**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**83

# Search results for: Ahmet Tekcan

##### 83 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t

**Authors:**
Ahmet Tekcan,
Betül Gezer,
Osman Bizim

**Abstract:**

Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.

**Keywords:**
Pell equation,
Diophantine equation.

##### 82 The Pell Equation x2 − Py2 = Q

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Canan Kocapınar,
Hatice Alkan

**Abstract:**

**Keywords:**
Pell equation,
solutions of Pell equation.

##### 81 The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Hatice Alkan

**Abstract:**

**Keywords:**
Diophantine equation,
Pell equation,
quadratic form.

##### 80 The Number of Rational Points on Singular Curvesy 2 = x(x - a)2 over Finite Fields Fp

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Singular curve,
elliptic curve,
rational points.

##### 79 The Number of Rational Points on Conics Cp,k : x2 − ky2 = 1 over Finite Fields Fp

**Authors:**
Ahmet Tekcan

**Abstract:**

Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.

**Keywords:**
Elliptic curve,
conic,
rational points.

##### 78 The Pell Equation x2 − (k2 − k)y2 = 2t

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Pell equation,
solutions of Pell equation.

##### 77 Neighbors of Indefinite Binary Quadratic Forms

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Quadratic form,
indefinite form,
cycle,
proper cycle,
right neighbor,
left neighbor.

##### 76 The Number of Rational Points on Elliptic Curves y2 = x3 + b2 Over Finite Fields

**Authors:**
Betül Gezer,
Hacer Özden,
Ahmet Tekcan,
Osman Bizim

**Abstract:**

Let p be a prime number, Fpbe a finite field and let Qpdenote the set of quadratic residues in Fp. In the first section we givesome notations and preliminaries from elliptic curves. In the secondsection, we consider some properties of rational points on ellipticcurves Ep,b: y2= x3+ b2 over Fp, where b ∈ F*p. Recall that theorder of Ep,bover Fpis p + 1 if p ≡ 5(mod 6). We generalize thisresult to any field Fnp for an integer n≥ 2. Further we obtain someresults concerning the sum Σ[x]Ep,b(Fp) and Σ[y]Ep,b(Fp), thesum of x- and y- coordinates of all points (x, y) on Ep,b, and alsothe the sum Σ(x,0)Ep,b(Fp), the sum of points (x, 0) on Ep,b.

**Keywords:**
Elliptic curves over finite fields,
rational points on elliptic curves.

##### 75 Positive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Binary quadratic form,
elliptic curves,
cubic congruence.

##### 74 Elliptic Divisibility Sequences over Finite Fields

**Authors:**
Betül Gezer,
Ahmet Tekcan,
Osman Bizim

**Abstract:**

**Keywords:**
Elliptic divisibility sequences,
singular elliptic divisibilitysequences,
elliptic curves,
singular curves.

##### 73 Some Algebraic Properties of Universal and Regular Covering Spaces

**Authors:**
Ahmet Tekcan

**Abstract:**

Let X be a connected space, X be a space, let p : X -→ X be a continuous map and let (X, p) be a covering space of X. In the first section we give some preliminaries from covering spaces and their automorphism groups. In the second section we derive some algebraic properties of both universal and regular covering spaces (X, p) of X and also their automorphism groups A(X, p).

**Keywords:**
covering space,
universal covering,
regular covering,
fundamental group,
automorphism group.

##### 72 The Number of Rational Points on Elliptic Curves and Circles over Finite Fields

**Authors:**
Betül Gezer,
Ahmet Tekcan,
Osman Bizim

**Abstract:**

**Keywords:**
Elliptic curves over finite fields,
rational points on
elliptic curves and circles.

##### 71 The Elliptic Curves y2 = x3 - t2x over Fp

**Authors:**
Ahmet Tekcan

**Abstract:**

Let p be a prime number, Fp be a finite field and t ∈ F*p= Fp- {0}. In this paper we obtain some properties of ellipticcurves Ep,t: y2= y2= x3- t2x over Fp. In the first sectionwe give some notations and preliminaries from elliptic curves. In the second section we consider the rational points (x, y) on Ep,t. Wegive a formula for the number of rational points on Ep,t over Fnp for an integer n ≥ 1. We also give some formulas for the sum of x?andy?coordinates of the points (x, y) on Ep,t. In the third section weconsider the rank of Et: y2= x3- t2x and its 2-isogenous curve Et over Q. We proved that the rank of Etand Etis 2 over Q. In the last section we obtain some formulas for the sums Σt∈F?panp,t for an integer n ≥ 1, where ap,t denote the trace of Frobenius.

