共查询到20条相似文献,搜索用时 78 毫秒
1.
一个实方阵A称为是S2NS阵,若所有与A有相同符号模式的矩阵均可逆,且它们的逆矩阵的符号模式都相同.若A是S2NS阵且A中任意一个零元换为任意非零元后所得的矩阵都不是S2NS阵,则称A是极大S2NS阵.设所有n阶极大S2NS阵的非零元个数所成之集合为S(n),Z4(n)={1/2n(n-1) 4,…,1/2n(n 1)-1},除了2n 1到3n一4间的一段和Z4(n)外,S(n)得到了完全确定.本文将用图论方法证明Z4(n)∩S(n)=(?). 相似文献
2.
Let T(n,R) be the Lie algebra consisting of all n × n upper triangular matrices over a commutative ring R with identity 1 and M be a 2-torsion free unital T(n,R)-bimodule.In this paper,we prove that every Lie triple derivation d : T(n,R) → M is the sum of a Jordan derivation and a central Lie triple derivation. 相似文献
3.
Let $D_n $ (${\cal O}_n$) be the semigroup of all finite order-decreasing (order-preserving) full transformations of an $n$-element chain, and let $D(n,r) = \{\alpha\in D_n: |\mbox{Im}\alpha| \leq r\}$ (${\cal C}(n,r) = D(n,r)\cap {\cal O}_n)$ be the two-sided ideal of $D_n $ ($D_n \cap {\cal O}_n$). Then it is shown that for $r \geq 2$, the Rees quotient semigroup $DP_r(n)= D(n,r) / D(n,r-1)$ (${\cal C}P_r(n)= {\cal C}(n,r)/{\cal C} (n,r-1)$) is an ${\cal R}$-trivial (${\cal J}$-trivial) idempotent-generated 0*-bisimple primitive abundant semigroup. The order of ${\cal C}P_r(n)$ is shown to be $1+ \left(\begin{array}{c} n-1 \\ r-1 \end{array} \right) \left(\begin{array}{c} n \\ r \end{array} \right)/(n-r+1)$. Finally, the rank and idempotent ranks of ${\cal C}P_r(n)\,(r<n)$ are both shown to be equal to $\left(\begin{array}{c} n-1 \\ r-1 \end{array} \right)$. 相似文献
4.
设$W_{\beta}(x)=\exp(-\frac{1}{2}|x|^{\beta})~(\beta > 7/6)$ 为Freud权, Freud正交多项式定义为满足下式$\int_{- \infty}^{\infty}p_{n}(x)p_{m}(x)W_{\beta}^{2}(x)\rd x=\left \{ \begin{array}{ll} 0 & \hspace{3mm} n \neq m , \\ 1 & \hspace{3mm}n = m \end{array} \right.$的 相似文献
5.
Green's Equivalences on Semigroups of Transformations Preserving Order and an Equivalence Relation 总被引:4,自引:0,他引:4
Let ${\cal T}_X$ be the full transformation semigroup on the set $X$,
\[
T_{E}(X)=\{f\in {\cal T}_X\colon \ \forall(a,b)\in E,(f(a),f(b))\in E\}
\]
be the subsemigroup of ${\cal T}_X$ determined by an equivalence
$E$ on $X$. In this paper the set $X$ under consideration is a
totally ordered set with $mn$ points where $m\geq 2$ and $n\geq
3$. The equivalence $E$ has $m$ classes each of which contains $n$
consecutive points. The set of all order preserving
transformations in $T_{E}(X)$ forms a subsemigroup of $T_E(X)$
denoted by
\[
{\cal O}_{E}(X)=\{f\in T_{E}(X)\colon \ \forall\, x, y\in X, \ x\leq
y \mbox{ implies } f(x)\leq f(y)\}.
\]
The nature of regular elements in ${\cal O}_{E}(X)$ is described
and the Green's equivalences on ${\cal O}_{E}(X)$ are
characterized completely. 相似文献
6.
