GCRIS Repository Collection: Collection of Mathematics / Matematik Bölümü koleksiyonu
https://hdl.handle.net/11147/8
Collection of Mathematics / Matematik Bölümü koleksiyonu
Thu, 12 Sep 2024 08:35:05 GMT
20240912T08:35:05Z

Endüstriyel matematik
https://hdl.handle.net/11147/14628
Title: Endüstriyel matematik
Authors: Tanoğlu, Gamze; Yurt, Canberk
Abstract: 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.
Mon, 01 Jan 2024 00:00:00 GMT
https://hdl.handle.net/11147/14628
20240101T00:00:00Z

Uniform asymptotic and input to state stability by indefinite Lyapunov functions
https://hdl.handle.net/11147/14270
Title: Uniform asymptotic and input to state stability by indefinite Lyapunov functions
Authors: Şahan, Gökhan; Özdemir, Durmuş
Abstract: In this work, we study uniform, uniform asymptotic, and inputtostate stability conditions for nonlinear timevarying systems. We introduce an easily verifiable condition for uniform attractivity by utilizing an indefinite sign upper bound for the derivative of the Lyapunov function. With this bounding structure, we propose novel conditions that enable us to test uniform stability, uniform asymptotic stability, and ISS, easily. As a result, the constraints on the coefficients of the bound that identify uniformity for stability and attractivity, and many of the available conditions have been relaxed. The results are also used for the perturbation problem of uniformly stable and uniformly asymptotically stable linear timevarying systems. Consequently, we demonstrate that uniform asymptotic stability of nonlinear timevarying systems can be robust for perturbations, but with special timevarying coefficients. © 2024 European Control Association
Mon, 01 Jan 2024 00:00:00 GMT
https://hdl.handle.net/11147/14270
20240101T00:00:00Z

Local wellposedness of the higherorder nonlinear Schrödinger equation on the halfline: Singleboundary condition case
https://hdl.handle.net/11147/14055
Title: Local wellposedness of the higherorder nonlinear Schrödinger equation on the halfline: Singleboundary condition case
Authors: Alkın, Aykut; Mantzavinos, Dionyssios; Özsarı, Türker
Abstract: We establish local wellposedness in the sense of Hadamard for a certain thirdorder nonlinear Schrödinger equation with a multiterm linear part and a general power nonlinearity, known as higherorder nonlinear Schrödinger equation, formulated on the halfline (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 initialboundary value problems, as it involves proving boundarytype 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 higherorder 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 initialboundary 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 initialboundary value problem for a partial differential equation associated with a multiterm linear differential operator. © 2023 Wiley Periodicals LLC.
Sun, 01 Jan 2023 00:00:00 GMT
https://hdl.handle.net/11147/14055
20230101T00:00:00Z

On purities relative to minimal right ideals
https://hdl.handle.net/11147/14028
Title: On purities relative to minimal right ideals
Authors: Alagöz, Yusuf; Alizade, Rafail; Büyükaşık, Engin; Sağbaş, Selçuk
Abstract: Abstract: We call a right module M weakly neatflat if (Formula presented.) is surjective for any epimorphism (Formula presented.) and any simple right ideal S . A left module M is called weakly absolutely spure if (Formula presented.) is monic, for any monomorphism (Formula presented.) and any simple right ideal S . These notions are proper generalization of the neatflat and the absolutely spure 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 neatflat and weakly absolutely spure modules, and investigate several classes of rings that are characterized via these modules. The relation between these modules and some wellknown 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 neatflat right R module is neatflat (moreover if R is right mincoherent) if and only if every weakly absolutely spure left R module is absolutely spure. The rings over which every weakly neatflat (resp. weakly absolutely spure) module is injective and projective are exactly the QF rings. Finally, we study enveloping and covering properties of weakly neatflat and weakly absolutely spure modules. The rings over which every simple right ideal has an epic projective envelope are characterized. © 2023, Pleiades Publishing, Ltd.
Sun, 01 Jan 2023 00:00:00 GMT
https://hdl.handle.net/11147/14028
20230101T00:00:00Z