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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 Open Access 2D hybrid meshes for direct simulation Monte Carlo solvers(Institute of Physics (IOP) Publishing, 2013) Şengil, Nevsan; Department of Mathematics; Şengil, Uluç; Master Student; Department of Mathematics; College of SciencesThe efficiency of the direct simulation Monte Carlo (DSMC) method decreases considerably if gas is not rarefied. In order to extend the application range of the DSMC method towards non-rarefied gas regimes, the computational efficiency of the DSMC method should be increased further. One of the most time consuming parts of the DSMC method is to determine which DSMC molecules are in close proximity. If this information is calculated quickly, the efficiency of the DSMC method will be increased. Although some meshless methods are proposed, mostly structured or non-structured meshes are used to obtain this information. The simplest DSMC solvers are limited with the structured meshes. In these types of solvers, molecule indexing according to the positions can be handled very fast using simple arithmetic operations. But structured meshes are geometry dependent. Complicated geometries require the use of unstructured meshes. In this case, DSMC molecules are traced cell-by-cell. Different cell-by-cell tracing techniques exist. But, these techniques require complicated trigonometric operations or search algorithms. Both techniques are computationally expensive. In this study, a hybrid mesh structure is proposed. Hybrid meshes are both less dependent on the geometry like unstructured meshes and computationally efficient like structured meshes.Publication Metadata only 3D convective Cahn-Hilliard equation(Amer Inst Mathematical Sciences-Aims, 2007) Eden, Alp; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; College of Sciences; 117655We consider the initial boundary value problem for the 3D convective Cahn - Hilliard equation with periodic boundary conditions. This gives rise to a continuous dynamical system on L-2(ohm). Absorbing balls in L-2(ohm), H-per(1)(ohm) and H-per(2)(ohm) are shown to exist. Combining with the compactness property of the solution semigroup we conclude the existence of the global attractor. Restricting the dynamical system on the absorbing ball in H-per(2)(ohm) and using the general framework in Eden et. all. [] the existence of an exponential attractor is guaranteed. This approach also gives an explicit upper estimate of the dimension of the exponential attractor, albeit of the global attractor.Publication Metadata only 3D shape correspondence by isometry-driven greedy optimization(IEEE Computer Soc, 2010) N/A; Department of Computer Engineering; Sahillioğlu, Yusuf; Yemez, Yücel; PhD Student; Faculty Member; Department of Computer Engineering; Graduate School of Sciences and Engineering; College of Engineering; 215195; 107907We present an automatic method that establishes 3D correspondence between isometric shapes. Our goal is to find an optimal correspondence between two given (nearly) isometric shapes, that minimizes the amount of deviation from isometry. We cast the problem as a complete surface correspondence problem. Our method first divides the given shapes to be matched into surface patches of equal area and then seeks for a mapping between the patch centers which we refer to as base vertices. Hence the correspondence is established in a fast and robust manner at a relatively coarse level as imposed by the patch radius. We optimize the isometry cost in two steps. in the first step, the base vertices are transformed into spectral domain based on geodesic affinity, where the isometry errors are minimized in polynomial time by complete bipartite graph matching. the resulting correspondence serves as a good initialization for the second step of optimization in which we explicitly minimize the isometry cost via an iterative greedy algorithm in the original 3D Euclidean space. We demonstrate the performance of our method on various isometric (or nearly isometric) pairs of shapes for some of which the ground-truth correspondence is available.Publication Metadata only A bias phenomenon on the behavior of Dedekind sums(Int Press Boston, Inc, 2008) Xiong, Maosheng; Zaharescu, Alexandru; Department of Mathematics; Alkan, Emre; Faculty Member; Department of Mathematics; College of Sciences; 32803In this paper we present a bias phenomenon on the behavior of Dedekind sums at visible points in a dilated region. Our results indicate that in more than three quarters of the time the Dedekind sum increases as one moves from one visible point to the next.Publication Metadata only A characterization of heaviness in terms of relative symplectic cohomology(Wiley, 2024) Mak, Cheuk Yu; Sun, Yuhan; Department of Mathematics; Varolgüneş, Umut; Department of Mathematics; College of SciencesFor a compact subset K$K$ of a closed symplectic manifold (M,omega)$(M, \omega)$, we prove that K$K$ is heavy if and only if its relative symplectic cohomology over the Novikov field is nonzero. As an application, we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results is also included.Publication Metadata only A characterization of the closed unital ideals