Matematik Bölümü

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https://hdl.handle.net/20.500.12402/654

Listeleniyor 1 - 20 / 31

Arf numerical semigroups with multiplicity eight
(Yıldız Teknik Üniversitesi, 2017-05) Süer, Meral; İlhan, Sedat; Karakaş, İbrahim
Arf sayısal yarıgrupları
(Çankaya Üniversitesi, 2013-06) Süer, Meral; İlhan, Sedat
Bazı saturated sayısal yarıgruplar üzerine
(Dicle Üniversitesi, 2016-12) Süer, Meral; İlhan, Sedat; Çelik, Ahmet
Bazı sayısal yarıgrupların tip dizileri
(Erciyes Üniversitesi, 2010-08) Süer, Meral; İlhan, Sedat
Conditions of numerical semigroups having maximal or almost maximal length
(International Journal of Physical Sciences, 2012-04-30) Süer, Meral; İlhan, Sedat
Fibonacci simetrik sayısal yarıgrupların bir sınıfı
(ODTÜ, 2015-06) Süer, Meral; İlhan, Sedat
Gaps of a class of pseudo symmetric numerical semigroups
(Acta Universitatis Apulensis, 2013) Süer, Meral; İlhan, Sedat
In this study, we give some results about the gaps, fundamental and special gaps of a pseudo symmetric numerical semigroup in the form of S=< 3, 3+ s, 3+ 2s> for s∈ Z+ and 3 s.
İndirgenme boyutu üç olan fibonacci simetrik sayısal yarıgruplarının bir sınıfı
(Batman Üniversitesi, 2015) Süer, Meral; İlhan, Sedat
Bu çalışmada, pozitif tam sayı, , ve , 3 ün tam katı olmamak üzere, Fibonacci sayıları için simetrik Fibonacci sayısal yarıgrubu şeklindeki özel bir sınıfını inceleyeceğiz ve bu sınıfta bazı sonuçları vereceğiz.
Katlılığı 6 olan saturated sayısal yarıgruplar üzerine
(Batman Üniversitesi, 2017) Süer, Meral; İlhan, Sedat; Çelik, Ahmet
İlk olarak sayısal yarıgrup problemi, “ Sayısal yarıgruba ait olmayan en büyük tamsayıyı üreteçleri cinsinden nasıl ifade edilebilir?” şeklinde olup, 19. yy sonunda karşımıza çıkmıştır. Sayısal yarıgrup çalışan ilk matematikçiler Frobenius ve Sylvester’dır. Sayısal yarıgrup kavramı günümüzde de hala matematikçilerin ilgi alanındadır. Sayısal yarıgrup problemleri, sayılar teorisi ile bağlantılı olduğu gibi matematiğin diğer alanlarında ve bilgisayar bilimleri ile de ilgilidir. Diophant moduler eşitsizliklerin çözümünde, liner tamsayı programlamada, şifrelemede, değişmeli cebir ve cebirsel geometrinin uygulamalarında özel ilgi alanı oluşturmuştur. Bu bağlamda saturated sayısal yarıgruplarda literatürde önemli çalışmalarda yer almış. Özellikle saturated halkaların, yarıgruplar teorisine geçişi olarak karşımıza çıkmış. Bu çalışmadaki amacımız katlılığı 6 ve kondüktörü C olan saturated sayısal yarıgruplar üzerine çalışmaktır. Burada C, 6 dan büyük veya eşit ve k negatif olamayan tamsayı olmak üzere 6k+1 den farklı olarak yazılabilen pozitif bir tamsayıdır. Katlılığı 6 ve kondüktörü C olan tüm saturated sayısal yarıgrupları elde edip bu sayısal yarıgrupların Frobenius sayısı, belirteç sayısı ve cinsini bu yarıgrupların üreteçleri ile ifade edeceğiz.
Katlılığı 9 ve 10 olan arf sayısal yarıgrupları üzerine
(Gazi Üniversitesi, 2019-06) Süer, Meral; İlhan, Sedat; Karakaş, İbrahim
Bu çalışmada, katlılığı 9 ve 10 olan ve keyfi bir ileticili bazı Arf sayısal yarıgruplarda tip dizisi, belirteç sayısı, Apery kümesi ve cins hakkında elde ettiğimiz birtakım sonuçları vereceğiz
On a class of Arf numerical semigroups
(Fırat Üniversitesi, 2016-05) Süer, Meral; İlhan, Sedat
A subset S of N is called a numerical semigroup if S is closed under addition and S has element 0 and N\S is finite where N denotes the set of nonnegative integers. In this study, we are interested two subclass of maximal embedding dimension numerical semigroups, which are those semigroups having the Arf property and saturated numerical semigroups. We introduce a new class of both Arf property and saturated numerical semigroups with multiplicity four. We consider numerical semigroups minimally generated by {4, k, k+1, k+2}. Where k is an integer greater than or equal to 5 and k is congruent to 1 (modulo 4). We prove that all these semigroups are both numerical semigroups with Arf property and saturated numerical semigroup. There is not any formulas to calculate invariants as Frobenius number, gaps, n(S) and genus of S even for numerical semigroup with multiplicity four. But this invariants have been calculated by imposing some conditions on elements of the numerical semigroup S. We calculate the Frobenius number, the genus and the set of gaps of each of these numerical semigroups. Additionally, we give a relation between the set of pseudo- Frobenius numbers and the set of all fundamental gaps of these numerical semigroups.
On a class of pseudo-symmetric numerical semigroups
(Pushpa Publishing House, 2011-12) Süer, Meral; İlhan, Sedat
On a family of saturated numerical semigroups with multiplicity four
(TÜBİTAK, 2017-01-16) Süer, Meral; İlhan, Sedat
In this study, we will give some results on Arf numerical semigroups of multiplicity four generated by {4, k, k + 1, k + 2} where k is an integer not less than 5 and k ≡ 1(mod 4).
On Arf closures of some numerical semigroups generated by three elements
(Harran Üniversitesi, 2017-05) Süer, Meral; İlhan, Sedat; Çelik, Ahmet
