共查询到20条相似文献,搜索用时 46 毫秒
1.
Ioannis Kontoyiannis 《Journal of Theoretical Probability》1998,11(3):795-811
Let
be a discrete-valued stationary ergodic process distributed according to P and let x=(..., x
–1, x
0, x
1,...) denote a realization from X. We investigate the asymptotic behavior of the recurrence time R
n defined as the first time that the initial n-block
reappears in the past of x. We identify an associated random walk,
on the same probability space as X, and we prove a strong approximation theorem between log R
n and
. From this we deduce an almost sure invariance principle for log R
n. As a byproduct of our analysis we get unified proofs for several recent results that were previously established using methods from ergodic theory, the theory of Poisson approximation and the analysis of random trees. Similar results are proved for the waiting time W
n defined as the first time until the initial n-block from one realization first appears in an independent realization generated by the same (or by a different) process. 相似文献
2.
Let S = x
1,...,x
n} be a finite subset of a partially ordered set P. Let f be an incidence function of P. Let
denote the n × n matrix having f evaluated at the meet
of x
i and x
j as its i, j-entry and
denote the n × n matrix having f evaluated at the join
of x
i and x
j as its i, j-entry. The set S is said to be meet-closed if
for all 1 i, j n. In this paper we get explicit combinatorial formulas for the determinants of matrices
and
on any meet-closed set S. We also obtain necessary and sufficient conditions for the matrices
and
on any meet-closed set S to be nonsingular. Finally, we give some number-theoretic applications. 相似文献
3.
The N-commutator
is conjecturally a well-defined nontrivial operation on
for x =
(x
1, ... ,
x
n
)
if and only if N =
n
2 +
2n - 2. This is
proved for n = 2 and confirmed by
computer experiments for n < 5.
Under 2- and 5-commutators the algebra of divergence-free
vector fields in two dimensions is an sh-Lie (strong homotopic
Lie) algebra in the sense of Stasheff. Similarly,
W(2) is an
sh-Lie algebra with respect to 2- and 6-commutators. 相似文献
4.
Wu Zhende 《数学学报(英文版)》1989,5(4):302-306
In this paper, we determine the groups
(k
i
are odd),
(k
i
are odd and
(k
i
are even andn>k
l
),
(k
i
are even andn>k
l
),
(k
i
are even andn>k
l
,k
l
12),J
n
1,2,J
n
2,3,J
n
1,4. And we obtain the relation Im
n
k
=J
n
l,k
. 相似文献
5.
A set of codewords isfix-free if it is both prefix-free and suffix-free: no codeword in the set is a prefix or a suffix of any other. A set of codewords {x
1,x
2,...,x
n
} over at-letter alphabet is said to becomplete if it satisfies the Kraft inequality with equality, so that
相似文献
6.
A. A. Shcherbakov 《Mathematical Notes》1977,22(6):948-953
It is proved that
, where U(a, r) is the ball of radius r with center at the pointa, is the smallest closed convex set containing the kernel of any sequence {yn} obtained from the sequence {xn} by means of a regular transformation (cnk) satisfying the condition
, where x, xn, cnk (n, k=1, 2,...) are complex numbers.Traslated from Matematicheskie Zametki, Vol. 22, No. 6, pp. 815–823, December, 1977. 相似文献
7.
In this paper, using the generalized Wronskian, we obtain a new sharp
bound for the generalized Masons theorem [1] for functions of several variables.
We also show that the Diophantine equation (The generalized Fermat-Catalan equation)
where
, such that k out of the
n-polynomials
are constant, and
under certain conditions for
has no non-constant solution.
Received: 20 March 2003 相似文献
8.
E. V. Podsypanin 《Journal of Mathematical Sciences》1979,11(2):306-311
A system of Diophantine equations is considered for integers n1,...,2, $$\phi ^{\left( k \right)} \left( {x_1 , \ldots ,x_s } \right) = n_k \left( {k = 1, \ldots ,2} \right)$$ , Ф(k)(x1,...,xs)=nk (k=1,...,ρ), where Ф(k) are integral forms of degree d is s variables. The singular integral and singular series of this problem are investigated. 相似文献
9.
E.E. Allen 《Journal of Algebraic Combinatorics》1994,3(1):5-16
Let R(X) = Q[x
1, x
2, ..., x
n] be the ring of polynomials in the variables X = {x
1, x
2, ..., x
n} and R*(X) denote the quotient of R(X) by the ideal generated by the elementary symmetric functions. Given a S
n, we let g
In the late 1970s I. Gessel conjectured that these monomials, called the descent monomials, are a basis for R*(X). Actually, this result was known to Steinberg [10]. A. Garsia showed how it could be derived from the theory of Stanley-Reisner Rings [3]. Now let R(X, Y) denote the ring of polynomials in the variables X = {x
1, x
2, ..., x
n} and Y = {y
1, y
2, ..., y
n}. The diagonal action of S
n on polynomial P(X, Y) is defined as
Let R
(X, Y) be the subring of R(X, Y) which is invariant under the diagonal action. Let R
*(X, Y) denote the quotient of R
(X, Y) by the ideal generated by the elementary symmetric functions in X and the elementary symmetric functions in Y. Recently, A. Garsia in [4] and V. Reiner in [8] showed that a collection of polynomials closely related to the descent monomials are a basis for R
*(X, Y). In this paper, the author gives elementary proofs of both theorems by constructing algorithms that show how to expand elements of R*(X) and R
*(X, Y) in terms of their respective bases. 相似文献
10.
The N-heap Wythoffs game is a two-player impartial game with
N piles of tokens of sizes
Players take turns removing any number of tokens from a single pile, or removing
(a1,..., aN)
from all piles - ai tokens from the i-th pile,
providing that
where is the nim addition. The first player that cannot make a move loses. Denote all the
P-positions (i.e., losing positions) by
Two conjectures were proposed on the game by Fraenkel [7]. When
are fixed, i) there exists an integer N1
such that when
. ii) there exist integers N2
and _2 such that when
, the golden section.In this paper, we provide a sufficient condition for the conjectures to hold, and subsequently
prove them for the three-heap Wythoffs game with the first piles having up to 10 tokens.AMS Subject Classification: 91A46, 68R05. 相似文献
11.
We compute the joint entropy ofd commuting automorphisms of a compact metrizable group. LetR
d
= [u
1
±1
,...,[d
1
±1
] be the ring of Laurent polynomials ind commuting variables, andM be anR
d
-module. Then the dual groupX
M
ofM is compact, and multiplication onM by each of thed variables corresponds to an action
M
of
d
by automorphisms ofX
M
. Every action of
d
by automorphisms of a compact abelian group arises this way. IffR
d
, our main formula shows that the topological entropy of
is given by
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