Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Spectrophotometry simultaneous determination of levamisole and triclabendazole in tablets by principal component regression and partial least squares chemometric methods(Chiminform DATA S A, 2008) Pektas, Gözde; Dinç, Erdal; Baleanu, DumitruPrincipal component regression (PCR) and partial least squares (PLS) chemometric methods were applied to the simultaneous quantitative analysis of levamisole (LVM) and triclabendazole (TCB) in tablets without using a preliminary separation, even in presence of the overlapping spectra of the above compounds. For both PCR and PLS, a concentration set containing 25 different mixtures of LVM and TCB in the linear concentration range was symmetrically prepared and then the absorbance values of the concentration set were measured at the wavelength set with Δλ=0.1 nm in the spectral region of 225-322.3 nm. PCR and PLS calibrations were obtained by applying the PCR and PLS algorithms to the concentration set data (y-block) and their corresponding absorbance data (x-block). The validity of PCR and PLS chemometric methods was performed by using the independent synthetic mixtures and the standard addition technique. Then, these analytical methods were applied to the commercial tablets and a good agreement was obtained between experimental results provided by the application of the PCR and PLS to the synthetic and real samples.Article Fractional Transmission Line with Losses(2014) Gómez-Aguilar, José Francisco; Baleanu, DumitruIn this manuscript, the fractional transmission line with losses is presented. The order of the Caputo derivative is considered as 0 < β ≤ 1 and 0 < γ ≤ 1 for the fractional equation in space and time domain, respectively. Two cases are solved, with fractional spatial and fractional temporal derivatives, and also numerical simulations were carried out, where there are taken both derivatives in simultaneous form. Two parameters σx and σt are introduced and a physical relation between these parameters is reported. Solutions in space and time are given in terms of the Mittag-Leffler functions. The classic cases are recovered when β and γ are equal to 1.Article FractionalHybridDifferential EquationsandCoupled Fixed-Point Results for α-Admissible F(ψ1, ψ2) − Contractions in M − Metric Spaces(2020) Karapınar, Erdal; Shimaa I., Moustafa; Shehata, Ayman; Agarwal, Ravi P.In this paper, we investigate the existence of a unique coupled fixed point for admissible mapping which is of contraction in the context of metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations with linear perturbations of second type and with three-point boundary conditions.Article Do Users Sacrifice Security for Speed and Ease-of-Use on Smartphones?: A Case Study on Attitude(IGI Global, 2020) Pusatlı, Tolga; Koyuncu, Murat; Nakip, MahirStoring credentials on smartphones to perform online activities increases ease-of-use (EoU) and speed. However, such practices increase security risks, especially if users use a number of applications or store data on their smartphones. Risks become more complicated by keeping smartphones online. This work aims to find potential relationships between security perceptions of smartphone users and their ease-of-use and speed preferences. Two user attitudes are defined as “not considering risk” and “risk exaggeration.” User ease-of-use and speed preferences are limited with the factors related to storing credentials on a smartphone and always keeping the device online. A survey of 154 participants was conducted through convenience sampling. Through regression analyses, logarithmic causality relations are found between EoU and speed and attitudes of not considering risk or risk exaggeration; so the participants preferred to take advantage of EoU and speed despite the fact that they were aware of the risks.Article A common fixed point theorem of a Greguš type on convex cone metric spaces(2011) Abdeljawad, Thabet; Karapinar, ErdalThe result of Ćirić [1] on a common fixed point theorem of Greguš type on metric spaces is extended to the class of cone metric spaces. Namely, a common fixed point theorem is proved in s-convex cone metric spaces under the normality of the cone and another common fixed point theorem is proved in convex cone metric spaces under the assumption that the cone is strongly minihedral.Article Complex b-spline collocation method for solving weaklysingular volterra integral equations of the second kind(Univ Miskolc Inst Math, 2015) Jafari, H.; Ramezani, M.; Johnston, S. J.; Baleanu, DumitruIn this paper we propose a new collocation type method for solving Volterra integral equations of the second kind with weakly singular kernels. In this method we use the complex B-spline basics in collocation method for solving Volterra integral. We compare the results obtained by this method with exact solution. A few numerical examples are presented to demonstrate the effectiveness of the proposed method.Book Part Cantor-type spherical-coordinate method for differential equationswithin local fractional derivatives(De Gruyter Open LTD, 2015) Rahmat, MRS; Baleanu, Dumitru; Yang, XJIn this article, we utilize the Cantor-type spherical coordinate method to investigate a family of local fractional differential operators on Cantor sets. Some examples are discussed to show the capability of this method for the damped wave, Helmholtz and heat conduction equations defined on Cantor sets. We show that it is a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type spherical-coordinate systems.Article Common fixed point theorems in cone Banach spaces(Hacettepe Univ, FAC Sci, 2011) Abdeljawad, Thabet; Karapınar, Erdal; Taş, Kenan; Tas, Aysegul; Kumar, AnilRecently, E. Karapınar (Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Applications, Article ID 609281, 9 pages, 2009) presented some fixed point theorems for self-mappings satisfying certain contraction principles on a cone Banach space. Here we will give some generalizations of this theorem.Book Optimal Approximation and Pricing of High- Dimensional Options(Lambert Academic Publishing, 2019) Kushpel, AlexanderThe book introduces an original general approach to the problem of multidimensional pricing which is applicable for a wide range of practically important examples. It gives a comprehensive and self-contained treatment of the problem of multidimensional pricing which provides the reader with all technical details. The book reflects a new stage of research in Quantitative Finance. It gives a particular fascination when apparently disjoint areas turn out to have a meaningful connection to each other. It demonstrates on concrete examples deep connections between Quantitative Finance and Numerical Analysis, Topology, Functional Analysis and Complexity Theory. The book can be considered as an inspirational source for practitioners, graduate and postgraduate students, MSc and PhD projects, to those working in Quantitative Finance and Economics.Article Numerical and Bifurcations Analysis for Multi Order Fractional Model of Hiv Infection of Cd4(+)T-Cells(Univ Politehnica Bucharest, 2016) Alipour, Mohsen; Arshad, Sadia; Baleanu, DumitruIn this paper, we solve the dynamical system of HIV infection of CD4(+) T cells within the multi-order fractional derivatives. The Bernstein operational matrices in arbitrary interval [a,b] are applied to obtain the approximate analytical solution of the model. In this way, the fractional differential equations are reduced to an algebraic easily solvable system. The obtained solutions are accurate and the method is very efficient and simple in implementation. With the help of bifurcation analysis, we acquired the critical value of viral death rate, that is, if viral death rate is greater than the critical value then level of virus particles starts to decline and thus free virus will eventually eliminate and patient is cured. Further, we found the threshold for viral infection rate analytically, which assures the stability of uninfected equilibrium and virus will ultimately eradicate.