Primal-Lower-Nice Property of Value Functions in Optimization and Control Problems

The paper studies value functions associated with optimization problems and with Mayer-type control problems. Using methods belonging to proximal analysis and control theory, we establish new results for the primal-lower-nice (pln) property of the value functions for these problems.     

Distance Function Associated to a Prox-regular set

Set-Valued and Variational Analysis - In this paper, we provide in a general Hilbert space new characterizations of uniform prox-regularity involving outside but sufficiently close points of...     

Methylerythritol Phosphate Pathway: Enzymatic Evidence for a Rotation in the LytB/IspH-Catalyzed Reaction

IspH/LytB, an oxygen-sensitive [4Fe-4S] enzyme, catalyzes the last step of the methylerythritol phosphate (MEP) pathway, a target for the development of new antimicrobial agents. This metalloenzyme converts (E)-4-hydroxy-3-methylbut-2-en-1-yl diphosphate (HMBPP) into the two isoprenoid precursors: isopentenyl diphosphate (IPP) and dimethylallyl diphosphate (DMAPP). Here, the synthesis of (S)-[4-²H₁]HMBPP and (R)-[4-²H₁]HMBPP is reported together with a detailed NMR analysis of the products formed after their respective incubation with E. coli IspH/LytB in the presence of the biological reduction system used by E. coli to reduce the [4Fe-4S] center. (S)-[4-²H₁]HMBPP was converted into [4-²H₁]DMAPP and (E)-[4-²H₁]IPP, whereas (R)-[4-²H₁]HMBPP yielded [4-²H₁]DMAPP and (Z)-[4-²H₁]IPP, hence providing the direct enzymatic evidence that the mechanism catalyzed by IspH/LytB involves a rotation of the CH₂OH group of the substrate to display it away from the [4Fe-4S].     

Controlled Growth of Ag Nanocrystals in a H-Bonded Open Framework

A procedure that enabled rational access to the first example of hybrid material made of NPs grown within a H-bonded framework is reported. To avoid competitive reactions with the framework units, the metal precursor was chemically trapped in the porous structure and subsequently photo-reduced to afford the hybrid material Ag@SPA-2 , which consists of Ag NPs of nanometric sizes (<15 nm) homogeneously distributed in the crystals of the host material. In a subsequent step, taking advantage of the porous matrix the silver NPs have been transformed in situ to Ag₂S NP by simple infiltration of H₂S. The supramolecular network is shown to play an important role in stabilizing the inorganic nanomaterials and thus in controlling their growth.     

Electrochemical behavior of CoSb<Subscript>3</Subscript> in sulfuric and oxalic acids over the potential range 0 to 40 V

The electrochemical behavior of pure Co, pure Sb, and CoSb₃ has been investigated over a large anodic potential range (0 to 40 V) in two acids, i.e., oxalic acid or sulfuric acid at different concentrations (0.01 to 1 M). Potentiodynamic polarizations performed on CoSb₃ plates reveal the possible formation of a passive layer between 1 and 3 V (vs SCE), on a passivation plateau. The oxidation of CoSb₃ at 2 V in sulfuric and oxalic acids results in the growth of an anodic conversion layer. This coating is mainly made of a porous layer of amorphous antimony oxides due to dealloying of CoSb₃. In the specific case of oxalic acid, rods of crystallized oxalates are tangled between the oxide sheets.     

Pyrromethene–BF2 complexes as laser dyes:1.

Condensations between 3-X-2,4-dimethylpyrroles (X = H, CH₃, C₂H₅, and CO₂C₂H₅) and acyl chlorides gave derivatives of 3,5,3′,5′-tetramethylpyrromethene (isolated as their hydrochloride salts): 6-methyl, 6-ethyl, 4,4′,6-trimethyl, 4,4′-diethyl-6-methyl, and 4,4′-dicarboethoxy-6-ethyl derivatives for conversion on treatment with boron trifluoride to 1,3,5,7-tetramethylpyrromethene–BF₂ complex (TMP–BF₂) and its 8-methyl (PMP–BF₂), 8-ethyl, 2,6,8-trimethyl (HMP–BF₂),2,6,-diethyl-8-methyl (PMDEP–BF₂), and 2,6-dicarboethoxy-8-ethyl derivatives. Chlorosulfonation converted, 1,3,5,7,8-pentamethylpyrromethene–BF₂ complex to its 2,6-disulfonic acid isolated as the lithium, sodium (PMPDS–BF₂), potassium, rubidium, cesium, ammonium, and tetramethylammonium disulfonate salts and the methyl disulfonate ester. Sodium 1,3,5,7-tetramethyl-8-ethylpyrromethene-2,6-disulfonate–BF₂ complex was obtained from the 8-ethyl derivative of TMP–BF₂. Nitration and bromination converted PMP–BF₂ to its 2,6-dinitro-(PMDNP–BF₂) and 2,6-dibromo- derivatives. The time required for loss of fluorescence by irradiation from a sunlamp showed the following order for P–BF₂ compounds (10⁻³ to 10⁻⁴ M) in ethanol: PMPDS–BF₂, 7 weeks; PMP–BF₂, 5 days; PMDNP–BF₂, 72 h; HMP–BF₂, 70 h; and PMDEP–BF₂, 65 h. Under similar irradiation PMPDS–BF₂ in water lost fluorescence after 55 h. The dibromo derivative was inactive, but each of the other pyrromethene–BF₂ complexes under flashlamp excitation showed broadband laser activity in the region λ 530–580 nm. In methanol PMPDS–BF₂ was six times more resistant to degradation by flashlamp pulses than was observed for Rhodamine-6G (R-6G). An improvement (up to 66%) in the laser power efficiency of PMPDS–BF₂ (10⁻⁴ M in methanol) in the presence of caffeine (a filter for light <300 nm) was dependent on flashlamp pulse width (2.0 to 7.0 μsec).