一类Nicholson's blowflies模型的全局吸引性和振动性

本文研究了带有多个滞后变量的Ｎｉｃｈｏｌｓｏｎ’ｓ ｂｌｏｗｆｌｉｅｓ动态模型Ｎ（ｔ）＝－δＮ（ｔ）＋ΣＰｉＮ（ｔ-τｉ）ｅ-ａｉＮ（ｔ-τｉ）的全局吸引性和振动性,获得了该方程的正平衡解为全局稳定的充分条件以及其所有正解关于该平衡解振动的充分条件．     

一般Lyness方程的周期性与振动性

本文研究一般的 Ｌｙｎｅｓｓ方程 其中ａ,β,ｒ,δ　∈［０,∝）且α＋β＞０,γ＋δ＞０．获得了方程（*）解具周期性的充要条件和具严格振动性的充分条件,作为应用,我们得到了 Ｇ． Ｌａｄａｓ在［４］中提出的一个悬而未决问题的一些解．     

时滞Logistic型差分方程的振动及稳定性

本文获得了如下Xn 1=xnexp(a bxn-k^p-cxn-1^q）时滞Logistic型差分方程所有正解关于其平衡点振动的充要条件，同时还获得了一个正平衡点渐近稳定的充分条件，其中A∈（0，∞），B∈（-∞，O]，C∈（0，∞），K,l∈N。     

虎皮鹦鹉(Melopsittacus undulatfus)的振动敏感性研究

本文研究了虎皮鹦鹉对正弦振动的敏感性,旨在探索其腿部存在赫氏小体,和阐明其震前声行为反应与地面振动的关系提供依据。虎皮鹦鹉对５０－８０Ｈｚ的正弦振动不敏感,振动位移约２００－５０μｍ才可能激起声行为反应．但对１００－２５０Ｈｚ的正弦振动具有显著的敏感性,反应阈值约１０－２μｍ。对１３０－１７０Ｈｚ和２００－２５０Ｈｚ阈值反应,约７０％的潜伏期（ＬＰ）分别为ＬＰ＜３０５和ＬＰ＜１５ｓ。     

带有分段常数变量的单种群模型的全局稳定性和振动性（英文）

研究了带有分段常数变量的单种群连续模型的全局稳定性和振动性.通过计算将连续模型转化为对应的差分模型,首先研究发现当模型的参数和初值条件满足一定条件时,差分方程的任一正解是单调有界的,且正平衡态是全局渐近稳定的.其次以参数β_1作为分类标准,在两种情况下研究得到当参数r属于某一区间时,差分方程的解是振动的.最后数值模拟验证了理论分析的正确性.     

一阶非线性多时滞微分方程的振动性

考虑一阶非线性多时滞微分方程x′（t）=f（t,x（t-r₁）,x（t-r₂）,…,x（t-r_n））,利用其线性近似方程x′（t）=∑i=1nD_i+1f（t,0,…,0）x（t-r_i）的振动性,给出了方程解振动的一个充分条件,所得结果推广了文献[5]的相关结果.     

非自治时滞Logistic方程的振动性

本文研究了时滞Logistic方程和它的线性化方程的振动性。在一定的条件下,我们证明了这两个方程在振动性上等价．所得结果推广和改进了〔1〕的相应结果,同时也给〔2〕的作者提出的问题一个肯定的回答．     

中立型时滞逻辑斯谛方程的全局渐近稳定性和振动性

本文研究中立型时滞Logistic方程N（t）=N（t）)〔a－bN(t－τ)－cN(t－τ)－dN(t)〕,t≥t_0(E),其中τ,φ∈［0,∞],a,b,c,d∈R,得到方程（E）的正解关于正常数平衡点全局渐近稳定和振动的充分条件．本文所用方法与其他文献不同,所得结果发展了文献[1—4]的结果,其中定理4回答了文献[10]所提出的一个公开问题．     

时滞逻辑斯谛方程的稳定性和振动性

本文研究时滞逻辑斯谛方程其中得到方程（E）关于正常数平衡点为渐近稳定和振动的条件,也得到方程（E）存在正周期解的条件,所得结果发展和推广了文献［1］,［2］的结果。     

一个造血模型的全局吸引性和周期解相交

本文将Mackey和Glass提出的一个造血模型推广到具有周期系数和无穷时滞的情形．研究该模型的全局吸引性和周期解相交,并相应地得到两个充分条件.     

