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Search results for: fractional derivations
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Functional delay fractional equations
PublicationIn this paper, we discuss functional delay fractional equations. A Banach fixed point theorem is applied to obtain the existence (uniqueness) theorem. We also discuss such problems when a delay argument has a form α(t) = αt, 0 < α < 1, by Rusing the method of successive approximations. Some existence results are also formulated in this case. An example illustrates the main result.
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Fractional Problems with Right-Handed Riemann-Liouville Fractional Derivatives
PublicationIn this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems...
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On Applications of Fractional Derivatives in Circuit Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the circuit theory. The properties of FO derivatives required for the circuit-level modelling 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 of formulations of the FO derivatives have limited...
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On Applications of Fractional Derivatives in Electromagnetic Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are analysed from the point of view of applications in the electromagnetic theory. The mathematical problems related to the FO generalization of Maxwell's equations are investigated. The most popular formulations of the fractional derivatives, i.e., Riemann-Liouville, Caputo, Grünwald-Letnikov and Marchaud definitions, are considered. Properties of these derivatives are...
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Fractional Derivatives Application to Image Fusion Problems
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Electromagnetic-based derivation of fractional-order circuit theory
PublicationIn this paper, foundations of the fractional-order circuit theory are revisited. Although many papers have been devoted to fractional-order modelling of electrical circuits, there are relatively few foundations for such an approach. Therefore, we derive fractional-order lumped-element equations for capacitors, inductors and resistors, as well as Kirchhoff’s voltage and current laws using quasi-static approximations of fractional-order...
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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
PublicationIn 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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Journal of Derivatives
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Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties
PublicationStarting 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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Progress on Chemistry and Application of Chitin and Its Derivatives
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Review of Derivatives Research
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Extracting functional groups of ALLINI to design derivatives of FDA‐approved drugs: Inhibition of HIV‐1 integrase
PublicationHIV‐1 integrase (IN) is crucial for integration of viral DNA into the host genome and a promising target in development of antiretroviral inhibitors. In this work, six new compounds were designed by linking the structures of two different class of HIV‐1 IN inhibitors (active site binders and allosteric IN inhibitors (ALLINIs)). Among newly designed compounds, INRAT10b was found most potent HIV‐1 IN inhibitor considering different...
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REACTIVE & FUNCTIONAL POLYMERS
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Fractional Differential Calculus
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Fractional Spectral and Fractional Finite Element Methods: A Comprehensive Review and Future Prospects
PublicationIn this article, we will discuss the applications of the Spectral element method (SEM) and Finite element Method (FEM) for fractional calculusThe so-called fractional Spectral element method (f-SEM) and fractional Finite element method (f-FEM) are crucial in various branches of science and play a significant role. In this review, we discuss the advantages and adaptability of FEM and SEM, which provide the simulations of fractional...
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Density Functional Theory Studies on Ir Spectra of the Triphenylene Derivatives. A Scaled Quantum Mechanical Force Field Approach
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Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator
PublicationA new approach is used to investigate the analytical solutions of the mathematical fractional Casson fluid model that is described by the Constant Proportional Caputo fractional operator having non-local and singular kernel near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, and the governing equations were then transformed in non-dimensional form. For the sake of generalized...
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A Note on Fractional Curl Operator
PublicationIn this letter, we demonstrate that the fractional curl operator, widely used in electromagnetics since 1998, is essentially a rotation operation of components of the complex Riemann–Silberstein vector representing the electromagnetic field. It occurs that after the wave decomposition into circular polarisations, the standard duality rotation with the angle depending on the fractional order is applied to the left-handed basis vector...
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Fractional problems with advanced arguments
PublicationThis paper concerns boundary fractional differential problems with advanced arguments. We investigate the existence of initial value problems when the initial point is given at the end point of an interval. Nonhomogeneous linear fractional differential equations are also studied. The existence of solutions for fractional differential equations with advanced arguments and with boundary value problems has been investigated by using...
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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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IR–Raman, NMR and density functional methods in the examination of tautomerism and features of N-methyl substituted 9-acridinamine derivatives
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ADVANCED FUNCTIONAL MATERIALS
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Functional Materials Letters
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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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Boundary problems for fractional differential equations
PublicationIn this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.
