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Search results for: jumarie fractional derivative
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Comments on “Closed Form Variable Fractional Time Delay Using FFT”
PublicationIn 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
PublicationIn 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
PublicationThis 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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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublicationThis 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
PublicationThis 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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On possible applications of media described by fractional-order models in electromagnetic cloaking
PublicationThe 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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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublicationIn 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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The Effect of Conjugation with Octaarginine, a Cell-Penetrating Peptide on Antifungal Activity of Imidazoacridinone Derivative
PublicationAcridine cell-penetrating peptide conjugates are an extremely important family of compounds in antitumor chemotherapy. These conjugates are not so widely analysed in antimicrobial therapy, although bioactive peptides could be used as nanocarriers to smuggle antimicrobial compounds. An octaarginine conjugate of an imidazoacridinone derivative (Compound 1-R8) synthetized by us exhibited high antifungal activity against reference...
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Multiple Solutions to Third-Order Differential Equations with Derivative Dependence and Deviating Arguments
PublicationIn this paper, we give some new results for multiplicity of positive (nonnegative) solutions for third-order differential equations with derivative dependence, deviating arguments and Stieltjes integral boundary conditions. We discuss our problem with advanced argument α and arbitrary β ∈ C([0,1],[0,1]), see problem (2). It means that argument β can change the character on [0,1], so β can be delayed in some set J ⊂ [0,1] and advanced...
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Proportional-Derivative and Model-Based Controllers for Control of a Variable Mass Manipulator
PublicationIn the paper, numerical analysis of dynamics of a variable mass manipulator is presented. A revolute joints composed manipulator is considered. Payload of the gripper is considered as the only element characterized by unknown value of its mass (variable between subsequent operations). As in other cases of the revolute joints composed manipulators, its behaviour dependents significantly on the pose of the manipulator. When the manipulator...
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Recurrent Neural Network Based Adaptive Variable-Order Fractional PID Controller for Small Modular Reactor Thermal Power Control
PublicationThis 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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On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces
PublicationIn this paper, we investigate the properties of the Fenchel–Moreau conjugate of G-function with respect to the coupling function c(x, A) = |A[x]2 |. We provide conditions that guarantee that the conjugate is also a G-function. We also show that if a G-function G is twice differentiable and its second derivative belongs to the Orlicz space generated by the Fenchel–Moreau conjugate of G then the modular generated by G is twice differentiable...
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Fuzzy Multi-Regional Fractional PID controller for Pressurized Water nuclear Reactor
PublicationThe 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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Successive Iterative Method for Higher-Order Fractional Differential Equations Involving Stieltjes Integral Boundary Conditions
PublicationIn 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.
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A Nyquist filter of fractional delay
PublicationIn 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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Photosensitive and pH-dependent activity of pyrazine-functionalized carbazole derivative as promising antifungal and imaging agent
PublicationCarbazole skeleton plays a significant role as a structural scaffold of many pharmacologically active compounds. Pyrazine-functionalized carbazole derivative was constructed by coupling 2-amino-5-bromo-3-methylaminepyrazine (ABMAP) into 3 and 6 positions of the carbazole ring. Multi-experimental methods were used, e.g., potentiometric, spectroscopic (ATR, UV, XRD powder,1H and13C NMR), electrochemical (cyclic voltammetry), and...
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Solvent-Free Synthesis of Phosphonic Graphene Derivative and Its Application in Mercury Ions Adsorption
PublicationFunctionalized graphene was efficiently prepared through ball-milling of graphite in the presence of dry ice. In this way, oxygen functional groups were introduced into material. The material was further chemically functionalized to produce graphene derivative with phosphonic groups. The obtained materials were characterized by spectroscopic and microscopic methods, along with thermogravimetric analysis. The newly developed material...
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublicationIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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Some applications of fractional order calculus
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Fractional Order Models of Dynamic Systems
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Optimal Control for Discrete Fractional Systems
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Fractional differential equations with deviating arguments
PublicationDla równań różniczkowych typu ułamkowego, zostały podane warunki dostateczne na istnienie jednego rozwiązania lub rozwiazań ekstremalnych. Nierówności różniczkowe są też doskutowane.
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Metabolism of antitumour agent 1-nitroacridine derivative, C-1748 in pancreatic cancer cell lines
PublicationPancreatic cancer has the highest mortality rate of all major cancers because of limited treatment options. Surgical removal of the tumour is possible only in its early stage, nevertheless the asymptomatic development very often makes unable an accurate diagnose. In the case of metastatic pancreatic cancer only chemotherapy, mainly with gemcitabine, can be offered to patients. However, common resistance towards gemcitabine imposes...
