一类Kolmogorov系统的动力性质

用定性分析的方法对一类Kolmogorov系统(dx)/(dt)=x(a_0-a_11x a_2x~(n-1)-a3x~n a_4xy~m),(dy)/(dt)=y(b_1x~n-b_2),进行了研究．讨论了系统平衡点的性态,给出了系统无闭轨的充分条件以及存在唯一稳定极限环的条件．包含并推广了文献[3]的相关结果．     

一类具功能反应的食饵-捕食者两种群模型的定性分析

对具功能反应的食饵-捕食者两种群模型x=xg(x)-y( )(x),y=y(-d+e( )(x)).在g(x)=α-baα,( )(x)=cxα(a,b,c＞0,1/2≤α＜1)且α使函数f(x)=x1/a在(-∞,+∞)上为偶函数时进行了研究,讨论了该系统平衡点的稳定性态,系统无环的充分条件以及在正平衡点外围存在惟一稳定极限环的条件.     

一类稀疏效应下食饵—捕食系统极限环的存在唯一性

本文研究如下一类具有稀疏效应的食饵－捕食模型dx/dt=bx^2(k-x)-bxy,dy/dt=-cy (βx-γy）y。应用常微分方程定性理论,对该系统的平衡点进行分析,得到了该系统极限环存在唯一的充分条件,并给出了生态解释。     

一类具有免疫反应的HollingⅡ型发生率病毒动力学模型

建立并讨论了一类具有潜伏期、抗体免疫反应和CTL免疫反应的Holling II型发生率病毒动力学模型.定义了决定这个模型动力学性质的五个阈值,借助适当的Lyapunov函数得到:当R_(01)≤1时,无病平衡点全局渐近稳定,病毒被清除;当R_(01)1,R_(02)≤1,R_(03)≤1时,无免疫平衡点全局渐近稳定;当R_(02)1,R_(04)≤1时,CTL免疫主导平衡点全局渐近稳定;当R_(03)〉1,R_(04)≤1时,抗体免疫主导平衡点全局渐近稳定;当R_(04)1,R′_(04)1时,正平衡点全局渐近稳定.     

对崔-Lawson氏种群增长模型的探讨

本文讨论了崔启武和Lawson在《模》文中所采用的研究方法以及所得结论中存在的错误,因为μ_c=μ_mX_m/X′_m,当X′_m(?)X_m时,模型(dX)/(Xdt)=μ_c(1-X/X_m)/(1-X/X′_m)不是转化为logistic方程,而是趋于(dX)/(Xdt)=0,不能认为崔-Lawson氏模型是对指数方程和logistic方程的扩充。     

一阶线性差分微分方程振动的充要条件及应用

本文的目的是建立一阶线性差分微分方程 (dx)/(dt)=-sum from i=1 to n p_i(t)x(t-i_x(t)) (1)的所有解关于θ振动的等价条件,然后把所得结果应用于生物自身调节反馈滞后型方程(dN(t))/(dt)=rN(t)[1-(N(t-i))/p] (2)的更一般形式     

一类具稀疏效应生态系统的极限环

研究如下一类具稀疏效应的生态系统模型dx/dt=bx^2(κ-x)-bxy/1 hx,dy/dt=cy dxy/1 hx。应用微分方程定性理论,对该系统的平衡点进行了分析,给出了极限环存在唯一性及不存在的参数范围。     

墨西哥落羽杉的化学成分

从墨西哥落羽杉(Taxodium mucronatum)枝叶中首次分离得到10个化合物,通过MS与NMR等方法将它们分别鉴定为quercetin 3′-methoxy-3-O-β-D-galactopyranoside(1),quercetin 3′-methoxy-3-O-β-D-arabinopyrano-side(2),quercetin 3′-methoxy-3-O-α-L-arabinofuranoside(3),quercetin(4),avicularin(5),quercetin 3-O-β-D-ga-lactopyranoside(6),(7′S,8′R)-4,7′-epoxy-3,3′-dimethoxy-4,9,3′,4′,9′-lignanepentol-4′-O-β-D-glucopyranoside(7),(7′S,8′S)-3,3′-dimethoxy-9,4′,9′-trihydroxy-4,8′-oxyneolignan-7′-O-β-D-glucopyranside(8),methyl shikimate(9)和β-sitosterol(10)。     

