A NECESSARY AND SUFFICIENT CONDITION FOR THE OSCILLATION OF HIGHER-ORDER NEUTRAL EQUATIONS WITH SEVERAL DELAYS

Consider the higher-order neutral delay differential equationd~t/dt~n(x(t)+sum from i=1 to lp_ix(t-τ_i)-sum from j=1 to mr_jx(t-ρ_j))+sum from k=1 to Nq_kx(t-u_k)=0,(A)where the coefficients and the delays are nonnegative constants with n≥2 even. Then anecessary and sufficient condition for the oscillation of (A) is that the characteristicequationλ~n+λ~nsum from i=1 to lp_ie~(-λτ_i-λ~n)sum from j=1 to mr_je~(-λρ_j)+sum from k=1 to Nq_ke~(-λρ_k)=0has no real roots.     

常系数非齐线性递推式的解的显式表示

本文给出常系数非齐线性递推式(?)的解的显式表达式 H(m)=sum from i=0 to k-1(sum from j=i to k-1 b_ja_(k-j+i))D_(m-k-i)+sum from i=0 to m-k D_if(m-i)(m≥k)其中D_m=sum x_1+2x_2+…+kx_k=m x_j≥0(i=1,2,…,k)(?)a_1~x1a_2~x2…a_k~xk.     

关于线性过程谱函数估计的弱不变原理的一点注记

设随机序列{X_n; n=0,±1…}可表示成为X_n=sum from j=-∞ to +∞(α_(j-n)ζ_j其中{α_j}是满足sum from j=-∞ to +∞(α_j~2)<∞的实数列,{ζ_j}是白噪声序列。通常用(?)_N(λ)=integral from 0 to λ(1/2πN)∣sum from k=1 to N(x_(?)e~(iμk)∣~2 dμ来估计{x_n}的未知的谱函数F(λ)。在一定的条件下,当{ζ_j}是独立同分布随机序列时,和[3]证明了:过程√(?)[(?)_N(λ)-F(λ)]的分布弱收敛到某个正态过程ζ(λ)在C[0,π]上产生的测度。本文在他们工作的基础上,运用鞅的极限定理和鞅不等式,改进了[3]中的两个关键引理,从而证明了当{ζ_j}是有控制分布的实四阶鞅差序列时,仍有相同的结果。     

二次指派问题的一个新的限界方法

二次指派问题(QAP)的数学模型是:min{z(x)=sum from i=1 to n sum from =1 to n a_(ip)x_(ip)+sum from i=1 to n sum from p=1 to n sum from j=1 to n sum from q=1 to n c_(ipjq)x_(ip)x_(jq)|x∈},(1)这里∈(n~2维布尔集)是满足如下约束的集合:sum from i=1 to n x_(ip)=1,1≤p≤n,(2)sum from p=1 to n x_(ip)=1,1≤i≤n,(3)x_(ip)=0,1,1≤i,p≤n.(4)因为 x_(ip)~2=x_(ip)并且有约束(2)和(3),我们可以约定 c_(ipjq)=0,当 i=j 或 p=q.如果所有二次项的系数都可以写成     

具有大稳定域的线性多步方法

§1.引言 解常微分方程初值问题:的线性k步方法为 sum from j=0 to k (α_jy_(n j)=h sum from j=0 to k (β_jf_(n j),(2)其中α_0~2 β_0~2≠0,α_k≠0.当β_k≠0时,(2)为隐式k步法;当β_k=0时,(2)为显式k步法. 若将(2)应用于单个方程 y′=λy,Reλ<0,则得差分方程 ρ(E)y_n=μσ(E)y_(?),μ=λh,     

数列的循环求和法——探索一类数列和的表达式

数列求和的方法很多,己有许多杂志刊登了各种数列求和方法的文章,本文提及的循环求和法,其思想方法是通过式子变形,使所求和重复出现,造成循环,亦即构造出含有所求和S的方程S=f(s),然后解出S。问题:求 sum from k=1 to n (k·2~k)sum from k=1 to n (k·2~k)=sum from k=0 to (n-1) ((k+1)2~(k+1))=2 sum from k=0 to (n-1) k2~k+sum from k= to (n-1) (2(k+1))=2[sum from k=1 to n (k·2~k-n·2~n)]+sum from k=1 to n 2~k∴ sum from k=1 to n (k·2~k)=n·2~(n+1)-(2~(n+1)-2) 有许多同志会感兴趣于研究sum from k=1 to n (k~p 2~k)     

稳定性参数区域之进一步估计

在[1]中,笔者用标量函数的方法研究了具有分解形式(dX_i)/(dt)=G_i(X_i,t) sum from i=1 j(?)i to r A_(ij)(t)X_j(t) sum from j=1 to r B_(ij)(t)[X_j(t-τ(ij))-X_j(t)](i=1,2,…,r)的复合系统(dX)/(dt)=H[t,X(t),X(t-τ)]及具有分解形式     

孤立波数值方法综述(Ⅱ)

