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Search results for: GENERALIZED TAYLOR FORMULA
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Generalized Taylor formula and shell structures for the analysis of the interaction between geosythetics and engineering structures of transportation lines
PublicationThe analysis of the interaction between geosynthetics and engineering structures (e.g. railroad bed, soil foundation, pipeline) assumes that the geosynthetic form elastic membranes or shell laid on different types of foundations. The mathematical description of that problems in continuous domain employs Laplace operator Δ or d’Alembert operator □. In this paper we demonstrate the analysis based on generalize Taylor formula, and...
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Magnetic-field-induced electric quadrupole moments for relativistic hydrogenlike atoms: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationWe consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function we derive a closed-form expression for the electric quadrupole moment induced...
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Second-order Stark effect and polarizability of a relativistic two-dimensional hydrogenlike atom in the ground state
PublicationThe second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb Green's function. A closed-form analytical expression for the static dipole polarizability of that system is found. The formula involves the generalized hypergeometric function ${}_{3}F_{2}$...
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Simple sufficient condition for subspace to be completely or genuinely entangled
PublicationWe introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We...
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Jednoelektronowy atom Diraca w słabym polu magnetycznym
PublicationW rozprawie przedstawiono opis wpływu zewnętrznego stałego, słabego, jednorodnego pola magnetycznego na jednoelektronowy atom Diraca. Wykorzystując funkcje gęstości ładunku elektrycznego oraz gęstości prądu elektrycznego, rozważono procesy indukowania się w atomie dodatkowych elektromagnetycznych momentów multipolowych. Dokonano analizy indukowanego momentu dipolowego, w wyniku której uzyskano wyrażenie dla magnetyzowalności atomu....
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Methods for displacement and rotation measurements of individual Taylor-Schneebeli grains.
PublicationW artykule przedtawiono autorską metodę pomiaru przemieszczeń oraz obrotów cząstek ośrodka analogowego Taylor-Schneebeli oraz propozycję interpretacji badań.
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Degree product formula in the case of a finite group action
PublicationLet V, W be finite dimensional orthogonal representations of a finite group G. The equivariant degree with values in the Burnside ring of G has been studied extensively by many authors. We present a short proof of the degree product formula for local equivariant maps on V and W.
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Seiberg-Witten invariants the topological degree and wall crossing formula
PublicationFollowing S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b 1 = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.
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Unifying Aspects of Generalized Calculus
PublicationNon-Newtonian calculus naturally unifies various ideas that have occurred over the years in the field of generalized thermostatistics, or in the borderland between classical and quantum information theory. The formalism, being very general, is as simple as the calculus we know from undergraduate courses of mathematics. Its theoretical potential is huge, and yet it remains unknown or unappreciated.
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Generalized adaptive notch smoothing revisited
PublicationThe problem of identification of quasi-periodically varying dynamic systems is considered. This problem can be solved using generalized adaptive notch filtering (GANF) algorithms. It is shown that the accuracy of parameter estimates can be significantly increased if the results obtained from GANF are further processed using a cascade of appropriately designed filters. The resulting generalized adaptive notch smoothing (GANS) algorithm...
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Taylor type predictor for pressure changes
PublicationCelem pracy jest ocena predykcji ciśnienia za pomocą rozwinięcia funkcji w szereg Taylora. Przewidywana wartość ciśnienia jest obliczana jako iloczyn wcześniejszych wartości mnożonych przez współczynniki wagowe wyznaczone w oparciu o szereg Taylora. Zaletą takiego podejścia jest możliwość analizy danych próbkowanych nierównomiernie. Podstawową wadą jest założenie, że ciśnienie jest dobrze aproksymowane przez wielomian niskiego...
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The ancient formula of master-apprentice relevance in contemporary architecture education.
PublicationThe universalization of the methodology for determining the quality of European higher education exposes the aspect of supporting the student in the education process, which takes the form of tutoring or supervising - a modern form of ancient master-apprentice relationship. The 'master' in architectural education has lawful building qualification and is a member in national architect association - a sine qua non with respect to...
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Generalized Dold sequences on partially-ordered sets
PublicationDold sequences constitute an important class of integer sequences that play an important role in combinatorics, number theory, topology and dynamical systems. We generalize the notion of Dold sequence for the case of partially ordered sets and describe their properties. In particular we give two alternative descriptions of generalized Dold sequences: by some class of elementary sequences as well as by different...
