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Search results for: LINEAR APPROXIMATION
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Stability by linear approximation for time scale dynamical systems
PublicationWe study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents...
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Stability by linear approximation for time scale dynamical systems
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Approximation of the non-linear roll damping
PublicationArtykuł omawia, jak otrzymać oszacowanie nieliniowego momentu tłumiącehgo kołysania boczne okretu za pomocą zapisu przebiegu kołysań swobodnych modelu okrętu. Udowadnia, że 1) moment tłumiący w kategoriach aproksymacji jest nieanalityczną funkcją nieparzystą prędkosci kołysań, 2) standardowa metoda, oparta na stosunku dwóch kolejnych amplitud, ma ograniczone zastosowanie, do niezbyt dużych amplitud kołysań. Zaproponowano nową metodą...
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Errors of a Linear Current Approximation in High-Speed PMSM Drives
PublicationCurrent sampling techniques and predictive algorithms used in the digital control of electric drives rely on a simple mathematical model that assumes linear current changes upon constant supplying voltages. This paper identifies rotor movement as a factor that makes this assumption invalid when the rotor covers an angular distance of a few tens of degrees during the control interval duration. The errors of the linear current approximation...
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Approximation Strategies for Generalized Binary Search in Weighted Trees
PublicationWe consider the following generalization of the binary search problem. A search strategy is required to locate an unknown target node t in a given tree T. Upon querying a node v of the tree, the strategy receives as a reply an indication of the connected component of T\{v} containing the target t. The cost of querying each node is given by a known non-negative weight function, and the considered objective is to minimize the total...
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Impact of Low Switching-to-Fundamental Frequency Ratio on Predictive Current Control of PMSM: A simulation study
PublicationPredictive current control algorithms for permanent magnet synchronous (PMSM) drives rely on an assumption that within short intervals motor currents can be approximated with linear functions. This approximation may result either from discretizing the motor model or from simplifications applied to the continuous-time model. As the linear current approximation has been recognized as inaccurate in case when the drive operates with...
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On FEM analysis of Cosserat-type stiffened shells. Static and stability linear analysis
PublicationThe present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads to the conforming shell and beam...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublicationIn this article, specific methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublicationIn this study, dedicated methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Constant-Factor Approximation Algorithm for Binary Search in Trees with Monotonic Query Times
PublicationWe consider a generalization of binary search in linear orders to the domain of weighted trees. The goal is to design an adaptive search strategy whose aim is to locate an unknown target vertex of a given tree. Each query to a vertex v incurs a non-negative cost ω(v) (that can be interpreted as the duration of the query) and returns a feedback that either v is the target or the edge incident to v is given that is on the path towards...
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Polypyrrole based gas sensor for ammonia detection
PublicationThe nature of polypyrrole response to toxic gases does not allow using the sensor in a conventional way. The main aim of this study is to acquire the information about the concentration using different approaches: a linear approximation, a non-linear approximation and a tangent method. In this paper a two-steps procedure for sensor response measurements has been utilized. Polypyrrole films were electrochemically synthesized on...
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Gas sensors based on conducting polymers-recent developments
PublicationThis work discusses sensing performance dependence of PEDOT polymer and its composites on the counter ions used in the polymerization process. The sensors based on PEDOT-RGO composite show reversible response to NO2, while on PEDOT/LiClO4 irreversible. As a result, PEDOT-RGO could be used as a typical gas sensor, while sensor based PEDOT/LiClO4 could be used as an integrating gas sensor, also known as an accumulating gas sensor....
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Drilling couples and refined constitutive equations in the resultant geometrically non-linear theory of elastic shells
PublicationIt is well known that distribution of displacements through the shell thickness is non-linear, in general. We introduce a modified polar decomposition of shell deformation gradient and a vector of deviation from the linear displacement distribution. When strains are assumed to be small, this allows one to propose an explicit definition of the drilling couples which is proportional to tangential components of the deviation vector....
