Sharp geometric condition for null-controllability of the heat equation on $$\mathbb {R}^d$$ and consistent estimates on the control cost

In this note we study the control problem for the heat equation on \(\mathbb {R}^d\), \(d\ge 1\), with control set \(\omega \subset \mathbb {R}^d\). We provide a necessary and sufficient condition (called \((\gamma , a)\)-thickness) on \(\omega \) such that the heat equation is null-controllable in any positive time. We give an estimate of the control cost with explicit dependency on the characteristic geometric parameters of the control set. Finally, we derive a control cost estimate for the heat equation on cubes with periodic, Dirichlet, or Neumann boundary conditions, where the control sets are again assumed to be thick. We show that the control cost estimate is consistent with the \(\mathbb {R}^d\) case.     

Integrating Operations Research in Constraint Programming

This paper presents Constraint Programming as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of propagation and tailored algorithms for global constraints. It also allows linear programming to be combined with propagation and novel and varied search techniques which can be easily expressed in CP. The paper describes how CP can be used to exploit linear programming within different kinds of hybrid algorithm. In particular it can enhance techniques such as Lagrangian relaxation, Benders decomposition and column generation.     

Solvent-free microwave-assisted extraction of fluoroquinolones from soil and liquid chromatography-fluorescence determination

Presented hereafter is a novel method entailing solvent free microwave-assisted extraction (MAE) and HPLC equipped with Fluorimetric Detector (HPLC-FD) for the simultaneous determination at μgkg(-1) concentration of eight fluoroquinolone antibiotics (FQs) (Ciprofloxacin, Danofloxacin, Enrofloxacin, Flerofloxacin, Levofloxacin, Marbofloxacin, Norfloxacin and Orbifloxacin) in agricultural soils. The extraction was quantitatively performed, in a single step, by using an aqueous solution containing Mg(II) as complexing agent, thus avoiding consumption of organic solvents. The optimal MAE conditions have been established through a chemometric approach by considering temperature, irradiation time and matrix moisture or solvent, as the most important recognized variables affecting the extraction yield. Satisfying recoveries (69-110%, spikes 0.03-0.5mgkg(-1)) were gained with a single MAE cycle of 20min, at 80°C in 20% (w/v) Mg(NO(3))(2) solution as leaching agent. MAE-SPE recoveries at 10μgkg(-1), concentration near method quantification limits (MQLs), were in the range 60-85%. Good repeatability and within-lab reproducibility were observed (both in the range 1-16%). The applicability of the method to real samples was assessed on natural contaminated soils. Compared to ultrasonic-assisted extraction (UAE), MAE was shown to be highly competitive in terms of extraction efficacy and analysis speed.     

The synthesis of 2-oxyalkyl-cyclohex-2-enones, related to the bioactive natural products COTC and antheminone A, which possess anti-tumour properties

The syntheses of five novel 2-oxyalkyl-cyclohex-2-enones, structurally related to the natural products COTC and antheminone A, are described. The target structures were selected in order to probe the influence of several key structural parameters on in vitro anti-cancer bioactivity. The results of a cytotoxicity bioassay of the compounds against non-small-cell lung cancer cell lines A549 and H460 are reported. The biological data provides useful information, which will help guide the future design of compounds in this class with enhanced anti-cancer activity.     

Synthesis of mixed Ar,Ar'-BIAN ligands (Ar,Ar'-BIAN = bis(aryl)acenaphthenequinonediimine). Measurement of the coordination strength of hemilabile ligands with respect to their symmetric counterparts

The synthesis of Ar,Ar'-BIAN ligands (Ar,Ar'-BIAN = bis(aryl)acenaphthenequinonediimine) having different aryl groups bound to the two nitrogen atoms is reported for the first time. The ligands were obtained by two different strategies: (i) by a transimination reaction starting from a symmetric Ar,Ar-BIAN ligand having aryl groups bearing strongly electron-withdrawing substituents or (ii) by a two-step-one-pot sequence. The ligands synthesized have been chosen so that the electronic difference between the two aryl groups is very large, but the steric difference is variable and, in one case, the ligand is almost sterically symmetric. The coordination strength of the new ligands towards three palladium complexes has been measured by a competition experiment following a protocol previously described by us. The coordination strength of the mixed ligands is the mean of those of the corresponding symmetric counterparts. The X-ray crystal structure of a palladium pi-allyl complex of the electronically asymmetric-sterically symmetric ligand (3,5-(CF(3))(2)C(6)H(3)),(3,5-Me(2)C(6)H(3))-BIAN has been solved, together with those of the two symmetric analogues to allow a comparison. Despite the fact that the dodecafluorinated ligand has a K(eq) value about three orders of magnitude lower than the non-fluorinated counterpart, no notable difference is observed in the N-Pd and Pd-C(allyl) distances in the three complexes. Calculations at the density functional level confirm that Pd-BIAN distances are not strictly correlated to the coordination energies, which are in qualitative agreement with the spectroscopic evidence. The bond length is thus not a good indication of the bond strength in these cases.     

Direct immobilisation of DNA probes for the development of affinity biosensors

An immobilisation procedure based on the direct coupling of thiolated probes (Probe-C6-SH) to bare gold sensor surfaces has been compared with a reference immobilisation method, based on the coupling of biotinylated probes onto a streptavidin-coated dextran-modified surface. The instrumentations used were a quartz crystal microbalance (QCM) and the optical instruments Biacore X and Spreeta based on surface plasmon resonance (SPR). The performances of the DNA-based sensors resulting from direct coupling of thiolated DNA probes onto electrodes of quartz crystals or gold SPR-chips have been studied in terms of the main analytical parameters, i.e. selectivity, sensitivity, reproducibility, etc. In particular, the two immobilisation approaches have been applied to the analysis of oligonucleotides, DNA amplified by polymerase chain reaction (PCR) and genomic DNA enzymatically digested.     

Solute-solvent interactions and chiral induction in liquid crystals

The induction of a cholesteric phase by doping an achiral nematic liquid crystal with an enantiopure solute is a phenomenon that, as in all general supramolecular phenomena of chiral amplification, depends in a subtle way on intermolecular interactions. The micrometric helical deformation of the phase director in the cholesteric phase is generated by the interplay of anisotropy and chirality of probe-medium interactions. In the case of a flexible chiral dopant, the solvent can influence the twisting power in two ways, difficult to disentangle: it is responsible for the solute orientational order, an essential ingredient for the emergence of phase chirality; but also it can affect the dopant conformational distribution and then the chirality of the structures present in the solution. In this work we have investigated methyl phenyl sulfoxide, a flexible, chiral molecule that, when dissolved in different nematics, can produce cholesteric phases of opposite handedness. This peculiar, intriguing sensitivity to the environment makes MPS a suitable probe for a thorough investigation of the effects of solute-solvent interactions on chiral induction in liquid crystals. NMR experiments in various nematic solvents have been performed in addition to twisting power measurements. From the analysis of partially averaged 1H-1H and 13C-1H dipolar couplings, the effects of solvent on solute conformation and orientational order are disentangled, and this information is combined with the modeling of the chirality of intermolecular interactions, within a molecular field theory. The integration of different techniques allows an unprecedented insight into the role of solvent in mediating the chirality transfer from molecule to phase.