共查询到20条相似文献,搜索用时 15 毫秒
1.
Chang Qing 《数学年刊B辑(英文版)》1988,9(2):161-166
Let $F$ denote a field, finite or infinite, with characteristic $\[p \ne 0\]$. In this paper, the
author obtains the following result: The symmetric polynomial on $t$ letters
$$\[{S_{sym(t)}}({x_1},{x_2}, \cdots ,{x_t}) = \sum\limits_{x \in sym(t)} {{X_{\pi 1}}{X_{\pi 2}} \cdots {X_{\pi t}}} \]$$
is a polynomial identity of $\[{M_n}(F)\]$ when $\[t \ge pn\]$, and this is sharp in the sense that if $\[t \le pn - 1\]$,it is not a polynomial identity of $\[{M_n}(F)\]$. 相似文献
2.
Wen Zhixiong 《数学年刊B辑(英文版)》1984,5(4):695-710
Zhang Yuanda has determined the groups of order $\[2_{{p^2}}^3\]$ (p is an odd prime$\[ \ne 3,7\]$). Now this paper is to determine the structures of groups of order $\[2_{pq}^3\]$(p,q are odd primes and p
相似文献
3.
Wu Xiaolong 《数学年刊B辑(英文版)》1988,9(4):436-441
In this paper, the author proves the following resu: It Let K be a skew field and A be an automorphism of SL(2, K). Then there exists A∈GL(2, K), an automorphism σ or an anti-automorphism τ of K, such that A is of theform AX=AX~σA~(-1) for all X∈SL(2, K)or AX=A(X~τ~2)~(-1)A~(-1) for all X∈SL(2, K),where X~σ, X~τ are the matrices obtained by applying σ, τ on X respee tively and X' is thetranspose of X. 相似文献
4.
Let $\[(\Omega ,F,\mu )\]$ be a probabilty space with an increasing family $\[{\{ {F_t}\} _{t > 0}}\]$ of sub-fields satisfying the usual conditions. The following results are obtained: for $\[f \in BMO\]$, we have $\[f = g - h\]$ with $\[g,h \in BLO\]$; if in addition, f satisfies
then for $\[s > 0\]$ arbitrary, g,h can be chosen such that $\[g,h \in BLO\]$, and
$$\[E({\varepsilon ^{(a - \varepsilon )(g - {g_t})}}|{F_t}) \le {C_{a,\beta ,\varepsilon }},E({\varepsilon ^{(\beta - \varepsilon )(h - {h_t})}}|{F_t}) \le {C_{a,\beta ,\varepsilon }}\]$$
and for weights z, we have
$\[z \in {A_p} \cap S \Leftrightarrow z = {z_1}z_2^{1 - p}\]$ with $\[{z_i} \in {A_i} \cap S,i = 1,2\]$,
where $\[S = \{ \begin{array}{*{20}{c}}
{weight}&{z:C{z_{{T^ - }}} \le {z_T} \le C{z_{{T^ - }}}}
\end{array}\} \]$, $\[\forall \]$ stopping times T, outside a null set }. 相似文献
5.
Sun Hesheng 《数学年刊B辑(英文版)》1988,9(4):429-435
In practical problems there appears the higher-order equations of changing type. But,there is only a few of papers, which studied the problems for this kind of equations. In this paper a kind of the higher-order m 相似文献
6.
Wu Liangsen 《数学年刊B辑(英文版)》1988,9(1):27-31
Let $A$, $B$ be unital $\[{C^*}\]$-algebras.
$\[{\chi _A} = \{ \varphi |\varphi \]$ are all completely postive linear maps from $\[{M_n}(C)\]$ to $A$ with $\[\left\| {a(\varphi )} \right\| \le 1\]$ $}$.
$\[(a(\varphi ) = \left( {\begin{array}{*{20}{c}}
{\varphi ({e_{11}})}& \cdots &{\varphi ({e_{1n}})}\{}& \cdots &{}\{\varphi ({e_{n1}})}& \cdots &{\varphi ({e_{nn}})}
\end{array}} \right),\]$ where $\[\{ {e_{ij}}\} \]$ is the matrix unit of $\[{M_n}(C)\]$.
