scholarly journals The zeros of the second derivative of the reciprocal of an entire function

1981 ◽  
Vol 263 (2) ◽  
pp. 501-501 ◽  
Author(s):  
Simon Hellerstein ◽  
Jack Williamson
Keyword(s):  
Entire Function ◽  
Second Derivative

scholarly journals Yet another characterization of the sine function

1981 ◽  
Vol 4 (2) ◽  
pp. 371-381
Author(s):  
Robert Gervais ◽  
Lee A. Rubel
Keyword(s):  
Entire Function ◽  
Complex Plane ◽  
Exponential Type ◽  
Second Derivative ◽  
Sine Function ◽  
Number Of Zeros ◽  
Expository Paper

In this expository paper, it is shown that if an entire function of exponential type vanishes at least once in the complex plane and if it has exactly the same number of zeros (counting multiplicities) as its second derivative, then this function must take the formAsin(Bz+C).

Functions in the Schwartz algebra that are invertible in the sense of Ehrenpreis

2019 ◽  
Vol 484 (1) ◽  
pp. 7-11
Author(s):  
N. F. Abuzyarova
Keyword(s):  
Entire Function ◽  
Exponential Type ◽  
Zero Set ◽  
Schwartz Algebra

We consider the problem of obtaining the restrictions on the zero set of an entire function of exponential type under which this function belongs to the Schwartz algebra and invertible in the sense of Ehrenpreis.

Second‐Derivative Spectra for Estimating Crop Residue Cover

1994 ◽  
Vol 86 (2) ◽  
pp. 349-354 ◽  
Author(s):  
Haiping Su ◽  
Michel D. Ransom ◽  
Edward T. Kanemasu ◽  
Tanvir H. Demetriades‐Shah
Keyword(s):  
Crop Residue ◽  
Second Derivative ◽  
Derivative Spectra ◽  
Second Derivative Spectra

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

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