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Search results for: FRACTAL CURVES
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Crystallization of space: Space-time fractals from fractal arithmetic
PublicationFractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated...
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Bifractal receiver operating characteristic curves: a formula for generating receiver operating characteristic curves in credit-scoring contexts
PublicationThis paper formulates a mathematical model for generating receiver operating characteristic (ROC) curves without underlying data. Credit scoring practitioners know that the Gini coefficient usually drops if it is only calculated on cases above the cutoff. This fact is not a mathematical necessity, however, as it is theoretically possible to get an ROC curve that keeps the same Gini coefficient no matter how big a share of lowest...
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Facial features extraction for color, frontal images
PublicationThe problem of facial characteristic features extraction is discussed. Several methods of features extraction for color en--face photographs are discussed. The methods are based mainly on the colors features related to the specific regions of the human face. The usefulness of presented methods was tested on a database of en--face photographs consisting of 100 photographs.
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Simple Fractal Calculus from Fractal Arithmetic
PublicationNon-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resulting definitions of derivatives and integrals are simpler from what one finds in the more traditional literature of the subject, and they often work in the cases where the standard methods fail. As an illustration, we perform a Fourier transform of a real-valued...
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Violence at the workplace—a questionnaire survey of nurses
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Waves Along Fractal Coastlines: From Fractal Arithmetic to Wave Equations
PublicationBeginning with addition and multiplication intrinsic to a Koch-type curve, we formulate and solve wave equation describing wave propagation along a fractal coastline. As opposed to examples known from the literature, we do not replace the fractal by the continuum in which it is embedded. This seems to be the first example of a truly intrinsic description of wave propagation along a fractal curve. The theory is relativistically...
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University of the future: a fractal oganization of knowledge
PublicationW opracowaniu przedstawiono wizję uniwersytetu przyszłości jako organizacji fraktalnej. Pokazano cechy wspólne organizacji fraktalnej i uniwersytetu ewoluującego w kierunku organizacji podporzadkowanej wiedzy.
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Fractal local fields in random composites
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Generating fractal tiles using Voronoi diagrams
PublicationPraca opisuje szczególną klasę podziałów powierzchni n-wymiarowego torusa na komórki o fraktalnym brzegu. Zbiór komórek przejawia nietypowe własności samopodobieństwa, może zostać użyty do wypełnienia przestrzeni R^n w sposób periodyczny lub aperiodyczny ze zmienną gęstością podziałów. Zaproponowany został algorytm do generowania takich podziałów używając diagramów Woronoja. Opisana metoda może mieć zastosowania w grafice komputerowej.
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Gas bubble dynamics - experiment and fractal analysis.
PublicationPrzedstawiono nieliniowe aspekty generowania pęcherzyków gazowych z dysz szklanych umieszczonych pod powierzchnią cieczy. W badaniach eksperymentalnych zastosowano układ laser diodowy- fotodetektor oraz hydrofon. Sygnały z fotodetektora i hydrofonu były wzmacniane, rejestrowane za pomocą karty dźwiękowej, a następnie poddane analzie fraktalnej. W wyniku obliczeń ustalono mapy występowania chaosu w funkcji strumienia objętości gazu.
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Statistical and fractal analysis of human heart dynamics.
PublicationPrzedstawiono sposób obliczania podstawowych i bardziej zaawansowanych (dyskrepancja) wielkości statystycznych do analizy dynamiki ludzkiego serca. Oprócz analizy statystycznej pokazano elementy analizy fraktalnej (wykresy Poincare). Przedstawiona analiza umożliwia wykrywanie patologicznych sytuacji i jest pomocna lekarzom w diagnostyce.
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Fractal analysis and modelling of gas bubble formation.
PublicationPrzedstawiono wyniki badań eksperymentalnych generowania pęcherzyków powietrznych z dysz o różnej średnicy, umieszczonych pod powierzchnią wody. Sygnał rejestrowany przez układ laser-fotodioda poddano analizie fraktalnej.
