Vertex-edge domination in graphs

In this paper we study graph parameters related to vertex-edge domination, where a vertex dominates the edges incident to it as well as the edges adjacent to these incident edges. First, we present new relationships relating the ve-domination to some other domination parameters, answering in the affirmative four open questions posed in the 2007 PhD thesis by Lewis. Then we provide an upper bound for the independent ve-domination number in terms of the ve-domination number for every nontrivial connected K_1,k-free graph, with k ≥ 3, and we show that the independent ve-domination number is bounded above by the domination number for every nontrivial tree. Finally, we establish an upper bound on the ve-domination number for connected C₅-free graphs, improving a recent bound given for trees.     

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.     

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.