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Öğe Fibonacci simetrik sayısal yarıgrupların bir sınıfı(ODTÜ, 2015-06) Süer, Meral; İlhan, SedatÖğe Pseudo simetrik sayısal yarıgruplar(Uludağ Üniversitesi, 2011-09) Süer, Meral; İlhan, SedatBu çalışmada pseudo simetrik sayısal yarıgrupların bazı özellikleri ve 3’ün katı olmayan s pozitif tam sayısı için S 3,3 s,3 2 s şeklindeki özel bir pseudo simetrik sayısal yarıgrubunun yapısı incelenmektedirÖğe Bazı sayısal yarıgrupların tip dizileri(Erciyes Üniversitesi, 2010-08) Süer, Meral; İlhan, SedatÖğe Katlılığı 9 ve 10 olan arf sayısal yarıgrupları üzerine(Gazi Üniversitesi, 2019-06) Süer, Meral; İlhan, Sedat; Karakaş, İbrahimBu 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 vereceğizÖğe Bazı teleskopik sayısal yarı grupların parametrizasyonu(Atılım Üniversitesi, 2017-09) Süer, MeralÖğe Arf sayısal yarıgrupları(Çankaya Üniversitesi, 2013-06) Süer, Meral; İlhan, SedatÖğe Pseudo simetrik sayısal yarıgruplar üzerine(Dicle Üniversitesi, 2013-09) Süer, Meral; İlhan, SedatÖğe Pseudo simetrik sayısal yarıgrupların bir sınıfının boşlukları(Hacettepe Üniversitesi, 2011-06) Süer, Meral; İlhan, SedatBu c¸alıs¸mada 3 un katı olmayan ¨ s ∈ Z + ic¸in S = h3, 3 + s, 3 + 2si s¸eklindeki bir pseudosimetrik sayısal yarıgrubunun bos¸lukları, temel ve ozel bos¸lukları hakkında bazı sonuc¸lar yer almak- ¨ tadır.Öğe On the numerical semigroups with generated by two elements with multiplicity 3(Harran Üniversitesi, 2017-05) Süer, Meral; İlhan, Sedat; Çelik, AhmetThroughout 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) xS :x mS 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 .Öğe Delta sets of some pseudo-symmetric numerical semigroups(IKSAD Publishing House, 2018-05-01) Süer, Meral; Çelik, ÖzkanA numerical semigroup is a submonoid of , the set of nonnegative integers, under addition and with finite complement in . If the numerical semigroup is the form with an integer not divisible by tree, then is a pseudo symmetric numerical semigroup with embedding dimension and multiplicity three. We present procedures to calculate the delta of pseudo- symmetric numerical semigroups as given above. Also, we will give a relation between the betti numbers and the delta sets of these semigroups.Öğe Betti numbers of some telescopic numerical semigroups(IKSAD Publishing House, 2018-05-01) Süer, Meral; Sezgin, Mehmet ŞirinLet be the set of nonnegative integers. A numerical semigroup is a nonempty subset M of that is closed under addition, contains the zero element, and whose complement in is finite. In this study, we will examine the Betti numbers of some telescopic numerical semigroup families with generated triply. And we will try to express in terms of generators of these numerical semigroup families. So we will find a formula for the Betti numbers of these numerical semigroup families.Öğe The special gaps of some Arf numerical semigroups(IKSAD Publishing House, 2018-05-01) Süer, Meral; Yalçın, Burak YasinThe concept of special gap of a numerical semigroup is used to by the problem of finding the set of all numerical semigroups containining a given numerical semigroup. In this study, we will find the specific gaps of some Arf numerical semigroups families and all numerical semigroups containining them.Öğe On Arf closures of some numerical semigroups generated by three elements(Harran Üniversitesi, 2017-05) Süer, Meral; İlhan, Sedat; Çelik, AhmetA 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.Öğe Some results in triply–generated telescopic numerical semigroups(Harran Üniversitesi, 2017-05) Süer, Meral; İlhan, SedatIn this study, we assume that ¥ = {0,1,2,...,n,...