PLA Electrospun Fibers Reinforced with Organic and Inorganic Nanoparticles: A Comparative Study

In this work, different poly (lactic acid) (PLA)-based nanocomposite electrospun fibers, reinforced with both organic and inorganic nanoparticles, were obtained. As organic fibers, cellulose nanocrystals, CNC, both neat and functionalized by “grafting from” reaction, chitosan and graphene were used; meanwhile, hydroxyapatite and silver nanoparticles were used as inorganic fibers. All of the nanoparticles were added at 1 wt% with respect to the PLA matrix in order to be able to compare their effect. The main aim of this work was to study the morphological, thermal and mechanical properties of the different systems, looking for differences between the effects of the addition of organic or inorganic nanoparticles. No differences were found in either the glass transition temperature or the melting temperature between the different electrospun systems. However, systems reinforced with both neat and functionalized CNC exhibited an enhanced degree of crystallinity of the electrospun fibers, by up to 12.3%. From a mechanical point of view, both organic and inorganic nanoparticles exhibited a decreased elastic modulus and tensile strength in comparison to neat electrospun PLA fibers, improving their elongation at break. Furthermore, all of the organic and inorganic reinforced systems disintegrated under composting conditions after 35 days.     

Two-time-scale Jump-Diffusion Models with Markovian Switching Regimes

This work is concerned with two-time-scale jump diffusion models modulated by continuous-time Markov chains. One of our motivations stems from generalization of insurance risk models. The models are hybrid in the sense that they involve both continuous dynamics and discrete events. Two cases are considered. One of them has a fast-varying switching process, and the other contains a rapidly fluctuating diffusion. Two-time scale is used for complexity reduction. Using weak convergence methods, we derive their limit processes. The insight and implication provided by the analysis are: to reduce the complexity, one can ignore the detailed variations and concentrate on the limit or the reduced models.     

Cascades of Hopf bifurcations from boundary delay

We consider a 1-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is given by the constant function u≡1. We show that if the delay is small, this equilibrium solution is asymptotically stable, similar as in the case without delay. We also show that, as the delay goes to infinity, this equilibrium becomes unstable and undergoes a cascade of Hopf bifurcations. The structure of this cascade will depend on the parameters appearing in the equation. This equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain.     

Some Thoughts on Mathematical Education

This paper explores the growth of mathematical studies in recent times and suggests future patterns that may occur in mathematical curricula. It is proposed that courses in the History and Methods of Mathematics, Mathematical Engineering (rather than Engineering Mathematics) and Mathematics and Education should be used to widen the curriculum choices for the mathematical student of the future. Finally, in illustrating the application of mathematics to the study of Noise and Vibration it is shown that, in such an investigation, mathematics cannot be an end in itself but can be greatly helped by a knowledge of other physical disciplines.

     

Operational Research Education for Practitioners and Managers∗

The paper reviews the history of education in operational research and indicates the needs both of a practitioner and of a manager. It describes how these can be met by standard course teaching and suggests some areas of development.