共查询到20条相似文献,搜索用时 109 毫秒
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本文,我们把递归算术系统简化为下列三个系统:A_0V_2、A_0V_1I_2θ_2及A_0V_1I_2θ_2~*,此处A_0为存在性公理,而V_n、I_n、θ_n、θ_n~*为唯一性规则,其定义如下:A_0是:给了H(x,y),存在一函数F(u,x),使得规则V_n是:此处是指“可推导出”,x为约束变元,它在前件中不能进行代入,I_n是V_n当H是么函数I(I(x)=x)时的特例,θ_n是V_n当H为θ(θ(x)=0)时的特例,θ_n~*又是θ_n当F(u_1,…,u_n,0)=0时的特例。 相似文献
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秦曾复 《高等学校计算数学学报》1980,(1)
龙贝格算法是数值积分的一个基本方法。Bauer等人(1963)曾经指出,用经典的倍增数列{δ_n}:δ_n=2~n来构成步长序列,被积函数的赋值次数增加太快,他们设计了一个增长稍慢的数列{τ_n}:τ_(2k)=3~k,τ_(2k+1)=2×3~k,并指出那个增长最慢的自然数列{V_n}:v_n=n+1是数值不稳定的。Bulirsch(1964)也认为经典的龙叹格算法工作量过 相似文献
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移不变性,则称{ψ_n}_1~∞ 具有平移不变性.记作{ψ_n}_1~∞具有 i.p.m.性质1.如果{(?)_n}_1~∞是数列空间 l~p(1≤p<∞)、C_0或 C 中的自然基,则{(?)_n}_1~∞具有 i.p.m.特别地,当 X 为 C_0,l′或 Hilbert 空间时,X 中的任何无条件基都具有 i.p.m.(?) 相似文献
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关于x_1,x_2,…,x_n的对称多项式都可表为初等对称多项式σ_1,σ_2,…,σ_n的多项式。本文推广了此定理的结论。定义设f_i=f_i(x_1,x_2,…,x_n)(i=1,2,…,n)为关于x_1,x_2,…,x_n的i次对称多项式,且由它们组成的方程组 (这里a_i(i=1,2,…,n)为常数)是独立的n个方程组成的方程组。即f_i不能表为上述其它n-1个多项式的多项式。则称f_i,f_2,…,f_n为n元对称多项式的一组基。引理对于任意的1≤i≤n,f_i可表为σ_1,σ_2,…,σ_i的多项式。证明因为f_i是x_1,x_2,…,x_n的i次对称多项式。由对称多项式的基本定理可设 f_i=g(σ_1,σ_2,…,σ_n)在多项式g(σ_1,σ_2,…,σ_n)中若存在含σ_i(i相似文献
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对角型拟线性蜕化椭圆型方程组广义解的处处 Holder 连续性 总被引:1,自引:0,他引:1
设 G 是 n 维欧氏空间 E~n 中的有界区域.B(x_0,r)记中心在 x 半径为 r 的球体,B(r)=B(0,r).W_2~1(G)和\mathring{W}_2^1(G)是通常的空间.[W_2~1(G)]~N 和[\mathring{W}_2^1(G)]~N为 N 维向量值函数的空间.限于 n≥3.在 G 中考虑方程... 相似文献
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设E是具弱序列连续对偶映像自反Banach空间, C是E中闭凸集, T:C→ C是具非空不动点集F(T)的非扩张映像.给定u∈ C,对任意初值x0∈ C,实数列{αn}n∞=0,{βn}∞n=0∈ (0,1),满足如下条件:(i)sum from n=α to ∞α_n=∞, α_n→0;(ii)β_n∈[0,α) for some α∈(0,1);(iii)sun for n=α to ∞|α_(n-1) α_n|<∞,sum from n=α|β_(n-1)-β_n|<∞设{x_n}_(n_1)~∞是由下式定义的迭代序列:{y_n=β_nx_n (1-β_n)Tx_n x_(n 1)=α_nu (1-α_n)y_n Then {x_n}_(n=1)~∞则{x_n}_(n=1)~∞强收敛于T的某不动点. 相似文献
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贵刊1991年第3期《标准正交基的一种求法》一文,给出用矩阵的合同变换把R~n的一个基{α_1.α_2,…,α_n}化为标准正交基{β_1,β_2,…,β_n}的一种方法。这种方法是以向量α_1的分量作为第i列(i=1,2,…,n)作出矩阵A,A′A是一个n阶正定矩阵,所以存在n阶可逆矩阵T 相似文献