芒果叶化学成分研究 II

为探讨芒果(Mangifera indica L.)的化学成分,从芒果叶的70%乙醇提取物中分离鉴定了13个化合物,经波谱分析,分别鉴定为:(–)-secoisolariciresinol-9′-O-D-glucopyranoside(1)、7S,8R-erythro-4,7,9-trihydroxy-3,3′-dimethoxy-8-O-4′-neolignan-9′-O-β-D-glucopyranoside(2)、7R,8R-threo-4,7,9-trihydroxy-3,3′-dimethoxy-8-O-4′-neolignan-9′-O-β-D-glucopyranoside(3)、(7R/S,8R)-7,8-dihydro-9′-hydroxyl-3′-methoxyl-8-hydroxymethyl-7-(4-hydroxy-3-methoxyphenyl)-1′-benzofuranpropanol 9′-O-β-D-glucopyranoside(4)、citrusin D(5)、丁香苷(6)、2,6-二甲氧基-4-羟基苯基-1-O-β-D-葡萄糖苷(7)、原儿茶酸(8)、没食子酸(9)、没食子酸甲酯(10)、没食子酸乙酯(11)、4,5-二羟基-3-甲氧基苯甲酸(12)、β-胡萝卜苷(13)。其中化合物1～7和12为首次从芒果属植物中分离得到。     

肋果茶中的萜类化学成分研究

从肋果茶(Sladenia celastrifolia)95％乙醇提取物的乙酸乙酯部位中分离得到15个萜类化合物,经波谱学方法分别鉴定为sladeniafolin A(1),grasshopper ketone (2),(3S,5R,6S,7E,9R) -7-megastigmene-3,6,9-triol (3),hedytriol (4),(3S,5R,6R,7E,9R) -3,5,6,9-tetrahydroxy-7-megastigmene(5),1′S*,4′R*-8-(4′-hydroxy-2′,6′,6′-trimethylcyclohex-2-enyl)-6-methyloct-3E,5E,7E-trien -2-one (6),2α,3α,19α,23-tetrahydroxyurs-12-en-28-oic acid (7),2α,3β,19α,23-tetrahydroxyurs-12-en-28-oic acid(8),pomolic acid(9),3-O-acetyl pomolic acid(10),ursaldehyde (11),camarolide (12),3β-hydroxyurs-11-en-13β(28) -olide (13),3β-hydroxy -11α,12α-epoxy-urs-13β,28-olide (14)和28-0-β-D-glucopyranosyl euscaphic acid (15).以上化合物均首次从该植物中分离得到,其中1为新的C9裂环烯醚萜.     

Multiallelic selection polymorphism

The existence and stability of an internal (i.e., completely polymorphic) equilibrium for viability selection at a single multiallelic locus is investigated. Generations are discrete and nonoverlapping; the population is panmictic, monoecious, and diploid. Various necessary and sufficient conditions for the existence of an internal equilibrium are established and applied to the loss of alleles. Some necessary conditions for the existence of an asymptotically stable internal equilibrium are also established. All these conditions are simpler and yield general biological conclusions more easily than the classical necessary and sufficient conditions.     

一类具常数接触率传染病模型的稳定性分析

本文研究了一类具常数接触率的传染病模型,用上下解方法和Liapnuov泛函讨论了地方病平衡点及无病平衡点的渐近行为,得到了各自全局稳定的充分条件.     

两个基因座位的遗传平衡原理

由于许多教科书中关于连锁平衡的介绍,多是引用结论或是推导不太严谨,使学生在学习群体遗传学时对理解连锁平衡的原理感到困难。本文从遗传平衡的基本条件出发,通过较严谨的数学推导,介绍了两个基因座的连锁平衡条件、平衡过程等原理,供教师和学生在群体遗传学教学中参考。Abstract: Because linkage equilibrium is introduced by directly quoting the conclusions or imprecise mathematical reasoning in most of textbooks, many students are puzzled with the problem of linkage equilibrium when they learn population genetics. Based on the radical conditions of genetic equilibrium, the principle of linkage equilibrium condition and process, for two gene loci is introduced by precise mathematical reasoning. The article may provide reference to teachers and students in the teaching and learning of population genetics.     

一个具有寄生虫病感染和恢复的捕食模型(英文)

本文假设感染的食饵有恢复率和对捕食者有收获,研究了一个对部分食饵和全部捕食者具有寄生虫病感染的捕食模型.用定性理论证明了边界和正平衡点的稳定性.结论表明恢复率和收获率对正平衡点的稳定性有影响.     

