The delayed feedback control (DFC) is a control method for stabilizing unstable periodic orbits in nonlinear autonomous differential equations. We give an important relationship between the characteristic multipliers of the linear variational equation around an unstable periodic solution of the equation and those of its delayed feedback equation. The key of our proof is a result about the spect...

A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state P = ρ. A wide class of self-similar solutions turn out to be unstable against kink mode perturbation. According to the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be a critical solutio...

The stability behavior of low immersion helical end milling processes is investigated in this paper. Low radial immersion milling operations involve interrupted cutting which induces chatter vibration under certain cutting conditions. Time Finite Element Analysis (TFEA) is suggested for an approximate solution for delayed differential equations encountered during interrupted milling. An improve...

We investigate singular and degenerate behavior of solutions of the unstable free boundary problem ∆u = −χ{u>0} . First, we construct a solution that is not of class C and whose free boundary consists of four arcs meeting in a cross-shaped singularity. This solution is completely unstable/repulsive from above and below which would make it hard to get by the usual methods, and even numerics is n...

Consider a one-mass system with two degrees of freedom, nonlin-early coupled, with parametric excitation in one direction. Assuming the internal resonance 1:2 and parametric resonance 1:2 we derive conditions for stability of the trivial solution by using both the harmonic balance method and the normal form method of averaging. If the trivial solution becomes unstable a stable periodic solution...

Many boronic acids, including 2-heterocyclic, vinyl, and cyclopropyl derivatives, are inherently unstable, which can limit their benchtop storage and/or efficient cross-coupling. We herein report the first general solution to this problem: in situ slow release of unstable boronic acids from the corresponding air-stable MIDA boronates. This remarkably general approach has transformed all three c...

Meshfree Collocation Method is used to solve linear two-dimensional problems. This method differs from weak form methods such as Galerkin method and no cellular networking and no numerical  integration. Therefore, this method has no constraints such as the integration accuracy and the integration CPU time, and equations can be isolated directly from the strong form of governing PDE. The fundame...