Let $J$ be an infinite set and let $I={\cal P}_{f}( J)$, i.e., $I$ is the collection of all non empty finite subsets of $J$. Let $\beta I$ denote the collection of all ultrafilters on the set $I$. In this paper, we consider $( \beta I,\uplus ),$ the compact (Hausdorff) right topological semigroup that is the {\it Stone-$\check{C}\!\!$ech} $Compactification$ of the semigroup $\left( I,\cup \right)$ equipped with the discrete topology. It is shown that there is an injective map $A\rightarrow \beta _{A}( I) $ of ${\cal P}( J) $ into ${\cal P}( \beta I) $ such that each $\beta _{A}( I) $ is a closed subsemigroup of $ ( \beta I,\uplus ) $, the set $\beta _{J}( I) $ is a closed ideal of $( \beta I,\uplus ) $and the collection $\{ \beta _{A}( I) \mid A\in {\cal P} ( J) \} $ is a partition of $\beta I$. The algebraic structure of $\beta I$ is explored. In particular, it is shown that {\bf (1)} $\beta _{J}\left( I\right) =\overline{K( \beta I) }$, i.e., $\beta _{J}( I) $is the closure of the smallest ideal of $\beta I$, and {\bf (2)} for each non empty $A\subset J$, the set ${\cal V}_{A}=\tbigcup \{ \beta_{B}( I) \mid B\subset A\} $is a closed subsemigroup of $( \beta I,\uplus ) ,$ $\beta _{A}( I) $ is a proper ideal of ${\cal V}_{A},$ and ${\cal V}_{A}$ is the largest subsemigroup of $( \beta I,\uplus ) $ that has $ \beta _{A}( I) $ as an ideal. 相似文献
7.
Mihaly Kovacs 《Semigroup Forum》2005,71(3):462-470
For a generator $A$ of a $C_0$-semigroup $T(\cdot)$ on a Banach space $X$ we consider the semi-norm $M^{k}_x:=\limsup_{t\to
0+}\|t^{-1}(T(t)-I)A^{k-1}x\|$ on the Favard space ${\cal F}_{k}$ of order $k$ associated with $A$. The use of this semi-norm
is motivated by the functional analytic treatment of time-discretization methods of linear evolution equations. We show that
sharp inequalities for bounded linear operators on ${\cal D}(A^k)$ can be extended to the larger space ${\cal F}_{k}$ by using
the semi-norm $M^{k}_{(\cdot)}$. We also show that $M^{k}_{(\cdot)}$ is a norm equivalent to the norms that are usually considered
in the literature if A has a bounded inverse. 相似文献
8.
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
9.
Abstract In the present paper, some basic properties of MP filters of Ro algebra M are investigated. It is proved that(FMP(M),包含,′∧^-∨^-,{1},M)is a bounded distributive lattice by introducing the negation operator ′, the meet operator ∧^-, the join operator ∨^- and the implicati on operator → on the set FMP(M) of all MP filters of M. Moreover, some conditions under which (FMP(M),包含,′∨^-,→{1},M)is an Ro algebra are given. And the relationship between prime elements of FMP (M) and prime filters of M is studied. Finally, some equivalent characterizations of prime elements of .FMP (M) are obtained. 相似文献
10.
