WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM

For Vilenkin-like system, the authors define a new operator H*f := supn |Hnf|, where Hnf is the weighted average for partial sums, and prove that H* is of type (Hp* (Gm), Lp(Gm)) for all 1/2 < p ≤∞. As a consequence, the authors prove the operator S*f := supn |Snf| is of type (p, p) for 1 < p < ∞, where Snf is the n-partial sum.     

Periodical Stability for a Class of Uncertain System Under Process Perturbation

Controlled object for a class of m × n flow show with infinite buffers, is a linear state space model in the sense of ordinary max-algebra R , ⊕, ? . S open[1~3]: ( ) ( ) ( )( ) ( ) X k A X k B u kY k C X k??? == ?? ⊕ ? , k = 1,2,L (1) where A ∈ R p × p , B ∈ R p × q ,C ∈ Rq ×p, p = mn, q = m + n. k denotes the processing batch of jobs J 1, J 2, …, J n; X = [ x1 1 , L , x1 n , x2 1 , L , xm 1 , L , xmn]T denotes the state vector; xi j is the time when job J j was processed…     

代数 一个求解联立多項式方程的方法

在P.H.Blundeff的论文中考虑了方程: Σa_(ij)x~ij~j=0; Σb_(ij)x~iy~j=0; 此时i,j≥0;i+j=≤n。通过求解一个线性方程组(该线性方程组的系数是某一网格点集,而此网格点又是满足有关的一对差分方程的),求出一个一元多项式,此多项式的根的值恰巧就是原联立方程组变元之一全部根的值,至于其他变元相应的值则是通过简单的公式而得到的。文中研究了n=5和n=7的实际情况,在n=5和当a_(ij),b_(ij)是整数时已没有任何困难。     

线性多时滞差分微分系统全时滞稳定的代数判据

考虑下列线性多时滞差分微分系统 ?(t)=A_0x(t)+sum from k=1 to N(A_kx(t-τk·r),其中X∈R~n,A_k(k=0,1,…,N)是n×n常数矩阵;τk=(τk1,τk2,…,τkM),τkj(k=1,…,N;j=1,…,M)是整数,r~T=(r_1,r_2,…,rM),τk·r=sum from j=1 to M(τkj·rj)。本文利用Liapunov函数和Liapunov泛函,给出了系统(*)全时滞稳定的代数判别准则;并具体讨论了n=3,N=1时,系统(*)全时滞稳定的代数条件,克服了Hale文中验证“超越”条件的困难,为实际工作者提供了十分有效而方便的判别方法。     

解一阶线性常微分方程组一般边值问题的线性最小二乘法

设有一阶线性常微分方程组边值问题 y_i＇(x)=sum from i=1 to n [a_(ij)(x)y_i(x)+f_i(x)]0相似文献   

On the l_2-stability of time-varying linear and nonlinear discrete-time MIMO systems

New conditions are derived for the 2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput(MIMO) systems, having a linear time time-invariant block with the transfer function Γ(z), in negative feedback with a matrix of periodic/aperiodic gains A(k), k = 0, 1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities■(■), without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions,which are derived in the frequency domain, have the following features: i) They involve the positive definiteness of the real part(as evaluated on |z| = 1) of the product of Γ(z) and a matrix multiplier function of z. ii) For periodic A(k), one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A(k), but for aperiodic A(k), which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of(A(k + 1), A(k)), k = 1, 2,.... iii) They are distinct from and less restrictive than recent results in the literature.     

关于分布参数系统最佳调节器的稳定裕度

本文直接证明 定理 假设 1.x(·)是dx(t)/dt=Ax(t) Bu(t),x(0)=x_0的mild解,其中A是Hilbert空间X上的强连续半群e~(At)(t≥0)的母元,u(·)∈L~2([0, ∞),Z), 2.当integral from n=0 to ∞ (‖u(t)‖~2dt< ∞)和integral from n=0 to ∞ (‖Lx(t)‖~2dt< ∞)时integral from n=0 to ∞ (‖x(t)‖~2dt< ∞) ; 3.P≥0满足A~TP PA L~TL-PBR~(-1)B~TP=0和integral from n=0 to ∞ (‖e~((A-BR~(-1)B~TP)t)‖~2dt< ∞,其中R(?)0; 4.n(·): Z→Z是强连续的,且存在k>0和β>0使得integral from n=0 to ∞ (‖n(n(t))‖~2dt≤k integral from n=0 to ∞ (‖u(t)‖~2dt,(1 β)/2)integral from n=0 to ∞ dt≤integral from n=0 to ∞ dt. 那末方程的mild解是渐近稳定的。     

