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In this paper we study the existence of periodic solutions to the partial functional differential equation { d y ( t ) d t = B y ( t ) + L ^ ( y t ) + f ( t , y t ) , ∀ t ≥ 0 , y 0 = φ ∈ C B . \begin{equation*} \left \{ \begin {array}{l} \frac {dy(t)}{dt}=By(t)+\hat {L}(y_{t})+f(t,y_{t}), \;\forall t\geq 0,\\ y_{0}=\varphi \in C_{B}. \end{array} \right . \end{equation*} where B : Y → Y B: Y \rightarrow Y is a Hille-Yosida operator on a Banach space Y Y . For C B ≔ { φ ∈ C ( [ − r , 0 ] ; Y ) : φ ( 0 ) ∈ D ( B ) ¯ } C_{B}≔\{\varphi \in C([-r,0];Y): \varphi (0)\in \overline {D(B)}\} , y t ∈ C B y_{t}\in C_{B} is defined by y t ( θ ) = y ( t + θ ) y_{t}(\theta )=y(t+\theta ) , θ ∈ [ − r , 0 ] \theta \in [-r,0] , L ^ : C B → Y \hat {L}: C_{B}\rightarrow Y is a bounded linear operator, and f : R × C B → Y f:\mathbb {R}\times C_{B}\rightarrow Y is a continuous map and is T T -periodic in the time variable t t . Sufficient conditions on B B , L ^ \hat {L} and f ( t , y t ) f(t,y_{t}) are given to ensure the existence of T T -periodic solutions. The results then are applied to establish the existence of periodic solutions in a reaction-diffusion equation with time delay and the diffusive Nicholson’s blowflies equation.

Biomineralization is a phenomenon in which organisms form crystals. Studies have shown that many fungi have the ability to biomineralize, it can exhibit calcium oxalate crystals on their hyphae and fruiting body. Schizophyllum commune is a common saprophytic fungus distributed all over the world, but there is little research on its biomineralization. In this paper, S. commune fruiting body from three different provinces of China were collected, and isolation for hyphal cultured to obtain several samples. Utilizing light microscope, FE-SEM, and EDAX, the existence of crystals on the fruiting body and mycelium of each strain was found, and their morphological characteristics and ion content were analyzed. It was ultimately established that biomineralization occurs on S. commune.

Interest in thermoelectric generators for waste heat recovery has flourished in recent years. Typically, the efficiency of thermoelectric generators (TEGs) is quite low. Investigations are conducted in this thesis to get better performance and efficiency. The segmented leg generator is investigated as it is a promising method to increase a conventional TEGs' efficiency. This project presents the simulation model of a TEG with eight pairs of segmented legs. The simulation model is built with exactly the same materials and the same size as a physical TEG reported in the literature. Then the simulation model is compared with the prototype physical model to testify the accuracy of the simulation. The error between them is around 10 percent which is acceptable. After achieving the model of a segmented TEG, several methods are explored to improve its output power and conversion efficiency. Those methods include raising the working temperature, replacing the thermoelectric materials and reconfiguring the TEG geometry. It was found that the original model can be further optimized. After optimization, the output power increases from 188.2mW to 354.7mW, 703.13mW, and 212.85mW, respectively. Conversion efficiency increases from 1.66 percent to 2.08 percent, 7.03 percent, and 1.85 percent, respectively. Finally, a general method to design a segmented TEG is developed, using all knowledge gained from the computer simulations.

We propose a stage-structured model of childhood infectious disease transmission dynamics, with the population demographics dynamics governed by a certain family and population planning strategy giving rise to nonlinear feedback delayed effects on the reproduction ageing and rate. We first describe the long-term aging-profile of the population by describing the pattern and stability of equilibrium of the demographic model. We also investigate the disease transmission dynamics, using the epidemic model when the population reaches the positive equilibrium (limiting equation). We establish conditions for the existence, uniqueness and global stability of the disease endemic equilibrium. We then prove the global stability of the endemic equilibrium for the original epidemic model with varying population demographics. The global stability of the endemic equilibrium allows us to examine the effects of reproduction ageing and rate, under different family planning strategies, on the childhood infectious disease transmission dynamics. We also examine demographic distribution, diseases reproductive number, infant disease rate and age distribution of disease, and as such, the work can be potentially used to inform targeted age group for optimal vaccine booster programs.