Wyniki wyszukiwania - Biblioteka Nauki

1

Fourier analysis for solving the load balancing problem

100%

Karagiorgos G. , Missirlis N. M.

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2002

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tom Vol. 27, No. 3

129-140

EN

A new approach based on Fourier analysis to study Diffusion-type methods for solving the load balancing problem is presented. This approach is applied on two newly introduced methods the Average Diffusion (ADF) and its extrapolated counterpart (EADF) for d-regular graphs. Necessary and sufficient conditions are found for their convergence, whereas the optimum value of the extrapolation parameter r is determined in terms of M and m, the second largest and smallest eigenvalues of the ADF iteration matrix. Instead of using matrix theory, we apply Fourier analysis to determine M and m in case the diffusion parameters Cij are not equal to a constant value, as is the usual assumption. Our approach is simpler than matrix analysis. Moreover, it is shown that EADF attains the same rate of convergence with the classical Diffusion (DF) method, exhibiting a better convergence behavior in certain applications (2D-torus) for large number of processors.

2

Modeling of vibration for functionally graded beams

100%

Yiğit G. , Şahin A. , Bayram M.

Open Mathematics

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2016

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tom 14

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nr 1

661-672

EN

In this study, a vibration problem of Euler-Bernoulli beam manufactured with Functionally Graded Material (FGM), which is modelled by fourth-order partial differential equations with variable coefficients, is examined by using the Adomian Decomposition Method (ADM).The method is one of the useful and powerful methods which can be easily applied to linear and nonlinear initial and boundary value problems. As to functionally graded materials, they are composites mixed by two or more materials at a certain rate. This mixture at a certain rate is expressed with an exponential function in order to try to minimize singularities from transition between different surfaces of materials as much as possible. According to the structure of the ADM in terms of initial conditions of the problem, a Fourier series expansion method is used along with the ADM for the solution of simply supported functionally graded Euler-Bernoulli beams. Finally, by choosing an appropriate mixture rate for the material, the results are shown in figures and compared with those of a standard (homogeneous) Euler-Bernoulli beam.

3

The higher order Riesz transform for Gaussian measure need not be of weak type (1,1)

100%

Forzani L. , Scotto R.

Studia Mathematica

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1998

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tom 131

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nr 3

205-214

EN

The purpose of this paper is to prove that the higher order Riesz transform for Gaussian measure associated with the Ornstein-Uhlenbeck differential operator $L:= d^2/dx^2 - 2xd/dx$, x ∈ ℝ, need not be of weak type (1,1). A function in $L^1(dγ)$, where dγ is the Gaussian measure, is given such that the distribution function of the higher order Riesz transform decays more slowly than C/λ.

4

Parametryzacja sygnałów dla celów e-diagnostyki obiektów końcowych sieci energetycznej

100%

Lisowiec A.

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2011

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tom Vol. 52, nr 7

15-17

PL

W artykule przedstawiono metody parametryzacji sygnałów elektrycznych związanych z wyłącznikiem średnich napięć dla celów diagnostyki wyłącznika w trakcie jego normalnej pracy. Szczególną uwagę poświęcono metodom obliczania widma sygnałów napięć i prądów fazowych. Omówiono metodę detekcji i dokładnego wyznaczania składowych anharmonicznych w sygnałach napięciowych.

EN

In the paper methods of the parametrization of medium voltage circuit breaker signals for the purpose of on - line diagnosis have been presented. Particular stress has been laid on the methods of phase and current signals spectrum estimation. The method of detection and parameters estimation of anharmonic signals has been described.

5

A note on the M. Riesz theorem for the conjugate function

88%

Papadopoulos S.

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1999

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tom Vol. 47, no 3

283-288

EN

In this note we shall prove that if p is a power of 2, i.e. p = 2[sup k], k [belongs to] N, and f(0) = 0, that is f has the Fourier series Sigma[...] with a[sub o] = 0, then [...].

6

Wpływ szumu na wymiar fraktalny profilu powierzchni ciała stałego modyfikowanego wiązką jonową

75%

Martan J. , Jaguś P.

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2008

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tom Vol. 49, nr 1

74-76

PL

Istnieją różne metody analizy chropowatości powierzchni ciał stałych, takie jak analiza statystyczna lub analiza fourierowska. W wypadku analizy statystycznej potrzebne są dziesiątki parametrów do opisu powierzchni, a analiza fourierowska sprawdza się tam, gdzie oczekuje się periodyczności w uzyskanym profilu powierzchni. Analiza fraktalna powierzchni ciała stałego opisuje profil powierzchni tylko jednym parametrem - wymiarem fraktalnym. Szum wprowadzany przez urządzenia pomiarowe ma wpływ na wartość wymiaru fraktalnego. Przedstawiono wyniki badań metod obliczania wymiaru fraktalnego (metody Hursta i Fouriera) pod kątem ich odporności na szum. Profil powierzchni uzyskano za pomocą programu komputerowego wykorzystującego algorytm z losowym przesunięciem punktu środkowego. Do otrzymanego w ten sposób profilu dodano pięć różnych procentowych udziałów szumu białego oraz gaussowskiego i obliczono wymiar fraktalny dla każdego z nich. Metoda Fouriera okazała się bardziej odporna na szum niż metoda Hursta.

