We obtain a sufficient condition for the existence of a (g, f)-factor in terms of vertex-deleted subgraphs. The following theorem is proved: Let G be a graph, k an even integer, g, f: V(G)→mathbb{Z} two functions such that g(x)≤f(x) for all x∈V(G), and {u0, u1, …, uk/2} the set of distinct vertices of G such that {u1, u2, …, uk/2}⊆NG(u0). If g(u0)≤k≤f(u0) and G-{ui} has a (g, f)-factor for all i=0, …, k/2, then G has a (g, f)-factor.
{"title":"Neighborhood conditions for the existence of ( g, f )-factors","authors":"Haruhide Matsuda","doi":"10.5036/MJIU.36.1","DOIUrl":"https://doi.org/10.5036/MJIU.36.1","url":null,"abstract":"We obtain a sufficient condition for the existence of a (g, f)-factor in terms of vertex-deleted subgraphs. The following theorem is proved: Let G be a graph, k an even integer, g, f: V(G)→mathbb{Z} two functions such that g(x)≤f(x) for all x∈V(G), and {u0, u1, …, uk/2} the set of distinct vertices of G such that {u1, u2, …, uk/2}⊆NG(u0). If g(u0)≤k≤f(u0) and G-{ui} has a (g, f)-factor for all i=0, …, k/2, then G has a (g, f)-factor.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"20 1","pages":"1-4"},"PeriodicalIF":0.0,"publicationDate":"2004-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75883416","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 object of our research is a piecewise Riemannian 2-polyhedron which is a combinatorial 2-polyhedron such that each 2-simplex is isometric to a triangle bounded by three smooth curves on some Riemannian 2-manifold. In the previous paper [4], which is a joint work with J. Itoh, we have introduced the concept of total curvature for piecewise Riemannian 2-polyhedra and proved a generalized Gauss-Bonnet theorem and a generalized Cohn-Vossen theorem. In this paper, we shall give a definition of flatness of piecewise Riemannian 2-polyhedra and characterize them.
{"title":"Structures of flat piecewise Riemannian 2-polyhedra","authors":"Fumiko Ohtsuka","doi":"10.5036/MJIU.36.57","DOIUrl":"https://doi.org/10.5036/MJIU.36.57","url":null,"abstract":"The object of our research is a piecewise Riemannian 2-polyhedron which is a combinatorial 2-polyhedron such that each 2-simplex is isometric to a triangle bounded by three smooth curves on some Riemannian 2-manifold. In the previous paper [4], which is a joint work with J. Itoh, we have introduced the concept of total curvature for piecewise Riemannian 2-polyhedra and proved a generalized Gauss-Bonnet theorem and a generalized Cohn-Vossen theorem. In this paper, we shall give a definition of flatness of piecewise Riemannian 2-polyhedra and characterize them.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"14 1","pages":"57-64"},"PeriodicalIF":0.0,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76680322","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 the present paper, the fine spectrum of the Cesaro operator in the sequence space c0 has been examined. Although the discussion is made for determination of the spectrum of the Cesaro operator in the sequence space c0 by Reade (14) and the others, our consequences are more refinement and include a remark concerning with the previous works. Further, a Mercerian theorem has also been given. Finally, the fine spectrum of the Cesaro operator in the sequence space c has been given, without proof.
{"title":"On the fine spectrum of the Cesàro operator in c0","authors":"A. Akhmedov, F. Başar","doi":"10.5036/MJIU.36.25","DOIUrl":"https://doi.org/10.5036/MJIU.36.25","url":null,"abstract":"In the present paper, the fine spectrum of the Cesaro operator in the sequence space c0 has been examined. Although the discussion is made for determination of the spectrum of the Cesaro operator in the sequence space c0 by Reade (14) and the others, our consequences are more refinement and include a remark concerning with the previous works. Further, a Mercerian theorem has also been given. Finally, the fine spectrum of the Cesaro operator in the sequence space c has been given, without proof.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"19 1","pages":"25-32"},"PeriodicalIF":0.0,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81120147","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":"Caloric morphisms with respect to radial metrics on mathbb{R}nbachslash{0}","authors":"Katsunori Shimomura","doi":"10.5036/MJIU.35.35","DOIUrl":"https://doi.org/10.5036/MJIU.35.35","url":null,"abstract":"","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"49 1","pages":"35-53"},"PeriodicalIF":0.0,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76481050","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}
~on S×S by (s1,t1)~(s2,t2) if s1+t2=s2+t1. We denote the equivalence class of (s,t) under~by s-t. Let G={s-t|s,t∈S}be the set of equivalence classes. Then G is a monoid with identity 0=s-s with each s∈S under the additive operation (s1-t1)+(s2-t2)=(s1+s2)-(t1+t2). Furthermore, each element s-t of G has the converse t-s and then G is a torsion-free Abelian group. Evidently S is a submonoid of the group G. The group G is called the quotient group of S. The quotient group of a monoid S is often denoted by q(S). Let S be a g-monoid with quotient group G. A subset I of G is called a fractional ideal of S if S+I⊆I and s+I⊆S for some element s∈S. A subset I of S is called an integral ideal of S if I+S⊆I. We shall denote the set of fractional ideals of S by F(S). For each element x of G, the set x+S={x+s|s∈S} is a fractional ideal of S and is called a principal ideal of S. The principal ideal x+S is simply denoted by (x).
