共查询到20条相似文献,搜索用时 875 毫秒
1.
David J. Grynkiewicz 《Combinatorica》2006,26(4):445-453
An n-set partition of a sequence S is a collection of n nonempty subsequences of S, pairwise disjoint as sequences, such that every term of S belongs to exactly one of the subsequences, and the terms in each subsequence are all distinct so that they can be considered
as sets. If S is a sequence of m+n−1 elements from a finite abelian group G of order m and exponent k, and if
is a sequence of integers whose sum is zero modulo k, then there exists a rearranged subsequence
of S such that
. This extends the Erdős–Ginzburg–Ziv Theorem, which is the case when m = n and wi = 1 for all i, and confirms a conjecture of Y. Caro. Furthermore, we in part verify a related conjecture of Y. Hamidoune, by showing that
if S has an n-set partition A=A1, . . .,An such that |wiAi| = |Ai| for all i, then there exists a nontrivial subgroup H of G and an n-set partition A′ =A′1, . . .,A′n of S such that
and
for all i, where wiAi={wiai |ai∈Ai}. 相似文献
2.
C. M. Reidys 《Annals of Combinatorics》2006,10(4):481-498
In this paper we study sequential dynamical systems (SDS) over words. An SDS is a triple consisting of: (a) a graph Y with vertex set {v1, ..., vn}, (b) a family of Y-local functions
, where K is a finite field and (c) a word w, i.e., a family (w1, ..., wk), where wi is a Y-vertex. A map
is called Y-local if and only if it fixes all variables
and depends exclusively on the variables
, for
. An SDS induces an SDS- map,
, obtained by the map-composition of the functions
according to w. We show that an SDS induces in addition the graph G(w,Y) having vertex set {1, ..., k} where r, s are adjacent if and only if ws, wr are adjacent in Y. G(w, Y) is acted upon by Sk via
and Fix(w) is the group of G(w, Y) graph automorphisms which fix w. We analyze G(w, Y)-automorphisms via an exact sequence involving the normalizer of Fix(w) in Aut(G(w, Y)), Fix(w) and Aut(Y). Furthermore we introduce an equivalence relation over words and prove a bijection between word equivalence classes and
certain orbits of acyclic orientations of G(w, Y).
Received September 12, 2004 相似文献
3.
Noriko Mizoguchi 《Mathematische Annalen》2007,339(4):839-877
A solution u of a Cauchy problem for a semilinear heat equation
is said to undergo Type II blowup at t = T if lim sup Let be the radially symmetric singular steady state. Suppose that is a radially symmetric function such that and (u
0)
t
change sign at most finitely many times. We determine the exact blowup rate of Type II blowup solution with initial data
u
0 in the case of p > p
L
, where p
L
is the Lepin exponent. 相似文献
4.
Using the bicomplex numbers
which is a commutative ring with zero divisors defined by
where i12 = − 1, i22 = − 1, j2 = 1 and i1i2 = j = i2i1, we construct hyperbolic and bicomplex Hilbert spaces. Linear functionals and dual spaces are considered on these spaces
and properties of linear operators are obtained; in particular it is established that the eigenvalues of a bicomplex self-adjoint
operator are in the set of hyperbolic numbers. 相似文献
5.
Let (,G, U) be a continuous representation of a Lie groupG by bounded operatorsg U (g) on the Banach space and let (,
,dU) denote the representation of the Lie algebra
obtained by differentiation. Ifa
1, ...,a
d
is a Lie algebra basis of
,A
i
=dU (a
i
) and
whenever =(i
1, ...,i
k
) we reconsider the operators
相似文献
6.
Kin Ming Hui 《Mathematische Annalen》2007,339(2):395-443
We prove the existence of a unique solution of the following Neumann problem , u > 0, in (a, b) × (0, T), u(x, 0) = u
0(x) ≥ 0 in (a, b), and , where if m < 0, if m = 0, and
m≤ 0, , and the case −1 < m ≤ 0, , for some constant p > 1 − m. We also obtain a similar result in higher dimensions. As a corollary we will give a new proof of a result of A. Rodriguez
and J.L. Vazquez on the existence of infinitely many finite mass solutions of the above equation in for any −1 < m ≤ 0. We also obtain the exact decay rate of the solution at infinity. 相似文献
7.
8.
We propose new formulas for eigenvectors of the Gaudin model in the sl(3) case. The central point of the construction is the
explicit form of some operator P, which is used for derivation of eigenvalues given by the formula
9.
For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator
10.
I. Kiguradze 《Georgian Mathematical Journal》1994,1(5):487-494
The properties of solutions of the equationu″(t) =p
1(t)u(τ1(t)) +p
2(t)u′(τ2(t)) are investigated wherep
i
:a, + ∞[→R (i=1,2) are locally summable functions τ1 :a, + ∞[→R is a measurable function, and τ2 :a, + ∞[→R is a nondecreasing locally absolutely continuous function. Moreover, τ
i
(t) ≥t (i = 1,2),p
1(t)≥0,p
2
2
(t) ≤ (4 - ɛ)τ
2
′
(t)p
1(t), ɛ =const > 0 and
. In particular, it is proved that solutions whose derivatives are square integrable on [α,+∞] form a one-dimensional linear
space and for any such solution to vanish at infinity it is necessary and sufficient that
. 相似文献
11.
We are interested in parabolic problems with L1 data of the type
12.
J. Tervo 《Aequationes Mathematicae》1990,40(1):201-234
The paper deals with the minimal and the maximal realizations (L
w
)~ and (L
w
):L
2L
2 of linear operators of Weyl type
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