Propagation of first-order electromagnetic discontinuities in an isotropic medium

The propagation of a first-order electromagnetic discontinuity is discussed. Expressions are obtained for the possible velocities of propagation as functions of the field strengths ahead of the surface of discontinuity. Expressions are also obtained for the growth in the magnitude of the discontinuity as the wave progresses.     

Highly Stereoselective Intermolecular Haloetherification and Haloesterification of Allyl Amides

An organocatalytic and highly regio‐, diastereo‐, and enantioselective intermolecular haloetherification and haloesterification reaction of allyl amides is reported. A variety of alkene substituents and substitution patterns are compatible with this chemistry. Notably, electronically unbiased alkene substrates exhibit exquisite regio‐ and diastereoselectivity for the title transformation. We also demonstrate that the same catalytic system can be used in both chlorination and bromination reactions of allyl amides with a variety of nucleophiles with little or no modification.     

18‐Crown‐6 Catalyzed Microwave‐mediated Synthesis of Symmetric Bis‐Heterocyclic Compounds under Solvent‐free Condition

An efficient, solvent‐free and 18‐crown‐6 catalyzed method for the synthesis of N‐alkyl‐4‐(4‐(5‐(2‐(alkyl‐amino)thiazol‐4‐yl)pyridin‐3‐yl)phenyl)thiazol‐2‐amine, N‐alkyl‐4‐(5‐(2‐alkyamino)thiazol‐4‐yl)pyridine‐3‐yl)thiazol‐2‐amine, and 4,4′‐bis‐{2‐[amino]‐4‐thiazolyl}biphenyl bis‐heterocyclic derivatives via microwave accelerated cyclization is presented.     

The characterisation of coumarins from selected structural classes by electrospray ionisation quadrupole time-of-flight tandem mass spectrometry

Electrospray ionisation quadrupole time-of-flight tandem mass spectrometry (ESI-QTOF-MS/MS) has been used for characterisation of a selection of naturally occurring and synthetic coumarins from different structural classes. The product ions, suggested in earlier studies by electrospray ionisation ion trap mass spectrometry (ESI-MS(n)), are unequivocally established for the representative coumarins by virtue of accurate mass measurement. Synthetic coumarins that are unsubstituted in the heterocyclic ring give rise to a major product ion by loss of CO(2), whereas those substituted in the heterocyclic ring generally undergo alternative fragmentation releasing neutral species such as ketene or methyl ketene. Naturally occurring coumarins, unsubstituted in the heterocyclic ring and substituted in the benzene ring with chains or rings of hydrocarbons and oxygen, principally fragment at the side chain releasing unsaturated hydrocarbons. The ESI-QTOF-MS/MS behaviour of some naturally occurring and synthetic quinolines which are structurally similar or fragment similarly are included where appropriate.     

Efficient complexation of pyrrole-bridged dizinc(II) bisporphyrin with fluorescent probe pyrene: synthesis, structure, and photoinduced singlet-singlet energy transfer

A diethylpyrrole‐bridged dizinc(II) bisporphyrin (Zn₂DEP) is reported that encapsulates fluorescent probe pyrene molecules through strong π–π interactions, which can relay information about the chemical environment in the interior of the host–guest supramolecular assembly. X‐ray structures of both Zn₂DEP and the encapsulated pyrene complex are reported, which provides a rare opportunity to investigate the structural changes upon guest binding. A comparative structural analysis demonstrated the exceptional ability of this bisporphyrin platform to open its binding pocket for pyrene encapsulation by a vertical displacement of more than 2.45 Å, although both Zn₂DEP and the pyrene complex have nearly parallel porphyrin ring orientations. The ¹H NMR spectrum of the encapsulated pyrene complex in solution shows the upfield shifts of the pyrene protons due to a strong ring current effect, which demonstrates the retention of the solid‐state structure in solution. To further assess the extent to which pyrene guests remain encapsulated in solution, a known fluorescence quencher, dimethylaniline, was added to the host–guest assembly, which shows no exciplex formation for days in nonpolar solvents. Thus, the assembly also retained the structural integrity in solution for a long time. The association constant (K_asso) for such a complexation process in solution was observed to be 1.78×10⁵ M ^?2 for 1:2 binding. Steady‐state fluorescence and lifetime studies indicate significant photoinduced singlet–singlet energy transformation from the excited state of pyrene to zinc bisporphyrin.     