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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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Fractional Order Dynamic Positioning Controller
PublicationImproving the performance of Dynamic Positioning System in such applications as station keeping, position mooring and slow speed references tracking requires improving the position and heading control precision. These goals can be achieved through the improvement of the ship control system. Fractional-order calculus is a very useful tool which extends classical, integer-order calculus and is used in contemporary modeling and control...
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Systems of Nonlinear Fractional Differential Equations
PublicationUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives D(T)(q)x and D(T)(q)y. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.
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Fractional differential equations with causal operators
PublicationWe study fractional differential equations with causal operators. The existence of solutions is obtained by applying the successive approximate method. Some applications are discussed including also the case when causal operator Q is a linear operator. Examples illustrate some results.
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Functional Materials
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FUNCTIONAL NEUROLOGY
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FUNCTIONAL ECOLOGY
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Progress in Fractional Differentiation and Applications
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Fractal and Fractional
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Fundamental properties of solutions to fractional-order Maxwell's equations
PublicationIn 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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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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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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A complex variable fractional-delay FIR filter structure
PublicationW 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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Square root RC Nyquist filter of fractional delay
PublicationIn this paper we propose a discrete-time FIR (finite impulse response) filter which couples the role of square root Nyquist filter with fractional delay filter. This filter enables to substitute for a cascade of square root RC (SRRC) Nyquist filter and fractional delay filter in one device/algorithm. The aim is to compensate for transmission delay in communication system. Statistically defined performances, e.g. BER (bit error...
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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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Fractional-order Systems and Synchronous Generator Voltage Regulator
PublicationModern regulators of synchronous generators, including voltage regulators, are digital systems, in their vast majority with standard structures contained in the IEEE standard. These are systems described with stationary differential equations of integral order. Differential equations of fractional order are not employed in regulators for synchronous generator control. This paper presents an analysis of the possibilities of using...
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Derivation of Schwinger variational principles.
PublicationZastosowano metodę Gerjuoy-Rau-Sprucha do skonstruowania zasad wariacyjnych Schwingera dla elementów macierzowych uogólnionego operatora przejścia.
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Functional differential equations
PublicationSformułowano dość ogólne warunki dostateczne na to, aby odpowiednio zdefiniowane ciągi monotoniczne były zbieżne do jedynego, w pewnym segmencie, rozwiązania zagadnienia początkowego dla funkcyjnych równań różniczkowych. Omawiane równanie jest ogólne, a np. zwyczajne równania różniczkowe czy równania różniczkowo-całkowe są jego szczególnymi przypadkami.
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Fractional Calculus and Applied Analysis
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COMPARATIVE AND FUNCTIONAL GENOMICS
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Briefings in Functional Genomics
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Annals of Functional Analysis
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GEOMETRIC AND FUNCTIONAL ANALYSIS
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JOURNAL OF FUNCTIONAL PROGRAMMING
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Functional Composites and Structures
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JOURNAL OF FUNCTIONAL ANALYSIS
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Journal of Functional Foods
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STEREOTACTIC AND FUNCTIONAL NEUROSURGERY
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Simulation of Signal Propagation Along Fractional-Order Transmission Lines
PublicationIn this paper, the simulation method of signal propagation along fractional-order (FO) transmission lines is presented. Initially, fractional calculus and the model of FO transmission line are introduced. Then, the algorithm allowing for simulation of the nonmonochromatic wave propagation along FO transmission lines is presented. It employs computations in the frequency domain, i.e., an analytical excitation is transformed to the...
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Simulation of Wave Propagation in Media Described by Fractional-Order Models
PublicationIn 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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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector
PublicationIn 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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Signal propagation in electromagnetic media described by fractional-order models
PublicationIn this paper, signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain. Then, their phasor representation is derived for one-dimensional case of the plane wave propagation. With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced....
