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Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation

100%
Özdemir N., Yavuz M.
Acta Physica Polonica A
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2017
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vol. 132
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issue 3
1050-1053
EN
In this study, a new application of multivariate Padé approximation method has been used for solving European vanilla call option pricing problem. Padé polynomials have occurred for the fractional Black-Scholes equation, according to the relations of "smaller than", or "greater than", between stock price and exercise price of the option. Using these polynomials, we have applied the multivariate Padé approximation method to our fractional equation and we have calculated numerical solutions of fractional Black-Scholes equation for both of two situations. The obtained results show that the multivariate Padé approximation is a very quick and accurate method for fractional Black-Scholes equation. The fractional derivative is understood in the Caputo sense.
2
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Measurement of Double Differential Cross-Section for Electron Impact Ionization of Argon at 348 eV

81%
Bozkurt G., Yavuz M., Ozer Z., Dogan M.
Acta Physica Polonica A
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2014
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vol. 125
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issue 2
343-344
EN
In this study, we report the angular distribution of double differential cross sections of ejected electrons from Ar in intermediate energy region. Double differential cross-sections for electron impact ionization of argon have been measured at 348 eV. A hemispherical energy analyzer is used to analyze the ejected electrons with energies between 25 and 325 eV and angles between 25° and 130°.
3
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Double Differential Cross-Section Measurements for Methane Molecule at 350 eV

71%
Yavuz M., Isik N., Ozer Z., Ulu M., Doğan M.
Acta Physica Polonica A
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2014
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vol. 125
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issue 2
442-444
EN
Double differential cross-sections have been measured after ionizing electron collisions with methane at primary energy of 350 eV using a conventional electron spectrometer. An electrostatic analyzer was used to measure angular distributions of secondary electrons with energies between 25 eV and 300 eV. Angles of emission were 25° to 130°. It was found that the outgoing electrons belong to one of the two energetically separated groups, either the fast electrons which are scattered mainly in forward direction or the slow electrons which are distributed isotropically into all angles. For higher ejection energies the maxima shifted towards smaller angles as expected from binary type collision.
4
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Comparison of Experimental and Theoretical Double Differential Cross Sections of CH₄ at 250 eV Impact Energy

52%
Isik N., Yavuz M., Aksoy E., Ozer Z., Ulu M., Sahlaoui M., Boumediene L., Bouamoud M., Dogan M.
Acta Physica Polonica A
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2015
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vol. 127
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issue 4
1112-1114
EN
In this study, experimental and theoretical double differential cross section (DDCS) data for methane-electron interaction mechanism after the impact of a 250 eV electron have been comprehensively determined for a wide energy range of the detected electron, from 50 to 225 eV. The first Born-One Coulomb wave modeling with Gamow factor has been calculated to analyze experimental DDCS results for a correct description of the electron impact ionization of methane molecule. It is found that these theoretical calculations are successful to describe the post-collision interaction effects due to the Coulomb long-range interaction between the outgoing electrons in the final state. A considerable agreement is found between experimental and theoretical results.
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