Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

Measurements of resistance and reactance in fish with the use of bioelectrical impedance analysis: sources of error

New technologies can be riddled with unforeseen sources of error, jeopardizing the validity and application of their advancement. Bioelectrical impedance analysis (BIA) is a new technology in fisheries research that is capable of estimating proximate composition, condition, and energy content in fish quickly, cheaply, and (after calibration) without the need to sacrifice fish. Before BIA can be widely accepted in fisheries science, it is necessary to identify sources of error and determine a means to minimize potential errors with this analysis. We conducted controlled laboratory experiments to identify sources of errors within BIA measurements. We concluded that electrode needle location, procedure deviations, user experience, time after death, and temperature can affect resistance and reactance measurements. Sensitivity analyses showed that errors in predictive estimates of composition can be large (>50%) when these errors are experienced. Adherence to a strict protocol can help avoid these sources of error and provide BIA estimates that are both accurate and precise in a field or laboratory setting.

Preparation, Surface Properties and Biological Activity of the Composite of Poly (lactide-co-glycolide) and Bioglass Nanoparticles Surface Grafted with Poly(L-lactide)

SiO2-CaO-P2O5 gel bioglass (BG) nanoparticles with the diameter of 40 nm were synthesized by sol-gel approach. The surface of BG nanoparticles was grafted through the ring-open polymerization of the L-lactide to yield poly (L-lactide) (PLLA) grafted gel particle (PLLA-g-BG). The PLLA-g-BG was further blended with poly(lactide-co-glycolide) (PLGA) to prepare the nanocomposites of PLLA-g-BG/PLGA with the various blend ratios of two phases. PLLA-g-BG accounted 10%, 20% and 40% in the composite, respectively. TGA, ESEM and EDX were used to analyze the graft ratio of PLLA-g-BG, the dispersion of nano-particles and the surface elements of the composites respectively. The rabbit osteoblasts were seeded and cultured on the thin films of composites in vitro. The cell adhesion, spreading and growth of osteoblasts were analyzed with FITC staining, NIH Image J software and MTT assay. The change of cell cycle was monitored by flow cytometry (FCM). The results demonstrated that the Surface modification of BG with PLLA could significantly improve the dispersing of the particles in the matrix of PLGA. The nanocomposite with 20% PLLA-g-BG exhibited superior surface properties, including roughness and plenty of silicon, calcium and phosper, to enhance the adhesion, spreading and proliferation of osteoblasts.

Computer simulation of miscibility and self-assembly structure for polymer-containing systems with special interactions

The miscibility and structure of A-B copolymer/C homopolymer blends with special interactions were studied by a Monte Carlo simulation in two dimensions. The interaction between segment A and segment C was repulsive, whereas it was attractive between segment B and segment C. In order to study the effect of copolymer chain structure on the morphology and structure of A-B copolymer/C homopolymer blends, the alternating, random and block A-B copolymers were introduced into the blends, respectively. The simulation results indicated that the miscibility of A-B block copolymer/C homopolymer blends depended on the chain structure of the A-B copolymer. Compared with alternating or random copolymer, the block copolymer, especially the diblock copolymer, could lead to a poor miscibility of A-B copolymer/C homopolymer blends. Moreover, for diblock A-B copolymer/C homopolymer blends, obvious self-organized core-shell structure was observed in the segment B composition region from 20% to 60%. However, if diblock copolymer composition in the blends is less than 40%, obvious self-organized core-shell structure could be formed in the B-segment component region from 10 to 90%. Furthermore, computer statistical analysis for the simulation results showed that the core sizes tended to increase continuously and their distribution became wider with decreasing B-segment component.

