The well-known Funk metric F (x, y) is projectively flat with constant flag curvature K = −1/4 and the Hilbert metric Fh(x, y) := (F (x, y) + F (x,−y))/2 is projectively flat with constant curvature K = −1. These metrics are the special solutions to Hilbert’s Fourth Problem. In this paper, we construct a non-trivial R-flat spray using the Funk metric. It is then an inverse problem in the calcul...

‎given a finite non-cyclic group $g$‎, ‎call $sigma(g)$ the smallest number of proper subgroups of $g$ needed to cover $g$‎. ‎lucchini and detomi conjectured that if a nonabelian group $g$ is such that $sigma(g) < sigma(g/n)$ for every non-trivial normal subgroup $n$ of $g$ then $g$ is textit{monolithic}‎, ‎meaning that it admits a unique minimal normal subgroup‎. ‎in this paper we show how thi...

The Ernst equation is formulated on an arbitrary Riemann surface. Analytically, the problem reduces to finding solutions of the ordinary Ernst equation which are periodic along the symmetry axis. The family of (punctured) Riemann surfaces admitting a non-trivial Ernst field constitutes a " partially discretized " subspace of the usual moduli space. The method allows us to construct new exact so...

We show how non-trivial form fields can induce an effective potential for the dilaton and metric moduli in compactifications of type II string theory and M–theory. For particular configurations, the potential can have a stable minimum. In cosmological compactifications of type II theories, we demonstrate that, if the metric moduli become fixed, this mechanism can then lead to the stabilization ...

Approximate solutions for optimization problems become of interest if the ‘true’ optimum cannot be found: this may happen for the simple reason that an optimum does not exist or because of the ‘bounded rationality’ (or bounded accuracy) of the optimizer. This paper characterizes several approximate solutions by means of consistency and additional requirements. In particular we consider invarian...

We discuss the existence of breather solutions for a Discrete Nonlinear Schrödinger equation in an infinite N-dimensional lattice, involving site dependent anharmonic parameter. We give a simple proof on the existence of (nontrivial) breather solutions based on variational approach, assuming that the sequence of anharmonic parameters is in an appropriate sequence space (decays with an appropria...

In this paper, we study a cubic predator-prey model with diffusion. We first establish the global stability of the trivial and nontrivial constant steady states for the reaction diffusion system, and then prove the existence and non-existence results concerning non-constant positive stationary solutions by using topological argument and the energy method, respectively.

Phenomenological evidence suggests the existence of non-trivial background fields in the QCD vacuum. On the other hand SU(3) gauge theory possessses three different classes of both non-generic and non-trivial strata that may be used as classical backgrounds. It is suggested that this threefold multiplicity of non-trivial vacua may be related to the existence of particle generations, which would...

We correct a flaw in the proof of [1, Lemma 2.3]. 1. Corrigendum. This Corrigendum concerns the proof of [1, Lemma 2.3]. In that proof there is a flaw in the estimate of log xk due to an incorrect inequality. We provide here a correct estimate of log xk in 1.5 which preserves the validity of Lemma 2.3. For the reader convenience we recall the statement of Lemma 2.3 and we give its complete proo...