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1.
For 30 years the Lempel–Ziv factorization LZ
x
of a string x = x[1..n] has been a fundamental data structure of string processing, especially valuable for string compression and for computing
all the repetitions (runs) in x. Traditionally the standard method for computing LZ
x
was based on Θ(n)-time (or, depending on the measure used, O(n log n)-time) processing of the suffix tree ST
x
of x. Recently Abouelhoda et al. proposed an efficient Lempel–Ziv factorization algorithm based on an “enhanced” suffix array – that is, a suffix array SA
x
together with supporting data structures, principally an “interval tree”. In this paper we introduce a collection of fast
space-efficient algorithms for LZ factorization, also based on suffix arrays, that in theory as well as in many practical
circumstances are superior to those previously proposed; one family out of this collection achieves true Θ(n)-time alphabet-independent processing in the worst case by avoiding tree structures altogether.
The work of the first and third authors was supported in part by grants from the Natural Sciences & Engineering Research Council
of Canada. 相似文献
2.
Elena Rubei 《Annali dell'Universita di Ferrara》2004,50(1):151-165
This paper deals with syzygies of the ideals of the Veronese embeddings. By Green’s Theorem we know thatO
P
n
(d) satisfies Green-Lazarsfeld’s PropertyN
p ∀d≥p, ∀n. By Ottaviani-Paoletti’s theorem ifn≥2, d≥3 and 3d−2≤p thenO
P
n
(d) does not satisfy PropertyN
p. The casesn≥3, d≥3, d<p<3d−2 are still open (exceptn=d=3). Here we deal with one of these cases, namely we prove thatO
P
n
(3) satisfies PropertyN
4 ∀n. Besides we prove thatO
P
n
(d) satisfiesN
p ∀n≥p iffO
P
n
(d) satisfiesN
p.
Sunto L’argomento di questo articolo sono le sizigie degli ideali delle varietà di Veronese. Per il teorema di Green sappiamo cheO P n (d) soddisfa la proprietàN p di Green-Lazarsfeld ∀d≥p, ∀n. Per il teorema di Ottaviani-Paoletti sen≥2, d≥3 and 3d−2≤p alloraO P n (d) non soddisfa la ProprietàN p. I casin≥3, d≥3, d<p<3d−2 sono ancora aperti (eccetton=d=3). Qui consideriamo uno di tali casi, precisamente proviamo cheO P n (3) soddisfa la ProprietàN 4 ∀n. Inoltre proviamo cheO P n (d) soddisfaN p ∀n≥p se e solo seO P p (d) satisfiesN p.相似文献
3.
Fix integers n, x, k such that n≥3, k>0, x≥4, (n, x)≠(3, 4) and k(n+1)<(
n
n+x
). Here we prove that the order x Veronese embedding ofP
n
is not weakly (k−1)-defective, i.e. for a general S⊃P
n
such that #(S) = k+1 the projective space | I
2S
(x)| of all degree t hypersurfaces ofP
n
singular at each point of S has dimension (
n
/n+x
)−1− k(n+1) (proved by Alexander and Hirschowitz) and a general F∈| I
2S
(x)| has an ordinary double point at each P∈ S and Sing (F)=S.
The author was partially supported by MIUR and GNSAGA of INdAM (Italy). 相似文献
4.
Given a (known) function f:[0,1]→(0,1), we consider the problem of simulating a coin with probability of heads f(p) by tossing a coin with unknown heads probability p, as well as a fair coin, N times each, where N may be random. The work of Keane and O’Brien (ACM Trans. Model. Comput. Simul. 4(2):213–219, 1994) implies that such a simulation scheme with the probability ℙ
p
(N<∞) equal to 1 exists if and only if f is continuous. Nacu and Peres (Ann. Appl. Probab. 15(1A):93–115, 2005) proved that f is real analytic in an open set S⊂(0,1) if and only if such a simulation scheme exists with the probability ℙ
p
(N>n) decaying exponentially in n for every p∈S. We prove that for α>0 noninteger, f is in the space C
α
[0,1] if and only if a simulation scheme as above exists with ℙ
p
(N>n)≤C(Δ
n
(p))
α
, where
\varDelta n(x):=max{?{x(1-x)/n},1/n}\varDelta _{n}(x):=\max\{\sqrt{x(1-x)/n},1/n\}. The key to the proof is a new result in approximation theory: Let B+n\mathcal{B}^{+}_{n} be the cone of univariate polynomials with nonnegative Bernstein coefficients of degree n. We show that a function f:[0,1]→(0,1) is in C
α
[0,1] if and only if f has a series representation ?n=1¥Fn\sum_{n=1}^{\infty}F_{n} with Fn ? B+nF_{n}\in \mathcal{B}^{+}_{n} and ∑
k>n
F
k
(x)≤C(Δ
n
(x))
α
for all x∈[0,1] and n≥1. We also provide a counterexample to a theorem stated without proof by Lorentz (Math. Ann. 151:239–251, 1963), who claimed that if some jn ? B+n\varphi_{n}\in\mathcal{B}^{+}_{n} satisfy |f(x)−φ
n
(x)|≤C(Δ
n
(x))
α
for all x∈[0,1] and n≥1, then f∈C
α
[0,1]. 相似文献
5.
