Analysis and Computation of the Derivative Function for an Isolated Lorentz Line.

1979 ◽  
Author(s):  
Stephen J. Young
Keyword(s):  
Derivative Function ◽  
Lorentz Line

scholarly journals A reverse Hardy–Hilbert-type integral inequality involving one derivative function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Qian Chen ◽  
Bicheng Yang
Keyword(s):  
Integral Inequality ◽  
Beta Function ◽  
Equivalent Form ◽  
Constant Factor ◽  
Weight Functions ◽  
Derivative Function ◽  
The Best Possible Constant ◽  
Type Integral ◽  
Hilbert Type ◽  
Hilbert Integral

AbstractIn this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.

scholarly journals The derivative function

2001 ◽  
pp. 41-57
Author(s):  
Casper Goffman ◽  
Togo Nishiura ◽  
Daniel Waterman
Keyword(s):  
Derivative Function

Formulation of Low-Carbon City Development Roadmap: Technical Elements and Recommendations

2017 ◽  
Vol 05 (04) ◽  
pp. 1750023 ◽  
Author(s):  
Guiyang ZHUANG ◽  
Zhen'ge ZHOU
Keyword(s):  
Decision Making ◽  
Ghg Emissions ◽  
National Development ◽  
Low Carbon ◽  
City Development ◽  
Intergovernmental Panel ◽  
Systematic Analysis ◽  
Derivative Function ◽  
Key Sectors ◽  
Low Carbon City

Promoting low-carbon development (LCD) is one of the basic requirements of building new-type urbanization with Chinese characteristics. Research on the formulation of low-carbon city development roadmap (hereinafter referred to as the “Roadmap”) is a necessity for systematic control of greenhouse gas (GHG) emission and the construction of low-carbon cities. Based on the actual conditions of cities as well as the regional and national development strategies, the Roadmap panoramically describes the strategic objectives, development plans, and key sectors' initiatives for the transformation of city development through planning techniques and solutions. Generally, the formulation of a low-carbon roadmap involves six steps: understanding the present situation of GHG emissions; analyzing the future emission scenarios; setting LCD targets; developing action plans for key sectors; assessing mitigation potential of low-carbon technologies/projects; and proposing measures for implementation. This paper, based on the practical experience in low-carbon city roadmap development and the needs of divisional management, establishes an analytical structure of GHG inventory for seven sectors, so as to link the key sectors for LCD, namely the seven major sectors for emissions reduction proposed by the Intergovernmental Panel on Climate Change (IPCC). Moreover, this paper integrates sectorial (industrial) low-carbon technology needs assessment (TNA) into the formulation of the Roadmap. It also provides several recommendations for better incorporating the two methods into the Roadmap: firstly, to strengthen the core function of GHG inventory by enhanced accounting quality and scientific and systematic analysis of the temporal and sectorial distribution of GHG emissions so as to serve the Roadmap formulation and decision-making. Secondly, to reinforce the derivative function of GHG inventory that serves the LCD planning, assessment, and decision-making by improving the quality and continuity of GHG inventory. Thirdly, to develop the derivative function of GHG inventory by integrating the improved GHG inventory and TNA into the formulation of the Roadmap.

A New Nonlinear Least Square Algorithm for Voigt Spectral Lines

1980 ◽  
Vol 34 (3) ◽  
pp. 351-360 ◽  
Author(s):  
R. J. Noll ◽  
A. Pires
Keyword(s):  
Least Square ◽  
Spectral Lines ◽  
Single Line ◽  
Second Derivatives ◽  
Fitting Algorithm ◽  
Starting Conditions ◽  
Data Points ◽  
Lorentz Line ◽  
Few Data ◽  
Raphson Method

In this paper a new fitting algorithm which works with Voigt functions is discussed. The fitting algorithm used is an extension of the rapidly convergent gradient method of Fletcher and Powell, who claim faster convergence than the Newton-Raphson method which has been used by Chang and Shaw for fitting Lorentz line widths. The Fletcher and Powell algorithm involves the effects of second derivatives although second derivatives are not explicitly calculated. In our algorithm, first and second derivatives are computed not numerically, but analytically via a modification to Drayson's Voigt function subroutine. This algorithm provides rapid convergence even when there are few data points. Profiles have been fitted with as few as five data points. Our typical line fits involve 40 points. The run time of the algorithm has been compared with the shrinking cube algorithm of Hillman and found to be at least 10 times faster under identical starting conditions. Sample single line and single line plus background are shown illustrating the speed and efficiency of the new algorithm, as well as the importance of good zero-order estimates to start the iterations.

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