Optimal control and numerical methods for hybrid stochastic SIS models

This work focuses on optimal controls of a class of stochastic SIS epidemic models under regime switching. By assuming that a decision maker can influence the infectivity period, our aim is to minimize the expected discounted cost due to illness, medical treatment, and the adverse effect on the society. In addition, a model with the incorporation of vaccination is proposed. Numerical schemes are developed by approximating the continuous-time dynamics using Markov chain approximation methods. It is demonstrated that the approximation schemes converge to the optimal strategy as the mesh size goes to zero. Numerical examples are provided to illustrate our results.     

Controllable Preparation of Plasmonic Gold Nanostars for Enhanced Photothermal and SERS Effects

Gold nanostars(Au NSs) are asymmetric anisotropic nanomaterials with sharp edge structure. As a promising branched nanomaterial, Au NS has excellent plasmonic absorption and scattering properties. In order to tune the plasmonic photothermal and surface-enhanced Raman scattering(SERS) activity of Au NSs to obtain the desired characteristics, the effects of reagents on the local surface plasmon resonance(LSPR) bands of Au NSs were studied and the morphology and size were regulated. Nanoparticles with different sharp edges were synthesized to make their local plasmon resonance mode tunable in the visible and near-infrared region. The effects of the number and sharpness of different tips under the control of AgNO₃ on the photothermal response of Au NSs and the SERS activity and their mechanism were discussed in detail. The results show that as the length of the branch tip becomes longer and the sharpness increases, the plasmonic photothermal effect of Au NSs is strengthened, and the photothermal conversion efficiency is the highest up to 40% when the length of Au NSs is the longest. Au NSs with high SERS activity are used for the Raman detection substrate. Based on this property, the quantitative detection of the pesticide thiram is achieved.     

Brownian motion with drift on spaces with varying dimension

Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in Chen and Lou (2018). In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation). Such a process can be conveniently defined by a regular Dirichlet form that is not necessarily symmetric. Through the method of Duhamel’s principle, it is established in this paper that the transition density of BMVD with drift has the same type of two-sided Gaussian bounds as that for BMVD (without drift). As a corollary, we derive Green function estimate for BMVD with drift.     

One injection for one-week controlled release: In vitro and in vivo assessment of ultrasound-triggered drug release from injectable thermoresponsive biocompatible hydrogels

Episodic release of bioactive compounds is often necessary for appropriate biological effects under specific physiological conditions. Here, we aimed to develop an injectable, biocompatible, and thermosensitive hydrogel system for ultrasound (US)-triggered drug release. An mPEG-PLGA-BOX block copolymer hydrogel was synthesized. The viscosity of 15 wt% hydrogel is 0.03 Pa*s at 25 °C (liquid form) and 34.37 Pa*s at 37 °C (gel form). Baseline and US-responsive in vitro release profile of a small molecule (doxorubicin) and that of a large molecule (FITC-dextran), from the hydrogel, was tested. A constant baseline release was observed in vitro for 7 d. When triggered by US (1 MHz, continuous, 0.4 W/cm²), the release rate increased by approximately 70 times. Without US, the release rate returned to baseline. Baseline and US-responsive in vivo release profile of doxorubicin was tested by subcutaneous injection in the back of mice and rats. Following injection into the subcutaneous layer, in vivo results also suggested that the hydrogels remained in situ and provided a steady release for at least 7 d; in the presence of the US-trigger, in vivo release from the hydrogel increased by approximately 10 times. Therefore, the mPEG-PLGA-BOX block copolymer hydrogel may serve as an injectable, biocompatible, and thermosensitive hydrogel system that is applicable for US-triggered drug release.     

Development and application of chip calorimeter as an X-ray detector

Radiotherapy for cancer patients requires accurate measurement of the absorbed dose of radiation in a treatment planning step. Various types of radiation detectors are currently utilized for dose measurement. Among them, calorimeters are known to be the most precise detector for measuring absorbed dose, but their on-site application is limited by the large size of the equipment. We developed a miniaturized chip calorimeter for application as a radiation detector. The calorimetric radiation detector was built using micro/nano fabrication techniques, and consists of an SU-8 photoresist absorber and high-sensitivity vanadium oxide (VO_x) thermistors. The thermistors had a temperature resolution of 135 μK, and the calorimeter showed a thermal conductance of 11 μW/K. The detector was irradiated with various X-ray dose rates from a linear accelerator, and the absorbed dose to SU-8 was measured. The detector responses showed high linearity with dose rates, demonstrating the feasibility of the radiation detector for practical uses.     

Leucine-coated cobalt ferrite nanoparticles: Synthesis,characterization and potential biomedical applications for drug delivery

This work was primarily focused on the synthesis, characterization and biomedical applications of cobalt ferrite (CoFe₂O₄) nanoparticles, which were synthesized by a facile solvothermal method using an amino acid of Leucine (Leu) as the surface coating agents. The morphology, structure and properties of the as-synthesized uncoated and Leu-coated CoFe₂O₄ nanoparticles were characterized in detail by means of XRD, SEM, TEM, DLS, FTIR, XPS, TGA and SQUID. More importantly, it was found that the Leu-coated CoFe₂O₄ nanoparticles can be used as the efficient drug delivery with a drug loading capacity of 0.32 mg/mg for doxorubicin hydrochloride (DOX), and the loaded DOX demonstrated a sustained and progressive release manner. The in vitro cytotoxicity studies towards the HeLa cells were carried out, and the results indicated that the Leu-coated CoFe₂O₄ nanoparticles exhibited a relatively high cell viability compared with that of bare CoFe₂O₄ nanoparticles and the DOX loaded Leu-coated CoFe₂O₄ nanoparticles presented an obvious cytotoxic effect on HeLa cells.     

立体化学教学中空间感观能力的培养

介绍了在有机物结构、有机反应机理和构象快速转换平衡的教学中培养学生构建空间感观的策略.教学实践表明,这些策略的实施具有较好的效果.     

Modeling of metallic foam morphology using the Representative Volume Element approach: Development and experimental validation

This paper focuses on the development of an algorithm capable of generating morphologically-representative foam structures using the Representative Volume Element (RVE) approach. Stereology, a sampling method based on direct observations of the foam cross-sections, is used to characterize the pore size and shape distributions. Using the morphology generation algorithm, the smallest RVEs corresponding to the numerically-convergent foam morphologies are calculated for different foam porosities. To validate the foam generation algorithm, the pore size and shape distributions of the numerically-generated foams are compared to those of the titanium foams manufactured by the space holder method.     

The ∞‐Besov capacity problem

A theory of ∞‐Besov capacities is developed and several applications are provided. In particular, we solve an open problem in the theory of limits of the ∞‐Besov semi‐norms, we obtain new restriction‐extension inequalities, and we characterize the pointwise multipliers acting on the ∞‐Besov spaces.