具周期脉冲的周期差分系统的全局性态

本文建立了具有常数脉冲和周期脉冲的周期差分系统,得到了常数脉冲系统全局稳定周期解存在的充分条件,并证明了周期脉冲的周期系统的周期解是全局吸引的。     

全退化型小参数问题周期解的存在性

运用拓扑度方法给出高维非自治系统全爱化型小参数问题周期解存在性的一些简明的判别方法,即在非线性项满足强制性条件时,无需计算便能判别周期解的存在。     

多滞量捕食模型的正周期解

利用重合度理论中的延拓定理讨论了多滞量捕食模型的正周期解的存在性,得到了保证周期解存在的充分条件,推广了已知的相关结果。     

Bony Healing of Unstable Thoracolumbar Burst Fractures in the Elderly Using Percutaneously Applied Titanium Mesh Cages and a Transpedicular Fixation System with Expandable Screws

IntroductionThere is a high incidence of vertebral burst fractures following low velocity trauma in the elderly. Treatment of unstable vertebral burst fractures using the same principles like in stable vertebral burst fractures may show less favourable results in terms of fracture reduction, maintenance of reduction and cement leakage. In order to address these shortcomings this study introduces cementless fixation of unstable vertebral burst fractures using internal fixators and expandable intravertebral titanium mesh cages in a one-stage procedure via minimum-invasive techniques.ResultsStabilization of the collapsed vertebral body was achieved in all 16 cases without any intraoperative complication. Surgical time averaged 102±6.6 minutes (71–194). The postoperative kyphotic angle (KA) and Cobb angle revealed significant improvements (KA 13.7° to 7.4°, p<0.001; Cobb 9.6° to 6.0°, p<0.002) with partial loss of reduction at final follow-up (KA 8.3°, Cobb 8.7°). VAS (Visual Analogue Scale) improved from 7.6 to 2.6 (p<0.001). Adjacent fractures were not observed. One minor (malposition of pedicle screw) complication was encountered.ConclusionCementless fixation of osteoporotic burst fractures revealed substantial pain relief, adequate maintenance of reduction and a low complication rate. Bony healing after unstable osteoporotic burst fractures is possible.

Trial Registration

www.germanctr.de DRKS00005657     

多种群阶段结构竞争系统的周期解与概周期解

研究具有阶段结构的多种群竞争系统,得到该系统一致持久,正周期解全局渐近稳定及概周期解的存在性与一致渐近稳定性的充分条件。     

周期中立型时滞捕食者-食饵系统正周期解的全局存在性

利用重合度理论建立了一类周期中立型时滞捕食者-食饵系统正周期解的全局存在性的充分条件．     

一类中心型半连续动力系统的周期解

讨论了一类中心型半连续动力系统的阶1周期解和阶2周期解的存在性、个数及其稳定性,给出该中心型系统存在唯一、两个、无穷多个阶1周期解和阶2周期解的条件,并给出了相应理论结果的数值模拟.     

具有阶段结构的两种群竞争系统的周期解

本文研究了具有阶段结构的两种群竞争系统的渐近行为.我们得到了系统持续生存的条件.由Brouwer不动点定理和李亚普诺夫函数,我们证明相应的周期系统在满足一定的条件下,存在一个唯一的全局渐近稳定的正周期解.最后我们把没有阶段结构的系统与有阶段结构的系统进行了比较.     

一类周期种群系统的稳定性分析及最优控制问题

本文讨论了一类线性时变周期种群系统的稳定性和最优控制问题.利用Lyapunov函数.对系统的稳定性进行了分析.给出了系统稳定的充分条件.并且利用Banach空间理论,证明了最优收获控制的存在性和唯一性.并且给出了最优控制所满足的必要性条件.     

一类捕食者-食铒系统正周期解的存在性

利用重合度理论中的延拓定理研究了一类具有HollingⅡ型功能性反应的捕食者-食铒系统非平凡周期解的存在性,其中食饵种群服从Smith增长,捕食者种群具有密度制约效应。得到了存在正周期解的充分性判据,推广并改进了已知的相关结果。     

带存放率的周期竞争扩散系统的稳定共存

应用上、下解方法和抛物型方程的极值原理,研究了带存放率的周期竞争系统ut-D1Δu=u（α-bu-cv）＋h,vt-D2Δv=v）d-eu-fv）＋k 在齐次Neumann边界条件下解的渐近性态,得到了该系统的全局渐近性．     

