Interaction of surface water waves with a vertical elastic plate: a hypersingular integral equation approach

In this paper, we present an alternative method to investigate scattering of water waves by a submerged thin vertical elastic plate in the context of linear theory. The plate is submerged either in deep water or in the water of uniform finite depth. Using the condition on the plate, together with the end conditions, the derivative of the velocity potential in the direction of normal to the plate is expressed in terms of a Green’s function. This expression is compared with that obtained by employing Green’s integral theorem to the scattered velocity potential and the Green’s function for the fluid region. This produces a hypersingular integral equation of the first kind in the difference in potential across the plate. The reflection coefficients are computed using the solution of the hypersingular integral equation. We find good agreement when the results for these quantities are compared with those for a vertical elastic plate and submerged and partially immersed rigid plates. New results for the hydrodynamic force on the plate, the shear stress and the shear strain of the vertical elastic plate are also evaluated and represented graphically.     

Osmium-carbonyl complexes of naphthylazoimidazoles. Single crystal X-ray structure of [Os(H)(CO)(PPh3)2(α-NaiEt)](PF6) {α-NaiEt = 1-ethyl-2-(naphthyl-α-azo)imidazole}

1-Alkyl-2-(naphthyl-α/β-azo)imidazole (α-NaiR 1; β-NaiR, 2) react with [Os(H)(Cl)(CO)(PPh₃)₃] in THF and synthesise [Os(H)(CO)(PPh₃)₂(α/β-NaiR)](PF₆) (3, 4). The X-ray structure of [Os(H)(CO)(PPh₃)₂(α-NaiEt)](PF₆) (3c) shows a distorted octahedral geometry. Other spectroscopic studies (IR, UV–Vis, NMR) support the stereochemistry of the complexes. Addition of Cl₂ in MeCN to 3 or 4 gives [Os(Cl)(CO)(α/β-NaiR)(PPh₃)₂](PF₆) (5, 6), which were characterized by spectroscopic studies. The redox properties of the complexes show Os(III)/Os(II), Os(IV)/Os(III) and azo reductions.     

Charge-transfer-induced twisting of the nitro group

Excited-state relaxation dynamics of 2-amino-7-nitrofluorene (ANF) and 2-dimethylamino-7-nitrofluorene (DMANF) has been investigated in two aprotic solvents, namely acetonitrile and DMSO using femtosecond transient absorption spectroscopic technique. Following photoexcitation to the highly dipolar excited singlet (S1) state, ANF and DMANF undergo mainly two concomitant relaxation processes, namely dipolar solvation and conformational relaxation via twisting of the nitro group to an orthogonal configuration with respect to the aromatic plane. Viscosity dependence of the relaxation dynamics of the S1 states of both ANF and DMANF suggests no involvement of the twisting motion of the amino or dimethylamino group in the charge-transfer process. The twisting of the nitro group is found to be a friction affected diffusive motion, which does not associate with any further charge transfer. The results presented in this paper resolve experimentally the dynamics of the twisting motion of the nitro group for the first time.     

A facile phenol-driven intramolecular diastereoselective thermal/base-catalyzed dipolar [2+2] annulation reactions: an easy access to complex bioactive natural and unnatural benzopyran congeners

The complex bioactive natural and unnatural benzopyran congeners have been synthesized using one-/two-step approaches in very good yields from the reactions of two different dihydroxyphthalides, natural resorcyclic acid derivative, and trihydroxybenzophenone with citral and/or farnesal, via the phenol-driven intramolecular diastereoselective thermal/base-catalyzed dipolar [2+2] cycloaddition reactions and three different thermal intramolecular cyclization reactions. The effects of the nature and the position of phenolic groups in the starting materials on the course of these cycloaddition reactions have also been described. Depending upon the absence or presence of intramolecular hydrogen bonding of the phenolic group with the carbonyl moiety in the starting materials, these phenol-driven intramolecular thermal/base-catalyzed dipolar [2+2] cycloaddition reactions either furnished the kinetically controlled products or directly formed the thermodynamically controlled rearranged products, respectively.     

