Mathematics / Matematik

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

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Citation - WoS: 53
Citation - Scopus: 58
Measurement of the WZ Production Cross Section in pp Collisions at S=13 TeV
(Elsevier, 2017) Khachatryan, V.; Sirunyan, A. M.; Tumasyan, A.; Adam, W.; Asilar, E.; Bergauer, T.; Woods, N.
The WZ production cross section in proton-proton collisions at root s = 13 Tev is measured with the CMS experiment at the LHC using a data sample corresponding to an integrated luminosity of 2.3 fb(-1). The measurement is performed in the leptonic decay modes WZ -> lVl'l', where l,l'=e,mu. The measured cross section for the range 60 WZ) = 39.9 +/- 3.2(stat)(2.9)(-3.1)(syst)+/- 0.4(theo)+/- 1.3(lumi)pb, consistent with the standard model prediction.
Endüstriyel Matematik
(01. Izmir Institute of Technology, 2024) Tanoğlu, Gamze; Yurt, Canberk; Yurt, Canberk; Tanoğlu, Gamze; 04.02. Department of Mathematics; 02.04. Department of Industrial Design; 04. Faculty of Science; 01. Izmir Institute of Technology; 02. Faculty of Architecture
Üniversitelerin öğrencilere meslek kazandırma misyonu dijital yüzyılda yeni nesil üniversiteler tanımı ile birlikte değişerek farklı bir misyona doğru evrilmiştir. Değişen bu misyon üniversitenin ürettiği bilimi toplumun diğer paydaşları ile paylaşarak toplumu dönüştürmek biçimde ifade edilebilir. İzmir Yüksek Teknoloji Enstitüsü, çocukları ve gençleri toplumun en değerli paydaşları görerek onların dönüşümüne ve gelişimine katkı sunmayı üniversitenin eğitim modeli olarak benimsemiştir. Bu atölye çalışması ile lise öğrencilerinin matematik müfredatında gördüğü konuları pekiştirerek öğrenmesi benimsenmiştir. Ayrıca, öğrencilerin bilgisayar yardımı ile özellikle de algoritma mantığı kullanarak ele alınan konuları deneyimleyerek öğrenmesini hedeflemektedir. Böylece bu çalıma ile ezberden uzak kalıcı öğrenme modeli sunulmuş olup matematiğin soyut yapısından somut yapısına bir köprü oluşturulması amaçlanmaktadır. Umuyorum bu atölye çalışması öğrencilere matematiğin günlük hayatta nerelerde kullanıldığı konusunda fikir vererek eğlenceli bir bilim olduğu konusunda da bir vizyon sunar.
Citation - WoS: 7
Citation - Scopus: 6
Local Well-Posedness of the Higher-Order Nonlinear Schrödinger Equation on the Half-Line: Single-Boundary Condition Case
(Wiley, 2023) Alkın, Aykut; Özsarı, Türker; Mantzavinos, Dionyssios; Özsarı, Türker; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We establish local well-posedness in the sense of Hadamard for a certain third-order nonlinear Schrödinger equation with a multiterm linear part and a general power nonlinearity, known as higher-order nonlinear Schrödinger equation, formulated on the half-line (Formula presented.). We consider the scenario of associated coefficients such that only one boundary condition is required and hence assume a general nonhomogeneous boundary datum of Dirichlet type at (Formula presented.). Our functional framework centers around fractional Sobolev spaces (Formula presented.) with respect to the spatial variable. We treat both high regularity ((Formula presented.)) and low regularity ((Formula presented.)) solutions: in the former setting, the relevant nonlinearity can be handled via the Banach algebra property; in the latter setting, however, this is no longer the case and, instead, delicate Strichartz estimates must be established. This task is especially challenging in the framework of nonhomogeneous initial-boundary value problems, as it involves proving boundary-type Strichartz estimates that are not common in the study of Cauchy (initial value) problems. The linear analysis, which forms the core of this work, crucially relies on a weak solution formulation defined through the novel solution formulae obtained via the Fokas method (also known as the unified transform) for the associated forced linear problem. In this connection, we note that the higher-order Schrödinger equation comes with an increased level of difficulty due to the presence of more than one spatial derivatives in the linear part of the equation. This feature manifests itself via several complications throughout the analysis, including (i) analyticity issues related to complex square roots, which require careful treatment of branch cuts and deformations of integration contours; (ii) singularities that emerge upon changes of variables in the Fourier analysis arguments; and (iii) complicated oscillatory kernels in the weak solution formula for the linear initial-boundary value problem, which require a subtle analysis of the dispersion in terms of the regularity of the boundary data. The present work provides a first, complete treatment via the Fokas method of a nonhomogeneous initial-boundary value problem for a partial differential equation associated with a multiterm linear differential operator. © 2023 Wiley Periodicals LLC.
