Invariants of a second-order curves under a special linear transformation

2019 ◽  
Vol 2019 (3) ◽  
pp. 19-24
Author(s):  
A. Artykbaev ◽  
B.M. Sultanov
Keyword(s):  
Linear Transformation ◽  
Second Order ◽  
Special Linear

scholarly journals Invariants of Surface Indicatrix in a Special Linear Transformation

2019 ◽  
Vol 7 (4) ◽  
pp. 106-115
Author(s):  
A. Artykbaev ◽  
B. M. Sultanov
Keyword(s):  
Linear Transformation ◽  
Special Linear

On the Product of Three Homogeneous Linear Forms. IV

1943 ◽  
Vol 39 (1) ◽  
pp. 1-21 ◽  
Author(s):  
H. Davenport
Keyword(s):  
Lower Bound ◽  
Real Number ◽  
Linear Transformation ◽  
Linear Forms ◽  
Special Linear ◽  
Absolute Value ◽  
Cubic Equation ◽  
Image Position ◽  
Homogeneous Linear

Let L1, L2, L3 be three homogeneous linear forms in u, v, w with real coefficients and determinant 1. Let M denote the lower bound offor integral values of u, v, w, not all zero. I proved a few years ago (1) thatmore precisely, thatexcept when L1, L2, L3 are of a special type, in which case If we denote by θ, ø, ψ the roots of the cubic equation t3+t2-2t-1 = 0, the special linear forms are equivalent, by an integral unimodular linear transformation, to(in any order), where λ1,λ2,λ3 are real number whose product is In this case, L1L2L3|λ1λ2λ3 is a non-zero integer, and the minimum of its absolute value is 1, giving

Linear transformation of pulse chirp through a cascaded optical second-order process

1995 ◽  
Vol 20 (14) ◽  
pp. 1521 ◽  
Author(s):  
R. Danielius ◽  
A. Dubietis ◽  
A. Piskarskas
Keyword(s):  
Linear Transformation ◽  
Second Order ◽  
Order Process ◽  
Pulse Chirp ◽  
Second Order Process

Spatial Homogenization of Stochastic Wave Equation with Large Interaction

2016 ◽  
Vol 59 (3) ◽  
pp. 542-552 ◽  
Author(s):  
Yongxin Jiang ◽  
Wei Wang ◽  
Zhaosheng Feng
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Wave Equation ◽  
Invariant Manifold ◽  
Linear Transformation ◽  
Second Order ◽  
Stochastic Wave Equation ◽  
Random Invariant Manifold ◽  
Large Interaction

AbstractA dynamical approximation of a stochastic wave equation with large interaction is derived. A random invariant manifold is discussed. By a key linear transformation, the random invariant manifold is shown to be close to the random invariant manifold of a second-order stochastic ordinary differential equation.

scholarly journals Compatibility aspects of the method of phase synchronization for decoupling linear second-order differential equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Willy Sarlet ◽  
Tom Mestdag
Keyword(s):  
General Theory ◽  
Differential Equations ◽  
Linear Transformation ◽  
Phase Synchronization ◽  
Second Order ◽  
Order System ◽  
Linear Transformations ◽  
Second Order Differential Equations ◽  
Geometric Context ◽  
The Given

<p style='text-indent:20px;'>The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather unusual approach because velocity-dependent transformations in general do not preserve the second-order character of differential equations. Moreover, at least in the case of linear transformations, such a velocity-dependent one defines by itself a second-order system, which need not have anything to do, in principle, with the given system or its reformulation. This aspect, and the related questions of compatibility it raises, seem to have been overlooked in the existing literature. The purpose of this paper is to clarify this issue and to suggest topics for further research in conjunction with the general theory of decoupling in a differential geometric context.</p>

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