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Fractal dimension for bending–torsion fatigue fracture characterisation
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Compact CPW-fed Sierpinski fractal monopole antenna.
PublicationZaproponowano nową wielozakresową strukturę antenową dla zastosowań wielosystemowych. Jest to zminiaturyzowana antena monopolowa planarna, której obwód zaprojektowano wykorzystując czwartego rzędu iterację trójkąta Sierpińskiego ze współczynnikiem skali d=1.5. Antenę wykonano na podłożu dielektrycznym i zasilono wykorzystując falowód koplanarny. Badania parametrów wykonanego modelu potwierdziły wielozakresową pracę struktury.
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Compact antenna array comprising fractal-shaped microstripradiators
PublicationA design method of antenna array consisting of eight microstrip patches modified with Sierpinski fractal curves has been presented andexperimentally validated in this paper. Method proposed has enabled the achievement of considerable miniaturization of array length (26%),together with multi-band behavior of the antenna, which proves the attractiveness of presented design methodology and its ability to be implemented in more complex...
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Fractal dimension for bending–torsion fatigue fracture characterisation
PublicationFracture surfaces after biaxial fatigue tests were compared using fractal dimension for three types of metallic materials in smooth and notched specimens made of S355J2 and 10HNAP steels and 2017-T4 aluminium alloy, considering both proportional and nonproportional cyclic loading. High-resolution optical 3D measurement studies were performed on the entire fracture surface. A direct correlation between fractal dimension and fatigue...
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Slow-wave fractal-shaped compact microstrip resonant cell
PublicationA novel fractal-shaped compact microstrip resonant cell (CMRC) featuring a strong slow-wave effect has been presented. Its vital usefulness in the process of microstrip line miniaturisation has been proved and experimentally validated on the basis of a compact 3-dB branch-line coupler illustrating the possibilities of the approach. A prototype example structure has been designed to mirror the characteristics of a conventional device,...
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Fractal analysis of the bending-torsion fatigue fracture of aluminium alloy
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Singular curves in the resultant thermomechanics of shells
PublicationSome geometric and kinematic relations associated with the curve moving on the shell base surface are discussed. The extended surface transport relation and the extended surface divergence theorems are proposed for the piecewise smooth tensor fields acting on the regular and piecewise regular surfaces. The recently formulated resultant, two-dimensionally exact, thermodynamic shell relations - the balances of mass, linear and angular...
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Prospects in elongation of railway transition curves
PublicationThe paper presents an analysis of the elongation of transition curves in relation to railway track alignment correction and modernisation. The analysis is based on numerical computations for a wide range of parameters describing a typical railway geometrical layout with transition curves. The differences between the horizontal ordinates of the existing layout and the layout with the elongated transition curves are evaluated and...
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Analytical design method of reverse curves
PublicationThe paper deals with a new approach relating to the design of the region of railway track direction alteration adapted to Mobile Satellite Measurements technique. The method may be particularly useful in situations when both the straights of the route directions cannot be connected in an elementary way using a circular arc with transition curves; this also refers to the application of a compound curve. Thus the only solution becomes...
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Novel microstrip low-pass filters with fractal defected ground structures
PublicationIn this study, three microstrip low-pass filters (LPFs) containing fractal-shaped defected ground structures have been designed and manufactured. To improve the performance of microstrip LPF, cascades of inductively coupled fractal resonators have been applied. Simultaneously, to achieve relatively constant microstrip impedance resulting in essentially low reflection losses, a modification of the strip geometry has been introduced....
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Sensivity of echo envelope fractal dimension to bottom type and bottom depth.
PublicationPrzedstawiono wynik badania zależności pomiędzy wymiarem fraktalnym obwiedni echa akustycznego od dna a rodzajem dna na wpływ głębokości dna na tę zależność. Wykorzystano sygnały ech otrzymane w wyniku numerycznych symulacji rozpraszania na granicy woda dno dla różnych głębokości dna.
