Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article The first observation of memory effects in the infrared (FT-IR) measurements: Do successive measurements remember each other?(Public Library Science, 2014) Nigmatullin, Raoul R.; Osokin, Sergey I.; Baleanu, Dumitru; Al-Amri, Sawsan; Azam, Ameer; Memic, AdnanOver the past couple of decades there have been major advances in the field of nanoscience and nanotechnology. Many applications have sprouted from these fields of research. It is essential, given the scale of the materials, to attain accurate, valid and reproducible measurements. Material properties have shown to be a function of their size and composition. Physiochemical properties of the nanomaterials can significantly alter material behavior compared to bulk counterparts. For example, metal oxide nanoparticles have found broad applications ranging from photo-catalysis to antibacterial agents. In our study, we synthesized CuO nanoparticles using well established sol-gel based methods with varying levels of Ni doping. However, upon analysis of measured infrared data, we discovered the presence of quasi-periodic (QP) processes. Such processes have previously been reported to be tightly associated with measurement memory effects. We were able to detect the desired QP process in these measurements from three highly accurate repetitive experiments performed on each Ni (1-7%) doped CuO sample. In other words, successive measurements performed in a rather short period of time remember each other at least inside a group of neighboring measurements.Article Citation - WoS: 8Citation - Scopus: 10The First Observation of Memory Effects in the Infrared (ft-Ir) Measurements: Do Successive Measurements Remember Each Other(Public Library Science, 2014) Osokin, Sergey I.; Baleanu, Dumitru; Al-Amri, Sawsan; Azam, Ameer; Memic, Adnan; Nigmatullin, Raoul R.Over the past couple of decades there have been major advances in the field of nanoscience and nanotechnology. Many applications have sprouted from these fields of research. It is essential, given the scale of the materials, to attain accurate, valid and reproducible measurements. Material properties have shown to be a function of their size and composition. Physiochemical properties of the nanomaterials can significantly alter material behavior compared to bulk counterparts. For example, metal oxide nanoparticles have found broad applications ranging from photo-catalysis to antibacterial agents. In our study, we synthesized CuO nanoparticles using well established sol-gel based methods with varying levels of Ni doping. However, upon analysis of measured infrared data, we discovered the presence of quasi-periodic (QP) processes. Such processes have previously been reported to be tightly associated with measurement memory effects. We were able to detect the desired QP process in these measurements from three highly accurate repetitive experiments performed on each Ni (1-7%) doped CuO sample. In other words, successive measurements performed in a rather short period of time remember each other at least inside a group of neighboring measurements.Article Citation - WoS: 21Citation - Scopus: 34New Relationships Connecting a Class of Fractal Objects and Fractional Integrals in Space(versita, 2013) Baleanu, Dumitru; Nigmatullin, Raoul R.Many specialists working in the field of the fractional calculus and its applications simply replace the integer differentiation and integration operators by their non-integer generalizations and do not give any serious justifications for this replacement. What kind of "Physics" lies in this mathematical replacement? Is it possible to justify this replacement or not for the given type of fractal and find the proper physical meaning? These or other similar questions are not discussed properly in the current papers related to this subject. In this paper new approach that relates to the procedure of the averaging of smooth functions on a fractal set with fractional integrals is suggested. This approach contains the previous one as a partial case and gives new solutions when the microscopic function entering into the structural-factor does not have finite value at N a parts per thousand << 1 (N is number of self-similar objects). The approach was tested on the spatial Cantor set having M bars with different symmetry. There are cases when the averaging procedure leads to the power-law exponent that does not coincide with the fractal dimension of the self-similar object averaged. These new results will help researches to understand more clearly the meaning of the fractional integral. The limits of applicability of this approach and class of fractal are specified.Article Citation - WoS: 18Citation - Scopus: 22The Derivation of the Generalized Functional