We consider an autonomous system admitting invariant manifold M. The following questions are discussed: (i) what the conditions ensuring exponential stability of manifold? (ii) does every motion attracting by M tend to some on (i.e. have asymptotic phase)? (iii) is geometrical structure set formed orbits approaching a given orbit? get answer in terms Lyapunov functions omitting assumption that ...

This paper deals with the asymptotic stabilization of a class port-Hamiltonian (pH) 1-D Partial Differential Equations (PDE) spatial varying parameters, interconnected linear Ordinary (ODE), control input on ODE. The considered ODE contains effect proportional term, that can be as action controller or spring in case mechanical systems. In this particular study, it is not possible to directly ad...

An inverse nodal problem has first been studied for the Sturm-Liouville equation with one turning point. The asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated and an asymptotic of the nodal points is obtained. For this problem, we give a reconstruction formula for the potential function. Furthermore, numerical examples have been established a...

In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...

For a class of linear autonomous delay differential equations with parameter α we give upper bounds for the integral ∞ 0 |X (t, α)| dt of the fundamental solution X (·, α). The asymptotic estimations are sharp at a critical value α0 where x = 0 loses stability. We use these results to study the stability properties of perturbed equations.

In this paper, we show that there is no negative upper bound for the sectional curvature of Teichmüller space of Riemann surfaces with the Weil–Petersson metric. Mathematics Subject Classifications (2000). 32G15, 53C21, 30F60.

introduction: it was shown in a previous study, that mcpip, a cilostamide derivative, increased atrial contraction force without changing contraction rate. to improve this property, two new derivatives of cilostamide were synthesized and their effects on pde3 activity and isolated rat atria contraction were investigated. methods: the inhibitory effect of each compound on pde3 enzyme was determi...

A large financial market is described by a sequence of standard general models of continuous trading. It turns out that the absence of asymptotic arbitrage of the first kind is equivalent to the contiguity of sequence of objective probabilities with respect to the sequence of upper envelopes of equivalent martingale measures, while absence of asymptotic arbitrage of the second kind is equivalen...