Banach空间二阶非线性微分-积分方程两点边值问题整体解的存在性

利用一个新的比较结果和Ｍｏｎｃｈ不动点定理,研究了Ｂａｎａｃｈ空间二阶非线性微分－积分方程两点边值问题整体解的存在性     

二阶Volterra型积分微分差分方程非线性边值问题的存在性与唯一性

本文利用微分不等式技巧研究了某一类Volterra型二阶积分微分差分方程非线性边值问题,在上下解存在的条件下,得到了解的存在性和唯一性定理.结果表明:这种技巧为其它边值问题的研究提出了崭新的思路.     

Banach空间二阶非线性微分—积分方程两点边值问题整体解的存在性

利用一个新的比较结果和Moench不动点定理，研究了Banach空间二阶非线性微分－积分方程两点边值问题整体解的存在性。     

一个环境依赖型二维纯竹林发展系统的古典解

对普通的森林纯林发展系统,已经有不少研究结果.对竹林系统一维问题有人进行过描述,二维问题还未见到有人研究.竹林是一类特殊的森林,它通过自主发笋进行更新.本文提出了一个环境依赖型二维竹林纯林发展系统模型,并针对这类系统边界状态有些混沌,不满足通常的三类条件之一的特点,采用在"竹龄-直径"存在区域内引进一类特殊的曲线族,避开了提边界条件问题.再利用适当地选择林木直径尺度量纲的技巧,提出了一个适定的二维纯林发展系统模型,最后综合拉特征线、先验估计、构造初始状态积分方程、迭代等技巧证明了这个系统整体古典解的存在唯一性.     

带超前项的二阶脉冲中立型积分微分方程解的存在性(英文)

应用不动点定理,研究了带超前项的二阶脉冲中立型积分微分方程解的存在性,建立了两个存在准则,并举例说明了准则的有效性.     

一类病菌模型初边值问题的动力性态

本文研究一个描述病菌传播的反应的散方程组,考虑它的初边值问题。用积分估计方法证明了整体吸引子的存在性。     

森林发展系统强解的存在唯一性及稳定性分析

对森林发展系统的动态数学模型,运用泛函分析和积分方程的理论,证明了系统强解的存在性和唯一性,并对系统的稳定性进行了讨论．     

具有捕食者饱和与竞争捕食模型解的存在性与唯一性（英文）

在本文中,我们考虑一类在Dirichlet边界条件下具有饱和与竞争项捕食模型的正解存在性.首先利用标准的不动点指数理论建立了正解的存在性和存在的充分必要条件.特别地,通过数学分析与积分不等式的技巧,得到了正解的唯一性。     

一个具有年龄结构的单种群离散反应扩散模型的波前解

利用上下解方法研究了一个具有年龄结构的单种群离散反应扩散模型波前解的存在性,并证明了存在具有临界波速的波前解.     

一类BAM随机神经网络的稳定性

对于一类双向联想记忆（BAM）随机神经网络。研究其全局稳定性和指数稳定性,利用Schwarz积分不等式和Ito积分性质,给出其稳定性判定的充分性条件．     

对分子置换法中积分半径选取方法的探讨

通过对晶胞中帕特逊向量的统计分布的研究,从理论上阐述了根据模型结构单元的线度确定旋转函数的积分半径这种作法的合理性,并且指出了估算积分半径取值范围的具体方法,以及自身旋转函数与交叉旋转函数的积分半径取值范围的区别。经过我们将此方法应用于酚胰岛素Ｂ链羰端六肽胰岛素的旋转函数求解,计算结果证实了这种积分半径的估算方法的可靠性。     

非线性年龄结构种群发展方程解的存在唯一性

本文讨论非线性年龄结构种群动力系统,证明了方程的解的存在唯一性．     

On the uniqueness of the positive solution of an integral equation which appears in epidemiological models

 In this paper, we show that the positive solution of a non-linear integral equation which appears in classical SIR epidemiological models is unique. The demonstration of this fact is necessary to justify the correctness of any approximate or numerical solution. The SIR epidemiological model is used only for simplicity. In fact, the methods used can be easily extended to prove the existence and uniqueness of the more involved integral equations that appear when more biological realities are considered. Thus the inclusion of a latent class (SLIR models) and models incorporating variability in the infectiousness with duration of the infection and spatial distribution lead to integral equations to which the results derived in this paper apply immediately. Received: 7 May 1999     

EXISTENCE OF MULTIPLE PERIODIC SOLUTIONS TO A NONLINEAR INTEGRAL EQUATION FROM THE THEORY OF EPIDEMICS

Thenonlinearintegralequation(1.1)isageneralizedmodelforthespreadofdiseaseswithseasonaldependence.Inthispaper,wehaveprovedtheexistenceofatleastthreenontrivialnonnegativeperiodicsolutionstothisequation.     

