An integral solution of the electromagnetic seismograph equation

1960 ◽  
Vol 50 (3) ◽  
pp. 461-465
Author(s):  
R. E. Ingram
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Integral Solution ◽  
Ground Movement ◽  
Ground Movements ◽  
Angular Movement ◽  
Electromagnetic Seismograph

ABSTRACT In investigating the response of an electromagnetic seismograph to various ground movements it is advantageous to have the solution of the differential equation as an integral. This is done by finding the Green's function, f(s), for the particular instrument. The angular movement of the galvanometer is then θ(t)=q∫0tf(s)x″(t−s)ds where x(t) is the ground movement and prime stands for the operator d/dt. It is sufficient to find one function, F(s), with dF/ds = f(s), to give the response to a displacement test, a tapping test, or a ground movement.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Green's function for a differential equation with a deviating argument

1975 ◽  
Vol 17 (3) ◽  
pp. 259-262
Author(s):  
I. N. Inozemtseva ◽  
Yu. V. Komlenko ◽  
S. A. Pak
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Deviating Argument

A Green's Function-Based Design for Deformation Control of a Microbeam With In-Domain Actuation

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Amir Badkoubeh ◽  
Guchuan Zhu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Control Design ◽  
Target System ◽  
Bernoulli Equation ◽  
Test Function ◽  
Deformation Control ◽  
Control Scheme

This paper presents a Green's function-based design for deformation control of a microbeam described by an Euler-Bernoulli equation with in-domain pointwise actuation. The Green's function is first used in control design to construct the test function that enables the solvability of a map between the original nonhomogeneous partial differential equation and a target system in standard boundary control form. Then a regularized Green's function is employed in motion planning, leading to a computationally tractable implementation of the control scheme combined by a single feedback stabilizing loop and feedforward controls. The viability and the applicability of the proposed approach are demonstrated through numerical simulations of a representative microbeam.

scholarly journals Maximal and minimal iterative positive solutions for $ p $-Laplacian Hadamard fractional differential equations with the derivative term contained in the nonlinear term

2021 ◽  
Vol 6 (11) ◽  
pp. 12583-12598
Author(s):  
Limin Guo ◽  
◽  
Lishan Liu ◽  
Ying Wang ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Nonlinear Term ◽  
Iterative Schemes ◽  
Hadamard Fractional Differential Equations ◽  
Equation Boundary ◽  
Derivative Term ◽  
Fractional Differential

<abstract><p>In this paper, the maximal and minimal iterative positive solutions are investigated for a singular Hadamard fractional differential equation boundary value problem with a boundary condition involving values at infinite number of points. Green's function is deduced and some properties of Green's function are given. Based upon these properties, iterative schemes are established for approximating the maximal and minimal positive solutions.</p></abstract>

scholarly journals LINEAR DIFFERENTIAL EQUATION WITH ADDITIONAL CONDITIONS AND FORMULAE FOR GREEN'S FUNCTION

2011 ◽  
Vol 16 (3) ◽  
pp. 401-417 ◽  
Author(s):  
Svetlana Roman
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence Condition ◽  
Linear Ordinary Differential Equation ◽  
Linearly Independent ◽  
Linear Differential

In this paper, we investigate the m-order linear ordinary differential equation with m linearly independent additional conditions. We have found the solution to this problem and give the formula and the existence condition of Green's function. We compare two Green's functions for two such problems with different additional conditions and apply these results to the problems with nonlocal boundary conditions.

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