Matematik Bölümü Koleksiyonu

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On Caputo fractional Bertrand curves in E3 and E31
(Univ Nis, Fac Sci Math, 2024) Taşdemir, Mert; Canfes, Elif Özkara; Uzun, Banu
In this article, we examine Bertrand curves in E3 and E31 by using the Caputo fractional derivative which we call alpha-Bertrand Curves. First, we consider alpha-Bertrand curves in E3 and we give a characterization of them. Then, we study alpha-Bertrand curves in E31 and we prove the necessary and sufficient condition for a alpha-Bertrand curves in E31 by considering time like, space like and null curves. We also give the related examples by using Python.
Optimization of wastewater treatment systems for growing industrial parks
(Elsevier B.V., 2023-12-20) Savun Hekimoğlu, Başak; İşler, Zülal; Hekimoğlu, Mustafa; Burak, Selmin; Karlı, Deniz; Yücekaya, Ahmet; Akpınar, Ersin; Ediger, Volkan Ş.
Wastewater treatment is one of the crucial functions of industrial parks as wastewater from industrial facilities usually contains toxic compounds that can cause damage to the environment. To control their environmental loads, industrial parks make investment decisions for wastewater treatment plants. For this, they need to consider technical and economic factors as well as future growth projections as substantial construction and operational costs of wastewater treatment plants have to be shared by all companies in an industrial park. In this paper, we consider the long-term capacity planning problem for wastewater treatment facilities of a stochastically growing industrial park. By explicitly modeling randomness in the arrival of new tenants and their random wastewater discharges, our model calculates the future mean and variance of wastewater flow in the industrial park. Mean and variance are used in a Mixed Integer Programming Model to optimize wastewater treatment plant selection over a long planning horizon (30 years). By fitting our first model to empirical data from an industrial park in Turkey, we find that considering the variance of wastewater load is critical for long-term planning. Also, we quantify the economic significance of lowering wastewater discharges which can be achieved by water recycling or interplant water exchange.
Modeling repair demand in existence of a nonstationary installed base
(Elsevier B.V., 2023-09) Hekimoğlu, Mustafa; Karlı, Deniz
Life cycles of products consist of 3 phases, namely growth, maturity, and decline phases. Modeling repair demand is particularly difficult in the growth and decline stages due to nonstationarity. In this study, we suggest respective stochastic models that capture the dynamics of repair demand in these two phases. We apply our theory to two different operations management problems. First, using the moments of spare parts demand, we suggest an algorithm that selects a parametric distribution from the hypergeometric family (Ord, 1967) for each period in time. We utilize the algorithm in a single echelon inventory control problem. Second, we focus on investment decisions of Original Equipment Manufacturers (OEMs) to extend economic lifetimes of products with technology upgrades. Our results indicate that the second moment is sufficient for growing customer bases, whereas using the third moment doubles the approximation quality of theoretical distributions for a declining customer base. From a cost minimization perspective, using higher moments of demand leads to savings up to 13.6% compared to the single-moment approach. Also, we characterize the optimal investment policy for lifetime extension decisions from risk-neutral and risk-averse perspectives. We find that there exists a critical level of investment cost and installed base size for profitability of lifetime extension for OEMs. From a managerial point of view, we find that a risk-neutral decision maker finds the lifetime extension problem profitable. In contrast, even a slight risk aversion can make the lifetime extension decision economically undesirable.
Graph surfaces invariant by parabolic screw motions with constant curvature in H²×R
(DergiPark, 2023-04-30) Dursun, Uğur
In this work we study vertical graph surfaces invariant by parabolic screw motions with pitch ? > 0 and constant Gaussian curvature or constant extrinsic curvature in the product space H² × R. In particular, we determine flat and extrinsically flat graph surfaces in H² × R. We also obtain complete and non-complete vertical graph surfaces in H² × R with negative constant Gaussian curvature and zero extrinsic curvature.