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Discrete identification of continuous non-linear and non-stationary dynamical systems that is insensitive to noise correlation and measurement outliers
PublicationThe paper uses specific parameter estimation methods to identify the coefficients of continuous-time models represented by linear and non-linear ordinary differential equations. The necessary approximation of such systems in discrete time in the form of utility models is achieved by the use of properly tuned `integrating filters' of the FIR type. The resulting discrete-time descriptions retain the original continuous parameterization...
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Sensitivity analysis of critical loads of I-columns
PublicationThe first order variation of critical buckling load of thin-walled columns with bisymmetric open cross-section due to some variations of the design variables such as: cross-section dimensions, or material characteristics is derived. The influence of the residual welding stresses is taken into account. In the numerical examples dealing with I-column the functions describing the effect of the variation of the dimensions of the flange...
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Application of regularized Savitzky–Golay filters to identification of time-varying systems
PublicationSavitzky–Golay (SG) filtering is a classical signal smoothing technique based on the local least squares approximation of the analyzed signal by a linear combination of known functions of time (originally — powers of time, which corresponds to polynomial approximation). It is shown that the regularized version of the SG algorithm can be successfully applied to identification of time-varying finite impulse response (FIR) systems....
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Fast Basis Function Estimators for Identification of Nonstationary Stochastic Processes
PublicationThe problem of identification of a linear nonsta-tionary stochastic process is considered and solved using theapproach based on functional series approximation of time-varying parameter trajectories. The proposed fast basis func-tion estimators are computationally attractive and yield resultsthat are better than those provided by the local least squaresalgorithms. It is shown that two...
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Electrostatic interactions in finite systems treated with periodic boundary conditions: Application to linear-scaling density functional theory
PublicationWe present a comparison of methods for treating the electrostatic interactions of finite, isolated systems within periodic boundary conditions (PBCs), within density functional theory (DFT), with particular emphasis on linear-scaling (LS) DFT. Often, PBCs are not physically realistic but are an unavoidable consequence of the choice of basis set and the efficacy of using Fourier transforms to compute the Hartree potential. In such...
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Artificial Thermal Ageing of Polyester Reinforced and Polyvinyl Chloride Coated Technical Fabric
PublicationArchitectural fabric AF9032 has been subjected to artificial thermal ageing to determine changes of the material parameters of the fabric. The proposed method is based on the accelerated ageing approach proposed by Arrhenius. 300 mm x 50 mm samples were cut in the warp and fill directions and placed in a thermal chamber at 80 °C for up to 12 weeks or at 90 °C for up to 6 weeks. Then after one week of conditioning at ambient temperature,...
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Enhancing capabilities of Atomic Force Microscopy by tip motion harmonics analysis
PublicationMotion of a tip used in an atomic force microscope can be described by the Lennard-Jones potential, approximated by the van der Waals force in a long-range interaction. Here we present a general framework of approximation of the tip motion by adding three terms of Taylor series what results in non-zero harmonics in an output signal. We have worked out a measurement system which allows recording of an excitation tip signal and its...
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Convergence of rational multistep methods of of Adams-Padé type
PublicationRational generalizations of multistep schemes, where the linear stiff part of a given problem is treated by an A-stable rational approximation, have been proposed by several authors, but a reasonable convergence analysis for stiff problems has not been provided so far. In this paper we directly relate this approach to exponential multistep methods, a subclass of the increasingly popular class of exponential integrators. This natural,...
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Global Optimization for Recovery of Clipped Signals Corrupted With Poisson-Gaussian Noise
PublicationWe study a variational formulation for reconstructing nonlinearly distorted signals corrupted with a Poisson-Gaussian noise. In this situation, the data fidelity term consists of a sum of a weighted least squares term and a logarithmic one. Both of them are precomposed by a nonlinearity, modelling a clipping effect, which is assumed to be rational. A regularization term, being a piecewise rational approximation of the ℓ0 function...
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Parameters’ Identification of Perzyna and Chaboche Viscoplastic Models for Aluminum Alloy at Temperature of 120◦C
PublicationThe main purpose of this paper is the parameters identification of the Perzyna and the Chaboche models for the aluminum alloy at elevated temperature. The additional purpose is comparison of the results for these viscoplastic models. The results have been verified by the numerical simulation of the laboratory tests. The material parameters have been calculated on the basis of the uniaxial tension test. The determination of the...
