Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Citation - WoS: 1
Citation - Scopus: 1
Applications of Class Numbers and Bernoulli Numbers To Harmonic Type Sums
(Korean Mathematical Society, 2021) Göral, Haydar; Sertbaş, Doğa Can; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
Divisibility properties of harmonic numbers by a prime number p have been a recurrent topic. However, finding the exact p-adic orders of them is not easy. Using class numbers of number fields and Bernoulli numbers, we compute the exact p-adic orders of harmonic type sums. Moreover, we obtain an asymptotic formula for generalized harmonic numbers whose p-adic orders are exactly one.
Arithmetic Progressions in Certain Subsets of Finite Fields
(Elsevier, 2023) Eyidoğan, Sadık; Göral, Haydar; Kutlu, Mustafa Kutay; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In this note, we focus on how many arithmetic progressions we have in certain subsets of finite fields. For this purpose, we consider the sets Sp = {t2 : t & ISIN; Fp} and Cp = {t3 : t & ISIN; Fp}, and we use the results on Gauss and Kummer sums. We prove that for any integer k & GE; 3 and for an odd prime number p, the number of k-term arithmetic progressions in Sp is given by p2 2k + R, where and ck is a computable constant depending only on k. The proof also uses finite Fourier analysis and certain types of Weil estimates. Also, we obtain some formulas that give the exact number of arithmetic progressions of length  in the set Sp when  & ISIN; {3,4, 5} and p is an odd prime number. For  = 4, 5, our formulas are based on the number of points on
Citation - WoS: 2
Citation - Scopus: 3
Biquandle Brackets and Knotoids
(World Scientific Publishing, 2021) Güğümcü, Neslihan; Nelson, Sam; Oyamaguchi, Natsumi; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
Biquandle brackets are a type of quantum enhancement of the biquandle counting invariant for oriented knots and links, defined by a set of skein relations with coefficients which are functions of biquandle colors at a crossing. In this paper, we use biquandle brackets to enhance the biquandle counting matrix invariant defined by the first two authors in (N. Gügümcü and S. Nelson, Biquandle coloring invariants of knotoids, J. Knot Theory Ramif. 28(4) (2019) 1950029). We provide examples to illustrate the method of calculation and to show that the new invariants are stronger than the previous ones. As an application we show that the trace of the biquandle bracket matrix is an invariant of the virtual closure of a knotoid.
Can Cpt Be Violated Through Extended Time Reversal?
(World Scientific Publishing, 2001) Erdem, Recai; Ufuktepe, Ünal; 04.05. Department of Pyhsics; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We consider the implications of the extension of time reversal through Wigner types and group extensions. We clarify its physical content and apply the results in a toy model. Finally we point out the possibility of violation of CPT in this framework.
Citation - WoS: 21
Citation - Scopus: 21
Cold Sintering of Soda-Lime Glass
(Elsevier Ltd., 2021) Karacasulu, Levent; Ögür, Ezgi; Pişkin, Cerem; Vakıfahmetoğlu, Çekdar; 03.09. Department of Materials Science and Engineering; 01. Izmir Institute of Technology; 01.01. Units Affiliated to the Rectorate; 03. Faculty of Engineering
Ordinary recycled soda lime glass powder was densified via cold sintering process with the aid of concentrated NaOH solution. Increase in processing time, temperature and concentration of the NaOH solution resulted in the formation of monolithic glass artifacts with higher relative densities. The sample densified the most (95.2%) was obtained when the sintering was performed at 250˚C with a 20 min dwell time using 15 M NaOH solution.