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Diffusion equations with spatially dependent coefficients and fractal Cauer-type networks
PublicationIn this article, we formulate and solve the representation problem for diffusion equations: giving a discretization of the Laplace transform of a diffusion equation under a space discretization over a space scale determined by an increment h > 0, can we construct a continuous in h family of Cauer ladder networks whose constitutive equations match for all h > 0 the discretization. It is proved that for a finite differences discretization...
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Dynamics of Railway Vehicles Movement on Transition Curves
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Floodable length curves based on probability of survival.
PublicationPrzedstawiono możliwość obliczanie krzywych grodziowych dla statku o mieszanym podziale grodziowym dla zadanej wartości mnożnika s, traktowanego jako parametr. Krzywe takie, dotąd nie stosowane, mogą znacznie ułatwić optymalizowanie podziału grodziowego względem wskaźnika niezatapialności.
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Identification of transition curves in vehicular roads and railways
PublicationIn the paper attention is focused on the necessity to systematize the procedure for determining the shape of transition curves used in vehicular roads and railway routes. There has been presented a universal method of identifying curvature in transition curves by using differential equations. Curvature equations for such known forms of transition curves as clothoid, quartic parabola, the Bloss curve, cosinusoid and sinusoid, have...
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Design of reverse curves adapted to the satellite measurements
PublicationThe paper presents a new method for designing railway route in the direction change area adapted to the Mobile Satellite Measurements technique. The method may be particularly useful in the situations when both tangents cannot be connected in an elementary way using a circular arc with transition curves. Thus, the only solution would be the application of two circular arcs of opposite curvature signs, that is, the use of an inverse...
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Design of compound curves adapted to the satellite measurements
PublicationThe paper deals with a novelty related to the design of a region for an alternative railway track direction adequate for mobile satellite measurements. The new approach may become particularly useful in the design of the existing track axis control when the determination of both the main track directions becomes impossible. The only solution in that case is to apply to the geometrical system two circular arcs of a different radius,...
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Curves of thermodynamic states in some fluids with dispersion
Publicationvariations in the thermodynamic state of a dispersive medium, caused by sound, are studied. A bubbly liquid and a Maxwell fluid are considered as examples. Curves in the plane of thermodynamic states are plotted. They are in fact pictorial images of linear relations of excess pressure and excess density in the acoustic wave which reflect irreversible attenuation of the sound energy. The curves account for the nonlinear generation...
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Assessing vehicle restraint systems on horizontal curves
PublicationHorizontal curves, an element of road infrastructure, have a statistically high number of accidents. Considering that horizontal curves in the last ten years have had app. 10% of all road accidents representing app. 14% of all fatalities on Polish roads, the issue is serious and requires more research and proper road safety treatments. Data for 2007 - 2016 show that in the case of accidents on horizontal curves app. 45% of the...
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Singular Surface Curves in the Resultant Thermodynamics of Shells
PublicationWithin six-parameter shells theory we discuss the governing equations of shells with material or non-material singular curves. By singular curve we mean a surface curve where are discontinuities in some surface fields. As an example we consider shells with junctions and shells undergoing stress-induced phase transitions.
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Hysteresis curves for some periodic and aperiodic perturbations in gases
PublicationEvolution of sound in a medium whose properties irreversibly vary in the course of wave propagation, is studied. For example, a gas that is a particular case of a Newtonian fluid is considered. Hysteresis curves, pictorial representations of irreversible attenuation of the sound energy, in the plane of thermodynamic states are plotted. The irreversible losses in internal energy are proportional to the total attenuation and depend...
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How to model ROC curves - a credit scoring perspective
PublicationROC curves, which derive from signal detection theory, are widely used to assess binary classifiers in various domains. The AUROC (area under the ROC curve) ratio or its transformations (the Gini coefficient) belong to the most widely used synthetic measures of the separation power of classification models, such as medical diagnostic tests or credit scoring. Frequently a need arises to model an ROC curve. In the biostatistical...
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Potential Energy Curves of Diatomic Alkali Molecules Datasets
PublicationThe datasets described in this article contain potential energy curves for several diatomic systems. The data was obtained via high-performance computing using MOLPRO, a system of ab initio programs for advanced molecular electronic structure calculations. The datasets allow to model bond lengths, energy levels, spectra and time-evolution of molecular dimers for which the data are presented.