of the Fourier-Stieltjes algebra B(G) of a locally compact amenable group G(Elsevier, 2003) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ALet G be a locally compact amenable group, B(G) its Fourier–Stieltjes algebra and I be a closed ideal of it. In this paper we prove the following result: The ideal I has a unit element iff it is principal. This is the noncommutative version of the Glicksberg–Host–Parreau Theorem. The paper also contains an abstract version of this theorem.Publication Metadata only A characterization of the invertible measures(Polish Acad Sciences Inst Mathematics, 2007) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ALet G be a locally compact abelian group and M(G) its measure algebra. Two measures mu and lambda are said to be equivalent if there exists an invertible measure pi such that pi * mu = lambda. The main result of this note is the following: A measure mu is invertible iff vertical bar(mu) over cap vertical bar >= epsilon on (G) over cap for some epsilon > 0 and mu is equivalent to a measure lambda of the form lambda = a + theta, where a is an element of L-1(G) and theta is an element of M(G) is an idempotent measure.Publication Open Access A comparison of game-theoretic models for parallel trade(World Scientific Publishing, 2018) Gnecco, Giorgio; Pammolli, Fabio; Department of Economics; Alpanda, Berna Tuncay; Faculty Member; Department of Economics; College of Administrative Sciences and EconomicsWithin the EU Single Market for medicines, differences in drug prices, regulations, and transaction costs may create, under suitable conditions, arbitrage opportunities well before patent expiration, giving an incentive to the occurrence of parallel trade. When this is permitted, parallel traders may obtain a profit from buying drugs in a country where prices are lower, then re-selling them in a country where prices are higher. This phenomenon may came inefficiencies from a global welfare perspective, and reduce the manufacturers' incentive to invest in Research and Development (R & D). Given this framework, in this paper, we investigate the efficiency (expressed in terms of the price of anarchy) of the subgame-perfect Nash equilibria associated with five dynamic noncooperative game-theoretic models for the parallel trade of pharmaceuticals. We also compare such models with regard to the manufacturer's incentive to invest in R & D. More specifically, first we find in closed form the optimal value of the global welfare of two countries, which is obtained by solving a suitable quadratic optimization problem modeling the decision-making process of a global planner. Then, we use such a result. to evaluate and compare the prices of anarchy of five games modeling the interaction between a manufacturer in the first country and a potential parallel trader in the second country. The first three games refer, respectively, to the cases of no parallel trade threat, parallel trade threat, and parallel trade occurrence at equilibrium. Then, we investigate two modifications of the third game, in which its transfer payment from the potential parallel trader to the manufacturer is, respectively, removed/determined by Nash bargaining. For completeness, we also consider a decision-theoretic model of no parallel trade threat. For what concerns the incentive for the manufacturer to invest in R & D, the results of our numerical comparison show that the decision-theoretic model of no parallel trade threat is always the one with the highest incentive, whereas the two game-theoretic models of parallel trade threat/occurrence that do not include the transfer payment provide typically the lowest incentives. Moreover, the latter two models have the highest prices of anarchy (i.e., their equilibria have the lowest efficiencies). From a policy-making perspective, improvements are obtained if suitable countermeasures are taken to help the manufacturer recover from the costs of R & D, such as the inclusion of a transfer payment in the model.Publication Metadata only A constant-factor approximation algorithm for multi-vehicle collection for processing problem(Springer Heidelberg, 2013) Gel, Esma S.; N/A; Department of Industrial Engineering; Department of Industrial Engineering; Yücel, Eda; Salman, Fatma Sibel; Örmeci, Lerzan; PhD Student; Faculty Member; Faculty Member; Department of Industrial Engineering; Graduate School of Sciences and Engineering; College of Engineering; College of Engineering; 235501; 178838; 32863We define the multiple-vehicle collection for processing problem (mCfPP) as a vehicle routing and scheduling problem in which items that accumulate at customer sites over time should be transferred by a series of tours to a processing facility. We show that this problem with the makespan objective (mCfPP()) is NP-hard using an approximation preserving reduction from a two-stage, hybrid flowshop scheduling problem. We develop a polynomial-time, constant-factor approximation algorithm to solve mCfPP(). The problem with a single site is analyzed as a special case with two purposes. First, we identify the minimum number of vehicles required to achieve a lower bound on the makespan, and second, we characterize the optimal makespan when a single vehicle is utilized.