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A Conception of Pairwise Comparisons Model for Selection of Appropriate Body Surface Area Calculation Formula
PublicationBody surface area (BSA) may be computed using a variety of formulas, but the computed BSA differs from real BSA values for particular subjects. This is presented in the paper by computing BSA values for selected subject and comparing them to the real BSA value obtained with the use of a 3D body scanner. The results show inequalities in the relevant BSA computing formulas. Hence, there is a need to determine a method that will allow...
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Measuring Tilt with an IMU Using the Taylor Algorithm
PublicationThis article addresses the important problem of tilt measurement and stabilization. This is particularly important in the case of drone stabilization and navigation in underwater environments, multibeam sonar mapping, aerial photogrammetry in densely urbanized areas, etc. The tilt measurement process involves the fusion of information from at least two different sensors. Inertial sensors (IMUs) are unique in this context because...
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Content of odd-numbered carbon fatty acids in the milk of lactating women and in infant formula and follow-on formula
PublicationBadano zależność pomiędzy występowaniem w mleku ludzkim kwasów pentadekanowego C15:0 (PA) i heptadekanowego C17:0 (HA) a rodzajem diety matek oraz oznaczono zawartość kwasów PA i HA w preparatach do początkowego i następnego żywienia niemowląt, dostępnych w sprzedaży. Badaniu poddano mleko ludzkie uzyskane od 34 zdrowych kobiet w wieku 24-33 lata. Matki podzielono na dwie grupy zgodnie ze spożywana przez nie dietą: grupa kobiet...
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The asymptotic formula for the error in orthogonal projection
PublicationW pracy podano formułę asymptotyczną błędu aproksymacji dla rzutów ortogonalnych w normie L^p.
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Effective Formula for Impact Damping Ratio for Simulation of Earthquake-induced Structural Pounding
PublicationStructural pounding during earthquakes may cause substantial damage to colliding structures. The phenomenon is numerically studied using different models of collisions. The aim of the present paper is to propose an effective formula for the impact damping ratio, as a parameter of the impact force model used to study different problems of structural pounding under seismic excitations. Its accuracy has been verified by four various...
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Critical Reappraisal of Casagrande and Taylor Methods for Coefficient of Consolidation
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Denaturation of proteins by surfactants studied by the Taylor dispersion analysis
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Periodic Solutions of Generalized Lagrangian Systems with Small Perturbations
PublicationIn this paper we study the generalized Lagrangian system with a small perturbation. We assume the main term in the system to have a maximum, but do not suppose any condition for perturbation term. Then we prove the existence of a periodic solution via Ekeland’s principle. Moreover, we prove a convergence theorem for periodic solutions of perturbed systems.
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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A simple way of increasing estimation accuracy of generalized adaptive notch filters
PublicationGeneralized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. It is shown that frequency biases, which arisein generalized adaptive notch filtering algorithms, can be significantly reduced by incorporating in the adaptive loop an appropriately chosen decision delay. The resulting performance...
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Generalized adaptive notch smoothers for real-valued signals and systems
PublicationSystems with quasi-periodically varying coefficients can be tracked using the algorithms known as generalized adaptive notch filters (GANFs). GANF algorithms can be considered an extension, to the system case, of classical adaptive notch filters (ANFs). We show that estimation accuracy of the existing algorithms, as well as their robustness to the choice of design parameters, can be considerably improved by means of compensating...
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Generalized temperature dependence model for anammox process kinetics
PublicationTemperature is a key operational factor influencing the anammox process kinetics. In particular, at temperatures below 15 °C, the specific anammox activity (SAA) considerably decreases. This study aimed to describe the temperature dependence of the anammox process kinetics in the temperature range from 10 to 55 °C, including the specific characteristics of“cold anammox”. The commonly used Arrhenius and extended and modifiedRatkowsky...
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A memoryless direct digital synthesizer based on Taylor series approach.
PublicationW pracy rozważono dwa podejścia do projektowania cyfrowego, kwadraturowego generatora syntezy bezpośredniej (DDS). Pierwsze z nich wykorzystuje małą pamięć na próbki jednego okresu bazowej sinusoidy zespolonej o małej szybkości próbkowania i interpolację tej sinusoidy szeregiem Taylora do docelowej, większej szybkości próbkowania. Drugie jest rozwiązaniem bezpamięciowym z bezpośrednią aproksymacją zespolonej sinusoidy za pomocą...
