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1.
2.
We prove that Generalized Mukai Conjecture holds for Fano manifolds X of pseudoindex i
X
≥ (dim X + 3)/3. We also give different proofs of the conjecture for Fano fourfolds and fivefolds. 相似文献
3.
Tobias Müller 《Combinatorica》2008,28(5):529-545
A random geometric graph G
n
is constructed by taking vertices X
1,…,X
n
∈ℝ
d
at random (i.i.d. according to some probability distribution ν with a bounded density function) and including an edge between
X
i
and X
j
if ‖X
i
-X
j
‖ < r where r = r(n) > 0. We prove a conjecture of Penrose ([14]) stating that when r=r(n) is chosen such that nr
d
= o(lnn) then the probability distribution of the clique number ω(G
n
) becomes concentrated on two consecutive integers and we show that the same holds for a number of other graph parameters
including the chromatic number χ(G
n
).
The author was partially supported by EPSRC, the Department of Statistics, Bekkerla-Bastide fonds, Dr. Hendrik Muller’s Vaderlandsch
fonds, and Prins Bernhard Cultuurfonds. 相似文献
4.
Haruko Okamura 《Graphs and Combinatorics》2005,21(4):503-514
Let k≥2 be an integer and G = (V(G), E(G)) be a k-edge-connected graph. For X⊆V(G), e(X) denotes the number of edges between X and V(G) − X. Let {si, ti}⊆Xi⊆V(G) (i=1,2) and X1∩X2=∅. We here prove that if k is even and e(Xi)≤2k−1 (i=1,2), then there exist paths P1 and P2 such that Pi joins si and ti, V(Pi)⊆Xi (i=1,2) and G − E(P1∪P2) is (k−2)-edge-connected (for odd k, if e(X1)≤2k−2 and e(X2)≤2k−1, then the same result holds [10]), and we give a generalization of this result and some other results about paths not containing
given edges. 相似文献
5.
Antonio Kirson 《Annali dell'Universita di Ferrara》2010,56(2):327-333
An automorphism σ of a projective variety X is said to be wild if σ(Y) ≠ Y for every non-empty subvariety
Y \subsetneq X{Y \subsetneq X} . In [1] Z. Reichstein, D. Rogalski, and J.J. Zhang conjectured that if X is an irreducible projective variety admitting a wild automorphism then X is an abelian variety, and proved this conjecture for dim(X) ≤ 2. As a step toward answering this conjecture in higher dimensions we prove a structure theorem for projective varieties
of Kodaira dimension 0 admitting wild automorphisms. This essentially reduces the Kodaira dimension 0 case to a study of Calabi-Yau
varieties, which we also investigate. In support of this conjecture, we show that there are no wild automorphisms of certain
Calabi-Yau varieties. 相似文献
6.
Li Wenxia 《数学学报(英文版)》1998,14(4):487-494
Corresponding to the irreducible 0–1 matrix (a
ij
)
n×n
, take similitude contraction mappingsϕ
ij
for eacha
ij
=1, ina
ij
=1, in R
d
with ratio 0<r
ij
<1. There are unique nonempty compact setsF
1,…,F
n
satisfying for each1≤i≤n, F
i. We prove that open set condition holds if and only ifF
i
is ans-set for some1≤i≤n, wheres is such that the spectral radius of matrix (r
ij
3
)
n x n
is 1.
Partly supported by Natural Science Foundation of China, and partly by Natural Science Foundation of Hubei Province 相似文献
7.
For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if, whenever N+X=M with M/X singular, we have X=M. Let ℘ be the class of all singular simple modules. Then δ(M)=Σ{ L≤ M| L is a δ-small submodule of M} = Re
jm(℘)=∩{ N⊂ M: M/N∈℘. We call M δ-coatomic module whenever N≤ M and M/N=δ(M/N) then M/N=0. And R is called right (left) δ-coatomic ring if the right (left) R-module R
R(RR) is δ-coatomic. In this note, we study δ-coatomic modules and ring. We prove M=⊕
i=1
n
Mi is δ-coatomic if and only if each M
i (i=1,…, n) is δ-coatomic. 相似文献
8.
Assume that X is a left Banach module over a unital C*-algebra A. It is shown that almost every n-sesquilinear-quadratic mapping h:X×X×Xn→A is an n-sesquilinear-quadratic mapping when holds for all x,y,z1,…,znX.Moreover, we prove the generalized Hyers–Ulam–Rassias stability of an n-sesquilinear-quadratic mapping on a left Banach module over a unital C*-algebra. 相似文献
9.
