One‐pot synthesis of new 3‐substituted coumarins by tandem reactions

The synthesis of new 3‐substituted coumarins appended to imidazolium, pyridinium, 3‐dimethylamino pyridinium, 3‐chloro pyridinium and 3‐bromo pyridinium salts is reported. These salts were prepared by tandem reactions, followed by quantitative anionic metathesis. The structure of these new 3‐substituted coumarins was established by NMR (¹H, ¹³C) and high‐resolution mass spectrometry.     

A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies

In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.     

Effect of thermooxidation on tinuvin 783 in LDPE films: Characterization by UV and ftir spectroscopy

The effect of thermooxidation on Tinuvin 783 which is a hindered amine light stabilizer in LDPE films has been investigated by UV and FTIR spectroscopy. Initially, a standard curve describing the variation of the concentration of Tinuvin 783 in LDPE films was plotted using the method of integration of the band area. The relation obtained was: band area = 19.6249 × [Tinuvin 783]. This equation was then applied to measure the variation of the concentration of Tinuvin 783 in the 0.2%_wt stabilized samples which have undergone thermooxidation at 90°C for 98 days. The results showed a considerable decrease in the concentration of Tinuvin 783 by 35% during the first 30 days due to probably the formation of nitroxyl radicals. After this, the concentration was observed to be unchanged and may correspond to the phase of nitroxyl radical regeneration. On the other hand, no chemical change in the stabilized LDPE films was observed by FTIR spectroscopy at 90°C during 98 days while the band characteristic of ketone groups (1720 cm⁻¹) was detected for the unstabilized samples after only 11 days. (LDPE: low density polyethylene; HALS: hindered amine light stabilizer)     

Energy harvesting in a Mathieu–van der Pol–Duffing MEMS device using time delay

This paper investigates quasi-periodic vibration-based energy harvesting in a delayed nonlinear MEMS device consisting of a delayed Mathieu–van der Pol–Duffing type oscillator coupled to a delayed piezoelectric coupling mechanism. We use the multiple scales method to approximate the quasi-periodic response and the related power output near the principal parametric resonance. The effect of time delay on the energy harvesting performance is studied. It is shown that for appropriate combination of time delay parameters, there exists an optimum range of excitation frequency beyond the resonance where quasi-periodic vibration-based energy harvesting is maximum. Numerical simulations are performed to confirm the analytical predictions.     

Multi-scale Modeling of Vision-Guided Remodeling and Age-Dependent Growth of the Tree Shrew Sclera During Eye Development and Lens-Induced Myopia

The sclera uses unknown mechanisms to match the eye’s axial length to its optics during development, producing eyes with good focus (emmetropia). A myopic eye is too long for its own optics. We propose a multi-scale computational model to simulate eye development based on the assumption that scleral growth is controlled by genetic factors while scleral remodeling is driven by genetic factors and the eye’s refractive error. We define growth as a mechanism that changes the tissue volume and mass while remodeling involves internal micro-deformations that are volume-preserving at the macro-scale. The model was fitted against longitudinal refractive measurements in tree shrews of different ages and exposed to three different visual conditions: (i) normal development; (ii) negative lens wear to induce myopia; and (iii) recovery from myopia by removing the negative lens. The model was able to replicate the age- and vision-dependent response of the tree shrew experiments. Scleral growth ceased at younger age than scleral remodeling. The remodeling rate decreased as the eye emmetropized but increased at any age when a negative lens was put on. The predictive power of the model was investigated by calculating the susceptibility to scleral remodeling and the response to form deprivation myopia in tree shrews. Both predictions were in good agreement with experimental data that were not used to fit the model. We propose the first model that distinguishes scleral growth from remodeling. The good agreement of our results with experimental data supports the notion that scleral growth and scleral remodeling are two independently controlled mechanisms during eye development.     

Numerical solution for a sub-diffusion equation with a smooth kernel

In this paper we study the numerical solution of an initial value problem of a sub-diffusion type. For the time discretization we apply the discontinuous Galerkin method and we use continuous piecewise finite elements for the space discretization. Optimal order convergence rates of our numerical solution have been shown. We compare our theoretical error bounds with the results of numerical computations. We also present some numerical results showing the super-convergence rates of the proposed method.     

Spin versus helicity: Processes involving transversity

We construct the spin formalism in order to deal naturally with processes involving transversity which are now of increasing popularity. The helicity formalism which is more appropriate for collision processes of definite helicity has been so far used to also manage processes with transversity, but at the price of computing numerous helicity amplitudes which generally involve unnecessary kinematical variables.     

Finite elastic deformations of transversely isotropic circular cylindrical tubes

We consider the finite radially symmetric deformation of a circular cylindrical tube of a homogeneous transversely isotropic elastic material subject to axial stretch, radial deformation and torsion, supported by axial load, internal pressure and end moment. Two different directions of transverse isotropy are considered: the radial direction and an arbitrary direction in planes normal locally to the radial direction, the only directions for which the considered deformation is admissible in general. In the absence of body forces, formulas are obtained for the internal pressure, and the resultant axial load and torsional moment on the ends of the tube in respect of a general strain-energy function. For a specific material model of transversely isotropic elasticity, and material and geometrical parameters, numerical results are used to illustrate the dependence of the pressure, (reduced) axial load and moment on the radial stretch and a measure of the torsional deformation for a fixed value of the axial stretch.