Harmonic resonance phenomena on nonlinear SH waves
(Işık University Press, 2023-04) Ahmetolan, Semra; Özdemir, Neşe; Peker Dobie, Ayşe; Demirci, Ali
The interaction of shear horizontal (SH) waves in a two layered elastic medium and its mth harmonic component is studied. The dispersion relation is analysed to obtain the wave number-phase velocity pairs where the third and fifth harmonic resonance phenomena emerge. By employing an asymptotic perturbation method it is shown that the balance between the weak nonlinearity and dispersion yields a coupled nonlinear Schrödinger (CNLS) equation for the slowly varying amplitudes of the fundamental wave and its fifth harmonic component. The nonlinearity effects of the materials and the ratio of layers’ thicknesses on the linear instabilities of solutions and the existence of solitary waves are examined.
Tulczyjew's triplet for Lie groups III: higher order dynamics and reductions for iterated bundles
(Serbian Society of Mechanics, 2021) Esen, Oğul; Gümral, Hasan; Sütlü, Serkan
Given a Lie group G, we elaborate the dynamics on T*T*G and T*TG, which is given by a Hamiltonian, as well as the dynamics on the Tul-czyjew symplectic space TT * G, which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the iterated bundles, we exploit all possible subgroup reductions (Poisson, symplectic or both) of higher order dynamics.
On pseudo-umbilical rotational surfaces with pointwise 1-type gauss map in E-2(4)
(Istanbul Technical Univ, 2017-01-01) Bektaş, Burcu; Canfes, Elif Özkara; Dursun, Uğur
In this work, we study two families of rotational surfaces in the pseudo Euclidean space 1E4 with profile curves lying in 2 dimensional planes. First, we obtain a classification of pseudo umbilical spacelike surfaces and timelike surfaces in these families. Then, we show that in this classification there exists no a pseudo umbilical rotational surface in 1E4 with pointwise 1 type Gauss map of second kind. Finally, we determine such pseudo umbilical rotational surfaces in 1E4 having pointwise 1 type Gauss map of first kind.
Cohomologies and generalized derivations of n-Lie algebras
(Electronic Journals Project, 2022) Ateşli, Begüm; Esen, Oğul; Sütlü, Serkan
A cohomology theory associated to an n-Lie algebra and a representation space of it is introduced. It is shown that this cohomology theory classifies generalized derivations of n-Lie algebras as 1-cocycles, and inner generalized derivations as 1-coboundaries.
Constant angle surfaces in the Lorentzian warped product manifold I ×f E²1
(Tübitak, 2022-09-14) Dursun, Uğur
Let I ×f E²1 be a 3-dimensional Lorentzian warped product manifold with the metric g˜ = dt² + f² (t)(dx² ? dy² ), where I is an open interval, f is a strictly positive smooth function on I, and E²1 is the Minkowski 2-plane. In this work, we give a classification of all space-like and time-like constant angle surfaces in I ×f E²1 with nonnull principal direction when the surface is time-like. In this classification, we obtain space-like and time-like surfaces with zero mean curvature, rotational surfaces, and surfaces with constant Gaussian curvature. Also, we have some results on constant angle surfaces of the anti-de Sitter space H³1(?1).
Tulczyjew's triplet with an Ehresmann connection I: Trivialization and reduction
(World Scientific, 2023-03-30) Esen, Oğul; Kudeyt, Mahmut; Sütlü, Serkan
We study the trivialization and the reduction of Tulczyjew's triplet, in the presence of a symmetry and an Ehresmann connection associated to it. We thus establish a geometric pathway for the Legendre transformations on singular dynamical systems.
Matching of cocycle extensions for second tangent groups
(American Institute of Physics Inc., 2022-11-07) Uçgun, Filiz Çağatay; Esen, Oğul; Sütlü, Serkan
We present the second-order tangent group of a Lie group as a cocycle extension of the first-order tangent group. We exhibit matching of the second-order tangent groups of two mutually interacting Lie groups. We examine the cocycle extension character of the matched second-order group and arrive at that matched pair of cocycle extensions is a cocycle extension by itself.
Bicocycle double cross constructions
(World Scientific, 2023-12-01) Esen, Oğul; Guha, Partha; Sütlü, Serkan
We introduce the notion of a bicocycle double cross product (sum) Lie group (algebra), and a bicocycle double cross product bialgebra, generalizing the unified products. On the level of Lie groups the construction yields a Lie group on the product space of two pointed manifolds, none of which being necessarily a subgroup. On the level of Lie algebras, a Lie algebra is obtained on the direct sum of two vector spaces, which are not required to be subalgebras. Finally, on the quantum level a bialgebra is obtained on the tensor product of two (co)algebras that are not necessarily sub-bialgebras.
