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Publication Metadata only ‘Anti-commutable’ local pre-Leibniz algebroids and admissible connections(Elsevier, 2023) Department of Physics; N/A; Dereli, Tekin; Doğan, Keremcan; Faculty Member; PhD Student; Department of Physics; College of Sciences; Graduate School of Sciences and Engineering; 201358; N/AThe concept of algebroid is convenient as a basis for constructions of geometrical frameworks. For example, metric-affine and generalized geometries can be written on Lie and Courant algebroids, respectively. Furthermore, string theories might make use of many other algebroids such as metric algebroids, higher Courant algebroids, or conformal Courant algebroids. Working on the possibly most general algebroid structure, which generalizes many of the algebroids used in the literature, is fruitful as it creates a chance to study all of them at once. Local pre-Leibniz algebroids are such general ones in which metric-connection geometries are possible to construct. On the other hand, the existence of the 'locality operator', which is present for the left-Leibniz rule for the bracket, necessitates the modification of torsion and curvature operators in order to achieve tensorial quantities. In this paper, this modification of torsion and curvature is explained from the point of view that the modification is applied to the bracket instead. This leads one to consider 'anti-commutable' local pre-Leibniz algebroids which satisfy an anti-commutativity-like property defined with respect to a choice of an equivalence class of connections. These 'admissible' connections are claimed to be the necessary ones while working on a geometry of algebroids. This claim is due to the fact that one can prove many desirable properties and relations if one uses only admissible connections. For instance, for admissible connections, we prove the first and second Bianchi identities, Cartan structure equations, Cartan magic formula, the construction of Levi-Civita connections, the decomposition of connection in terms of torsion and non-metricity. These all are possible because the modified bracket becomes anti-symmetric for an admissible connection so that one can apply the machinery of almost-or pre-Lie algebroids. We investigate various algebroid structures from the literature and show that they admit admissible connections which are metric-compatible in some generalized sense. Moreover, we prove that local pre-Leibniz algebroids that are not anti-commutable cannot be equipped with a torsion-free, and in particular Levi-Civita, connection.Publication Metadata only Blow up of solutions to the initial boundary value problem for quasilinear strongly damped wave equations(Academic Press Inc Elsevier Science, 2013) N/A; Department of Mathematics; Bilgin, Bilgesu Arif; Kalantarov, Varga; PhD Student; Faculty Member; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 117655We obtain sufficient conditions on initial functions for which the initial boundary value problem for second order quasilinear strongly damped wave equations blow up in a finite time. (C) 2013 Elsevier Inc. All rights reserved.Publication Metadata only Computing the nadir point for multiobjective discrete optimization problems(Springer, 2015) N/A; N/A; Department of Business Administration; Kirlik, Gökhan; Sayın, Serpil; PhD Student; Faculty Member; Department of Business Administration; Graduate School of Sciences and Engineering; College of Administrative Sciences and Economics; N/A; 6755We investigate the problem of finding the nadir point for multiobjective discrete optimization problems (MODO). The nadir point is constructed from the worst objective values over the efficient set of a multiobjective optimization problem. We present a new algorithm to compute nadir values for MODO with objective functions. The proposed algorithm is based on an exhaustive search of the -dimensional space for each component of the nadir point. We compare our algorithm with two earlier studies from the literature. We give numerical results for all algorithms on multiobjective knapsack, assignment and integer linear programming problems. Our algorithm is able to obtain the nadir point for relatively large problem instances with up to five-objectives.Publication Metadata only Existence of an attractor and determining modes for structurally damped nonlinear wave equations(Elsevier Science Bv, 2018) N/A; Department of Mathematics; Bilgin, Bilgesu Arif; Kalantarov, Varga; PhD Student; Faculty Member; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 117655The paper is devoted to the study of asymptotic behavior as t -> +infinity of solutions of initial boundary value problem for structurally damped semi-linear wave equation partial derivative(2)(t)u(x, t) - Delta u(x, t)+gamma(-Delta)(theta)partial derivative(t) u(x,t) + f(u) = g(x), theta is an element of(0, 1), x is an element of Omega, t > 0 under homogeneous Dirichlet's boundary condition in a bounded domain Omega subset of R-3. We proved that the asymptotic behavior as t -> infinity of solutions of this problem is completely determined by dynamics of the first N Fourier modes, when N is large enough. We also proved that the semigroup generated by this problem when theta is an element of(1/2, 1) possesses an exponential attractor. (C) 2017 Elsevier B.V. All rights reserved.Publication Metadata only Faster simulation methods for the non-stationary random vibrations of non-linear mdof systems(A A Balkema, 1995) Department of Mathematics; Department of Mathematics; N/A; N/A; Aşkar, Attila; Köylüoğlu, Hasan Uğur; Çakmak, Ayşe Selin; Nielsen, Susanne Ramtung; Faculty Member; Teaching Faculty; Other; Other; Department of Mathematics; College of Sciences; College of Sciences; N/A; N/A; 178822 N/A; N/A; N/AN/APublication Metadata only Inventory control and pricing for perishable products under age and price dependent stochastic demand(Springer, 2018) Kaya, Onur; N/A; Ghahroodi, Sajjad Rahimi; Master Student; Graduate School of Sciences and Engineering; N/APerishable products have a short lifetime and cause a high amount of wastage when