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2-Coloring number revisited
Publication2-Coloring number is a parameter, which is often used in the literature to bound the game chromatic number and other related parameters. However, this parameter has not been precisely studied before. In this paper we aim to fill this gap. In particular we show that the approximation of the game chromatic number by the 2-coloring number can be very poor for many graphs. Additionally we prove that the 2-coloring number may grow...
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Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines: Complexity and Algorithms
PublicationIn this paper, the problem of scheduling on parallel machines with a presence of incompatibilities between jobs is considered. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine. The paper provides several results concerning schedules, optimal or approximate with respect to the two most popular criteria of optimality:...
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Analysis of Floodplain Inundation Using 2D Nonlinear Diffusive Wave Equation Solved with Splitting Technique
PublicationIn the paper a solution of two-dimensional (2D) nonlinear diffusive wave equation in a partially dry and wet domain is considered. The splitting technique which allows to reduce 2D problem into the sequence of one-dimensional (1D) problems is applied. The obtained 1D equations with regard to x and y are spatially discretized using the modified finite element method with the linear shape functions. The applied modification referring...
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Electron scattering from tin tetrachloride (SnCl4) molecules
PublicationAbsolute grand-total cross section (TCS) for electron scattering from a tin tetrachloride, SnCl4, molecule was measured at electron-impact energies ranging from 0.6 to 300 eV, in the linear electron-transmission experiment. The measured TCS energy dependence shows two very pronounced enhancements peaking near 1.2 eV and around 9.5 eV, separated with a deep minimum centered close to 3 eV. The low energy structure is attributed to...
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Stateczność i niezawodność pełnomorskich platform wiertniczych
PublicationW pracy przedstawiono wieloletnie doświadczenia Autora w zakresie wybranych aspektów numerycznej analizy pełnomorskich platform wiertniczych, w szczególności stacjonarnych platform stalowych poddanych działaniu fal wiatrowych i wiatru. W opisie zachowania się platform uwzględniono współoddziaływanie trzech ośrodków: materiału konstrukcji, morskich fal wiatrowych i podłoża gruntowego. Przyjęcie do opisu stochastycznych właściwości...
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Efficient Multi-Fidelity Design Optimization of Microwave Filters Using Adjoint Sensitivity
PublicationA simple and robust algorithm for computationally efficient design optimiza-tion of microwave filters is presented. Our approach exploits a trust-region (TR)-based algorithm that utilizes linear approximation of the filter response obtained using adjoint sensitivity. The algorithm is sequentially executed on a family of electromagnetic (EM)-simulated models of different fidelities, starting from a coarse-discretization one, and...
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Noise sources in Raman spectroscopy of biological objects
PublicationWe present an overview of noise sources deteriorating the quality of the recorded biological Raman spectra and the ability to determine the specimen composition. The acquired Raman spectra exhibit intense additive noise components or drifts because of low intensity of the scattered light. Therefore we have to apply expensive or bulky measurement setups to limit their inherent noise or to apply additional signal processing to reduce...
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Application of the Monte Carlo algorithm for solving volume integral equation in light scattering simulations
PublicationVarious numerical methods were proposed for analysis of the light scattering phenomenon. Important group of these methods is based on solving the volume integral equation describing the light scattering process. The popular method from this group is the discrete dipole approximation (DDA). DDA uses various numerical algorithms to solve the discretized integral equation. In the recent years, the application of the Monte Carlo (MC)...
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Thermal visualization of Ostwald-de Waele liquid in wavy trapezoidal cavity: Effect of undulation and amplitude
PublicationThe present study is concerned with the numerical simulations of Ostwald-de Waele fluid flow in a wavy trapezoidal cavity in the presence of a heated cylinder situated at the center of the cavity. The work consists in characterizing the mixed convection as a function of the intensity of heat flow. The flow behaviour and temperature distribution in a cavity are the main focus of this study. The lower wall of the cavity is fixed...
