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1.
《代数通讯》2013,41(9):2957-2975
ABSTRACT Let F m (N) be the free left nilpotent (of class two) Leibniz algebra of finite rank m, with m ≥ 2. We show that F m (N) has non-tame automorphisms and, for m ≥ 3, the automorphism group of F m (N) is generated by the tame automorphisms and one more non-tame IA-automorphism. Let F(N) be the free left nilpotent Leibniz algebra of rank greater than 1 and let G be an arbitrary non-trivial finite subgroup of the automorphism group of F(N). We prove that the fixed point subalgebra F(N) G is not finitely generated. 相似文献
2.
Let G be a permutation group acting on a set with N elements such that every permutation with more than m fixed points is the identity. It is easy to verify that |G| divides N(N − 1) ··· (N − m). We show that if gcd(|G|, m!) = 1, then |G| divides (N − i)(N − j) for some i and j satisfying 0 ≤ i < j ≤ m. We use this to show that any almost perfect 1-factorization of K2n has an automorphism group whose cardinality divides (2n − i)(2n − j) for some i and j with 0 ≤ i < j ≤ 2 as long as n is odd. An almost perfect 1-factorization (or APOF) is a 1-factorization in which the union of any three distinct 1-factors is connected. This result contrasts with an example of an APOF on K12 given by Cameron which has PSL(2, ℤ11) as its automorphism group [with cardinality 12(11)(5)]. When n is even and the automorphism group is solvable, we show that either G acts vertex transitively and n is a power of two, or |G| divides 2n − 2a for some integer a with 2a dividing 2n, or else |G| divides (2n − i)(2n − j) for some i and j with 0 ≤ i < j ≤ 2. We also give a number of structure results concerning these automorphism groups. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 355–380, 1998 相似文献
3.
4.
Alexander Katsevich 《Mathematische Nachrichten》2005,278(4):437-450
Consider the Poincare unit disk model for the hyperbolic plane H 2. Let Ξ be the set of all horocycles in H 2 parametrized by (θ, p), where eiθ is the point where a horocycle ξ is tangent to the boundary |z| = 1, and p is the hyperbolic distance from ξ to the origin. In this paper we invert the dual Radon transform R* : μ(θ, p) → (z) under the assumption of exponential decay of μ and some of its derivatives. The additional assumption is that Pm(d/dp)(μm(p)ep) be even for all m ∈ ?. Here Pm(d/dp) is a family of differential operators introduced by Helgason, and μm(p) are the coefficients of the Fourier series expansion of μ(θ, p). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
Let M be a closed Willmore hypersurface in the sphere S^n+1(1) (n ≥ 2) with the same mean curvature of the Willmore torus Wm,n-m, if SpecP(M) = Spec^P(Wm,n-m ) (p = 0, 1,2), then M is Wm,n-m. 相似文献
6.
Yehoram Gordon 《Israel Journal of Mathematics》1969,7(2):151-163
Given 1≦p<∞ and a real Banach spaceX, we define thep-absolutely summing constantμ
p(X) as inf{Σ
i
=1/m
|x*(x
i)|p
p Σ
i
=1/m
‖x
i‖p
p]1
p}, where the supremum ranges over {x*∈X*; ‖x*‖≤1} and the infimum is taken over all sets {x
1,x
2, …,x
m} ⊂X such that Σ
i
=1/m
‖x
i‖>0. It follows immediately from [2] thatμ
p(X)>0 if and only ifX is finite dimensional. In this paper we find the exact values ofμ
p(X) for various spaces, and obtain some asymptotic estimates ofμ
p(X) for general finite dimensional Banach spaces.
This is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof.
A. Dvoretzky and Prof. J. Lindenstrauss. 相似文献
7.
Let A be a commutative integral domain that is a finitely generated algebra over a field k of characteristic 0 and let ø be a k-algebra automorphism of A of finite order m. In this note we study the ring D(A;ø of differential operators introduced by A.D. Bell. We prove that if A is a free module over the fixed sub-ring A ø, with a basis containing 1, then D(A;ø) is isomorphic to the matrix ring Mm(D(A ø). It follows from Grothendieck's Generic Flatness Theorem that for an arbitrary A there is an element c?Asuch that D(A[c-1];ø)?M m(D(A[c-1]ø)). As an application, we consider the structure of D(A;ø)when A is a polynomial or Laurent polynomial ring over k and ø is a diagonalizable linear automorphism. 相似文献
8.
We prove that, given a countable groupG, the set of countable structures (for a suitable languageL)U
G
whose automorphism group is isomorphic toG is a complete coanalytic set and ifG ≄H thenU
G
is Borel inseparable fromU
H
. We give also a model theoretic interpretation of this result. We prove, in contrast, that the set of countable structures
forL whose automorphism group is isomorphic to ℤ
p
ℕ
,p a prime number, is Π
1
1
&σ
1
1
-complete. 相似文献
9.