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在正实轴上考虑函数系,其中Reμ_n>0,n=1,2,…,且用S_k表示μ_k在{μ_1,μ_2,…,μ_k}中出现的次数,P_k表示μ_k在序列{U_n}_1~∞中出现的次数,已知 Mntz-Szasz定理:要使函数系在空间L~2[0, ∞)中完备,即对任意f(x)∈L~2《0, ∞),对任给ε>0,存在P_n(x)=sum from k=1 to n(c_ke~(-μ_ke~x)x~(S_(k-1)))使得 相似文献
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Wu Zhengchang 《数学年刊B辑(英文版)》1993,14(2):189-196
Let ${V_k}^{+\infinity}_{k=-\infinity}$ be a multiresolution analysis generated by a function $\phi(x)\in L^2(R^2)$. Under this multiresolution framework the key point for studying wavelet decompositions in $L^2(R^2)$ is to study the properties of Wo which is the orthogonal complement of $V_0$ in $V_1:V_1=V_0\oplus W_0$.In this paper the author studies the structure of W_0 and furthermore shows that a box spline of three directions can generate a wavelet decomposition of $L^2(R^2)$. 相似文献
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By using the rank methods of matrix, a necessary and sufficient condition is established for reverse order law $$\begin{gathered} WA_{d,W} W = (W_n (A_n )_{d,W_n } W_n )(W_{n - 1} (A_{n - 1} )_{d,W_{n - 1} } W_{n - 1} ) \hfill \\ ... (W_1 (A_1 )_{d,W_1 } W_1 ) \hfill \\ \end{gathered} $$ to hold for the W-weighted Drazin inverses, whereA =A 1 A 2 … A n andW =W n W n-1 …W 1. This result is the extension of the result proposed by [Linear Algebra Appl., 348(2002)265-272] and the result proposed by [J. Math. Research and Exposition. 19(1999)355-358]. 相似文献
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赵长健 《数学年刊A辑(中文版)》2014,35(4):501-510
Milman曾提出过一个问题;在混合体积理论,是否存在Marcus-Lopes型和Bergstrom型不等式?即对R~n上任意凸体K与L且i=0,…,n-1,是否成立(W_i(K+L))/(W_i+1(K+L))≥(W_i(K))/(W_i+1(K))+(W_i(L))/(W_i+1(L))?这里W_i表示凸体的i次均值积分.当且仅当i=n-1或i=n-2时,这个问题是正确的,已被证明.作者考虑了一个对偶问题,证明了:若K与L是R~n上的星体,n-2≤i≤n-1且i∈R,则(W_i(K+L))/(W_i+1(K+L))≤(W_i(K))/(W_i+1(K))+(W_i(L))/(W_i+1(L))/(W_i+1(L))其中W_i表示星体的i次对偶均值积分. 相似文献
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<正> 导言伯恩斯坦曾经证明:设 F(x)是偶的整函数,其泰勒系数不是负数,并且它的性(род,genus)大于零.如果 f(x)在(—∞,∞)上连续,并且适合 相似文献
15.