Let $P$ be a set of $n$ points in $\Re^d$. The {\em
radius} of a $k$-dimensional flat ${\cal F}$ with
respect to $P$, which we denote by ${\cal RD}({\cal F},P)$,
is defined to be $\max_{p \in P} \mathop{\rm dist}({\cal F},p)$, where
$\mathop{\rm dist}({\cal F},p)$ denotes the Euclidean distance between
$p$ and its projection onto ${\cal F}$. The $k$-flat
radius of $P$, which we denote by ${R^{\rm opt}_k}(P)$, is the
minimum, over all $k$-dimensional flats ${\cal F}$, of
${\cal RD}({\cal F},P)$. We consider the problem of
computing ${R^{\rm opt}_k}(P)$ for a given set of points $P$. We
are interested in the high-dimensional case where $d$ is
a part of the input and not a constant. This problem is
NP-hard even for $k = 1$. We present an algorithm that,
given $P$ and a parameter $0 < \eps \leq 1$, returns a
$k$-flat ${\cal F}$ such that ${\cal RD}({\cal F},P) \leq (1 +
\eps) {R^{\rm opt}_k}(P)$. The algorithm runs in $O(nd
C_{\eps,k})$ time, where $C_{\eps,k}$ is a constant that
depends only on $\eps$ and $k$. Thus the algorithm runs
in time linear in the size of the point set and is a
substantial improvement over previous known algorithms,
whose running time is of the order of $d
n^{O(k/\eps^c)}$, where $c$ is an appropriate constant. 相似文献
11.
12.
设$F$ 为域, $n\geq 3$, $\bf{N}$$(n,\mathbb{F})$ 为域$\mathbb{F}$ 上所有$n\times n$ 阶严格上三角矩阵构成的严格上三角矩阵李代数, 其李运算为$[x,y]=xy-yx$. $\bf{N}$$(n, \mathbb{F})$ 上一线性映射$\varphi$ 称为积零导子,如果由$[x,y]=0, x,y\in \bf{N}$$(n,\mathbb{F})$,总可推出 $[\varphi(x), y]+[x,\varphi(y)]=0$. 本文证明 $\bf{N}$$(n,\mathbb{F})$上一线性映射 $\varphi$ 为积零导子当且仅当 $\varphi$ 为$\bf{N}$$(n,\mathbb{F})$ 上内导子, 对角线导子, 极端导子, 中心导子和标量乘法的和. 相似文献
13.
Jianxun He 《Applicable analysis》2013,92(2):495-512
Let SL (2, C ) be the special linear group of 2 ‐ 2 complex matrices with determinant 1 and SU (2) its maximal compact subgroup. Then SL (2, C )/ SU (2) can be realized as the quaternionic upper half-plane $ {\cal H}^c $ . Let SL (2, C ) = NASU (2) be the Iwasawa decomposition and M the centerlizer of A in SU (2). Then P = NA and P a = NAM are the automorphism groups of $ {\cal H}^c $ . In this article, we define the unitary representations of P and P a on L 2 ( C , H ; dz ). From the viewpoint of square integrable group representations we discuss the wavelet transforms, and obtain the orthogonal direct sum decompositions for the function spaces $ L^2({\cal H}^c, \fraca {(dz\, d\rho)}{\rho ^3}) $ and $ L^2({\bf R}^2\times {\bf R}^2, \fraca {dx\, dy\, dx^{\prime }dy^{\prime }}{{({x^{\prime }}^2 + {y^{\prime }}^2)^{\fraca {3}{2}})}} $ . 相似文献
14.
Joseph A. Wolf 《Results in Mathematics》2001,40(1-4):321-338
Consider the set S(q, Γ) of isometry classes of q-dimensional spherical space forms whose fundamental groups are isomorphic to a fixed group Γ. We define a certain group ${\cal A}(q,\Gamma)$ of transformations on the finite set ${\cal S}(q,\Gamma)$ , prove that any two elements in the same ${\cal A}(q,\Gamma)$ -orbit are strongly isospectral, and study some consequences. Then a number of the results are carried over to riemannian quotients of oriented real Grassmann manifolds. Some of these results were first obtained by Ikeda, mostly for the special case (Γ cyclic) of lens spaces, and by Gilkey and Ikeda for the case where every Sylow subgroup of Γ is cyclic. 相似文献
15.