We introduce a class of sparse matrices U m (A p 1 ) of order m by m, where m is a composite natural number, p 1 is a divisor of m, and A p 1 is a set of nonzero real numbers of length p 1. The construction of U m (A p 1 ) is achieved by iteration, involving repetitive dilation operations and block-matrix operations. We prove that the matrices U m (A p 1 ) are invertible and we compute the inverse matrix (U m (A p 1 ))?1 explicitly. We prove that each row of the inverse matrix (U m (A p 1 ))?1 has only two nonzero entries with alternative signs, located at specific positions, related to the divisors of m. We use the structural properties of the matrix (U m (A p 1 ))?1 in order to build a nonlinear estimator for prediction of nearly periodic time series of length m with fixed period. 相似文献
10.
Let A be a finitely generated abelian group. We describe the automorphism group Aut(A) using the rank of A and its torsion part p-part A
p
.
For a finite abelian p-group A of type (k
1, ..., k
n
), simple necessary and sufficient conditions for an n × n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k
1, k
2) is analyzed.
This work has begin during the visit of the second author to the Faculty of Mathematics and Computer Science, Nicolaus Copernicus
University during the period July 31–August 13, 2005. This visit was supported by the Nicolaus Copernicus University and a
grant from Cnpq. 相似文献
11.
Ameer Athavale 《Integral Equations and Operator Theory》2010,68(2):255-262
We consider an important class of subnormal operator m-tuples M
p
(p = m,m + 1, . . .) that is associated with a class of reproducing kernel Hilbert spaces Hp{{\mathcal H}_p} (with M
m
being the multiplication tuple on the Hardy space of the open unit ball
\mathbb B2m{{\mathbb B}^{2m}} in
\mathbb Cm{{\mathbb C}^m} and M
m+1 being the multiplication tuple on the Bergman space of
\mathbb B2m{{\mathbb B}^{2m}}). Given any two C*-algebras A{\mathcal A} and B{\mathcal B} from the collection {C*(Mp), C*([(M)\tilde]p): p 3 m}{\{C^*({M}_p), C^*({\tilde M}_p): p \geq m\}} , where C*(M
p
) is the unital C*-algebra generated by M
p
and C*([(M)\tilde]p){C^*({\tilde M}_p)} the unital C*-algebra generated by the dual [(M)\tilde]p{{\tilde M}_p} of M
p
, we verify that A{\mathcal A} and B{\mathcal B} are either *-isomorphic or that there is no homotopy equivalence between A{\mathcal A} and B{\mathcal B} . For example, while C*(M
m
) and C*(M
m+1) are well-known to be *-isomorphic, we find that C*([(M)\tilde]m){C^*({\tilde M}_m)} and C*([(M)\tilde]m+1){C^*({\tilde M}_{m+1})} are not even homotopy equivalent; on the other hand, C*(M
m
) and C*([(M)\tilde]m){C^*({\tilde M}_{m})} are indeed *-isomorphic. Our arguments rely on the BDF-theory and K-theory. 相似文献
12.
Let G be a finite group and π(G) be the set of all prime divisors of its order. The prime graph GK(G) of G is a simple graph with vertex set π(G), and two distinct primes p, q ∈ π(G) are adjacent by an edge if and only if G has an element of order pq. For a vertex p ∈ π(G), the degree of p is denoted by deg(p) and as usual is the number of distinct vertices joined to p. If π(G) = {p
1, p
2,...,p
k
}, where p
1 < p
2 < ... < p
k
, then the degree pattern of G is defined by D(G) = (deg(p
1), deg(p
2),...,deg(p
k
)). The group G is called k-fold OD-characterizable if there exist exactly k non-isomorphic groups H satisfying conditions |H| = |G| and D(H) = D(G). In addition, a 1-fold OD-characterizable group is simply called OD-characterizable. In the present article, we show that
the alternating group A
22 is OD-characterizable. We also show that the automorphism groups of the alternating groups A
16 and A
22, i.e., the symmetric groups S
16 and S
22 are 3-fold OD-characterizable. It is worth mentioning that the prime graph associated to all these groups are connected. 相似文献
13.
DuBeiliang 《高校应用数学学报(英文版)》2001,16(2):107-110
Abstract. In this paper, it is shown that a sufficient condition for the existence of a 相似文献
14.
