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Search results for: almost periodic function
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CELL STRUCTURE AND FUNCTION
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Journal of Function Spaces
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TREES-STRUCTURE AND FUNCTION
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Green function diagonal for a class of heat equations
PublicationA construction of the heat kernel diagonal is considered as element of generalized zeta function theory, which gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expressions of the Green function in the case of finite-gap potential coefficient of the heat equation are constructed. An algorithm and program for Mathematica are presented...
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Acceleration of the discrete Green's function computations
PublicationResults of the acceleration of the 3-D discrete Green's function (DGF) computations on the multicore processor are presented. The code was developed in the multiple precision arithmetic with use of the OpenMP parallel programming interface. As a result, the speedup factor of three orders of magnitude compared to the previous implementation was obtained thus applicability of the DGF in FDTD simulations was significantly improved.
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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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Left-handed propagation characteristics of a dielectric and metal-loaded periodic circular waveguide
PublicationIn this paper, a periodic dielectric/metallic rod is located in a circular waveguide to obtain left-handed operation. Two geometries of the dielectric/metallic rod are proposed and examined. The dispersion characteristics of the investigated waveguides are obtained using a surface impedance model. Moreover, equivalent circuit models are proposed allowing for calculation of the dispersion characteristics and scattering parameters...
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Magnetoacoustic Heating in Nonisentropic Plasma Caused by Different Kinds of Heating-Cooling Function
PublicationThe nonlinear phenomena which associate with magnetoacoustic waves in a plasma are analytically studied. A plasma is an open system with external inflow of energy and radiation losses. A plasma’s flow may be isentropically stable or unstable. The nonlinear phenomena occur differently in dependence on stability or instability of a plasma’s flow. The nonlinear instantaneous equation which describes dynamics of nonwave entropy mode...
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Local basis function method for identification of nonstationary systems
PublicationThis thesis is focused on the basis function method for the identification of nonstationary processes. The first chapter describes a group of models that can be identified using the basis function method. The next chapter describes the basic version of the basis function method, including its algebraic and statistical properties. The following section introduces the local basis function (LBF) method: its properties are described...
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Immunizing the Hillcast Method against the Known-Plaintext Attack using Periodic Key Exchange
PublicationThis paper considers a Joint Fingerprinting and Decryption method, called Hillcast, for the copyright protection and traitor tracing in case of Video on Demand services. Because the method is based on the Hill cipher, it is vulnerable to a known-plaintext attack. The goal of this paper is to present an efficient periodic key exchange mechanism to make this method secure without compromising its scalability, imperceptibility or...
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Almost homoclinics for nonautonomous second order Hamiltonian systems by a variational approach
PublicationW artykule badamy problem istnienia rozwiązań prawie homoklinicznych dla nieautonomicznych układów Hamiltona w R^n z potencjałem V(t,x) postaci -1/2(L(t)x,x)+W(t,x) oraz zaburzeniem f(t) (ang. forcing term) z L^2. Zakładamy, że L jest funkcją ciągłą z prostej w zbiór macierzy kwadratowych nxn taką, że macierze L(t) są symetryczne i dodatnio określone jednostajnie względem zmiennej t. Potencjał W(t,x) jest klasy C^1 i nadkwadratowy...
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Two almost homoclinic solutions for second-order perturbed Hamiltonian systems
PublicationW niniejszym artykule badamy problem istnienia rozwiązań prawie homoklinicznych (rozwiązań znikających w nieskończonościach) dla układów Hamiltonowskich drugiego rzędu (układów Newtonowskich) z zaburzeniem. Nasz wynik jest uogólnieniem twierdzenia Rabinowitza-Tanaki o istnieniu rozwiązania homoklinicznego dla układów bez zaburzenia [Math. Z. 206 (1991) 473-499]. O zaburzeniu zakładamy, że jest dostatecznie małe w przestrzeni funkcji...
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Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms
PublicationWe apply the representation of Lefschetz numbers of iterates in the form of periodic expansion to determine the minimal sets of Lefschetz periods of Morse–Smale diffeomorphisms. Applying this approach we present an algorithmic method of finding the family of minimal sets of Lefschetz periods for Ng, a non-orientable compact surfaces without boundary of genus g. We also partially confirm the conjecture of Llibre and Sirvent (J Diff...