Citation - WoS: 7
Citation - Scopus: 8
Diffraction of Flexural-Gravity Waves by a Vertical Cylinder of Non-Circular Cross Section
(Elsevier Ltd., 2020) Dişibüyük, Nazile Buğurcan; Korobkin, A. A.; Yılmaz, Oğuz; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
The linear three-dimensional problem of flexural-gravity wave (hydro-elastic wave) diffraction by a vertical cylinder of an arbitrary smooth cross section is studied using an asymptotic approach combined with the vertical mode method for water of finite depth. The surface of the water is covered by an infinite, continuous elastic ice plate. The rigid cylinder extends from the sea bottom to the ice surface. The ice plate is frozen to the cylinder. The ice deflection is described by the equation of a thin elastic plate of constant thickness with clamped edge conditions at the cylinder. The flow under the ice is described by the linear theory of potential flows. The coupled problem of wave diffraction is solved in two steps. First, the problem is solved without evanescent waves similar to the problem of water waves diffracted by a vertical cylinder. This solution does not satisfy the edge conditions. Second, a radiation problem with a prescribed motion of the ice plate edge is solved by the vertical mode method. The sum of these two solutions solve the original problem. Both solutions are obtained by an asymptotic method with a small parameter quantifying a small deviation of the cylinder cross section from a circular one. Third-order asymptotic solutions are obtained by solving a set of two-dimensional boundary problems for Helmholtz equations in the exterior of a circle. Strains along the edge, where the ice plate is frozen to the cylinder, are investigated for nearly square and elliptic cross sections of the vertical cylinders depending on the characteristics of ice and incident wave. The strains are shown to be highest in the places of high curvatures of the cross sections. The derived asymptotic formulae can be used in design of vertical columns in ice. They directly relate the strains in ice plate to the shape of the column. © 2020 Elsevier Ltd
Citation - WoS: 3
Citation - Scopus: 3
Dual Kasch rings
(World Scientific Publishing, 2023) Lomp, Christian; Büyükaşık, Engin; Yurtsever, Haydar Baran; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
It is well known that a ring R is right Kasch if each simple right R-module embeds in a projective right R-module. In this paper we study the dual notion and call a ring R right dual Kasch if each simple right R-module is a homomorphic image of an injective right R-module. We prove that R is right dual Kasch if and only if every finitely generated projective right R-module is coclosed in its injective hull. Typical examples of dual Kasch rings are self-injective rings, V-rings and commutative perfect rings. Skew group rings of dual Kasch rings by finite groups are dual Kasch if the order of the group is invertible. Many examples are given to separate the notion of Kasch and dual Kasch rings. It is shown that commutative Kasch rings are dual Kasch, and a commutative ring with finite Goldie dimension is dual Kasch if and only if it is a classical ring (i.e. every element is a zero divisor or invertible). We obtain that, for a field k, a finite dimensional k-algebra is right dual Kasch if and only if it is left Kasch. We also discuss the rings over which every simple right module is a homomorphic image of its injective hull, and these rings are termed strongly dual Kasch.
Citation - WoS: 2
Citation - Scopus: 6
Dynamical Properties of Generalized Traveling Waves of Exactly Solvable Forced Burgers Equations With Variable Coefficients
(Elsevier, 2021) Atılgan Büyükaşık, Şirin; Bozacı, Aylin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
The initial value problem for a generalized forced Burgers equation with variable coefficients U-t + ((mu)over dot(t)/mu(t))U + UUX = (1/2 mu(t))U-xx - a(t)U-x + b(t)(xU)(x) - omega(2)(t)x + f(t), x is an element of R , t > 0, is solved using Cole-Hopf linearization and Wei-Norman Lie algebraic approach for finding the evolution operator of the associated linear diffusion type equation. As a result, solution of the initial value problem is obtained in terms of a corresponding linear second-order inhomogeneous ordinary differential equation and a standard Burgers model. Then, using the translation and Galilean invariance of standard Burgers equation, families of generalized nonlinear waves propagating according to a Newtonian type equation of motion are constructed. The influence of the damping, dilatation and forcing terms on the dynamics of shocks, multi-shocks, triangular and N-shaped generalized traveling waves and rational type solutions with moving singularities is investigated. Finally, exactly solvable models with concrete time-variable coefficients are introduced and dynamical properties of certain particular solutions are discussed. (C) 2020 Elsevier B.V. All rights reserved.
Citation - WoS: 9
Citation - Scopus: 11
An Efficient Approach for Solving Nonlinear Multidimensional Schrodinger Equations
(Elsevier, 2021) İmamoğlu Karabaş, Neslişah; Korkut, Sıla Övgü; Tanoğlu, Gamze; Aziz, Imran; Siraj-ul-Islam; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
An efficient numerical method is proposed for the solution of the nonlinear cubic Schrodinger equation. The proposed method is based on the Frechet derivative and the meshless method with radial basis functions. An important characteristic of the method is that it can be extended from one-dimensional problems to multi-dimensional ones easily. By using the Frechet derivative and Newton-Raphson technique, the nonlinear equation is converted into a set of linear algebraic equations which are solved iteratively. Numerical examples reveal that the proposed method is efficient and reliable with respect to the accuracy and stability.
Es-W
(Taylor & Francis, 2021) Ay Saylam, Başak; Hamdi, Haleh; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We introduce and study the notion of ES-w-stability for an integral domain R. A nonzero ideal I of R is called ES-w-stable if (I-2)(w) = (JI)(w) for some t-invertible ideal J of R contained in I, and I is called weakly ES-w-stable if I-w = (JE)(w) for some t-invertible fractional ideal J of R and w-idempotent fractional ideal E of R. We define R to be an ES-w-stable domain (resp., a weakly ES-w-stable domain) if every nonzero ideal of R is ES-w-stable (resp., weakly ES-w-stable). These notions allow us to generalize some well-known properties of ES-stable and weakly ES-stable domains.
