compact spaces. At the end of each section, we provide some examples to demonstrate that the spaces studied and their counterparts, introduced in [9], are independent of each other.","PeriodicalId":42784,"journal":{"name":"Missouri Journal of Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46776947","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 purpose of this paper is to introduce and investigate strongly fully stable acts relative to an ideal as a concept generalizing strongly fully stable modules relative to an ideal, but is stronger than that of fully stable acts. In this study, we consider some properties and characterizations of the class of strongly fully stable acts relative to an ideal, as well as the relations between this class and other classes. Among these classes are quasi-injective acts, strongly quasi-injective acts, acts which satisfy Baer's criterion, acts satisfying the strongly Baer's criterion, and duo acts. The product of strongly fully stable acts relative to an ideal need not be a strongly fully stable act relative to that ideal. The coproduct of any family of strongly fully stable acts relative to an ideal need not be a strongly fully stable act relative to that ideal. Also, we have that strongly fully stable acts relative to an ideal are equivalent to an $S$-act that satisfies the strongly Baer's criterion relative to an ideal $I$ for cyclic subacts. The strongly fully stable act relative to $I$ is equivalent to the strongly quasi-injective act relative to the ideal $I$ and duo act with a commutative monoid.
{"title":"Strongly Fully Stable Acts Relative to an Ideal","authors":"A. K. Mutashar, H. Baanoon","doi":"10.35834/2020/3201110","DOIUrl":"https://doi.org/10.35834/2020/3201110","url":null,"abstract":"The purpose of this paper is to introduce and investigate strongly fully stable acts relative to an ideal as a concept generalizing strongly fully stable modules relative to an ideal, but is stronger than that of fully stable acts. In this study, we consider some properties and characterizations of the class of strongly fully stable acts relative to an ideal, as well as the relations between this class and other classes. Among these classes are quasi-injective acts, strongly quasi-injective acts, acts which satisfy Baer's criterion, acts satisfying the strongly Baer's criterion, and duo acts. The product of strongly fully stable acts relative to an ideal need not be a strongly fully stable act relative to that ideal. The coproduct of any family of strongly fully stable acts relative to an ideal need not be a strongly fully stable act relative to that ideal. Also, we have that strongly fully stable acts relative to an ideal are equivalent to an $S$-act that satisfies the strongly Baer's criterion relative to an ideal $I$ for cyclic subacts. The strongly fully stable act relative to $I$ is equivalent to the strongly quasi-injective act relative to the ideal $I$ and duo act with a commutative monoid.","PeriodicalId":42784,"journal":{"name":"Missouri Journal of Mathematical Sciences","volume":"32 1","pages":"110-117"},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41410930","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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