On Purities Relative To Minimal Right Ideals
(Pleiades Publishing, 2023) Alagöz, Yusuf; Büyükaşık, Engin; Alizade, Rafail; Alizade, Rafail; Büyükaşık, Engin; Alagöz, Yusuf; Sağbaş, Selçuk; 04.02. Department of Mathematics; 01. Izmir Institute of Technology; 04. Faculty of Science
Abstract: We call a right module M weakly neat-flat if (Formula presented.) is surjective for any epimorphism (Formula presented.) and any simple right ideal S . A left module M is called weakly absolutely s-pure if (Formula presented.) is monic, for any monomorphism (Formula presented.) and any simple right ideal S . These notions are proper generalization of the neat-flat and the absolutely s-pure modules which are defined in the same way by considering all simple right modules of the ring, respectively. In this paper, we study some closure properties of weakly neat-flat and weakly absolutely s-pure modules, and investigate several classes of rings that are characterized via these modules. The relation between these modules and some well-known homological objects such as projective, flat, injective and absolutely pure are studied. For instance, it is proved that R is a right Kasch ring if and only if every weakly neat-flat right R -module is neat-flat (moreover if R is right min-coherent) if and only if every weakly absolutely s-pure left R -module is absolutely s-pure. The rings over which every weakly neat-flat (resp. weakly absolutely s-pure) module is injective and projective are exactly the QF rings. Finally, we study enveloping and covering properties of weakly neat-flat and weakly absolutely s-pure modules. The rings over which every simple right ideal has an epic projective envelope are characterized. © 2023, Pleiades Publishing, Ltd.
Citation - WoS: 2
Citation - Scopus: 1
On Schrödinger Operators Modified by Δ Interactions
(Academic Press, 2023) Akbaş, Kaya Güven; Erman, Fatih; Erman, Fatih; Turgut, O. Teoman; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We study the spectral properties of a Schrödinger operator H0 modified by δ interactions and show explicitly how the poles of the new Green's function are rearranged relative to the poles of original Green's function of H0. We prove that the new bound state energies are interlaced between the old ones, and the ground state energy is always lowered if the δ interaction is attractive. We also derive an alternative perturbative method of finding the bound state energies and wave functions under the assumption of a small coupling constant in a somewhat heuristic manner. We further show that these results can be extended to cases in which a renormalization process is required. We consider the possible extensions of our results to the multi center case, to δ interaction supported on curves, and to the case, where the particle is moving in a compact two-dimensional manifold under the influence of δ interaction. Finally, the semi-relativistic extension of the last problem has been studied explicitly. © 2023 Elsevier Inc.
Citation - WoS: 1
Citation - Scopus: 1
Euler-Zagier Sums Via Trigonometric Series
(Publishing House of the Romanian Academy, 2023) Çam Çelik, Şermin; Göral, Haydar; Göral, Haydar; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In this note, we study the evaluations of Euler sums via trigonometric series. It is a commonly believed conjecture that for an even weight greater than seven, Euler sums cannot be evaluated in terms of the special values of the Riemann zeta function. For an even weight, we reduce the evaluations of Euler sums into the evaluations of double series and integrals of products of Clausen functions. We also re-evaluate Euler sums of odd weight using a new method based on trigonometric series.
Arithmetic Progressions in Certain Subsets of Finite Fields
(Elsevier, 2023) Eyidoğan, Sadık; Göral, Haydar; 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: 7
Citation - Scopus: 6
Exponential Stability and Boundedness of Nonlinear Perturbed Systems by Unbounded Perturbation Terms
(Elsevier, 2023) Şahan, Gökhan; 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: 3
Citation - Scopus: 3
Dual Kasch rings
(World Scientific Publishing, 2023) Lomp, Christian; Büyükaşık, Engin; 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.
The Adjoint Reidemeister Torsion for Compact 3-Manifolds Admitting a Unique Decomposition
(TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2023) Erdal, Esma Dirican
Let M be a triangulated, oriented, connected compact 3 -manifold with a connected nonempty boundary. Such a manifold admits a unique decomposition into △ -prime 3 -manifolds. In this paper, we show that the adjoint Reidemeister torsion has a multiplicative property on the disk sum decomposition of compact 3 -manifolds without a corrective term.