Ye Cinan 《数学年刊B辑(英文版)》1986,7(3):384-396
Suppose that there is a variance components model
$$\[\left\{ {\begin{array}{*{20}{c}}
{E\mathop Y\limits_{n \times 1} = \mathop X\limits_{n \times p} \mathop \beta \limits_{p \times 1} }\{DY = \sigma _2^2{V_1} + \sigma _2^2{V_2}}
\end{array}} \right.\]$$
where $\[\beta \]$,$\[\sigma _1^2\]$ and $\[\sigma _2^2\]$ are all unknown, $\[X,V > 0\]$ and $\[{V_2} > 0\]$ are all known, $\[r(X) < n\]$. The author estimates simultaneously $\[(\sigma _1^2,\sigma _2^2)\]$. Estimators are restricted to the class $\[D = \{ d({A_1}{A_2}) = ({Y^''}{A_1}Y,{Y^''}{A_2}Y),{A_1} \ge 0,{A_2} \ge 0\} \]$. Suppose that the loss function is $\[L(d({A_1},{A_2}),(\sigma _1^2,\sigma _2^2)) = \frac{1}{{\sigma _1^4}}({Y^''}{A_1}Y - \sigma _1^2) + \frac{1}{{\sigma _2^4}}{({Y^''}{A_2}Y - \sigma _2^2)^2}\]$.
This paper gives a necessary and sufficient condition for $\[d({A_1},{A_2})\]$ to be an equivariant D-asmissible estimator under the restriction $\[{V_1} = {V_2}\]$, and a sufficient condition and a necessary condition for $\[d({A_1},{A_2})\]$ to equivariant D-asmissible without the restriction. 相似文献
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Let M be a compact orientable manifold, and F be an essential closed surface which cuts M into two 3-manifolds M
1 and M
2. Let be a Heegaard splitting for i = 1, 2. We denote by d(S
i
) the distance of . If d(S
1), d(S
2) ≥ 2(g(M
1) + g(M
2) − g(F)), then M has a unique minimal Heegaard splitting up to isotopy, i.e. the amalgamation of and .
Ruifeng Qiu is supported by NSFC(10625102). 相似文献
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Liu Quan-sheng 《数学年刊B辑(英文版)》1989,10(2):214-220
The paper considers the random L-Dirichlet seriesf(s,ω)=sum from n=1 to ∞ P_n(s,ω)exp(-λ_ns)and the random B-Dirichlet seriesψτ_0(s,ω)=sum from n=1 to ∞ P_n(σ iτ_0,ω)exp(-λ_ns),where {λ_n} is a sequence of positive numbers tending strictly monotonically to infinity, τ_0∈R is a fixed real number, andP_n(s,ω)=sum from j=1 to m_n ε_(nj)a_(nj)s~ja random complex polynomial of order m_n, with {ε_(nj)} denoting a Rademacher sequence and {a_(nj)} a sequence of complex constants. It is shown here that under certain very general conditions, almost all the random entire functions f(s,ω) and ψ_(τ_0)(s,ω) have, in every horizontal strip, the same order, given byρ=lim sup((λ_nlogλ_n)/(log A_n~(-1)))whereA_n=max |a_(nj)|.Similar results are given if the Rademacher sequence {ε_(nj)} is replaced by a steinhaus seqence or a complex normal sequence. 相似文献
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I. P. Gavrilyuk 《Journal of Mathematical Sciences》1992,58(1):1-11