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublicationIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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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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Point to point control of fractional differential linear control systems
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Numerical solution of fractional neutron point kinetics in nuclear reactor
PublicationThis 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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Variable Fractional Delay Filter Design Using a Symmetric Window
PublicationIn 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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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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efficient fractional delay hilbert transform filter in the farrow structure
PublicationIn this paper the design and application of a Fractional Delay Hilbert Transform Filter (FDHTF) into an adaptive sub-sample delay estimation between two separated sinusoidal signals is considered. The FDHTF incorporates the functions of Hilbertian and variable fractional delay filtering of the incoming signal simultaneously, in one stage. In traditional approach each of these operations was performed separately. Obtained value...
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Fractional equations of Volterra type involving a Riemann Liouville derivative
PublicationIn 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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On Sample Rate Conversion Based on Variable Fractional Delay Filters
PublicationThe sample rate conversion algorithm based on variable fractional delay filters is often used if the resampling ratio cannot be expressed as the ratio of small integer numbers or if it is not constant. The main advantage of such solution is that it allows for arbitrary resampling ratios which can even be changed during the resampling process. In this paper a discussion on influence of different approaches to fractional filter...
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Parabolic Equations with Functional Dependence
PublicationWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence and prove theorems on the existence of solutions to parabolic differential-functional equations.
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Difference functional inequalities and applications.
PublicationThe paper deals with the difference inequalities generated by initial boundary value problems for hyperbolic nonlinear differential functional systems. We apply this result to investigate the stability of constructed difference schemes. The proof of the convergence of the difference method is based on the comparison technique, and the result for difference functional inequalities is used. Numerical examples are presented.
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Functional safety and managing competence
PublicationSą nowe wyzwania związane z badaniami, edukacją i szkoleniem w obszarach bezpieczeństwa i ochrony systemów i sieci krytycznych. W rozdziale podkreśla się, że kompetencje specjalistów powinny być kształtowane w zintegrowanych procesach edukacji i szkolenia. Dlatego uzasadnione jest, aby opracować w Europie standardy i programy kształcenia na bazie odpowiednich prac badawczych i najlepszych doświadczeń z praktyki przemysłowej w celu...
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Functional safety and human factors
PublicationRozdział przedstawia istotny problem uwzględnienia czynników ludzkich (H&OF) w analizie bezpieczeństwa funkcjonalnego, które wpływają istotnie na bezpieczeństwo przemysłowych obiektów podwyższonego ryzyka, nie ujęty jednak w normach bezpieczeństwa funkcjonalnego. Przedstawia się metody analizy niezawodności człowieka (HRA) w kontekście tych czynników, które wpływają na błędy człowieka. Czynniki ludzkie i organizacyjne powinny być...
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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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Signal Propagation in Electromagnetic Media Modelled by the Two-Sided Fractional Derivative
PublicationIn this paper, wave propagation is considered in a medium described by a fractional-order model, which is formulated with the use of the two-sided fractional derivative of Ortigueira and Machado. Although the relation of the derivative to causality is clearly specified in its definition, there is no obvious relation between causality of the derivative and causality of the transfer function induced by this derivative. Hence, causality...
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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublicationIn 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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Neural Approximators for Variable-Order Fractional Calculus Operators (VO-FC)
PublicationThe 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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Farrow structure implementation of fractional delay filter optimal in Chebyshev sense
PublicationW pracy omówiono problematykę implementacji filtrów ułamkowych opóźniających o zmiennym opóźnieniu w oparciu o strukturę Farrowa. Podejście to polega na obliczeniu próbek nowej odpowiedzi impulsowej filtru dla każdego wymaganego opóźnienia w opraciu o wielomiany o współczynnikach niezależnych od opóźnienia. Prowadzi to do znacznego zmniejszenia kosztów numerycznych implementacji w zastosowaniach wymagających częstej zmiany opóźnienia...
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Ultracapacitor modeling and control with discrete fractional order artificial neural network
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Adaptive Feedback Control of Fractional Order Discrete State-Space Systems
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A NUMERICAL STUDY ON THE DYNAMICS OF DENGUE DISEASE MODEL WITH FRACTIONAL PIECEWISE DERIVATIVE
PublicationThe 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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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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Variable Ratio Sample Rate Conversion Based on Fractional Delay Filter
PublicationIn 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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Fractional delayor application in self-tuning sub-sample delay estimator
PublicationW artykule przedstawiono nowe rozwiązanie samonastrajalnego estymatora opóźnienia sygnału sinusoidalnego. Estymator działa w czasie dyskretnym. Proponowane rozwiązanie wykorzystuje kaskadowe połączenie cyfrowego filtru ułamkowo opóźniającego służącego do synchronizacji próbkowania i liniowo-fazowego cyfrowego filtru Hilberta. Oryginalność polega na zastosowaniu tu filtrów cyfrowych o bardzo małej złożoności numerycznej. Jest ona...