III Finite Element Methods We take element, I=sum from j=1 to N (I_j). Let Φ_h and Ψ_h be the trail function space and test function space respectively with basis (x) and (x). We suppose U~h(x,t)=sum from j=1 to N (U_i(t)(?)_j(x)), x∈I,t≥0. The usual Galerkin method is to find U~h∈L~∞(0,T;Φ_h) satisfying (21) In order to improve the stability and convergence, the dissipative finite element     

退缩椭圆型方程的边值问题

<正> 在 R~n 的有界凸区域Ω上考虑椭圆型方程Lu≡sum from i,j=1 to n (a_(ij)(x)u_(xi)_(xj)+sum from i=1 to n b_i(x)u_i+c(x)u=f(x),(1)设对 x∈(?)及所有的实数组(ξ_1,ξ_2,…,ξ_n)sum from i,j=1 to n a_(ij)(x)ξ_iξ_j≥λ(x)sum from i=1 to n ξ_i~2≥0,a_(ji)(x)∈C(?),即算子 L(u)可能退缩而为退缩椭圆型算子。记(?)的边界为∑,∑上满足 sum from ij=1 to n a_(ij)n_in_j=0的点集为∑_0,(n_1,…,n_n)表示∑上的内单位法向量,∑_3=∑\∑_0,设其 n-1维测度非零,则对方程(1)可提如下的边值问题:     

具多滞量和正负系数中立型微分方程解的渐近性质

该文考虑多滞量和正负系数中立型方程[x(t)-sum from n=1 to l(1/n)C_A(t)x(t-r_n)] sum from i=1 to (1/i)P_i(t)x()t-τ_i)-sum from j=1 to n(1/j)Q_j(t)x(t-σ_j)=0,其中C_A(k=1,…,l),P_i(i=1,…,m),Q_j(j=1…,n)∈C([to,∞co),R~ ),0≤τ_l<…<τ_m,0≤σ_1<…<σ_n,0相似文献   

Estimating a survival function with incomplete cause-of-death data

We propose a random censorship model which permits uncertainty in the cause of death assessments for a subset of the subjects in a survival experiment. A nonparametric maximum likelihood approach and a “self-consistency” approach are considered. The solution sets corresponding to both approaches are found. They are infinite and identical. Only some of the solutions are consistent; i.e., the MLEs and self-consistent estimators are not consistent in general. Two estimates are thus proposed and their asymptotic properties are studied. It is shown that both estimates are strongly consistent and converge to Gaussian processes. The covariance structures of these Gaussian processes are derived.     

关于(余)反射的等价性和可扩张性及其应用

该文研究了（余）反射的等价性和可扩张性及应用，得到的主要结果如下：(1) 余反射余代数范畴和反射代数范畴是等价的．(2) 反射和余反射都具有可扩张性．使用这些结果可以用来推广和化简［1-4］中部分结论     

On covering mappings on solenoids

Covering mappings on the dyadic solenoid are studied. Some results stated by Zhou Youcheng (2000) are discussed in a more detailed way by indicating certain inaccuracies in their proofs. These are either corrected or supplemented, or else suitable counterexamples are constructed. Some open questions are asked and connections with related results are considered.

     

直觉模糊关系的截集性质

定义了直觉模糊关系的截集以及并给出了它们的基本性质,同时分别讨论了自反、对称、传递直觉模糊关系与经典二元关系之间的等价刻画;其次,提出直觉模糊关系的定义域与值域的概念;最后,分析了直觉模糊关系合成的截集性质.     

Depth notions for orthogonal regression

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.     

近程空中目标航路研究

本文在等加速俯冲飞行假定下,分析了近程空中目标航路的特点,并据此提出了目标航路模型.经过投影变换,把目标航路模型转化为二次函数,从而使目标航路的滤波及预报问题得到简化,采用弟推最小二乘(RLS)原理,给出了目标航路的滤波器及预报器,最后,对本文方法进行了仿真,并对仿真结果进行了分析.     

Enumeration of point-determining graphs

Point-determining graphs are graphs in which no two vertices have the same neighborhoods, co-point-determining graphs are those whose complements are point-determining, and bi-point-determining graphs are those both point-determining and co-point-determining. Bicolored point-determining graphs are point-determining graphs whose vertices are properly colored with white and black. We use the combinatorial theory of species to enumerate these graphs as well as the connected cases.     

Magnetically created instability in a collisionless plasma

In the Vlasov–Maxwell theory we prove that there are homogeneous equilibria that are monotone decreasing in every direction and are arbitrarily close to a Maxwellian. They are unstable under certain electromagnetic perturbations, but are stable under purely electric perturbations as well as under electromagnetic perturbations of sufficiently short period. These statements are valid both in the linear and nonlinear senses.     

Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof.Lu Jinake

In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.     

Games with vector payoffs

Two-person games are defined in which the payoffs are vectors. Necessary and sufficient conditions for optimal mixed strategies are developed, and examples are presented.