Global solutions for superlinear parabolic equations involving the biharmonic operator for initial data with optimal slow decay

We are interested in stability/instability of the zero steady state of the superlinear parabolic equation u _t + Δ² u = |u| ^p-1 u in , where the exponent is considered in the “super-Fujita” range p > 1 + 4/n. We determine the corresponding limiting growth at infinity for the initial data giving rise to global bounded solutions. In the supercritical case p > (n + 4)/(n−4) this is related to the asymptotic behaviour of positive steady states, which the authors have recently studied. Moreover, it is shown that the solutions found for the parabolic problem decay to 0 at rate t ^−1/(p-1).     

Similar Structural Dynamics for the Degradation of CH3NH3PbI3 in Air and in Vacuum

We investigate the degradation path of MAPbI₃ (MA=methylammonium) films over flat TiO₂ substrates at room temperature by means of X‐ray diffraction, spectroscopic ellipsometry, X‐ray photoelectron spectroscopy, and high‐resolution transmission electron microscopy. The degradation dynamics is found to be similar in air and under vacuum conditions, which leads to the conclusion that the occurrence of intrinsic thermodynamic mechanisms is not necessarily linked to humidity. The process has an early stage, which drives the starting tetragonal lattice in the direction of a cubic atomic arrangement. This early stage is followed by a phase change towards PbI₂. We describe how this degradation product is structurally coupled with the original MAPbI₃ lattice through the orientation of its constituent PbI₆ octahedra. Our results suggest a slight octahedral rearrangement after volatilization of HI+CH₃NH₂ or MAI, with a relatively low energy cost. Our experiments also clarify why reducing the interfaces and internal defects in the perovskite lattice enhances the stability of the material.     

Condensed‐Phase,Halogen‐Bonded CF3I and C2F5I Adducts for Perfluoroalkylation Reactions

A family of practical, liquid trifluoromethylation and pentafluoroethylation reagents is described. We show how halogen bonding can be used to obtain easily handled liquid reagents from gaseous CF₃I and CF₃CF₂I. The synthetic utility of the new reagents is exemplified by a novel direct arene trifluoromethylation reaction as well as adaptations of other perfluoroalkylation reactions.     

Effect of a plant fortifier (Boundary) on pests and predators of greenhouse vegetable crops

Boundary, a plant fortifier composed of extracts of Sophora flavescens Aiton and brown algae, was tested for control of the leaf miner Tuta absoluta (Meyrick) on tomato (three trials) and of the red spider mite Tetranychus urticae Koch on eggplant (one trial) and for side effects on the whitefly predator Macrolophus pygmaeus (Kambur) (two trials) on tomato and on the thrips predators Orius laevigatus (Fieber) and Amblyseius swirskii Athias-Henriot (two trials) on pepper, all in cold greenhouses in South Italy. Control rates for T. absoluta were moderate (40–70%) in the autumn crop but very high and comparable to those for emamectin benzoate in the spring crops (96–100%). Boundary compared well with abamectin against T. urticae, with near complete control. M. pygmaeus was moderately injured in late autumn, but not in early autumn. At the tested application rate and predator population density Boundary was safe for O. laevigatus and A. swirskii.     

Azidoethoxyphenylalanine as a Vibrational Reporter and Click Chemistry Partner in Proteins

An unnatural amino acid, 4‐(2‐azidoethoxy)‐L ‐phenylalanine (AePhe, 1 ), was designed and synthesized in three steps from known compounds in 54 % overall yield. The sensitivity of the IR absorption of the azide of AePhe was established by comparison of the frequency of the azide asymmetric stretch vibration in water and dimethyl sulfoxide. AePhe was successfully incorporated into superfolder green fluorescent protein (sfGFP) at the 133 and 149 sites by using the amber codon suppression method. The IR spectra of these sfGFP constructs indicated that the azide group at the 149 site was not fully solvated despite the location in sfGFP and the three‐atom linker between the azido group and the aromatic ring of AePhe. An X‐ray crystal structure of sfGFP‐149‐AePhe was solved at 1.45 Å resolution and provides an explanation for the IR data as the flexible linker adopts a conformation which partially buries the azide on the protein surface. Both sfGFP‐AePhe constructs efficiently undergo a bioorthogonal strain‐promoted click cycloaddition with a dibenzocyclooctyne derivative.     

Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks

In this paper, we investigate the application of penalty and relaxation methods to the problem of optimal placement and operation of control valves in water supply networks, where the minimization of average zone pressure is the objective. The optimization framework considers both the location and settings of control valves as decision variables. Hydraulic conservation laws are enforced as nonlinear constraints and binary variables are used to model the placement of control valves, resulting in a mixed-integer nonlinear program. We review and discuss theoretical and algorithmic properties of two solution approaches. These include penalty and relaxation methods that solve a sequence of nonlinear programs whose stationary points converge to a stationary point of the original mixed-integer program. We implement and evaluate the algorithms using a benchmarking water supply network. In addition, the performance of different update strategies for the penalty and relaxation parameters are investigated under multiple initial conditions. Practical recommendations on the numerical implementation are provided.     