线性规划中的多项式型算法

<正> 我们考虑由具有整系数a_(ij),b_i的关于n≥2个实变元x_1,…,x_j,…,X_n的m≥2个线性不等式 a_(il)X_1+…+a_(in)X_n≤b_i i=1,2,…,m(1)所组成的系统。令 L=[sum from i,j=1 to m,n(log_2(|a_(ij)|+1))+sum from ?=1 to m(log_2(|b_i|+1)+log_2nm)]+1 是系统的输入的长度,亦即为了把(1)写成二进制形式所需要的符号0,1的个数。     

Lower estimation of approximation rate for neural networks

Let SFd and Πψ,n,d = { nj=1bjψ(ωj·x+θj) :bj,θj∈R,ωj∈Rd} be the set of periodic and Lebesgue’s square-integrable functions and the set of feedforward neural network (FNN) functions, respectively. Denote by dist (SF d, Πψ,n,d) the deviation of the set SF d from the set Πψ,n,d. A main purpose of this paper is to estimate the deviation. In particular, based on the Fourier transforms and the theory of approximation, a lower estimation for dist (SFd, Πψ,n,d) is proved. That is, dist(SF d, Πψ,n,d) (nlogC2n)1/2 . T...     

解实对称矩阵特征值并行快速Jacobi方法

<正> 本文对传统的Jacobi 变换进行变形,且在此基础上设计了快速方法。对一次扫描而言,进行变形可省2·(((n(n-1))/2)-2[(n+1)/2]+1)次矩阵乘法([x]表示≤x 的最大整数),快速方法对固定j 而言,省了一次开平方计算。一、Jacobi 变换变形对n 阶实对称矩阵A=[a_(ij)=[(?)]i,j=1,2,…n,鉴于A 的对称性,仅考虑i相似文献   

Selection of Secure Hyperelliptic Curves of g = 2 Based on a Subfield

In the implementation of hyperelliptic curve cryptosystems, a siginificant step is the selection of secure hyperelliptic curves on which the Jacobian is constructed. In this paper, we discuss the hyperelliptic curves of g=2 such as v2 uv=f and v2 v=f(u) defined on GF(2r). The curves defined on GF(4) and GF(8) are expanded to the curves defined on GF(4)k and GF(8)t respectively, where 38相似文献   

数据结构典型考题与分析(下)

本文针对数据结构中的典型考题进行分析讲解,希望广大考生朋友能够对数据结构概念和算法有深刻的理解,并能够灵活的运用。1.请问下面这个程序片断的时间复杂度是多少?voidselect_sort(inta[],intn)｛//将a中整数序列重新排列成自小至大有序的整数序列for(i=0;i相似文献   

充满魅力的计算机艺术图

利用计算机自动生成一些漂亮的艺术图形,这是十分有趣的,也充满魅力。在计算机自动生成艺术图形的方法中,有一种是利用函数迭代的方法来生成。其迭代公式为:x=a[k]*x+b[k]*y+e[k],y=c[k]*x+d[k]*y+f[k]。其中k取1、2、…、n,每一个k对应的一组参数a[k]、b[k]、c[k]、d[k]、e[k]、f[k]代表一种迭代法则,共有n种法则。在实际中,n可取4(本程序如此),并预先给定每组参数。在迭代     

一类特殊类型数学规划的解法及其在金融业的应用

1.问题的描述 假设国际金融界有n种货币可以发生直接的兑换.用a_(ij)表示国际市场兑换率.它的含义是,i货币每单位可以换取j货币的最大数量,若i货币不能直接兑换成j货币,则取a_(ij)=0.顺便指出,a_(ij)=1.由于买入价和卖出价之间有个差价,所以通常情况下a_(ij)a_(ji)≤1.在实际问题中,a_(ij)a_(ji)往往接近于某个常数,常见的是0.995.     