Let $\[\alpha \]$ be the natural action of $\[SU(n)\]$ on $\[{M_n}(C)\]$
For $\[n \ge 3\]$, if $\[\Phi \]$ is an $\[\alpha \]$-invariant affine isomorphism between $\[{\chi _A}\]$ and $\[{\chi _B}\]$, $\[\Phi (0) = 0\]$, then $A$ and $B$ are $\[^*\]$-isomorphic
In this paper a counter example is given for the case $\[n = 2\]$. 相似文献
7.
Liang Zhongchao 《数学年刊B辑(英文版)》1982,3(1):79-84
In this paper, the existence and uniqueness of solution of the limit boundary value problem
$\[\ddot x = f(t,x)g(\dot x)\]$(F)
$\[a\dot x(0) + bx(0) = c\]$(A)
$\[x( + \infty ) = 0\]$(B)
is considered, where $\[f(t,x),g(\dot x)\]$ are continuous functions on $\[\{ t \ge 0, - \infty < x,\dot x < + \infty \} \]$ such that the uniqueness of solution together with thier continuous dependence on initial value are ensured, and assume: 1)$\[f(t,0) \equiv 0,f(t,x)/x > 0(x \ne 0);\]$; 2) f(t,x)/x is nondecreasing in x>0 for fixed t and non-increasing in x<0 for fixed t, 3)$\[g(\dot x) > 0\]$,
In theorem 1, farther assume: 4) $\[\int\limits_0^{ \pm \infty } {dy/g(y) = \pm \infty } \]$
Condition (A) may be discussed in the following three cases
$x(0)=p(p \neq 0)$(A_1)
$\[x(0) = q(q \ne 0)\]$(A_2)
$\[x(0) = kx(0) + r{\rm{ }}(k > 0,r \ne 0)\]$(A_3)
The notation $\[f(t,x) \in {I_\infty }\]$ will refer to the function f(t,x) satisfying $\[\int_0^{ + \infty } {\alpha tf(t,\alpha )dt = + \infty } \]$ for each $\alpha \neq 0$,
Theorem. 1. For each $p \neq 0$, the boundary value problem (F), (A_1), (B) has a solution if and only if $f(t,x) \in I_{\infty}$
Theorem 2. For each$q \neq 0$, the boundary value problem (F), (A_2), (B) has a solution if and only if $f(t, x) \in I_{\infty}$.
Theorem 3. For each k>0 and $r \neq 0$, the boundary value problem (F), (A_3), (B) has a solution if and only if f(t, x) \in I_{\infty},
Theorem 4. The boundary value problem (F), (A_j), (B) has at most one solution for j=l, 2, 3. . 相似文献
8.
The number $\[A({d_1}, \cdots ,{d_n})\]$ of solutions of the equation
$$\[\sum\limits_{i = 0}^n {\frac{{{x_i}}}{{{d_i}}}} \equiv 0(\bmod 1),0 < {x_i} < {d_i}(i = 1,2, \cdots ,n)\]$$
where all the $\[{d_i}s\]$ are positive integers, is of significance in the estimation of the number $\[N({d_1}, \cdots {d_n})\]$ of solutiohs in a finite field $\[{F_q}\]$ of the equation
$$\[\sum\limits_{i = 1}^n {{a_i}x_i^{{d_i}}} = 0,{x_i} \in {F_q}(i = 1,2, \cdots ,n)\]$$
where all the $\[a_i^''s\]$ belong to $\[F_q^*\]$. the multiplication group of $\[F_q^{[1,2]}\]$. In this paper, applying the inclusion-exclusion principle, a greneral formula to compute $\[A({d_1}, \cdots ,{d_n})\]$ is obtained.