Zbigniew Grande 《Central European Journal of Mathematics》2011,9(4):772-777
A sequence (f
n
)
n
of functions f
n
: X → ℝ almost decreases (increases) to a function f: X → ℝ if it pointwise converges to f and for each point x ∈ X there is a positive integer n(x) such that f
n+1(x) ≤ f
n
(x) (f
n+1(x) ≥ f
n
(x)) for n ≥ n(x). In this article I investigate this convergence in some families of continuous functions. 相似文献
6.
A. N. Dyogtev 《Algebra and Logic》1996,35(2):80-85
Let A⊆N={0,1,2,...} and β be an n-ary Boolean function. We call A a β-implicatively selector (β-IS) set if there exists an
n-ary selector general recursive function f such that (∀x1,...,xn)(β(χ(x1),...,χ(xn))=1⟹f(x1,...,xn)∈A), where χ is the characteristic function of A. Let F(m), m≥1, be the family of all d
m+1
*
-IS sets, where
, F(0)=N, and F(∞) is the class of all subsets in N. The basic result of the article says that the family of all β-IS sets coincides with one
of F(m), m≥0, or F(∞), and, moreover, the inclusions F(0)⊂F(1)⊂...⊂F(∞) hold.
Translated fromAlgebra i Logika, Vol. 35, No. 2, pp. 145–153, March–April, 1996. 相似文献
7.
A. G. Baskakov 《Mathematical Notes》2000,67(6):690-698
We obtain conditions for the invertibility and the Fredholm property of the difference operator (Dx)(n)=x(n) -U(n)x(n − 1),n ε ℤ, in the Banach space l
p
(ℤ, X),p ε [1, ∞], of vector sequences, whereX is a Banach space andU is a bounded operator function.
Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 816–827, June, 2000. 相似文献
8.
Consider a sequence of stationary tessellations {Θ
n
}, n=0,1,…, of ℝ
d
consisting of cells {C
n
(x
i
n
)}with the nuclei {x
i
n
}. An aggregate cell of level one, C
0
1(x
i
0), is the result of merging the cells of Θ1 whose nuclei lie in C
0(x
i
0). An aggregate tessellation Θ0
n
consists of the aggregate cells of level n, C
0
n
(x
i
0), defined recursively by merging those cells of Θ
n
whose nuclei lie in C
n
−1(x
i
0).
We find an expression for the probability for a point to belong to atypical aggregate cell, and obtain bounds for the rate
of itsexpansion. We give necessary conditions for the limittessellation to exist as n→∞ and provide upperbounds for the Hausdorff dimension of its fractal boundary and forthe spherical contact distribution function
in the case ofPoisson-Voronoi tessellations {Θ
n
}.
Received: 3 June 1999 / Revised version: 22 November 2000 / Published online: 24 July 2001 相似文献
9.
Sandra Lucente 《Annali dell'Universita di Ferrara》2006,52(2):317-335
Abstract In this paper, we deal with some global existence results for the large data smooth solutions of the Cauchy Problem associated
with the semilinear weakly hyperbolic equations
Here u=u(x,t),
and for λ≥ 0, aλ≥ 0 is a continuous function that behaves as |t–t0|λ close to some t0>0. We conjecture the existence of a critical exponent pc(λ1,λ2,n) such that for p≤ pc(λ1,λ2,n) a global existence theorem holds. For suitable λ1,λ2,n, we recall some known results and add new ones.
Keywords: Critical exponents for semilinear equations, Weak hyperbolicity 相似文献
10.
