On the stability of impulsive functional differential equations with infinite delays

In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. By using Lyapunov functions and the Razumikhin technique, some new theorems on the uniform stability and uniform asymptotic stability are obtained. The obtained results are milder and more general than several recent works. Two examples are given to demonstrate the advantages of the results

Bio-mimetic multimodal nanostructured surfaces fabricated with self-assembling biopolymer and its applications

Nanotechnology will revolutionize the industrial world in 21st century. Almost every country has invested in research to unfold the mysteries of nanomaterials and for their applications. A major driving force of nanomaterial research is through the imitation of living system and materials, also known as biomimetics. Polymeric biomaterials have a critical role in the advancement of medicine and sustainable green materials. In this dissertation I demonstrate the roles that the polysaccharide biopolymer chitin has as the major structural component of the arthropod cuticle and the potential that chitin has as a versatile component to novel biomaterial applications. Chitin is a polysaccharide that is a polymer of N-acetylglucosamine, chitin is the second most abundant biopolymer on the planet and a primary component of insect, arthropod and fungal exoskeletons/cuticles. Various factors contribute to the mechanical properties of an insect cuticle including cuticle thickness and composition. In my dissertation research I have also shown that nanoscale chitin polymer alignment may be another factor that contributes to the optical, surface, and mechanical properties of a cuticle. Purified chitin self-assembles into 20 nm chitin nanofibers that serve as the foundation for all higher order chitin structures in the cuticles of insects and other arthropods via interactions with structural cuticle proteins. In addition to this I have also demonstrated that purified chitin and its deacetylated form of chitosan have great potential as a substrate for many nanofabrication technique and thus provide a new and novel material in place of traditional synthetic polymers. In my dissertation is shown that the chitin and chitosan have great potential as the substrate for nanosphere lithography for the production of the generation of flexible antimicrobial and antifogging nanostructured surfaces. Metal nanoparticles are critical for many application and industrial processes, however the methods needed for their synthesis often are energy intensive and environmentally unfriendly. I demonstrate that chitin and chitosan are powerful tools for the green synthesis of metal nanoparticles. While arthropod cuticles are traditional examples for bio-mineralization and bio-metalization, I have found that a primary component of these process is due in fact to chitin and I use chitin to develop a novel class of composite nanomaterial which has important implications for a broad range of applications including antimicrobial surfaces, bioremediation, and cell scaffolds for biomedical engineering and regenerative medicine

SATURATED AND ASYMMETRIC SATURATED IMPULSIVE CONTROL SYNCHRONIZATION OF COUPLED DELAYED INERTIAL NEURAL NETWORKS WITH TIME-VARYING DELAYS

This paper considers control systems with impulses that are saturated and asymmetrically saturated which are used to examine the synchronization of inertial neural networks (INNs) with time-varying delay and coupling delays. Under the theoretical discussions, mixed delays, such as transmission delay and coupling delay are presented for inertial neural networks. The addressed INNs are transformed into first order differential equations utilizing variable transformation on INNs and then certain adequate conditions are derived for the exponential synchronization of the addressed model by substituting saturation nonlinearity with a dead-zone function. In addition, an asymmetric saturated impulsive control approach is given to realize the exponential synchronization of addressed INNs in the leader-following synchronization pattern. Finally, simulation results are used to validate the theoretical research findings