For some special cases more convenient formulas for $\[A({d_1}, \cdots ,{d_n})\]$ are also given, for
example, if $\[{d_i}|{d_{i + 1}},i = 1, \cdots ,n - 1\]$, then
$$\[A({d_1}, \cdots ,{d_n}) = ({d_{n - 1}} - 1) \cdots ({d_1} - 1) - ({d_{n - 2}} - 1) \cdots ({d_1} - 1) + \cdots + {( - 1)^n}({d_2} - 1)({d_1} - 1) + {( - 1)^n}({d_1} - 1).\]$$ 相似文献
9.
Ding Tongren 《数学年刊B辑(英文版)》1984,5(4):687-694
This note is concerned with the equation
$$\[\frac{{{d^2}x}}{{d{t^2}}} + g(x) = p(t)\begin{array}{*{20}{c}}
{}&{(1)}
\end{array}\]$$
where g(x) is a continuously differentiable function of a $\[x \in R\]$, $\[xg(x) > 0\]$ whenever $\[x \ne 0\]$, and
$\[g(x)/x\]$ tends to $\[\infty \]$ as \[\left| x \right| \to \infty \]. Let p(t) be a bounded function of $\[t \in R\]$. Define its norm by
$\[\left\| p \right\| = {\sup _{t \in R}}\left| {p(t)} \right|\]$
The study of this note leads to the following conclusion which improves a result due to
J. E. Littlewood,
For any given small constants $\[\alpha > 0,s > 0\]$, there is a continuous and roughly periodic(with respect to $\[\Omega (\alpha )\]$) function p(t) with $\[\left\| p \right\| < s\]$ such that the corresponding equation (1)
has at least one unbounded solution. 相似文献
10.
Huang Xinzhong 《数学年刊B辑(英文版)》1986,7(2):139-146
Let S~* be the class of functionsf(z)analytic,univalent in the unit disk|z|<1 andmap|z|<1 onto a region which is starlike with respect to w=0 and is denoted as D_f.Letr_0=r_0(f)be the radius of convexity of f(2).In this note,the author proves the following result:(d_0/d~*)≥0.4101492,where d_0= f(z),d~*=|β|. 相似文献
11.
Consider initial value probiom v_t-u_x=0, u_t+p(v)_x=0, (E), v(x, 0)=v_0(x), u(x, 0)=u_0(x), (I), where A≥0, p(v)=K~2v~(-γ), K>0, 0<γ<3. As 0<γ≤1, the authors give a sufficient condition for that (E), (I) to have a unique global smooth solution, As 1≤γ<3, a necessary condition is given for that. 相似文献
12.
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
13.
To indicate precisely the requirements for smoothness of symbols,generalizations ofH(?)rmander's classes of symbols,S_(ρ,k(?),v)~m and S_(ρ,k(?),v(?))~m,are introduced.The main results areas follows:(1)An optimal L~2-boundedness result is obtained for the pseudo-differentialoperators with double symbols(amplitude)a(x,(?),y);(2)By means of the interpolationtheorem due to Fefferman and Stein,new L~p-boundedness results are established.Theseresults are not only sharp with respect to upper index,but also sharp(p≥2)or almost sharp(1
相似文献
14.
In this paper, the authors prove following result:Let M~n be a complete Bechner-Kaehler submanifold of complex dimension (n≥4) in a complex projective space CP~(n p)(1) of complex dimension n p, endowed with the FubiniStudy metric of constant holomorphic sectional curvature 1. If the sectional curvature K of M~n satisfies K<1, then codimension p of M~n is not less then n(n 1)/2. 相似文献
15.
Zhang Yongzheng 《数学年刊B辑(英文版)》1992,13(3):315-326
Let $K(n,\mu _j,m),n=2r+1$,denote the Lie algebra of characteristic p=2,which is defined in [4].In the paper the restrictability of $K(n,\mu _j,m)$ is discussed and it is proved that,when $r\equiv 1(mod 2)$ and $r>1,I(ad f)=n+1$ if and only if $0\neq f \in $. Then the invariance of some filtrations of K(n,\mu,m) and the condition of isomorphism of K(n,\mu _i,m) and K(n',\mu _j ^',m') are obtained.Besides,the generators and the derivation algebra of K(n,\mu _i,m) are discussed.The results also hold,when $r\equiv 0 (mod 2)$ and r>0. 相似文献
16.
