共查询到20条相似文献,搜索用时 421 毫秒
1.
Amitai Regev 《Israel Journal of Mathematics》1999,113(1):15-28
The numbers
% MathType!End!2!1!, λ ⊢n appear in the enumeration of various objects, as well as coefficients inS
nrepresentations associated with products of higher commutators. We study their asymptotics asn→∞ and show that if (λ1, λ2, …)≈(α
1,α
2, …)n, if (λ′1, λ′2, …)≈(β
1,β
2, …)n and ifγ=1− Σ
k⩽1(α
k⩽1+β
k⩽1), then
% MathType!End!2!1!.
Work partially supported by N.S.F. Grant No. DMS 94-01197. 相似文献
2.
V. M. Prokip 《Ukrainian Mathematical Journal》2012,63(8):1314-1320
Polynomial n × n matrices A(x) and B(x) over a field
\mathbbF \mathbb{F} are called semiscalar equivalent if there exist a nonsingular n × n matrix P over
\mathbbF \mathbb{F} and an invertible n × n matrix Q(x) over
\mathbbF \mathbb{F} [x] such that A(x) = PB(x)Q(x). We give a canonical form with respect to semiscalar equivalence for a matrix pencil A(x) = A
0x
- A
1, where A
0 and A
1 are n × n matrices over
\mathbbF \mathbb{F} , and A
0 is nonsingular. 相似文献
3.
The additive subgroup generated by a polynomial 总被引:3,自引:0,他引:3
C. -L. Chuang 《Israel Journal of Mathematics》1987,59(1):98-106
SupposeR is a prime ring with the centerZ and the extended centroidC. Letp(x
1, …,x
n) be a polynomial overC in noncommuting variablesx
1, …,x
n. LetI be a nonzero ideal ofR andA be the additive subgroup ofRC generated by {p(a
1, …,a
n):a
1, …,a
n ∈I}. Then eitherp(x
1, …,x
n) is central valued orA contains a noncentral Lie ideal ofR except in the only one case whereR is the ring of all 2 × 2 matrices over GF(2), the integers mod 2. 相似文献
4.
Let {S
n
, n=0, 1, 2, …} be a random walk (S
n
being thenth partial sum of a sequence of independent, identically distributed, random variables) with values inE
d
, thed-dimensional integer lattice. Letf
n
=Prob {S
1 ≠ 0, …,S
n
−1 ≠ 0,S
n
=0 |S
0=0}. The random walk is said to be transient if
and strongly transient if
. LetR
n
=cardinality of the set {S
0,S
1, …,S
n
}. It is shown that for a strongly transient random walk with p<1, the distribution of [R
n
−np]/σ √n converges to the normal distribution with mean 0 and variance 1 asn tends to infinity, where σ is an appropriate positive constant. The other main result concerns the “capacity” of {S
0, …,S
n
}. For a finite setA inE
d
, let C(A=Σ
x∈A
) Prob {S
n
∉A, n≧1 |S
0=x} be the capacity ofA. A strong law forC{S
0, …,S
n
} is proved for a transient random walk, and some related questions are also considered.
This research was partially supported by the National Science Foundation. 相似文献
5.
Morris Newman 《Linear and Multilinear Algebra》2013,61(4):363-366
Let Rbe a principal ideal ringRn the ring of n× nmatrices over R, and dk (A) the kth determinantal divisor of Afor 1 ? k? n, where Ais any element of Rn , It is shown that if A,BεRn , det(A) det(B:) ≠ 0, then dk (AB) ≡ 0 mod dk (A) dk (B). If in addition (det(A), det(B)) = 1, then it is also shown that dk (AB) = dk (A) dk (B). This provides a new proof of the multiplicativity of the Smith normal form for matrices with relatively prime determinants. 相似文献
6.
LetK be a field, charK=0 andM
n
(K) the algebra ofn×n matrices overK. If λ=(λ1,…,λ
m
) andμ=(μ
1,…,μ
m
) are partitions ofn
2 let
wherex
1,…,x
n
2,y
1,…,y
n
2 are noncommuting indeterminates andS
n
2 is the symmetric group of degreen
2.
The polynomialsF
λ, μ
, when evaluated inM
n
(K), take central values and we study the problem of classifying those partitions λ,μ for whichF
λ, μ
is a central polynomial (not a polynomial identity) forM
n
(K).
