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Öğe On the fundamental gaps of some saturated numerical semigroups with multiplicity 4(Hikari, 2016) Süer, Meral; İlhan, Sedat; Çelik, AhmetIn 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.Öğe Radiation dose estimation and mass attenuation coefficients ofcement samples used in Turkey(Elsevier, 2009-12-16) Damla, Nevzat; Çevik, Uğur; Kobya, Ali İhsan; Çelik, Ahmet; Çelik, Necati; Grieken, R. VanDifferent cement samples commonly used in building construction in Turkey have been analyzed for natural radioactivity using gamma-ray spectrometry. The mean activity concentrations observed in the cement samples were 52, 40 and 324 Bq kg−1 for 226Ra, 232Th and 40K, respectively. The measured activity concentrations for these radionuclides were compared with the reported data of other countries and world average limits. The radiological hazard parameters such as radium equivalent activities (Raeq), gamma index (Iγ) and alpha index (Iα) indices as well as terrestrial absorbed dose and annual effective dose rate were calculated and compared with the international data. The Raeq values of cement are lower than the limit of 370 Bq kg−1, equivalent to a gamma dose of 1.5 mSv y−1. Moreover, the mass attenuation coefficients were determined experimentally and calculated theoretically using XCOM in some cement samples. Also, chemical compositions analyses of the cement samples were investigated.Öğe Assessment of natural radiation exposure levels and mass attenuation coefficients of lime and gypsum samples used in Turkey(Springer Nature, 2009-11-17) Damla, Nevzat; Çevik, Uğur; Kobya, Ali İhsan; Çelik, Ahmet; Çelik, NecatiThe activity concentrations of 226Ra, 232Th, and 40K in lime and gypsum samples used as building materials in Turkey were measured using gamma spectrometry. The mean activity concentrations of 226Ra, 232Th, and 40K were found to be 38 ± 16, 20 ± 9, and 156 ± 54 Bq kg − 1 for lime and found to be 17 ± 6, 13 ± 5, and 429 ± 24 Bq kg − 1 for gypsum, respectively. The radiological hazards due to the natural radioactivity in the samples were inferred from calculations of radium equivalent activities (Raeq), indoor absorbed dose rate in the air, the annual effective dose, and gamma and alpha indices. These radiological parameters were evaluated and compared with the internationally recommended limits. The experimental mass attenuation coefficients (μ/ρ) of the samples were determined in the energy range 81–1,332 keV. The experimental mass attenuation coefficients were compared with theoretical values obtained using XCOM. It is found that the calculated values and the experimental results are in good agreement.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 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.
