Endüstri Mühendisliği Bölümü Koleksiyonu

Permanent URI for this collectionhttps://gcris.khas.edu.tr/handle/20.500.12469/48

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Now showing 1 - 7 of 7

Citation Count: 0
Chebyshev nets formed by Ricci curves in a 3-dimensional Weyl space
(Elsevier Science Bv, 2005) Yıldırım, Gülçin Çivi; Özdeğer, Abdülkadir
In this paper Ricci curves in a 3-dimensional Weyl space W-3(g T) are defined and it is shown that any 3-dimensional Chebyshev net formed by the three families of Ricci curves in a W-3(g T) having a definite metric and Ricci tensors is either a geodesic net or it consists of a geodesic subnet the members of which have vanishing second curvatures. In the case of in indefinite Ricci tensor only one of the members of the geodesic subnet under consideration has a vanishing second curvature. (c) 2004 Elsevier B.V. All rights reserved.
Citation Count: 1
The critical point of a sigmoidal curve
(Babeș-Bolyai University, 2020) Bilge, Ayşe Hümeyra; Özdemir, Yunus
Let y(t) be a monotone increasing curve with lim(t ->+/-infinity) y((n))(t) = 0 for all n and let t(n) be the location of the global extremum of the nth derivative y((n))(t). Under certain assumptions on the Fourier and Hilbert transforms of y(t), we prove that the sequence {t(n)} is convergent. This implies in particular a preferred choice of the origin of the time axis and an intrinsic definition of the even and odd components of a sigmoidal function. In the context of phase transitions, the limit point has the interpretation of the critical point of the transition as discussed in previous work [3].
Citation Count: 5
Epidemic models for phase transitions: application to a physical gel
(Taylor & Francis Ltd, 2017) Bilge, Ayşe Hümeyra; Pekcan, Önder; Kara, Selim; Öğrenci, Arif Selçuk
Carrageenan gels are characterized by reversible sol-gel and gel-sol transitions under cooling and heating processes and these transitions are approximated by generalized logistic growth curves. We express the transitions of carrageenan-water system as a representative of reversible physical gels in terms of a modified Susceptible-Infected-Susceptible epidemic model as opposed to the Susceptible-Infected-Removed model used to represent the (irreversible) chemical gel formation in the previous work. We locate the gel point T-c of sol-gel and gel-sol transitions and we find that for the sol-gel transition (cooling) T-c > T-sg (transition temperature) i.e. T-c is earlier in time for all carrageenan contents and moves forward in time and gets closer to T-sg as the carrageenan content increases. For the gel-sol transition (heating) T-c is relatively closer to T-gs
Citation Count: 6
An Integrated Fuzzy Best-Worst-TOPSIS Method for Evaluation of Hotel Website and Digital Solutions Provider Firms
(Hindawi Limited, 2020) Samanlıoğlu, Funda; Burnaz, Ayşe Nur; Diş, Berke; Tabaş, Mehmet Doğukan; Adıgüzel, Mehmet
In todays world where technology is rapidly evolving, hotels need to be the best in all conditions to be one step ahead of other competitors. Digital marketing and hotel website solutions play a lead role in this competition. Therefore, hotel websites need to be innovative, user-friendly, and descriptive. The main purpose of the study is to evaluate and rank potential hotel websites and digital solutions provider firms. Since there are various potentially competing quantitative and qualitative criteria to take into consideration in the decision-making process, a multicriteria decision-making (MCDM) method is needed. As the MCDM method, fuzzy best-worst method (FBWM) is integrated with the Fuzzy Technique for Order Preference by Similarity to Ideal Solution (F-TOPSIS). In this integration, FBWM is applied to determine fuzzy evaluation criteria weights and then F-TOPSIS is implemented to rank alternatives utilizing the obtained fuzzy weights. A case study is presented, where 4 alternative hotel websites and digital solutions provider firms for Paloma Hotels in Turkey are evaluated based on 9 criteria by 3 hotel managers.
Citation Count: 8
Mathematical Characterization of Thermo-reversible Phase Transitions of Agarose Gels
(Taylor & Francis Inc, 2018) Bilge, Ayşe Hümeyra; Pekcan, Önder; Kara, Selim; Bilge, Ayşe Hümeyra
The thermal phase transition temperatures of high (HMP) and low melting point (LMP) agarose gels were investigated by using UV-vis spectroscopy techniques. Transmitted light intensities from the gel samples with different agarose concentrations were monitored during the heating (gel-sol) and cooling (sol-gel) processes. It was observed that the transition temperatures T-m defined as the location of the maximum of the first derivative of the sigmoidal transition paths obtained from the UV-vis technique slightly increased by increasing the agarose concentration in both the HMP and LMP samples. Here we express the phase transitions of the agar-water system as a representative of reversible physical gels in terms of a modified Susceptible-Infected-Susceptible epidemic model whose solutions are the well-known 5-point sigmoidal curves. The gel point is hard to determine experimentally and various computational techniques are used for its characterization. Based on previous work we locate the gel point T-0 of sol-gel and gel-sol transitions in terms of the horizontal shift in the sigmoidal transition curve. For the gel-sol transition (heating) T-0 is greater than T-m i.e. later in time and the difference between T-0 and T-m is reduced as the agarose content increases. For the sol-gel transition (cooling) T-0 is again greater than T-m but it is earlier in time for all agarose contents and moves forward in time and gets closer to T-m as the agarose content increases.
Citation Count: 10
A MATHEMATICAL DESCRIPTION OF THE CRITICAL POINT IN PHASE TRANSITIONS
(World Scientific Publ Co Pte Ltd, 2013) Bilge, Ayşe Hümeyra; Pekcan, Önder
Let y(x) be a smooth sigmoidal curve, y((n)) be its nth derivative and {x(m,i)} and {x(a,i)}, i = 1, 2, ... , be the set of points where respectively the derivatives of odd and even order reach their extreme values. We argue that if the sigmoidal curve y(x) represents a phase transition, then the sequences {x(m,i)} and {x(a,i)} are both convergent and they have a common limit x(c) that we characterize as the critical point of the phase transition. In this study, we examine the logistic growth curve and the Susceptible-Infected-Removed (SIR) epidemic model as typical examples of symmetrical and asymmetrical transition curves. Numerical computations indicate that the critical point of the logistic growth curve that is symmetrical about the point (x(0), y(0)) is always the point (x(0), y(0)) but the critical point of the asymmetrical SIR model depends on the system parameters. We use the description of the sol-gel phase transition of polyacrylamide-sodium alginate (SA) composite (with low SA concentrations) in terms of the SIR epidemic model, to compare the location of the critical point as described above with the "gel point" determined by independent experiments. We show that the critical point t(c) is located in between the zero of the third derivative t(a) and the inflection point t(m) of the transition curve and as the strength of activation (measured by the parameter k/eta of the SIR model) increases, the phase transition occurs earlier in time and the critical point, t(c), moves toward t(a).
Citation Count: 7
On sectional curvatures of a Weyl manifold
(2006) Özdeğer, Abdülkadir
In this paper it is proved that if at each point of a Weyl manifold the sectional curvature is independent of the plane chosen then the Weyl manifold is locally conformal to an Einstein manifold and that the scalar curvature of the Weyl manifold is prolonged covariant constant.

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