Bio-based nonionic antimicrobial polymers with isatin or indole functionality

Infections by pathogenic microorganisms remain one of the most serious concerns in several areas, particularly in hygienic applications. Antimicrobials have been used to combat these infections. Using small molecular antimicrobials as additives or coatings is an industrially adopted strategy. However, small antimicrobial agents always suffer from many drawbacks, such as leaching potential, toxicity to the environment, antimicrobial resistance. The development of antimicrobial polymers provides a promising strategy to overcome these issues. Compared to small molecular antimicrobials, antimicrobial polymers have advantages like enhanced antimicrobial efficiency, reduced toxicity, longer lifetime and lower risk to develop antimicrobial resistance.Most research has been focused on cationic antimicrobial polymers which can disrupt bacterial membranes by electrostatic interactions. The major issues with cationic antimicrobial polymers are their undesirable high-water solubility, toxicity, fouiling potential and poor miscibility with nonionic polymer matrices. To solve these problems, continued exploration of new nonionic antimicrobial polymers is highly valuable and that is where this thesis has been focusing on.In this work, we have designed and synthesized different nonionic antimicrobial polymers with isatin or indole functionality, including hyperbranched and linear structures. The antimicrobial properties against various bacteria of these polymers were evaluated. In general, these bio-based polymers exhibited significant antimicrobial activity, higher than their corresponding small model compounds. We also found that ether unit may have a synergistic effect to interact with certain bacterial membranes. It was also observed that the N-H moiety of indole in the polymer’s structure facilitate the hydrogen bonding with the C=O moiety of polyesters, which improved their miscibility. Finally, we evaluated the hemolytic activity and cytotoxicity of the obtained polymers. As a result, they showed negligible cytotoxic effect to red blood cells and MG-63 osteoblast-like cells, which indicates their potential in biomedical applications

A polynomial-time algorithm to solve the large scale of airplane refueling problem

Airplane refueling problem is a nonlinear combinatorial optimization problem with $n!$ feasible feasible solutions. Given a fleet of $n$ airplanes with mid-air refueling technique, each airplane has a specific fuel capacity and fuel consumption rate. The fleet starts to fly together to a same target and during the trip each airplane could instantaneously refuel to other airplanes and then be dropped out. The question is how to find the best refueling policy to make the last remaining airplane travels the farthest. To solve the large scale of the airplane refueling problem in polynomial-time, we propose the definition of the sequential feasible solution by employing the data structural properties of the airplane refueling problem. We prove that if an airplane refueling problem has feasible solutions, it must have sequential feasible solutions, and its optimal feasible solution must be the optimal sequential feasible solution. Then we present the sequential search algorithm which has a computational complexity that depends on the number of sequential feasible solutions referred to $Q_n$, which is proved to be upper bounded by $2^{n-2}$ as an exponential bound that lacks of applicability on larger input for worst case. Therefore we investigate the complexity behavior of the sequential search algorithm from dynamic perspective, and find out that $Q_n$ is bounded by $\frac{m^2}{n}C_n^m$ when the input $n$ is greater than $2m$. Here $m$ is a constant and $2m$ is regarded as the "inflection point" of the complexity of the sequential search algorithm from exponential-time to polynomial-time. Moreover, we build an efficient computability scheme according to which we shall predict the specific complexity of the sequential search algorithm to choose a proper algorithm considering the available running time for decision makers or users.Comment: 18 pages, 2 figure

The nn-vehicle exploration problem is NP-complete

The $n$-vehicle exploration problem (NVEP) is a combinatorial optimization problem, which tries to find an optimal permutation of a fleet to maximize the length traveled by the last vehicle. NVEP has a fractional form of objective function, and its computational complexity of general case remains open. We show that Hamiltonian Path $\leq_P$ NVEP, and prove that NVEP is NP-complete.Comment: 5 pages, 6 figure