managed ineffectively, due to their deterioration over time. We consider coordinated inventory and pricing decisions for perishable products in a periodically-reviewed inventory system with an age and price dependent random demand. We consider the products with a fixed shelf lifetime and use dynamic programming to model this system. We prove certain structural characteristics of the optimal solution and also analyze the effect of different parameters on the optimal solution through numerical experiments. In addition, we analyze simple-to-implement inventory control policies, namely quantity-based and age-based policies, and investigate their effectiveness.Publication Metadata only Linearization of one-dimensional nonautonomous jump-diffusion stochastic differential equations(World Scientific Publ Co Pte Ltd, 2007) Unal, Gazanfer; Khalique, C. Masood; N/A; İyigünler, İsmail; Master Student; Graduate School of Sciences and Engineering; N/ANecessary and sufficient conditions for the linearization of one-dimensional nonautonomous jump-diffusion stochastic differential equations are given. Stochastic integrating factor is introduced to solve the linear jump-diffusion stochastic differential equations. Closed form solutions to certain linearizable jump-diffusion stochastic differential equations are obtained.Publication Metadata only Modeling and simulation of metabolic networks for estimation of biomass accumulation parameters(Elsevier, 2009) Biegler, L.; Karasozen, Bülent; N/A; Department of Industrial Engineering; Kaplan, Uğur; Türkay, Metin; PhD Student; Faculty Member; Department of Industrial Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; 24956Metabolic networks are defined as the collection of biochemical reactions within a cell that define the functions of that cell. Due to the growing need to understand the functions of biological organisms for industrial and medical purposes, modeling and simulation of metabolic networks has attracted a lot of attention recently. Traditionally, metabolic networks are modeled such as flux-balance analysis that considers the steady state nature of the cell. However, it is important to consider the dynamic behavior of a cell since the environmental conditions change continuously. Sometimes due to the critical changes in the environment some of the reactions exhibit completely different behavior leading to discrete changes in the metabolic network. Therefore, a cell exhibits discrete-continuous behavior in continuous time. Since hybrid systems exhibit the same characteristics modeling a cell as a hybrid system gives an accurate representation. The aim of this paper is to develop a simulation framework to model the evolving structure of the cell metabolism under changes in the environment. The metabolic responses that cell gives, against multiple changes in the environment are not fully understood. Therefore, in this study, a cell is modeled as a hybrid system that is composed of a system of differential and algebraic equations. The changes in the concentration of metabolites in the environment are represented by Ordinary Differential Equations and the intracellular cell metabolism is represented by a set of algebraic equations. TO understand the feedback relationship between intracellular and extracellular changes, the system is solved considering the effects of extracellular stresses on the metabolic responses. (c) 2008 Elsevier B.V. .Publication Metadata only Modeling cutting forces for five axis milling of sculptured surfaces(Trans Tech Publications Ltd, 2011) Erdim, H.; N/A; Department of Mechanical Engineering; Boz, Yaman; Lazoğlu, İsmail; Master Student; Faculty Member; Department of Mechanical Engineering; Manufacturing and Automation Research Center (MARC); Graduate School of Sciences and Engineering; College of Engineering; N/A; 1793915-axis ball-end milling processes are used in various industries such as aerospace, automotive, die-mold and biomedical industries. 5-axis machining provides reduced cycle times and more accurate machining via reduction in machining setups, use of shorter tools due to improved tool accessibility. However, desired machining productivity and precision can be obtained by physical modeling of machining processes via appropriate selection of process parameters. In response to this gap in the industry this paper presents a cutting force model for 5-axis ball-end milling cutting force prediction. Cutter-workpiece engagement is extracted via developed solid modeler based engagement model. Simultaneous 5-axis milling tests are conducted on A17075 workpiece material with a carbide cutting tool. Validation of the proposed model is performed for impeller hub roughing toolpaths. Validation test proves that presented model is computationally efficient and cutting forces can be predicted reasonably well. The result of validation test and detailed comparison with the simulation are also presented in the paper.Publication Metadata only Newsvendor models with dependent random supply and demand(Springer Heidelberg, 2014) N/A; N/A; Department of Industrial Engineering; Department of Industrial Engineering; Okyay, Hayrettin Kaan; Karaesmen, Fikri; Özekici, Süleyman; Master Student; Faculty Member; Faculty Member; Department of Industrial Engineering; Graduate School of Sciences and Engineering; College of Engineering; College of Engineering; N/A; 3579; 32631The newsvendor model is perhaps the most widely analyzed model in inventory management. In this single-period model, the only source of randomness is the demand during the period and one tries to determine the optimal order quantity in view of various cost factors. We consider an extention where supply is also random so that the quantity ordered is not necessarily received in full at the beginning of the period. Such models have been well-received in the literature with the assumption of independence between demand and supply. In this setting, we suppose that the random demand and supply are not necessarily independent. We focus on the resulting optimization problem and provide interesting characterizations on the optimal order quantity.