ON THE JOINT SPECTRUM FOR N-TUPLE OF HYPONORMAL OPERATORS 总被引:1,自引:0,他引:1
Let A=(A_1,…,A,)be an n-tuple of double commuting hyponormal operators.It is-proved that:1.The joint spectrum of A has a Cartesian decomposition:Re[Sp(A)]=S_p(ReA),Im[Sp(A)]=Sp(ImA);2.The.joint resolvent of A satisfies the growth condition:‖()‖=1/(dist(z,Sp(A)));3.If 0σ(A_i),i=1,2,…,n,then‖A‖=γ_(sp)(A). 相似文献
16.
We develop structural formulas
satisfied by some families of
orthogonal matrix polynomials of size $2\times 2$ satisfying
second-order differential equations with polynomial coefficients. We consider
here two one-parametric families of weight matrices,
namely
\[
H_{a,1}(t)\;=\;e^{-t^2} \left( \begin{array}{@{}cc@{}}
1+\vert a\vert ^2t^2 & at \\bar at & 1 \end{array} \right) \quad {\rm and} \quad H_{a,2}(t)\;=\;e^{-t^2} \left( \begin{array} {@{}cc@{}}
1+\vert a\vert ^2t^4 & at^2 \\bar at^2 & 1
\end{array} \right),
\]
$a\in \mbox{\bf C} $ and $t\in \mbox{\bf R} $, and their corresponding orthogonal
polynomials. 相似文献
17.
研究了正交g-模V上的Clifford代数C(V)的支配权,其中g-模C(V)是Kostant给出的旋模Spin(V)的倍数.设Δ(V)是V的非零权组成的集合.证明了Δ(V)任一正凸半的半和总是C(V)的一个支配权.反之,如果某一个半和是C(V)的重数为2(m_V(O)+dimV)/2的最高权,那么该半和一定是Δ(V)的某个正凸半的半和. 相似文献
18.
Ronald L. Graham Jeffrey C. Lagarias Colin L. Mallows Allan R. Wilks Catherine H. Yan 《Discrete and Computational Geometry》2006,35(1):37-72
This paper gives $n$-dimensional analogues of the Apollonian circle packings in Parts I and II. Those papers considered circle
packings described in terms of their Descartes configurations, which are sets of four mutually touching circles. They studied
packings that had integrality properties in terms of the curvatures and centers of the circles. Here we consider collections
of $n$-dimensional Descartes configurations, which consist of $n+2$ mutually touching spheres. We work in the space $M_D^n$
of all $n$-dimensional oriented Descartes configurations parametrized in a coordinate system, augmented curvature-center coordinates,
as those $(n+2) \times (n+2)$ real matrices $W$ with $W^T Q_{D,n} W = Q_{W,n}$ where $Q_{D,n} = x_1^2 + \cdots + x_{n+2}^2
- ({1}/{n})(x_1 +\cdots +
x_{n+2})^2$ is the $n$-dimensional Descartes quadratic form, $Q_{W,n} = -8x_1x_2 + 2x_3^2 + \cdots + 2x_{n+2}^2$, and $\bQ_{D,n}$
and $\bQ_{W,n}$ are their corresponding symmetric matrices. On the parameter space $M_D^n$
of augmented curvature-center matrices, the group ${\it Aut}(Q_{D,n})$ acts on the left and ${\it Aut}(Q_{W,n})$ acts on
the right. Both these groups are isomorphic to the $(n+2)$-dimensional Lorentz group $O(n+1,1)$, and give two
different "geometric" actions. The right action of ${\it Aut}(Q_{W,n})$
(essentially) corresponds to Mobius transformations acting on the underlying
Euclidean space $\rr^n$ while the left action of ${\it Aut}(Q_{D,n})$ is
defined only on the parameter space $M_D^n$. We introduce $n$-dimensional analogues of the Apollonian group, the dual Apollonian
group and the super-Apollonian group. These are finitely generated groups in ${\it Aut}(Q_{D,n})$, with
the following integrality properties: the dual Apollonian group consists of integral matrices in all dimensions, while the
other two consist of rational matrices, with denominators having prime divisors drawn from a finite set $S$ depending on the
dimension. We show that the Apollonian group and the dual Apollonian group are finitely presented, and are Coxeter groups.
