Coexistence and harvesting control policy in a food chain model with mutual defense of prey

A model is proposed to understand the dynamics in a food chain (one predator‐two prey). Unlike many approaches, we consider mutualism (for defense against predators) between the two groups of prey. We investigate the conditions for coexistence and exclusion. Unlike Elettreby's (2009) results, we show that prey can coexist in the absence of predators (as expected since there is no competition between prey). We also show the existence of Hopf bifurcation and limit cycle in the model, and numerically present bifurcation diagrams in terms of mutualism and harvesting. When the harvest is practiced for profit making, we provide the threshold effort value that determines the profitability of the harvest. We show that there is zero profit when the constant effort is applied. Below (resp. above) , there will always be gain (resp. loss). In the case of gain, we provide the optimal effort and optimal steady states that produce maximum profit and ensure coexistence. Recommendations for resource managers As a result of our investigation, we bring the following to the attention of management:

• 1. In the absence of predators, different groups of prey can coexist if they mutually help each other (no competition among them).
• 2. There is a maximal effort to invest in order to gain profit from the harvest. Above , the investment will result in a loss.
• 3. In the case of profit from harvest, policy makers should recommend the optimal effort to be applied and the optimal stock to harvest. This will guarantee maximum profit while ensuring sustainability of all species.

     

Synthesis of high molecular weight and narrow molecular weight distribution poly(acrylonitrile) via RAFT polymerization

Well‐defined polyacrylonitrile (PAN) of high viscosity‐average molecular weight (M_η = 405,100 g/mol) was successfully synthesized using reversible addition‐fragmentation chain transfer polymerization. The polymerization exhibits controlled characters: molecular weights of the resultant PANs increasing approximately linearly with monomer conversion and keeping narrow molecular weight distributions. The addition of 0.01 equiv (relative to monomer acrylonitrile) of Lewis acid AlCl₃ in the polymerization system afforded the obtained PAN with an improved isotacticity (by 8%). In addition, the influence of molecular weights and molecular weight distributions of PANs on the morphology of the electrospun fibers was investigated. The results showed that, under the same conditions of electrospinning, average diameter (247–1094 nm) of fibers increased with molecular weights of PANs, and it was much easier to get “uniform” diameter fibers while using PANs with narrow molecular weight distributions as the precursor of electrospinning. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Well‐Defined High Molecular Weight Polystyrene with High Rates and High Livingness Synthesized via Two‐Stage RAFT Emulsion Polymerization

A highly living polymer with over 100 kg mol⁻¹ molecular weight is very difficult to achieve by controlled radical polymerization since the unavoidable side reactions of irreversible radical termination and radical chain transfer to monomer reaction become significant. It is reported that over 500 kg mol⁻¹ polystyrene with high livingness and low dispersity could be synthesized by a facile two‐stage reversible addition–fragmentation transfer emulsion polymerization. The monomer conversion reaches 90% within 10 h. High livingness of the product is ascribed to the extremely low initiator concentration and the chain transfer constant for monomer unexpectedly much lower than the well‐accepted values in the conventional radical polymerization. The two‐stage monomer feeding policy much decreases the dispersity of the product.

     

Systematic Tuning and Switching of Neutral and Ionic Phases in a Donor–Acceptor Chain Compound by Doping with Less‐Active Donors and by Pressure Application

The temperature‐induced stepwise neutral–ionic (N–I) phase transition in the covalently bonded donor–acceptor chain compound [Ru₂(2,3,5,6‐F₄PhCO₂)₄DMDCNQI] ? 2(p‐xylene) (2,3,5,6‐F₄PhCO₂^?=2,3,5,6‐tetrafluorobenzoate; DMDCNQI=2,5‐dimethyl‐N,N′‐dicyanoquinodiimine) was systematically tuned over a wide temperature range using two techniques: 1) A chemical technique based on doping with a less‐active donor unit [Ru₂^II,II(F₅PhCO₂)₄] (F₅PhCO₂^?=pentafluorobenzoate), thereby providing an isostructural doped series [{Ru₂^II,II(2,3,5,6‐F₄PhCO₂)₄}_1?x{Ru₂^II,II(F₅PhCO₂)₄}_xDMDCNQI] ? 2(p‐xylene), with x=0.06, 0.10, 0.21, and 0.24; and 2) a physical technique, which was the application of hydrostatic pressure to the doped compounds. The stepwise N–I transition observed in the original compound was systematically varied in terms of the viewpoints of both transition temperature and transition features (stepwise or monotonic) dependent on the amount of dopants x. Application of pressure efficiently tuned the N–I transitions, with the oxidation phases being dramatically modified by applying only weak pressure up to 4 kbar. Even in cases that led to N–I transitions in small domains of the chains at ambient pressure, the application of pressure caused an expansion of the domains that enabled N–I transitions, finally leading to a complete change in the oxidation state of the chains, from neutral to ionic, accompanied by a change from a paramagnetic state to a ferrimagnetically ordered state.     