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Quasi-solutions for generalized second order differential equations with deviating arguments
PublicationThis paper deal with boundary value problems for generalized second order differential equations with deviating arguments. Existence of quasi-solutions and solutions are proved by monotone iterative method. Examples with numerical results are added.
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Automated microwave planar filter design with generalized Chebyshev characteristics.
PublicationIn this paper a technique of automatization of design of microwave filters with generalized Chebyshev characteristics is presented. A full wave electromagnetic simulator linked with the Matlab computing environment is used to ensure a rigorous numerical analysis while at the same time allowing automatization. To decrease time of optimization and overall design process, the Cauchy interpolation technique was used. An automated design...
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Multistage generalized adaptive notch filter with improved accuracy
PublicationGeneralized adaptive notch filters (GANFs) are estimators of coefficients of quasi-periodically time-varying systems. Current state of the art GANFs can deliver highly accurate estimates of system variations’ frequency, but underperform in terms of accuracy of the coefficient estimates. The paper proposes a novel multistage GANF with accuracy improved in this aspect. The processing pipeline consists of three stages. The preliminary...
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Generalized adaptive notch filters with frequency debiasing for tracking of polynomial phase systems
PublicationGeneralized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. For general patterns of frequency variation the generalized adaptive notch filtering algorithms yield biased frequency estimates. We show that when system frequencies change slowly in a smooth way, the estimation bias can...
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A self-optimization mechanism for generalized adaptive notch smoother
PublicationTracking of nonstationary narrowband signals is often accomplished using algorithms called adaptive notch filters (ANFs). Generalized adaptive notch smoothers (GANSs) extend the concepts of adaptive notch filtering in two directions. Firstly, they are designed to estimate coefficients of nonstationary quasi-periodic systems, rather than signals. Secondly, they employ noncausal processing, which greatly improves their accuracy and...
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Generalized adaptive comb filter with improved accuracy and robustness properties
PublicationGeneralized adaptive comb lters can be used to identify/track parameters of quasi-periodically varying systems.In a special, signal case they reduce down to adaptive comblters, applied to elimination or extraction of nonstationarymulti-harmonic signals buried in noise. We proposea new algorithm which combines, in an adaptive way, resultsyielded by several, simultaneously working generalizedadaptive comb lters. Due to its highly...
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On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation
PublicationIn this note, we establish the property of convergence for a finite-difference discretization of a diffusive partial differential equation with generalized Burgers convective law and generalized Hodgkin–Huxley reaction. The numerical method was previously investigated in the literature and, amongst other features of interest, it is a fast and nonlinear technique that is capable of preserving positivity, boundedness and monotonicity....
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On tracking properties of real-valued generalized adaptive notch filters
PublicationGeneralized adaptive notch filters (GANFs) are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. The paper presents results of local performance analysis of a real-valued GANF algorithm, i.e., algorithm designed to track parameters of a real-valued system. This is an extension of the previous work which focused...
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A multirate approach to DDS algorithm versus Taylor-series expansion technique.
PublicationPokazano, że cyfrowy generator syntezy bezpośredniej (DDS) można traktować jako algorytm wieloszybkościowy. Rozważono i porównano dwa sposoby wykorzystania pamięci. W pierwszym z nich zastosowano filtr ułamkowo-opóźniający o strukturze Farrowa. Drugie podejście oparto na rotacji fazy na podstawie rozwinięcia w szereg Taylora. Eksperymenty pokazują, że za pomocą obu tych sposobów, dla sinusoidy zespolonej generowanej w kwadraturowym...
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Non-standard contact conditions in generalized continua: microblock contact model for a Cosserat body
PublicationGeneralized continuum theories involve non-standard boundary conditions that are associated with the additional kinematic variables introduced in those theories, e.g., higher gradients of the displacement field or additional kinematic degrees of freedom. Accordingly, formulation of a contact problem for such a continuum necessarily requires that adequate contact conditions are formulated for the additional kinematic variables and/or...
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Regularized Identification of Time-Varying FIR Systems Based on Generalized Cross-Validation
PublicationA new regularization method is proposed and applied to identification of time-varying finite impulse response systems. We show, that by a careful design of the regularization constraint, one can improve estimation results, especially in the presence of strong measurement noise. We also show that the the most appropriate regularization gain can be found by direct optimization of the generalized cross-validation criterion.
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Mazur-Orlicz theorem and asymptotic formula for the error in supreme norm.
PublicationObliczono formułę asymptotyczną błędu interpolacji dla normy supremum.
