二阶抽象微分方程的多项式有界解的极大子空间

受文de Laubenfels[1](1997,Isreal Journal ofM athem atics,98:189~207)的启发,引进空间W(A,k)和H(A,ω),它们分别是使得该二阶抽象Cauchy问题有在[0,∞)一致连续且O((1 t)k)有界和O(eωt)有界的弱解的x∈X的全体.讨论Banach空间X上二阶抽象Cauchy问题的具有多项式有界解或指数有界解的极大子空间问题.由W ang and W ang[2](1996,Functional Analysis in Ch ina.K luwer,333~350)知,该Cauchy问题适定的充要条件是该Cauchy问题中的X上闭算子A生成一个强连续Cosine算子函数.处理该Cauchy问题不适定的情况.证明或指出了如下结论:.W(A,k)和H(A,ω)均为Banach空间,且W(A,k)和H(A,ω)均连续嵌入X;.部分算子A|W(A,k)生成一个多项式有界的余弦算子函数{C(t)}t∈R ,使‖C(t)‖W(A,k)≤2(1 t)k;.部分算子A|H(A,ω)生成一个指数有界的余弦算子函数{C(t)}t∈R ,使‖C(t)‖H(A,ω)≤2eωt;.W(A,k)和H(A,ω)分别是极大的.即若有Banach空间Y连续嵌入X,且使A|Y生成一个O((1 t)k)有界的余弦算子函数,那么Y连续嵌入W(A,k);而若使A|Y生成一个O(eωt)有界的余弦算子函数,那么Y连续嵌入H(A,ω).     

有限集S上变换的标准分解及其应用

通过研究集合S={ 1,2 ,… ,n}上变换σ的动力系统性质 :(1)得到了σ的标准分解式 :σ =(q11q12 …q1t1 ) ∧ (q2 1q2 2 …q2t2 ) ∧ … (qm1qm2 …qmtm) ∧ (j11j12 …j1n1 ) (j2 1j2 2 …j2n2 )… (jk1jk2 …jknk) ;(2 )证明了 :｜H n ｜ =∑ni =0Cin(n-i) i(n-i) ! ,其中H n ={σ∈Hn｜σk+ 1=σ ,k =1,2 ,3,… } .     

Heisenberg型的群上的Radon变换

令H={(z,t):z∈Cn,t∈Rm}表示Heisenberg型群,对于(z,t),(z',t')∈H,群乘法法则为(z,t)°(z',t')=(z+z',t+t'+1/2zJz't),其中zJ z't=(z U(1)z't,z U(2)z't,…,z U(m)z't),z't表示z'的转置,U(j)(j=1,2,…,m)是2n×2n反对称实正交矩阵,文章给出了H上的Radon变换,并通过Fourier变换得到了与映射J相关的逆公式.     

类Gauss映射

设E_i~n是符号为(q,n-q)的伪欧氏空间,M_p~m是E_q~n的非退化子流形.如果M_p~m不是E_q~n的极小子流形,则定义一个映射H∶M_p~m→Q=S_q~(n-1)(1)或H_q~n=I(1)(伪黎曼球面与伪双曲空间),使得H(x)=h(x)/||h(x)||,x∈M_p~m,h(r)表示M_p~m在点x的平均曲率向量.称H为类Gauss映射.当M_p~m是E_q~n的超曲面时,H就是经典的Gauss映射.绘出了一个类Gauss映射是位似的充要条件.在一定条件下,得到了类Gauss映射的极小性并讨论了具有全测地类Gauss像的子流形.     

由Levy过程驱动的随机偏微分方程解的逼近

K和H为可分的希尔伯特空间,Z是一个巴拿赫空间.采用逐步逼近方法研究如下由Levy过程驱动的随机偏微分方程dx(t)=[Ax(t)+f(t,x(t))]dt+g((t,x(t))d W(t)+z乙h(t,x(t-),z)譙(dt,dz)解的逼近,并证明其局部温和解的存在性和唯一性.其中A∶D(A)奂H→H是H上的压缩半群(S(t))t≥0的无穷小生成元,f∶[0,T]×H→H,g∶[0,T]×H→L2(K,H),h∶R+×Ω×Z→H,满足局部非利普希茨条件.     

一类变保费双Cox风险模型的鞅分析

讨论一类带有投资收益和再保险的变保费双Cox风险模型:U(t)=u+V1(t)=u1+u2+∑〖DD(〗M1(t)〖〗i=1〖DD)〗Xi-∑〖DD(〗M2(t)
〖〗j=1〖DD)〗Zj+u2W(t).假设保单数量过程M1(t)与索赔次数过程M2(t)相依, 使用鞅方法得到了该模型最终破产概率的一个上界表达式e-ru·C(r), 并在特定条件M1(t)=β(t)M2(t)下, 给出了最终破产概率的一个明确上界ψ(u)≤e-Ru, 其中R为Lundberg指数.     