A. Krajka 《Acta Appl Math》2007,96(1-3):327-338
Let
be a probability space with a nonatomic measure P and let (S,ρ) be a separable complete metric space. Let {N
n
,n≥1} be an arbitrary sequence of positive-integer valued random variables. Let {F
k
,k≥1} be a family of probability laws and let X be some random element defined on
and taking values in (S,ρ).
In this paper we present necessary and sufficient conditions under which one can construct an array of random elements {X
n,k
,n,k≥1} defined on the same probability space and taking values in (S,ρ), and such that
, and moreover
as n→∞. Furthermore, we consider the speed of convergence
to X as n→∞.
相似文献
10.
ZhiXiangWU 《数学学报(英文版)》2005,21(2):249-260
In this paper, we prove that R is a two-sided Artinian ring and J is a right annihilator ideal if and only if (i) for any nonzero right module, there is a nonzero linear map from it to a projective module; (ii) every submodule of RR is not a radical module for some right coherent rings. We call a ring a right X ring if Homa(M, R) = 0 for any right module M implies that M = 0. We can prove some left Goldie and right X rings are right Artinian rings. Moreover we characterize semisimple rings by using X rings. A famous Faith‘s conjecture is whether a semipimary PF ring is a QF ring. Similarly we study the relationship between X rings and QF and get many interesting results. 相似文献
11.
M. Andreatta 《manuscripta mathematica》1995,87(1):359-367
LetX be a complex projective variety with log terminal singularities admitting an extremal contraction in terms of Minimal Model
Theory, i.e. a projective morphism φ:X→Z onto a normal varietyZ with connected fibers which is given by a (high multiple of a) divisor of the typeK
x+rL, wherer is a positive rational number andL is an ample Cartier divisor. We first prove that the dimension of anu fiberF of φ is bigger or equal to (r-1) and, if φ is birational, thatdimF≥r, with the equalities if and only ifF is the projective space andL the hyperplane bundle (this is a sort of “relative” version of a theorem of Kobayashi-Ochiai). Then we describe the structure
of the morphism φ itself in the case in which all fibers have minimal dimension with the respect tor. If φ is a birational divisorial contraction andX has terminal singularities we prove that φ is actually a “blow-up”. 相似文献
12.
Jia Feng Lü 《数学学报(英文版)》2009,25(6):1015-1030
The so-called weakly d-Koszul-type module is introduced and it turns out that each weakly d-Koszul-type module contains a d-Koszul-type submodule. It is proved that, M ∈ W H J^d(A) if and only if M admits a filtration of submodules: 0 belong to U0 belong to U1 belong to ... belong to Up = M such that all Ui/Ui-1 are d-Koszul-type modules, from which we obtain that the finitistic dimension conjecture holds in W H J^d(A) in a special case. Let M ∈ W H J^d(A). It is proved that the Koszul dual E(M) is Noetherian, Hopfian, of finite dimension in special cases, and E(M) ∈ gr0(E(A)). In particular, we show that M ∈ W H J^d(A) if and only if E(G(M)) ∈ gr0(E(A)), where G is the associated graded functor. 相似文献
13.
Vugar E. Ismailov 《Proceedings Mathematical Sciences》2009,119(1):45-52
Let X
1, …, X
n
be compact spaces and X = X
1 × … × X
n
. Consider the approximation of a function ƒ ∈ C(X) by sums g
1(x
1)+…+g
n
(x
n
), where g
i
∈ C(X
i
), i = 1, …, n. In [8], Golomb obtained a formula for the error of this approximation in terms of measures constructed on special points
of X, called ‘projection cycles’. However, his proof had a gap, which was pointed out by Marshall and O’Farrell [15]. But the
question if the formula was correct, remained open. The purpose of the paper is to prove that Golomb’s formula holds in a
stronger form. 相似文献
14.
Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all
root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen root number. The condition “f satisfies the Wecken property is known to be equivalent to |deg(f)|≤N R[f]/(1−χ(M
2)−χ(M
10/(1−χ(M
2)) for maps between closed orientable surfaces. In the case of nonorientable surfaces the condition is A(f)≤N R[f]/(1−χ(M
2)−χ(M
2)/(1−χ(M
2)). Also we construct, for each integer n≥3, an example of a map f: K
n
→N from an n-dimensionally connected complex of dimension n to an n-dimensional manifold such that we cannot deform f in a way that all the Nielsen root classes reach the minimal number of points at the same time. 相似文献
15.
For a natural number k, define an oriented site percolation on ℤ2 as follows. Let x
i
, y
j
be independent random variables with values uniformly distributed in {1, …, k}. Declare a site (i, j) ∈ℤ2
closed if x
i
= y
j
, and open otherwise. Peter Winkler conjectured some years ago that if k≥ 4 then with positive probability there is an infinite oriented path starting at the origin, all of whose sites are open.