Citation - WoS: 7
Citation - Scopus: 6
Exponential Stability and Boundedness of Nonlinear Perturbed Systems by Unbounded Perturbation Terms
(Elsevier, 2023) Şahan, Gökhan; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We study the exponential stability and boundedness problem for perturbed nonlinear time-varying systems using Lyapunov Functions with indefinite derivatives. As the limiting function for the perturbation term, we use different forms and give stability and boundedness conditions in terms of the coefficients in these bounds. Contrary to most of the available conditions, we allow the coefficients to be unbounded. But instead, we put forward a condition that requires a series produced by coefficients to be limited and exponentially decaying. We perform our results on Linear time-varying systems and generalize many of the available results. & COPY; 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.
Citation - WoS: 5
Citation - Scopus: 5
Exponential Stability for the Nonlinear Schrodinger Equation With Locally Distributed Damping
(Taylor and Francis Ltd., 2020) Cavalcanti, Marcelo M.; Correa, Wellington J.; Özsarı, Türker; Sepulveda, Mauricio; Vejar-Aseme, Rodrigo; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In this paper, we study the defocusing nonlinear Schrodinger equation with a locally distributed damping on a smooth bounded domain as well as on the whole space and on an exterior domain. We first construct approximate solutions using the theory of monotone operators. We show that approximate solutions decay exponentially fast in the L-2-sense by using the multiplier technique and a unique continuation property. Then, we prove the global existence as well as the L-2-decay of solutions for the original model by passing to the limit and using a weak lower semicontinuity argument, respectively. The distinctive feature of the paper is the monotonicity approach, which makes the analysis independent from the commonly used Strichartz estimates and allows us to work without artificial smoothing terms inserted into the main equation. We in addition implement a precise and efficient algorithm for studying the exponential decay established in the first part of the paper numerically. Our simulations illustrate the efficacy of the proposed control design.
Holomorphic Realization of Non-Commutative Space-Time and Gauge Invariance
(IOP Publishing, 2003) Mir-Kasimov, Rufat M.; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
The realization of the Poincare Lie algebra in terms of noncommutative differential calculus over the commutative algebra of functions is considered. The algebra of functions is defined on the spectrum of the unitary irreducible representations of the De Sitter group. Corresponding space-time carries the noncommutative geometry. Gauge invariance principle consistent with this noncommutative space is considered.
Citation - WoS: 2
Citation - Scopus: 2
An Inverse Parameter Problem With Generalized Impedance Boundary Condition for Two-Dimensional Linear Viscoelasticity
(Society for Industrial and Applied Mathematics Publications, 2021) Ivanyshyn Yaman, Olha; Le Louer, Frederique; 04.02. Department of Mathematics; 01. Izmir Institute of Technology; 04. Faculty of Science
We analyze an inverse boundary value problem in two-dimensional viscoelastic media with a generalized impedance boundary condition on the inclusion via boundary integral equation methods. The model problem is derived from a recent asymptotic analysis of a thin elastic coating as the thickness tends to zero [F. Caubet, D. Kateb, and F. Le Louer, J. Elasticity, 136 (2019), pp. 17-53]. The boundary condition involves a new second order surface symmetric operator with mixed regularity properties on tangential and normal components. The well-posedness of the direct problem is established for a wide range of constant viscoelastic parameters and impedance functions. Extending previous research in the Helmholtz case, the unique identification of the impedance parameters from measured data produced by the scattering of three independent incident plane waves is established. The theoretical results are illustrated by numerical experiments generated by an inverse algorithm that simultaneously recovers the impedance parameters and the density solution to the equivalent boundary integral equation reformulation of the direct problem.
Citation - WoS: 1
Citation - Scopus: 1
Irreducibility and Primality in Differentiability Classes
(Michigan State University Press, 2023) Batal, Ahmet; Eyidoğan, S.; Göral, Haydar; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In this note, we give criteria for the irreducibility of functions in Cm [0, 1], where m ∈ {1, 2, 3, ...} ∪ {∞} ∪ {ω}. We also discuss irreducibility in multivariable differentiability classes. Moreover, we characterize irreducible functions and maximal ideals in C∞ [0, 1]. In fact, irreducible and prime smooth functions are the same, and every maximal ideal of C∞ [0, 1] is principal. © 2023 Michigan State University Press. All rights reserved.
