Superconvergence results of iterated projection methods for linear Volterra integral equations of second kind

In this paper, we develop the iteration techniques for Galerkin and collocation methods for linear Volterra integral equations of the second kind with a smooth kernel, using piecewise constant functions. We prove that the convergence rates for every step of iteration improve by order \({\mathcal {O}}(h^{2})\) for Galerkin method, whereas in collocation method, it is improved by \({\mathcal {O}}(h)\) in infinity norm. We also show that the system to be inverted remains same for every iteration as in the original projection methods. We illustrate our results by numerical examples.     

Phenylboronic Acid Appended Pyrene‐Based Low‐Molecular‐Weight Injectable Hydrogel: Glucose‐Stimulated Insulin Release

A pyrene‐containing phenylboronic acid (PBA) functionalized low‐molecular‐weight hydrogelator was synthesized with the aim to develop glucose‐sensitive insulin release. The gelator showed the solvent imbibing ability in aqueous buffer solutions of pH values, ranging from 8–12, whereas the sodium salt of the gelator formed a hydrogel at physiological pH 7.4 with a minimum gelation concentration (MGC) of 5 mg mL^?1. The aggregation behavior of this thermoreversible hydrogel was studied by using microscopic and spectroscopic techniques, including transmission electron microscopy, FTIR, UV/Vis, luminescence, and CD spectroscopy. These investigations revealed that hydrogen bonding, π–π stacking, and van der Waals interactions are the key factors for the self‐assembled gelation. The diol‐sensitive PBA part and the pyrene unit in the gelator were judiciously used in fluorimetric sensing of minute amounts of glucose at physiological pH. The morphological change of the gel due to addition of glucose was investigated by scanning electron microscopy, which denoted the glucose‐responsive swelling of the hydrogel. A rheological study indicated the loss of the rigidity of the native gel in the presence of glucose. Hence, the glucose‐induced swelling of the hydrogel was exploited in the controlled release of insulin from the hydrogel. The insulin‐loaded hydrogel showed thixotropic self‐recovery property, which hoisted it as an injectable soft composite. Encouragingly, the gelator was found to be compatible with HeLa cells.     

Reductive Cleavage of Carbon Monoxide by a Disilenide

The complete reductive cleavage of the triple bond in carbon monoxide was achieved using a lithium disilenide at room temperature. The C? C‐coupled product can be regarded as a silanone dimer with pending alkyne and silirene moieties and incorporates two equivalents of CO per disilenide unit. A formation mechanism via ketenyl intermediates is proposed on the basis of DFT calculations and elucidated experimentally by employing Group 6 metal carbonyls as both stabilizing entity and source of CO in the reaction with disilenide. The isolation of cyclic silylene complexes with weakly donating ketenyl donor groups further supports the mechanistic scenario.     

Curvature condensation and bifurcation in an elastic shell

We study the formation and evolution of localized geometrical defects in an indented cylindrical elastic shell using a combination of experiment and numerical simulation. We find that as a symmetric localized indentation on a semicylindrical shell increases, there is a transition from a global mode of deformation to a localized one which leads to the condensation of curvature along a symmetric parabolic defect. This process introduces a soft mode in the system, converting a load-bearing structure into a hinged, kinematic mechanism. Further indentation leads to twinning wherein the parabolic defect bifurcates into two defects that move apart on either side of the line of symmetry. A qualitative theory captures the main features of the phenomena but leads to further questions about the mechanism of defect nucleation.     

I2/TBHP promoted oxidative C–N bond formation at room temperature: Divergent access of 2-substituted benzimidazoles involving ring distortion

A new ‘one pot’ tandem synthesis of 2-substituted benzimidazoles has been developed from 2-aminobenzyl alcohol/2-aminobenzamide and different coupling partners (nitriles, aldehydes and 1,3-diketones) via iodine and TBHP promoted oxidative ring contraction. The present strategy involves sequential C–N bond formation, cyclization, subsequent ring contraction and dehydrogenation to afford various medicinally important benzimidazole derivatives in moderate to good yields. This operationally simple synthetic approach proceeds at room temperature under base-free condition, broadly applicable to a wide array of nitriles and aldehydes bearing oxidation prone functional groups and noteworthy to mention that various acyclic 1,3-diketones undergo selective C–C bond cleavage leading to 2-alkyl benzimidazoles under mild condition.     