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THE FUNCTION OF GREENERY IN A SKYSCRAPER: THE PLACEMENT AND ITS INFLUENCE
PublicationThe contrast between the high rise buildings; with their mostly geometric shapes, and the organic form of the greenery was visible even in the idea of a skyscraper. Yet the realizations and recent projects show emerging interest and the link between them. To better understand the developing function of the greenery in the context of a skyscraper, both literature and case studies are conducted. The aim is to relate the location...
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Accuracy of the discrete Green's function computations
PublicationThis paper discusses the accuracy of the discrete Green's function (DGF) computations. Recently closed-form expression of the DGF and its efficient numerical implementation were presented which facilitate the DGF applications in FDTD simulations of radiation and scattering problems. By carefully comparing the DGF results to those of the FDTD simulation, one can make conclusions about the range of the applicability of the DGF for...
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Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces
PublicationLet f be a smooth self-map of a closed connected manifold of dimension m⩾3. The authors introduced in [G. Graff, J. Jezierski, Minimizing the number of periodic points for smooth maps. Non-simply connected case, Topology Appl. 158 (3) (2011) 276-290] the topological invariant NJD_r[f], where r is a fixed natural number, which is equal to the minimal number of r-periodic points in the smooth homotopy class of f. In this paper smooth...
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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
PublicationLet M be a smooth closed simply-connected 4-dimensional manifold, f be a smooth self-map of M with fast grow of Lefschetz numbers and r be a product of different primes. The authors calculate the invariant equal to the minimal number of r-periodic points in the smooth homotopy class of f.
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Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublicationLet $r$ be an odd natural number, $M$ a compact simply-connected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simply-connected. We consider $f$, a $C^1$ self-maps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$-periodic points...
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Windowing of the Discrete Green's Function for Accurate FDTD Computations
PublicationThe paper presents systematic evaluation of the applicability of parametric and nonparametric window functions for truncation of the discrete Green's function (DGF). This function is directly derived from the FDTD update equations, thus the FDTD method and its integral discrete formulation can be perfectly coupled using DGF. Unfortunately, the DGF computations require processor time, hence DGF has to be truncated with appropriate...
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Port-based approach to distributed transfer function method
PublicationIn the paper there is presented an uniform, port-based approach to modeling of both lumped and distributed parameter systems. Port-based model of distributed system has been defined by application of distributed transfer function method (DTFM). The approach proposed combines versatility of port - based modeling and accuracy of distributed transfer function method. It enables to formulate appropriate input data for computer analysis...
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Minimal number of periodic points for smooth self-maps of simply-connected manifolds
Open Research DataThe problem of finding the minimal number of periodic points in a given class of self-maps of a space is one of the central questions in periodic point theory. We consider a closed smooth connected and simply-connected manifold of dimension at least 4 and its self-map f. The topological invariant D_r[f] is equal to the minimal number of r-periodic points...
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The Concept of Using the Decision-Robustness Function in Integrated Navigation Systems
PublicationThe diversity and non-uniformity of the positioning systems available in maritime navigation systems often impede the watchkeeping officer in the selection of the appropriate positioning system, in particular, in restricted basins. Thus, it is necessary to introduce a mathematical apparatus to suggest, in an automated manner, which of the available systems should be used at the given moment of a sea trip. Proper selection of the...
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Local basis function estimators for identification of nonstationary systems
PublicationThe problem of identification of a nonstationary stochastic system is considered and solved using local basis function approximation of system parameter trajectories. Unlike the classical basis function approach, which yields parameter estimates in the entire analysis interval, the proposed new identification procedure is operated in a sliding window mode and provides a sequence of point (rather than interval) estimates. It is...
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Tuning the work function of graphite nanoparticles via edge termination
PublicationGraphite nanoparticles are important in energy materials applications such as lithium-ion batteries (LIBs), supercapacitors and as catalyst supports. Tuning the work function of the nanoparticles allows local control of lithiation behaviour in LIBs, and the potential of zero charge of electrocatalysts and supercapacitors. Using large scale density functional theory (DFT) calculations, we find that the surface termination of multilayer...
