Filtry
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Wyniki wyszukiwania dla: FRACTIONAL FOURIER TRANSFORM
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Numerical solution of fractional neutron point kinetics in nuclear reactor
PublikacjaThis paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme...
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Neural Approximators for Variable-Order Fractional Calculus Operators (VO-FC)
PublikacjaThe paper presents research on the approximation of variable-order fractional operators by recurrent neural networks. The research focuses on two basic variable-order fractional operators, i.e., integrator and differentiator. The study includes variations of the order of each fractional operator. The recurrent neural network architecture based on GRU (Gated Recurrent Unit) cells functioned as a neural approximation for selected...
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The Hough transform in the classification process of inland ships
PublikacjaThis article presents an analysis of the possibilities of using image processing methods for feature extraction that allows kNN classification based on a ship’s image delivered from an on-water video surveillance system. The subject of the analysis is the Hough transform which enables the detection of straight lines in an image. The recognized straight lines and the information about them serve as features in the classification...
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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
PublikacjaIn this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited...
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Study on polymer modified road asphalt mixture
PublikacjaThe formulation of ternary asphalt-additives blend composed of crumb rubber : low-density polyethylene (CR : LDPE) and crumb rubber : textile fiber (CR : TF) couples, and quaternary asphalt additives-blend composed of (CR : LDPE : TF) triplets on the virgin asphalt to optimize the asphalt basic and rheological properties and to use the extrusion process of two or three additives to obtain composite materials of them, as well as...
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Molecular transformation of dissolved organic matter in manganese ore-mediated constructed wetlands for fresh leachate treatment
PublikacjaThe organic matter (OM) and nitrogen in Fresh leachate (FL) from waste compression sites pose environmental and health risks. Even though the constructed wetland (CW) can efficiently remove these pollutants, the molecular-level transformations of dissolved OM (DOM) in FL remain uncertain. This study reports the molecular dynamics of DOM and nitrogen removal during FL treatment in CWs. Two lab-scale vertical-flow CW systems were...
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Numerical Investigation of Nuclear Reactor Kinetic and Heat Transfer Fractional Model with Temperature Feedback
PublikacjaAbstract—In the paper, the numerical results concerning the kinetics and proposed heat exchange models in nuclear reactor based on fractional calculus are presented for typical inputs. Two fractional models are proposed and compared with the model based on ordinary derivative. The first fractional model is based on one of the generalized Cattaneo equations. The second one is based on replacing the ordinary to fractional order of...
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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector
PublikacjaIn this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their...
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Fractional equations of Volterra type involving a Riemann Liouville derivative
PublikacjaIn this paper, we discuss the existence of solutions of fractional equations of Volterra type with the Riemann Liouville derivative. Existence results are obtained by using a Banach fixed point theorem with weighted norms and by a monotone iterative method too. An example illustrates the results.
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Approximation of Fractional Order Dynamic Systems Using Elman, GRU and LSTM Neural Networks
PublikacjaIn the paper, authors explore the possibility of using the recurrent neural networks (RNN) - Elman, GRU and LSTM - for an approximation of the solution of the fractional-orders differential equations. The RNN network parameters are estimated via optimisation with the second order L-BFGS algorithm. It is done based on data from four systems: simple first and second fractional order LTI systems, a system of fractional-order point...
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Simulation of Wave Propagation in Media Described by Fractional-Order Models
PublikacjaIn this paper, algorithms for simulation of the wave propagation in electromagnetic media described by fractional-order (FO) models (FOMs) are presented. Initially, fractional calculus and FO Maxwell's equations are introduced. The problem of the wave propagation is formulated for media described by FOMs. Then, algorithms for simulation of the non-monochromatic wave propagation are presented which employ computations in the time...
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Monometallic nanoparticles decorated and rare earth ions doped KTaO3/K2Ta2O6 photocatalysts with enhanced pollutant decomposition and improved H2 generation
PublikacjaNew, monometallic nanoparticles (MNPs) decorated surface and rare earth (RE) ions doped lattice of perovskite-type (KTaO3)/pyrochlore-type (K2Ta2O6) photocatalysts were successfully prepared by facile hydrothermal incorporation of RE ions into KTaO3/K2Ta2O6 lattices followed by photodeposition of MNPs. The impact of noble metal type (MNPs = Au, Pt, Rh) and rare earth dopant type (RE = Er, Pr) on the physicochemical properties correlated...