关于最大信息熵原理与群体遗传平衡一致性的探讨

汪小龙等建立了用最大信息熵原理推导一个基因座上群体遗传平衡的统一数学模型,并给出了模型的最大值解,此解正是Hardy-Weinberg平衡定律所给出的基因型频率。这说明当群体基因型信息熵最大时,群体基因型频率不再变化,达到平衡状态,从而证明了最大信息熵原理与Hardy-Weinberg平衡定律具有一致性,同时指出这一结论可以推广至有迁移、突变、选择、遗传漂变、近亲交配的群体以及多个基因座情形。概括地说就是：最大信息熵原理与群体遗传平衡具有一致性。但是,他们仅仅证明了最大信息熵原理与一个基因座上Hardy-Weinberg平衡定律具有一致性,本文在这个范围内将其推广至多个基因座,且每一个基因座均为复等位基因情形。至于最大信息熵原理是否与其它的群体遗传平衡具有一致性,他们的结论仅仅是猜想,并未严格推导。事实上,要想将这种一致性推广到迁移、突变、随机漂变和近亲交配等群体,则不见得正确。      

最大信息熵原理与群体遗传平衡

建立了用最大信息熵原理推导群体遗传平衡定律的统一数学模型,并给出了模型的统一解,此解正是Hardy-Weinberg定律所给出的平衡群体的基因型频率,说明当群体信息熵达到最大时,群体基因型频率不再变化,即达到“平衡”。这证明了最大熵分布就是Hardy-Weinberg平衡分布。Hardy-Weinberg平衡定律与最大信息熵原理的内在一致性说明,杂交和随机交配是一个不可逆过程,使群体基因型信息熵增大,无序性增,是选择和近亲交配使群体的信息熵降低,有序性增加,育种过程实际就是调节群体信息熵的过程。过程信息熵的含义是表示一个概率分布的不确定性,最大熵原理意味着在一定的约束条件,选择具有最大不确定性的分布,从而其分布是最为随机的。最大熵原理在信息,工程,天文,地理,图像处理,模式识别等自然科学和社会科学领域都有广泛的成功应用,本文从群体遗传学角度证明了这一原理具有普遍适用性。熵是描述系统状态的函数,而最大熵原理则表明了系统发展变化的趋势,系统的最终状态必然是熵增加至最大值的状态,对于任何系统都是如此。因此,群体遗传系统的平衡定律可以统一用最大熵原理进行判定和描述;任意群体的基因型信息熵在随机交配世代传递时有不断增加的趋势;在一定约束条件下基因型信息熵达到最大值时,就称之为达到遗传平衡。本文将信息论原理应用于群体遗传学研究,揭示了基因信息熵的生物学意义,并表明可以用信息学和控制论的原理和方法来研究群体遗传学问题。     

Ecology and evolution of symbiosis in metapopulations

We present a model for symbionts in plant host metapopulation. Symbionts are assumed not only to form a systemic infection throughout the host and pass into the host seeds, but also to reproduce and infect new plants by spores. Thus, we study a metapopulation of qualitatively identical patches coupled through seeds and spores dispersal. Symbionts that are only vertically inherited cannot persist in such a uniform environment if they lower the host's fitness. They have to be beneficial in order to coexist with the host if they are not perfectly transmitted to the seeds; but evolution selects for 100% fidelity of infection inheritance. In this model we want to see how mixed strategies (both vertical and horizontal infection) affect the coexistence of uninfected and infected plants at equilibrium; also, what would evolution do for the host, for the symbionts and for their association. We present a detailed classification of the possible equilibria with examples. The stability of the steady states is rigorously proved for the first time in a metapopulation set-up.     

Saturation recovery leads to multiple endemic equilibria and backward bifurcation

The number of patients need to be treated may exceed the carry capacity of local hospitals during the spreading of a severe infectious disease. We propose an epidemic model with saturation recovery from infective individuals to understand the effect of limited resources for treatment of infectives on the emergency disease control. It is shown that saturation recovery from infective individuals leads to vital dynamics, such as bistability and periodicity, when the basic reproduction number R₀ is less than unity. An interesting dynamical behavior of the model is a backward bifurcation which raises many new challenges to effective infection control.     

Orthobaric Densities from Simulations of the Liquid Vapour Interface

Molecular dynamics studies of the liquid vapour interface of a Lennard-Jones fluid performed on a CYBER 205 are reported for kT/ε = 0.70, 0.85, and 1.10. The main emphasis is on the orthobaric fluid densities: their dependence on different cut-off radii and long range corrections as well as their comparison with the coexisting densities from bulk fluid simulations. As previously reported bubble densities from bulk simulations differ by about 3 per cent at kT/ε = 1.10, phase equilibrium was redetermined there with the NpT + test particle method. Concerning the bubble densities from the interface simulations, increase of the cut-off radius and use of long range corrections shift them up rather close to the “bulk” values. The dew densities from the interface simulations which for the usual cut-off radius of 2.5 [sgrave] are mostly too high by a factor of 3 are decreased dramatically by accounting for the long range part of the potential. For a cut-off radius of 5 [sgrave] and long range corrections they agree with the “bulk” values within the accuracy of the latters which, however, is estimated to be only by about 20 per cent. Some characteristic density profiles are also shown.