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Antifungal action of the oxathiolone-fused chalcone derivative
PublicationAMG-148, pochodna chalkonu z pierścieniem oksatiolonowym, wykazuje aktywność przeciwgrzybową in vitro wobec szczepów grzybowych patogennych dla człowieka, z wartościami minimalnych stężeń hamujących wzrost mieszczących się w zakresie 1-16 mikrogramów na mililitr, natomiast w wyższych stężeniach związek ten działa grzybobójczo. Obecność głównych białek oporności wielolekowej, Cdr1p, Cgr2p lub Mdr1p nie wpływa znacząco na aktywność...
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Metal dusting phenomena of 501 AISI furnace tubes in refinery fractional distillation unit
PublicationThe purpose of this investigation was to conduct the failure analysis of 501 AISI furnace tubes places before distillation column in fractional distillation unit. The investigated furnace tubes were planned to work for ten years however after just two years of exploitation <30% of the material left. The observed corrosion process had the intense and complex character. The well-adhered shiny black deposits and deep, round pits were...
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Thermodynamic, Anticoagulant, and Antiproliferative Properties of Thrombin Binding Aptamer Containing Novel UNA Derivative
PublicationThrombin is a serine protease that plays a crucial role in hemostasis, fibrinolysis, cell proliferation, and migration. Thrombin binding aptamer (TBA) is able to inhibit the activity of thrombin molecule via binding to its exosite I. This 15-nt DNA oligonucleotide forms an intramolecular, antiparallel G-quadruplex structure with a chair-like conformation. In this paper, we report on our investigations on the influence of certain...
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Synthesis and application of oligomer with hydroxy groups based on peroxy derivative of ED-24 epoxy resin and POLYTHF-2000 oligoether
PublicationNew oligomer with peroxy, primary and secondary hydroxy groups has been synthesized on the basis of peroxy derivative of ED-24 epoxy resin (PO) and PolyTHF-2000 oligoether according to the developed procedure. The effect of the catalysts nature and amount, temperature and process time on the reaction rate has been studied. Benzyltriethylammonium chloride, potassium hydroxide,1,4-diazobicyclooctane and the mixture composed of benzyltriethylammonium...
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Fractional Derivatives Application to Image Fusion Problems
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Two-Rate Based Low-Complexity Variable Fractional-Delay FIR Filter Structures
PublicationThis paper considers two-rate based structures for variable fractional-delay (VFD) finite-length impulse response (FIR) filters. They are single-rate structures but derived through a two-rate approach. The basic structure considered hitherto utilizes a regular half-band (HB) linear-phase filter and the Farrow structure with linear-phase subfilters. Especially for wide-band specifications, this structure is computationally efficient...
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Epoxy Composites Filled with Natural Calcium Carbonate. 1. Epoxy Composites Obtained in the Presence of Monoperoxy Derivative of Epidian-6 Epoxy Resin
PublicationPhysico-mechanical properties of the products based on filled epoxy-oligomeric mixtures composed of Epidian-5 epoxy resin, oligoesteracrylate TGM-3 and monoperoxide derivative of Epidian-6 epoxy resin (PO) have been investigated. CaCO3 was used as a filler and polyethylene polyamine was a curing agent. The effect of PO and CaCO3 on the gel-fraction content and physico-mechanical properties was examined. Using a scanning electron...
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Investigation of an elutable N-propylphosphonic acid chitosan derivative composition with a chitosan matrix prepared from carbonic acid solution
PublicationPorous chitosan composites using CO2 dissolution procedure and including water soluble N-propylphosphonic chitosan derivative (p-CHI) were obtained and characterized. In contrast to the control material, composites containing modified chitosan distinguished by a rapid moisture absorption and good adhesion to the skin. The FTIR analysis confirmed the presence of propylphosphonic group in the structure of the polymer. The porosity...
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Fractional Delay Filter Design for Sample Rate Conversion
PublicationRosnąca liczba różnych standardów szybkości próbkowania stwarza potrzebę stosowania algorytmów konwersji szybkości próbkowania ciągów dyskretnych. Jeżeli współczynnik przepróbkowania nie jest wyrażony jako stosunek małych liczb całkowitych albo gdy nie jest on stały, to rozwiązaniem może być użycie filtrów ułamkowoopóźniających. Umożliwiają one realizację przepróbkowania z dowolną krotnością. Dokładność przepróbkowania algorytmów...
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Fractional Delay Filter Design with Extracted Window Offsetting
PublicationW pracy przedstawiono koncepcję projektowania filtrów ułamkowoopóźniających (FD) bazującą na metodzie okien. W zaproponowanym podejściu w projektowaniu jest używane okno wyodrębnione z odpowiedzi impulsowej filtru optymalnego offsetowanego o opóźnienie ułamkowe projektowanego filtru. Poszczególne filtry FD zaprojektowany w ten sposób nie są optymalnymi filtrami FD, jednak oferują lepszą jakość w zastosowaniu do zmiany szybkości...