高阶色散方程的柯西问题

主要研究了高阶色散方程ut+2j+1xu=j+1x(u2)+j-1x(ux2),j≥2,j∈N,x,t∈R的柯西问题.使用修正傅里叶限制范数方法和Strichartz估计以及修正Bourgain空间,证明了这个问题在修正的Sobolev空间H(s,1/2j)(s-j/2+3/4)上是局部适定的.使用迭代技巧,也证明了这个问题在H(s,w)(0w1/2j)中,对于任意的s∈R,流映射不是C2的.     

孟家段水库鲢、鳙鱼生长规律的研究

孟家段水库的主要养殖鱼类鲢鱼和鳙鱼的体长(L)和体重(W)的关系分别为WH=0.035 2L2.862H和WA=0.079 4L2.6912A,该库的鲢鱼体长和体重的Von Bertalanffy方程分别为:LH=75.576 5[1-e-0.1544(t 0.3982)],WH=8 482.15[1-e-01544(t 0.3982)]2.8620;鳙鱼体长和体重的Von Bertalanffy方程分别为:LA=80.961 0[1-e-0.161(t 07794)],WA=10 848.58[1-e-0161(t 0.7794)]2.6912.并根据此方程计算出其生长速度和生长加速度的方程.该库鲢、鳙的生长参数为:L∞(H)=75.576 5 cm,W∞(H)=8 482.15 g,L∞(A)=80.961 0 cm,W∞(A)=10 848.58 g,KH=-0.154 4,KA=-0.161 1;t0(H)=0.398 2,t0(A)=0.7794;生长拐点分别为2 478.14 g(0.292W∞(H)和3 107.60 g(0.286 W∞(A)).比较几个不同纬度水体同种鱼类的vov Bertalanffy方程的系数可知其生长速度较为缓慢.     

THE COMPOUND BOUNDARY VALUE PROBLEM FOR A CLASS OF NONLINEAR PSEUDOPARABOLIC SYSTEMS

Let D be N+1 connected bounded domain in plane. Suppose the contour of D consists of N+1 simple-ly closed curves _0, _1…, _N and _1… _N are in the interior of domain circumscribed byC_μ~1(0 <μ< 1). In addition, assume that there are n mutually exclusive contour γ_,j=1,…,n,in interi-or of D,γ=γ_i; ∈C_μ~1. Denote D_j is the bounded domain circumscribed by γ_j,j=1,…,n, D~-=D_1+…+D.,D~+=D-D~-,D_t~ =D~ ×E, E=[0,T] (T>0), z=0∈D~+.We consider the following pseudoparabolic complex equation on D_t~ : / t[W_Z- Q_1(z)W_z- Q_2(z) _ - A_1(z)W - A_2(Z) ]= H(t,z,W,W-_2,W_2), (z,t) ∈D_t~ , (1)     

三阶p-Laplacian中立型泛函微分方程的周期解

利用Mawhin重合度理论,研究一类三阶p-Laplacian中立型泛函微分方程[φp(x(t)-∑n j=1cjx(t-r))″]′+f(x(t))x′(t)+α(t)g(x(t))+∑n j=1βj(t)g(x(t-γj(t)))=p(t)周期解的存在性,得到了这类方程至少存在一个T周期解的充分条件.     

误差为鞅差时的非参数回归模型

本文讨论了描述海水含盐量与年度月份变化之间关系的非参数多元回归模型Y~(j)(X_(in))=g(X_(in))+e~(j)(X_(in))获得了未知数函数g(x)的估计量的相合性。     

由混合序列生成的线性过程加权和的极限定理

假设线性过程Xt=∑〖DD(〗∞〖〗j=0〖DD)〗ajξt-j, t≥1, 其中{ξt,t∈Z}为一零均值的混合序列, {aj, j≥0}为一实数序列, 满足∑〖DD(〗∞〖〗j=0〖DD)〗j〖JB(|〗aj〖JB)|〗<∞, {ani,1≤i≤n,n≥1}为一实值的三角阵列, 在适当的假设条件下, 利用混合序列的中心极限定理及相应的概率不等式, 证明了由混合序列生成线性过程加权和的极限定理.     

The genome of a motile marine Synechococcus

Marine unicellular cyanobacteria are responsible for an estimated 20-40% of chlorophyll biomass and carbon fixation in the oceans. Here we have sequenced and analysed the 2.4-megabase genome of Synechococcus sp. strain WH8102, revealing some of the ways that these organisms have adapted to their largely oligotrophic environment. WH8102 uses organic nitrogen and phosphorus sources and more sodium-dependent transporters than a model freshwater cyanobacterium. Furthermore, it seems to have adopted strategies for conserving limited iron stores by using nickel and cobalt in some enzymes, has reduced its regulatory machinery (consistent with the fact that the open ocean constitutes a far more constant and buffered environment than fresh water), and has evolved a unique type of swimming motility. The genome of WH8102 seems to have been greatly influenced by horizontal gene transfer, partially through phages. The genetic material contributed by horizontal gene transfer includes genes involved in the modification of the cell surface and in swimming motility. On the basis of its genome, WH8102 is more of a generalist than two related marine cyanobacteria.     