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Almost homoclinic solutions for a certain class of mixed type functional differential equations
PublicationW pracy opisano pewną metodę aproksymacyjną szukania rozwiązań prawie homoklinicznych dla równań różniczkowo funkcyjnych z opóźnionym i przyśpieszonym argumentem. Podano również przykłady zastosowań tej metody.
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Computer-assisted pronunciation training—Speech synthesis is almost all you need
PublicationThe research community has long studied computer-assisted pronunciation training (CAPT) methods in non-native speech. Researchers focused on studying various model architectures, such as Bayesian networks and deep learning methods, as well as on the analysis of different representations of the speech signal. Despite significant progress in recent years, existing CAPT methods are not able to detect pronunciation errors with high...
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An Analysis of Periodic Arrangements of Cylindrical Objects of Arbitrary Convex Cross Sections with the Use of Field Matching Method
PublicationA problem of electromagnetic wave scattering from multilayered frequency selective surfaces is presented. Each surface is composed of periodically arranged cylindrical posts of arbitrary convex cross-section. The method of analysis is based on the direct field matching technique for a single cell, and the transmission matrix method with the lattice sums technique for periodic arrangement of scatterers.
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Streaming caused by non periodic ultrasound.
PublicationOpracowano wzory na generację przepływów rotacyjnych przez falę akustyczną dowolnego typu. Równania ewolucyjne wyprowadzone, wyniki porównywane są teorią dla wielkości uśrednionych. Impuls dodatniej polarności służy przykładem fali akustycznej. Przedstawiono czasowe, przestrzenne wykresy na podstawie obliczeń numerycznych oraz linie pędu przepływu rotacyjnego.
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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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Magnetoacoustic Heating of Plasma Caused by Periodic MagnetosoundPerturbations with Discontinuities in a Quasi-Isentropic Magnetic Gas
PublicationThe magnetoacoustic heating of plasma by harmonic or periodic saw-tooth perturbations at a trans-ducer is theoretically studied. The planar fast and slow magnetosound waves are considered. The wavevector may form an arbitrary angleθwith the equilibrium straight magnetic field. In view of variableθand plasma-β, the description of magnetosound perturbations and appropriate magnetosound heatingis fairly difficult. The scenario of...
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Roughness evaluation of turned composite surfaces by analysis of the shape of Autocorrelation Function
PublicationIn this paper, the application of an Autocorrelation Function for the characterisation of surface topography was validated. The roughness evaluation of turned composite surfaces was supported by sophisticated studies of the Autocorrelation Function properties, considering especially the shape of the function. Details were measured with the optical method. The selection of the surface roughness evaluation procedures was carried...
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Ethnographica. Periodic Publication of the Peloponnese Folklore Foundation
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Validation of dynamic electrochemical impedance spectrograms using autocorrelation function
PublicationValidation of impedance data is essential for checking the reliability of experimental data. Kramers – Kronig transformation is used to verify data obtained from classical Electrochemical Impedance Spectroscopy (EIS) measurements. Data obtained from Dynamic Electrochemical Impedance Spectroscopy (DEIS) could be validated in the same way, but in this case, there is no information about internal consistency between every single spectrum...
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High frequency dynamics of an isotropic Timoshenko periodic beam by the use of the Time-domain Spectral Finite Element Method
PublicationIn this work results of numerical simulations and experimental measurements related to the high frequency dynamics of an aluminium Timoshenko periodic beam are presented. It was assumed by the authors that the source of beam structural periodicity comes from periodical alterations to its geometry due to the presence of appropriately arranged drill-holes. As a consequence of these alterations dynamic characteristics of the beam...
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Regularized Local Basis Function Approach to Identification of Nonstationary Processes
PublicationThe problem of identification of nonstationary stochastic processes (systems or signals) is considered and a new class of identification algorithms, combining the basis functions approach with local estimation technique, is described. Unlike the classical basis function estimation schemes, the proposed regularized local basis function estimators are not used to obtain interval approximations of the parameter trajectory, but provide...
