Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing

We study the large-time behavior and rate of convergence to the invariant measures of the processes dX (t)=b(X) (t)) dt + (X (t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/² , the transition density has a good lower bound and when the process has run for about exp( – )/², it is very close to the invariant measure. LetL =(²/2) – U · be a second-order differential operator on ^d. Under suitable conditions,L ^z has the discrete spectrum

Two-generator subgroups of soluble groups and their Fitting subgroups

For soluble groups, the Fitting length is bounded by a function of the maximum order of the Fitting subgroups of 2-generator subgroups.     

Measurability implies continuity for solutions of functional equations - even with few variables

Summary. We prove that - under certain conditions - measurable solutions $f$ of the functional equation $f(x)=h(x,y,f(g_{1}(x,y)),\ldots,f(g_{n}(x,y))),\quad(x,y)\in D \subset \mathbb{R}^{s} \times \mathbb{R}^{l}$ are continuous, even if $1\le l\le s$. As a tool we introduce new classes of functions which - roughly speaking - interpolate between continuous and Lebesgue measurable functions. Connection between these classes are also investigated.     

The Solow model improved through the logistic manpower growth law

In this paper the neo-classical economic Solow-Swan model (1956) has been improved replacing its Malthusian manpower law with the Verhulst (logistic) one. The relevant ordinary differential equation for the ratio capital/work has been then integrated in closed form via the Hypergeometric function₂ F ₁. The logistic growth injection for the manpower is detected to induce a more slow dynamics onto the Solow-Swan system, which keeps its stability. Increasing developments are displayed as the technologic progress rises. Further sceneries are tested and the congruence of the new solution with the classical one is shown switching to zero the selflimitation coefficent in the logistic law. Research supported by MURST grant:Metodi matematici in economia     

Hypersurfaces of the Euclidean sphere with nonnegative Ricci curvature

In this paper we prove that a compact oriented hypersurface of a Euclidean sphere with nonnegative Ricci curvature and infinite fundamental group is isometric to an H(r)-torus with constant mean curvature. Furthermore, we generalize, whithout any hypothesis about the mean curvature, a characterization of Clifford torus due to Hasanis and Vlachos. Received: 19 March 2002     

A remark on the moduli field of a curve

We give a purely algebro-geometric proof of the fact that every nonsingular projective curve can be defined over a finite extension of its moduli field. This extends a result byWolfart [7] to curves over fields of arbitrary characteristic. Received: 30 November 2001     

Harmonicity and gauge transformations in dimension 3

Let (M, ) be a contact manifold. Consider a particular class of gauge transformations for the contact form . In this note we study the harmonicity of the identity map of the manifold M, of dimension three, endowed with the Webster metric g and with another metric $\widetilde{g}$ obtained from g after a gauge transformation.     

End effects for pre-stressed and pre-polarized piezoelectric solids in anti-plane shear

This paper is concerned with investigation of the influence of pre-stress and pre-polarization on the decay of Saint-Venant end effects in piezoelectric solids. This issue is examined within the framework of incremental anti-plane shear states for prestressed and prepolarized solids. Attention is confined to a specific class of materials, namely those of hexagonal 6mm or 4mm symmetry. It is shown that the mechanical and electrical fields uncouple in this case, and the governing system of coupled second-order linear partial differential equations uncouple to a single homogeneous second-order equation with constant coefficients for the displacement and a Poisson equation for the electric potential. The exact decay rate for mechanical and electrical end effects is determined and the influence of pre-stress and pre-polarization is assessed. Motivation for this work arises from the current rapid developments in smart materials technology.     

On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

 We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond–J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Perron algorithm. Received September 30, 2001; in revised form January 8, 2002