**Keywords:**
Elliptic curves over finite fields,
rational points onelliptic curves,
rank,
trace of Frobenius.

##### 70 Quadratic Irrationals, Quadratic Ideals and Indefinite Quadratic Forms II

**Authors:**
Ahmet Tekcan,
Arzu Özkoç

**Abstract:**

Let D = 1 be a positive non-square integer and let δ = √D or 1+√D 2 be a real quadratic irrational with trace t =δ + δ and norm n = δδ. Let γ = P+δ Q be a quadratic irrational for positive integers P and Q. Given a quadratic irrational γ, there exist a quadratic ideal Iγ = [Q, δ + P] and an indeﬁnite quadratic form Fγ(x, y) = Q(x−γy)(x−γy) of discriminant Δ = t 2−4n. In the ﬁrst section, we give some preliminaries form binary quadratic forms, quadratic irrationals and quadratic ideals. In the second section, we obtain some results on γ, Iγ and Fγ for some speciﬁc values of Q and P.

**Keywords:**
Quadratic irrationals,
quadratic ideals,
indefinite quadratic forms,
extended modular group.

##### 69 The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4

**Authors:**
Armend Sh. Shabani

**Abstract:**

**Keywords:**
Pell's equation,
solutions of Pell's equation.

##### 68 Effect of Derating Factors on Photovoltaics under Climatic Conditions of Istanbul

**Authors:**
Bihter Yerli,
Mustafa K. Kaymak,
Ercan İzgi,
Ahmet Öztopal,
Ahmet D. Şahin

**Abstract:**

**Keywords:**
Efficiency,
Derating Factor,
Istanbul,
Photovoltaic.

##### 67 Decomposition of Homeomorphism on Topological Spaces

**Authors:**
Ahmet Z. Ozcelik,
Serkan Narli

**Abstract:**

**Keywords:**
Generalized closed set,
homeomorphism,
gsghomeomorphism,
sgs-homeomorphism.

##### 66 On Submaximality in Intuitionistic Topological Spaces

**Authors:**
Ahmet Z. Ozcelik,
Serkan Narli

**Abstract:**

**Keywords:**
Intuitionistic set; intuitionistic topology;intuitionistic submaximality and mega-connectedness.

##### 65 On Generalizing Rough Set Theory via using a Filter

**Authors:**
Serkan Narlı,
Ahmet Z. Ozcelik

**Abstract:**

**Keywords:**
Rough set,
fuzzy set,
membership function,
knowledge representation and processing,
information theory

##### 64 The Challenge of Large-Scale IT Projects

**Authors:**
Ahmet Denker

**Abstract:**

**Keywords:**
Software engineering,
software economics,
project
management,
large-scale projects.

##### 63 Investigation of the Effect of Phosphorous on the Flame Retardant Polyacrylonitrile Nanofiber

**Authors:**
Mustafa Yılmaz,
Ahmet Akar,
Nesrin Köken,
Nilgün Kızılcan

**Abstract:**

Commercially available poly(acrylonitrile-co-vinyl acetate) P(AN-VA) or poly(acrylonitrile-co-methyl acrylate) P(AN-MA) are not satisfactory to meet the demand in flame and fire-resistance. In this work, vinylphosphonic acid is used during polymerization of acrylonitrile, vinyl acetate, methacrylic acid to produce fire-retardant polymers. These phosphorus containing polymers are successfully spun in the form of nanofibers. Properties such as water absorption of polymers are also determined and compared with commercial polymers.

**Keywords:**
Flame retardant,
nanofiber,
polyacrylonitrile,
phosphorous compound,
membrane.

##### 62 Sliding Mode Based Behavior Control

**Authors:**
Selim Yannier,
Asif Sabanovic,
Ahmet Onat,
Muhammet Bastan

**Abstract:**

**Keywords:**
Autonomous Mobile Robot,
Behavior Based Control,
Fast Local Obstacle Avoidance,
Sliding Mode Control.

##### 61 A Comparative Analysis of the Perceived Bureaucracy in a Turkish State University

**Authors:**
Ahmet C. Kutlu,
Seçkin Polat

**Abstract:**

**Keywords:**
Degree of bureaucratization,
Hall's Organizational
Inventory,
perceived bureaucracy.

##### 60 Transferring Route Plan over Time

**Authors:**
Barıs Kocer,
Ahmet Arslan

**Abstract:**

**Keywords:**
genetic algorithms,
transfer learning,
travellingsalesman problem

##### 59 Performance Comparison of a Low Cost Air Quality Sensor with a Commercial Electronic Nose

**Authors:**
Ünal Kızıl,
Levent Genç,
Sefa Aksu,
Ahmet Tapınç

**Abstract:**

**Keywords:**
Air quality,
electronic nose,
environmental quality,
gas sensor.

##### 58 Comparative Performance Analysis of Nonlinearity Cancellation Techniques for MOS-C Realization in Integrator Circuits