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Generalized adaptive comb filters/smoothers and their application to the identification of quasi-periodically varying systems and signals
PublicationThe problem of both causal and noncausal identification of linear stochastic systems with quasiharmonically varying parameters is considered. The quasi-harmonic description allows one to model nonsinusoidal quasi-periodic parameter changes. The proposed identification algorithms are called generalized adaptive comb filters/smoothers because in the special signal case they reduce down to adaptive comb algorithms used to enhance...
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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublicationIn this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some...
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Generalized Pareto ranking bisection for computationally feasible multi-objective antenna optimization
PublicationMulti-objective optimization (MO) allows for obtaining comprehensive information about possible design trade-offs of a given antenna structure. Yet, executing MO using the most popular class of techniques, population-based metaheuristics, may be computationally prohibitive when full-wave EM analysis is utilized for antenna evaluation. In this work, a low-cost and fully deterministic MO methodology is introduced. The proposed generalized...
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Generalized Chebyshev Bandpass Filters With Frequency-Dependent Couplings Based on Stubs
PublicationThis paper presents an accurate synthesis method for inline and cross-coupled generalized Chebyshev bandpass filters with frequency-dependent couplings implemented via open and short stubs. The technique involves the synthesis of a lumped-element prototy pe in the form of a coupling matrix with a frequency-dependent term and the conversion of this prototype to a distributed-element mode l composed of sections of TEM lines. This...
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Frequency Guided Generalized Adaptive Notch Filtering - Tracking Analysis and Optimization
PublicationGeneralized adaptive notch filters (GANFs) are estimators of coefficients of quasi-periodically time-varying systems, encountered e.g., in RF applications when Doppler effect takes place. Current state of the art GANFs can deliver highly accurate estimates of system variations’ frequency, but underperform in terms of accuracy of system coefficient estimates. The paper proposes a novel multistage GANF with improved coefficient...
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Category Adaptation Meets Projected Distillation in Generalized Continual Category Discovery
Publication"Generalized Continual Category Discovery (GCCD) tackles learning from sequentially arriving, partially labeled datasets while uncovering new categories. Traditional methods depend on feature distillation to prevent forgetting the old knowledge. However, this strategy restricts the model’s ability to adapt and effectively distinguish new categories. To address this, we introduce a novel technique integrating a learnable projector...
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Low-Cost Multi-Objective Optimization of Antennas By Means Of Generalized Pareto Ranking Bisection Algorithm
PublicationThis paper introduces a generalized Pareto ranking bisection algorithm for low-cost multi-objective design optimization of antenna structures. The algorithm allows for identifying a set of Pareto optimal sets of parameters (that represent the best trade-offs between considered objectives) by iterative partitioning of the intervals connecting previously found designs and executing a Pareto-ranking-based poll search. The initial...
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A Novel Coupling Matrix Synthesis Technique for Generalized Chebyshev Filters With Resonant Source–Load Connection
PublicationThis paper reports a novel synthesis method for microwave bandpass filters with resonant source–load connection. In effect, a network realizing N+1 transmission zeros (where N is the number of reflection zeros) is obtained. The method is based on a prototype transversal coupling matrix (N+2, N+2) with source and load connected by a resonant circuit formed by a capacitor in parallel with a frequency-invariant susceptance. To complement...
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TelePOVM - A generalized quantum teleportation scheme.
PublicationPokazano, że kwantowa teleportacja jest specjalnym przypadkiem uogólnionej nielokalności EPR.
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A Generalized Version of the Lions-Type Lemma
PublicationIn this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma generalizes some results for a class of Orlicz–Sobolev spaces. What matters here is the behavior of the integral, not the space
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Generalized Dobrushin Coefficients on Banach Spaces
PublicationThe asymptotic behavior of iterates of bounded linear operators (not necessarily positive), acting on Banach spaces, is studied. Through the Dobrushin ergodicity coefficient, we generalize some ergodic theorems obtained earlier for classical Markov semigroups acting on L1 (or positive operators on abstract state spaces).
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Self-optimizing generalized adaptive notch filters - comparison of three optimization strategies
PublicationThe paper provides comparison of three different approaches to on-line tuning of generalized adaptive notch filters (GANFs) the algorithms used for identification/tracking of quasi-periodically varying dynamic systems. Tuning is needed to adjust adaptation gains, which control tracking performance of ANF algorithms, to the unknown and/or time time-varying rate of system nonstationarity. Two out ofthree compared approaches are classical...