On continuous parametrization of a family of separators of a locally connected curve

The question (raised in [7]) whether every homogeneous family of separators of a locally connected metrizable space Y, which is a partition of Y and has the continuum power, admits a continuous parametrization, is studied in the realm of locally connected curves

Symmetrization in a Neumann problem

Let w be a weak solution of the Neumann problem for a second order elliptic equation in divergence form, in abounded open subset G of Rn . In the case that the right hand side of the equation is a continuous linear functional on H1(G) , we give some symmetrization results and an estimate of the norm of w

Existence theorems for completely non convex problems

In this note we give some existence theorems for integral functionals with non convex integrand. We consider first the simpler case in which minimization is taken on decomposable spaces and successively we prove an existence theorem also for the minimum of an integral functional on non-decomposable space

Riesz spaces valued submeasures and application to group-valued finitely additive measures

As a consequence of a general Domination Theorem given for a subadditive measure with values in a Riesz space, we prove the arcwise connectedness of the range of a L.C.V.T.S.-valued and of a group-valued finitely additive measure

The nonlinear continuum traffic equilibrium problem and a related Dirichlet problem for quasilinear elliptic equations

In the framework of continuum models, a system-optimization problem for transportation networks is studied in nonlinear case. Some results of convex analysis are used to prove the existence theorems and to derive variational inequalities for optimal flow. A nonhomogeneous Dirichlet problem is proved to solve the minimization problem, provided that some non standard conditions on first derivatives of the solutions are fulfilled

An almost sure invariance principle for the maps S_a(x)=ax(1-x) in the interval [0,1]

In this paper we consider the family of maps in the unit interval defined by Sa(x)=ax(1-x), x∈[0,1], a∈[0,4]. For a countable set of values of a for which the a.c. Sa-invariant measure μa exists, we show an almost sure invariance principle for the process {f∘ Sia}, with f a function of bounded p-variation; from this the previously proved central limit theorem with respect to μa follows again; moreover log-log-laws and weak invariance principles for the process {f∘ Sia} follow