Lineer uzaylar ve kutupsal uzaylar üzerine
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Date
2006
Authors
Kılınç, Nuri
Journal Title
Journal ISSN
Volume Title
Publisher
Uludağ Üniversitesi
Abstract
Yedi bölümden oluşan bu çalışmada lineer uzaylar ve kutupsal uzaylar ele alınmıştır. Birinci bölümde ilerideki bölümlere hazırlık olması amacıyla bazı temel kavramlar tanıtılmıştır. İkinci bölümde lineer uzayların genel özellikleri incelenip, lineer uzay örnekleri üzerinde durulmuştur. Üçüncü bölümde D.R. Stinson’un belli sonlu lineer uzayların yokluğunu araştırdığı “The non-existence of certain finite lineer spaces” adlı makalesi incelenmiştir. Dördüncü bölümde L.M. Batten’in “The non-existence of finite lineer spaces with ϑ=n 2 and b=n2 +n+2 lines” makalesi incelenmiştir. Beşinci bölümde yine L.M. Batten’in “A characterization of finite lineer spaces on ϑ points, n2 ≤ ϑ< (n+1)2 , and b=n2 +n+3 lines n ≥ 10” makalesi incelenmiştir. Altıncı bölümde Klaus Metsch’in “Proof of Dowling-Wilson Konjecture” adlı makalesi incelenmiştir. Yedinci bölümde ise kutupsal uzaylar tanıtılıp, konunun ortaya çıkışının tarihçesi özetlenmiştir.
In this work which consist of seven sections, linear spaces and polar spaces are examined. In section one, some of the main concepts are introduced as a preparation for the following sections. In section two, general properties of linear spaces are exemined and linear space examples are stressed upon. In section three, the article : “The nonexistence of certain finite linear space” , in which D.R. Stinson make a study of nonexistence of certain finite linear space is examined. In section four, L.M. Batten’s “The nonexistence of finite linear space with ϑ=n 2 and b=n2 +n+2 lines” article is examined. In section five, another study of L.M. Batten is examined on “ A characterization of finite lineer spaces on ϑ points, n2 ≤ ϑ< (n+1)2 , and b=n2 +n+3 lines n ≥ 10” In section six, the study of Klaus Metsch on “Proof of DowlingWilson Konjecture” is examined. And in section seven , the polar spaces are introduced and the history of the subject is summerized.
In this work which consist of seven sections, linear spaces and polar spaces are examined. In section one, some of the main concepts are introduced as a preparation for the following sections. In section two, general properties of linear spaces are exemined and linear space examples are stressed upon. In section three, the article : “The nonexistence of certain finite linear space” , in which D.R. Stinson make a study of nonexistence of certain finite linear space is examined. In section four, L.M. Batten’s “The nonexistence of finite linear space with ϑ=n 2 and b=n2 +n+2 lines” article is examined. In section five, another study of L.M. Batten is examined on “ A characterization of finite lineer spaces on ϑ points, n2 ≤ ϑ< (n+1)2 , and b=n2 +n+3 lines n ≥ 10” In section six, the study of Klaus Metsch on “Proof of DowlingWilson Konjecture” is examined. And in section seven , the polar spaces are introduced and the history of the subject is summerized.
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Keywords
Lineer uzay, Sonlu lineer uzayların karakterizasyonu, Kutupsal uzay, Sonlu lineer uzay, Dowling Wilson konjektörü, Lineer space, Polar space, Finite lineer space, Dowling-Wilson konjecture, Characterization of finite lineer spaces
Citation
Kılınç, N. (2006). Lineer uzaylar ve kutupsal uzaylar üzerine. Yayınlanmamış yüksek lisans tezi. Uludağ Üniversitesi Fen Bilimleri Enstitüsü.