The behaviors and sources of dissolved arsenic and antimony in Bohai Bay

In this paper, we determined the concentrations of antimony species (antimonite (Sb(III)), antimonate (Sb(V)) and dissolved inorganic antimony (DISb)) and arsenic, in Bohai Bay seawaters, as well as the relationships of the analytes with environmental factors such as seawater characteristics (e.g., suspended particulate material (SPM), salinity and total organic carbon (TOC)), heavy metals, nutrients and phytoplankton species, and evaluated the sources of arsenic and antimony. Dissolved arsenic and antimony concentrations in the surface waters were ranging spatially from 1.03 to 1.26 ng/ml and 0.386 to 1.075 ng/ml, with mean values of 1.18 and 0.562 ng/ml, respectively. Sb(V) as the prominent chemical species constituted about 89%. Regarding arsenic concentrations in the surface waters, there was a tendency for a small variation. However, antimony species concentrations were much variable than arsenic. The highest arsenic and antimony concentrations were found near the Haihe Estuary. These distribution patterns were controlled mainly by environmental factors, biological activities and sources. In this region, DISb and Sb(V) negatively correlated with salinity. Besides, arsenic and antimony correlated well with the nutrients, chlorophyll a and phytoplankton, implying that arsenic and antimony had been involved in biological cycling. In addition, according to our estimate, about 333.5 x 10(8) mg/year of arsenic and 454.2 x 10(8) mg/year of antimony reached Bohai Bay via rivers. (C) 2010 Elsevier Ltd. All rights reserved.

Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

The synthesis and biological evaluation of lanostane and cholestane-type natural products

The main objective of this thesis is to outline the synthetic chemistry involved in the preparation of a range of novel lanostane and cholestane derivatives, and subsequent investigation into their biological activity in cancer cells. The biological results obtained throughout the project have driven the strategic synthesis of new compounds, in an effort to optimise the anti cancer potential of lanostane and cholestane derivatives. The first chapter begins with an overview of steroidal compounds and details a literature review of the natural sources of these moieties, as well as their biosynthesis and reported synthetic derivatives. The biological activity of interesting natural and synthetic analogues is also discussed. In addition, an insight into some currently prescribed pharmaceutical compounds, with functional groups relevant to this project, is presented. The second chapter discusses the methods employed for the synthesis of these novel lanostane and cholestane derivatives, and comprises three main sections. Firstly, various oxidation products of lanosterol are synthesised, mainly via epoxidations of the C-8,9 and C- 24,25 alkenes, and also allylic oxidations at these positions. Secondly, amine derivatives of lanosterol are formed by cleaving the lanostane side chain, thereby yielding a new cholestane nucleus, and performing several reductive aminations on the resulting key aldehyde intermediates. Various amines such as piperidine, morpholine, diethylamine and aniline are employed in the reductive amination reactions to yield novel cholestane steroids with amine side chains. Finally, starting from stigmasterol and proceeding with the same methodology of cleaving the steroidal side chain and subsequently performing reductive aminations, novel cholestane derivatives of the biologically active amines are synthesised. The cytotoxicity of these compounds against CaCo-2 and U937 cell lines is presented in terms of percentage viability of cells, IC50 value and apoptosis. The MTT assay is used to determine the percentage viability of cells, and the IC50 data is generated from the MTT results. Apoptosis is measured in terms of fold increase relative to a carrier control. In summary, the compounds formed are discussed in terms of chemical synthesis, spectroscopic interpretation and biological activity. The main reaction pathways involved in the chemistry within this project are various oxidations and reductive amination. The final chapter is a detailed account of the full experimental procedures for the compounds synthesised during this work, including characterisation using spectroscopic and analytical data.

Comparison of encapsulant curing with convention and microwave systems

Comparison of the performance of a conventional convection oven system with a dual-section microwave system for curing thermosetting polymer encapsulant materials has been performed numerically. A numerical model capable of analysing both the convection and microwave cure processes has been developed and is breifly outliines. The model is used to analyse the curing of a commercially available encapsulant material using both systems. Results obtained from numerical solutions are presented, confirming that the VFM system enables the cure process to be carried out far more rapidly than with the convection oven system. This capability stems from the fundamental heating processes involved, namely that microwave processing enables the heating rate to be varied independently of the material temperature. Variations in cure times, curing rates, maximum temperatures and residual stresses between the processes are fully discussed.