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Stability of Discrete Fractional Order State-space Systems
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Comparison and validation of integer and fractional order ultracapacitor models
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Time domain validation of ultracapacitor fractional order model
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Diffusion process modeling by using fractional-order models
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Synthesis and properties of carboxy derivative of Epidian 6 monomethacrylate (in English)
PublicationWe present the synthesis of an oligomer with carboxy and methacrylic groups based on Epidian 6. The effect of the catalyst nature and amount, solvent nature and process temperature on the rate of the reaction between Epidian6 monomethacrylate and adipic acid was examined at 313, 323 and 333 K in the presence of 4-dimethylaminopyridine, 1,4-diazobicyclo[2.2.2]octane, and benzyltriammonium chloride. The synthesized oligomer was characterized...
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On the derivative of the Legendre function of the first kind with respect to its degree
PublicationPokazano, że pochodna po indeksie funkcji Legendre'a pierwszego rodzaju, obliczona dla całkowitej wartości indeksu, może być wyrażona przez funkcje elementarne. Skonstruowano kilka jawnych reprezentacji tej pochodnej. Zaprezentowano przykłady zastosowań otrzymanych wzorów.
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Unexpected thioketene derivative formation during thioacyl dithiophosphate synthesis.
PublicationZbadano zakres i ograniczenia tioacylowania opartego na ditiofosforanach tioacylu. Ditiofosforany tioacylo otrzymano w wyniku reakcji ditiofosforanów acylu z kwasem ditiofosforowym. Obecność dwóch podstawników w pozycji alfa we fragmencie acylowym faworyzowała tworzenie pochodnych tioketenu tym samym obniżając wydajność oczekiwanych ditiofosforanów tioacylu.
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Carboxy derivative of dioxydiphenylpropane diglycydyl ether monomethacrylate as an addtive for composites
PublicationThe modifier of composites was used in the presence of polyetylene polyamine. Physico-mechanical properties and chemical stability of coatings thus obtained were analyzed.
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Proportional-Derivative and Model-based Controllers used for a Serial Type Manipulator in case of a Variable Mass Payload
PublicationIn the paper, numerical analysis of dynamics of a variable mass system is considered. Its reference example is a serial-like manipulator composed of revolute joints and rigid bodies. Payload of its gripper is considered as its variable mass element (mass and inertia irregularly between subsequent payloads). For the rest of the system, inertia parameters are considered as known (precisely identified during the assembling process)....
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Antitumor 1-nitroacridine derivative C-1748 induces significant apoptosis in pancreatic cancer cells.
PublicationPancreatic cancer is the fifth leading cause of cancer death and has the lowest survival rate of any solid cancer in the industrial countries. The poor prognosis of pancreatic cancer results from its tendency for late presentation, aggressive invasion, early metastasis, and resistance to chemotherapy. Gemcitabine still remains the best chemotherapeutic agent available for the treatment of advanced pancreatic cancer. However, gemcitabine...
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Improvement of time difference of arrival measurements resolution by using fractional delay filters in a direct sequence-code division multiple access radionavigation system
PublicationThis study presents a method of improving time measurements resolution in a direct sequence-code division multiple access receiver by using a fine code tracking loop based on fractional delay filtering of a despreading sequence. It briefly describes the structure of a generic digital code tracking loop and the proposed modification which allows to measure time difference of arrival values with the subsample resolution, together...
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Application of the Fractional Fourier Transform for dispersion compensation in signals from a fiber-based Fabry-Perot interferometer
PublicationOptical methods of measurement do not require contact of a probe and the object under study, and thus have found use in a broad range of applications such as nondestructive testing (NDT), where noninvasive measurement is crucial. Measuring the refractive index of a material can give a valuable insight into its composition. Low‑coherence radiation sources enable measurement of the sample’s properties across a wide spectrum, while...
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A nearly optimal fractional delay filter design with asymmetric window
PublicationW pracy przedstawiono wyniki badań nad zastosowaniem asymetrycznego okna wyodrębnionego zawczasu z filtru optymalnego. Pokazano, że takie podejście przy zastosowaniu dodatkowej korekcji wzmocnienia filtru zależnej od opóźnienia filtru pozwala na projektowanie filtrów prawie optymalnych. W efekcie zaproponowana metoda łączy prostotę metody okien z jakością porównywalną do jakości filtrów optymalnych. Efektywność zaprezentowanej...
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A COMPUTATIONAL ALGORITHM FOR THE NUMERICAL SOLUTION OF NONLINEAR FRACTIONAL INTEGRAL EQUATIONS
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Frequency response based identification of fractional order dynamical systems
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Modelling heat transfer in heterogeneous media using fractional calculus
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Modeling Heat Transfer in Heterogeneous Media Using Fractional Calculus
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