We give a formula that allows us to evaluateF
λ, μ
inM(K) in general and we prove that if λ andμ are not both derived in a suitable way from the partition δ=(1, 3,…, 2n−3, 2n−1), thenF
λ, μ
is a polynomial identity forM
n
(K). As an application, we exhibit a new class of central polynomials forM
n
(K).
In memory of Shimshon Amitsur
Research supported by a grant from MURST of Italy. 相似文献
7.
V. V. Makeev 《Journal of Mathematical Sciences》2011,175(5):572-573
Let X be an affine cross-polytope, i.e., the convex hull of n segments A
1
B
1,…, A
n
B
n
in
\mathbbRn {\mathbb{R}^n} that have a common midpoint O and do not lie in a hyperplane. The affine flag F(X) of X is the chain O ∈ L
1 ⊂⋯ ⊂ L
n
=
\mathbbRn {\mathbb{R}^n} , where L
k
is the k-dimensional affine hull of the segments A
1
B
1,…, A
k
B
k
, k ≤ n. It is proved that each convex body K ⊂
\mathbbRn {\mathbb{R}^n} is circumscribed about an affine cross-polytope X such that the flag F(X) satisfies the following condition for each k ∈{2,…, n}:the (k−1)-planes of support at A
k
and B
k
to the body L
k
∩ K in the k-plane L
k
are parallel to L
k
−1.Each such X has volume at least V(K)/2
n(n−1)/2. Bibliography: 5 titles. 相似文献
8.
Let A , B be two unital C*-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h : A → B which satisfies h(2 n uy) = h(2 n u)h(y) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2, … , is a homomorphism. Also, we establish the generalized Hyers-Ulam-Rassias stability of *-homomorphisms on unital C*-algebras. 相似文献
9.
Let A and B denote two families of subsets of an n-element set. The pair (A,B) is said to be ℓ-cross-intersecting iff |A∩B|=ℓ for all A∈ A and B∈B. Denote by P
e
(n) the maximum value of |A||B| over all such pairs. The best known upper bound on P
e
(n) is Θ(2
n
), by Frankl and R?dl. For a lower bound, Ahlswede, Cai and Zhang showed, for all n ≥ 2ℓ, a simple construction of an ℓ-cross-intersecting pair (A,B) with |A||B| = $
\left( {{*{20}c}
{2\ell } \\
\ell \\
} \right)
$
\left( {\begin{array}{*{20}c}
{2\ell } \\
\ell \\
\end{array} } \right)
2
n−2ℓ
= Θ(2
n
/$
\sqrt \ell
$
\sqrt \ell
), and conjectured that this is best possible. Consequently, Sgall asked whether or not P
e
(n) decreases with ℓ. 相似文献
10.
We consider the system $$ \dot x = A\left( \cdot \right)x + B\left( \cdot \right)u, u = S\left( \cdot \right)x, t \geqslant t_0 , $$ where A(·) ∈ ? n×n , B(·) ? n×p , and S(·) ∈ ? p×n . The entries of matrices A(·), B(·), and S(·) are arbitrary bounded functionals. We consider the problem of constructing a matrix H > 0 and finding relations between the entries of the matrices B(·) and S(·) such that for a given constant matrix R the inequality $$ V\left( {x\left( t \right)} \right) < V\left( {x\left( {t_0 } \right)} \right) + \int\limits_{t_0 }^t {x*\left( \tau \right)Rx\left( \tau \right)d\tau ,} $$ where V(x) = x*Hx, is satisfied. This problem is solved for the cases where matrix A(·) has p sign-definite entries on the upper part of some subdiagonal or on the lower part of some superdiagonal. It is assumed also that all entries located to the left (or to the right) of the sign-definite entries are equal to zero. 相似文献
11.
Harri Nyrhinen 《Journal of Theoretical Probability》2009,22(1):1-17
Let {S
n
;n=1,2,…} be a random walk in R
d
and E(S
1)=(μ
1,…,μ
d
). Let a
j
>μ
j
for j=1,…,d and A=(a
1,∞)×⋅⋅⋅×(a
d
,∞). We are interested in the probability P(S
n
/n∈A) for large n in the case where the components of S
1 are heavy tailed. An objective is to associate an exact power with the aforementioned probability. We also derive sharper
asymptotic bounds for the probability and show that in essence, the occurrence of the event {S
n
/n∈A} is caused by large single increments of the components in a specific way.