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Fast implementation of FDTD-compatible green's function on multicore processor
PublicationIn this letter, numerically efficient implementation of the finite-difference time domain (FDTD)-compatible Green's function on a multicore processor is presented. Recently, closed-form expression of this discrete Green's function (DGF) was derived, which simplifies its application in the FDTD simulations of radiation and scattering problems. Unfortunately, the new DGF expression involves binomial coefficients, whose computations...
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
PublicationFor a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m 4, we provide an algorithm for estimating the values of the topological invariant D^m_r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing D^m_r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013),...
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Implementation of FDTD-Compatible Green's Function on Graphics Processing Unit
PublicationIn this letter, implementation of the finite-difference time domain (FDTD)-compatible Green's function on a graphics processing unit (GPU) is presented. Recently, closed-form expression for this discrete Green's function (DGF) was derived, which facilitates its applications in the FDTD simulations of radiation and scattering problems. Unfortunately, implementation of the new DGF formula in software requires a multiple precision...
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Computational Methods and Function Theory
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Journal of Function Spaces and Applications
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Graph decomposition for improving memoryless periodic exploration
PublicationW ostatnich latach często badanym problem jest eksploracja anonimowych grafów z lokalnymi etykietami portów przy każdym wierzchołku. Niedawno pokazano [Czyzowicz et al., Proc. SIROCCO'09], że dla każdego grafu istnieje poetykietowanie prowadzące do eksploracji przez automat bezpamięciowy z okresem co najwyżej 13n/3. W niniejszej pracy poprawiamy to ograniczenie do 4n-2, stosując całkowicie nową technikę dekompozycji grafu.
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Existence of periodic orbits for a perturbed vector field
PublicationPrzy nałożeniu pewnego warunku na odwzorowanie Poincarego, wyrażonego w języku indeksów iteracji, dowodzi się istnienia orbit periodycznych dla zaburzonego pola wektorowego.
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Elastostatic problems in multicomponent, multilayered periodic composites
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Periodic Points for Sphere Maps Preserving MonopoleFoliations
PublicationLet S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in...
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Single and Series of Multi-valued Decision Diagrams in Representation of Structure Function
PublicationStructure function, which defines dependency of performance of the system on performance of its components, is a key part of system description in reliability analysis. In this paper, we compare two approaches for representation of the structure function. The first one is based on use of a single Multi-valued Decision Diagram (MDD) and the second on use of a series of MDDs. The obtained results indicate that the series of MDDs...
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Follow-up assessment of the microvascular function in patients with long COVID
PublicationLong COVID is a complex pathophysiological condition. However, accumulating data suggests that COVID-19 is a systemic microvascular endothelial dysfunction with different clinical manifestations. In this study, a microvascular function was assessed in long COVID patients (n = 33) and healthy controls (n = 30) using flow-mediated skin fluorescence technique (FMSF), based on measurements of nicotinamide adenine dinucleotide fluorescence...
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Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds
PublicationLet M be a closed smooth connected and simply connected manifold of dimension m at least 3, and let r be a fixed natural number. The topological invariant D^m_r [f], defined by the authors in [Forum Math. 21 (2009), 491-509], is equal to the minimal number of r-periodic points in the smooth homotopy class of f, a given self-map of M. In this paper, we present a general combinatorial scheme of computing D^m_r [f] for arbitrary dimension...
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Hybridization of the FDTD method with use of the discrete Green's function
PublicationIn this contribution, a hybrid technique is presented which combines the finite-difference time-domain (FDTD) method and the discrete Green's function (DGF) formulation of this method. FDTD is a powerful technique for the analysis of complex penetrable objects but its application is not efficient when the computational domain includes many free-space cells. Therefore, the hybrid method was developed which is applicable to complex...
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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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On the dervative of the Legendre function of the first kind with respect to its degree [Corrigendum]
PublicationSkorygowano błąd matematyczny w pracy: R. Szmytkowski, On the derivative of the Legendre function of the first kind with respect to its degree, J. Phys. A: Math. Gen. Vol. 39(2006) s. 15147-15172 [744014]