Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Author: search.filters.author.Nigmatullin, Raoul R.

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Now showing 1 - 10 of 15
  • Article
    Citation - WoS: 6
    Citation - Scopus: 8
    Spectral Analysis of Hiv Drugs for Acquired Immunodeficiency Syndrome Within Modified Non-Invasive Methods
    (Chiminform Data S A, 2013) Nigmatullin, Raoul R.; Baleanu, Dumitru; Baleanu, Dumitru; Al-Zhrani, Abdulrahim A.; Alhamed, Yahia A.; Zahid, Adnan H.; Youssef, Tamer E.; Matematik
    In this study a chromatographic separation of active ingredients for four drugs namely Combivir Kaletra, Valcyte and Viramune was performed on thin layer chromatography (TLC). Their spectra were analyzed for acquired immunodeficiency syndrome by using the Fourier transform infrared spectroscopy spectra combined with the new procedure of the optimal linear smoothing. Fourier transform of the second type was applied as the fitting function based on some significant set of frequencies for the smoothed signals. The obtained results show that the proposed method is efficient and easy to apply in extracting of a hidden information from signals corresponding to the four investigated drugs.
  • 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, Adnan
    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
    Extraction of Reliable Information from Time-Domain Pressure and Flow Signals Measured By Means of Forced Oscillation Techniques
    (Chiminform Data, 2014) Nigmatullin, Raoul R.; Osokin, Sergey I.; Ionescu, Clara; Baleanu, Dumitru
    This paper aims to give a proof-of-concept for the possible application of the forced oscillation lung function test to assess the viscoelastic properties of the airways and tissue. In particular, a novel signal processing algorithm is employed on non-stationary, noisy, (relatively) short time series of respiratory pressure and flow signals. This novel technique is employed to filter the useful information from the signals acquired under two measurement conditions: pseudo-functional residual capacity (PFRC) and pseudo-total lung capacity (PTLC). The PFRC is the measurement performed at lowest lung volume with maximum deflation, and the PTLC is measurement performed at the maximum lung volume under maximum inflation. The results suggest that the proposed technique is able to extract information on the viscoelastic properties of the lung tissue at a macroscopic level. The conclusion of this preliminary study is that the proposed combination of signal processing method and lung function test is suited to be employed on a large database in order to deliver reference values and perform further statistical analysis.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 10
    The 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: 6
    Citation - Scopus: 7
    Raman Spectra of Nanodiamonds: New Treatment Procedure Directed for Improved Raman Signal Marker Detection
    (Hindawi Ltd, 2013) Baleanu, Dumitru; Povarova, Diana; Salah, Numan; Habib, Sami S.; Memic, Adnan; Nigmatullin, Raoul R.
    Detonation nanodiamonds (NDs) have shown to be promising agents in several industries, ranging from electronic to biomedical applications. These NDs are characterized by small particle size ranging from 3 to 6 nm, while having a reactive surface and a stable inert core. Nanodiamonds can exhibit novel intrinsic properties such as fluorescence, high refractive index, and unique Raman signal making them very attractive imaging agents. In this work, we used several nanodiamond preparations for Raman spectroscopic studies. We exposed these nanodiamonds to increasing temperature treatments at constant heating rates (425-575 degrees C) aiding graphite release. We wanted to correlate changes in the nanodiamond surface and properties with Raman signal which could be used as a detection marker. These observations would hold potential utility in biomedical imaging applications. First, the procedure of optimal linear smoothing was applied successfully to eliminate the high-frequency fluctuations and to extract the smoothed Raman spectra. After that we applied the secondary Fourier transform as the fitting function based on some significant set of frequencies. The remnant noise was described in terms of the beta-distribution function. We expect this data treatment to provide better results in biomolecule tracking using nanodiamond base Raman labeling.
  • Article
    Citation - WoS: 21
    Citation - Scopus: 34
    New 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: 3
    Citation - Scopus: 6
    Linear Discrete Systems With Memory: a Generalization of the Langmuir Model
    (de Gruyter Poland Sp Z O O, 2013) Nigmatullin, Raoul R.; Baleanu, Dumitru
    In this manuscript we analyzed a general solution of the linear nonlocal Langmuir model within time scale calculus. Several generalizations of the Langmuir model are presented together with their exact corresponding solutions. The physical meaning of the proposed models are investigated and their corresponding geometries are reported.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 8
    New Method and Treatment Technique Applied To Interband Transition in Gaas1-Xpx Ternary Alloys
    (versita, 2011) Nigmatullin, Raoul R.; Cetin, Saime Sebnem; Baleanu, Dumitru; Ozcelik, Suleyman; Baleanu, Cristina-Mihaela
    In this paper we presented a new method (Eigen-Coordinates (ECs)) that can be used for calculations of the critical points (CPs) energy of the interband-transition edges of the heterostructures. This new method is more accurate and complete in comparison with conventional ones and has a wide range of application for the calculation of the fitting parameters related to nontrivial functions that initially have nonlinear fitting parameters that are difficult to evaluate. The new method was applied to determine the CPs energies from the dielectric functions of the MBE grown GaAs1-xP (x) ternary alloys obtained using spectroscopic ellipsometry (SE) measurements at room temperature in the 0.5-5 eV photon energy region. The obtained results are in good agreement with the results of the other methods.
  • Article
    Citation - WoS: 18
    Citation - Scopus: 22
    The 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: 14
    Citation - Scopus: 14
    On 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.