Semiclassical study of quantum coherence and isotope effects in ultrafast electron transfer reactions coupled to a proton and a phonon bath

The linearized semiclassical initial value representation is employed to describe ultrafast electron transfer processes coupled to a phonon bath and weakly coupled to a proton mode. The goal of our theoretical investigation is to understand the influence of the proton on the electronic dynamics in various bath relaxation regimes. More specifically, we study the impact of the proton on coherences and analyze if the coupling to the proton is revealed in the form of an isotope effect. This will be important in distinguishing reactions in which the proton does not undergo significant rearrangement from those in which the electron transfer is accompanied by proton transfer. Unlike other methodologies widely employed to describe nonadiabatic electron transfer, this approach treats the electronic and nuclear degrees of freedom consistently. However, due to the linearized approximation, quantum interference effects are not captured accurately. Our study shows that at small phonon bath reorganization energies, coherent oscillations and isotope effect are observed in both slow and fast bath regimes. The coherences are more substantially damped by deuterium in comparison to the proton. Further, in contrast to the dynamics of the spin-boson model, the coherences are not long-lived. At large bath reorganization energies, the decay is incoherent in the slow and fast bath regimes. In this case, the extent of the isotope effect depends on the relative relaxation timescales of the proton mode and the phonon bath. The isotope effect is magnified for baths that relax on picosecond timescales in contrast to baths that relax in femtoseconds.     

Studies on the Synthesis and Characterization of Pd?TiO2?SiO2 Nanocomposite for Electroanalytical Applications

A nanocomposite of Pd? TiO₂? SiO₂ is developed through a sol‐gel process from the reaction products of titanium isopropoxide followed by mixing the same with palladium linked 3‐glycidoxypropyltrimethoxysilane. The reaction product is sonicated and calcinated to obtain the nanocomposite of Pd? TiO₂? SiO₂. The calcination at 600 °C yielded an amorphous structure whereas at 900 °C it resulted into a nanocrystalline structure. The nanocomposite of palladium was further characterized by TEM, XRD, IR and EDS. The material acts as an efficient electrocatalyst. Electrocatalysis of ascorbic acid is observed at 0.1 V vs. Ag/AgCl, shows linearity between 1 µM and 1 mM in 0.1 M phosphate buffer (pH 7.0).     

Mild preparation of functionalized [2.2]paracyclophanes via the Pummerer rearrangement

[2.2]Paracyclophanes, incorporating functional groups in the aliphatic bridges, suitable for elimination to give [2.2]paracyclophanedienes, are synthesized through a novel approach. It relies on a double Pummerer rearrangement on dithiacyclophane precursors, followed by ring contraction through a photochemical sulfur extrusion, and it is compatible with aryl moieties possessing very different electronic properties.     

Dynamic lot-sizing in sequential online retail auctions

Retailers often conduct non-overlapping sequential online auctions as a revenue generation and inventory clearing tool. We build a stochastic dynamic programming model for the seller’s lot-size decision problem in these auctions. The model incorporates a random number of participating bidders in each auction, allows for any bid distribution, and is not restricted to any specific price-determination mechanism. Using stochastic monotonicity/stochastic concavity and supermodularity arguments, we present a complete structural characterization of optimal lot-sizing policies under a second order condition on the single-auction expected revenue function. We show that a monotone staircase with unit jumps policy is optimal and provide a simple inequality to determine the locations of these staircase jumps. Our analytical examples demonstrate that the second order condition is met in common online auction mechanisms. We also present numerical experiments and sensitivity analyses using real online auction data.