The aim of this paper is to construct indecomposable positive definite Z-lattices withgiven rank n(2≤n≤9) and discriminant a,a being composite and square-free,but for afinite number of exceptions.And all exceptional cases for 3≤n≤9 are determined.Theseare unsettled cases of a paper of O’Meara in 1975. 相似文献
17.
Liang Zhaojun 《数学年刊B辑(英文版)》1984,5(1):37-42
In this paper, we consider the relative position of limit cycles for the system
$$\[\begin{array}{*{20}{c}}
{\frac{{dx}}{{dt}} = \delta x - y + mxy - {y^2}}\{\frac{{dy}}{{dt}} = x + a{x^2}}
\end{array}\]$$
under the condition
$$\[a < 0,0 < \delta \le m,m \le \frac{1}{a} - a\]$$
The main result is as follows:
(i)Under Condition (2), if $\[\delta = \frac{m}{2} + \frac{{{m^2}}}{{4a}} \equiv {\delta _0}\]$, then system $\[{(1)_{{\delta _0}}}\] $ has no limit cycles and
on singular closed trajectory through a saddle point in the whole plane,
(ii)Under condition (2), the foci 0 and R'' cannot be surrounded by the limit cycles of system (1) simultaneously. 相似文献
18.
Zhou Yi 《数学年刊B辑(英文版)》1993,14(2):225-236
The author studies the life span of classical solutions to the following Cauchy problem $\[B \simeq Ma{t_m}(kD)\]$,
$t=0:u=\epsilon\phi(x),u_t=\epsilon\psi(x),x\in R^2$
where $\phi,\psi\in C_0^\infinity(R^2)$ and not both identically zero,$\[\square = \partial _t^2 - \partial _1^2 - \partial _2^2,p \geqslant 2\]$ is a real number and $\epsilon > 0$ is a small parameter, and obtains respectively upper and lower bounds of the same order of magnitude for the life span for $2\leq p \leq p_0$, where $p_0$ is the positive root of the quadratic $X^2-3X-2=0$. 相似文献
19.
Zhan Tao 《数学年刊B辑(英文版)》1989,10(2):227-235
Let L(x) denote the number of square-full integers not exceeding x. It is proved in [1] thatL(x)~(ζ(3/2)/ζ(3))x~(1/2) (ζ(2/3)/ζ(2))x~(1/3) as x→∞,where ζ(s) denotes the Riemann zeta function. Let △(x) denote the error function in the asymptotic formula for L(x). It was shown by D. Suryanaryana~([2]) on the Riemann hypothesis (RH) that1/x integral from n=1 to x |△(t)|dt=O(x~(1/10 s))for every ε>0. In this paper the author proves the following asymptotic formula for the mean-value of △(x) under the assumption of R. H.integral from n=1 to T (△~2(t/t~(6/5))) dt~c log T,where c>0 is a constant. 相似文献
20.
Sun Xiehua 《数学年刊B辑(英文版)》1987,8(4):468-470
To answer the rest part of the problem of Boas R. P. on derivative of polynomial, it is shown that if $\[p(z)\]$ is a polynomial of degree n such that $\[\mathop {\max }\limits_{\left| z \right| \le 1} \left| {p(z)} \right| \le 1\]$ and $\[{p(z) \ne 0}\]$ in $\[\left| z \right| \le k,0 < k \le 1\]$, then $\[\left| {{p^''}(z)} \right| \le n/(1 + {k^n})\]$ for $\[\left| z \right| \le 1\]$. The above estimate is sharp and the equation holds for $\[p(z) = ({z^n} + {k^n})/(1 + {k^n})\]$. 相似文献