Polynomial Reproduction in Subdivision

We study conditions on the matrix mask of a vector subdivision scheme ensuring that certain polynomial input vectors yield polynomial output again. The conditions are in terms of a recurrence formula for the vectors which determine the structure of polynomial input with this property. From this recurrence, we obtain an algorithm to determine polynomial input of maximal degree. The algorithm can be used in the design of masks to achieve a high order of polynomial reproduction.     

Effects of tributyltin(IV) chloride on the gametes and fertilization of Ascidia malaca (Ascidiacea: Tunicata)

Ascidia malaca gametes before fertilization incubated in 10^?5 or 10^?7 M solutions of tributyltin(IV) chloride, TBTCl, for 3 h appear highly damaged under transmission electron microscopy observation. Also, the fertilization process is affected by the compound: the damaged spermatozoa are present in the vitelline coat and the egg does not cleave. An increase of microbodies, structurally similar to peroxisomes, have been detected in the egg peripheral cytoplasm, probably in relation to their role in alleviating damage to some cellular components. The results have shown that the reproduction of ascidians under unfavourable environmental conditions is prevented. Copyright © 2003 John Wiley & Sons, Ltd.     

Mathematical analysis of the dynamics of COVID-19 in Africa under the influence of asymptomatic cases and re-infection

Coronavirus pandemic (COVID-19) hit the world in December 2019, and only less than 5% of the 15 million cases were recorded in Africa. A major call for concern was the significant rise from 2% in May 2020 to 4.67% by the end of July 15, 2020. This drastic increase calls for quick intervention in the transmission and control strategy of COVID-19 in Africa. A mathematical model to theoretically investigate the consequence of ignoring asymptomatic cases on COVID-19 spread in Africa is proposed in this study. A qualitative analysis of the model is carried out with and without re-infection, and the reproduction number is obtained under re-infection. The results indicate that increasing case detection to detect asymptomatically infected individuals will be very effective in containing and reducing the burden of COVID-19 in Africa. In addition, the fact that it has not been confirmed whether a recovered individual can be re-infected or not, then enforcing a living condition where recovered individuals are not allowed to mix with the susceptible or exposed individuals will help in containing the spread of COVID-19.     

Dynamical analysis of age-structured pertussis model with covert infection

An age-structured pertussis model with covert infection is proposed to understand the effect of covert infection on the recurrence of pertussis. It is found that vaccination only for young children does not have a decisive effect on whooping cough control. It is shown that although the vaccine coverage rate is relatively high, the model has a backward bifurcation for a larger covert infection rate. In addition, sufficient conditions for the disease-free steady state to be globally asymptotically stable are obtained.     

Multistrain edge‐based compartmental model on networks

Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models.     

两大部类持续扩大再生产的优化

基于经典的马克思两大部类社会再生产公式,建立了离散确定型的持续扩大再生产的优化问题的动态规划模型.在生产资料部类的不变资本产出率高于另一部类的条件下,动态规划的指标函数是作为决策变量的生产资料部类积累率的单调函数,因而可以使用逆序解法或者顺序解法,获得唯一的最优策略和最优指标函数.借助《资本论》中的一个举例,计算验证了最优解.     

A Color Appearance Model Applicable in Mesopic Vision

We propose a color vision model that can be used to predict color appearance in mesopic vision as well as photopic and scotopic vision. It is based on a two-stage model which consists of the cone and opponent stages and it assumes rod intrusion at the opponent stage. The model has the following features to describe the color appearance in mesopic vision. First, it includes a gradual and nonlinear shift in spectral luminous efficiency from V (LD) to V (LD) to cope with the spectral sensitivity difference between photopic and scotopic vision and the nonlinearity of rod influence on the luminance channel. Second, the model assumes decrease of the chromatic component with decreasing illuminance to explain the reduction of saturation at low illuminance levels. Third, it assumes that red/green and yellow/blue components change with illuminance levels independently, thus explaining hue shifts with decreasing illuminance. We applied the model for color appearance simulation of natural scenes in a mesopic visual environment.     

基于Zernike多项式表示色域边界的色域映射

在彩色图像的跨媒体复制中,由于不同媒体有不同的色域,所以在大多数情况下色域映射是不可避免的。不论采用何种映射算法,色域映射的第一步是确定有关媒体的色域边界。目前大多数的色域边界都是用一组测量的或用其它方法得到的离散数据来表示的。然而,由于这种表示方式是利用一组离散数据来实施色域映射的两个基本处理(即确定任一指定的等色调面平面中色域的边缘线以及确定色域边界与一条映射线的交点),比较复杂和费时,因此希望找到一种色域边界的解析表达式来解决这一问题。简述了不久前提出的一种解析函数色域边界表示方法,并用实例说明了如何利用这种解析表示(Zernike多项式)来实现上述的边缘线确定和交点确定。最后给出了几种映射算法的色域映射完整过程及其结果。