**Authors:**
Hasan Çiçekli,
Ahmet Gökçen,
Uğur Çam

**Abstract:**

**Keywords:**
Integrator circuits,
MOS-C realization,
nonlinearity
cancellation,
tunable resistors.

##### 57 A Diagnostic Fuzzy Rule-Based System for Congenital Heart Disease

**Authors:**
Ersin Kaya,
Bulent Oran,
Ahmet Arslan

**Abstract:**

**Keywords:**
Congenital heart disease,
Fuzzy rule-basedclassifiers,
Classification

##### 56 Testing the Relationship between Economic Freedoms and Growth by Panel Causality Application: Case of Middle East Countries

**Authors:**
Ahmet Ay,
Hakan Acet,
Ceyhun Can Özcan

**Abstract:**

Economic freedoms, most emphasized issue in the recent years, are considered to affect economic growth and performance via institutional structure. In this context, a model that includes Turkey and Middle East Countries, and where the effects of economic freedom on growth are examined, was formed. For the groups of countries determined, in the study carried out by using the dataset belonging the period of 2004 - 2009, between economic freedoms and growth, a negative relationship was observed as group. In the sense of individual effects, it was identified that there was a positive relationship in terms of some Middle East Countries and Turkey.

**Keywords:**
Economic Freedoms,
Economic Growth,
Freedoms.

##### 55 Improving Classification Accuracy with Discretization on Datasets Including Continuous Valued Features

**Authors:**
Mehmet Hacibeyoglu,
Ahmet Arslan,
Sirzat Kahramanli

**Abstract:**

**Keywords:**
Data mining classification algorithms,
entropy-baseddiscretization method

##### 54 A Look at the Gezi Park Protests through the Lens of Media

**Authors:**
Süleyman Hakan Yılmaz,
Yasemin Gülşen Yılmaz

**Abstract:**

The Gezi Park protests of 2013 have significantly changed the Turkish agenda and its effects have been felt historically. The protests, which rapidly spread throughout the country, were triggered by the proposal to recreate the Ottoman Army Barracks to function as a shopping mall on Gezi Park located in Istanbul’s Taksim neighbourhood despite the oppositions of several NGOs and when trees were cut in the park for this purpose. Once the news that the construction vehicles entered the park on May 27 spread on social media, activists moved into the park to stop the demolition, against whom the police used disproportioned force. With this police intervention and the then prime-minister Tayyip Erdoğan's insistent statements about the construction plans, the protests turned into anti- government demonstrations, which then spread to the rest of the country, mainly in big cities like Ankara and Izmir. According to the Ministry of Internal Affairs’ June 23rd reports, 2.5 million people joined the demonstrations in 79 provinces, that is all of them, except for the provinces of Bayburt and Bingöl, while even more people shared their opinions via social networks. As a result of these events, 8 civilians and 2 security personnel lost their lives, namely police chief Mustafa Sarı, police officer Ahmet Küçükdağ, citizens Mehmet Ayvalıtaş, Abdullah Cömert, Ethem Sarısülük, Ali İsmail Korkmaz, Ahmet Atakan, Berkin Elvan, Burak Can Karamanoğlu, Mehmet İstif, and Elif Çermik, and 8163 more were injured. Besides being a turning point in Turkish history, the Gezi Park protests also had broad repercussions in both in Turkish and in global media, which focused on Turkey throughout the events. Our study conducts content analysis of three Turkish reporting newspapers with varying ideological standpoints, Hürriyet, Cumhuriyet ve Yeni Şafak, in order to reveal their basic approach to news casting in context of the Gezi Park protests. Headlines, news segments, and news content relating to the Gezi protests were treated and analysed for this purpose. The aim of this study is to understand the social effects of the Gezi Park protests through media samples with varying political attitudes towards news casting.

**Keywords:**
Gezi Park,
media,
news casting,
tree.