A Sharp Upper Bound for the¶Torsional Rigidity of Rods¶by Means of Web Functions

Using web functions, we approximate the Dirichlet integral which represents the torsional rigidity of a cylindrical rod with planar convex cross-section Ω. To this end, we use a suitably defined piercing function, which enables us to obtain bounds for both the approximate and the exact value of the torsional rigidity. When Ω varies, we show that the ratio between these two values is always larger than ¾; we prove that this is a sharp lower bound and that it is not attained. Several extremal cases are also analyzed and studied by numerical methods.     

Searching for gallium bioactive compounds: Gallium(III) complexes of tridentate salicylaldehyde semicarbazone derivatives

In the search for gallium bioactive compounds five Ga(III) complexes, [Ga^III(L-H)₂](NO₃), with tridentate salicylaldehyde semicarbazone derivatives as ligands (L) have been synthesized and characterized in the solid state and in solution by different techniques. The crystal structure of [Ga^III(L4-H)₂](NO₃)·2H₂O, where L4 is 3-ethoxysalicylaldehyde semicarbazone, was solved by X-ray diffraction methods. The gallium(III) ion is in a distorted octahedral environment, coordinated to two nearly planar and mutually perpendicular 3-ethoxysalicylaldehyde semicarbazonato anions acting as tridentate ligands through their phenol and carbonyl oxygen atoms and their azomethine nitrogen atom. Their biological potential has been explored by evaluating their activity on Mycobacterium tuberculosis, causative agent of tuberculosis, and their cytotoxicity on tumor cell lines. Three different human tumor cell lines were selected that show different degrees of resistance to metallodrugs: ovarian A2780 (low resistance), breast MCF7 (medium resistance) and prostate PC3 (high resistance) cells. Although the complexes have not shown activity on M. tuberculosis, complexation with gallium has led to the enhancement of the cytotoxic potencies of the organic compounds. Those complexes that contain a bromide substituent at the phenolate ring have shown the highest cytotoxicities. In particular, [Ga^III(L2-H)₂](NO₃), where L2 is 5-bromosalicylaldehyde semicarbazone,·has shown a remarkable cytotoxicity on A2780 tumor cell line with an IC₅₀ value of the same order than cisplatin (IC_{50 Ga-L2} = 2.4 ± 0.3 μM; IC_{50 cisplatin} = 2.0 ± 0.1 μM, 72 h incubation at 37 °C). Interestingly, this complex has also shown moderate cytotoxicity against MCF7 and PC3 cells (IC_{50 MCF7} = 30 ± 6; IC_{50 PC3} = 18 ± 3 μM). Therefore, this gallium compound could be considered a promising wide spectrum potential anti-tumor agent.     

Solvent and TMEDA effects on the configurational stability of chiral lithiated aryloxiranes

The employment of hexane/N,N,N',N'-tetramethylethylenediamine (TMEDA) dramatically hinders the racemization of those lithiated styrene oxides (trifluoromethyl-, chloro-, and phenylthio-substituted) that have been proven to be configurationally unstable in THF on the timescale of their reactions. The barriers to inversion and the activation parameters, calculated (Eyring equation) for reactions performed in THF, THF/TMEDA, and hexane/TMEDA, suggest the intervention of particular enantiomerization mechanisms for each case. The role of TMEDA in both coordinating and noncoordinating solvents has also been questioned and discussed in light of the kinetic data gathered and a model for deprotonation in hexane/TMEDA has also been proposed. The synthetic benefits of our results became apparent on establishing an asymmetric synthesis of an industrially important antifungal agent.     

Panchromatic ruthenium sensitizer based on electron-rich heteroarylvinylene π-conjugated quaterpyridine for dye-sensitized solar cells

The first example of a heteroarylvinylene π-conjugated quaterpyridine Ru(II) sensitizer (N1044) was synthesized and used in dye-sensitized solar cells; the dye has an effective panchromatic absorption band, covering the entire visible spectrum up to the NIR region, and superior electrochemical characteristics (HOMO/LUMO and bandgap energies) with respect to previous representative Ru(II) bi- and quaterpyridine sensitizers. A record IPCE curve ranging from 360 to 920 nm has been measured with a maximum of 65% at 646 nm and still 33% efficiency at 800 nm; this leads to substantially increased photocurrent (19.2 mA cm(-2)) when compared to the prototype N719 Ru(II) sensitizer.