Browsing by Author "Psihoyios, G."
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Item Applications of hecke operator to generalized dedekind eta functions(Amer Inst Pyhsics, 2009) Açıkgöz, Mehmet; Kim, Daeyeoul; Şimşek, Yılmaz; Simos, T. E.; Psihoyios, G.; Tsitouras, C.; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; J-3505-2017; 57189022403The aim of this paper is to give relations between generalized Dedekind eta functions, theta functions, Dedekind sums, Hardy-Berndt sums and Hecke operators.Item Calculation of the minimal polynomial of 2cos(π/n) over Q with Maple(American Inst Physics, 2012) Simos, T. E.; Psihoyios, G.; Tsitouras, C.; Anastassi, Z.; Yurttaş, Aysun; Özgür, Birsen; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-0700-5774; ABA-6206-2020; ABI-4127-2020; J-3505-2017; AAG-8470-2021; 37090056000; 54403501400; 57189022403The number lambda(q) = 2cos pi/q, q is an element of N, q >= 3, appears in the study of Hecke groups which are Fuchsian groups and in the study of regular polyhedra. There are many results about the minimal polynomial of this algebraic number. Here we obtain the minimal polynomial of these numbers over the field of rationals by means of the better known Chebycheff polynomials and the Maple language.Item Determination of genus of normal subgroups of discrete groups(Amer Inst Physics, 2010) Karpuz, Eylem Güzel; Ateş, Fırat; Psihoyios, G.; Tsitouras, C.; Cangül, İsmail Naci; Demirci, Musa; Yurttaş, Aysun; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; AAG-8470-2021; J-3505-2017; 57189022403; 23566581100; 37090056000In this work, subgroups of a special class of discrete subgroups of PLS(2, R), namely the ones of the first kind with genus 0, have been studied. We establish a technique to compute the genus of these subgroups in terms of the genus of easier groups. The method established here can be used for triangle groups, surface groups and Hecke groups (including the well-known modular group).Item Deterrmining the minimal polynomial of cos(2π/n) over Q with Maple(Amer Inst Physics, 2012) Simos, T. E.; Psihoyios, G.; Tsitouras, C.; Anastassi, Z.; Özgür, Birsen; Yurttaş, Aysun; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-0700-5774; AAG-8470-2021; J-3505-2017; ABA-6206-2020; ABI-4127-2020; 54403501400; 37090056000; 57189022403The number lambda(q) = 2cos pi/q, q is an element of N, q >= 3, appears in the study of Hecke groups which are Fuchsian groups, and in the study of regular polyhedra. There are many results about the minimal polynomial of this algebraic number and in some of these methods, the minimal polynomials of several algebraic numbers are used. Here we obtain the minimal polynomial of one of those numbers, cos(2 pi/n), over the field of rationals by means of the better known Chebycheff polynomials for odd q and give some of their properties. We calculated this minimal polynomial for n is an element of N by using the Maple language and classifying the numbers n is an element of N into different classes.Item Generalization for Estrada index(Amer Inst Physics, 2010) Güngör, Ayşe Dilek; Çevik, Ahmet Sinan; Karpuz, Eylem Güzel; Ateş, Fırat; Psihoyios, G.; Tsitouras, C.; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017; 57189022403In this paper the Estrada index of Hermite matrix is firstly defined and investigated. In fact this is a natural generalization of Estrada, distance Estrada and Laplacian Estrada indices. Thus all properties about them can be handled by this new index.Item A p-adic Look at the Diophantine equation x2 + 112k = yn(Amer Inst Physics, 2009) Şimşek, Yılmaz; Soydan, Gökhan; Simos, T. E.; Psihoyios, G.; Tsitouras, C.; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; 57189022403We find all solutions of Diophantine equation x(2) + 11(2k) = y(n), x >= 1, y >= 1, k is an element of N, n >= 3. We give p-adic interpretation of this equation.Item Primes in Z[exp(2πi/3)](Amer Inst Physics, 2010) Namlı, Dilek; Çevik, Ahmet Sinan; Güngör, Ayşe Dilek Maden; Tekcan, Ahmet; Psihoyios, G.; Tsitouras, C.; Naci, İsmail Cangül; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017; 57189022403In this paper, we study the primes in the ring Z[w], where w = exp(2 pi i/3) is a cubic root of unity. We gave a classification of them and some results related to the use of them in the calculation of cubic residues are obtained.Item Some formulae for the Zagreb indices of graphs(Amer Inst Physics, 2012) Çevik, Ahmet Sinan; Simos, T. E.; Psihoyios, G.; Tsitouras, C.; Anastassi, Z.; Cangül, İsmail Naci; Yurttaş, Aysun; Togan, Müge; Uludaǧ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-0700-5774; AAG-8470-2021; J-3505-2017; ABA-6206-2020; 57189022403; 37090056000; 54403978300In this study, we first find formulae for the first and second Zagreb indices and coindices of certain classical graph types including path, cycle, star and complete graphs. Secondly we give similar formulae for the first and second Zagreb coindices.