A stochastic maximum principle for processes driven by fractional Brownian motion

We prove a stochastic maximum principle for controlled processes X(t)=X^(u)(t) of the form

dX(t)=b(t,X(t),u(t)) dt+σ(t,X(t),u(t)) dB^(H)(t),

where B^(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter . As an application we solve a problem about minimal variance hedging in an incomplete market driven by fractional Brownian motion.     

An algorithm for the computation of consistent initial values for differential–algebraic equations

We use boundary value methods to compute consistent initial values for fully implicit nonlinear differential-algebraic equations. The obtained algorithm uses variable order formulae and a deferred correction technique to evaluate the error. A rigorous theory is stated for nonlinear index 1, 2 and 3 DAEs of Hessenberg form. Numerical tests on classical index 1, 2 and 3 DAE problems are reported. This revised version was published online in June 2006 with corrections to the Cover Date.     

Segments and Hilbert schemes of points

Using results obtained from a study of homogeneous ideals sharing the same initial ideal with respect to some term order, we prove the singularity of the point corresponding to a segment ideal with respect to a degreverse term order (as, for example, the degrevlex order) in the Hilbert scheme of points in Pⁿ. In this context, we look into the properties of several types of “segment” ideals that we define and compare. This study also leads us to focus on the connections between the shape of generators of Borel ideals and the related Hilbert polynomial, thus providing an algorithm for computing all saturated Borel ideals with a given Hilbert polynomial.     

Convex Hamilton-Jacobi Equations Under Superlinear Growth Conditions on Data

Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness of viscosity solutions growing at most like o(1+|x| ^p ) at infinity for such HJB equations and more generally for degenerate parabolic equations with a superlinear convex gradient nonlinearity. If the corresponding control problem has a bounded diffusion with respect to the control, then our results apply to a larger class of solutions, namely those growing like O(1+|x| ^p ) at infinity. This latter case encompasses some equations related to backward stochastic differential equations.     

Bifurcation and symmetry breaking for a class of semilinear elliptic equations in an annulus

In this paper we consider the problem $$\left\{ \begin{array}{ll} -\Delta u=u^p+\lambda u & \quad\hbox{ in }A,\\ u > 0&\quad \hbox{ in }A,\\ u=0 &\quad \hbox{ on }\partial A, \end{array}\right. $$ where A is an annulus of ${\mathbb{R}^N,N\ge2}$ and p?>?1. We prove bifurcation of nonradial solutions from the radial solution in correspondence of a sequence of exponents {p _k } and for expanding annuli.     

Differential Inclusions and Monotonicity Conditions for Nonsmooth Lyapunov Functions

In this paper we address the problem of characterizing the infinitesimal properties of functions which are nonincreasing along all the trajectories of a differential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous differential inclusions. Moreover, we show that the same criterion applies also in the case of Lipschitz continuous functions and continuous differential inclusions.     

Dynamic crossover in hydration water of curing cement paste: the effect of superplasticizer

The influence of a new comb-shaped polycarboxylate-based superplasticizer (CSSP) on the hydration kinetics and transport properties of aged cement pastes has been investigated by high-resolution quasi-elastic neutron scattering (QENS) and low temperature differential scanning calorimetry (LT-DSC). A new method of analysis of QENS spectra is proposed. By applying the refined method we were able to access to four independent physical parameters including the self-diffusion coefficient of the hydration water confined in the cement paste. Mean squared displacement (MSD) of the hydrogen atom for mobile water molecules displays a dynamic crossover temperature in agreement with DSC data. The experimental results indicate that CSSP polymer added into cement paste moderates the hydration process and decreases the dynamic crossover temperature of the hydration water.     

Towards modelling the vibrational signatures of functionalized surfaces: carboxylic acids on H-Si(111) surfaces

In this work, we investigate the adsorption process of two carboxylic acids (stearic and undecylenic) on a H-Si(111) surface via the calculation of structural and energy changes as well as the simulation of their IR and Raman spectra. The two molecules adsorb differently at the surface since the stearic acid simply physisorbs while the undecylenic acid undergoes a chemical reaction with the hydrogen atoms of the surface. This difference is observed in the change of geometry during the adsorption. Indeed, the chemisorption of the undecylenic acid has a bigger impact on the structure than the physisorption of the stearic acid. Consistently, the former is also characterized by a larger value of adsorption energy and a smaller value of the tilting angle with respect to the normal plane. For both the IR and Raman signatures, the spectra of both molecules adsorbed at the surface are in a first approximation the superposition of the spectra of the Si cluster and of the carboxylic acid considered individually. The main deviation from this simple observation is the peak of the stretching Si-H (ν(Si-H)) mode, which is split into two peaks upon adsorption. As expected, the splitting is bigger for the chemisorption than the physisorption. The modes corresponding to atomic displacements close to the adsorption site display a frequency upshift by a dozen wavenumbers. One can also see the disappearance of the peaks associated with the C=C double bond when the undecylenic acid chemisorbs at the surface. The Raman and IR spectra are complementary and one can observe here that the most active Raman modes are generally IR inactive. Two exceptions to this are the two ν(Si-H) modes which are active in both spectroscopies. Finally, we compare our simulated spectra with some experimental measurements and we find an overall good agreement.     

Interpreting technical evidence from spectral imaging of paintings by Édouard Manet in the Courtauld Gallery

The paintings by Édouard Manet in The Courtauld Gallery Déjeuner sur l'herbe (1863–68), Marguerite de Conflans en Toilette de Bal (1870–1880), Banks of the Seine at Argenteuil (1874), and A Bar at the Folies–Bergère (1882) were investigated for the first time using a range of non-invasive in situ analyses. The aims of the study were to investigate the painting techniques and materials used for this group of works and to critically evaluate the technical evidence derived from the integrated use of imaging techniques and portable spectroscopic methods in this context. The paintings were investigated by means of macro X-ray fluorescence (MA-XRF), reflection spectral imaging, portable UV–Vis–NIR spectroscopy, portable Raman spectroscopy, and reflection FTIR. MA-XRF and reflection spectral imaging allowed visualising elements in the compositions that were not visible using traditional methods of technical study. For example, MA-XRF analysis of Déjeuner sur l'herbe revealed elements of the development of the composition that provided new evidence to consider its relationship to other versions of the composition. The study also highlighted questions about the interpretation of elemental distribution maps and spectral images that did not correspond to the reworking visible in X-radiographs. For example, in A Bar at the Folies–Bergère Manet made numerous changes during painting, which were not clearly visualised with any of the techniques used. The research has wider implications for the study of Impressionist paintings, as the results will support technical studies of works by other artists of the period who used similar materials and painting methods.