The Experts below are selected from a list of 49584 Experts worldwide ranked by ideXlab platform
D M Khripunov - One of the best experts on this subject based on the ideXlab platform.
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instrumental broadening of spectral line profiles due to discrete representation of a continuous physical quantity
Journal of Quantitative Spectroscopy & Radiative Transfer, 2008Co-Authors: E N Dulov, D M KhripunovAbstract:It is the usual situation in spectroscopy that a continuous physical quantity, which plays the role of a spectral Function Argument (i.e. the abscissa of a spectrum), is sampled electronically as discrete point clouds or channels. Each channel corresponds to the midpoint of a small interval of the continuous Argument. The experimentally registered value of intensity in the channel describes the averaged spectral intensity in this interval. However, an approximation of spectra by a continuous theoretical model Function often assumes that the interval is small enough, and tabulation of the theoretical model Function may be used without appreciable disadvantages for the fitting results. At this point, a new type of approximation error appears, such as the error of midpoint approximation to a definite integral in the rectangle method of numeric integration. This paper aims at quantitative estimation of this error in the cases of a pure Lorentz lineshape and a generalized Voigt contour. It is shown that discrete representation of continuous spectral data leads to some non-physical broadening in comparison with the tabulated model Function. As a first approximation it is normal broadening. We show that even in the case of a Lorentz true lineshape we must use the tabulated Voigt Function measured in channels fixed Gauss linewidth rather than a tabulated Lorentzian. Application of the results of this paper is demonstrated on Mossbauer spectra.
E N Dulov - One of the best experts on this subject based on the ideXlab platform.
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instrumental broadening of spectral line profiles due to discrete representation of a continuous physical quantity
Journal of Quantitative Spectroscopy & Radiative Transfer, 2008Co-Authors: E N Dulov, D M KhripunovAbstract:It is the usual situation in spectroscopy that a continuous physical quantity, which plays the role of a spectral Function Argument (i.e. the abscissa of a spectrum), is sampled electronically as discrete point clouds or channels. Each channel corresponds to the midpoint of a small interval of the continuous Argument. The experimentally registered value of intensity in the channel describes the averaged spectral intensity in this interval. However, an approximation of spectra by a continuous theoretical model Function often assumes that the interval is small enough, and tabulation of the theoretical model Function may be used without appreciable disadvantages for the fitting results. At this point, a new type of approximation error appears, such as the error of midpoint approximation to a definite integral in the rectangle method of numeric integration. This paper aims at quantitative estimation of this error in the cases of a pure Lorentz lineshape and a generalized Voigt contour. It is shown that discrete representation of continuous spectral data leads to some non-physical broadening in comparison with the tabulated model Function. As a first approximation it is normal broadening. We show that even in the case of a Lorentz true lineshape we must use the tabulated Voigt Function measured in channels fixed Gauss linewidth rather than a tabulated Lorentzian. Application of the results of this paper is demonstrated on Mossbauer spectra.
Zoltan Porkolab - One of the best experts on this subject based on the ideXlab platform.
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practical heuristics to improve precision for erroneous Function Argument swapping detection in c and c
Journal of Systems and Software, 2021Co-Authors: Richard Szalay, Abel Sinkovics, Zoltan PorkolabAbstract:Abstract Argument selection defects, in which the programmer chooses the wrong Argument to pass to a parameter from a potential set of Arguments in a Function call, is a widely investigated problem. The compiler can detect such misuse of Arguments only through the Argument and parameter type for statically typed programming languages. When adjacent parameters have the same type or can be converted between one another, a swapped or out of order call will not be diagnosed by compilers. Related research is usually confined to exact type equivalence, often ignoring potential implicit or explicit conversions. However, in current mainstream languages, like C++, built-in conversions between numerics and user-defined conversions may significantly increase the number of mistakes to go unnoticed. We investigated the situation for C and C++ languages where developers can define Functions with multiple adjacent parameters that allow Arguments to pass in the wrong order. When implicit conversions – such as parameter pairs of types – are taken into account, the number of mistake-prone Functions markedly increases compared to only strict type equivalence. We analysed a sample of projects and categorised the offending parameter types. The empirical results should further encourage the language and library development community to emphasise the importance of strong typing and to restrict the proliferation of implicit conversions. However, the analysis produces a hard to consume amount of diagnostics for existing projects, and there are always cases that match the analysis rule but cannot be “fixed”. As such, further heuristics are needed to allow developers to refactor effectively based on the analysis results. We devised such heuristics, measured their expressive power, and found that several simple heuristics greatly help highlight the more problematic cases.
