Mathematics / Matematik

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

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Now showing 1 - 20 of 707

Citation - WoS: 3
Citation - Scopus: 3
A1-L10 Phase Boundaries and Anisotropy Via Multiple-Order Theory for an Fcc Alloy
(European Mathematical Society Publishing House, 2003) Tanoğlu, Gamze; Braun, Richard J.; Cahn, John W.; McFadden, Geoffrey B.; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
The dependence of thermodynamic properties of planar interphase boundaries (IPBs) and antiphase boundaries (APBs) in a binary alloy on an fcc lattice is studied as a function of their orientation. Using a recently developed diffuse interface model based on three non-conserved order parameters and the concentration, and a free energy density that gives a realistic phase diagram with one disordered phase (A1) and two ordered phases (L12 and L10) such as occur in the Cu-Au system, we are able to find IPBs and APBs between any pair of phases and domains, and for all orientations. The model includes bulk and gradient terms in a free energy functional, and assumes that there is no mismatch in the lattice parameters for the disordered and ordered phases.We catalog the appropriate boundary conditions for all IPBs and APBs. We then focus on the IPB between the disordered A1 phase and the L10 ordered phase. For this IPB we compute the numerical solution of the boundary value problem to find its interfacial energy, γ as a function of orientation, temperature, and chemical potential (or composition). We determine the equilibrium shape for a precipitate of one phase within the other using the Cahn-Hoffman "-vector" formalism. We find that the profile of the interface is determined only by one conserved and one non-conserved order parameter, which leads to a surface energy which, as a function of orientation, is "transversely isotropic" with respect to the tetragonal axis of the L10 phase. We verify the model's consistency with the Gibbs adsorption equation.
Citation - WoS: 7
Citation - Scopus: 5
Abelian Chern-Simons Vortices and Holomorphic Burgers Hierarchy
(Pleiades Publishing, 2007-07) Pashaev, Oktay; Gürkan, Zeynep Nilhan; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We consider the Abelian Chern-Simons gauge field theory in 2+1 dimensions and its relation to the holomorphic Burgers hierarchy. We show that the relation between the complex potential and the complex gauge field as in incompressible and irrotational hydrodynamics has the meaning of the analytic Cole-Hopf transformation, linearizing the Burgers hierarchy and transforming it into the holomorphic Schrödinger hierarchy. The motion of planar vortices in Chern-Simons theory, which appear as pole singularities of the gauge field, then corresponds to the motion of zeros of the hierarchy. We use boost transformations of the complex Galilei group of the hierarchy to construct a rich set of exact solutions describing the integrable dynamics of planar vortices and vortex lattices in terms of generalized Kampe de Feriet and Hermite polynomials. We apply the results to the holomorphic reduction of the Ishimori model and the corresponding hierarchy, describing the dynamics of magnetic vortices and the corresponding lattices in terms of complexified Calogero-Moser models. We find corrections (in terms of Airy functions) to the two-vortex dynamics from the Moyal space-time noncommutativity.
Citation - WoS: 17
Citation - Scopus: 18
The Ablowitz-Ladik Lattice System by Means of the Extended (g' / G)-Expansion Method
(Elsevier Ltd., 2010-07) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We analyzed the Ablowitz-Ladik lattice system by using the extended (G′ / G)-expansion method. Further discrete soliton and periodic wave solutions with more arbitrary parameters are obtained. We observed that some previously known results can be recovered by assigning special values to the arbitrary parameters. © 2010 Elsevier Inc. All rights reserved.
Absolute Co-Supplement and Absolute Co-Coclosed Modules
(Hacettepe Üniversitesi, 2013) Tütüncü, Derya Keskin; Toksoy, Sultan Eylem; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
A module M is called an absolute co-coclosed (absolute co-supplement) module if whenever M ≅ T/X the submodule X of T is a coclosed (supplement) submodule of T. Rings for which all modules are absolute co-coclosed (absolute co-supplement) are precisely determined. We also investigate the rings whose (finitely generated) absolute co-supplement modules are projective. We show that a commutative domain R is a Dedekind domain if and only if every submodule of an absolute co-supplement R-module is absolute co-supplement. We also prove that the class Coclosed of all short exact sequences 0→A→B→C→0 such that A is a coclosed submodule of B is a proper class and every extension of an absolute co-coclosed module by an absolute co-coclosed module is absolute co-coclosed.
