Time irregularity of generalized Ornstein--Uhlenbeck processes

The paper is concerned with the properties of solutions to linear evolution equation perturbed by cylindrical L\'evy processes. It turns out that solutions, under rather weak requirements, do not have c\`adl\`ag modification. Some natural open questions are also stated

Gold(I)-Catalyzed Reactivity of Furan-ynes with N-Oxides: Synthesis of Substituted Dihydropyridinones and Pyranones

[Image: see text] The reactivity of “furan-ynes” in combination with pyridine and quinoline N-oxides in the presence of a Au(I) catalyst, has been studied, enabling the synthesis of three different heterocyclic scaffolds. Selective access to two out of the three possible products, a dihydropyridinone and a furan enone, has been achieved through the fine-tuning of the reaction conditions. The reactions proceed smoothly at room temperature and open-air, and were further extended to a broad substrate scope, thus affording functionalized dihydropyridinones and pyranones

Controllability and Qualitative properties of the solutions to SPDEs driven by boundary L\'evy noise

Let $u$ be the solution to the following stochastic evolution equation (1) du(t,x)& = &A u(t,x) dt + B \sigma(u(t,x)) dL(t),\quad t>0; u(0,x) = x taking values in an Hilbert space \HH, where $L$ is a \RR valued L\'evy process, $A:H\to H$ an infinitesimal generator of a strongly continuous semigroup, \sigma:H\to \RR bounded from below and Lipschitz continuous, and B:\RR\to H a possible unbounded operator. A typical example of such an equation is a stochastic Partial differential equation with boundary L\'evy noise. Let \CP=(\CP_t)_{t\ge 0} %{\CP_t:0\le t<\infty}$the corresponding Markovian semigroup. We show that, if the system (2) du(t) = A u(t)\: dt + B v(t),\quad t>0 u(0) = x is approximate controllable in time$T>0$, then under some additional conditions on$B$and$A$, for any$x\in H$the probability measure$\CP_T^\star \delta_x$is positive on open sets of$H$. Secondly, as an application, we investigate under which condition on$\HH$and on the L\'evy process$L$and on the operator$A$and$B$ the solution of Equation [1] is asymptotically strong Feller, respective, has a unique invariant measure. We apply these results to the damped wave equation driven by L\'evy boundary noise

Selective Synthesis of a Salt and a Cocrystal of the Ethionamide-Salicylic Acid System

Herein is presented a rare example of salt/cocrystal polymorphism involving the adduct between ethionamide (ETH) and salicylic acid (SAL). Both the salt and cocrystal forms have the same stoichiometry and composition and are both stable at room temperature. The synthetic procedure was successfully optimized in order to selectively obtain both polymorphs. The two adducts' structures were thoroughly investigated by means of single-crystal X-ray diffraction, solid-state NMR spectroscopy, and density functional theory (DFT) calculations. From the solid-state NMR point of view, the combination of mono- and multinuclear experiments (1H MAS, 13C and 15N CPMAS, 1H-{14N} D-HMQC, 1H-14N PM-S-RESPDOR) provided undoubted spectroscopic evidence about the different positions of the hydrogen atom along the main N\ub7\ub7\ub7H\ub7\ub7\ub7O interaction. In particular, the 1H-14N PM-S-RESPDOR allowed N-H distance measurements through the 1H detected signal at a very high spinning speed (70 kHz), which remarkably agree with those derived by DFT optimized X-ray diffraction, even on a natural abundance real system. The thermodynamic relationship between the salt and the cocrystal was inquired from the experimental and computational points of view, enabling the characterization of the two polymorphs as enantiotropically related. The performances of the two forms in terms of dissolution rate are comparable to each other but significantly higher with respect to the pure ETH

Linear Operator Inequality and Null Controllability with Vanishing Energy for unbounded control systems

We consider linear systems on a separable Hilbert space $H$, which are null controllable at some time $T_0>0$ under the action of a point or boundary control. Parabolic and hyperbolic control systems usually studied in applications are special cases. To every initial state $y_0 \in H$ we associate the minimal "energy" needed to transfer $y_0$ to $0$ in a time $T \ge T_0$ ("energy" of a control being the square of its $L^2$ norm). We give both necessary and sufficient conditions under which the minimal energy converges to $0$ for $T\to+\infty$. This extends to boundary control systems the concept of null controllability with vanishing energy introduced by Priola and Zabczyk (Siam J. Control Optim. 42 (2003)) for distributed systems. The proofs in Priola-Zabczyk paper depend on properties of the associated Riccati equation, which are not available in the present, general setting. Here we base our results on new properties of the quadratic regulator problem with stability and the Linear Operator Inequality.Comment: In this version we have also added a section on examples and applications of our main results. This version is similar to the one which will be published on "SIAM Journal on Control and Optimization" (SIAM