Pure Multiplicative Noises Induced Population Extinction in an Anti-tumor Model under Immune Surveillance

The dynamical characters of a theoretical anti-tumor model under immune surveillance subjected to a pure multiplicative noise are investigated. The effects of pure multiplicative noise on the stationary probability distribution （SPD） and the mean first passage time （MFPT） are analysed based on the approximate Fokker-Planck equation of the system in detail. For the anti-tumor model, with the multiplieative noise intensity D increasing, the tumor population move towards to extinction and the extinction rate can be enhanced. Numerical simulations are carried out to check the approximate theoretical results. Reasonably good agreement is obtained.     

Periodic Solution of a Nonautonomous Diffusive Food Chain System of Three Species with Time Delays

Abstract By using the continuation theorem of coincidence degree theory,the existence of a positive periodicsolution for a nonautonomous diffusive food chain system of three species. dx_1(t)/dt=x_1(t)[r_1(t)-a_(11)(t)x_1(t)-a_(12)(t)x_2(t)]+D_1(t)[y(t)-x_1(t)], dx_2(t)/dt=x_2(t)[-r_2(t)+a_(21)(t)x_1(t-r_1)-a_(22)(t)x_2(t)-a_(23)(t)x_3(t)], dx_3(t)/dt=x_3(t)[-r_3(t)+a_(32)(t)x_2(t-r_2)-a_(33)(t)x_3(t)], dy(t)/dt=y(t)[r_4(t)-a_(44)(t)y(t)]+D_2(t)[x_1(t)-y(t)]+D_2(t)[x_1(t)-y(t)],is established,where,r_i(t),a_(ii)(t)(i=1,2,3,4),D_i(t)(i=1,2),a_(12)(t),a_(21)(t),a_(23)(t)and a_(32)(t) are all positiveperiodic continuous functions with period w>0,T_i(i=1,2)are positive constants.     

居高声自远,非是藉秋风——诗句中的声学原理

这首脍炙人口的五绝名篇《蝉》，是唐代诗人虞世南（558～638）所作．当您反复吟诵这美丽的诗句时，蝉那饮清露而生，栖高桐而歌的高洁清远的意境就仿佛重现在您的眼前，真是美不胜收．可是，您可曾想到，在这洗练的诗句中还凝聚着诗人对声学现象的敏锐洞察力!     

一类具年龄结构n维食物链模型的最优收获控制

研究一类具有年龄结构n维食物链模型的最优收获控制.利用不动点定理,证明了系统非负解的存在性和唯一性.由Mazur定理,证明了最优控制策略的存在性,同时由法锥概念的特征刻画,还得到了控制问题最优解存在的必要条件.     

权马尔可夫链在人口死亡率时序误差预测中的应用

针对人口死亡率时间序列既有摆动又有一定趋势的特点,首先对人口死亡率的时间趋势项进行拟合,然后对人口死亡率的误差序列进行分析,提出了以规范化的自相关系数为权,用加权的马尔可夫链来预测人口死亡率状况。并通过实例对该方法进行了具体的应用。     

具有空间扩散和年龄结构竞争模型的正平衡态

讨论了具有空间扩散和年龄结构的竞争模型在Neumann边界条件下正常数解的稳定性,并用两种不同的方法给出了非常数正解不存在的条件,即在此条件下不会发生斑图现象.     

SYNTHESIS AND CHARACTERIZATION OF POLY(PHTHALAZINONE ETHER PHOSPHINE OXIDE)S BY N―C COUPLING REACTION

<正>Based on several unsymmetrical,twist,noncoplanar phthalazinone-containing monomers 2a-2e and an active bis(4-fluorophenyl)phenyl phosphine oxide(BFPPO) monomer,a series of novel poly(phthalazinone ether phosphine oxide)s (PPEPO) was synthesized by anhydrous K_2CO_3 mediated N—C coupling reaction in DMAc.The polymers exhibited good thermal properties with T_gs ranging from 267℃to 306℃and 5%weight loss temperatures in nitrogen higher than 430℃, together with high char yield upon prolonged heating at 800℃(35%—56%).Moreover,the polymers were readily soluble in common organic solvents,such as N-methyl-2-pyrrolidone,chloroform and m-cresol.These polymers had inherent viscosities in the range of 0.45-0.72 dL/g and could be cast into flexible and colorless films by spin coating or casting approach.     

揭秘“153”的数学神奇之旅

在古希腊，没有社会保险号码，没有电话号码，没有人口调查统计数字，没有选举后的投票数字，没有统计数据．当时，世界还没有数字化，但数字在希腊知识分子的头脑中至关重要．毕达哥拉斯的“万物皆数”的论断就证明了这一点．     

一类具年龄结构种群动力系统的最优控制

研究一类具年龄结构种群线性动力系统的最优控制问题 .由Mazur’s定理 ,我们证明了最优控制问题 (OH)最优解的存在性 ,同时借助于法锥概念 ,我们还得到了最优控制问题 (OH)最优解存在的必要条件     

黄冈市人口增长模型的研究

分析了1978年以来黄冈市人口发展的现状,选择黄冈市1978~2004年的总人口统计数据来建立马尔萨斯人口模型和L og istic人口模型,运用2005~2006年的总人口数据来验证模型,并对黄冈市未来8年的总人口数进行了预测.