Örgü kavramı ve minumum geçişli 3-örgüler
Braid concept and minumum crossing with 3-braids
Yazar: OSMAN KARTAL
Danışman: YRD. DOÇ. DR. HAKAN ŞİMŞEK
Kırıkkale Üniversitesi / Fen Bilimleri Enstitüsü / Matematik Ana Bilim Dalı
Derece: Yüksek Lisans, 2007
Konu: Matematik = Mathematics

Özet:
Bu tez dört bölümden olusmaktadır. Birinci bölüm giris için ayrılmıstır. kincibölümde bazı temel tanımlar ve kavramlar ile örgünün tanımı hakkında kısa bilgiverildi. Artin örgü temsili ve Konfigürasyon uzayına baglı tanımı verildi.Konfigürasyon uzayı incelendi. Üçüncü bölümde ise, N = 3 ifadesine yönelik biralgoritma irdelenecektir. n-bilesenli örgü verildigi zaman minimal uzunluga sahip, B,Artin örgü temsilini bulan algoritma için bir örnek verildi. Minimal geçisli örgü eldeetme problemi notasyon olarak çözümde ve çizimde ekonomik yollar vermektedir.Artin örgü kelimesinin uzunlugu ile bahsedilen kavram örgü diyagramında verilengeçitlerin sayısıdır. Minimum geçit sayısı örgünün kompleksligiyle ilgili bir ölçütverir. Fiziksel anlamda ise toplam manyetik alanların büyüklügünün tahmini içinkullanılmaktadır. Dördüncü bölüm ise tartısma ve sonuç için ayrılmıstır.Anahtar Kelimeler: Örgü, Dügüm Teorisi, Artin Temsili, Wraplar

Abstract:
This work (thesis work) is classified into four sections. The first section isallocated to foreword. In second section some basic definitions and concepts alsodefinition of braid with it are mentioned in brief. Braid description of Artin isintroduced and definition of this description in related to configuration space is alsomade. We researched on that configuration space in this section too. In third sectiona algorithm based on N = 3 valve will be scrutinized. If a braid with component n isgiven, B braid description of Artin in minimal length sets an example for algorithm.The problem of obtaining minimal crossing braid offers as notation economicalways in solution and diagram. The concept denoted by length of word of Artin braidis the number of crossing in braid diagram. Minimum number of crossing sets acriteria of complexity of braid. It is used in physical sense for estimation purpose ofsize of complete magnetic surfaces. Last section is allocated to discussion andconclusion.iiKey Words: Braid, Knot Theory, Description of Artin, WrapsThis work (thesis work) is classified into four sections. The first section isallocated to foreword. In second section some basic definitions and concepts alsodefinition of braid with it are mentioned in brief. Braid description of Artin isintroduced and definition of this description in related to configuration space is alsomade. We researched on that configuration space in this section too. In third sectiona algorithm based on N = 3 valve will be scrutinized. If a braid with component n isgiven, B braid description of Artin in minimal length sets an example for algorithm.The problem of obtaining minimal crossing braid offers as notation economicalways in solution and diagram. The concept denoted by length of word of Artin braidis the number of crossing in braid diagram. Minimum number of crossing sets acriteria of complexity of braid. It is used in physical sense for estimation purpose ofsize of complete magnetic surfaces. Last section is allocated to discussion andconclusion.iiKey Words: Braid, Knot Theory, Description of Artin, WrapsThis work (thesis work) is classified into four sections. The first section isallocated to foreword. In second section some basic definitions and concepts alsodefinition of braid with it are mentioned in brief. Braid description of Artin isintroduced and definition of this description in related to configuration space is alsomade. We researched on that configuration space in this section too. In third sectiona algorithm based on N = 3 valve will be scrutinized. If a braid with component n isgiven, B braid description of Artin in minimal length sets an example for algorithm.The problem of obtaining minimal crossing braid offers as notation economicalways in solution and diagram. The concept denoted by length of word of Artin braidis the number of crossing in braid diagram. Minimum number of crossing sets acriteria of complexity of braid. It is used in physical sense for estimation purpose ofsize of complete magnetic surfaces. Last section is allocated to discussion andconclusion.iiKey Words: Braid, Knot Theory, Description of Artin, WrapsThis work (thesis work) is classified into four sections. The first section isallocated to foreword. In second section some basic definitions and concepts alsodefinition of braid with it are mentioned in brief. Braid description of Artin isintroduced and definition of this description in related to configuration space is alsomade. We researched on that configuration space in this section too. In third sectiona algorithm based on N = 3 valve will be scrutinized. If a braid with component n isgiven, B braid description of Artin in minimal length sets an example for algorithm.The problem of obtaining minimal crossing braid offers as notation economicalways in solution and diagram. The concept denoted by length of word of Artin braidis the number of crossing in braid diagram. Minimum number of crossing sets acriteria of complexity of braid. It is used in physical sense for estimation purpose ofsize of complete magnetic surfaces. Last section is allocated to discussion andconclusion.iiKey Words: Braid, Knot Theory, Description of Artin, Wraps