An inequality concerning the growth bound of an evolution family and the norm of a convolution operator

Let \(\mathcal {U}=\{U(t,s)\}_{t\ge s\ge 0}\) be a strongly continuous and exponentially bounded evolution family acting on a complex Banach space X and let \(\mathcal {X}\) be a certain Banach function space of X-valued functions. We prove that the growth bound of the family \(\mathcal {U}\) is less than or equal to \(-\frac{1}{c(\mathcal {U}, \mathcal {X})}\) provided that the convolution operator \(f\mapsto \mathcal {U}*f\) acts on \(\mathcal {X}.\) It is well known that under the latter assumption, the convolution operator is bounded and then \(c(\mathcal {U}, \mathcal {X})\) denotes (ad-hoc) its norm in \(\mathcal {L}(\mathcal {X}).\) As a consequence, we prove that if \(\sup \nolimits _{s\ge 0}\int \nolimits _{s}^\infty \Vert U(t,s)\Vert dt=u_1(\mathcal {U})<\infty ,\) then \(\omega _0(\mathcal {U})u_1(\mathcal {U})\le -1.\) Finally, we give an example showing that the accuracy of the estimates may be quite accurate.     

Parametric generation of twin photons in vertical triple microcavities

We report the realization of a monolithic vertical-cavity, surface emitting micro-optical parametric conversion nanostructure, triply resonant with the parametric frequencies, allowing parametric oscillation with ultra-low pump power threshold. The photonic phase-space naturally provides triple resonance for the parametric frequencies, together with built-in cavity phase-matching for the pump wave at normal incidence. Parametric oscillation is observed in both the strong and weak exciton–photon coupling regime, allowing a high operating temperature. Signal and idler beams can be collected at 0° or at finite angles. The OPO threshold is low enough to envisage the realization of an all-semiconductor electrically-pumped micro-parametric oscillator. To cite this article: C. Diederichs et al., C. R. Physique 8 (2007).     

Synthesis of C8-glycomimetics as potential glycosidases inhibitors

The synthesis of C8-glycomimetics is described from C₂-symmetrical polyhydroxylated cyclooctenes derived from carbocyclisation of enantiomerically pure 1,9-dienes by ring closing metathesis. Their obtention notably involved either hydroboration followed by oxidation to carbasugars or to cyclooctanones then reductive amination, or formation of a cis-cyclic sulfate followed by successive introduction of an azido group, reduction and subsequent reductive amination. The biological activity of the C8-carbasugars and related aminocyclitols, analogous to voglibose, has been evaluated towards several commercially available glycosidases.     

Guest Covalent Capture by a Host: A Biomimetic Strategy for the Selective Functionalization of a Cavity

A biomimetic strategy for the monofunctionalization of a calix[6]arene core is described. It is based on host–guest chemistry (mimicking the Michaelis–Menten adduct in enzymes) and allows the finely tuned pre‐organization of the substrate (an alkyne) with respect to the reactant (three azido groups introduced at the calixarene large rim). It is shown that the thermal Huisgen reaction implemented in this work proceeds under very mild conditions with total regioselectivity of the cycloaddition process. The scope of the reaction was explored and the results suggest that such a supramolecular strategy is quite versatile and could be applied to the selective functionalization of other cavitands bearing different recognition patterns. A detailed structural, thermodynamic, and kinetic study is also reported, highlighting interesting biomimetic features: The importance of the host–guest adduct strength, the high sensitivity of the reaction to the pre‐organization of the reactive partners (alkyne vs. azide), and a significant impact of the embedment on the transition state. The self‐coordination of the monofunctionalized products was also studied and an “endo/exo” switch of the internal side‐chain could be triggered by adding competitive ligands.     

Evaluation of recombinant green fluorescent protein, under various culture conditions and purification with HiTrap hydrophobic interaction chromatography resins

To determine the influence of various culture conditions, transformed cells of Escherichia coli expressing recombinant green fluorescent protein (GFPuv) were grown in nine cultures with four variable conditions (storage of inoculated broth at 4°C prior to incubation, agitation speed, isopropyl-β-d-thiogalactopyranoside [IPTG] concentration, and induction time). The pelleted cells were resuspended in extraction buffer and subjected to the three-phase partitioning (TPP) extraction method. To determine the most appropriate purification resin, protein extracts were eluted through one of four types of HiTrap hydrophobic interaction chromatography (HIC) columns prepacked with methyl, butyl, octyl, or phenyl resins and analyzed further on a 12% sodium dodecylsulfatepolyacrylamidegel. With Coomassie staining, a single band between 27 (standard GFPuv) and 29 kDa (molecular weight standard) was visualized for every HIC column sample. TPP extraction with HIC elution provided about 90% of the GFPuv recovered and eight-fold GFPuv enrichment related to the specific mass. Rotary speed and IPTG concentration showed, respectively, greater negative and positive influences on GFPuv expression at the beginning of the logarithmic phase for the set culture conditions (37°C, 24-h incubation).     

Self-induced "electroclick" immobilization of a copper complex onto self-assembled monolayers on a gold electrode

We report the self-induced "electroclick" immobilization of the [Cu(II)(6-ethynyl-TMPA)(H(2)O)](2+) complex, by its simple electro-reduction, onto a mixed azidoundodecane-/decane-thiol modified gold electrode. The redox response of the grafted [Cu(II/I)(TMPA)] at the modified electrode is fully reversible indicating no Cu coordination change and a fast electron transfer.     

Synthesis and spectral properties of 7‐chloro‐5‐[(o‐ and p‐R1)phenyl]‐1‐R2‐3H‐[1,4]benzodiazepin‐2‐ones

A series of twelve new 7‐chloro‐5‐[(o‐ and p‐R₁)phenyl]‐1‐R₂‐3H‐[1,4] benzo‐diazepin‐2‐ones, which have possible pharmacological properties were synthesized. The synthesis of all the final compounds was carried out by four steps. The structure of all final products was corroborated by ir, ¹H nmr, ¹³C nmr and ms, and have been obtained in 35‐94% yield.     

Synthesis and spectral properties of 2‐methylthio‐3H‐7‐[(o‐; m‐ and p‐substituted)phenoxy]‐4‐(p‐substituted‐phenyl)‐[1,5]benzodiazepines

A series of eleven new 2‐methylthio‐3H‐7‐[(o‐; m‐ and p‐substituted) phenoxy]‐4‐(p‐substituted‐phenyl)‐[1,5]benzodiazepines, which have potentially useful pharmacological activities, has been synthesized by condensing the 4‐[(o‐; m‐ and p‐R₁)phenoxy]‐1,2‐phenylendiamines with 3,3‐dimercapto‐1‐(p‐R₂‐phenyl)‐2‐propen‐1‐one. Afterward the lH‐[1,5]benzodiazepine‐2‐thiones obtained were treated with sodium hydride and methyl iodide. The structure of all products was corroborated by ir, ¹H nmr, ¹³C nmr and ms.