Citation - Scopus: 1
Level Set Estimates for the Discrete Frequency Function
(Springer Verlag, 2019-07) Temur, Faruk; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We introduce the discrete frequency function as a possible new approach to understanding the discrete Hardy-Littlewood maximal function. Considering that the discrete Hardy-Littlewood maximal function is given at each integer by the supremum of averages over intervals of integer length, we define the discrete frequency function at that integer as the value at which the supremum is attained. After verifying that the function is well-defined, we investigate size and smoothness properties of this function.
Citation - WoS: 4
Citation - Scopus: 5
Lung Parenchyma Segmentation From Ct Images With a Fully Automatic Method
(Springer, 2023) Mousavi Moghaddam, Reza; Aghazadeh, Nasser; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
For the last three years, the world has been facing an infectious disease that primarily affects the human breathing organ. The disease has caused many deaths worldwide so far and has imposed high economic costs on all countries. Therefore, attention to computer-aided detection/diagnosis (CAD) systems to help diagnose and treat diseases related to the human respiratory system should be given more attention so that countries’ health systems can treat patients in epidemics. Considering the importance of CAD systems, we proposed a two-step automatic algorithm. In the first step, we obtain the primary boundary of the lobes in CT lung scan images with the help of some conventional image processing tools. In the second stage, we obtained a more precise boundary of the lung lobes by correcting the unusual dimples and valleys (which are sometimes caused by the presence of juxtapleural nodules). This proposed method has low implementation time. Given that a precise boundary of the pulmonary lobes is essential in the more accurate diagnosis of lung-related diseases, an attempt has been made to ensure that the final segmentation of the lung parenchyma has an acceptable score in terms of evaluation criteria so that the proposed algorithm can be used in the diagnosis procedure. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Citation - WoS: 8
Citation - Scopus: 9
Max-Projective Modules
(World Scientific Publishing, 2020) Alagöz, Yusuf; Büyükaşık, Engin; 01. Izmir Institute of Technology; 04.02. Department of Mathematics; 04. Faculty of Science
Weakening the notion of R-projectivity, a right R-module M is called max-projective provided that each homomorphism f: M ? R/I, where I is any maximal right ideal, factors through the canonical projection : R ? R/I. We study and investigate properties of max-projective modules. Several classes of rings whose injective modules are R-projective (respectively, max-projective) are characterized. For a commutative Noetherian ring R, we prove that injective modules are R-projective if and only if R = A × B, where A is QF and B is a small ring. If R is right hereditary and right Noetherian then, injective right modules are max-projective if and only if R = S × T, where S is a semisimple Artinian and T is a right small ring. If R is right hereditary then, injective right modules are max-projective if and only if each injective simple right module is projective. Over a right perfect ring max-projective modules are projective. We discuss the existence of non-perfect rings whose max-projective right modules are projective. © 2020 World Scientific Publishing Company.
Citation - WoS: 6
Citation - Scopus: 6
A Numerical Method Based on Legendre Wavelet and Quasilinearization Technique for Fractional Lane-Emden Type Equations
(Springer, 2023) İdiz, Fatih; Tanoğlu, Gamze; Aghazadeh, Nasser; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In this research, we study the numerical solution of fractional Lane-Emden type equations, which emerge mainly in astrophysics applications. We propose a numerical approach making use of Legendre wavelets and the quasilinearization technique. The nonlinear term in fractional Lane-Emden type equations is iteratively linearized using the quasilinearization technique. The linearized equations are then solved using the Legendre wavelet collocation method. The proposed method is quite effective to overcome the singularity in fractional Lane-Emden type equations. Convergence and error analysis of the proposed method are given. We solve some test problems to compare the effectiveness of the proposed method with some other numerical methods in the literature.
Citation - WoS: 4
Citation - Scopus: 4
Numerical Solution of a Generalized Boundary Value Problem for the Modified Helmholtz Equation in Two Dimensions
(Elsevier, 2021) Ivanyshyn Yaman, Olha; Özdemir, Gazi; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We propose numerical schemes for solving the boundary value problem for the modified Helmholtz equation and generalized impedance boundary condition. The approaches are based on the reduction of the problem to the boundary integral equation with a hyper-singular kernel. In the first scheme the hyper-singular integral operator is treated by splitting off the singularity technique whereas in the second scheme the idea of numerical differentiation is employed. The solvability of the boundary integral equation and convergence of the first method are established. Exponential convergence for analytic data is exhibited by numerical examples. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.Y. All rights reserved.

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