~on S×S by (s1,t1)~(s2,t2) if s1+t2=s2+t1。我们用s-t表示(s,t)在~下的等价类。设G={s-t|s,t∈s}是等价类的集合。则在加性运算(s1-t1)+(s2-t2)=(s1+s2)-(t1+t2)下，G是一个单位元0=s-s的单阵。进一步，G的每个元素s-t都有逆t-s，因此G是一个无扭阿贝尔群。显然S是群G的子单群。群G称为S的商群。单群S的商群通常用q(S)表示。设S为具有商群G的G -单拟子G，如果对某些元素S∈S, S+I和S+I∈S，则G的子集I称为S的分数理想。S的一个子集I称为S的一个积分理想，如果I+S≠I。我们用F(S)表示S的分数理想集合。对于G中的每一个元素x，集合x+S={x+ S | S∈S}是S的分数理想，称为S的主理想。主理想x+S简记为(x)。
{"title":"On the dual of an ideal of a g-monoid","authors":"A. Okabe","doi":"10.5036/MJIU.35.1","DOIUrl":"https://doi.org/10.5036/MJIU.35.1","url":null,"abstract":"~on S×S by (s1,t1)~(s2,t2) if s1+t2=s2+t1. We denote the equivalence class of (s,t) under~by s-t. Let G={s-t|s,t∈S}be the set of equivalence classes. Then G is a monoid with identity 0=s-s with each s∈S under the additive operation (s1-t1)+(s2-t2)=(s1+s2)-(t1+t2). Furthermore, each element s-t of G has the converse t-s and then G is a torsion-free Abelian group. Evidently S is a submonoid of the group G. The group G is called the quotient group of S. The quotient group of a monoid S is often denoted by q(S). Let S be a g-monoid with quotient group G. A subset I of G is called a fractional ideal of S if S+I⊆I and s+I⊆S for some element s∈S. A subset I of S is called an integral ideal of S if I+S⊆I. We shall denote the set of fractional ideals of S by F(S). For each element x of G, the set x+S={x+s|s∈S} is a fractional ideal of S and is called a principal ideal of S. The principal ideal x+S is simply denoted by (x).","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"27 1","pages":"1-9"},"PeriodicalIF":0.0,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78033297","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 present some results concerned with the problem of the unicity of immediate maximal extensions of a valued field.
本文给出了关于值域的直接极大扩展的唯一性问题的一些结果。
{"title":"On the unicity of immediate maximal extensions of valued fields","authors":"M. Vâjâitu, A. Zaharescu","doi":"10.5036/MJIU.35.29","DOIUrl":"https://doi.org/10.5036/MJIU.35.29","url":null,"abstract":"In this paper we present some results concerned with the problem of the unicity of immediate maximal extensions of a valued field.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"91 1","pages":"29-33"},"PeriodicalIF":0.0,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81607872","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}
(S3)E⊆E★ and (E★)★=E★. We shall denote the set of semistar operations (resp. the set of star operations) on D by SStar (D) (resp. Star (D)) as in [5]. The main purpose of this paper is to investigate semistar operations on conducive domains. We also study the number of semistar operations. We shall denote the cardinality of a set X by |X| and the symbol⊂means "proper inclusion" . Throughout this paper, D denotes an integral domain with quotient field K and D the integral closure of D. Furthermore we always assume D≠K. Any unexplained terminology is standard, as in [7].
{"title":"Semistar operations on conductive domains","authors":"A. Okabe","doi":"10.5036/MJIU.35.11","DOIUrl":"https://doi.org/10.5036/MJIU.35.11","url":null,"abstract":"(S3)E⊆E★ and (E★)★=E★. We shall denote the set of semistar operations (resp. the set of star operations) on D by SStar (D) (resp. Star (D)) as in [5]. The main purpose of this paper is to investigate semistar operations on conducive domains. We also study the number of semistar operations. We shall denote the cardinality of a set X by |X| and the symbol⊂means \"proper inclusion\" . Throughout this paper, D denotes an integral domain with quotient field K and D the integral closure of D. Furthermore we always assume D≠K. Any unexplained terminology is standard, as in [7].","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"12 1","pages":"11-19"},"PeriodicalIF":0.0,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83160116","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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