scholarly journals Rational Implementation of Fractional Calculus Operator Based on Quadratic Programming

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhisong Xu ◽  
Mingqiu Li
Keyword(s):  
Fractional Calculus ◽  
Quadratic Programming ◽  
Frequency Domain ◽  
Frequency Band ◽  
Rational Approximation ◽  
Least Squares Method ◽  
Approximation Accuracy ◽  
Approximation Function ◽  
Fractional Calculus Operators ◽  
Quadratic Programming Method

When fractional calculus operators and models are implemented rationally, there exist some problems such as low approximation accuracy of rational approximation function, inability to specify arbitrary approximation frequency band, or poor robustness. Based on the error criterion of the least squares method, a quadratic programming method based on the frequency-domain error is proposed. In this method, the frequency-domain error minimization between the fractional operator s ± r and its rational approximation function is transformed into a quadratic programming problem. The results show that the construction method of the optimal rational approximation function of fractional calculus operator is effective, and the optimal rational approximation function constructed can effectively approximate the fractional calculus operator and model for the specified approximation frequency band.

scholarly journals Improvement of the Approximation Accuracy of LED Radiation Patterns

Electronics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 337 ◽  
Author(s):  
Ivan Rachev ◽  
Todor Djamiykov ◽  
Marin Marinov ◽  
Nikolay Hinov
Keyword(s):  
Least Squares ◽  
Mathematical Analysis ◽  
Least Squares Method ◽  
Weighting Function ◽  
Radiation Patterns ◽  
Approximation Accuracy ◽  
Light Emitting ◽  
Approximation Function ◽  
Wide Range ◽  
Optoelectronic Systems

For the great variety of light-emitting diodes (LEDs), there exists a wide range of LED radiation patterns. An approach for constructing patterns of higher accuracy is here considered. The latter is required when the design of optoelectronic systems or their optimization is carried out analytically. A weighting function is introduced that allows increasing the gradient of the diagram of different widths. It has been selected through mathematical analysis of the emission diagrams of different LEDs used in optoelectronic systems. Based on the least squares method an algorithm is created, and programs are developed in MATLAB environment to estimate the parameters of the approximation function. Its accuracy is evaluated by comparison with the approximation with Lambert source of order n. The results show higher accuracy of the proposed approximation function compared to those obtained by conventional methods. Recommendations on the application of the proposed approach are given.

On some Hardy-type inequalities for fractional calculus operators

2017 ◽  
Vol 11 (2) ◽  
pp. 438-457 ◽  
Author(s):  
Sajid Iqbal ◽  
Josip Pečarić ◽  
Muhammad Samraiz ◽  
Zivorad Tomovski
Keyword(s):  
Fractional Calculus ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Fractional Calculus Operators

scholarly journals Optimal use of quadratic programming method for alignment of geodesic networks

2019 ◽  
Vol 15 (2) ◽  
pp. 38-42
Author(s):  
O.S. Goncharenko ◽  
V.N. Gladilin ◽  
L. Šiaudinytė
Keyword(s):  
Quadratic Programming ◽  
Programming Method ◽  
Quadratic Programming Method

Integrated and frequency-band magnitude, two alternative measures of the size of an earthquake

1970 ◽  
Vol 60 (3) ◽  
pp. 917-937 ◽  
Author(s):  
B. F. Howell ◽  
G. M. Lundquist ◽  
S. K. Yiu
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Frequency Band ◽  
Transfer Functions ◽  
Body Wave ◽  
Average Amplitude ◽  
Equivalent Quantity ◽  
Short Period ◽  
Alternative Measures ◽  
Body Wave Magnitude

Abstract Integrated magnitude substitutes the r.m.s. average amplitude over a pre-selected interval for the peak amplitude in the conventional body-wave magnitude formula. Frequency-band magnitude uses an equivalent quantity in the frequency domain. Integrated magnitude exhibits less scatter than conventional body-wave magnitude for short-period seismograms. Frequency-band magnitude exhibits less scatter than body-wave magnitude or integrated magnitude for both long- and short-period seismograms. The scatter of frequency-band magnitude is probably due to real azimuthal effects, crustal-transfer-function variations, errors in compensation for seismograph response, microseismic moise and uncertainties in the compensation for attenuation with distance. To observe azimuthal variations clearly, the crustal-transfer functions and seismograph response need to be known more precisely than was the case in this experiment, because these two sources of scatter can be large enough to explain all of the observed variations.

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