{"title":"COUPON COLLECTOR PROBLEM WITH PENALTY COUPON","authors":"","doi":"10.57016/mv-bgon6192","DOIUrl":"https://doi.org/10.57016/mv-bgon6192","url":null,"abstract":"","PeriodicalId":54181,"journal":{"name":"Matematicki Vesnik","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70913560","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, we use the notions of lower set $L_{R}(A)$ and the upper set $U_{R}(A)$ to define the interior operator ${rm int}_{R}^{A}$ and the closure operator ${rm cl}_{R}^{A}$ associated with a set $A$ in an approximation space $(X,R)$. These operators generate an approximation topological space different from the generated Nano topological space in $(X,R)$. Ideal approximation spaces $(X,R, ell)$ based on an ideal $ell$ joined to the approximation space $(X,R)$ are introduced as well. The approximation continuity and the ideal approximation continuity are defined. The lower separation axioms $T_{i}, i= 0,1,2$ are introduced in the approximation spaces and also in the ideal approximation spaces. Examples are given to explain the definitions. Connectedness in approximation spaces and ideal connectedness are introduced and the differences between them are explained. The interior and the closure operators are deduced using a grill ${cal G}$ defined on $(X,R)$, yielding the same results.
{"title":"APPROXIMATION SPACES VIA IDEALS AND GRILLS","authors":"","doi":"10.57016/mv-fuvt2928","DOIUrl":"https://doi.org/10.57016/mv-fuvt2928","url":null,"abstract":"In this paper, we use the notions of lower set $L_{R}(A)$ and the upper set $U_{R}(A)$ to define the interior operator ${rm int}_{R}^{A}$ and the closure operator ${rm cl}_{R}^{A}$ associated with a set $A$ in an approximation space $(X,R)$. These operators generate an approximation topological space different from the generated Nano topological space in $(X,R)$. Ideal approximation spaces $(X,R, ell)$ based on an ideal $ell$ joined to the approximation space $(X,R)$ are introduced as well. The approximation continuity and the ideal approximation continuity are defined. The lower separation axioms $T_{i}, i= 0,1,2$ are introduced in the approximation spaces and also in the ideal approximation spaces. Examples are given to explain the definitions. Connectedness in approximation spaces and ideal connectedness are introduced and the differences between them are explained. The interior and the closure operators are deduced using a grill ${cal G}$ defined on $(X,R)$, yielding the same results.","PeriodicalId":54181,"journal":{"name":"Matematicki Vesnik","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70913689","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 SUBTRACTIVE SUBSEMIMODULE-BASED GRAPH OF SEMIMODULES","authors":"","doi":"10.57016/mv-e8296tae","DOIUrl":"https://doi.org/10.57016/mv-e8296tae","url":null,"abstract":"","PeriodicalId":54181,"journal":{"name":"Matematicki Vesnik","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70913783","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":"COVERINGS, ACTIONS AND QUOTIENTS IN $text{CAT}^1$-GROUPOIDS","authors":"","doi":"10.57016/mv-spdf3739","DOIUrl":"https://doi.org/10.57016/mv-spdf3739","url":null,"abstract":"","PeriodicalId":54181,"journal":{"name":"Matematicki Vesnik","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70914062","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":"MULTIPLICITY OF SOLUTIONS FOR ANISOTROPIC DISCRETE BOUNDARY VALUE PROBLEMS","authors":"","doi":"10.57016//mv-mznh3231","DOIUrl":"https://doi.org/10.57016//mv-mznh3231","url":null,"abstract":"","PeriodicalId":54181,"journal":{"name":"Matematicki Vesnik","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70913587","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":"CONSTRUCTION OF UNIVALENT HARMONIC MAPPINGS AND THEIR CONVOLUTIONS","authors":"","doi":"10.57016/mv-gjwe5662","DOIUrl":"https://doi.org/10.57016/mv-gjwe5662","url":null,"abstract":"","PeriodicalId":54181,"journal":{"name":"Matematicki Vesnik","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70913699","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":"CONSTRUCTION OF THE TYPE 2 DEGENERATE POLY-EULER POLYNOMIALS AND NUMBERS","authors":"","doi":"10.57016/mv-nr25pm82","DOIUrl":"https://doi.org/10.57016/mv-nr25pm82","url":null,"abstract":"","PeriodicalId":54181,"journal":{"name":"Matematicki Vesnik","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70913971","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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