Stabilizing non-trivial solutions of the generalized Kuramoto–Sivashinsky equation using feedback and optimal control

Non-trivial solutions to a linear equation in integers

For k ≥ 3 let A ⊂ [1, N ] be a set not containing a solution to a1x1 + · · · + akxk = a1xk+1 + · · · + akx2k in distinct integers. We prove that there is an ε > 0 depending on the coefficients of the equation such that every such A has O(N) elements. This answers a question of I. Ruzsa. Introduction The problems of estimating the size of a largest subset of [1, N ] not containing a solution to ...

Exact Solutions of the Generalized Kuramoto-Sivashinsky Equation

In this paper we obtain  exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems.    The methods used  to determine the exact solutions of the underlying equation are the Lie group analysis  and the simplest equation method. The solutions obtained are  then plotted.

on the relationship between using discourse markers and the quality of expository and argumentative academic writing of iranian english majors

the aim of the present study was to investigate the frequency and the type of discourse markers used in the argumentative and expository writings of iranian efl learners and the differences between these text features in the two essay genres. the study also aimed at examining the influence of the use of discourse markers on the participants’ writing quality. to this end the discourse markers us...

Non-trivial periodic solutions of a non-linear Hill’s equation with positively homogeneous term

The existence of non-trivial periodic solutions of a general family of second order differential equations whose main model is a Hill’s equation with a cubic nonlinear term arising in different physical applications is proved. c © 2005 Elsevier Ltd. All rights reserved.

non-linear control distillation column using approximate feedback linearization