Backward Stochastic Riccati Equations and Infinite Horizon L-Q Optimal Control with Infinite Dimensional State Space and Random Coefficients

We study the Riccati equation arising in a class of quadratic optimal control problems with infinite dimensional stochastic differential state equation and infinite horizon cost functional. We allow the coefficients, both in the state equation and in the cost, to be random. In such a context backward stochastic Riccati equations are backward stochastic differential equations in the whole positive real axis that involve quadratic non-linearities and take values in a non-Hilbertian space. We prove existence of a minimal non-negative solution and, under additional assumptions, its uniqueness. We show that such a solution allows to perform the synthesis of the optimal control and investigate its attractivity properties. Finally the case where the coefficients are stationary is addressed and an example concerning a controlled wave equation in random media is proposed.     

A biomimetic approach to the chemical inactivation of chrysotile fibres by lichen metabolites

Some lichens were recently reported to modify the surface state of asbestos. Here we report some new insight on the physico-chemical modifications induced by natural chelators (lichen metabolites) on two asbestos samples collected in two different locations. A biomimetic approach was followed by reproducing in the laboratory the weathering effect of lichen metabolites. Norstictic, pulvinic and oxalic acid (0.005, 0.5 and 50 mM) were put in contact with chrysotile fibres, either in pure form (A) or intergrown with balangeroite, an iron-rich asbestiform phase (B). Mg and Si removal, measured by inductively coupled plasma atomic emission spectrometry (ICP-AES) and scanning electron microscopy-energy dispersive X-ray spectroscopy (SEM-EDS), reveals an incongruent dissolution for pure chrysotile (A), with Mg removal always exceeding that of Si, while chrysotile-balangeroite (B) follows a congruent dissolution pattern in all cases except in the presence of 50 mM oxalic acid. A much larger removal of Mg than Si in the solutions of 0.5 and 50 mM oxalic acid with chrysotile (A) suggests a structural collapse, which in the case of chrysotile-balangeroite (B) only occurs with 50 mM oxalic acid; in these cases both samples are converted into amorphous silica (as detected by X-ray diffraction (XRD)). Subsequent to incubation, some new phases (Fe(2)O(3), CaMg(CO(3))(2), Ca(C(2)O(4)) x H(2)O and Mg(C(2)O(4))2 x H(2)O), similar to those observed in the field, were detected by XRD and micro-Raman spectroscopy. The leaching effect of lichen metabolites also modifies the Fenton activity, a process widely correlated with asbestos pathogenicity: pure chrysotile (A) activity is reduced by 50 mM oxalic acid, while all lichen metabolites reduce the activity of chrysotile-balangeroite (B). The selective removal of poorly coordinated, highly reactive iron ions, evidenced by NO adsorption, accounts for the loss in Fenton activity. Such fibres were chemically close to the ones observed in the field. Chrysotile-rich rocks, colonised by lichens, could be exposed to a natural bioattenuation and considered as a transient environmental hazard.     

Pyroxene inclusions in paleo-Christian mosaic tesserae: a new tool for constraining the glass manufacturing temperature

The mineral inclusions of two orange glass tesserae from paleo-Christian mosaics were investigated in order to derive the melting temperature reached during their production (sourced from Padua and Vicenza, Veneto region, Italy). In particular, clinopyroxene crystals were studied by single-crystal X-ray diffraction and electron microprobe WDS analysis. The crystals show C2/c symmetry, typical of disordered Ca/Na and Mg/Al distributions indicating high-temperature of formation (>700°C). The cation site populations were obtained by combining results from the two experimental techniques enabled us to derive the following stoichiometric formula:

Ergodic BSDEs under weak dissipative assumptions

In this paper we study ergodic backward stochastic differential equations (EBSDEs) dropping the strong dissipativity assumption needed in Fuhrman et al. (2009) [12]. In other words we do not need to require the uniform exponential decay of the difference of two solutions of the underlying forward equation, which, on the contrary, is assumed to be non-degenerate.We show the existence of solutions by the use of coupling estimates for a non-degenerate forward stochastic differential equation with bounded measurable nonlinearity. Moreover we prove the uniqueness of “Markovian” solutions by exploiting the recurrence of the same class of forward equations.Applications are then given for the optimal ergodic control of stochastic partial differential equations and to the associated ergodic Hamilton-Jacobi-Bellman equations.     

Glaucopine C, a new diterpene from the fruiting bodies of Sarcodon glaucopus

In this work the mushroom Sarcodon glaucopus was studied. A new cyathane, glaucopine C (1), was isolated from the hexane extract and identified by 1H and 13C NMR spectra analysis. Glaucopine C showed anti-inflammatory acitvity.     

IR and theoretical studies of monocarbonyl Ni complexes formed by adsorption of CO at low pressure on silica-supported Ni(II) ions

This work reports on the reactivity of coordination vacancies of Ni(II) ions grafted onto the tridentate silica support (Ni(II)(3c) ions) with respect to CO used as a probe molecule. The adsorption of CO at 77 K in the 0.3 to 3.5 Pa CO pressure range is studied by FTIR on two samples differing in the dispersion of nickel. Quantum chemical calculations by the DFT method are performed to investigate, using a cluster approach, the binding of Ni to silica and, after CO adsorption, the geometry of the resulting carbonyl Ni complexes. Silica is modeled by using clusters composed of three types of monodentate ligands, SiO(-), SiOSi and/or SiOH, found on the surface of silica. This work is devoted to the monocarbonyl complexes. Whatever the sample, only one type of monocarbonyl is formed from Ni(II)(3c) ions. It is shown that the charge of the silica cluster is the major parameter influencing the CO IR frequency whereas the nature and the size of the silica cluster do not affect the CO bond length, confirming that local electrostatic interactions predominate. Only the 1- charged silica cluster Si(5)O(3)(-), composed of SiO(-), 2SiOSi fragments, respectively, reproduces the Ni[bond]O distances derived from EXAFS for the Ni(II)(3c) grafted site and gives CO frequencies in good agreement with the experimental values. It is shown that CO is stabilized by a magnetic transition from the (3)Ni(2+) triplet to the (1)Ni(2+) singlet state occurring upon adsorption.     

Linear-quadratic optimal control under non-Markovian switching

We study a finite-dimensional continuous-time optimal control problem on finite horizon for a controlled diffusion driven by Brownian motion, in the linear-quadratic case. We admit stochastic coefficients, possibly depending on an underlying independent marked point process, so that our model is general enough to include controlled switching systems where the switching mechanism is not required to be Markovian. The problem is solved by means of a Riccati equation, which turned out to be a backward stochastic differential equation driven by the Brownian motion and by the random measure associated with the marked point process.     

Lab‐on‐a‐Chip Reactor Imaging with Unprecedented Chemical Resolution by Hadamard‐Encoded Remote Detection NMR

The development of microfluidic processes requires information‐rich detection methods. Here we introduce the concept of remote detection exchange NMR spectroscopy (RD‐EXSY), and show that, along with indirect spatial information extracted from time‐of‐flight data, it provides unique information about the active regions, reaction pathways, and intermediate products in a lab‐on‐a‐chip reactor. Furthermore, we demonstrate that direct spatial resolution can be added to RD‐EXSY efficiently by applying the principles of Hadamard spectroscopy.     

Stochastic maximum principle for optimal control of SPDEs

In this Note, we give the stochastic maximum principle for optimal control of stochastic PDEs in the general case (when the control domain need not be convex and the diffusion coefficient can contain a control variable).