Citation - WoS: 13
Citation - Scopus: 13
Absolutely S-Pure Modules and Neat-Flat Modules
(Taylor and Francis Ltd., 2015-02) Büyükaşık, Engin; Durğun, Yılmaz; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
Let R be a ring with an identity element. We prove that R is right Kasch if and only if injective hull of every simple right R-modules is neat-flat if and only if every absolutely pure right R-module is neat-flat. A commutative ring R is hereditary and noetherian if and only if every absolutely s-pure R-module is injective and R is nonsingular. If every simple right R-module is finitely presented, then (1)R R is absolutely s-pure if and only if R is right Kasch and (2) R is a right (Formula presented.) -CS ring if and only if every pure injective neat-flat right R-module is projective if and only if every absolutely s-pure left R-module is injective and R is right perfect. We also study enveloping and covering properties of absolutely s-pure and neat-flat modules. The rings over which every simple module has an injective cover are characterized. © 2015 Taylor & Francis Group, LLC.
The Adjoint Reidemeister Torsion for Compact 3-Manifolds Admitting a Unique Decomposition
(TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2023) Erdal, Esma Dirican; 01. Izmir Institute of Technology
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.
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.
Citation - WoS: 13
Citation - Scopus: 15
Analysis of a Corner Layer Problem in Anisotropic Interfaces
(Southwest Missouri State University, 2006-03) Alikakos, N. D.; Bates, P. W.; Cahn, J. W.; Fife, P. C.; Fusco, G.; Tanoğlu, Gamze; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We investigate a model of anisotropic diffuse interfaces in ordered FCC crystals introduced recently by Braun et al and Tanoglu et al [3, 18, 19], focusing on parametric conditions which give extreme anisotropy. For a reduced model, we prove existence and stability of plane wave solutions connecting the disordered FCC state with the ordered Cu3Au state described by solutions to a system of three equations. These plane wave solutions correspond to planar interfaces. Different orientations of the planes in relation to the crystal axes give rise to different surface energies. Guided by previous work based on numerics and formal asymptotics, we reduce this problem in the six dimensional phase space of the system to a two dimensional phase space by taking advantage of the symmetries of the crystal and restricting attention to solutions with corresponding symmetries. For this reduced problem a standing wave solution is constructed that corresponds to a transition that, in the extreme anisotropy limit, is continuous but not differentiable. We also investigate the stability of the constructed solution by studying the eigenvalue problem for the linearized equation. We find that although the transition is stable, there is a growing number 0(1/ε), of critical eigenvalues, where 1/ε ≫ 1 is a measure of the anisotropy. Specifically we obtain a discrete spectrum with eigenvalues λn = ε2/3 μn with μn ∼ Cn2/3, as n → +∞. The scaling characteristics of the critical spectrum suggest a previously unknown microstructural instability.
Citation - WoS: 6
Citation - Scopus: 6
Analysis of Covid 19 Disease With Sir Model and Taylor Matrix Method
(American Institute of Mathematical Sciences, 2022) Uçar, Deniz; Çelik, Elçin; 01. Izmir Institute of Technology
Covid 19 emerged in Wuhan, China in December 2019 has continued to spread by affecting the whole world. The pandemic has affected over 328 million people with more than 5 million deaths in over 200 countries which has severely disrupted the healthcare system and halted economies of the countries. The aim of this study is to discuss the numerical solution of the SIR model on the spread of Covid 19 by the Taylor matrix and collocation method for Turkey. Predicting COVID-19 through appropriate models can help us to understand the potential spread in the population so that appropriate action can be taken to prevent further transmission and prepare health systems for medical management of the disease. We deal with Susceptible–Infected–Recovered (SIR) model. One of the proposed model’s improvements is to reflect the societal feedback on the disease and confinement features. We obtain the time dependent rate of transmission of the disease from susceptible β(t) and the rate of recovery from infectious to recovered γ using Turkey epidemic data. We apply the Taylor matrix and collocation method to the SIR model with γ, β(t) and Covid 19 data of Turkey from the date of the first case March 11, 2020 through July 3, 2021. Using this method, we focus on the evolution of the Covid 19 in Turkey. We also show the estimates with the help of graphics and Maple.