Triallylstannyllithium-allyllithium as an initiator for the anionic reversible chain transfer polymerization of 1,3-butadiene

The anionic polymerization of 1,3-butadiene using a novel metalloidal anion initiator, triallylstannyllithium (TALi)-allyllithium (ALi), was studied. The TALi-ALi initiated anionic polymerization of 1,3-butadiene gave the star polymer along with the linear polybutadiene (PBD). The star polymer consisted of three PBD branches and a central tin atom. What is striking is a fact that the number-average molecular weights (M_n) and molecular weight distribution of three PBD branches and linear PBD were almost identical. A reversible chain transfer polymerization mechanism, which includes the equilibrium between tri(macroallyl)-stannyllithium and macroallylic anion, is proposed. © 1996 John Wiley & Sons, Inc.     

COMPUTER SIMULATION TECHNIQUES FOR A MOBILE SATELLITE COMMUNICATION CHANNEL

This paper gives a brief and systematic presentation of the computer simulation techniques of satellite communications, especially for a mobile satellite channel, based on a summarization of the author's exploration and experience in this area. It includes the equivalent complex baseband notation (ECBN) method, a very convenient mathematical form for software simulation; development of a multi-functional and expandable channel simulation system on a computer from L-band to Ka-band; channel impulse or frequency response estimation in real time by the technique burst-mode link analyser with least-squares algorithm (BMLA/LS), modelling and simulation of the channel fast fading due to multipath and shadowing; acquisition of the equivalent normalized binary signal-to-noise ratio (E_b/N₀) data at the channel input; and bit-error rate (BER) evaluation by the directly error-counting approach and the computational approach at the channel output in simulation.     

基于故事情景链语法的偶动画短片分析与建模

偶动画是动画领域一个重要的分支,与传统手绘动画同步出现,甚至更早。偶动画作品以其独特的拍摄方法和艺术魅力,为众多艺术家和观众所喜爱。偶动画影片设计周期长、工作量大、生产过程复杂、经济风险高,用传统手工工艺制作完成一部5 min的定格动画影片,通常需要数年。本文以丹麦知名动画导演克里多夫·皮拉丹的《柏树山上的风》及德国格里高利·祖坎导演的《龙焰火枪》为例,提出以故事情节(storyline(i)),?i∈1,2,…,n?与情景链（scenario?chain）语法有限集的形式语言表达式分解偶动画电影的故事元素,通过叙事空间（narrative?space）中镜头画面的组接逻辑,形成不同叙事结构,以分析定格动画电影的故事寓意（implied?meaning）,从故事计算的角度将其转化为标准化设计流程,为构建偶动画电影故事建模理论以及辅助智能计算提供思路,方法提高了偶动画电影的设计与制作效率,为多学科协同创作提供了新模式,使普通偶动画爱好者也能参与创作。     

单链和寡链等规聚苯乙烯聚集体的结晶行为

自1960年Hoffman等提出聚合物结晶成核理论以来,人们对聚合物结晶生长速率、片晶的侧向尺寸随过冷度的变化等现象成功地进行了理论描述．1997年,Hoffman等对聚合物结晶成核理论进行修正,将de Gennes的聚合物“蛇行”概念。引入表面成核理论,通过对单根分子链从过冷熔体“卷绕”到晶体前沿所需的时间进行估算,其结果远远低于Flory预言时间约3～5个数量级,据此,Hoff-man认为,在聚合物结晶过程中,分子链在强迫稳态下的“蛇行”运动有足够的时间解缠结和结晶。     

可列值随机变量序列的一个小偏差定理

本文得到了可列值随机变量序列的用不等式表示的强极限定理,即小偏差定理,包含了［１］的结果．［１］中研究的是相对于齐次Ｍａｒｋｏｖ 链的偏差,而本文允许非齐次的情形．