Matematik Bölümü
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Browsing Matematik Bölümü by browse.metadata.publisher "Amer Scientific Publishers"
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Article Citation - WoS: 15Citation - Scopus: 14Analysis of a Nanofilm of the Mercaptophenyl Diazonium Modified Gold Electrode Within New Statistical Parameters(Amer Scientific Publishers, 2010) Baleanu, Dumitru; Dinc, Erdal; Ustundag, Zafer; Solak, Ali Osman; Kargin, Roman V.; Nigmatullin, Raoul R.The main aim of this study is to characterize the nanosurface of the mercaptophenyl diazonium modified gold (Au) surface by a new statistical approach. In this study the gold electrode surfaces were self-assembled in ethyl alcohol by 1.0 mM mercaptophenyl diazonium. FT-IR spectra of the surface modifier molecules in both solid and nanofilm of mercaptophenyl diazonium (MCP-Au) forms were recorded in the spectral range of 600-4,000 cm(-1). The FT-IR spectra of solid mercaptophenyl diazonium tetrafluoroborate salt were obtained by using KBr pellets. The above FT-IR spectra of both bare Au and its nanofilm of mercaptophenyl diazonium were processed by new statistical approach to reach optimal smoothing trend for the characterization of the modified electrode surface consisting of the nanofilm of gold-mercaptophenyl diazonium. In the frame of new statistical approach all measured spectra have been 'read' in terms of a set of universal statistical parameters. These new parameters help to establish the statistical proximity of the smoothed spectra compared and give a possibility to classify the measured spectra in accordance with new set of statistical and robust quantitative values. Besides, there is a possibility to receive the relative fluctuations and the smoothed spectra of the second order. So, thanks to new approach we do not loose any measured information: the smoothed spectra and accompanied them noise (relative fluctuations) can be analyzed separately for detection of possible influence of predominant external factors that can be essential for this type of measurements.Article Citation - WoS: 1An Analysis of Analytic and Approximate Solutions of the Nonlinear Foam-Drainage Equation and Its Applications(Amer Scientific Publishers, 2018) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu IsaIn this study, the modified Kudryashov and Riccati-Bernoulli (sub-ODE) methods are applied to construct some analytical solutions of the nonlinear Foam-drainage equation which plays an important part in the formation and evolution of liquid foams. Kink type, singular and logarithmic function solutions are obtained. Then, the residual power series method (RPSM) is used to analyze the numerical behavior of the equation by considering all the exact solutions. We observed that the modified Kudryashov and Riccati Bernoulli sub-ODE methods are powerful techniques for finding the exact solutions to various nonlinear models. Also, the RPSM is efficient for examining numerical behavior of nonlinear models. Some interesting figures are shown to show the reliability of the methods.Article Citation - WoS: 1Citation - Scopus: 1Analysis of the Nano-Surface of a Modified Glassy Carbon Electrode by Pseudo Phase Plane Method(Amer Scientific Publishers, 2011) Baleanu, Dumitru; Dinc, Erdal; Solak, Ali Osman; Eksi, Haslet; Guzel, Remziye; Tenreiro Machado, J. A.This paper presents the Pseudo phase plane (PPP) method for detecting the existence of a nanofilm on the nitroazobenzene-modified glassy carbon electrode (NAB-GC) system. This modified electrode systems and nitroazobenze-nanofilnn were prepared by the electrochemical reduction of diazonium salt of NAB at the glassy carbon electrodes (GCE) in nonaqueous media. The IR spectra of the bare glassy carbon electrodes (GCE), the NAB-GC electrode system and the organic NAB film were recorded. The IR data of the bare GC, NAB-GC and NAB film were categorized into five series consisting of FILM1, GC-NAB1, GC1; FILM2, GC-NAB2, GC2; FILM3, GC-NAB3, GC3 and FILM4, GC-NAB4, GC4 respectively. The PPP approach was applied to each group of the data of unmodified and modified electrode systems with nanofilm. The results provided by PPP method show the existence of the NAB film on the modified GC electrode.Article Citation - WoS: 9Citation - Scopus: 14Characterization Approach To Modified Glassy Carbon Electrode-Nanofilm System Within Multidimensional Scaling(Amer Scientific Publishers, 2011) Baleanu, Dumitru; Dinc, Erdal; Solak, All Osman; Eksi, Haslet; Guzel, Remziye; Tenreiro Machado, J. A.The aim of this work is to characterize the nanofilm consisting of the benzoic acid-modified glassy carbon (GC) electrode system through multidimensional scaling space analysis. The surface modification is based on the electrochemical reaction between the GC electrode and benzoic acid-diazonium salt (BA-DAS). As a result, the nonofilms regarding the benzoic acid-glassy carbon (BA-GC) electrode surface was obtained. For the analysis of the naonfilm of BC-GC electrode system, the IR spectra of the modified BA-GC electrode surface, GC surface and BA-DAS were recorded in the spectral range of 599.84 - 3996.34 [cm(-1)]. The IR data vectors of the above three forms were processed by the using the multidimensional scaling space approach to demonstrate the existence of a nanofilm on the modified BA-GC electrode system. Two- and three-dimensional MDS profiles obtained by application of multidimensional scaling approach to the data sets {CG1, ... ,CG10}, {BA-GC1, ... ,BA-GC10} and {FILM1, ... ,FILM10} allow a good recognition of the nanofilm on the modified glassy carbon (GC) electrode system.Article Citation - WoS: 1Citation - Scopus: 1Factor Analysis for the Characterization of the Nano-Surface of the Nitroazobenzene-Modified Glassy Carbon Electrode(Amer Scientific Publishers, 2012) Baleanu, Dumitru; Solak, Ali Osman; Eksi, Haslet; Guzel, Remziye; Dinc, ErdalFactor analysis with orthogonal varimax rotation was applied to determine the existence of a nano-structure on the nitroazobenze-modified glassy carbon electrode (NAB-GC) system. The NAB-GC electrode systems and benzoic acid-nanofilm (NAB-FILM) were obtained by using the electrochemical surface modification experiments. The IR spectra of the bare glassy carbon electrodes (GC), the NAB-GC electrode system and NAB-FILM were recorded. The IR data of the bare GC, BA-GC and BA-FILM were categorized into five series consisting of FILM1, GC-NAB1, GC1; FILM2, GC-NAB2, GC2; FILM3, GC-NAB3, GC3; FILM4, GC-NAB4, GC4; FILM5, GC-NAB5, GC5, respectively. The factor loadings were extracted by making use of the factor analysis approach applied to each group. The orthogonal varimax rotation technique was used to obtain the rotated factor loadings corresponding to the first two factors. After the estimation of the relationship among and within groups, the results predict the existence of the NAB-FILM on the NAB modified glassy carbon electrodes.Article Citation - WoS: 4Invariant Subspace and Lie Symmetry Analysis, Exact Solutions and Conservation Laws of a Nonlinear Reaction-Diffusion Murray Equation Arising in Mathematical Biology(Amer Scientific Publishers, 2018) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu IsaReaction-diffusion type equations are seen as models of pattern formation in biology and chemistry. The concept of Lie symmetry and invariant subspace (ISM) methods play a vital role in the study of partial differential equations (PDEs). Lie symmetry method helps to derive point symmetries, symmetry algebra and exact solution by reducing the PDEs to and ordinary differential equation (ODEs), while the invariant subspace method determines an invariant subspace and construct exact solutions of the PDEs by also reducing the PDEs to ODEs. In this article, the two methods are applied to derive the exact solutions of a nonlinear reaction-diffusion murray equation appearing in mathematical biology. Several kinds of solutions of the model are presented, including topological, singular and exponential function solutions. We classify the conservation laws (Cls) of the model using the multipliers approach. The paper conclude by giving a comprehensive physical interpretations and comparative study of the results showing the molecular nature of the acquired solutions.Article Nonlinear Self-Adjointness and Nonclassical Solutions of a Population Model With Variable Coefficients(Amer Scientific Publishers, 2018) Inc, M.; Akgul, A.; Baleanu, D.; Hashemi, M. S.In this work, the size-structured population model with variable coefficients is considered to construct the exact solutions with nonclassical symmetries in the light of the heir equations. Nonlinear self-adjointness is shown and conservation laws are calculated too. Some scientific theorems have been given in this paper.Article Citation - WoS: 1Optical Solitary Wave Solutions for the Conformable Perturbed Nonlinear Schrodinger Equation With Power Law Nonlinearity(Amer Scientific Publishers, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Gulsen, Selahattin; Baleanu, Dumitru; Inc, MustafaIn this study, we apply three integration schemes to extract optical soliton solutions for the conformable perturbed nonlinear Schrodinger equation (CPNLSE) with power law nonlinearity (PLN). The integration schemes that are used to carry out such solutions are Sine-Cosine (SC), generalized tanh (GT), and Ricatti-Bernoulli (RB) sub-ODE methods. The constraints conditions for the existence of the solutions are reported. The solutions are obtained using newly proposed fractional derivative called conformable derivative. Numerical simulations of some of the obtained solutions are also illustrated.Article Citation - WoS: 2Optical Solitons for Complex Ginzburg-Landau Model With Beta Derivative in Nonlinear Optics(Amer Scientific Publishers, 2018) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, AbdullahiIn this paper, we present some new optical solitons for Complex Ginzburg-Landau equation (CGLE) involving Kerr Law in nonlinear optics. Two integration schemes which are extended Jacobi elliptic function (EJEF) and generalized projective ricatti (GPR) methods are applied to reach such solutions. The governing equation in the present paper involves beta derivative. The constraints conditions for the existence of soliton solutions are reported. Numerical simulations of some of the obtained solutions are illustrated.Article Citation - WoS: 3Solitons and Conservation Laws for the (2+1)-Dimensional Davey-Stewartson Equations With Conformable Derivative(Amer Scientific Publishers, 2018) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, AbdullahiThis research obtains some new solitons for the Davey-Stewartson equation (DSE) with conformable derivative. The well known projective Ricatti equation ansatz (PREA) is employed to reach such solitons. The constraints conditions for the existence of soliton solutions are reported. Moreover, the conservation laws (Cls) for the governing equation is studied via multiplier technique. Physical features of some solutions are illustrated in Figures 1-8.
