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Yayın Positive solutions for a sum-type singular fractional integro-differential equation with m-point boundary conditions(Politechnica University of Bucharest, 2017) Aydoğan, Seher Melike; Nazemi, Sayyedeh Zahra; Rezapour, ShahramWe study the existence and uniqueness of positive solutions for a sum-type singular fractional integro-differential equation with m-point boundary condition. Also, we provide an example to illustrate our main result.Yayın Temperature effect on drying and swelling of kappa carrageenan gels: A steady state fluorescence study(Wiley-V C H Verlag GMBH, 2008) Tarı İlgin, Özlem; Pekcan, Mehmet ÖnderA novel technique based on in situ steady state fluorescence (SSF) measurements is introduced for studying drying and swelling Of kappa(-) carrageenan (kappa carrageenan) gels at various temperatures. kappa(-) carrageenan gels were completely dried and then swelled in water vapor. Pyranine was embedded in kappa(-) carrageenan and used as a fluorescence probe. Scattered light intensities, I-SC and fluorescence intensities, I were monitored during the drying and swelling Of kappa(-) carrageenan gels. it was observed that the fluorescence intensity decreased linearly as drying time was increased. A simple model consisting of Case II diffusion was used to quantify the drying processes of the kappa(-) carrageenan gels. This moving boundary model provided packing constant, kappa(o). During swelling, fluorescence intensity increased exponentially as time is increased. The increase in I, was modeled using Li-Tanaka equation from which swelling time constants, tau(c) and cooperative diffusion coefficients, D-c were determined. It was observed that swelling time constants, tau(c) decreased and diffusion coefficients, D-c increased as the swelling temperature was increased. Activation energies for drying and swelling were also obtained and found to be 53.9 and 47.2 kJ mol(-1), respectively.Yayın Monovalent and divalent cation effects on phase transitions of iota-carrageenan(Sage Publications Ltd, 2007-01) Kara, Selim; Arda, Ertan; Pekcan, Mehmet ÖnderPhase transitions Of L-carrageenan in a variety of monovalent (Li, Na, K) and divalent (Mg, Ca, Sr) cation solutions were studied during heating and cooling by using photon transmission technique. Photon transmission intensity (I-tr) was monitored against temperature to determine the transition temperatures and activation energies during the heating and cooling processes in the monovalent and divalent systems. Three distinct transition regions were observed during the heating and cooling cycles for the carrageenan-divalent salt system. At the first step of the heating process, dimer groups were transformed into dimers that presented (g-d) transitions, then these dimers were directly converted into a double helix by undergoing a (d-h) transition. In the higher temperature region, a double helix-to-coil (h-c) transition took place. During the cooling process, these transitions are arranged in the order of (c-h), (h-d), and (d-g). The carrageenan-monovalent salt system presented only coil-to-rod-like helix (c-r) and rod-like helix-to-coil (r-c) transitions during the cooling and heating processes, respectively. A hysteresis was observed between (r-c)-(c-r) and (g-d)-(d-g) transitions for the monovalent and divalent cations, respectively.Yayın Interactions of nonlinear waves in fluid-filled elastic tubes(Verlag Z Naturforsch, 2007-02) Demiray, HilmiIn this work, treating an artery as a prestressed thin-walled elastic tube and the blood as an inviscid fluid, the interactions of two nonlinear waves propagating in opposite directions are studied in the longwave approximation by use of the extended PLK (Poincare-Lighthill-Kuo) perturbation method. The results show that up to O(k(3)), where k is the wave number, the head-on collision of two solitary waves is elastic and the solitary waves preserve their original properties after the interaction. The leading-order analytical phase shifts and the trajectories of two solitons after the collision are derived explicitly.Yayın Molecular alignment during gel formation from methyl methacrylate: An excimer fluorescence study(Taylor & Francis Ltd, 2005-05) Kaya Aktaş, Demet; Erdoğan, Matem; Pekcan, Mehmet ÖnderGlass transition during bulk polymerization was studied in free-radical cross-linking copolymerization (FCC) of methyl methacrylate (MMA) using the steady-state fluorescence (SSF) technique. Naphthalene (N) was used as a monomer and excimer forming probe. Changes in the viscosity of the pregel solutions due to gel formation dramatically enhance both monomer and excimer fluorescent yield of N molecules. The reaction time at which the monomer and excimer intensities exhibit a sudden increase corresponds to the reaction time at which the rate of polymerization becomes maximum resulting from the gel effect. This effect was used to study the gelation of MMA, as a function of time, in various N concentrations. The results were interpreted in the view of percolation theory. The gel fraction, beta, and weight average degree of polymerization, gamma, exponents beta=0.40 +/- 0.02 and gamma=1.70 +/- 0.07 were found in agreement with percolation results for both monomer and excimer measurements, respectively.Yayın On a class of functional equations of the Wiener-Hopf type and their applications in n-part scattering problems(Oxford Univ Press, 2003-12) İdemen, Mehmet Mithat; Alkumru, AliAn asymptotic theory for the functional equation K-phi=f, where K : X-->Y stands for a matrix-valued linear operator of the form K=K1P1+K2P2+...