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Development of biocompatible iron oxide-silicon oxide core-shell nanoparticles as subcellular delivery platform for glucosamine-6-phosphate synthase inhibitors
PublikacjaIn order to develop the preparation of iron oxide-silica coreshell nanoparticles (CSNPs), thesis deeply explores the cetyltrimethylammonium (CTA+) directed silica coating methods of the oleic-acid capped iron oxide nanoparticles (OA-IONPs) initialized under near-neutral pH conditions. It is demonstrated that the initial alkaline hydrolysis of ethyl acetate in the presence of CTA+ and OA-IONPs induces an unusual ligand exchange...
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Degradation of cefadroxil drug by newly designed solar light responsive alcoholic template-based lanthanum ferrite nanoparticles
PublikacjaIn this work, lanthanum ferrite nanoparticles were synthesized via a simple co-precipitation method. Two different templates, namely sorbitol and mannitol, were used in this synthesis to tune the optical, structural, morphological, and photocatalytic properties of lanthanum ferrite. The synthesized lanthanum ferrite-sorbitol (LFOCo-So) and lanthanum ferrite-mannitol (LFOCo-Mo) were investigated through Ultraviolet–Visible (UV–Vis),...
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Heterojunction of (P, S) co-doped g-C3N4 and 2D TiO2 for improved carbamazepine and acetaminophen photocatalytic degradation
PublikacjaNovel photocatalysts of phosphorus and sulfur co-doped graphitic carbon nitride incorporated in 2D TiO2 structure were successfully fabricated and applied for solar-driven degradation of emerging pollutants from the group of pharmaceuticals not susceptible to biodegradation. The hybrid photocatalysts with different loadings of (P, S)-doped g-C3N4 were characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR),...
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Wavelet Transform Analysis of Temperature Modulated Gas Sensor Response
PublikacjaThe aim of the study was to evaluate whether it is possible to extract the information about the gas concentration despite the influence of humidity. Commercial semiconductor sensor response was examined under the application of a periodic temperature change. The data was collected using measurement protocol for different concentrations of ammonia at specified levels of relative humidity. In this work we focused on the evaluation...
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Variable Ratio Sample Rate Conversion Based on Fractional Delay Filter
PublikacjaIn this paper a sample rate conversion algorithm which allows for continuously changing resampling ratio has been presented. The proposed implementation is based on a variable fractional delay filter which is implemented by means of a Farrow structure. Coefficients of this structure are computed on the basis of fractional delay filters which are designed using the offset window method. The proposed approach allows us to freely...
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Variable Fractional Delay Filter Design Using a Symmetric Window
PublikacjaIn this paper a numerically efficient method for designing a nearly optimal variable fractional delay (VFD) filter based on a simple and well-known window method is presented. In the proposed method a single window extracted from the optimal filter with fixed fractional delay (FD) is divided into even and odd part. Subsequently, the odd part is discarded and symmetric even part of the extracted window is used to design a family...
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FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations
PublikacjaIn this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive relations and the Grünwald–Letnikov definition of a fractional derivative. Then the FDTD algorithm, which includes memory effects and energy dissipation of the considered media, is introduced....
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Numerical solution analysis of fractional point kinetics and heat exchange in nuclear reactor
PublikacjaThe paper presents the neutron point kinetics and heat exchange models for the nuclear reactor. The models consist of a nonlinear system of fractional ordinary differential and algebraic equations. Two numerical algorithms are used to solve them. The first algorithm is application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. The second involves building an analog scheme in the FOMCON Toolbox...
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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublikacjaIn this paper, control engineering methods are presented with regard to modelling and simulations of signal propagation in time-fractional (TF) electrodynamics. That is, signal propagation is simulated in electromagnetic media described by Maxwell’s equations with fractional-order constitutive relations in the time domain. We demonstrate that such equations in TF electrodynamics can be considered as a continuous-time system of...
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Fundamental properties of solutions to fractional-order Maxwell's equations
PublikacjaIn this paper, fundamental properties of solutions to fractional-order (FO) Maxwell's equations are analysed. As a starting point, FO Maxwell's equations are introduced in both time and frequency domains. Then, we introduce and prove the fundamental properties of electromagnetic field in FO electromagnetics, i.e. energy conservation, uniqueness of solutions, and reciprocity. Furthermore, the algorithm of the plane wave simulation...
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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublikacjaWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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Critical Case Stochastic Phylogenetic Tree Model via the Laplace Transform
PublikacjaBirth–and–death models are now a common mathematical tool to describe branching patterns observed in real–world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth–and–death model that is compatible with phylogenetic trees of both influenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the...