We define an Apollonian cluster ensemble to be any orbit under the Apollonian group, with similar notions for the other two
groups. We determine in which dimensions there exist rational Apollonian cluster ensembles (all curvatures are rational) and
strongly rational Apollonian sphere ensembles (all augmented curvature-center coordinates are rational). 相似文献
19.
Given a function ψ in
the affine (wavelet) system generated by ψ, associated to an invertible matrix a and a lattice Γ, is the collection of functions
In this paper we prove that the set of functions generating affine systems that are a Riesz basis of
${\cal L}^2({\Bbb R}^d)$ is dense in We also prove that a stronger result is true for affine systems that are a frame of
In this case we show that the generators associated to a fixed but arbitrary dilation are a dense set. Furthermore, we analyze
the orthogonal case in which we prove that the set of generators of orthogonal (not necessarily complete) affine systems,
that are compactly supported in frequency, are dense in the unit sphere of
with the induced metric. As a byproduct we introduce the p-Grammian of a function and prove a convergence result of this
Grammian as a function of the lattice. This result gives insight in the problem of oversampling of affine systems. 相似文献
20.
Ronald L. Graham Jeffrey C. Lagarias Colin L. Mallows Allan R. Wilks Catherine H. Yan 《Discrete and Computational Geometry》2005,34(4):547-585
Apollonian circle packings arise by repeatedly filling the interstices
between four mutually tangent circles with further tangent circles.
We observe that there exist Apollonian packings which have strong integrality
properties, in which all circles in the packing have integer curvatures and
rational centers such that (curvature) $\times$ (center) is an integer vector. This series of papers explain such properties.
A Descartes configuration is a set of four mutually tangent circles with disjoint interiors. An Apollonian circle packing
can be described in terms of the Descartes configuration it contains. We describe the
space of all ordered, oriented Descartes configurations using a coordinate system $M_ D$ consisting of those $4 \times
4$ real matrices $W$ with $W^T Q_{D} \bW = Q_{W}$ where $Q_D$ is the matrix of the Descartes quadratic form $Q_D= x_1^2 +
x_2^2+ x_3^2 + x_4^2 - \frac{1}{2}(x_1 +x_2 +x_3 + x_4)^2$ and $Q_W$ of the quadratic form $Q_W = -8x_1x_2 + 2x_3^2 + 2x_4^2$.
On the parameter space
$M_ D$ the group $\mathop{\it Aut}(Q_D)$ acts on the left, and $\mathop{\it Aut}(Q_W)$ acts on the right, giving two different
"geometric" actions. Both these groups are isomorphic to the Lorentz group $O(3, 1)$. The right action of $\mathop{\it Aut}(Q_W)$
(essentially) corresponds to Mobius transformations acting on the underlying Euclidean space $\rr^2$ while the left action
of $\mathop{\it Aut}(Q_D)$ is defined only on the parameter space. We observe that
the Descartes configurations in each Apollonian packing form an orbit of a single Descartes configuration under a certain
finitely generated discrete subgroup of $\mathop{\it Aut}(Q_D)$, which we call the Apollonian group. This group consists
of $4 \times 4$ integer matrices, and its integrality properties lead to the integrality properties observed in some Apollonian
circle packings. We introduce two more related finitely generated groups in $\mathop{\it Aut}(Q_D)$, the dual Apollonian
group produced from the Apollonian group by a "duality" conjugation, and the super-Apollonian group which is the group generated
by the Apollonian and
dual Apollonian groups together. These groups also consist of integer $4 \times 4$ matrices. We show these groups are hyperbolic
Coxeter groups. 相似文献