Equations Describing Self-Similar Processes(Walter de Gruyter Gmbh, 2012) Baleanu, Dumitru; Nigmatullin, Raoul R.The generalized functional equations describing a wide class of different self-similar processes are derived. These equations follow from the observation that microscopic function describing an initial self-similar process increases monotonically or even cannot have a certain value. The last case implies the behavior of trigonometric functions cos(z zeta (n) ), sin(z zeta (n) ) at zeta > 1 and n a parts per thousand << 1 that can enter to the microscopic function and when the limits of the initial scaling region are increasing and becoming large. The idea to obtain the desired functional equations is based on the approximate decoupling procedure reducing the increasing microscopic function to the linear combination of the same microscopic functions but having smaller scales. Based on this idea the new solutions for the well-known Weierstrass-Mandelbrot function were obtained. The generalized functional equations derived in this paper will help to increase the limits of applicability in description of a wide class of self-similar processes that exist in nature. The procedure that is presented in this paper allows to understand deeper the relationship between the procedure of the averaging of the smoothed functions on discrete self-similar structures and continuous fractional integrals.Article Citation - WoS: 14Citation - Scopus: 14On the Laplace Integral Representation of Multivariate Mittag-Leffler Functions in Anomalous Relaxation(Wiley, 2016) Khamzin, Airat A.; Baleanu, Dumitru; Nigmatullin, Raoul R.In the given paper, a special method of representation of the Mittag-Leffler functions and their multivariate generalizations in the form of the Laplace integrals is suggested. The method is based on the usage of the generalized multiplication Efros theorem. The possibilities of a new method are demonstrated on derivation of the integral representations for relaxation functions used in the anomalous dielectric relaxation in time domain. Copyright (C) 2016 JohnWiley & Sons, Ltd.Article Citation - WoS: 1Citation - Scopus: 2Dielectric Response of Different Complex Materials(Ieee-inst Electrical Electronics Engineers inc, 2012) Zhang, Wei; Baleanu, Dumitru; Nigmatullin, Raoul R.In this paper we describe novel results of the application of the non-orthogonal amplitude-frequency analysis of the smoothed signals (NAFASS) approach [1] for the analysis of the dielectric response of some complex materials. Our goal is to convince experimentalists that the NAFASS approach can serve as a useful tool in the cases when an underlying physical model is absent or in cases when it is necessary to calibrate the equipment with uncertain quantitative characteristics. The parameters obtained in the frame of the NAFASS approach can be used as metrological parameters for comparison of electromagnetic responses associated with properties of different dielectric materials.Article Citation - WoS: 65Citation - Scopus: 72Newtonian Law With Memory(Springer, 2010) Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Nigmatullin, Raoul R.; Baleanu, DumitruIn this study we analyzed the Newtonian equation with memory. One physical model possessing memory effect is analyzed in detail. The fractional generalization of this model is investigated and the exact solutions within Caputo and Riemann-Liouville fractional derivatives are reported.Article Citation - WoS: 18Citation - Scopus: 18Characterization of a Benzoic Acid Modified Glassy Carbon Electrode Expressed Quantitatively by New Statistical Parameters(Elsevier, 2009) Baleanu, Dumitru; Dinc, Erdal; Solak, Ali Osman; Nigmatullin, Raoul R.The main aim of this study is to characterize the nanosurface of the benzoic acid modified glassy carbon (GC) electrode by using a new statistical approach. In this study, the electrode surfaces were modified by cyclic voltametry in the potential range of +0.4 and -0.8 V at a scan rate 200 mV s(-1) for four cycles versus Ag/Ag+ electrode in acetonitrile containing 0.1 M tetrabutylammonium tetraflouroborate (TBATFB). FT-IR spectra of the surface modifier molecules in both solid (GC and nanofilm (GC-benzoic acid)) forms were recorded in the spectral range 600-4000 cm(-1). The FT-IR spectra of p-aminobenzoic acid were obtained by using KBr pellets. The above FT-IR spectra of both GC and its nanofilm with benzoic acid were processed by new statistical approach to reach optimal smoothing trend for the characterization of the modified electrode surface consisting of the nanofilm of GC-benzoic acid. In the frame of new statistical approach all measured spectra have been 'read' in terms of a set of universal statistical parameters. (C) 2008 Elsevier B.V. All rights reserved.