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Radiative lifetime of a BODIPY dye as calculated by TDDFT and EOM-CCSD methods: solvent and vibronic effects
PublicationThe radiative emission lifetime and associated S1 excited state properties of a BODIPY dye are investigated with TDDFT and EOM-CCSD calculations. The effects of a solvent are described with the polarizable continuum model using the linear response (LR) approach as well as state-specific methods. The Franck–Condon (FC), Herzberg–Teller (HT) and Duschinsky vibronic effects are evaluated for the absorption and emission spectra, and...
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Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines
PublicationIn this paper we consider a problem of job scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine. Our research stems from the works of Bodlaender, Jansen, and Woeginger (1994) and Bodlaender and Jansen (1993). In particular, we pursue the...
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Joint experimental and theoretical study on electron scattering from titanium tetrachloride (TiCl4) molecule
PublicationAbsolute grand-total cross section for electron scattering from titanium tetrachloride, TiCl4, molecule was measured at electron-impact energies ranging from 0.3 to 300 eV, in the linear electron-transmission experiment. The elastic integral, differential, momentum transfer, and total ionization cross sections for TiCl4 molecule were also calculated for low and intermediate collisional energies at the level of various theories. The...
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The Experimental Determination of Bearings Dynamic Coefficients in a Wide Range of Rotational Speeds, Taking into Account the Resonance and Hydrodynamic Instability
PublicationMethods for the experimental determination of dynamic coefficients are commonly used for the analysis of various types of bearings, including hydrodynamic, aerodynamic and foil bearings. There are currently several algorithms that allow estimating bearing dynamic coefficients. Such algorithms usually use various excitation techniques applied to rotor–bearings systems. So far only a small number of scientific publications show how...
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Cross-sections for electron-scattering from 2-methyl-1-buten-3-yne, C 5 H 6 , molecules
PublicationtCross-sections for electron collisions with the 2-methyl-1-buten-3-yne [H2C C(CH3)C CH] moleculewere measured and calculated. Absolute grand-total electron-scattering cross-section (TCS) was takenat impact energies from 0.6 to 300 eV in the linear electron-transmission experiment. The TCS energydependence for the electron–C5H6collision has two prominent enhancements separated with a deepminimum located near 1.8 eV. In addition,...
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approximation of photonic crystal fibres with large air holes by the step index fibre model
PublicationAn equivalent step index fibre with a silica core and air cladding is used to model photonic crystal fibres with large air holes. We model this fibre for linear polarisation (we focus on the lowest few transverse modes of the electromagnetic field). The equivalent step index radius is obtained by equating the lowest two eigenvalues of the model to those calculated numerically for the photonic crystal fibres. The step index parameters...
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Scattering of electrons by a 1,2-butadiene (C4H6) molecule: measurements and calculations
PublicationWe present the results of experimental and theoretical study on electron collisions with a 1,2-butadiene (H2C=C=CHCH3) molecule. Absolute grand-total cross sections (TCSs) were measured using a linear electron-transmission method for collision energies in the 0.5–300 eV range. Two distinct features in the TCS energy curve were detected: a narrow peak located at 2.3 eV and a broad enhancement centered around 9 eV. We attributed...
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Synteza układu sterowania statkiem morskim dynamicznie pozycjonowanym w warunkach niepewności
PublicationNiniejsza monografia obejmuje zagadnienia związane z syntezą układu dynamicznego pozycjonowania statku w środowisku morskim z zastosowaniem wybranych nieliniowych metod sterowania. W ramach pracy autorka rozważała struktury sterowania z zastosowaniem wektorowej adaptacyjnej metody backstep oraz metod jej pokrewnych, takich jak regulatory MSS (ang. multiple surface sliding), DSC (ang. dynamic surface control), NB (ang. neural backstepping)....
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Optimization of the Hardware Layer for IoT Systems using a Trust Region Method with Adaptive Forward Finite Differences
PublicationTrust-region (TR) algorithms represent a popular class of local optimization methods. Owing to straightforward setup and low computational cost, TR routines based on linear models determined using forward finite differences (FD) are often utilized for performance tuning of microwave and antenna components incorporated within the Internet of Things systems. Despite usefulness for design of complex structures, performance of TR methods...
