In this paper, let Σ ⊂ R be a compact convex hypersurface. We prove that if Σ carries only finitely many geometrically distinct closed characteristics, then at least two of them must possess irrational mean indices. Moreover, if Σ carries exactly three geometrically distinct closed characteristics, then at least two of them must be elliptic.

This paper is among the first to investigate impact of over-education and over-skilling on workers’ wages using a unique pan-European database covering twenty-eight countries for year 2014, namely CEDEFOP’s European Skills Jobs (ESJ) survey. Overall, results suggest existence wage penalty associated with over-education. When educational skills mismatches are interacted each other in order disti...

We consider a special class of Lagrangians that play a fundamental role in the theory of second order Lagrangian systems: Twist systems. This subclass of Lagrangian systems is deened via a convenient monotonicity property that such systems share. This monotonicity property (Twist property) allows a nite dimensional reduction of the variational principle for nding closed characteristics in xed e...

On the energy manifolds of fourth order conservative systems closed characteristics can be found inmany cases via analogues of Twist-maps. The ‘Twist property’ implies the existence of a generating function which leads to second order recurrence relations. We study these recurrence relations to find simple closed characteristics andwe give conditionswhen fourth order systems satisfy the ‘Twist ...

We prove that closed simply connected K-contact manifolds with minimal number of closed characteristics are homeomorphic to odd-dimensional spheres.

For a large class of second order Lagrangian dynamics, one may reformulate the problem of finding periodic solutions as a problem in solving second-order recurrence relations satisfying a twist condition. We project periodic solutions of such discretized Lagrangian systems onto the space of closed braids and apply topological techniques. Under this reformulation, one obtains a gradient flow on ...

For any given compact C2 hypersurface Σ in R2n bounding a strictly convex set with nonempty interior, in this paper an invariant ̺n(Σ) is defined and satisfies ̺n(Σ) ≥ [n/2] + 1, where [a] denotes the greatest integer which is not greater than a ∈ R. The following results are proved in this paper. There always exist at least ̺n(Σ) geometrically distinct closed characteristics on Σ. If all the geom...

We consider the problem of allocating a given workload among the stations in a multi-server product-form closed queueing network to maximize the throughput. We first investigate properties of the throughput function and prove that it is pseudoconcave for some special cases. Some other characteristics of the optimal workload and its physical interpretation are also provided. We then develop two ...