A multi-structured epidemic problem with direct and indirect transmission in heterogeneous environments

In this work, we analyse a deterministic epidemic mathematical model motivated by the propagation of a hantavirus (Puumala hantavirus) within a bank vole population (Clethrionomys glareolus). The host population is split into juvenile and adult individuals. A heterogeneous spatial chronological age and infection age structure is considered, and also indirect transmission via the environment. Maturation rates for juvenile individuals are adult density-dependent. For the reaction-diffusion systems with age structures derived, we give global existence, uniqueness and global boundedness results. A model with transmission to humans is also studied here.     

A multi-structured epidemic problem with direct and indirect transmission in heterogeneous environments

In this work, we analyse a deterministic epidemic mathematical model motivated by the propagation of a hantavirus (Puumala hantavirus) within a bank vole population (Clethrionomys glareolus). The host population is split into juvenile and adult individuals. A heterogeneous spatial chronological age and infection age structure is considered, and also indirect transmission via the environment. Maturation rates for juvenile individuals are adult density-dependent. For the reaction–diffusion systems with age structures derived, we give global existence, uniqueness and global boundedness results. A model with transmission to humans is also studied here.     

方向数据密度函数的最近邻估计

设Ｘ为取值于ｄ＋１维空间中单位球面上的单位随机向量,具有概率密度函数ｆ（ｘ）本文讨论密度函数ｆ（ｘ）的估计问题,给出了基于方向数据的最近邻估计,并建立这种最近邻估计的逐点强,弱相合性,一致强相合性及渐近正态性,得到了与欧氏情形（Ｒ＾ｄ）基本一致的结果。     

Interval Estimation of Simple Difference under Independent Negative Binomial Sampling

When the sample size is not large or when the underlying disease is rare, to assure collection of an appropriate number of cases and to control the relative error of estimation, one may employ inverse sampling, in which one continues sampling subjects until one obtains exactly the desired number of cases. This paper focuses discussion on interval estimation of the simple difference between two proportions under independent inverse sampling. This paper develops three asymptotic interval estimators on the basis of the maximum likelihood estimator (MLE), the uniformly minimum variance unbiased estimator (UMVUE), and the asymptotic likelihood ratio test (ALRT). To compare the performance of these three estimators, this paper calculates the coverage probability and the expected length of the resulting confidence intervals on the basis of the exact distribution. This paper finds that when the underlying proportions of cases in both two comparison populations are small or moderate (≤0.20), all three asymptotic interval estimators developed here perform reasonably well even for the pre-determined number of cases as small as 5. When the pre-determined number of cases is moderate or large (≥50), all three estimators are essentially equivalent in all the situations considered here. Because application of the two interval estimators derived from the MLE and the UMVUE does not involve any numerical iterative procedure needed in the ALRT, for simplicity we may use these two estimators without losing efficiency.     

随机时污染源影响的单种群微生物的灭绝分析

建立了污染物排放对微生物种群生灭影响的模型,研究了随机时刻灭绝概率Ψ(x,T)的一致渐近性,并最终得到一致渐近公式Ψ(x,T)～Eλ(T)(?).     