We construct a commutative algebra
Ax{\mathcal{A}}_{x}
of difference operators in ℝ
p
, depending on p+3 parameters, which is diagonalized by the multivariable Racah polynomials R
p
(n;x) considered by Tratnik (J. Math. Phys. 32(9):2337–2342, 1991). It is shown that for specific values of the variables x=(x
1,x
2,…,x
p
) there is a hidden duality between n and x. Analytic continuation allows us to construct another commutative algebra
An{\mathcal{A}}_{n}
in the variables n=(n
1,n
2,…,n
p
) which is also diagonalized by R
p
(n;x). Thus, R
p
(n;x) solve a multivariable discrete bispectral problem in the sense of Duistermaat and Grünbaum (Commun. Math. Phys. 103(2):177–240, 1986). Since a change of the variables and the parameters in the Racah polynomials gives the multivariable Wilson polynomials
(Tratnik in J. Math. Phys. 32(8):2065–2073, 1991), this change of variables and parameters in
Ax{\mathcal{A}}_{x}
and
An{\mathcal{A}}_{n}
leads to bispectral commutative algebras for the multivariable Wilson polynomials. 相似文献
11.
D. R. Heath-Brown 《Proceedings Mathematical Sciences》1994,104(1):13-29
LetF(x) =F[x1,…,xn]∈ℤ[x1,…,xn] be a non-singular form of degree d≥2, and letN(F, X)=#{xεℤ
n
;F(x)=0, |x|⩽X}, where
. It was shown by Fujiwara [4] [Upper bounds for the number of lattice points on hypersurfaces,Number theory and combinatorics, Japan, 1984, (World Scientific Publishing Co., Singapore, 1985)] thatN(F, X)≪X
n−2+2/n
for any fixed formF. It is shown here that the exponent may be reduced ton - 2 + 2/(n + 1), forn ≥ 4, and ton - 3 + 15/(n + 5) forn ≥ 8 andd ≥ 3. It is conjectured that the exponentn - 2 + ε is admissable as soon asn ≥ 3. Thus the conjecture is established forn ≥ 10. The proof uses Deligne’s bounds for exponential sums and for the number of points on hypersurfaces over finite fields.
However a composite modulus is used so that one can apply the ‘q-analogue’ of van der Corput’s AB process.
Dedicated to the memory of Professor K G Ramanathan 相似文献
12.
Consider the standard non-linear regression model y
i
= g(x
i
, θ
0)+ε
i
, i = 1, ... ,n where g(x, θ) is a continuous function on a bounded closed region X × Θ, θ
0 is the unknown parameter vector in Θ ⊂ R
p
, {x
1, x
2, ... , x
n
} is a deterministic design of experiment and {ε1, ε2, ... , ε
n
} is a
sequence of independent random variables. This paper establishes the existences of M-estimates and the asymptotic uniform linearity of M-scores in a family of non-linear regression models when the errors are independent and identically distributed. This result
is then used to obtain the asymptotic distribution of a class of M-estimators for a large class of non-linear regression models. At the same time, we point out that Theorem 2 of Wang (1995)
(J. of Multivariate Analysis, vol. 54, pp. 227–238, Corrigenda. vol. 55, p. 350) is not correct.
This research was supported by the Natural Science Foundation of China (Grant No. 19831010 and grant No. 39930160) and the
Doctoral Foundation of China 相似文献
13.
W. T. Gowers 《Israel Journal of Mathematics》1990,69(2):129-151
We show that if 0<ε≦1, 1≦p<2 andx
1, …,x
n is a sequence of unit vectors in a normed spaceX such thatE ‖∑
l
n
εi
x
l‖≧n
1/p, then one can find a block basisy
1, …,y
m ofx
1, …,x
n which is (1+ε)-symmetric and has cardinality at leastγn
2/p-1(logn)−1, where γ depends on ε only. Two examples are given which show that this bound is close to being best possible. The first
is a sequencex
1, …,x
n satisfying the above conditions with no 2-symmetric block basis of cardinality exceeding 2n
2/p-1. This sequence is not linearly independent. The second example is a sequence which satisfies a lowerp-estimate but which has no 2-symmetric block basis of cardinality exceedingCn
2/p-1(logn)4/3, whereC is an absolute constant. This applies when 1≦p≦3/2. Finally, we obtain improvements of the lower bound when the spaceX containing the sequence satisfies certain type-condition. These results extend results of Amir and Milman in [1] and [2].
We include an appendix giving a simple counterexample to a question about norm-attaining operators. 相似文献
14.
The h-super connectivity κh and the h-super edge-connectivity λh are more refined network reliability indices than the conneetivity and the edge-connectivity. This paper shows that for a connected balanced digraph D and its line digraph L, if D is optimally super edge-connected, then κ1(L) = 2λ1 (D), and that for a connected graph G and its line graph L, if one of κ1 (L) and λ(G) exists, then κ1(L) = λ2(G). This paper determines that κ1(B(d, n) is equal to 4d- 8 for n = 2 and d ≥ 4, and to 4d-4 for n ≥ 3 and d ≥ 3, and that κ1(K(d, n)) is equal to 4d- 4 for d 〉 2 and n ≥ 2 except K(2, 2). It then follows that B(d,n) and K(d, n) are both super connected for any d ≥ 2 and n ≥ 1. 相似文献
15.