Michael J. Johnson 《Constructive Approximation》2004,20(2):303-324
We show that the Lp-approximation order of surface spline interpolation
equals m+1/p for p in the range 1 \leq p \leq 2, where m is an integer
parameter which specifies the surface spline. Previously it was known that this
order was bounded below by m + &frac; and above by m+1/p. With
h denoting the fill-distance between the interpolation points and the domain
, we show specifically that the Lp()-norm of the error between f
and its surface spline interpolant is O(hm + 1/p) provided that f belongs
to an appropriate Sobolev or Besov space and that \subset
Rd is open, bounded, and has the C2m-regularity
property. We also show that the boundary effects (which cause the rate of
convergence to be significantly worse than O(h2m)) are confined to a
boundary layer whose width is no larger than a constant multiple of
h |log h|. Finally, we state numerical evidence which supports the
conjecture that the
Lp-approximation order of surface spline interpolation is m + 1/p for
2 < p \leq \infty. 相似文献
15.
G.J. Lovegrove 《Journal of Algebraic Combinatorics》2003,18(3):159-170
The automorphism group of the Steiner triple system of order v 3 (mod 6), obtained from the Bose construction using any Abelian Group G of order 2s + 1, is determined. The main result is that if G is not isomorphic to Z
3
n
× Z
9
m
, n 0, m 0, the full automorphism group is isomorphic to Hol(G) × Z
3, where Hol(G) is the Holomorph of G. If G is isomorphic to Z
3
n
× Z
9
m
, further automorphisms occur, and these are described in full. 相似文献
16.
On Hua-Tuan’s conjecture 总被引:2,自引:0,他引:2
Let G be a finite group and |G| = pn, p be a prime. For 0 m n, sm(G) denotes the number of subgroups of of order pm of G. Loo-Keng Hua and Hsio-Fu Tuan have ever conjectured: for an arbitrary finite p-group G, if p > 2, then sm(G) ≡ 1, 1 + p, 1 + p + p2 or 1 + p + 2p2 (mod p3). In this paper, we investigate the conjecture, and give some p-groups in which the conjecture holds and some examples in which the conjecture does not hold. 相似文献
17.
In this article, the authors establish the conditions for the extinction of solutions, in finite time, of the fast diffusive polytropic filtration equation u t ?=?div(|?u m | p?2?u m )?+?a∫Ω u q (y,?t)dy with a, q, m?>?0, p?>?1, m(p???1)?1, in a bounded domain Ω???R N (N?>?2). More precisely speaking, it is shown that if q?>?m(p???1), any non-negative solution with small initial data vanishes in finite time, and if 0?q?m(p???1), there exists a solution which is positive in Ω for all t?>?0. For the critical case q?=?m(p???1), whether the solutions vanish in finite time or not depends on the comparison between a and μ, where μ?=?∫?Ωφ p?1(x)dx and φ is the unique positive solution of the elliptic problem ?div(|?φ| p?2?φ)?=?1, x?∈?Ω; φ(x)?=?0, x?∈??Ω. 相似文献
18.
In this paper we either prove the non‐existence or give explicit construction of primitive symmetric (v, k, λ) designs with v=pm<2500, p prime and m>1. The method of design construction is based on an automorphism group action; non‐existence results additionally include the theory of difference sets, multiplier theorems in particular. The research involves programming and wide‐range computations. We make use of software package GAP and the library of primitive groups which it contains. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 141–154, 2010 相似文献
19.
Klaus Pinn 《Complexity》1999,4(3):41-46
A number of observations are made on Hofstadter's integer sequence defined by Q(n) = Q(n − Q(n − 1)) + Q(n − Q(n − 2)), for n > 2, and Q(1) = Q(2) = 1. On short scales, the sequence looks chaotic. It turns out, however, that the Q(n) can be grouped into a sequence of generations. The k‐th generation has 2k members that have “parents” mostly in generation k − 1 and a few from generation k − 2. In this sense, the sequence becomes Fibonacci type on a logarithmic scale. The variance of S(n) = Q(n) − n/2, averaged over generations, is ≅2αk, with exponent α = 0.88(1). The probability distribution p*(x) of x = R(n) = S(n)/nα, n ≫ 1, is well defined and strongly non‐Gaussian, with tails well described by the error function erfc. The probability distribution of xm = R(n) − R(n − m) is given by pm(xm) = λm p*(xm/λm), with λm → √2 for large m. © 1999 John Wiley & Sons, Inc. 相似文献
20.
Suppose that AmLp(D,) is the space of all m-analytic functions on the disk D={z:|z| < 1} which are pth power integrable over area with the weight (1-|z|2), > -1. In the paper, we introduce subspaces AkLp
0(D,), k=1,2,...,m, of the space A
mLp(D,) and prove that A
mLp(D,) is the direct sum of these subspaces. These results are used to obtain growth estimates of derivatives of polyanalytic functions near the boundary of arbitrary domains. 相似文献