}, S Í ¥ and ¢ integer set. S is a numerical semigroup if a + b Î S, for a,b Î S , 0Î S and ¥ \S is finite. Let S be a numerical semigroup and X Ì ¥ . X is called minimal system of generators of S if S = < X > and there is not any subset Y Ì X such that S = < Y > . = < > 1 2 3 S s ,s ,s is called a triply-generated telescopic numerical semigroup if Î < > 1 2 3 , s s s d d where = 1 2 d gcd(s s ) (Here, gcd(S)= greatest common divisor the element of S ). Let S be a numerical semigroup, then m(S) = min{x Î S: x > 0} is called as multiplicity of S . The number F(S) = max(¢ \S) is called Frobenius number of S . A numerical semigroup S can be written the form { } - = < > = = = + ® 1 2 0 1 2 1 , ,..., 0, , ,..., , ( ) 1, ... n n n S a a a s s s s s F S , where + < i i 1 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 x Î ¥ and x Ï S , then x is called gap of S . We denote the set of gaps ofS , H(S) = ¥ \S . The number G(S) = #(H(S)) is called the genus ofS . Let S be a numerical semigroup and m Î S ,m> 0. Then Ap(S,m) x S :x mS is called Apery set of S according to m . Ap(S,m) is formed by the smallest elements of S belonging to the different congruence classes mod m. Thus # (Ap(S,m)) = m and the Frobenius number of S equal to max(Ap(S,m)) - m ( where #(A) stands for Cardinality (A) ). The number n(S) = #({0,1,2,...,F(S)}ÇS) is called determine of numerical semigroup S . Also, It is known that G(S) = F(S)+ 1- n(S) . In this study, we will give some results about gaps, fundamental gaps and the determine number of S triply-generated telescopic numerical semigroups with arbitrary multiplicity.Öğe Saturated numerical semigroups with multiplicity four(Fırat Üniversitesi, 2016-05) Süer, Meral; İlhan, SedatA 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. A numerical semigroup S is saturated if the following condition holds: s, s1,s2, …,sk belongs to S are such that s1 < s or equal to s, for all 1 < I < k or i=1 and i=k , and c1,c2,…,ck belongs to are such that c1s1+c2s2+…+cksk > 0 or equal to 0, then s+ c1s1+c2s2+…+cksk belongs to S. The frobenius number of S is the maximum integer not belonging to S, which is denoted by F(S). H(S)= N\S is the set of the elements gaps of S, and the cardinality elements of H(S) is called genus of S, and denoted by g(S). It is said that an integer x is a Pseudo-Frobenius number if x+s belongs to S for s > 0, s belongs to S and x belongs to \S. In this study, we will characterize the all families of Saturated numerical semigroups with multiplicity four. These numerical semigroups generated by 4,k,k 1,k 2 for k>5 or k=5, k=1(mod4), and 4,k,k 2,k 3 for k > 7 or k=7, k=3(mod4), and 4,k,k t,k t 2 for k > 6 or k=6, k=2(mod 4), respectively. We will prove that Saturated numerical semigroups such that multiplicity four. Also, we will give formulas Frobenius number F S( ) , Pseudo Frobenius number PF S( ) , gaps H S( ) and genus g S( ) of these numerical semigroups.Öğe On a class of Arf numerical semigroups(Fırat Üniversitesi, 2016-05) Süer, Meral; İlhan, SedatA 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.Öğe Some results on telescopic numerical semigroups(Yıldız Teknik Üniversitesi, 2017-05) Süer, Meral; İlhan, SedatÖğe Some results on Arf numerical semigroups with multiplicity 8(Harran Üniversitesi, 2017-05) Süer, Meral; İlhan, SedatA 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 ¥ . Note also that up to isomorphism the set of numerical semigroups classify the set of all submonoids of ( , ) ¥ + . Let S be submonoid of ¥ , the condition of having finite complement in ¥ is equivalent to saying that the greatest common divisor (gcd for short) of its elements is one. Those positive integers which do not belong to S are called gaps of S . The number of gaps of S is called the genus of S and it is denoted by G S( ) . The largest gaps of S is F S( ) if S is different from ¥ . m S s S s ( ) min : 0 = Î > { } are called multiplicity of S , respectively. Also, n S Card F S S ( ) 0,1,2,..., ( ) = Ç ({ } ) is called the number determine of S . If a Î ¥ and a S Ï , 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 known that G S F S n S ( ) ( ) 1 ( ) = + - . A numerical semigroup S is called Arf if x y z S + - Î for all x y z S , , Î , where x y z ³ ³ . This definition was first given by C. Arf in 1949. In the study, we intend to examine the Arf numerical semigroup with multiplicity eight and fixed conductor. We will also able to compute the notable elements and special sets of these numerical semigroups.Öğe Arf numerical semigroups with multiplicity eight(Yıldız Teknik Üniversitesi, 2017-05) Süer, Meral; İlhan, Sedat; Karakaş, İbrahimÖğe On the dirichlet problem for semilinear eliptic equations(Yıldız Technical University, 2020) Harman, Aziz; Harman, Ezgi