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A complex variable fractional-delay FIR filter structure
PublikacjaW artykule wprowadzamy strukturę zespolonego filtru o skończonej odpowiedzi impulsowej (ang. finite impulse response - FIR) ze zmiennym opóźnieniem ułamkowym (ang. fractional delay - FD). Strukturę tę otrzymujemy na podstawie przestrajanego filtru FD FIR o współczynnikach rzeczywistych. Stanowi ona połączenie zbioru liniowo-fazowych filtrów FIR o współczynnikach stałych rzeczywistych i dwóch łańcuchów mnożąco-akumulujących, zawierających...
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Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties
PublikacjaStarting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality...
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Fourier based stabilization of thermal images in dynamic thermography
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Comments on “Closed Form Variable Fractional Time Delay Using FFT”
PublikacjaIn this letter drawbacks of the aforementioned paper are pointed out. The proposed approach is improved with minor modifications of the discrete frequency response. This allows for design of fractional delay filters which are close to optimal and can be efficiently implemented in the frequency domain using the sliding DFT based structure. Alternatively, the derived equivalent closed form formulae for offset windows can be used...
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Fractional Order Circuit Elements Derived from Electromagnetism
PublikacjaIn this paper, derivations of fractional-order (FO) circuit-element equations from electromagnetism are presented. Whilst many papers are devoted to FO modelling of electrical circuits, there are no strong foundations for such an approach. Therefore, we investigate relations between the FO electromagnetism and the FO circuit theory. Our derivations start from quasi-static (QS) approximations of Maxwell's equations in media with...
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Fractional neutron point kinetics equations for nuclear reactor dynamics – Numerical solution investigations
PublikacjaThis paper presents results concerning numerical solutions to a fractional neutron point kinetics model for a nuclear reactor. The paper discusses and expands on results presented in (Espinosa-Paredes et al., 2011). The fractional neutron point kinetics model with six groups of delayed neutron precursors was developed and a numerical solution using the Edwards’ method was proposed (Edwards et al., 2002). The mathematical model...
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Crank–Nicolson FDTD Method in Media Described by Time-Fractional Constitutive Relations
PublikacjaIn this contribution, we present the Crank-Nicolson finite-difference time-domain (CN-FDTD) method, implemented for simulations of wave propagation in media described by time-fractional (TF) constitutive relations. That is, the considered constitutive relations involve fractional-order (FO) derivatives based on the Grünwald-Letnikov definition, allowing for description of hereditary properties and memory effects of media and processes....
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublikacjaThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublikacjaThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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Advancement of Non-Newtonian Fluid with Hybrid Nanoparticles in a Convective Channel and Prabhakar’s Fractional Derivative—Analytical Solution
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On possible applications of media described by fractional-order models in electromagnetic cloaking
PublikacjaThe purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use...
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Evaluation of Hilbert transform filter performance
PublikacjaW pracy rozpatrzono zagadnienie adaptacyjnej estymacji ułamkowego opóźnienia pomiędzy dwoma sygnałami sinusoidalnymi. Zastosowano tu nowy, zagregowany, zespolony filtr Hilberta, który łączy w sobie funkcje filtracji Hilberta i kompensacji ułamkowego opóźnienia. W eksperymentach wykorzystano efektywną implementację tego filtru w strukturze Farrowa, której jedynym parametrem o zmiennej wartości jest bieżące opóźnienie ułamkowe.
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The Farrow structure for the Hilbert transform filter
PublikacjaPrzedstawiono nową implementację cyfrowego filtru Hilberta, wykonaną w strukturze Farrowa. Jest to filtr zespolony, realizujący jednocześnie dwie różne operacje liniowe, wykonywane dotychczas za pomocą osobnych filtrów. Pierwsza z nich polega na standardowej filtracji hilbertowskiej. Tworzy ona zespolony "analityczny" odpowiednik rzeczywistego sygnału wejściowego. Drugą, osiąganą za pomocą prze-próbkowania ze współczynnikiem, w...
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublikacjaIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Investigations of the Methods of Time Delay Measurement of Stochastic Signals Using Cross-correlation with the Hilbert Transform
PublikacjaThe article presents the results of simulation studies of four methods of estimating time delay for random signals using cross-correlation with the Hilbert Transform. Selected models of mutually delayed stochastic signals were used in the simulations, corresponding to the signals obtained from scintillation detectors in radioisotope measurements of liquid-gas two-phase flow. Standard deviations of the values of the individual functions...