On extensions, Lie-Poisson systems, and dissipation
(Heldermann Verlag, 2022-07-06) Esen, Oğul; Özcan, Gökhan; Sütlü, Serkan
Lie-Poisson systems on the dual spaces of unified products are studied. Having been equipped with a twisted 2-cocycle term, the extending structure framework allows not only to study the dynamics on 2-cocycle extensions, but also to (de)couple mutually interacting Lie-Poisson systems. On the other hand, symmetric brackets; such as the double bracket, the Cartan-Killing bracket, the Casimir dissipation bracket, and the Hamilton dissipation bracket are worked out in detail. Accordingly, the collective motion of two mutually interacting irreversible dynamics, as well as the mutually interacting metriplectic flows, are obtained. The theoretical results are illustrated in three examples. As an infinite-dimensional physical model, decompositions of the BBGKY hierarchy are presented. As for the finite-dimensional examples, the coupling of two Heisenberg algebras, and the coupling of two copies of 3D dynamics are studied.
Inverse solution of thermoacoustic wave equation for cylindrical layered media
(Frontiers Media S.A., 2022-03-30) Elmas, Demet; Ünalmış Uzun, Banu
Thermoacoustic imaging is a crossbred approach taking advantages of electromagnetic and ultrasound disciplines, together. A significant number of current medical imaging strategies are based on reconstruction of source distribution from information collected by sensors over a surface covering the region to be imaged. Reconstruction in thermoacoustic imaging depends on the inverse solution of thermoacoustic wave equation. Homogeneous assumption of tissue to be imaged results in degradation of image quality. In our paper, inverse solution of the thermoacoustic wave equation using layered tissue model consisting of concentric annular layers on a cylindrical cross-section is investigated for cross-sectional thermoacustic imaging of breast and brain. By using Green’s functions and surface integral methods we derive an exact analytic inverse solution of thermoacoustic wave equation in frequency domain. Our inverse solution is an extension of conventional solution to layered cylindrical structures. By carrying out simulations, using numerical test phantoms consisting of thermoacoustic sources distributed in the layered model, our layered medium assumption solution was tested and benchmarked with conventional solutions based on homogeneous medium assumption in frequency domain. In thermoacoustic image reconstruction, where the medium is assumed as homogeneous medium, the solution of nonhomogeneous thermoacoustic wave equation results in geometrical distortions, artifacts and reduced image resolution due to inconvenient medium assumptions.
Slant curves in the Lorentzian warped product manifold - I× fE²
(Birkhauser, 2022-03-15) Dursun, Uğur
In this work, we study slant curves in the 3-dimensional Lorentzian warped product - I× fE², where E² is a 2-dimensional Euclidean plane, I? R is an open interval equipped with the metric dt², and f is a positive smooth function on I. First we give a characterization of slant curves, and then we obtain a classification of all slant curves in - I× fE². We also compute their curvature and torsion, and we obtaine some results on slant curves and helices in the de Sitter space S13(1) and in the Minkowski space E13. Moreover we determined some biharmonic slant curves in S13(1).
Sönümlemeli sistemlerin eşlenmesi üzerine
(Afyon Kocatepe Üniversitesi, 2021) Esen, Oğul; Özcan, Gökhan; Sütlü, Serkan
Bu makalede karşılıklı etki tepki içindeki iki sönümlemeli sistemin beraber (kollektif- eşlenmiş) hareketinin analizi üzerine bir yöntem öneriyoruz. Aşikardır ki; eşlenmiş hareketi kontrol eden diferansiyel denklemler iki sistemin denklemlerini bir arada yazmak dışında karşılıklı etki tepkinin doğurduğu fazladan terimler içerecektir. Karşılıklı etkiyi belirleyen ilave terimler, Lie cebirlerinin karşılıklı etkisi ile üretilecektir ve bu şekilde pür geometrik/cebirsel bir inşa gerçekleştirilecektir. Sonrasında elde ettiğimiz sonuçları 3 ve 4 boyutlu örneklerde göstereceğiz.