Refractometric Sensing with Silicon Quantum Dots Coupled to a Microsphere

Quantum dots (QDs) coupled to an optical microsphere can be used as fluorescent refractometric sensors. The QD emission couples to the whispering gallery resonances of the microsphere, leading to sharp, periodic maxima in the fluorescence spectrum. Silicon QDs (Si-QDs) are especially attractive fluorophores because of their low toxicity and ease of handling. In this work, a thin layer of Si-QDs was coated onto the surface of a microsphere made by melting the end of a tapered optical fiber. Refractometric sensing experiments were conducted using two methods. First, the sphere was immersed directly into a cuvette containing methanol–water mixtures. Second, the sphere was inserted into a silica capillary and the solutions were pumped through the capillary channel. The latter method enables microfluidic operation, which is otherwise difficult to achieve with a microsphere. In both geometries, high-visibility (V?=?0.83) modes were observed with Q factors up to 1,700. Using standard signal processing methods applied to the whispering gallery mode (WGM) spectrum, sensorgram-type measurements were conducted using single Si-QD-coated microspheres. The WGM resonances shifted as a function of the refractive index of the analyte solution, giving sensitivities ranging from ~30 to 100 nm/refractive index unit (RIU) for different microspheres and a detection limit on the order of 10^?4 RIU.     

Gause比率依赖型捕食者-食饵系统的周期解

考虑一类Gause比率依赖型捕食者-食饵系统,利用重合度理论中的延拓定理, 研究了全局周期解的存在性,得到保证周期解存在的充分条件．     

TGF-Mediated Dynamics in a System of Many Coupled Nephrons

This paper presents a mathematical model of a system of many coupled nephrons branching from a common cortical radial artery, and accompanying analysis of that system. This modeling effort is a first step in understanding how coupling magnifies the tendency of nephrons to oscillate owing to tubuloglomerular feedback. Central to the present work is the single nephron integral model (as in Pitman et al., The IMA Volumes in Mathematics and Its Applications, vol. 129, pp. 345–364, 2002 and in Zaritski, Ph.D. Dissertation, 1999) which is a simplification of the single nephron PDE model of Layton et al. (Am. J. Physiol. 261, F904–F919, 1991). A second principal idea used in the present model is a coupling of model nephrons, generalizing the work of Pitman et al. (Bull. Math. Biol. 66, 1463–1492, 2004) who proposed a model of two coupled nephrons. In this study, we couple nephrons through a nearest neighbor interaction. Speaking generally, our results suggest that a series of similar nephrons coupled to their nearest neighbors are more prone to be found in an oscillatory mode, relative to a single nephron with the same properties. More specifically, we show analytically that, for N coupled identical nephrons, the region supporting oscillatory solutions in the time delay–gain parameter plane increases with N. Numerical simulations suggest that, if N nephrons have gains and time delays that do not differ by much, the system is, again, more prone to oscillate, relative to a single nephron, and the oscillations tend to be approximately synchronous and in-phase. We examine the effect of parameters on bifurcation. We also examine alternative models of coupling; this analysis allows us to conclude that the increased propensity of coupled nephrons to oscillate is a robust finding, true for several models of nephron interaction.     

Periodic Solutions of N-Species Competition System with Time Delays

1IntroductionWeconsiderherethefollowingpeiodicn-speCiescompetitionSyStemwithtimedelaystogetherwithinitialvalueconditionswherer,(i=1,..',n)arepeitivecontinuousdeperiedicfUnctionsandail,ry(i,j=1,...f,n)arenormeqativeconStants.Whenr.(i=1,..',n)arepeitiveconStants,(1.1)isknoWnasan"speCies~a-VolterracompetitionsystemintheliteratureonmathematicaleCOIOgyandhashostudiedextensivelybySevelal.thorstl-j.ShibataandAntot')haveshownthetimedelaysinatwcrspeCies~a-Volterra~itionsystemcanleadto"~ic~ior".O…     

具有周期传染率的SIR传染病模型的周期解

考虑了具有周期传染率的SIR流行病模型,定义了基本再生数^-R0=β／（μ＋γ）,分析了该模型的动力学性态,证明了当^-R0〈1时无病平衡点是全局稳定的;^-R0〉1时,无病平衡点是不稳定的,模型至少存在一个周期解。对小振幅的周期传染率模型,给出了模型周期解的近似表达式,证明了该周期解的稳定性,最后做了数值模拟,结果显示周期解可能是全局稳定的。