Zur numerischen Auswertung von Schnittflächenverteilungen. IV

In this paper a general integral equation is given for the connection between the size distribution of similar formed objects and the size distribution of their sections with zero thickness. The spherical problem is enclosed in this solution. The integral kernels for six simple polyhedrons are numerically given. The integral geometry is the theoretical basis for this paper, and the computer simulation of the section process is the practical method for the numerical calculation of integral kernels.     

Global asymptotic stability of density dependent integral population projection models

Many stage-structured density dependent populations with a continuum of stages can be naturally modeled using nonlinear integral projection models. In this paper, we study a trichotomy of global stability result for a class of density dependent systems which include a Platte thistle model. Specifically, we identify those systems parameters for which zero is globally asymptotically stable, parameters for which there is a positive asymptotically stable equilibrium, and parameters for which there is no asymptotically stable equilibrium.     

Mathematical analysis of an integral equation arising from population dynamics

In this paper, we establish the existence of travelling wave solution to an intrinsically non-linear differential–integral equation formed as a result of mathematical modelling of the evolution of an asexual population in a changing environment. This equation is first converted to a non-linear integral equation. The discretization and manipulation of the corresponding eigenvalue problem allows us to use the theory of positive matrices to get some very useful estimates and then to confirm the existence of solution. We also exhibit numerical simulation results and explain the biological meaning of the results.     

Integral dose: Comparison between four techniques for prostate radiotherapy

Aim

Comparisons of integral dose delivered to the treatment planning volume and to the whole patient body during stereotactic, helical and intensity modulated radiotherapy of prostate.

Background

Multifield techniques produce large volumes of low dose inside the patient body. Delivered dose could be the result of the cytotoxic injuries of the cells even away from the treatment field. We calculated the total dose absorbed in the patient body for four radiotherapy techniques to investigate whether some methods have a potential to reduce the exposure to the patient.

Materials and methods

We analyzed CyberKnife plans for 10 patients with localized prostate cancer. Five alternative plans for each patient were calculated with the VMAT, IMRT and TomoTherapy techniques. Alternative dose distributions were calculated to achieve the same coverage for PTV. Integral Dose formula was used to calculate the total dose delivered to the PTV and whole patient body.

Results

Analysis showed that the same amount of dose was deposited to the treated volume despite different methods of treatment delivery. The mean values of total dose delivered to the whole patient body differed significantly for each treatment technique. The highest integral dose in the patient''s body was at the TomoTherapy and CyberKnife treatment session. VMAT was characterized by the lowest integral dose deposited in the patient body.

Conclusions

The highest total dose absorbed in normal tissue was observed with the use of a robotic radiosurgery system and TomoTherapy. These results demonstrate that the exposure of healthy tissue is a dosimetric factor which differentiates the dose delivery methods.     

Poisson convergence on continuous time Branching Random Walks and multistage carcinogenesis

A theorem for Poisson convergence on realizations of twodimensional Branching Random Walks with an underlying continuous time Markov Branching Process is proved. This result can be used to gain an approximation for the number of cells having sustained a certain deficiency after a long time in multistage carcinogenesis.     

Convergent exaptation and adaptation in solitary island lizards

Independent evolutionary lineages often display similar characteristics in comparable environments. Three kinds of historical hypotheses could explain this convergence. The first is adaptive and evolutionary: nonrandom patterns may result from analogous evolutionary responses to shared conditions. The second explanation is exaptive and ecological: species may be filtered by their suitability for a particular type of environment. The third potential explanation is a null hypothesis of random colonization from a historically nonrandom source pool. Here we demonstrate that both exaptation and adaptation have produced convergent similarity in different size-related characters of solitary island lizards. Large sexual size dimorphism results from adaptive response to solitary existence; uniform, intermediate size results from ecological filtering of potential colonizers. These results demonstrate the existence of deterministic exaptive convergence and suggest that convergent phenomena may require historical explanations that are ecological as well as evolutionary.