+KnPn, is developed. Here X and Y refer to certain Hilbert spaces, {P-alpha} denotes a partition of the unit operator in X while K-alpha are certain operators from X to Y. One assumes that the partition {P-alpha} as well as the operators K-alpha depend on a complex parameter nu such that all K-alpha are multi-valued around certain branch points at nu=k(+) and nu=k(-) while the inverse operators K-alpha(-1) exist and are bounded in the appropriately cut nu-plane except for certain poles. Then, for a class of {P-alpha} having certain analytical properties, an asymptotic solution valid for \k(+/-)\-->infinity is given. The basic idea is the decomposition of phi into a sum of projections on n mutually orthogonal subspaces of X. The results can be extended in a straightforward manner to the cases of no or more branch points. If there is no branch point or n=2, then the results are all exact. The theory may have effective applications in solving some direct and inverse multi-part boundary-value problems connected with high-frequency waves. An illustrative example shows the applicability as well as the effectiveness of the method.Yayın Percolation approach to film formation from surfactant-free polystyrene particles(Taylor & Francis, 2005-09) Uğur, Şaziye; Pekcan, Mehmet ÖnderIn this study, a film formation process from surfactant-free polystyrene (PS) latex particles is reported. Steady state fluorescence (SSF) and photon transmission (UVV) techniques were used to study the evolution of film formation. The latex films were prepared from pyrene (P)-labeled PS particles at room temperature and annealed at time intervals of 2.5 min above the glass transition temperature (T-g) of PS. During the annealing processes, the transparency of the film changed considerably. Fluorescence intensity (I-0P) from P was measured after each annealing step to monitor the stages of film formation. Evolution of transparency of latex films were monitored by using photon transmission intensity, I-tr. A drastic increase in I-tr and I-0P above the critical annealing times, t(r) and t(c) were attributed, respectively to percolation behavior of PS material from one side to the other side of the latex film. Critical exponents, beta of percolation clusters were measured and found to be around 0.35 and 0.25 for I-tr and I-0P measurements, respectively.Yayın An analysis of higher order terms for ion-acoustic waves by use of the modified Poincar,-Lighthill-Kuo method(Springer India, 2015-10) Demiray, HilmiIn this work, by utilizing the modified Poincar,-Lighthill-Kuo (PLK) method, we studied the propagation of weakly nonlinear waves in a collisionless cold plasma and obtained the governing evolution equations of various order terms in the perturbation expansion. Seeking a progressive wave solution to these evolution equations we obtained the speed correction terms so as to remove some possible secularities. The result obtained here is exactly the same with those of the modified reductive perturbation and re-normalization methods. The method presented here is quite simple and based on introducing a new set of stretched coordinates.Yayın In situ fluorescence study of swelling, sorption and desorption processes in and out of PAAm gels(Wiley-V C H Verlag GMBH, 2008-05) Evingür, Gülşen Akın; Karslı, Kadir; Pekcan, Mehmet ÖnderSmall molecule sorption and desorption in and out of polyacrylamide (PAAm) gels were studied at various temperatures. Pyranine (P(y)) dissolved in water used as a probe. Fluorescence emission intensity, I(p) from P(y) was monitored for studying sorption and desorption processes. Scattered light intensities, I(SC) from PAAm gel was also monitored to observed structural variations during sorption and desorption process. Li-Tanaka model was applied to produce the swelling time constants, tau(C) and sorption coefficients, D(C) for the swelling processes. on the other hand, sorption and desorption processes were studied and coefficients were produced by using Fickian model. Related activation energies were also calculated from the corresponding physical processes.Yayın Study on critical behaviour in N-isopropyl acrylamide gels by using fluorescence technique(Taylor & Francis Group, 2006-11) Kaya Aktaş, Demet; Pekcan, Mehmet ÖnderThe steady state fluorescence (SSF) technique was used to study the sol-gel transition for the solution free radical crosslinking copolymerization of N-isopropyl acrylamide (NIPA), with N,N'-methylenebis (acrylamide) (BIS) as crosslinker in the presence of ammonium persulfate (APS) as an initiator. Pyranine (8-hydroxypyrene-1,3,6-trisulfonic acid, trisodium salt, HPTS) was used as a floroprobe for monitoring the polymerization. Pyranine molecules start to bind to NIPA polymer chains upon the initiation of the polymerization, thus the spectra of the bonded pyranines shift to the shorter wavelengths. The get fraction exponent beta and the weight average degree of polymerization exponent gamma' agree best with the mean-field (Flory-Stockmayer) results near the gel point for various crosslinker contents.