I.e., there is an infinite path P = (i
0, j
0)(i
1, j
1) · · · such that 0 = i
0≤i
1≤· · ·, 0 = j
0≤j
1≤· · ·, and each site (i
n
, j
n
) is open. Rather surprisingly, this conjecture is still open: in fact, it is not known whether the conjecture holds for any value of k. In this note, we shall prove the weaker result that the corresponding assertion holds in the unoriented case: if k≤ 4 then the probability that there is an infinite path that starts at the origin and consists only of open sites is positive.
Furthermore, we shall show that our method can be applied to a wide variety of distributions of (x
i
) and (y
j
). Independently, Peter Winkler [14] has recently proved a variety of similar assertions by different methods.
Received: 4 March 1999 / Revised version: 27 September 1999 / Published online: 21 June 2000 相似文献
16.
We study the asymptotic behavior of a set of random vectors ξi, i = 1,..., m, whose coordinates are independent and identically distributed in a space of infinitely increasing dimension. We investigate
the asymptotics of the distribution of the random vectors, the consistency of the sets M
m(n) = ξ1,..., ξm and X
nλ = x ∈ X
n: ρ(x) ≤ λn, and the mutual location of pairs of vectors.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1706–1711, December, 1998. 相似文献
17.
S. J. Dilworth E. Odell T. Schlumprecht A. Zsák 《Foundations of Computational Mathematics》2008,8(6):703-736
Let (e
i
) be a dictionary for a separable infinite-dimensional Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn
usually from a ‘finite alphabet’. We investigate several approximation properties of this type and connect them to the Banach
space geometry of X. The existence of a total minimal system with one of these properties, namely the coefficient quantization property, is shown to be equivalent to X containing c
0. We also show that, for every ε>0, the unit ball of every separable infinite-dimensional Banach space X contains a dictionary (x
i
) such that the additive group generated by (x
i
) is (3+ε)−1-separated and 1/3-dense in X.
相似文献
18.
Let G be a finite group andA be a normal subgroup ofG. We denote by ncc(A) the number ofG-conjugacy classes ofA andA is calledn-decomposable, if ncc(A)= n. SetK
G = {ncc(A)|A ⊲ G}. LetX be a non-empty subset of positive integers. A groupG is calledX-decomposable, ifK
G =X.
Ashrafi and his co-authors [1-5] have characterized theX-decomposable non-perfect finite groups forX = {1, n} andn ≤ 10. In this paper, we continue this problem and investigate the structure ofX-decomposable non-perfect finite groups, forX = {1, 2, 3}. We prove that such a group is isomorphic to Z6, D8, Q8, S4, SmallGroup(20, 3), SmallGroup(24, 3), where SmallGroup(m, n) denotes the mth group of ordern in the small group library of GAP [11]. 相似文献
19.
In this paper we estimate the size of the ρn’s in the famous L. Zalcman’s Lemma. With it, we obtain a uniqueness theorem for entire functions and their first derivatives,
which improves and generalizes the related results of Rubel and Yang and of Li and Yi. Some examples are provided to show
the sharpness of our result. As an application, we prove that R. Brück’s conjecture is true for a class of functions.
Received: 30 October 2008, Revised: 5 February 2009 相似文献
20.
Gebhard Böckle 《manuscripta mathematica》1998,96(2):231-246
We will study the generic fiber over of the universal deformation ring R
Q
, as defined by Mazur, for deformations unramified outside a finite set of primes Q of a given Galois representation , E a number field, k a finite field of characteristic l. The main result will be that, if ˉρ is tame and absolutely irreducible, and if one assumes the Leopoldt conjecture for the
splitting field E
0 of , then defines a smooth l-adic analytic variety, near the trivial lift ρ0 of ˉρ, whose dimension is given by cohomological constraints and as predicted by Mazur. As a corollary it follows that, in
the cases considered here, R
Q
is a quotient of by an ideal I generated by exactly m equations, where and . Under the above assumptions for and ˉρ odd, using ideas of Coleman, Gouvêa and Mazur it should now be possible to show that modular points are Zariski-dense
in the component of , that contains the trivial lift ρ0, provided this lift satisfies the Artin conjecture and E
0 satisfies the Leopoldt conjecture.
Furthermore, in the Borel case, we show that the Krull dimension of R
Q
can exceed any given number, provided Q is chosen appropriately. At the same time, we present some evidence that despite this fact, one might however expect that
the dimension of the generic fiber is given by the same cohomological formula as in the tame case.
Received: 12 December 1997 / Revised version: 5 February 1998 相似文献