Palladium‐Catalyzed Annulation of Diarylamines with Olefins through CH Activation: Direct Access to N‐Arylindoles

A palladium‐catalyzed dehydrogenative coupling between diarylamines and olefins has been discovered for the synthesis of substituted indoles. This intermolecular annulation approach incorporates readily available olefins for the first time and obviates the need of any additional directing group. An ortho palladation, olefin coordination, and β‐migratory insertion sequence has been proposed for the generation of olefinated intermediate, which is found to produce the expected indole moiety.     

Ab Initio Molecular Dynamics Simulations of the Interaction between Organic Phosphates and Goethite

Today’s fertilizers rely heavily on mining phosphorus (P) rocks. These rocks are known to become exhausted in near future, and therefore effective P use is crucial to avoid food shortage. A substantial amount of P from fertilizers gets adsorbed onto soil minerals to become unavailable to plants. Understanding P interaction with these minerals would help efforts that improve P efficiency. To this end, we performed a molecular level analysis of the interaction of common organic P compounds (glycerolphosphate (GP) and inositol hexaphosphate (IHP)) with the abundant soil mineral (goethite) in presence of water. Molecular dynamics simulations are performed for goethite–IHP/GP–water complexes using the multiscale quantum mechanics/molecular mechanics method. Results show that GP forms monodentate (M) and bidentate mononuclear (B) motifs with B being more stable than M. IHP interacts through multiple phosphate groups with the 3M motif being most stable. The order of goethite–IHP/GP interaction energies is GP M < GP B < IHP M < IHP 3M. Water is important in these interactions as multiple proton transfers occur and hydrogen bonds are formed between goethite–IHP/GP complexes and water. We also present theoretically calculated infrared spectra which match reasonably well with frequencies reported in literature.     

Graphical Representation of the Supermode Theory of a Waveguide Directional Coupler

A novel graphical representation of the supermode theory of a waveguide directional coupler based on phasor analysis is described. Following this approach, dependence of the magnitudes and phases of the output fields on the splitting ratio of a directional coupler is discussed. Both the cases of phase-matched (identical) and non-phase-matched (non-identical) waveguides constituting a directional coupler are investigated. This approach directly illustrates the fact that the phase shift suffered by the coupled light relative to the throughput light is π/2, regardless of the splitting ratio for identical guides, which is not the case for couplers with non-identical waveguides. It also yields additional information about the phases of the output fields of a directional coupler. The usefulness of this approach in the context of wavelength-flattened couplers, wavelength division multiplexing couplers, and polarization effects in directional couplers is also discussed. This approach should also be helpful in the analysis of guided wave interferometric devices such as wavelength interleave filters and modulators, based on concatenated directional couplers.     

Synthesis and antimicrobial activity of a new class of methyleneamine‐linked bis‐heterocycles

A new class of methyleneamine‐linked bis‐heterocycles that exhibit antimicrobial activity was synthesized. Bromination of 1 followed by condensation with thiourea gave 3 . The reaction of 3 with propargyl bromide in dry toluene under inert atmosphere led to the formation of 4 . Its subsequent reaction with different aromatic azides 5 using CuSO₄.5H₂O‐sodiumascorbate system in a 2:1 mixture of water and tert‐butylalcohol yielded the title compounds 6a , 6b , 6c , 6d , 6e , 6f , 6g , 6h , 6i , 6j in good yields. The identities of these compounds were confirmed following elemental analysis, IR, ¹H, ¹³C NMR, and mass spectral studies. All the title compounds exhibited pronounced in vitro antibacterial and antifungal activities. J. Heterocyclic Chem., (2011).     

Entrapment and kinetic resolution of stabilized axial and equatorial conformers of spiro-β-lactams

The facile synthesis of the stabilized axial and equatorial conformers of spiro-β-lactams was achieved via entrapment of cyclohexanone imines (Schiff bases) with acetoxyacetyl chloride in a [2 + 2]-cycloaddition reaction followed by their kinetic resolution. The immobilization of the racemic substrates on an inert solid support significantly reduced the reaction time and improved the enantioselectivity of conformers during kinetic resolution. The mechanism of the formation of the spiro-β-lactams was explored using B3LYP/6-31+G* level quantum chemical calculations.     

A 3-approximation algorithm for the facility location problem with uniform capacities

We consider the facility location problem where each facility can serve at most U clients. We analyze a local search algorithm for this problem which uses only the operations of add, delete and swap and prove that any locally optimum solution is no more than 3 times the global optimum. This improves on a result of Chudak and Williamson who proved an approximation ratio of ${3+2\sqrt{2}}$ for the same algorithm. We also provide an example which shows that any local search algorithm which uses only these three operations cannot achieve an approximation guarantee better than 3.     

New approach for fractional Schrödinger-Boussinesq equations with Mittag-Leffler kernel

In this paper, we find the solution and analyse the behaviour of the obtained results for the nonlinear Schrödinger-Boussinesq equations using q -homotopy analysis transform method (q -HATM) within the frame of fractional order. The considered system describes the interfaces between intermediate long and short waves. The projected fractional operator is proposed with the help of Mittag-Leffler function to incorporate the nonsingular kernel to the system. The projected algorithm is a modified and accurate method with the help of Laplace transform. The convergence analysis is presented with the help of the fixed point theorem in the form existence and uniqueness. To validate and illustrate the effectiveness of the algorithm considered, we exemplified considered system with respect of arbitrary order. Further, the behaviour of achieved results is captured in contour and 3D plots for distinct arbitrary order. The results show that the projected scheme is very effective, highly methodical and easy to apply for complex and nonlinear systems and help us to captured associated behaviour diverse classes of the phenomenon.