线性过程的大数定律与中心极限定理

设{Xt}是一个线性过程Xt=∑∞j=0cjεt-j,其中{cj}是常数列,{εi,Fi}是一个适应的鞅差序列,∑∞j=0cj2Eε2t-j<∞,t=1,2,….本文利用线性过程的Beveridge-Nelson分解,得到了一类线性过程的大数定律和中心极限定理,推广和改进了Philips和Solo文中的相应结果.     

Extraction and Application of Natural Mordant Dyes from Eichhornia Crassipes (Water Hyacinth)

Metallic salts are often added as extra mordant when dyeing the fabrics with natural dyes. Eichhornia crassipes,namely water hyacinth( WH),is an environmentally problematic aquatic weed with high affinity for metals. In this paper,WH was selected as the source of natural mordant dyes,and extracted by absolute ethyl alcohol using a soxhlet apparatus. The colorants in WH were extracted and separated by column chromatography and thin layer chromatography( TLC). UV-visible spectrophotometer( UV-VIS),mass spectrometry, chemical identification with chromogenic reaction,and Fourier transform infrared spetroscopy( FTIR) were used to identify the main components of each pigment band. The total metal contents before and after extracting of the WH were determined by using an inductively coupled plasma atomic emission detector. The WH extracts were then used to dye wool fabric. The dyeing properties of WH extracts with and without metal mordant were investigated and compared. The results show that the main components of WH extracts are pheophytin and phyllins. The major metallic elements identified in WH are magnesium, manganese,zinc,and iron. Samples dyed with WH extracts without metal mordant exhibits high K / S values and good dyeing properties. This study indicates that the WH extracts can be used as a natural mordant dye on wool fabrics directly.     

多项目投资决策的一种数学规划模型

在已知各项目的现金流量yit和各时期提供的投资资金数量Mk情况下，把多项目投资的最优决策问题归结为数学规划模型：maxF=n/∑/t=1m/∑/j=1yjt(1 4)^n-tZj s.t.t/∑/k=1(Mk m/∑/j=1yjkZj)(1 r)^t-k≥0,t=1,…,n Zj=0,1,j=1,2,…,m此模型侧重于反映剩余资金可以向以后时期转移并获得增值的特点，在实际应用时可适当增加其它约束条件。     

Positive periodic solutions for three species Lotka-Volterra mixed ecosystems with periodic stocking

0　IntroductionPredator preysystemsandcompetitionsystemshavebeenstudiedextensively[1 5] .Mostofthepreviouspapersfocusedonthepredator preyandcompetitionsystemswithoutstocking .BrauerandSoudack[4,5] studiedsomepredator preysys temsunderconstantratestocking .Toourknowledge,fewpapershavebeenpublishedontheexistenceofperiodicsolutionsforLotka Volterramixedsystemswithperiodicstocking .Inthispaper,weinvestigatethefollowingmixedsystems:x1 ′(t) =x1 (t) (b1 (t) -a1 1 (t)x1 (t) -a1 2 (t)x2 (t) -a1 3(t…     

水击和调压室水力实验装置研制

自主研制的水击和调压室水力实验装置,可测定阀门不同启闭规律和管道上不同流速条件下的最大水击压力、水击压力过程线、沿管道水击压力分布以及调压室最高最低涌浪水位和水位波动的衰减过程;并且利用计算机测控,一次完成水击和调压室水力实验测控过程及数据采集和波型回放;通过实验证明,压力管道最大水击的实测值和理论计算值吻合,设置调压室时,调压室最高、最低涌浪水位和水位波动过程与实际情况完全吻合。     

高阶线性微分方程亚纯解的增长性

利用亚纯函数值分布理论,研究了亚纯系数高阶线性微分方程f^(k)+A_k-1(z)f^(k-1)+…+A₀(z)f=0解的增长性,证明了如果A₀(z)以∞为亏值,A_j(z)(1≤j≤k-1)满足某些条件,则上述方程的每个非零亚纯解都为无穷级,得到解的超级的下界估计.     

关于泛函微分中值点渐近性的进一步讨论

本在赋范线性空间上讨论微分中值点的渐近性,利用泛函的微积分理论给出了f^(i)(x0)h^(i)=0,g^(i)(x0)h^(i)=0(i=1,2…n-1,j=1.2…m-1),f^(n)(x0)h^(n),g^(m)(x0)h^(m)都不存在时泛函微分中值点渐近性的估计式。