Optimal control of an SIQRS epidemic model with three measures on networks

Nonlinear Dynamics - At present, the main measures for disease control are vaccination, quarantine and treatment. Taking the three measures into consideration, time-varying optimal control problems...     

First-principles study on the crystal, electronic structure and mechanical properties of hexagonal Al3RE (RE = La, Ce, Pr, Nd, Sm, Gd) intermetallic compounds

The structural properties, elastic properties and electronic structures of hexagonal Al₃RE intermetallic compounds are calculated by using first-principles calculations based on density functional theory. Since there exists strong on-site Coulomb repulsion between the highly localized 4f electrons of RE atoms, we present a combination of the GGA and the LSDA+U approaches in order to obtain the appropriate results. The GGA calculated lattice constants for the hexagonal Al₃RE intermetallic compounds are in good agreement with available experimental values. The results of cohesive energy indicate that these compounds can be stable under absolute zero Kelvin and the stability of Al₃Gd is the strongest in all of the hexagonal Al₃RE compounds. The densities of states for GGA and LSDA+U approaches are also obtained for the Al₃RE intermetallic compounds. The mechanical properties are calculated from the GGA method in this paper. According to the computed single crystal elastic constants, Al₃La, Al₃Sm and Al₃Gd are mechanically unstable, while Al₃Ce, Al₃Pr and Al₃Nd are stable. The polycrystalline elastic modulus and Poisson’s ratio have been deduced by using Voigt-Reuss-Hill (VRH) approximations, and the calculated ratio of bulk modulus to shear modulus indicates that Al₃La compound is ductile material, but Al₃Ce, Al₃Pr, Al₃Nd, Al₃Sm and Al₃Gd are brittle materials.     

微波传输路由的数学模型

在微波通讯中，电波射束和障碍物之间应留有足够的余隙，以保证能量的有效传输．本文考虑地球表面自然凸特征，建立在此意义下的余隙的数学模型，从而获得微波传输路由的数学模型．利用此模型的解与海拔制高点的余隙进行比较，便可获得工程建设中的最佳余隙值及相联系的有效的经济的路由设计．     

矩阵的奇异值分解的应用

本文通过引入矩阵奇异值的说明率及其模型考核的相关指标将矩阵的奇异值分解（ＳＶＤ）应用于我国育龄妇女接龄生育率数据的数学建模之中，得到了按龄生育率的可用于进行预测的按龄线性模型。     

Type I photosensitizers based on phosphindole oxide for photodynamic therapy: apoptosis and autophagy induced by endoplasmic reticulum stress

Photodynamic therapy (PDT) is considered a pioneering and effective modality for cancer treatment, but it is still facing challenges of hypoxic tumors. Recently, Type I PDT, as an effective strategy to address this issue, has drawn considerable attention. Few reports are available on the capability for Type I reactive oxygen species (ROS) generation of purely organic photosensitizers (PSs). Herein, we report two new Type I PSs, α-TPA-PIO and β-TPA-PIO, from phosphindole oxide-based isomers with efficient Type I ROS generation abilities. A detailed study on photophysical and photochemical mechanisms is conducted to shed light on the molecular design of PSs based on the Type I mechanism. The in vitro results demonstrate that these two PSs can selectively accumulate in a neutral lipid region, particularly in the endoplasmic reticulum (ER), of cells and efficiently induce ER-stress mediated apoptosis and autophagy in PDT. In vivo models indicate that β-TPA-PIO successfully achieves remarkable tumor ablation. The ROS-based ER stress triggered by β-TPA-PIO-mediated PDT has high potential as a precursor of the immunostimulatory effect for immunotherapy. This work presents a comprehensive protocol for Type I-based purely organic PSs and highlights the significance of considering the working mechanism in the design of PSs for the optimization of cancer treatment protocols.

Phosphindole oxide-based photosensitizers with Type I reactive oxygen species generation ability are developed and used for endoplasmic reticulum stress-mediated photodynamic therapy of tumors.     

Adaptive finite-time outer synchronization between two complex dynamical networks with noise perturbation

Nonlinear Dynamics - In this paper, the finite-time outer synchronization between two complex dynamical networks with noise perturbation is considered. Combing the adaptive and finite-time control...     

Stability and bifurcation analysis for a discrete-time model of Lotka-Volterra type with delay

A discrete model of Lotka-Volterra type with delay is considered, and a bifurcation analysis is undertaken for the model. We derive the precise conditions ensuring the asymptotic stability of the positive equilibrium, with respect to two characteristic parameters of the system. It is shown that for certain values of these parameters, fold or Neimark-Sacker bifurcations occur, but codimension 2 (fold-Neimark-Sacker, double Neimark-Sacker and resonance 1:1) bifurcations may also be present. The direction and the stability of the Neimark-Sacker bifurcations are investigated by applying the center manifold theorem and the normal form theory.     

Carathéodory条件下三阶半正边值问题的正解

不要求非线性项f(t,u)连续且下方有界,在f(t,u)满足Carathéodory条件下,讨论了三阶半正边值问题u+λf(t,u)=0,0t1,u(0)=u′(0)=u″(1)=0.当λ>0且充分小时正解的存在性,应用的工具为锥上的不动点.