Effect of precursor sol pH on microstructural, optical and photocatalytic properties of vacuum annealed zinc tin oxide thin films on glass

Dip coated vacuum annealed zinc tin oxide thin films on soda lime silica glass have been deposited from the precursor sols containing zinc acetate dihydrate and tin (IV) chloride pentahydrate (Zn:Sn = 67:33, atomic ratio in percentage) in 2-methoxy ethanol by varying sol pH (0.85–5.5). Crystallinity, morphology, optical and photocatalytic properties of the films strongly depend on sol pH. Measurement of grazing incidence X-ray diffraction confirms the presence of hexagonal nano ZnO in the films derived from the sols of pH < 5.5. Film crystallinity deteriorates on increasing sol pH and the film deposited from the sol of pH 5.5 shows XRD amorphous but the selected area diffraction pattern and HRTEM image evidence the presence of nano Zn₂SnO₄ (size, 5–6 nm). Direct band gap energy of films increases on increasing sol pH. To visualize the film surface microstructure, FESEM study has been done and a rod-like surface feature is revealed in the film deposited from the sol of pH 2.85. A dependence of precursor sol pH on the photocatalytic activity of films towards degradation of Rhodamine 6G dye under UV (254 nm) irradiation is found and the highest decomposition rate constant, ‘k’ value is obtained from the film prepared from the sol of pH 5.5. The presence of zinc deficient nano Zn₂SnO₄ in the film may consider for generating the highest ‘k’ value. We also measure gelling time, viscosity of sols as well as UV and FTIR studies on the films and propose chemical reactions.     

Intramolecularly Double-Donor-Stabilized Stannylene and Its Coordination towards Ag(I) and Au(I) Centers

The intramolecularly double-donor-stabilized stannylene 1 has been synthesized from the salt-metathesis reaction between two equivalents of lithium pyridine ene-amide L1 and SnCl₂. Compound 1 exhibits dipolar behavior when reacted with B(C₆F₅)₃ leading to the zwitterionic compound 2 . The reaction of 1 with one equivalent and 0.5 equivalent of AgOTf (OTf=trifluoromethane sulfonate) result in the formation of a stannylene-AgOTf complex 3 and a homoleptic distannylene-silver ionic complex 4 , respectively. Analogous to complex 4 , the gold(I) complex 5 has been synthesized from the reaction between two equivalents of 1 and 0.5 equivalent of AuCl.SMe₂/Me₃SiOTf. Complex 5 is the first example of homoleptic stannylene-Au(I) ionic complex among the very scarce reports on stannylene-gold(I) coordination complexes. All compounds have been structurally characterized using single crystal X-ray crystallography. Solution-state characterization have been performed using multinuclear NMR techniques. Detailed DFT calculations on the optimized geometries 1 o , 3 o – 5 o reveal the change in sp- hybridization on the pyramidal Sn(II) center upon metal coordination and their bonding overlaps.     

Metal assisted synthesis of mono and diamino substituted pyridines

A microwave assisted Buchwald-Hartwig amination protocol is reported for a series of dihalopyridine precursors. Using this procedure, selective substitution of one halogen by aryl or alkylamines is possible in very short time, usually 30 min. Mild base (K₂CO₃) can be used successfully, which broadens the substrate scope. The second halogen can then be substituted using alkylamines under nucleophilic substitution condition or via a Suzuki-Miyaura cross-coupling reaction. The target compounds are potential inducers of cardiomyogenesis as innovative approach in regenerative medicine.