Effects of boundary conditions on pattern formation in a nonlocal prey–predator model

Effects of periodic and Neumann boundary conditions on a nonlocal prey–predator model are investigated. Two types of kernel functions with finite supports are used to characterize the nonlocal interactions. These kernel functions are modified to handle the Neumann boundary condition. Numerical techniques to find the Turing and spatial-Hopf thresholds for Neumann boundary condition are also described. For a fixed range of nonlocal interaction with a given kernel function, Turing bifurcation curves corresponding to both the boundary conditions are close to each other. The same is true for the spatial-Hopf bifurcation curves too. However, the nonlinear solutions inside the Turing domain as well as spatial-Hopf domain depend on the boundary condition. Thus, boundary conditions play important roles in a nonlocal model of prey-predator interaction.     

The shelf space and pricing strategies for a retailer-dominated supply chain with consignment based revenue sharing contracts

Consider a two-echelon supply chain consisting of two manufacturers and a dominant retailer, such as big supermarkets like Walmart. Under a consignment contract with revenue sharing, the two manufacturers sell through the retailer two substitutable products whose demands are dependent on their shelf space and sales prices. The two manufacturers may compete horizontally for shelf space and pricing by three scenarios: Nash game, Stackelberg game, and collusion, and play vertically the retailer-Stackelberg game with the retailer. For each of these horizontal scenarios, we present all participators’ equilibrium strategies and their corresponding profits, based on which the impacts of manufacturers’ cost difference and moving sequence are investigated. Additionally, we discuss whether a horizontal collusion among manufacturers occurs when they choose their scenarios and whether centralization is always beneficial for the entire chain under the considered consignment contract. The study reveals the following results: (i) When the manufacturers compete horizontally, the high-cost manufacturer always sets a high-price and less shelf space strategy, while the low-cost manufacturer always adopts a low-price and more shelf space strategy, which is not affected by their moving sequence. If they collude horizontally, it is just reverse. (ii) When the two manufacturers compete horizontally, all participators’ equilibrium strategies and their corresponding profits are significantly influenced by manufacturers’ moving sequence. (iii) A horizontal collusion between the manufacturers can occur only when their cost difference is relatively small; this finding supplements existing literature. (iv) When the cost difference between manufacturers is relatively big, then centralization may be detrimental to the entire chain, which can explain why several supply chains adopt vertical competition strategies in practice. In addition, we find that these results still hold for the limited shelf space scenario and shelf-space limitation enhances the horizontal and vertical competition intensity by increasing shelf space fee.     

Polycyclic codes as invariant subspaces

Polycyclic codes are a powerful generalization of cyclic and constacyclic codes. Their algebraic structure is studied here by the theory of invariant subspaces from linear algebra. As an application, a bound on the minimum distance of these codes is derived which outperforms, in some cases, the natural analogue of the BCH bound.     

离散分红下障碍期权的间接级数展开定价方法

人们投资股票市场的最大动力,除了从股票本身的升值中获利,还包括收益分红.提出了带有离散分红的障碍期权的一种新型的近似方法,以向上敲出看涨障碍期权为例,固定分红的次数,通过泰勒级数展开得到关于关键变量的仿射函数,给出了一个只带有一维积分的定价公式,提高了计算速度.该方法还可以用于回望期权等其它衍生品的定价,对在市场上进行期权交易有一定指导意义.     

Constructions of optimal LCD codes over large finite fields

In this paper¹, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction methods include random sampling in the orthogonal group, code extension, matrix product codes and projection over a self-dual basis.     

