Determination of traces of perchlorate in chlorate solutions

Perchlorate present in chlorate solutions is determined gravimetrically as tetraphenylphosphonium perchlorate after destruction of chlorate by addition of hydrochloric acid. Interference of Fe(III) and Cr(III) is prevented by complexing with tarartic acid. Replicate analyses of a sodium chlorate solution containing NaClO(3), NaCl, Na(2)Cr(2)O(7), and 390 ppm NaClO(4) showed 405 ppm NaClO(4) (standard deviation 19 ppm, 12 results).     

Hypercontractivity properties of nonsymmetric ornstein-uhlenbeck semigroups in hilbert spaces

We prove hypercontractivity of nonsymmetric Ornstein-Uhlenbeck semigroups in Hilbert spaces, using direct probabilistic arguments. Our results imply exponential convergence at infinity for the semigroup. We show by examples that in our setting logarithmic Sobolev inequalities do not hold in general     

A new σ‐transform based Fourier‐Legendre‐Galerkin model for nonlinear water waves

This paper presents a new spectral model for solving the fully nonlinear potential flow problem for water waves in a single horizontal dimension. At the heart of the numerical method is the solution to the Laplace equation which is solved using a variant of the $\sigma$‐transform. The method discretizes the spatial part of the governing equations using the Galerkin method and the temporal part using the classical fourth‐order Runge‐Kutta method. A careful investigation of the numerical method's stability properties is carried out, and it is shown that the method is stable up to a certain threshold steepness when applied to nonlinear monochromatic waves in deep water. Above this threshold artificial damping may be employed to obtain stable solutions. The accuracy of the model is tested for: (i) highly nonlinear progressive wave trains, (ii) solitary wave reflection, and (iii) deep water wave focusing events. In all cases it is demonstrated that the model is capable of obtaining excellent results, essentially up to very near breaking.     

Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem

We study a stochastic optimal control problem for a partially observed diffusion. By using the control randomization method in Bandini et al. (2018), we prove a corresponding randomized dynamic programming principle (DPP) for the value function, which is obtained from a flow property of an associated filter process. This DPP is the key step towards our main result: a characterization of the value function of the partial observation control problem as the unique viscosity solution to the corresponding dynamic programming Hamilton–Jacobi–Bellman (HJB) equation. The latter is formulated as a new, fully non linear partial differential equation on the Wasserstein space of probability measures. An important feature of our approach is that it does not require any non-degeneracy condition on the diffusion coefficient, and no condition is imposed to guarantee existence of a density for the filter process solution to the controlled Zakai equation. Finally, we give an explicit solution to our HJB equation in the case of a partially observed non Gaussian linear–quadratic model.     

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.     

Sums of generators of analytic semigroups and multivalued linear operators

Let A and B be generators of analytic semigroups in a Banach space. Under some conditions on the commutator of the resolvents of A and B, already considered in the literature and not implying relative boundedness, we prove that the closure of A+B (or a proper extension of it) also generates an analytic semigroup, and we characterize interpolation spaces related to it. As a tool, we use approximation and interpolation results for multivalued linear operators.     

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).     

Determination and differentiation of nitrilotriacetic acid and ethylenediaminetetra-acetic acid

Ethylenediaminetetra-acetic acid (EDTA) and nitrilotri-acetic acid (NTA) can be differentiated and determined by titration with metal ions to visual metallochromic dye end-points. EDTA can be determined without interference from NTA, either by titrating with copper(II) at pH 5 using PAN indicator, or by titrating with iron(III) at pH 6 and 70 degrees using Tiron indicator. The total chelating power (EDTA + NTA) can be determined either by titrating with lead(II) at pH 4.4 using dithizone indicator, or by titrating with iron(III) at pH 3.5 using Tiron indicator ; NTA is determined by difference. The lowest concentration at which NTA can be determined in EDTA by titration to the iron(III)-Tiron end-point is about 1 wt.%. The apparent stability constants of the iron(III)-Tiron complexes under the conditions of the titration at pH 3.5 and pH 6 have been determined using the method of continuous variations.     

Backward stochastic differential equations associated to jump Markov processes and applications

In this paper we study backward stochastic differential equations (BSDEs) driven by the compensated random measure associated to a given pure jump Markov process X$X$ on a general state space K$K$. We apply these results to prove well-posedness of a class of nonlinear parabolic differential equations on K$K$, that generalize the Kolmogorov equation of X$X$. Finally we formulate and solve optimal control problems for Markov jump processes, relating the value function and the optimal control law to an appropriate BSDE that also allows to construct probabilistically the unique solution to the Hamilton–Jacobi–Bellman equation and to identify it with the value function.