Citation - Scopus: 1
Analysis of the Logistic Growth Model With Taylor Matrix and Collocation Method
(Etamaths Publishing, 2023) 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: 21
Citation - Scopus: 21
An Analytic Approach To a Class of Fractional Differential-Difference Equations of Rational Type Via Symbolic Computation
(John Wiley and Sons Inc., 2015-01) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
Fractional derivatives are powerful tools in solving the problems of science and engineering. In this paper, an analytical algorithm for solving fractional differential-difference equations in the sense of Jumarie's modified Riemann-Liouville derivative has been described and demonstrated. The algorithm has been tested against time-fractional differentialdifference equations of rational type via symbolic computation. Three examples are given to elucidate the solution procedure. Our analyses lead to closed form exact solutions in terms of hyperbolic, trigonometric, and rational functions, which might be subject to some adequate physical interpretations in the future. Copyright © 2013 JohnWiley & Sons, Ltd.
Citation - WoS: 14
Citation - Scopus: 16
Analytic Investigation of a Reaction-Diffusion Brusselator Model With the Time-Space Fractional Derivative
(Walter de Gruyter GmbH, 2014-04) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
It is well known that many models in nonlinear science are described by fractional differential equations in which an unknown function appears under the operation of a derivative of fractional order. In this study, we propose a reaction-diffusion Brusselator model from the viewpoint of the Jumarie's modified Riemann-Liouville fractional derivative. Based on the (G'/G)-expansion method, various kinds of exact solutions are obtained. Our results could be used as a starting point for numerical procedures as well.
Citation - WoS: 16
Citation - Scopus: 16
Analytic Investigation of the (2 + 1)-Dimensional Schwarzian Korteweg–de Vries Equation for Traveling Wave Solutions
(Elsevier Ltd., 2011-02-15) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
By means of the two distinct methods, the Exp-function method and the extended (G0/G)-expansion method, we successfully performed an analytic study on the (2 + 1)-dimensional Schwarzian Korteweg–de Vries equation. We exhibited its further closed form traveling wave solutions which reduce to solitary and periodic waves. New rational solutions are also revealed.
Citation - WoS: 26
Citation - Scopus: 27
Analytic Solutions To Nonlinear Differential-Difference Equations by Means of the Extended (g'/g)-expansion Method
(IOP Publishing Ltd., 2010-10) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In this paper, a discrete extension of the (G′/G)-expansion method is applied to a relativistic Toda lattice system and a discrete nonlinear Schrödinger equation in order to obtain discrete traveling wave solutions. Closed form solutions with more arbitrary parameters, which reduce to solitary and periodic waves, are exhibited. New rational solutions are also obtained. The method is straightforward and concise, and its applications in physical sciences are promising. © 2010 IOP Publishing Ltd.
Citation - WoS: 77
Citation - Scopus: 110
Analytic Study on Two Nonlinear Evolution Equations by Using the (g'/g)-expansion Method
(Elsevier Ltd., 2009-03) Aslan, İsmail; Öziş, Turgut; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
The validity and reliability of the so-called (G′/G)-expansion method is tested by applying it to two nonlinear evolutionary equations. Solutions in more general forms are obtained. When the parameters are taken as special values, it is observed that the previously known solutions can be recovered. New rational function solutions are also presented. Being concise and less restrictive, the method can be applied to many nonlinear partial differential equations.