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Gain deficit effect in the fractional delay filter design by the window method
PublicationMetoda okien jest sposobem szybkiego i skutecznego projektowania filtrów ułamkowoopóźniających. Jednakże wzmocnienie tak zaprojektowanego filtru różni się od zakładanej wartości idealnej. To zjawisko, nazywane deficytem wzmocnienia, negatywnie wpływa na jakoś projektowanego filtru. Artykuł poświęcono wynikom badań oraz metodom korekcji tego problemu. Omówiono wpływ współczynnika korekcji deficytu wzmocnienia na charakterystykę...
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Existence results to delay fractional differential equations with nonlinear boundary conditions
PublicationPraca dotyczy problemów brzegowych dla ułamkowych równań różniczkowych z opóźnionym argumentem. Podano warunki dostateczne na istnienie rozwiązań ekstremalnych takich zagadnień.
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Extracted window offsetting using maximally flat fractional delay filter
PublicationW pracy przedstawiono koncepcję projektowania filtru ułamkowoopóźniającego (FD) z wykorzystaniem metody okien offsetowanych. W zaproponowanym podejściu jako okna prototypowego, offsetowanego o opóźnienie ułamkowe projektowanego filtru, użyto okna wyodrębnionego z odpowiedzi impulsowej filtru optymalnego. Zaprojektowane w ten sposób filtry FD nie są optymalne jednak zapewniają lepszą jakość algorytmu zmiany szybkości próbkowania...
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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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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublicationWe 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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Inner derivations of special subrings of matrix rings and outerplanar digraphs.
PublicationTematem artykułu jest specjalny podpierścień pierścienia macierzy wyznaczony przez relację oraz digraf reprezentujący tę relację. Rozważane są takie relacje, dla których reprezentujące je digrafy są zewnętrznie planarne. W tym przypadku zostały udowodnione warunki konieczne i wystarczające na to, aby różniczkowanie pierścienia było wewnętrzne.
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Nanocrystalline cathode functional layer for SOFC
PublicationRecently, it was shown that thin functional layers introduced between an electrolyte and cathode might improve cathode performance. However, the mechanism of this improvement still needs analysis. In this paper, a thin (∼140 nm), spin-coated perovskite layer (La0.6Sr0.4Co0.2Fe0.8O3-δ) was placed between a cathode (La0.6Sr0.4Co0.2Fe0.8O3-δ) and an electrolyte (Ce0.8Gd0.2O2-δ) and the effects of this investigated. The microstructure...
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Multislice CT in functional cardiac exploration.
PublicationArtykuł przedstawia analizę oraz omówienie wykonanych badań w zastosowaniu tomografia wielorzędowej w diagnostyce czynnościowej serca. Pokazano zarówno aspekty technicznej metody jak i możliwości zastosowań medycznych.
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Functional differential equations of second order.
PublicationPraca dotyczy problemu brzegowego dla równań różniczkowo-funkcyjnych 2-go rzędu. Stosując metodę kwasilinearyzacji pokazano, że odpowiednio skonstruowane ciągi monotoniczne są zbieżne do jedynego rozwiązania danego problemu i ustalono szybkość tej zbieżności. Pokazano również pewną relację pomiędzy rozwiązaniami odpowiednich liniowych równań różniczkowo-funkcyjnych z warunkami brzegowymi.
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Security aspects in functional safety analysis
PublicationA security level of distributed control and protection system may have a significant impact on the results of functional safety analysis. However, the issue of integrating the safety and security aspects is difficult and usually is neglected during the functional safety analysis. This article presents a method of functional safety analysis which takes into consideration a concept of integrating these two aspects. It is based on...