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Wyniki wyszukiwania dla: 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
PublikacjaThe 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
PublikacjaWe 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
PublikacjaThe 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
PublikacjaWe 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
PublikacjaW 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.
PublikacjaW 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
PublikacjaLet 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
PublikacjaFollowing 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
PublikacjaNon-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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Taylor type predictor for pressure changes
PublikacjaCelem 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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Generalized adaptive notch smoothing revisited
PublikacjaThe 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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The ancient formula of master-apprentice relevance in contemporary architecture education.
PublikacjaThe 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
PublikacjaDold 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
PublikacjaBody 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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Content of odd-numbered carbon fatty acids in the milk of lactating women and in infant formula and follow-on formula
PublikacjaBadano 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
PublikacjaW 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
PublikacjaStructural 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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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublikacjaConsider 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...