Citation - WoS: 2
Citation - Scopus: 2
Analytical Improvement on the Electromagnetic Scattering From Deformed Spherical Conducting Objects
(Institute of Electrical and Electronics Engineers, 2021) Ateş, Barış; Kuştepeli, Alp; Çetin, Zebih; 03.05. Department of Electrical and Electronics Engineering; 03. Faculty of Engineering; 01. Izmir Institute of Technology
In this paper, electromagnetic scattering from con-ducting deformed spheres is considered analytically by employing the perturbation method and utilizing Debye potentials. To be able to analyze a wide variety of scattering problems, azimuthal variation is indispensable and therefore the geometries of the scatterers considered in this study do not have rotational symmetry, hence they are dependent on the θ and φ angles in spherical coordinates. Analyses are carried up to the second order explicitly to obtain more accurate results and thus scattered fields are obtained with second order corrections. The coefficients used to determine the scattered field are expressed in terms of Clebsch-Gordan coefficients, which enables one to obtain the results for new geometries only by simple algebraic manipulations. Numerical results and their comparisons are also presented for various deformation functions and parameters. IEEE
Citation - WoS: 21
Citation - Scopus: 28
Angular Analysis of the Decay B+-> K*(892)(+)mu(+)mu(-) in Proton-Proton Collisions at Root S=8 Tev
(Springer, 2021) CMS Collaboration; Karapınar, Güler; 01. Izmir Institute of Technology
Angular distributions of the decay B+-> K*(892)(+)mu(+)mu(-) are studied using events collected with the CMS detector in root s = 8 TeV proton-proton collisions at the LHC, corresponding to an integrated luminosity of 20.0 fb(-1). The forward-backward asymmetry of the muons and the longitudinal polarization of the K*(892)(+) meson are determined as a function of the square of the dimuon invariant mass. These are the first results from this exclusive decay mode and are in agreement with a standard model prediction.
Citation - WoS: 146
Citation - Scopus: 194
Angular Analysis of the Decay B0 → K⁎0μ+μ− From Pp Collisions at √s=8 Tev
(Elsevier B.V., 2016) Khachatryan, V.; Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Asilar, E.; Bergauer, T.; Puerta Pelayo, J.; 01. Izmir Institute of Technology
The angular distributions and the differential branching fraction of the decay B0→K⁎(892)0μ+μ− are studied using data corresponding to an integrated luminosity of 20.5 fb−1 collected with the CMS detector at the LHC in pp collisions at s=8 TeV. From 1430 signal decays, the forward–backward asymmetry of the muons, the K⁎(892)0 longitudinal polarization fraction, and the differential branching fraction are determined as a function of the dimuon invariant mass squared. The measurements are among the most precise to date and are in good agreement with standard model predictions. © 2015 CERN for the benefit of the CMS Collaboration
Citation - WoS: 91
Citation - Scopus: 103
Angular Coefficients of Z Bosons Produced in Pp Collisions at S=8 Tev and Decaying To Μ+μ− as a Function of Transverse Momentum and Rapidity
(Elsevier B.V., 2015) Khachatryan, V.; Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Bergauer, T.; Dragicevic, M.; Gigi, D.; 01. Izmir Institute of Technology
Measurements of the five most significant angular coefficients, A0 through A4, for Z bosons produced in pp collisions at s=8 TeV and decaying to μ+μ− are presented as a function of the transverse momentum and rapidity of the Z boson. The integrated luminosity of the dataset collected with the CMS detector at the LHC corresponds to 19.7fb−1. These measurements provide comprehensive information about the Z boson production mechanisms, and are compared to the QCD predictions at leading order, next-to-leading order, and next-to-next-to-leading order in perturbation theory. © 2015 CERN for the benefit of the CMS Collaboration
Citation - WoS: 21
Anonymity and One-Way Authentication in Key Exchange Protocols
(Springer Verlag, 2013-05) Goldberg, Ian; Stebila, Douglas; Ustaoğlu, Berkant; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
Key establishment is a crucial cryptographic primitive for building secure communication channels between two parties in a network. It has been studied extensively in theory and widely deployed in practice. In the research literature a typical protocol in the public-key setting aims for key secrecy and mutual authentication. However, there are many important practical scenarios where mutual authentication is undesirable, such as in anonymity networks like Tor, or is difficult to achieve due to insufficient public-key infrastructure at the user level, as is the case on the Internet today. In this work we are concerned with the scenario where two parties establish a private shared session key, but only one party authenticates to the other; in fact, the unauthenticated party may wish to have strong anonymity guarantees. We present a desirable set of security, authentication, and anonymity goals for this setting and develop a model which captures these properties. Our approach allows for clients to choose among different levels of authentication. We also describe an attack on a previous protocol of Øverlier and Syverson, and present a new, efficient key exchange protocol that provides one-way authentication and anonymity. © 2012 Springer Science+Business Media, LLC.

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