Given an integer n ≥ 2, let λ(n) := (log n)/(log γ(n)), where γ(n) = Π
p|n p, stand for the index of composition of n, with λ(1) = 1. We study the distribution function of (λ(n) – 1) log n as n runs through particular sets of integers, such as the shifted primes, the values of a given irreducible cubic polynomial
and the shifted powerful numbers.
Research supported in part by a grant from NSERC.
Research supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA.
Professor M.V. Subbarao passed away on February 15, 2006.
Received: 3 March 2006 Revised: 28 October 2006 相似文献
16.
D. M. Smirnov 《Algebra and Logic》1998,37(2):92-100
The dimension of a variety V of algebras is the greatest length of a basis (i.e., of an independent generating set) for an
SC-theory SC(V), consisting of strong Mal'tsev conditions satisfied in V. The variety V is assumed infinite-dimensional if
the lengths of the bases in SC(V) are not bounded. A simple algorithm is found for constructing a variety of any finite dimension
r≥1. Using the sieve of Eratosthenes, r distinct primes p1, p2,…, pr are written and their product n=p1p2…pr computed. The variety Gn of algebras (A, f) with one n-ary operation satisfying the identity f(x1, x2,…,xn)=f(x2,…,xn, x1) has, then, dimension r.
Translated fromAlgebra i Logika, Vol. 37, No. 2, pp. 167–180, March–April, 1998. 相似文献
17.
D. M. Smirnov 《Algebra and Logic》2005,44(5):348-352
We deal with varieties with one basic operation f(x1,...,xn) and one defining identity f(x1,..., xn) = f(xπ(1),...,xπ(n)), where π is a permutation whose cyclic set consists of distinct primes p1,...,pr, with the sum p1+...+pr = n. Their interpretability types, together with the greatest element 1 in a lattice
int, are said to be arithmetic. It is proved that the arithmetic types constitute a distributive lattice
ar, which is dual to a lattice Sub
fΠ of finite subsets of the set Π of all primes. It is shown that for n ⩾ 2, the poset
ar(
n) of arithmetic types defined by permutations in
n, for n fixed, is a lattice iff n = 2, 3, 4, 6, 8, 9, 11.
__________
Translated from Algebra i Logika, Vol. 44, No. 5, pp. 622–630, September–October, 2005. 相似文献
18.
Paul-Emile Maingé 《Positivity》2008,12(2):269-280
This paper deals with a viscosity iteration method, in a real Hilbert space , for minimizing a convex function over the fixed point set of , a mapping in the class of demicontractive operators, including the classes of quasi-nonexpansive and strictly pseudocontractive
operators. The considered algorithm is written as: x
n+1
:= (1 − w) v
n
+ w
T
v
n
, v
n
:= x
n
− α
n
Θ′(x
n
), where w ∈ (0,1) and , Θ′ is the Gateaux derivative of Θ. Under classical conditions on T, Θ, Θ′ and the parameters, we prove that the sequence (x
n
) generated, with an arbitrary , by this scheme converges strongly to some element in Argmin
Fix(T) Θ.
相似文献
19.
Raffaele Mosca 《Graphs and Combinatorics》2001,17(3):517-528
Let G be a graph with n vertices, and denote as γ(G) (as θ(G)) the cardinality of a minimum edge cover (of a minimum clique cover) of G. Let E (let C) be the edge-vertex (the clique-vertex) incidence matrix of G; write then P(E)={x∈ℜ
n
:Ex≤1,x≥0}, P(C)={x∈ℜ
n
:Cx≤1,x≥0}, α
E
(G)=max{1
T
x subject to x∈P(E)}, and α
C
(G)= max{1
T
x subject to x∈P(C)}. In this paper we prove that if α
E
(G)=α
C
(G), then γ(G)=θ(G).
Received: May 20, 1998?Final version received: April 12, 1999 相似文献
20.
Giampiero Chiaselotti 《Annali di Matematica Pura ed Applicata》2001,180(3):359-372
We simplify the Steinberg presentation of SL
n
(F
d
), where n≥1 and F
d
is any finite field with d elements. That presentation has the elementary matrices e
ij
(r), with i,j∈{1,...,n}, i≠=j and r∈F
d
, as generators, and (E1)–(E3), described at the opening of this work, as relations. The presentation that we shall obtain
reduces the number of generators e
ij
(r) and relations (E1)–(E3). In particular, relations (E3) are considerably reduced.
Received: March 16, 1998; in final form: November 3, 2000?Published online: October 2, 2001 相似文献