A difference scheme is constructed for the solution of the variational equation $$\begin{gathered} a\left( {u, v} \right)---u \geqslant \left( {f, v---u} \right)\forall v \varepsilon K,K \{ vv \varepsilon W_2^2 \left( \Omega \right) \cap \mathop {W_2^1 \left( \Omega \right)}\limits^0 ,\frac{{\partial v}}{{\partial u}} \geqslant 0 a.e. on \Gamma \} ; \hfill \\ \Omega = \{ x = (x_1 ,x_2 ):0 \leqslant x_\alpha< l_\alpha ,\alpha = 1, 2\} \Gamma = \bar \Omega - \Omega ,a(u, v) = \hfill \\ = \int\limits_\Omega {\Delta u\Delta } vdx \equiv (\Delta u,\Delta v, \hfill \\ \end{gathered} $$ The following bound is obtained for this scheme: $$\left\| {y - u} \right\|_{W_2 \left( \omega \right)}^2 = 0(h^{(2k - 5)/4} )u \in W_2^k \left( \Omega \right),\left\| {y - u} \right\|_{W_2^2 \left( \omega \right)} = 0(h^{\min (k - 2;1,5)/2} ),u \in W_\infty ^k \left( \Omega \right) \cap W_2^3 \left( \Omega \right)$$ The following bounds are obtained for the mixed boundary-value problem: $$\begin{gathered} \left\| {y - u} \right\|_{W_2^2 \left( \omega \right)} = 0\left( {h^{\min \left( {k - 2;1,5} \right)} } \right),u \in W_\infty ^k \left( \Omega \right),\left\| {y - u} \right\|_{W_2^2 \left( \omega \right)} = 0\left( {h^{k - 2,5} } \right), \hfill \\ u \in W_2^k \left( \Omega \right),k \in \left[ {3,4} \right] \hfill \\ \end{gathered} $$ . 相似文献
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S. B. Stechkin 《Mathematical Notes》1970,7(4):248-255
A class Pn of even positive trigonometric polynomials tn(?)=a0 + a1 cos ?+ ... + an cos · n?, satisfying the conditions: ak ≥0 (k = 0,1, ..., n), a0 < a1 is considered. The behavior of the sequence of functionals $$v_n = _{t_n \mathop { \in P_n }\limits^{\inf } } \frac{{t_n \left( 0 \right) - a_o }}{{\left( {\sqrt {a_1 } - \sqrt {a_o } } \right)}}$$ , is studied; two-sided estimations are given for Vn and \(V_\infty = \mathop {\lim }\limits_{n \to \infty } V_n \) . 相似文献
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We show that there do not exist computable functions f 1(e, i), f 2(e, i), g 1(e, i), g 2(e, i) such that for all e, i ∈ ω, (1) $ {\left( {W_{{f_{1} {\left( {e,i} \right)}}} - W_{{f_{2} {\left( {e,i} \right)}}} } \right)} \leqslant _{{\rm T}} {\left( {W_{e} - W_{i} } \right)}; $ (2) $ {\left( {W_{{g_{1} {\left( {e,i} \right)}}} - W_{{g_{2} {\left( {e,i} \right)}}} } \right)} \leqslant _{{\rm T}} {\left( {W_{e} - W_{i} } \right)}; $ (3) $ {\left( {W_{e} - W_{i} } \right)} \not\leqslant _{{\rm T}} {\left( {W_{{f_{1} {\left( {e,i} \right)}}} - W_{{f_{2} {\left( {e,i} \right)}}} } \right)} \oplus {\left( {W_{{g_{1} {\left( {e,i} \right)}}} - W_{{g_{2} {\left( {e,i} \right)}}} } \right)}; $ (4) $ {\left( {W_{e} - W_{i} } \right)} \not\leqslant _{{\rm T}} {\left( {W_{{f_{1} {\left( {e,i} \right)}}} - W_{{f_{2} {\left( {e,i} \right)}}} } \right)}{\text{unless}}{\left( {W_{e} - W_{i} } \right)} \leqslant _{{\rm T}} {\emptyset};{\text{and}} $ (5) $ {\left( {W_{e} - W_{i} } \right)} \leqslant _{{\rm T}} {\left( {W_{{g_{1} {\left( {e,i} \right)}}} - W_{{g_{2} {\left( {e,i} \right)}}} } \right)}{\text{unless}}{\left( {W_{e} - W_{i} } \right)} \leqslant _{{\rm T}} {\emptyset}. $ It follows that the splitting theorems of Sacks and Cooper cannot be combined uniformly. 相似文献