A Halogen-Bond-Driven Artificial Chloride-Selective Channel Constructed from 5-Iodoisophthalamide-based Molecules

Despite considerable emphasis on advancing artificial ion channels, progress is constrained by the limited availability of small molecules with the necessary attributes of self-assembly and ion selectivity. In this study, a library of small molecules based on 5-haloisophthalamide and a non-halogenated isophthalamide were examined for their ion transport properties across the lipid bilayer membranes, and the finding demonstrates that the di-hexyl-substituted 5-iodoisophthalamide derivative exhibits the highest level of activity. Furthermore, it was established that the highest active compound facilitates the selective chloride transport that occurs via an antiport-mediated mechanism. The crystal structure of the compound unveils a distinctive self-assembly of molecules, forming a zig-zag channel pore that is well-suited for the permeation of anions. Planar bilayer conductance measurements proved the formation of chloride selective channels. A molecular dynamics simulation study, relying on the self-assembled component derived from the crystal structure, affirmed the paramount significance of intermolecular hydrogen bonding in the formation of supramolecular barrel-rosette structures that span the bilayer. Furthermore, it was demonstrated that the transport of chloride across the lipid bilayer membrane is facilitated by the synergistic effects of halogen bonding and hydrogen bonding within the channel.     

Di­methyl 6‐methoxy‐4aβ‐methyl‐9‐oxo‐1,2,3,4,4a,9,10,10aβ‐octa­hydro­phenanthrene‐1,1‐di­carboxyl­ate

In the title tricyclic keto‐diester, C₂₀H₂₄O₆, a potential intermediate in the synthesis of bioactive podocarpic acid, the outer cyclo­hexane ring (in a chair conformation) is cis fused to the central cyclo­hexanone ring (in a half‐chair conformation). The conformational analysis of the compound, investigated by semi‐empirical quantum mechanical AM1 calculations, shows a good agreement with the X‐ray structure, except for the orientation of the methyl, methoxy­phenyl and methoxy­carbonyl substituents.     

Lanthanide‐Based Layer‐Type Two‐Dimensional Coordination Polymers Featuring Slow Magnetic Relaxation,Magnetocaloric Effect and Proton Conductivity

Three lanthanide‐based two‐dimensional (2D) coordination polymers (CPs), [Ln(L)(H₂O)₂]_n, {H₃L=(HO)₂P(O)CH₂CO₂H; Ln=Dy³⁺ (CP 1 ), Er³⁺ (CP 2 )} and [{Gd₂(L)₂(H₂O)₃}^.H₂O]_n, (CP 3 ) were hydrothermally synthesized using phosphonoacetic acid as a linker. Structural features revealed that the dinuclear Ln³⁺ nodes were present in the 2D sheet of CP 1 and CP 2 while in the case of CP 3 , nodes were further connected to each other forming a chain‐type arrangement throughout the network. The magnetic studies show field‐induced slow magnetic relaxation property in CP 1 and CP 2 with U_eff values of 72 K (relaxation time, τ₀=3.05×10^?7 s) and 38.42 K (relaxation time, τ₀=4.60×10^?8 s) respectively. Ab‐initio calculations suggest that the g tensor of Kramers doublet of the lanthanide ion (Dy³⁺ and Er³⁺) is strongly axial in nature which reflects in the slow magnetic relaxation behavior of both CPs. CP 3 exhibits a significant magnetocaloric effect with ?ΔS_m=49.29 J kg^?1 K^?1, one of the highest value among the reported 2D CPs. Moreover, impedance analysis of all the CPs show high proton conductivity with values of 1.13×10^?6 S cm^?1, 2.73×10^?3 S cm^?1 and 2, 6.27×10^?6 S cm^?1 for CPs 1 – 3 , respectively, at high temperature (>75 °C) and maximum 95 % relative humidity (RH).     

Synthesis of novel benzoxazocino quinoliniums and quinolones under PTC conditions and their application in Suzuki cross coupling reaction for the construction of polynuclear heteroaromatics

A general and highly efficient synthetic protocol under phase transfer catalytic condition has been established for the synthesis of fused tetracyclic oxazocinoquinolone analogues which served as the precursors for novel biaryl quinolones using microwave assisted Suzuki cross coupling reaction.     

Inventory models for defective items incorporating marketing decisions with variable production cost

This paper investigates the finite replenishment inventory models of a single product with imperfect production process. In this process, a certain fraction or a random number of produced items are defective. These non-conforming items are rejected or reworked or if they reached to the customer, refunded. Here, a generalised unit cost function is formulated incorporating the several factors like raw material, labour, replenishment rate and others factors of the manufacturing system. The rate of replenishment is considered to be a variable. The selling price of an unit is determined by a mark-up over the production cost. Optimum production of the product is suggested to have maximum profit using a gradient based mathematical programming technique for optimization. Finally, numerical examples are given to illustrate the results and the significant features of the production system. As a particular case, the result of the perfect system (without defective items) are obtained. Also, the effect of changes in the selling rate, defectiveness, production cost and other parameters on the optimal average profit are graphically presented. Some interesting decisions regarding production policy are established.