A numerical semigroup is a subset of the set of nonnegative integers (denoted here by ¥ ) closed under addition, containing the zero element and with finite complement in ¥ . A numerical semigroup is a set of the form 1, 2 , , 1 2 ... p p S = u u ¼ u = u ¥ + u ¥ + + u ¥ where are positive integers, such that ( ) 1 2 gcd , , , 1 p u u ¼ u = . The condition is saying that S has finite complement in ¥ (where short gcd is the greatest common divisor),( Barucci, Dobbs & Fontana, 1997; .Fröberg, Gottlieb & Haggkvist, 1987; . Rosales &Garcia-Sanchez, 2009). If S is a numerical semigroup, then F(S) = max(¢ \S) is called Frobenius number of S . Any numerical semigroup write this form { } 1 2 0 1 2 , ,..., 0 , , ,..., ( ) 1, ... n n S = < a a a > = = s s s s = F S + ® . Where “® ” means that every integer greater than F(S)+ 1 belongs to the set. A numerical semigroup S is called Arf if x + y - z Î S for all x, y, z Î S , where x ³ y ³ z . The smallest Arf numerical semigroup containing a numerical semigroup S is called the Arf closure of S , and it is denoted by Arf (S) . Arf numerical semigroup and their applications to algebraic error corerecting codes have been a special interest in recent times (Brass-Amaros, 2004; Campillo, Farran & Munuera, 2000). The families of Arf numerical semigroups are related with the problem solution of singularities in curve.In this presentation, we will give some results between numerical semigroups and theirs Arf closure. Also, we will obtain some relation for Arf closure of these numerical semigroups.
On Arf numerical semigroups
(SCIK Publishing Corporation, 2016) Süer, Meral; İlhan, Sedat
In this study, we obtain an Arf semigroup by means of a sequence. We also establish some results on the Arf semigroup
On telescopic numerical semigroup families with embedding dimension 3
(Erzincan Üniversitesi, 2019-03-24) Süer, Meral; İlhan, Sedat
In this study, the set of all telescopic numerical semigroups families with embedding dimension three is obtained for some fixed multiplicity by some parameters. Also, some invariants of these families are calculated in term of their generators
On the fundamental gaps of some saturated numerical semigroups with multiplicity 4
(Hikari, 2016) Süer, Meral; İlhan, Sedat; Çelik, Ahmet
In this study, we calculate the number of fundamental gaps of the some numerical semigroups which are for and and for and and or. Also, we give the type sequence of these numerical semigroups.
On the numerical semigroups with generated by two elements with multiplicity 3
(Harran Üniversitesi, 2017-05) Süer, Meral; İlhan, Sedat; Çelik, Ahmet
Throughout this study, we assume that ¥ and ¢ be the sets of nonnegative integers and integers, respectively. The subset S of ¥ is a numerical semigroup if 0 Î S , x + y Î S, for all x, y Î S , and Card(¥ \S)< ¥ ( this condition is equivalent to gcd(S)= 1 , gcd(S)= greatest common divisor the element of S ) . Let S be a numerical semigroup, then F(S) = max(¢ \S) and m(S) = min{s Î S: s > 0} are called Frobenius number and multiplicity of S , respectively. Also, n(S) = Card ({0,1,2,...,F(S)}ÇS)is called the number determine of S . If S is a numerical semigroup such that 1 2 , ,..., r S = < a a a > , then we observe that { } 1 2 0 , 2 1 , ,..., 0, , ,..., , ( ) 1, ... r n n S a a a s s s s s F S - = < > = = = + ® where 1 , ( ) i i s s n n S + < = , and the arrow means that every integer greater than F(S) + 1 belongs to S , for i = 1,2,...,n = n(S) . If a Î ¥ and a Ï S , then a is called gap of S . We denote the set of gaps of S , by H(S) , i.e, H(S) = ¥ \S .The G(S) = Card(H(S)) is called the genus of S . Also, It is known that G(S) = F(S) + 1- n(S) . Let S be a numerical semigroup andm Î S ,m > 0 . Then Ap(S,m)  xS :x mS  is called Apery set of S according to m . A numerical semigroup S is Arf if a+ b- c Î S , for all a,b,c Î S such that a ³ b ³ c. The intersection of any family of Arf numerical semigroups is again an Arf numerical semigroup. Thus, since ¥ is an Arf numerical semigroup, one can consider the smallest Arf numerical semigroup containing a given numerical semigroup. The smallest Arf numerical semigroup containing a numerical semigroup S is called the Arf closure of S , and it is denoted by Arf (S) . In this presentation, we will give some results about gaps, the determine number, Apery set and Arf closure of S numerical semigroup such that S = 3, x .
On the one half of an Arf numerical semigroup
(SCIK Publishing Corporation, 2015) Süer, Meral; İlhan, Sedat
In this study, we will characterize the Arf numerical semigroup that is computed in a quotient of an Arf numerical semigroup by an positive integer. We will also obtain the one half of this special Arf numerical semigroup and give some results about this numerical semigroup.
On the saturated numerical semigroups
(Open Mathematics, 2016-11) Süer, Meral; İlhan, Sedat
In this study, we characterize all families of saturated numerical semigroups with multiplicity four. We also present some results about invariants of these semigroups.

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