Citation - Scopus: 1
Analysis of the Logistic Growth Model With Taylor Matrix and Collocation Method
(Etamaths Publishing, 2023) Çelik, Elçin; Çelik, Elçin; Uçar, Deniz; 01. Izmir Institute of Technology
Early analysis of infectious diseases is very important in the spread of the disease. The main aim of this study is to make important predictions and inferences for Covid 19, which is the current epidemic disease, with mathematical modeling and numerical solution methods. So we deal with the logistic growth model. We obtain carrying capacity and growth rate with Turkey epidemic data. The obtained growth rate and carrying capacity is used in the Taylor collocation method. With this method, we estimate and making predictions close to reality with Maple. We also show the estimates made with the help of graphics and tables. © 2023 the author(s).
Citation - WoS: 4
Citation - Scopus: 3
A New Construction Method for Keystream Generators
(IEEE, 2023) Gül, Çağdaş; Kara, Orhun; Kara, Orhun; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We introduce a new construction method of diffusion layers for Substitution Permutation Network (SPN) structures along with its security proofs. The new method can be used in block ciphers, stream ciphers, hash functions, and sponge constructions. Moreover, we define a new stream cipher mode of operation through a fixed pseudorandom permutation and provide its security proofs in the indistinguishability model. We refer to a stream cipher as a Small Internal State Stream (SISS) cipher if its internal state size is less than twice its key size. There are not many studies about how to design and analyze SISS ciphers due to the criterion on the internal state sizes, resulting from the classical tradeoff attacks. We utilize our new mode and diffusion layer construction to design an SISS cipher having two versions, which we call DIZY. We further provide security analyses and hardware implementations of DIZY. In terms of area cost, power, and energy consumption, the hardware performance is among the best when compared to some prominent stream ciphers, especially for frame-based encryptions that need frequent initialization. Unlike recent SISS ciphers such as Sprout, Plantlet, LILLE, and Fruit; DIZY does not have a keyed update function, enabling efficient key changing. © 2005-2012 IEEE.
Citation - WoS: 4
Citation - Scopus: 5
Lung Parenchyma Segmentation From Ct Images With a Fully Automatic Method
(Springer, 2023) Mousavi Moghaddam, Reza; Aghazadeh, Nasser; 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.
On Classification of Sequences Containing Arbitrarily Long Arithmetic Progressions
(World Scientific Publishing, 2023) Cam Çelik, Şermin; Göral, Haydar; Eyidoğan, Sadık; Göral, Haydar; Sertbaş, Doğa Can; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In this paper, we study the classification of sequences containing arbitrarily long arithmetic progressions. First, we deal with the question how the polynomial map n(s) can be extended so that it contains arbitrarily long arithmetic progressions. Under some growth conditions, we construct sequences which contain arbitrarily long arithmetic progressions. Also, we give a uniform and explicit arithmetic progression rank bound for a large class of sequences. Consequently, a dichotomy result is deduced on the finiteness of the arithmetic progression rank of certain sequences. Therefore, in this paper, we see a way to determine the finiteness of the arithmetic progression rank of various sequences satisfying some growth conditions.
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; Aghazadeh, Nasser; Tanoğlu, Gamze; 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.
Akışkan-yapı etkileşimi problemlerinde birleşik sayısal/asimtotik algoritmalar: baraj yıkımı ile oluşan akış ve diğer uygulamalar
(TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2014) Korobkin, Alexander; Iafrati, Alessandro; Yılmaz, Oğuz; Neslitürk, Ali İhsan; Çiçek, Barış; Kaya, Adem; Isıdıcı, Damla; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
Baraj güvenliği ile ilgili ilk yasa acil durumlarda uygulanmak üzere Fransa’da 1968 yılında çıkmıştır. Günümüzde daha büyük barajların yapılması ile daha yeni düzenlemeler getirilmiştir. Baraj güvenliği acil eylem planı şunları içerir; potansiyel risklerin tespiti, bu riskleri önleyecek önlemlerin alınması, yerel yönetimlerin acil durumlardaki sorumluluk tanımı ve bilginin halka iletilmesi. Günümüzde baraj operatörlerinin acil eylem planı ışığında baraj yapılmadan önce risk değerlendirme çalışması yapması gerekmektedir. Baraj yıkıldıktan sonraki ilk 15 dakika içinde selin ulaşamadığı en yakın güvenli bölgeyi ve selin ulaşabileceği en uzak alanın tesbiti bu risk değerlendirmeleri içerisindedir.
