Pub Date : 2012-01-01DOI: 10.1007/978-3-642-28592-9_22
Liu Xin
{"title":"An FLP Complementary Slackness Theorem Based on Fuzzy Relationship","authors":"Liu Xin","doi":"10.1007/978-3-642-28592-9_22","DOIUrl":"https://doi.org/10.1007/978-3-642-28592-9_22","url":null,"abstract":"","PeriodicalId":16294,"journal":{"name":"Journal of Liaoning Normal University","volume":"67 1","pages":"213-228"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74478570","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 : 2009-01-01DOI: 10.4324/9781315731834-25
Dai Lian-rong
The short-range interaction mechanisms are totally different in the chirial SU(3) quark model and in the extended chiral SU(3) quark model.One is from the one-gluon exchange and another is from the vector meson exchange.In this work,we study the Ξ*-Ω interaction in these two models.The results show that it could be deeply bound states in these two models with totally different interaction mechanisms.The possible reasons of forming(Ξ*Ω)ST=012 stangeness-5 bound states are given.From the results,we can see that the chiral σ meson exchange is important,which dominantly provides the attractive interaction.Also we find that the quark exchange effect give attraction to this system,which means the special symmetry is important.Both reasons are helpful to form Ξ*-Ω deeply bound states.
{"title":"The study of Ξ~*-Ω interaction","authors":"Dai Lian-rong","doi":"10.4324/9781315731834-25","DOIUrl":"https://doi.org/10.4324/9781315731834-25","url":null,"abstract":"The short-range interaction mechanisms are totally different in the chirial SU(3) quark model and in the extended chiral SU(3) quark model.One is from the one-gluon exchange and another is from the vector meson exchange.In this work,we study the Ξ*-Ω interaction in these two models.The results show that it could be deeply bound states in these two models with totally different interaction mechanisms.The possible reasons of forming(Ξ*Ω)ST=012 stangeness-5 bound states are given.From the results,we can see that the chiral σ meson exchange is important,which dominantly provides the attractive interaction.Also we find that the quark exchange effect give attraction to this system,which means the special symmetry is important.Both reasons are helpful to form Ξ*-Ω deeply bound states.","PeriodicalId":16294,"journal":{"name":"Journal of Liaoning Normal University","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86279558","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 algorithm terminates after a finite number of iterations, since b is replaced in each iteration by the remainder r = a mod b, which is a nonnegative integer that is strictly smaller than b. Therefore, the algorithm terminates after at most b iterations. We show now that the algorithm is correct. We denote by 〈a, b〉 the set {ax + by | x, y ∈ Z}; this set is called the ideal generated by a and b in the ring of integers. Notice that if 〈a, b〉 contains the integers c and d, then 〈c, d〉 is a subset of 〈a, b〉. Lemma 1 If b 6= 0, then 〈a, b〉 = 〈b, a mod b〉. Proof. The ideal 〈a, b〉 contains the remainder r = a mod b, since r = a− qb with q = ba/bc. Thus, if b 6= 0 then the ideal 〈b, a mod b〉 is a subset of 〈a, b〉.
算法在有限次迭代后终止，因为b在每次迭代中被余数r = a mod b所取代，而余数r = a mod b是一个严格小于b的非负整数，因此算法最多迭代b次后终止。现在我们证明算法是正确的。我们用< a, b >表示集合{ax + by | x, y∈Z};这个集合称为由整数环中的a和b生成的理想集合。注意，如果< a, b >包含整数c和d，则< c, d >是< a, b >的子集。引理1如果b6 = 0，则< a, b > = < b, a mod b >。证明。理想< a, b >包含余数r = a mod b，因为r = a−qb且q = ba/bc。因此，如果b6 = 0，则理想< b, a mod b >是< a, b >的子集。
{"title":"On the Extended Euclidean Algorithm","authors":"Dong Xue","doi":"10.3840/08003652","DOIUrl":"https://doi.org/10.3840/08003652","url":null,"abstract":"The algorithm terminates after a finite number of iterations, since b is replaced in each iteration by the remainder r = a mod b, which is a nonnegative integer that is strictly smaller than b. Therefore, the algorithm terminates after at most b iterations. We show now that the algorithm is correct. We denote by 〈a, b〉 the set {ax + by | x, y ∈ Z}; this set is called the ideal generated by a and b in the ring of integers. Notice that if 〈a, b〉 contains the integers c and d, then 〈c, d〉 is a subset of 〈a, b〉. Lemma 1 If b 6= 0, then 〈a, b〉 = 〈b, a mod b〉. Proof. The ideal 〈a, b〉 contains the remainder r = a mod b, since r = a− qb with q = ba/bc. Thus, if b 6= 0 then the ideal 〈b, a mod b〉 is a subset of 〈a, b〉.","PeriodicalId":16294,"journal":{"name":"Journal of Liaoning Normal University","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89692160","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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