关于由映射Z←1/Z~n发生的分形

证明了负n阶Mandelbrot分形图M-n具有n+1条对称轴,其方程为z=rei(2j-1)πn+1(j=1,…,n+1;r为实数)。从而,可用轴对称旋转时间逃逸算法快速构造负n阶Mandelbrot分形图。     

1996年全国计算机等级考试试题及部分解析(续)

(41)设有如下程序: # include main() {int ＊＊k, ＊j,i = 100; j = &i; k = &j; printf("%d\n", ＊＊k); } 上述程序的输出结果是 A)运行错误 B)100 C)i的地址 D)j的地址答案:B。k为指向指针的指针,如图示:     

三要素法在暂态电路中的推广应用

在一阶电路中,由于含有动态元件L、C,当电路换路后,就有一个暂态过程,其响应有三种情况：零输入响应可用公式f（t）=f（0₊）e^-t/τ计算;零状态响应时对于状态量可用公式f（t）=f（∞）(1-e^-t/τ)计算;对于非状态量和全响应则用f（t）=f（∞）+[f（0₊）-f（∞）]e^-τ/t计算。     

On the structure of binary feedforward inverses with delay 2

Let M‘=S(Mα,f)be a semi-input-memory finite automaton with input alphabet Y and output alphabet X.If X=Y={0,1},then M‘ is a feedforware inverse with delay 2 if and only if there exists a cycle c of state diagram of Mαsuch that f(y0,…,yc,λα（t)0 can be expressed in the form of f ^(1)(y0,…,yc-1,λα（t)) yc for any state t in C and y0,y1,…,yc in Y;or of f^(2)(y0,…,yc-2,λα（t)) yc-c for any state t in Cand y0,y1,…,yc in Y;or for any state t in Cand y0,y1,…yc,in Y,y0,y1…yc satisfies the D[t] condition.The socalled y0,y1…yc satisfying the D[t] condition is that:for some i,j,(i,j)∈{(1,2),(1,3),(2,1),(2,2),(3,1),(3,2)},there exists a (c 2-k)-ary function f^(k),k=1,2,3,such that the Equation(1)and Equation (2)hokl simultaneously for all y‘c-2,…,y‘c 1∈Y. Equation (1);f(y0,…,yc-i,y‘c-i 1,…y‘c,λα（t))=f^(j)(y0,…yc-i,λα（t）） y‘c-i 1 Equation (2):f(y1,…,yc-j 1,y‘c-j 2,…,y‘c 1,λα（t））=f^(j)(y1,…,yc-j 1,λα（t）） y‘c-j s where t=δα（t）and if (i,j)=(1,2)then one and only one of the following conditions C1 and C2 holds for all y‘c-1,y‘c,y‘c 1∈Y.Condition C1:there exists a c-ary function g^(1),such that f(y0,…,yc-2,y‘c-1,y‘c,λα（t））=g^(1),(y0,…,yc-2,λα（t）） y‘c-1( )y‘c;Condition C2:there exists a (c-1)-ary functiong g^(2)such that f(y1,…,yc-2,y‘c-1,y‘c,y‘c 1,λα（t））=g^(2)(y1,…,yc-2,λα（t）） y‘c-1 y‘c,where t=δα(t).     

Ω上三重积分优化复化Simpson数值算法

设空间区域 Ω={(x,y,z)|α≤x≤b,φ_1(x)≤y≤φ_2(x),φ_1(x,y)≤z≤φ_2(x,y)}。(1)f(x,y,z)在Ω及其邻域内具有四阶连续偏导数,φ_1(x)与φ_2(x)在[α,a]内可导,φ_1(x,y)与φ_2(x,y)在Ω的投影(xoy面)区域上具有连续偏导数。下面介绍三重积分 I=∫∫∫f(x,y,z)dxdydz (2)的优化复化Simpson数值积分算法。首先将Ω进行划分,把[α,b]分为2m等分,步长与分点为 h_1=(b-α) /2m,x_i=α+ih_1(i=0,1,2,…,2m)。 (3)在x_(2i+1)处把[φ_1(x_(2i+1)),φ_2(x_(2i+1))分为2n等分,步长与分点为 g_(1,2i+1) =((φ_2(x_(2i+1)))-(φ_1(x_(2i+1))))/2n (i=o,1,2,…,m-1), (4) y_(2i+1,j)=φ_1(x_(2i+1))+jg_(1,2i+1) (j=0,1,2,…,2n)。     

基于量-质特征转化与定性映射的模式识别和形象"涌现"

1定性映射[1～5] 定义1 设a(o)为对象(object)的某属性,x∈X(∪)R,为a(o)的某个量特征值,pj(o)∈Po,是a(o)的某质特征或性质,Γ={(αj,βj)|(αj,βj)是a(o)的第j(j=1,…,m)个性质pj(o)的定性基准},称τ:X×Γ→{0,1}×Po是以(αj,βj)为基准对x进行的定性映射(Qualitative Mapping,QM)或定性判断,如果对任意x∈X,存在[αj,βj]∈Γ和以[αj,βj]为定性基准的性质pj(o)∈P,使得: