In Theorem 1, we generalize the results of Szabó [Sz1, Sz2] for Berwald metrics that are not necessary strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F . Further, we investigate geodesic equivalence of Berwald metrics. Theorem 2 gives a system of PDE that has a (nontrivial) solution if and only if the given essentially Berwa...

This paper discusses nonlinear proportional-integral (PI) current control with anti-windup of reluctance synchronous machines (RSMs) for which the flux linkage maps are known. The nonlinear controller design is based on the tuning rule “Magnitude Optimum criterion” [1]. Due to the nonlinear flux linkage, the current dynamics of RSMs are highly nonlinear and, so, the parameters of the PI control...

We construct a new exact solution of Einstein's equations in vacuo in terms of Weyl canonical coordinates. This solution may be interpreted as a black hole in a space-time which is periodic in one direction and which behaves asymptotically like the Kasner solution with Kasner index equal to 4M L −1 , where L is the period and M is the mass of the black hole. Outside the horizon, the solution is...

S. P. Novikov developed an analog of the Morse theory for closed 1-forms. In this paper we suggest an analog of the Lusternik Schnirelman theory for closed 1-forms. For any cohomology class ξ ∈ H1(X,R) we define an integer cl(ξ) (the cuplength associated with ξ); we prove that any closed 1-form representing ξ has at least cl(ξ)− 1 critical points. The number cl(ξ) is defined using cup-products ...

In this paper we consider the nonlinear equation involving differential forms on a compact Riemannian manifold δdξ = f ′(〈ξ, ξ〉)ξ. This equation is a generalization of the semilinear Maxwell equations recently introduced in a paper by Benci and Fortunato. We obtain a multiplicity result both in the positive mass case (i.e. f ′(t) ≥ ε > 0 uniformly) and in the zero mass case (f ′(t) ≥ 0 and f ′(...

We investigate a problem of approximate non-linear sampling recovery of functions on the interval I:=[0,1] expressing the adaptive choice of n sampled values of a function to be recovered, and of n terms from a given family of functions Φ. More precisely, for each function f on I, we choose a sequence ξ = {ξs} s =1 n of n points in I, a sequence a = {as}s=1} n of n functions defined on n and a ...