相似文献
12.
For given 2n×2n matricesS
13,S
24 with rank(S
13,S
24)=2n
we consider the eigenvalue problem:u′=A(x)u+B(x)v,v′=C
1(x;λ)u-A
T(x)v with
相似文献
13.
Mohamed Ali Toumi 《Czechoslovak Mathematical Journal》2010,60(1):85-94
Let A and B be two Archimedean vector lattices and let (A′)′
n
and (B′)′
n
be their order continuous order biduals. If Ψ: A × A → B is a positive orthosymmetric bimorphism, then the triadjoint Ψ***: (A′)′
n
× (A′)′
n
→ (B′)′
n
of Ψ is inevitably orthosymmetric. This leads to a new and short proof of the commutativity of almost f-algebras. 相似文献
14.
LetA=(A
1,...,A
n
),B=(B
1,...,B
n
)εL(ℓ
p
)
n
be arbitraryn-tuples of bounded linear operators on (ℓ
p
), with 1<p<∞. The paper establishes strong rigidity properties of the corresponding elementary operators ε
a,b
on the Calkin algebraC(ℓ
p
)≡L(ℓ
p
)/K(ℓ
p
);
, where quotient elements are denoted bys=S+K(ℓ
p
) forSεL(ℓ
p
). It is shown among other results that the kernel Ker(ε
a,b
) is a non-separable subspace ofC(ℓ
p
) whenever ε
a,b
fails to be one-one, while the quotient
is non-separable whenever ε
a,b
fails to be onto. These results extend earlier ones in several directions: neither of the subsets {A
1,...,A
n
}, {B
1,...,B
n
} needs to consist of commuting operators, and the results apply to other spaces apart from Hilbert spaces.
Supported by the Academy of Finland, Project 32837. 相似文献
15.
J. C. Gupta 《Proceedings Mathematical Sciences》2000,110(4):415-430
Let G
n,k
be the set of all partial completely monotone multisequences of ordern and degreek, i.e., multisequencesc
n(β1,β2,…, β
k
), β1,β2,…, βk
= 0,1,2,…, β1+β2 + … +β
k
≤n,c
n(0,0,…, 0) = 1 and
whenever β0 ≤n - (β1 + β2 + … + β
k
) where Δc
n(β1,β2,…, β
k
) =c
n(β1 + 1, β2,…, β
k
)+c
n(β1,β2+1,…, β
k
)+…+c
n (β1,β2,…, β
k
+1) -c
n(β1,β2,…, β
k
). Further, let Π
n,k
be the set of all symmetric probabilities on {0,1,2,…,k}
n
. We establish a one-to-one correspondence between the sets G
n,k
and Π
n,k
and use it to formulate and answer interesting questions about both. Assigning to G
n,k
the uniform probability measure, we show that, asn→∞, any fixed section {it{cn}(β1,β2,…, β
k
), 1 ≤ Σβ
i
≤m}, properly centered and normalized, is asymptotically multivariate normal. That is,
converges weakly to MVN[0, Σ
m
]; the centering constantsc
0(β1, β2,…, β
k
) and the asymptotic covariances depend on the moments of the Dirichlet (1, 1,…, 1; 1) distribution on the standard simplex
inR
k. 相似文献
16.
Let A and B be Banach function algebras on compact Hausdorff spaces X and Y and let ‖.‖
X
and ‖.‖
Y
denote the supremum norms on X and Y, respectively. We first establish a result concerning a surjective map T between particular subsets of the uniform closures of A and B, preserving multiplicatively the norm, i.e. ‖Tf Tg‖
Y
= ‖fg‖
X
, for certain elements f and g in the domain. Then we show that if α ∈ ℂ {0} and T: A → B is a surjective, not necessarily linear, map satisfying ‖fg + α‖
X
= ‖Tf Tg + α‖
Y
, f,g ∈ A, then T is injective and there exist a homeomorphism φ: c(B) → c(A) between the Choquet boundaries of B and A, an invertible element η ∈ B with η(Y) ⊆ {1, −1} and a clopen subset K of c(B) such that for each f ∈ A,
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