A boundary-value problem for Hamilton-Jacobi equations in hilbert spaces

We study a Hamilton-Jacobi equation in infinite dimensions arising in optimal control theory for problems involving both exit times and state-space constraints. The corresponding boundary conditions for the Hamilton-Jacobi equation, of mixed nature, have been derived and investigated in [19], [2], [5], and [15] in the finite-dimensional case. We obtain a uniqueness result for viscosity solutions of such a problem and then prove the existence of a solution by showing that the value function is continuous.The work of P. Cannarsa was partially supported by the Italian National Project Equazioni Differenziali e Calcolo delle Variazioni. H. M. Soner's work was supported by National Science Foundation Grant DMS-90-02249.     

Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension

In this paper, we study an economic model, where internal habits play a role. Their formation is described by a more general functional form than is usually assumed in the literature, because a finite memory effect is allowed. Indeed, the problem becomes the optimal control of a standard ordinary differential equation, with the past of the control entering both the objective function and an inequality constraint. Therefore, the problem is intrinsically infinite dimensional. To solve this model, we apply the dynamic programming approach and we find an explicit solution for the associated Hamilton–Jacobi–Bellman equation, which lets us write the optimal strategies in feedback form. Therefore, we contribute to the existing literature in two ways. Firstly, we fully develop the dynamic programming approach to a type of problem not studied in previous contributions. Secondly, we use this result to unveil the global dynamics of an economy characterized by generic internal habits.     

Unobserved Component models applied to the assessment of wear in railway points: A case study

Railways are experiencing a fundamental transformation. The introduction of high speed networks and the increased traffic levels on suburban routes and freight lines require new technologies for both railway infrastructure and trains, all of which must be subjected to rigorous quality control before and during operation and must be supported with effective maintenance processes during their operating lives. Safety in railway infrastructure provision must be ensured by all the main components operating reliably all the time. From an economic, quality and safety point of view, points are probably one of the most critical infrastructure elements in railway transportation.     

Twist points of the von Koch snowflake

It is known that the set of twist points in the boundary of the von Koch snowflake domain has full harmonic measure. We provide a new, simple proof, based on the doubling property of the harmonic measure, and on the existence of an equivalent measure, invariant and ergodic with respect to the shift.

     

A regularity result for a class of non-uniformly elliptic operators

Archiv der Mathematik - We obtain an explicit Hölder regularity result for viscosity solutions of a class of second order fully nonlinear equations led by operators that are neither...     

R-Matrices for Leibniz Algebras

Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties.     

The visibility function revisited

The visibility function of a compact setS E ^d assigns to eachx S the Lebesgue outer measure of its star inS. This function was introduced by G. Beer in 1972. In 1991, A. Forte Cunto characterized the points of discontinuity of the visibility function in the boundary of a planar Jordan domain. The basic intention of this paper is to extend this characterization to a compact subset ofE ^d . Under certain assumptions, it is proved here that the visibility function of such a set is continuous at a point if and only if the set of restricted visibility of this point has null Lebesgue outer measure.This paper was written as part of Argentine Research Project 01/TX38.     

Harnack inequality for two‐weight subelliptic p ‐Laplace operators

In this note, we prove a Harnack inequality for two‐weight subelliptic p ‐Laplace operators together with an upper bound of the Harnack constant associated with such inequality. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Complexes of tetracyclines with divalent metal cations investigated by stationary and femtosecond-pulsed techniques

Spectroscopic techniques both in steady-state (in absorption and emission) and pulsed (absorption of excited states with femtosecond resolution) conditions were used to study the complexation process between six molecules belonging to the tetracycline family and Mg(2+); in the case of TC the study was extended to the metal ions Ca(2+) and Cu(2+). The study was carried out in aqueous solution at various pH values, where one acid-base form of the substrate prevails over the others. The processing of experimental results, performed by means of Singular Value Decomposition and Global Analysis methods, allowed us to evaluate the extent of interaction through the association constants, to identify the number of equilibria present in solution and the stoichiometry (1:1 or 1:2) of the tetracycline:metal ion complex, and to define the spectral and photophysical properties of the latter (in terms of fluorescence quantum yields, lifetimes and rate constants). In fact, the (allowed) radiative decay process is a minor root for the lowest excited state of the complexes which mainly decay to the ground state by internal conversion. Details of the complexation sites are proposed for the various protonated forms of tetracyclines, and for the various cations in the case of TC. In particular, the molecular structure seems to affect significantly the dynamics of interaction when the upper peripheral region of tetracycline is rich in additional hydroxyl groups. Moreover, the state of protonation of the substrate produces changes in the order of the complexation sites, whose affinity for the cation increases significantly when they are negatively charged owing to the loss of protons. Magnesium and calcium (hard cations) give similar interactions, at least in acid solution, while copper(ii) (borderline cation) binds more efficiently on different sites, thus forming complexes with different properties.     

Low temperature Fourier transform infrared spectra and hydrogen bonding in polycrystalline uracil and thymine

The FTIR spectra of pure NH and isotopically diluted (NH/ND and ND/NH) polycrystalline uracil and thymine were measured in the range 4000-400 cm(-1) at temperatures from 300 to 10K. For the first time, the essentially narrow bands corresponding to the uncoupled stretching (nu(1)) and out of plane bending (nu(4)) NH proton modes of uracil and thymine were observed in the solid phase. It was found that in the nu(4) region the spectra reveal more details on the H-bond interactions present in both solids than in the nu(1) range. The frequencies of the various bands observed in both spectral regions were used for estimation of the H-bond energy, using empirical correlations between this property and both the red shift of nu(1) and the blue shift of nu(4) that occur upon crystallization due to the establishment of the H-bonds. The results are compared with known thermodynamic, structural and theoretical data. The IR data also suggest that the H-bond networks of both crystals contain, besides the two NH...O=C bonds revealed by X-ray experiments, additional types of H-bonds, which do not show long range periodicity and, thus, cannot be detected by the conventional structural methods. The assignment of some other bands in the spectra of both substances was also reviewed.