A Midpoint Method for Generalized Equations Under Mild Differentiability Condition

2011 ◽  
Vol 116 (3) ◽  
pp. 269-279 ◽  
Author(s):  
Catherine Cabuzel
Keyword(s):  
Generalized Equations ◽  
Differentiability Condition ◽  
Midpoint Method ◽  
Mild Differentiability Condition

The midpoint method: Magnetic interpretation of dikes and faults

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 834-839 ◽  
Author(s):  
I. V. Radhakrishna Murthy
Keyword(s):  
Characteristic Point ◽  
The Other ◽  
Magnetic Interpretation ◽  
Midpoint Method ◽  
Vertical Gradients

A method of magnetic interpretation of arbitrarily magnetized dikes and faults is developed, based on the properties of a new characteristic point called the “midpoint.” Anomaly profiles at two levels are considered, the maximum and minimum anomalies on them are located, and their midpoints are plotted. The rate of shift of the midpoint with elevation is a measure of the direction of magnetization. The distances between the points of maximum and minimum anomalies and the ratio of horizontal to vertical gradients in the case of faults are used to calculate the other parameters. I also suggest application of the method to anomalies of sheet‐like bodies.

Half division two-dimensional method for simple sinusoidal quantities parameters accurate measurement

2021 ◽  
pp. 16-21
Author(s):  
Kirill Yu. Solomentsev ◽  
Vyacheslav I. Lachin ◽  
Aleksandr E. Pasenchuk
Keyword(s):  
Measuring Instruments ◽  
Measured Signal ◽  
Two Dimensional ◽  
Measuring Device ◽  
New Approach ◽  
Precision Measuring ◽  
Useful Signal ◽  
Midpoint Method ◽  
Order Of Magnitude ◽  
Current Measuring

Several variants of half division two-dimensional method are proposed, which is the basis of a fundamentally new approach for constructing measuring instruments for sinusoidal or periodic electrical quantities. These measuring instruments are used in the diagnosis of electric power facilities. The most general variant, called midpoint method, is considered. The proposed midpoint method allows you to measure much smaller than using widespread methods, alternating currents or voltages, especially when changing the amplitude of the measured signal in very wide ranges, by 1–2 orders of magnitude. It is shown that using the midpoint method it is possible to suppress sinusoidal or periodic interference in the measuring path, in particular, to measure small alternating current when sinusoidal or periodic interference is 1–2 orders of magnitude higher than the useful signal. Based on the results of comparative tests, it was found that the current measuring device implementing the midpoint method is an order of magnitude more sensitive than the currently used high-precision measuring instruments.

Newton's method for fully parameterized generalized equations

Optimization ◽  
2018 ◽  
Vol 67 (11) ◽  
pp. 2061-2080 ◽  
Author(s):  
Wei Ouyang ◽  
Binbin Zhang
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Generalized Equations
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