Palladium-mediated intramolecular aryl amination on furanose derivatives: an expedient approach to the synthesis of chiral benzoxazocine derivatives and tricyclic nucleosides

Pd-catalyzed intramolecular arylamination on sugar derivatives has been accomplished by using bulky biaryl phosphine ligands. An application of this methodology on a variety of D-glucose-derived substrates, 2a-f, led to the synthesis of highly functionalized cis-fused tricyclic oxazocines, 3a-e. The products could subsequently be transformed to the optically active benzoxazocine derivative 4 and tricyclic nucleoside 6. This is the first example of the synthesis of eight-membered rings via intramolecular cycloamination of furanose derivatives, which provides a very useful method for the catalytic synthesis of medium-ring heterocycles.     

Rotating beams and non-rotating beams with shared eigenpair for pinned-free boundary condition

In this paper we look for a rotating beam, with pinned-free boundary conditions, whose eigenpair (frequency and mode-shape) is same as that of a uniform non-rotating beam for a particular mode. It is seen that for any given mode, there exists a flexural stiffness function (FSF) for which the ith mode eigenpair of a rotating beam with uniform mass distribution, is identical to that of a corresponding non-rotating beam with same length and mass distribution. Inserting these derived FSF’s in a finite element code for a rotating pinned-free beam, the frequencies and mode shapes of a non-rotating pinned-free beam are obtained. For the first mode, a physically realistic equivalent rotating beam is possible, but for higher modes, the FSF has internal singularities. Strategies for addressing these singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test functions for rotating beam codes and also for targeted destiffening of rotating beams.     

Emeritus Professor Shan-Fu Shen,Cornell University

A numerical analysis of blood flow in a rigid artery has been performed to observe the variations in flow pattern and haemodynamic parameters under the influence of multiple (double) stenoses. The interspacing distance, degree of stenotic severity and Reynolds number of flow have been varied. It is found that two stenoses interact when the interspacing distance is lower than a critical value that corresponds to the redevelopment length of fully developed flow after the proximal stenosis. In the case of non-interacting stenoses the haemodynamic parameters, like the peak centreline velocity (representing the peak systolic velocity ratio in medical term), the maximum wall shear stress, region of low shear stress and the irrecoverable pressure drop at the stenosis site, repeat themselves at each individual stenosis. However, when the stenoses interact hydrodynamically because of their proximity, the parameters behave differently, which can lead to a different haemodynamic profile in the arteries and pose difficulties in their pathological interpretation. This work evaluates the influence of double stenoses on the variations in the key haemodynamic features under different degree of stenoses and interspacing distance between the stenoses.     

Wave theory of light leading to the generalized vectorial laws of reflection and refraction

This paper deals with the application of Huygens’ wave theory of light for the derivation of the generalized vectorial laws of reflection and refraction discovered by the author in 2005. The long-running literature falls short of such a theoretical proof of the generalized vectorial laws of reflection and refraction on the basis of wave theory. As such the present work is novel and original. At the same time it also enhances the theoretical foundation of the discovery of the generalized vectorial laws of reflection and refraction there by proving the efficiency and increasing the range of applicability of the wave theory of light as well.     

Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams

In this paper, the governing equations for free vibration of a non-homogeneous rotating Timoshenko beam, having uniform cross-section, is studied using an inverse problem approach, for both cantilever and pinned-free boundary conditions. The bending displacement and the rotation due to bending are assumed to be simple polynomials which satisfy all four boundary conditions. It is found that for certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, the assumed polynomials serve as simple closed form solutions to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of analytical polynomial functions possible for material mass density, shear modulus and elastic modulus distributions, which share the same frequency and mode shape for a particular mode. The derived results are intended to serve as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of rotating non-homogeneous Timoshenko beams.     