EN

There are different methods of the surface roughness analysis of solids including a statistical or Fourier analysis. However, in order to describe the surface with a usage of these methods, dozens of parameters are needed. Fractal analysis of the solid state surface describes it with one real number parameter only which is a fractal dimension. One of the problems in calculating the fractal dimension is the fact that measurement data of surface profiles contain noise. Noise has an impact on the fractal dimension value. In this paper different methods for calculating the fractal dimension of waveforms (including box counting dimension estimation, Hurst analysis and Fourier analysis) were investigated in order to find the one that is the most resistant to noise. Measurement data were generated using computer programs (methods of midpoint displacement, fractal Brownian motion and Fourier series were used). Five different levels of noise were added to the generated data and fractal dimension of such data was calculated.

7

Wave Characteristics in Breaststroke Technique with and Without Snorkel Use

75%

Conceição A. , Silva A. J. , Boaventura J. , Marinho D. A. , Louro H.

Journal of Human Kinetics

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2013

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tom 39

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nr 1

185-194

EN

The purpose of this paper was to examine the characteristics of waves generated when swimming with and without the use of Aquatrainer® snorkels. Eight male swimmers performed two maximal bouts of 25 m breaststroke, first without the use of a snorkel (normal condition) and then using a snorkel (snorkel condition). The body landmarks, centre of the mass velocity, stroke rate, stroke length, stroke index, and Strouhal number (St) were quantified. Fourier analysis was conducted to determine the frequency, amplitude, and phase characteristics of the vertical undulations. We also determined the undulation period, the first and second harmonic wave percentage, and the contribution of these components to the power of each of the wave signals. The first wave harmonics had a frequency of 0.76 Hz (normal condition) and 0.78 Hz (snorkel condition), and the second wave harmonics had a frequency of 1.52 Hz (normal condition) and 1.56 Hz (snorkel condition). Under the normal conditions, the wave amplitude was higher on the vertex (0.72 m) and cervical (0.32 m) than that produced under snorkel conditions (0.71 m and 0.28 m, respectively). The lowest values were found in the hip (0.03 m in normal conditions, and 0.02 m in snorkel conditions) and in the trunk (0.06 m in normal conditions, and 0.04 m in snorkel conditions). It can be concluded that snorkel use seems to lead to slight changes in the biomechanical pattern in swimming velocity, as well as several stroke mechanical variables.

8

Wykorzystanie analizy fourierowskiej w analizie cyfrowych obrazów cząstek zużycia

63%

Wrona M.

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2007

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tom nr 6

235-245

PL

W pracy dokonano oceny tekstury powierzchni cząstek zużycia metodą analizy Fouriera z zastosowaniem komputerowej analizy obrazów uzyskanych w mikroskopie świetlnym. Wyznaczono widmo amplitudowe jednowymiarowej transformaty Fouriera oraz zbadano zależność paramtrów liczbowych widma od tekstury powierzchni cząstek. Na podstawie przeprowadzonych badań stwierdzono, że metoda analizy Fouriera może znaleźć zastosowanie przy identyfikacji cząstek zużycia tribologicznego, a pośrednio także mechanizmu zużycia.

EN

The evaluation of wear particles surface texture has been performed using the computer analysis of images acquired by means of the light microscope. The 1D Fast Fourier Transformation was computed and dependence between spectrum numerical parameters and particles texture surface was evaluated. On the basis of realized researches was found that the Fourier analysis method could be helpful in wear particle identification.

9

Istotność statystyczna wniosków z analiz ilościowych na przykładzie badań górnego czwartorzędu

51%

Walanus A.

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2000

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tom T. 26, z. 4

469-527

PL

Statystyka matematyczna jest jednym z narzędzi geologii, wykorzystywanym szczególnie w badaniu młodszych okresów, gdzie szerzej stosowane są metody ilościowe. W przedstawionym tekście, który jest podsumowaniem kilkunastu opublikowanych prac, zawarta jest propozycja pewnego podejścia do wnioskowania statystycznego. Kluczowe w tym spojrzeniu jest pojęcie istotności statystycznej, którego sens rozszerzono dla zwiększenia jego stosowalności w geologii. Wskazano kilka metod weryfikacji poprawności wyznaczania poziomu istotności. Podano pewne algorytmy i zasady postępowania, nie wymagające ani zaawansowanej matematyki ani technik obliczeniowych wykraczających poza możliwości arkusza kalkulacyjnego. Materiał merytoryczny zilustrowano przykładami z prac badawczych dotyczących skal czasu od 15000 lat do 5 dni

EN

Mathematical statistics is an unavoidable tool in modern geology, especially in Quaternary and Recent period, where quantitative approach based on measurements is widely applicable. Statistical methods consists not only of more or less advanced calculations but involves also difficult reasoning of special statistical kind. Proposed here, the way of statistical thinking is based on the, slightly modified idea of statistical significance level. As applied to the complicated environment of geological quantities, which are mutually interrelated and dependent on many unknown influences, significance level calculation result frequently only in rough estimation of reliability of suggested thesis. Some methods are proposed here to avoid gross errors in statistical significance level appreciation. Some sources of such errors are indicated. Neither advanced mathematics is necessary in the given approach nor sophisticated calculations (Excel is enough). Examples are presented, which came from scientific research of Late Glacial and the Holocene period, as well as from historical, up to the modern data