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A NUMERICAL STUDY ON THE DYNAMICS OF DENGUE DISEASE MODEL WITH FRACTIONAL PIECEWISE DERIVATIVE
PublikacjaThe aim of this paper is to study the dynamics of Dengue disease model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative are examined for the aforementioned problem. The suggested...
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MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION
PublikacjaThe purpose of this work is to study the memory effect analysis of Caputo–Fabrizio time fractional diffusion equation by means of cubic B-spline functions. The Caputo–Fabrizio interpretation of fractional derivative involves a non-singular kernel that permits to describe some class of material heterogeneities and the effect of memory more effectively. The proposed numerical technique relies on finite difference approach and cubic...
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Application of discrete wavelet transform in seismic nonlinear analysis of soil–structure interaction problems
PublikacjaSimulation of soil-structure interaction (SSI) effects is a time-consuming and costly process. However, ignoring the influence of SSI on structural response may lead to inaccurate results, especially in the case of seismic nonlinear analysis. In this paper, wavelet transform methodology has been utilized for investigation of the seismic response of soil-structure systems. For this purpose, different storey outrigger braced buildings...
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Recurrent Neural Network Based Adaptive Variable-Order Fractional PID Controller for Small Modular Reactor Thermal Power Control
PublikacjaThis paper presents the synthesis of an adaptive PID type controller in which the variable-order fractional operators are used. Due to the implementation difficulties of fractional order operators, both with a fixed and variable order, on digital control platforms caused by the requirement of infinite memory resources, the fractional operators that are part of the discussed controller were approximated by recurrent neural networks...
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Non-Destructive Diagnostics of Concrete Beams Strengthened with Steel Plates Using Modal Analysis and Wavelet Transform
PublikacjaExternally bonded reinforcements are commonly and widely used in civil engineering objects made of concrete to increase the structure load capacity or to minimize the negative effects of long-term operation and possible defects. The quality of adhesive bonding between a strengthened structure and steel or composite elements is essential for effective reinforcement; therefore, there is a need for non-destructive diagnostics of adhesive...
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Fuzzy Multi-Regional Fractional PID controller for Pressurized Water nuclear Reactor
PublikacjaThe paper presents the methodology for the synthesis of a Fuzzy Multi-Regional Fractional Order PID controller (FMR-FOPID) used to control the average thermal power of a PWR nuclear reactor in the load following mode. The controller utilizes a set of FOPID controllers and the fuzzy logic Takagi-Sugeno reasoning system. The proposed methodology is based on two optimization parts. The first part is devoted to finding the optimal...
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NO-BROADCASTING OF NON-SIGNALLING BOXES VIA OPERATIONS WHICH TRANSFORM LOCAL BOXES INTO LOCAL ONES
PublikacjaWe deal with families of probability distributions satisfying non-signalling condition, called non-signalling boxes and consider a class of operations that transform local boxes into local ones (the one that admit LHV model). We prove that any operation from this class cannot broadcast a bipartite non-local box with 2 binary inputs and outputs. We consider a function called anti-Robustness which can not decrease under these operations....
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Application of wavelet transform in analysis of guided wave propagation signals for damage detection in a steel plate
PublikacjaThe paper presents results of experimental investigations on damage detection using guided wave propagation technique. The tested specimen was a steel plate with a defect in the form of a rectangular notch. Lamb waves were excited by a PZT actuator and sensed by a laser vibrometer. Since reflections from damage in registered signals are often masked by measurement noise, for identification of time of reflections from damage, continuous...
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A Nyquist filter of fractional delay
PublikacjaIn the paper a novel discrete-time FIR fractonal delay specjal filter is investigated. This is a Nyquist filter which, besides the traditional its attribute (interymbol interference (ISI) free property), has the ability to compensate for subsample transmission delay involved, for example, in multipath propagation channel. The performance of the filter is analysed and illustrated.
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Wavelet transform-based approach to defect identification in railway carbon contact strips.
PublikacjaPantographs of electric rail vehicles are fitted with carbon contact strips, which slide along the contact wire of catenary to provide constant electrical contact. Contact strips are exposed to wear and damages. Using damaged contact strips significantly increases the risk of catenary rupture. Therefore, their technical condition has to be inspected frequently. In previous work a 3D laser scanning system was proposed for recording...
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Successive Iterative Method for Higher-Order Fractional Differential Equations Involving Stieltjes Integral Boundary Conditions
PublikacjaIn this paper, the existence of positive solutions to fractional differential equations with delayed arguments and Stieltjes integral boundary conditions is discussed. The convergence of successive iterative method of solving such problems is investigated. This allows us to improve some recent works. Some numerical examples illustrate the results.