Structural, dielectric relaxation and piezoelectric characterization of Sr substituted modified PMS-PZT ceramic

Pyrochlore phase free [Pb_0.94Sr_0.06] [(Mn_1/3Sb_2/3)_0.05(Zr_0.53Ti_0.47)_0.95] O₃ ceramics has been synthesized with pure Perovskite phase by semi-wet route using the columbite precursor method. The field dependences of the dielectric response and the conductivity have been measured in a frequency range from 50 Hz to 1 MHz and in a temperature range from 303 K to 773 K. An analysis of the real and imaginary parts of the dielectric permittivity with frequency has been performed, assuming a distribution of relaxation times. The scaling behavior of the dielectric loss spectra suggests that the distribution of the relaxation times is temperature independent. The SEM photographs of the sintered specimens present the homogenous structures and well-grown grains with a sharp grain boundary. The material exhibits tetragonal structure. When measured at frequency (100 Hz), the polarization shows a strong field dependence. Different piezoelectric figures of merit (k_p, d₃₃ and Q_m) of the material have also been measured obtaining their values as 0.53, 271 pC/N and 1115, respectively, which are even higher than those of pure PZT with morphotropic phase boundary (MPB) composition. Thus the present ceramics have the optimal overall performance and are promising candidates for the various high power piezoelectric applications.     

La(OTf)3-catalyzed one-pot synthesis of meso-substituted porphyrinic thiazolidinones

Abstract  

An improved synthetic procedure is developed for the regioselective nitration of a phenyl group of meso-tetraphenylporphyrin by using NaNO₂ in a mixture of trichloroacetic acid and AcOH. The meso-(4-nitrophenyl)porphyrins are successfully reduced to corresponding meso-(4-aminophenyl)porphyrins by SnCl₂ under acidic conditions. In addition, an efficient one-pot methodology for synthesizing a series of novel meso-substituted porphyrinic thiazolidinone conjugates is developed by reacting meso-(4-aminophenyl)porphyrins with various aromatic aldehydes and mercaptoacetic acid in refluxing toluene using La(OTf)₃ as a catalyst. The products obtained are characterized on the basis of their spectral data. Preliminary photophysical properties of the newly synthesized compounds are reported.     

Solid supported palladium(0) nano/microparticle: a ligand-free efficient recyclable heterogeneous catalyst for mono- and β,β-double-Heck reaction

Solid supported palladium nano/microparticles were found to be active catalysts to perform mono- and β,β-double-Heck reactions. Different β-unsubstituted and substituted alkenes including acrylate, methacrylate, crotonate, styrene, acrylonitrile, and acrylamide were investigated successfully for mono- and β,β-double-Heck reactions with aryl iodide under milder reaction condition. One-pot β,β-double-Heck reaction of aryl iodides with α,β-unsaturated ester, amide, nitrile, and styrene derivatives were also performed under standard reaction conditions. Wide functional group tolerance, easy catalyst recovery, and recyclability up to twelve times without significant loss of catalytic activity added extra importance to the present process.     

Vibration suppression of a string through cyclic application and removal of constraints

A new method for the control of string vibration is presented. The method relies on application and removal of a constraint at one point on the string close to one of its boundaries. Application of the constraint temporarily results in two vibrating strings, one of which is significantly shorter in length than the other. The vibration of the shorter length string decays rapidly due to high damping and results in reduction in the overall energy of the system. Removal of the constraint does not change the energy of the system but allows the constraint to be applied repeatedly for vibration suppression. A mathematical model of the cycle of constraint application and removal is presented and multiple cycles of constraint application and removal are simulated. Experiments were performed with a coiled extension spring which behaves like a lightly damped string. Simulation and experimental results match well with each other and demonstrate the efficacy of the simple control strategy.     

Singularity-free dark energy star

We propose a model for an anisotropic dark energy star where we assume that the radial pressure exerted on the system due to the presence of dark energy is proportional to the isotropic perfect fluid matter density. We discuss various physical features of our model and show that the model satisfies all the regularity conditions and is stable as well as singularity-free.