{"title":"On the adjacent eccentric distance sum of graphs","authors":"H. Bielak, Katarzyna Wolska","doi":"10.1515/UMCSMATH-2015-0001","DOIUrl":"https://doi.org/10.1515/UMCSMATH-2015-0001","url":null,"abstract":"In this paper we show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree and minimum degree. We extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum, Vol. 7 (2002) no. 26, 1289–1294]. The adjacent eccentric distance sum index of the graph (G) is defined as [xi ^{sv} (G)= sum_{vin V(G)}{frac{varepsilon (v) D(v)}{deg(v)}},] where (varepsilon(v)) is the eccentricity of the vertex (v), (deg(v)) is the degree of the vertex (v) and [D(v)=sum_{uin V(G)}{d(u,v)}] is the sum of all distances from the vertex (v).","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"78 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114146811","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":"Renormings of $c_0$ and the minimal displacement problem","authors":"Łukasz Piasecki","doi":"10.1515/UMCSMATH-2015-0008","DOIUrl":"https://doi.org/10.1515/UMCSMATH-2015-0008","url":null,"abstract":"The aim of this paper is to show that for every Banach space ((X, |cdot|)) containing asymptotically isometric copy of the space (c_0) there is a bounded, closed and convex set (C subset X) with the Chebyshev radius (r(C) = 1) such that for every (k geq 1 ) there exists a (k)-contractive mapping (T : C to C) with (| x - Tx | > 1 − 1/k) for any (x in C).","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130951509","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":"Properties of the determinant of a rectangular matrix","authors":"A. Makarewicz, P. Pikuta, D. Szalkowski","doi":"10.2478/UMCSMATH-2014-0004","DOIUrl":"https://doi.org/10.2478/UMCSMATH-2014-0004","url":null,"abstract":"In this paper we present new identities for the Radic’s determinant of a rectangular matrix. The results include representations of the determinant of a rectangular matrix as a sum of determinants of square matrices and description how the determinant is affected by operations on columns such as interchanging columns, reversing columns or decomposing a single column.","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114816161","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":"The Fekete–Szegö problem for a class of analytic functions defined by Carlson–Shaffer operator","authors":"O. Ahuja, H. Orhan","doi":"10.2478/UMCSMATH-2014-0001","DOIUrl":"https://doi.org/10.2478/UMCSMATH-2014-0001","url":null,"abstract":"In the present investigation we solve Fekete-Szego problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions. In the present investigation we solve Fekete-Szego problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions.","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127440204","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 a subordination result for analytic functions defined by convolution","authors":"E. Oyekan, T. Opoola","doi":"10.2478/UMCSMATH-2014-0007","DOIUrl":"https://doi.org/10.2478/UMCSMATH-2014-0007","url":null,"abstract":"In this paper we discuss some subordination results for a subclass of functions analytic in the unit disk U.","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120861425","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":"The Turàn number of the graph 3P4","authors":"H. Bielak, S. Kieliszek","doi":"10.2478/UMCSMATH-2014-0003","DOIUrl":"https://doi.org/10.2478/UMCSMATH-2014-0003","url":null,"abstract":"Let (ex(n, G)) denote the maximum number of edges in a graph on (n) vertices which does not contain (G) as a subgraph. Let (P_i) denote a path consisting of (i) vertices and let (mP_i) denote (m) disjoint copies of (P_i). In this paper we count (ex(n, 3P_4)).","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127667490","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 birational gonalities of smooth curves","authors":"E. Ballico","doi":"10.2478/UMCSMATH-2014-0002","DOIUrl":"https://doi.org/10.2478/UMCSMATH-2014-0002","url":null,"abstract":"Let (C) be a smooth curve of genus (g). For each positive integer (r) the birational (r)-gonality (s_r(C)) of (C) is the minimal integer (t) such that there is (Lin mbox{Pic}^t(C)) with (h^0(C,L) =r+1). Fix an integer (rge 3). In this paper we prove the existence of an integer (g_r) such that for every integer (gge g_r) there is a smooth curve (C) of genus (g) with (s_{r+1}(C)/(r+1) > s_r(C)/r), i.e. in the sequence of all birational gonalities of (C) at least one of the slope inequalities fails.","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130395431","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":"Weighted sub-Bergman Hilbert spaces","authors":"M. Nowak, R. Rososzczuk","doi":"10.2478/UMCSMATH-2014-0006","DOIUrl":"https://doi.org/10.2478/UMCSMATH-2014-0006","url":null,"abstract":"We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces (A^2_{alpha}), (−1 < alpha < infty). These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers.","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114781881","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":"The constructions of general connections on second jet prolongation","authors":"Mariusz Płaszczyk","doi":"10.2478/UMCSMATH-2014-0008","DOIUrl":"https://doi.org/10.2478/UMCSMATH-2014-0008","url":null,"abstract":"We determine all natural operators D transforming general connections Γ on fibred manifolds Y → M and torsion free classical linear connections ∇ on M into general connections D(Γ,∇) on the second order jet prolongation J 2 Y → M of Y → M.","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121089083","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 path-quasar Ramsey numbers","authors":"Binlong Li, Bo Ning","doi":"10.1515/umcsmath-2015-0002","DOIUrl":"https://doi.org/10.1515/umcsmath-2015-0002","url":null,"abstract":"Let (G_1) and (G_2) be two given graphs. The Ramsey number (R(G_1,G_2)) is the least integer (r) such that for every graph (G) on (r) vertices, either (G) contains a (G_1) or (overline{G}) contains a (G_2). Parsons gave a recursive formula to determine the values of (R(P_n,K_{1,m})), where (P_n) is a path on (n) vertices and (K_{1,m}) is a star on (m+1) vertices. In this note, we study the Ramsey numbers (R(P_n,K_1vee F_m)), where (F_m) is a linear forest on (m) vertices. We determine the exact values of (R(P_n,K_1vee F_m)) for the cases (mleq n) and (mgeq 2n), and for the case that (F_m) has no odd component. Moreover, we give a lower bound and an upper bound for the case (n+1leq mleq 2n-1) and (F_m) has at least one odd component.","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128770443","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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