Çizgilerin Castelnuovo-Mumford regülaritesi ve döngü-kıran komplekslerin topolojisi
(TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2014) Civan, Yusuf; Bıyıkoğlu, Türker; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
Bu proje çalışmasının iki temel amacı vardır. Bunlardan ilki, en genel anlamıyla her hangi bir kare-serbest monomial I idealinin Castelnuovo-Mumford regülaritesinin hesaplanması ve bu hesapta kullanılabilecek etkin yöntemlerin keşfedilmesi olarak betimlenebilir. Genel olarak regülarite hesabı oldukça zor olduğu için direkt hesaplamaların yanısıra regülariteye altan veya üsten etkin sınırların bulunması da önemli bir işlem olarak kabul görmektedir. Her ne kadar regülarite bir cebirsel değişmez olsa da, bu çalışmanın temel yaklaşımı kombinatoriyaldir. Özellikle çizgeler teorisinin temel enstrümanları bu değişmezin hesaplanması veya sınırlandırılmasında etkin bir şekilde kullanılmıştır. Bu amaç doğrultusunda proje kapsamında ulaşılan sonuçlar temel başlıklar altında şöyledir: • Her hangi bir kare-serbest monomial idealin regülaritesinin ilintili bir iki-çoklu çizgeden hesaplanabileceği ispatlanmıştır. • Köşe-parçalanabilir ve ardıl-sökülebilir çizgelerin regülariteleri belirlenmiştir. • Asal çizge kavramı tanımlanarak, regülarite hesabının bir çizgenin indirgenmiş asal parçalanışlarının bulunması problemiyle eşlenmiştir. • 2K2-serbest ve regülaritesi istenildiği kadar büyük çizgelerin varlığı tespit edilmiştir. Çizge operasyonlarının regülariteye etkileri tespit edilmiştir. İkinci amacımız, çizgelerin döngü-kıran komplekslerinin veya daha genel haliyle yoksunluk komplekslerinin topolojisini incelemek olmuştur. Bu komplekslerin (topolojik) bağlantılılık sayılarının çizgelerin bir takım bilinen nümerik değişmezlerin belirlenmesinde veya sınırlandırılmasında etki sahibi olması, bu noktadaki çalışmalarımızın temel motivasyonu olmuştur.
Hirota Bilinear Method and Relativistic Dissipative Soliton Solutions in Nonlinear Spinor Equations
(Springer, 2023) Pashaev, Oktay; Pashaev, Oktay; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
A new relativistic integrable nonlinear model for real, Majorana type spinor fields in 1+1 dimensions, gauge equivalent to Papanicolau spin model, defined on the one sheet hyperboloid is introduced. By using the double numbers, the model is represented as hyperbolic complex valued relativistic massive Thirring type model. By Hirota’s bilinear method, an exact one and two dissipative soliton solutions of this model are constructed. Calculation of first three integrals of motion for one dissipation solution shows that the last one represents a particle-like nonlinear excitation, with relativistic dispersion and highly nonlinear mass. A nontrivial solution of the system of algebraic equations, showing fusion and fission of relativistic dissipations is found. Asymptotic analysis of exact two dissipaton solution confirms resonant character of our dissipaton interactions. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 1
Maximally Entangled Two-Qutrit Quantum Information States and De Gua’s Theorem for Tetrahedron
(Springer, 2023) Pashaev, Oktay; Pashaev, Oktay; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
Geometric relations between separable and entangled two-qubit and two-qutrit quantum information states are studied. For two qubit states a relation between reduced density matrix and the concurrence allows us to characterize entanglement by double area of a parallelogram, expressed by determinant of the complex Hermitian inner product metric. We find similar relation in the case of generic two-qutrit state, where the concurrence is expressed by sum of all 2 × 2 minors of 3 × 3 complex matrix. We show that for maximally entangled two-retrit state this relation is just De Gua’s theorem or a three-dimensional analog of the Pythagorean theorem for triorthogonal tetrahedron areas. Generalizations of our results for arbitrary two-qudit states are discussed © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Parity of an Odd Dominating Set
(2022) Batal, Ahmet; Batal, Ahmet; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
For a simple graph $G$ with vertex set $V(G)={v_1,...,v_n}$, we define the closed neighborhood set of a vertex $u$ as $N[u]={v in V(G) ; | ; v ; text{is adjacent to} ; u ; text{or} ; v=u }$ and the closed neighborhood matrix $N(G)$ as the matrix whose $i$th column is the characteristic vector of $N[v_i]$. We say a set $S$ is odd dominating if $N[u]cap S$ is odd for all $uin V(G)$. We prove that the parity of the cardinality of an odd dominating set of $G$ is equal to the parity of the rank of $G$, where rank of $G$ is defined as the dimension of the column space of $N(G)$. Using this result we prove several corollaries in one of which we obtain a general formula for the nullity of the join of graphs.

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