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Recent Submissions

Sonlu cisimler üzerindeki x^k-cx-d polinomlarının iki uygulaması üzerine ve daha fazlası
İrimağzı, Canberk; Özbudak, Ferruh (Springer, Cham, 2023-1-11)
For integers k∈[2,q−2] coprime to q−1 , we first bound the number of zeroes of the family of polynomials xk−cx−d∈Fq[x] where q=2n such that q−1 is a prime or q=3n such that (q−1)/2 is a prime. This gives us bounds on...
On two applications of polynomials x^k-cx-d over finite fields and more
İrimağzı, Canberk; Özbudak, Ferruh (Springer, Cham, 2023-01-01)
For integers k∈[2,q−2] coprime to q−1 , we first bound the number of zeroes of the family of polynomials xk−cx−d∈Fq[x] where q=2n such that q−1 is a prime or q=3n such that (q−1)/2 is a prime. This gives us bounds on...
The Hasse Norm Principle in Global Function Fields
Uysal, Rabia Gülşah; Özman, Ekin; Newton , Rachel; Manzateanu , Adalina; Sutherland, Nichole (Springer Nature, 2022-02-01)
LetLbe a finite extension ofFq(t)" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; font-size: 18px; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction...
An Introduction to Sobolev Spaces
Pişkin, Erhan; Okutmuştur, Baver (Bentham Science Publishers, 2021-11-01)
Sobolev spaces were firstly defined by the Russian mathematician, Sergei L. Sobolev (1908-1989) in the 1930s. Several properties of these spaces have been studied by mathematicians until today. Functions that account ...
Structure-preserving Reduced Order Modeling of non-traditional Shallow Water Equation
Uzunca, Murat; Karasözen, Bülent; Yıldız, Süleyman (Springer, London/Berlin , 2021-04-01)
An energy- preserving reduced -order model (ROM) is developed for the non-traditional shallow water equation (NTSWE) with full Coriolis force. The NTSWE in the noncanonical Hamiltonian/Poisson form is discretized in space ...
Domain Structured Dynamics: Unpredictability, chaos, randomness, fractals, differential equations and neural networks
Akhmet, Marat (Institute of Physics Publishing (IOP), 2021-03-01)
Domain structured dynamics introduces a way for analysis of chaos in fractals, neural networks and random processes. It starts with newly invented abstract similarity sets and maps, which are in the basis of the abstract s...
Finite Difference Solutions of 2D Magnetohydrodynamic Channel Flow in a Rectangular Duct
Arslan, Sinem (Springer, Cham, 2021-01-01)
2020 International Conference on Information Security and Cryptology ISCTURKEY 2020 3-4 December 2020 Middle East Technical University Ankara, TURKEY
Sağıroğlu, Şeref; Özbudak, Ferruh; Akleylek, Sedat; Canbay, Yavuz (IEEE Publications, 2020-12-01)
xiiPREFACEInternational Conference on Information Security and Cryptology Conference (ISCTurkey) has been held since 2006. The 13th conference was completed in Ankara, Turkey, between December 3-4, 2020 via online due to t...
Construction of Efficient Codes for High-Order Direct Sum Masking
Carlet, Claude; Guılley, Sylvain; Güneri, Cem; Mesnager, Sihem; Özbudak, Ferruh (IOS Press, 2020-03-01)
Linear complementary dual (LCD) codes and linear complementarypairs (LCP) of codes have been proposed as counter-measures against side-channelattacks (SCA) and fault injection attacks (FIA) in the context of direct sum mas...
A Survey on Hilbert Spaces and Reproducing Kernels
Okutmuştur, Baver (IntechOpen, 2020-02-01)
The main purpose of this chapter is to provide a brief review of Hilbert space with its fundamental features and introduce reproducing kernels of the corresponding spaces. We separate our analysis into two parts. In ...
Dynamics with Chaos and Fractals
Akhmet, Marat (Springer, London/Berlin , 2020-02-01)
Stands as the first book presenting theoretical background on the unpredictable point and mapping of fractals.Introduces the concepts of unpredictable functions, abstract self-similarity, and similarity map.Discusses unpre...
An Extrapolated Crank Nicholson VMS-POD Methodfor Darcy Brinkman Equations.
Güler Eroğlu, Fatma; Kaya Merdan, Songül (Springer, Cham, 2020-01-01)
This study presents a variational multiscale (VMS) reduced order model (ROM) based on proper orthogonal decomposition (POD) for the Darcy Brinkman equations. The idea of POD consists of extracting the dominant features of ...
A FIRST COURSE IN ANALYSIS - Introductory Calculus
Okutmuştur, Baver (Nobel Yayın Dağıtım, 2019-09-01)
This book has been prepared in accordance with the programs of Basic Mathematics I, Analysis I or Calculus I courses which are taught at the undergraduate level of the Faculties of Science and Engineering as well as ...
Almost periodicity, chaos, and asymptotic equivalence
Akhmet, Marat (Springer, 2019-06-01)
The central subject of this book is Almost Periodic Oscillations, the most common oscillations in applications and the most intricate for mathematical analysis. Prof. Akhmet's lucid and rigorous examination proves these os...
Scalar Conservation Laws
Okutmuştur, Baver (IntechOpen, 2019-04-01)
We present a theoretical aspect of conservation laws by using simplest scalar models with essential properties. We start by rewriting the general scalar conserva- tion law as a quasilinear partial differential equation a...
Kindergarteners’ and first-graders’ development of numbers representing length and area: stories of measurement
Sevinç, Şerife (Springer, 2019-01-01)
Numerical Analysis
Tezer, Münevver; Bozkaya, Canan (ODTÜ Basım İşliği, 2018-05-01)
Gözleme Dayalı Yöntemler
Doğan, Celal Deha; Nayır, Funda; Arastaman, Gökhan; Kurum, Gül; Demir, Kamile; Yılmaz, Kürşat; Demirkasımoğlu, Nihan; Taneri, Pervin Oya; Kuru Çetin, Saadet; Fidan, Tuncer; Akın, Uğur; Kondakçı, Yaşar (Anı Yayınevi, 2018-01-01)
Constructions of Cyclic Subspace Codes and Maximum Rank Distance Codes
Özbudak, Ferruh (Springer, 2018-01-01)
This chapter is a survey of the recent results on the constructions of cyclicsubspace codes and maximum rank distance codes. Linearized polynomials are themain tools used to introduce both constructions in this chapter. In...
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