Thermochemical and Toxic Element Behavior during Co-Combustion of Coal and Municipal Sludge

The thermochemical and kinetic behavior of co-combustion of coal, municipal sludge (MS) and their blends at different ratios were investigated by thermogravimetric analysis. Simulation experiments were performed in a vacuum tube furnace to determine the conversion behavior of toxic elements. The results show that the combustion processes of the blends of coal and municipal sludge are divided into three stages and the combustion curves of the blends are located between those of individual coal and municipal sludge samples. The DTG_max of the sample with 10% sludge addition reaches a maximum at the heating rate of 20 °C/min, indicating that the combustion characteristics of coal can be improved during co-combustion. Strong interactions were observed between coal and municipal sludge during the co-combustion. The volatilization rates of toxic elements decrease with an increasing proportion of sludge in the blends during co-combustion, which indicates that the co-combustion of coal and sludge can effectively reduce the volatilization rate of toxic elements. The study reflects the potential of municipal sludge as a blended fuel and the environmental effects of co-combustion of coal and municipal sludge.     

1D atom localization via probe absorption spectrum in a four-level cascade-type atomic system

We present a simple scheme of atom localization in a subwavelength domain via manipulation of probe absorption spectrum in a four-level atomic system. Due to the joint quantum interference induced by the standing-wave and radio-frequency driving fields, the localization peak position and number as well as the conditional position probability can be controlled by properly adjusting the system parameters. The proposed scheme may provide a promising way to achieve high-precision and high-resolution 1D atom localization.     

Solid–liquid equilibria of long chain n-alkanes (C18–C28) in N,N-dimethylacetamide

Solid–liquid equilibria (SLE) of the n-alkanes (octadecane, nonadecane, eicosane, heneicosane, docosane, tricosane, tetracosane, pentacosane, hexacosane, heptacosane and octacosane) in N,N-dimethylacetamide (DMA) are reported. The data has been measured by the dynamic method from 275 K to the melting temperatures of the n-alkane. The experimental results have been correlated by the Redlich–Kister equation with two and three parameters and the NRTL equation.     

Sr0.955Al2-xBxSi2O8:0.025Eu2+荧光粉的制备、晶体结构及发光性能

通过高温固相反应在弱还原气氛下制备了Sr_0.955Al_2-xB_xSi₂O₈：0.025Eu²⁺（x=0~0.9）一系列荧光粉,研究了B（Ⅲ）取代基质晶格中的Al（Ⅲ）对荧光粉晶体结构和Eu²⁺发光性能的影响。B（Ⅲ）以类质同相取代基质晶格中Al（Ⅲ）,形成了连续固溶体。随着B（Ⅲ）取代量的增加,荧光粉的晶胞参数（a、b、c）和晶胞体积（V）呈线性递减,而晶胞参数（β）呈线性递增。荧光粉的激发光谱为位于225~400 nm的宽峰,表观峰值位于350 nm,激发峰的半高宽（FWHM）随着B（Ⅲ）取代量的增加,从90 nm减小到102 nm。发射光谱位于370~600 nm的宽峰,可拟合为409和447 nm两个峰,表观峰值位于409 nm。随着B（Ⅲ）取代量的增加,2个拟合峰位均出现蓝移且2个峰强度比呈线性递减。根据试样荧光光谱,通过Van Uitert经验公式计算得出SrAl₂Si₂O₈：Eu²⁺中Sr²⁺的配位数为9。随着B（Ⅲ）取代Al（Ⅲ）进入基质晶格,造成发光中心Eu与配体O距离增加,使得Eu²⁺所处的晶体场强度减小,发光中心Eu²⁺的5d能级分裂减小,造成Eu²⁺最低发射能级重心上移,2个拟合谱峰峰位均呈线性蓝移。     

Light-induced shape morphing of thin films

Shape transformation of thin two-dimensional sheets into three-dimensional structures using light is of great interest for remotely controlled fabrication, surface modulation, and actuation. Over the last few decades, significant efforts have been made to develop material systems incorporating photochemical or photothermal elements to drive deformation in response to illumination. However, the full extent of the interplay between chemistry, optics, and mechanics in these materials is poorly understood. In this review, we introduce principles of shape morphing in these systems by considering the underlying physics of photoinduced stresses and how these have been used in recent literature. In addition, we provide a critical overview of the important design characteristics of both photochemical and photothermal system and offer our view on the open opportunities and challenges in this rapidly growing field.