关于《一类具时滞的神经网络模型的收敛性》的注记

本文研究了一类具有时滞的神经网络模型     

How and why are uniformly polarization-sensitive retinae subject to polarization-related artefacts? Correction of some errors in the theory of polarization-induced false colours

If the photoreceptors of a colour vision system are polarization sensitive, the system detects polarization-induced false colours. Based on the functional similarities between polarization vision and colour vision, earlier it was believed that a uniformly polarization-sensitive (insect) retina (UPSR)-in which receptors of all spectral types have the same polarization sensitivity ratio and microvilli direction-cannot detect polarization-induced false colours. Here we show that, contrary to this belief, a colour vision based on a UPSR is subject to polarization-related artefacts, because both the degree and the angle of polarization of light reflected from natural surfaces depend on wavelength. Our second goal is to correct certain errors in the theory of polarizational false colours. The quantitative estimation of the influence of polarization sensitivity on colour vision was recently motivated by the suggestion that certain Papilio butterflies detect such false colours. The theoretical basis of this subject is to calculate the colour loci in the colour space of a visual system from the quantum catches of polarization-sensitive receptors of different spectral types. Horváth et al. (J. Exp. Biol. 205 (2002) 3281) gave the first exact mathematical and receptor-physiological derivation of formulae for these calculations. Here we prove that the two formulae given earlier by others are inappropriate or erroneous. This, however, does not influence the validity of the experimental data and the principal conclusions drawn about the colour vision and polarization sensitivity in Papilio butterflies.     

UMP(U)‐Tests for a Binomial Parameter: A Paradox

We consider uniformly most powerful (UMP) as well as uniformly most powerful unbiased (UMPU) tests and their non‐randomized versions for certain hypotheses concerning a binomial parameter. It will be shown that the power function of a UMP(U)‐test based on sample size n can coincide on the entire parameter space with the power function of the corresponding test based on sample size n + 1. A complete characterization of this paradox will be derived. Apart some exceptional cases for two‐sided tests and equivalence tests the paradox appears if and only if a test based on sample size n is non‐randomized.     

Point Estimation on Relative Risk under Inverse Sampling

When the underlying disease is rare, to control the coefficient of variation for the sample proportion of cases, we may wish to apply inverse sampling. In this paper, we derive the uniformly minimum variance unbiased estimator (UMVUE) of relative risk and its variance in closed form under inverse sampling. On the basis of a Monte Carlo simulation, we demonstrate that using the UMVUE of relative risk can substantially reduce the mean-squared-error of using the maximum likelihood estimator, especially when the number of index cases in both comparison samples is small. For a given fixed total cost, we include a program that can be used to find the optimal allocation for the number of index cases to minimize the variance of the UMVUE as well.     

The centromere1 (CEN1) region of Arabidopsis thaliana: architecture and functional impact of chromatin

We have analysed the centromere 1 (CEN1) of Arabidopsis thaliana by integration of genetic, sequence and fluorescence in situ hybridisation (FISH) data. CEN1 is considered to include the centromeric core and the flanking left and right pericentromeric regions, which are distinct parts by structural and/or functional properties. CEN1 pericentromeres are composed of different dispersed repetitive elements, sometimes interrupted by functional genes. In contrast the CEN1 core is more uniformly structured harbouring only two different repeats. The presented analysis reveals aspects concerning distribution and effects of the uniformly shaped heterochromatin, which covers all CEN1 regions. A lethal mutation tightly linked to CEN1 enabled us to measure recombination frequencies within the heterochromatin in detail. In the left pericentromere, the change from eu- to heterochromatin is accompanied by a gradual change in sequence composition but by an extreme change in recombination frequency (from normal to 53-fold decrease) which takes place within a small region spanning 15 kb. Generally, heterochromatin is known to suppress recombination. However, the same analysis reveals that left and right pericentromere, though similar in sequence composition, differ markedly in suppression (53-fold versus 10-fold). The centromeric core exhibits at least 200-fold if not complete suppression. We discuss whether differences in (fine) composition reflect quantitative and qualitative differences in binding sites for heterochromatin proteins and in turn render different functional properties. Based on the presented data we estimate the sizes of Arabidopsis centromeres. These are typical for regional centromeres of higher eukaryotes and range from 4.4 Mb (CEN1) to 3.55 Mb (CEN4).