A new form of Kakutani fixed point theorem and intersection theorem with applications
(Ministry Communications & High Technologies, 2021) Farajzadeh, Ali P.; Zanganehmehr, Parastoo; Hasanoğlu, Elman
The first aim of this paper is to extend the Kakutani's fixed point theorem from locally convex topological vector spaces to linear topological spaces. The second goal is to present sufficient conditions under which the intersection of a family of sets is nonempty. The third step is to provide an existence theorem for a set valued mapping. Finally, as an application, an existence result of a solution for quasi-equilibrium problem is given.
Epidemiyolojideki kompartman modellerinin eşlenmiş Hamilton analizi
(Marmara Üniversitesi Fen Bilimleri Enstitüsü, 2021-01-13) Ateşli, Begüm; Esen, Oğul; Sütlü, Serkan
Epidemiyolojideki SIR, SEIR, 2-SIR ve 2-SEIR modellerinin Hamilton formülasyonu verildi. Eşlenmiş Lie-Poisson sistemleri yazıldı. SIR ve SEIR modellerinin eşlenmiş Lie-Poisson sistemi oldukları gösterildi. Bir Lie cebiri için bükülmüş eşçevrim genişlemesi çalışıldı. Bu genişlemenin dual uzayı üzerinde eşlenmiş Lie-Poisson denklemleri elde edildi. SIR ve SEIR kompartman modellerinin iki popülasyon karşılığı olan 2-SIR ve 2-SEIR modellerinin bükülmüş eşçevrim genişlemesiyle elde edilmiş Lie-Poisson sistemi olarak ifade edilebilecekleri gösterildi.
Eşlenmiş Lie grupları üzerindeki Lagrange fark denklemleri
(Marmara Üniversitesi Fen Bilimleri Enstitüsü, 2021-03-09) Esen, Oğul; Kudeyt, Mahmut; Sütlü, Serkan
Bu makalede, kesikli (discrete) dinamiğin Lagrange formülasyonu eşlenmiş (matched pair) Lie grupları üzerinde çalışılmıştır. Sonuç olarak, karşılıklı etkileşim altındaki iki sistemin kolektif davranışını belirleyen eşlenmiş (Lagrange) fark denklemleri elde edilmiştir. İki örnek verilmiştir. İlki, bir Lie grubunun tanjant grubu üzerindeki fark denklemleri, ikincisi ise Heisenberg grubu üzerindeki fark denklemleridir.
Lie cebiroidleri üzerindeki Lagrange dinamiğinin eşlenmesi problemi üzerine
(Süleyman Demirel Üniversitesi, 2021-08-15) Esen, Oğul; Kaya, Hanife Kübra; Sütlü, Serkan
Lie cebiroidleri, bir anlamda tanjant demetini ve Lie cebiri yapısını beraber ihtiva eden ve fakat daha genel olan geometrik inşaalardır. Lagrange dinamiğinin en genel ifadesi Lie cebiroidleri üzerinde mümkündür. Bu makalede, karşılıklı (Lie cebiroidi üzerinde tanımlı) etki içindeki iki Lagrange dinamiğinin beraber davranışı, geometrik ve cebirsel bir yol ile elde edilecektir. Bu bakış açısı ile etkileşim, Lie cebiroidlerinin birbirleri üzerine olan lineer temsilleri (etkileri) ifade edilecektir. Böylece, belirli uyumluluk şartını sağlayan karşılıklı etki içindeki iki Lie cebiroidinin eşlenmesi, diğer bir ifade ile tek bir Lie cebiroidi olarak yazılması sağlanacaktır. Sonrasında ise eşlenmiş Lie cebiroidi üzerinde Lagrange dinamiği yazılacaktır. Elde edilecek kollektif (eşlenmiş) hareket denklemleri, bireysel davranışların gözlemlenmesinin yanı sıra karşılıklı etki terimlerinin de belirlenmesine olanak verecektir. Çalışmamız esnasında bir çok örnek sunularak teorik tanımların daha net anlatımı yakalanmaya çalışılacaktır.

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