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a novel modified star-triangular fractal (MSTF) monopole antenna for super-wideband applications
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a novel modified star-triangular fractal (MSTF) monopole antenna for super-wideband applications
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Lamb wave based structural damage detection using cointegration and fractal signal processing
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Higuchi fractal dimension analysis of surface EMG signals and determination of active electrode positions
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The Study of Geometry of the Selected Transition Curves in the Design of Circular Roads
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Quasirelativistic potential energy curves and transition dipole moments of NaRb
PublicationWe report on extensive calculations of quasi-relativistic potential energy curves and, for the first time, transition dipole moments including spin-orbit and scalar-relativistic effects of the NaRb molecule. The calculated curves of the 0+, 0-, 1, 2 and 3 molecular states correlate for large internuclear separation with the fourteen lowest atomic energies up to the Na(3s ^2S_{1/2}) + Rb(7s ^2S_{1/2}) atomic limit. Several new features...
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Potential energy curves, transition and permanent dipole moments of KRb
PublicationWe present extensive calculations of 48 adiabatic potential energy curves of the KRb molecule. Efforts have been focused on preparing the appropriate basis sets. Compared to previous approaches, the set of new potential energy curves is extended to higher excitations, including the single-excited K(4s2S)+Rb(5d2D) and double-excited K(4p2P)+Rb(5p2P) atomic limits. Larger distances between nuclei are also taken into account. New...
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Hysteresis curves for some periodic and aperiodic perturbations in magnetosonic flow
PublicationA thermodynamic relation between perturbations of pressure and mass density in the magnetohydrodynamic flow is theoretically studied. Planar magnetohydrodynamic perturbations with the wave vector, which forms a constant angle with the equilibrium magnetic field, are under study. The theory considers thermal conduction of a plasma and the deviation from adiabaticity of a flow due to some kind of heating–cooling function. It also...
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Time-current tripping curves of arc fault detection devices
PublicationTripping curves of arc fault detection devices, in accordance with PN-EN 62606 “General requirements for arc fault detection devices” have been presented in the paper. Consequently the most fundamental differences in arc fault detection devices tripping compared to circuit-breakers and residual current devices have been indicated.
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Improved selectivity compact band-stop filter with gosper fractal-shaped defected ground structures
PublicationA novel band-stop filter using Gosper fractal-shaped defected ground structures has been designed and manufactured. The improvement in the filter selectivity has been achieved by introducing a multiresonance fractal-shaped defect leading to a higher filter order, simultaneously maintaining its compact size. The experimental results prove the validity of proposed solution and its utility in novel miniaturized and severe requirement...
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Self-assembly of vertically oriented graphene nanostructures: multivariate characterisation by Minkowski functionals and fractal geometry
PublicationThe enormous self-assembly potential that graphene and its derived layered materials offer for responding to the contemporary environmental challenges has made it one of the most investigated materials. Hence, tuning its extraordinary properties and understanding the effect at all scales is crucial to tailoring highly customised electrodes. Vertically oriented graphene nanostructures, also known as carbon nanowalls (CNWs), due...
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The J-curve phenomenon revisited
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Smoothed transition curve for railways
PublicationThe work draws attention to the existing situation in the area of transition curves used in the geometric layouts of the railway track. Difficulties in the practical implementation and maintenance of very small horizontal ordinates of the transition curve and the ordinates of the gradient due to cant in the initial section, appearing on smooth transition curves, were indicated. The main reason for this situation was the excessive...
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Kinematic the flaying frontal rising kick
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Optoelectronic properties of curved carbon systems
PublicationSystematic investigation of optoelectronic properties of curved carbon systems has been performed and the results have been compared with the representatives of flat carbon systems. Moreover, the application of third order dispersion corrected density functional tight binding method (with third order corrections of self-consistent charges) including Becke-Johnson dumping (DFTB3-D3(BJ)) has been validated in order to obtain reliable...