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Electron collisions with methyl-substituted ethylenes: Cross section measurements and calculations for 2-methyl–2-butene and 2,3-dimethyl–2-butene
PublicationWe report electron-scattering cross sections determined for 2-methyl–2-butene [(H3C)HC==C(CH3)2] and 2,3-dimethyl–2-butene [(H3C)2C=C(CH3)2] molecules. Absolute grand-total cross sections (TCSs) were measured for incident electron energies in the 0.5–300 eV range, using a linear electron-transmission technique. The experimental TCS energy dependences for the both targets appear to be very similar with respect to the shape. In each...
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Structural properties of hydration shell around various conformations of simple polypeptides
PublicationIn this paper we investigate structural properties of water within the solvation shell around the peptide core created by a well-defined conformation of polypeptide chain. The following secondary structures are investigated: linear (straight chain), and three helices PII (polyproline-like), 310, and α. We propose using the two-particle contribution to entropy as a rational measure of the water structural ordering within the solvation...
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Direct Constraint Control for EM-Based Miniaturization of Microwave Passives
PublicationHandling constraints imposed on physical dimensions of microwave circuits has become an important design consideration over the recent years. It is primarily fostered by the needs of emerging application areas such as 5G mobile communications, internet of things, or wearable/implantable devices. The size of conventional passive components is determined by the guided wavelength, and its reduction requires topological modifications,...
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Representation of magnetic hysteresis in a circuit model of a single-phase transformer
PublicationThe paper presents a mathematical model for the hysteresis phenomenon in a multi-winding single-phase core type transformer. The set of loop differential equations was developed for K-th winding transformer model where the flux linkages of each winding includes a flux common Φ to all windings as function of magneto motive force Θ of all windings. The first purpose of this paper is to determine a hysteresis nonlinearity involved...
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Scheduling of compatible jobs on parallel machines
PublicationThe dissertation discusses the problems of scheduling compatible jobs on parallel machines. Some jobs are incompatible, which is modeled as a binary relation on the set of jobs; the relation is often modeled by an incompatibility graph. We consider two models of machines. The first model, more emphasized in the thesis, is a classical model of scheduling, where each machine does one job at time. The second one is a model of p-batching...
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Entropy of water calculated from harmonic approximation: estimation of the accuracy of method
PublicationSome molecular dynamics simulations were performed for liquid TIP4P and SPC water at a constant density (1.00 g/cm(3)) and within the temperature range of 5-90 degrees C. By using harmonic approximation, both the entropy of water S-H and the specific heat c(v) were calculated, and the results were compared to literature data. It was found that harmonic approximation overestimates absolute entropy of TIP4P water by 5.6 J/mol K (similar...
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PROPERTIES OF ONE DIMENSIONAL OPEN-CHANNEL STEADY FLOW EQUATIONS
PublicationIn this paper properties of discrete forms of one dimensional steady gradually varied flow equations are discussed. Such forms of flow equations are obtained as a result of approximation of their differential forms, which is required to solve them numerically. For such purpose explicit or implicit numerical approximation schemes for ordinary differential equations can be applied. It turns out that dependently on the chosen approximation...
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Improved magnitude estimation of complex numbers using alpha max and beta min algorithm
PublicationThe paper presents an improved algorithm for calculating the magnitude of complex numbers. This problem, which is a special case of square rooting, occurs for example, in FFT processors and complex FIR filters. The proposed method of magnitude calculation makes use of the modified alpha max and beta min algorithm. The improved version of the algorithm allows to control the maximum magnitude approximation error by using an adequate...
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On the approximation of the UWB dipole elliptical arms with stepped-edge polygon
PublicationA simple method of approximation of the ellipticalpatch with stepped-edge polygon is proposed as an introductionto wider studies over the planar ultrawideband (UWB) antennas.The general idea is to replace the elliptical patch with an equivalentpolygonal patch, with minimum loss in the performance. Theprinciples of the proposed method are presented in this letter, aswell as the results of performed numerical studies and its experimentalverification....