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the role of implicit conversions in erroneous Function Argument swapping in c
Source Code Analysis and Manipulation, 2020Co-Authors: Richard Szalay, Abel Sinkovics, Zoltan PorkolabAbstract:Argument selection defects, in which the programmer has chosen the wrong Argument to a Function call is a widely investigated problem. The compiler can detect such misuse of Arguments based on the Argument and parameter type in case of statically typed programming languages. When adjacent parameters have the same type, or they can be converted between one another, the potential error will not be diagnosed. Related research is usually confined to exact type equivalence, often ignoring potential implicit or explicit conversions. However, in current mainstream languages, like C++, built-in conversions between numerics and user-defined conversions may significantly increase the number of mistakes to go unnoticed. We investigated the situation for C and C++ languages where Functions are defined with multiple adjacent parameters that allow Arguments to pass in the wrong order. When implicit conversions are taken into account, the number of mistake-prone Function declarations significantly increases compared to strict type equivalence. We analysed the outcome and categorised the offending parameter types. The empirical results should further encourage the language and library development community to emphasise the importance of strong typing and the restriction of implicit conversion.
C Thiele - One of the best experts on this subject based on the ideXlab platform.
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weighted martingale multipliers in the non homogeneous setting and outer measure spaces
Advances in Mathematics, 2015Co-Authors: C Thiele, Sergei Treil, Alexander VolbergAbstract:Abstract We investigate the unconditional basis property of martingale differences in weighted spaces L 2 ( w d ν ) in the non-homogeneous situation, that is when the reference measure ν is not doubling. Specifically, we prove that finiteness of the quantity [ w ] A 2 = sup I 〈 w 〉 I 〈 w − 1 〉 I , defined through averages 〈 ⋅ 〉 I relative to the reference measure ν, implies that Haar subspaces form an unconditional basis in the weighted space L 2 ( w d ν ) . Moreover, we prove that the unconditional basis constant of this system grows at most linearly in [ w ] A 2 . The problem is reduced to the sharp weighted estimates of the so-called Haar multipliers. Even in the classical case of the standard dyadic lattice in R d with Lebesgue reference measure our result is new in that our estimates are independent of the dimension n. Our approach combines the technique of outer measure spaces with the Bellman Function Argument.
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weighted martingale multipliers in non homogeneous setting and outer measure spaces
arXiv: Analysis of PDEs, 2014Co-Authors: C Thiele, Sergei Treil, Alexander VolbergAbstract:We investigate the unconditional basis property of martingale differences in weighted $L^2$ spaces in the non-homogeneous situation (i.e. when the reference measure is not doubling). Specifically, we prove that finiteness of the quantity $[w]_{A_2}=\sup_I \, _I _I$, defined through averages $ _I$ relative to the reference measure $\nu$, implies that each martingale transform relative to $\nu$ is bounded in $L^2(w\, d\nu)$. Moreover, we prove the linear in $[w]_{A_2}$ estimate of the unconditional basis constant of the Haar system. Even in the classical case of the standard dyadic lattice in $\mathbb{R}^n$, where the results about unconditional basis and linear in $[w]_{A_2}$ estimates are known, our result gives something new, because all the estimates are independent of the dimension $n$. Our approach combines the technique of outer measure spaces with the Bellman Function Argument.
Alexander Volberg - One of the best experts on this subject based on the ideXlab platform.
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weighted martingale multipliers in the non homogeneous setting and outer measure spaces
Advances in Mathematics, 2015Co-Authors: C Thiele, Sergei Treil, Alexander VolbergAbstract:Abstract We investigate the unconditional basis property of martingale differences in weighted spaces L 2 ( w d ν ) in the non-homogeneous situation, that is when the reference measure ν is not doubling. Specifically, we prove that finiteness of the quantity [ w ] A 2 = sup I 〈 w 〉 I 〈 w − 1 〉 I , defined through averages 〈 ⋅ 〉 I relative to the reference measure ν, implies that Haar subspaces form an unconditional basis in the weighted space L 2 ( w d ν ) . Moreover, we prove that the unconditional basis constant of this system grows at most linearly in [ w ] A 2 . The problem is reduced to the sharp weighted estimates of the so-called Haar multipliers. Even in the classical case of the standard dyadic lattice in R d with Lebesgue reference measure our result is new in that our estimates are independent of the dimension n. Our approach combines the technique of outer measure spaces with the Bellman Function Argument.
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weighted martingale multipliers in non homogeneous setting and outer measure spaces
arXiv: Analysis of PDEs, 2014Co-Authors: C Thiele, Sergei Treil, Alexander VolbergAbstract:We investigate the unconditional basis property of martingale differences in weighted $L^2$ spaces in the non-homogeneous situation (i.e. when the reference measure is not doubling). Specifically, we prove that finiteness of the quantity $[w]_{A_2}=\sup_I \, _I _I$, defined through averages $ _I$ relative to the reference measure $\nu$, implies that each martingale transform relative to $\nu$ is bounded in $L^2(w\, d\nu)$. Moreover, we prove the linear in $[w]_{A_2}$ estimate of the unconditional basis constant of the Haar system. Even in the classical case of the standard dyadic lattice in $\mathbb{R}^n$, where the results about unconditional basis and linear in $[w]_{A_2}$ estimates are known, our result gives something new, because all the estimates are independent of the dimension $n$. Our approach combines the technique of outer measure spaces with the Bellman Function Argument.
