共查询到20条相似文献,搜索用时 218 毫秒
1.
Let ƒ be a birational map of C
d
,and consider the degree complexity or asymptotic degree growth rate δ(ƒ) = limn → ∞ (deg(ƒn))1/n.We introduce a family of elementary maps, which have the form ƒ = L o J, where L is (invertible) linear, and J(x
1
−1
,..., xd) = (x
1
−1
,...,x
d
−1
.We develop a method of regularization and show how it can be used to compute δ for an elementary map. 相似文献
2.
Jian Wang 《高校应用数学学报(英文版)》2008,23(3):345-350
A K1,k-factorization of λKm,n is a set of edge-disjoint K1,k-factors of λKm,n, which partition the set of edges of λKm,n. In this paper, it is proved that a sufficient condition for the existence of K1,k-factorization of λKm,n, whenever k is any positive integer, is that (1) m ≤ kn, (2) n ≤ km, (3) km-n = kn-m ≡ 0 (mod (k^2- 1)) and (4) λ(km-n)(kn-m) ≡ 0 (mod k(k- 1)(k^2 - 1)(m + n)). 相似文献
3.
Franz Kinzl 《Semigroup Forum》1989,38(1):105-118
Let S be a locally compact semigroup. We study the sequence (λn) of the convolution powers of a probability measure λ on S and their shifts by a probability measure η on S. We shall give
sufficient conditions for lim ‖λn−η*λn‖ = 0 (where ‖.‖ denotes the norm). In particular we consider the case the η is a point measure and we study the subsemigroup
LO(λ) = {x ∈ S : lim ‖λn−δX*λn‖ = 0}. We shall give necessary and sufficient conditions for Lo(λ)=S. In this case we want to treat the problem of the convergence of the sequence (λn). 相似文献
4.
Tien-Cuong Dinh 《Journal of Geometric Analysis》2007,17(2):227-244
Let f be a holomorphic endomorphism of ℙ
k
having an attracting setA. We construct an attracting current and an equilibrium measure associated toA. The attracting current is weakly laminar and extremal in the cone of invariant currents. The equilibrium measure is mixing
and has maximal entropy onA. 相似文献
5.
Dimitra Kosta 《Proceedings of the Steklov Institute of Mathematics》2009,264(1):102-109
Let X be a complete intersection of two hypersurfaces F
n
and F
k
in ℙ5 of degree n and k, respectively, with n ≥ k, such that the singularities of X are nodal and F
k
is smooth. We prove that if the threefold X has at most (n + k − 2)(n − 1) − 1 singular points, then it is factorial. 相似文献
6.
Let S′ be the class of tempered distributions. For ƒ ∈ S′ we denote by J
−α
ƒ the Bessel potential of ƒ of order α. We prove that if J
−α
ƒ ∈ BMO, then for any λ ∈ (0, 1), J
−α
(f)λ ∈ BMO, where (f)λ = λ−n
f(φ(λ−1)), φ ∈ S. Also, we give necessary and sufficient conditions in order that the Bessel potential of a tempered distribution of order
α > 0 belongs to the VMO space. 相似文献
7.
Let λK
m,n be a bipartite multigraph with two partite sets having m and n vertices, respectively. A P
v-factorization of λK
m,n is a set of edge-disjoint P
v
-factors of λK
m,n which partition the set of edges of λK
m,n. When v is an even number, Ushio, Wang and the second author of the paper gave a necessary and sufficient condition for the existence
of a P
v
-factorization of λK
m,n. When v is an odd number, we proposed a conjecture. However, up to now we only know that the conjecture is true for v = 3. In this paper we will show that the conjecture is true when v = 4k − 1. That is, we shall prove that a necessary and sufficient condition for the existence of a P
4k−1-factorization of λK
m,n is (1) (2k − 1)m ⩽ 2kn, (2) (2k − 1)n ⩽ 2km, (3) m + n ≡ 0 (mod 4k − 1), (4) λ(4k − 1)mn/[2(2k − 1)(m + n)] is an integer. 相似文献
8.
Let ∑
n
−1 be the unit sphere in the n-dimensional Euclidean space ℝ
n
. For a funcion ƒ∈L(∑
n
−1) denote by σδ
N
(ƒ) the Cesàro means of order δ of the Fourier-Laplace series of ƒ. The special value of δ is known as the critical index. In the case when n is even, this paper proves the existence of the ‘rare’ sequence {n
k
} such that the summability
takes place at each Lebesgue point satisfying some antipole conditions.
Received June 28, 1999, Revised August 11, 1999, Accepted February 16, 2000 相似文献
9.
10.
Carlo Magagna 《Monatshefte für Mathematik》2008,23(2):59-81
For a positive integer N, we define the N-rank of a non singular integer d × d matrix A to be the maximum integer r such that there exists a minor of order r whose determinant is not divisible by N. Given a positive integer r, we study the growth of the minimum integer k, such that A
k
− I has N-rank at most r, as a function of N. We show that this integer k goes to infinity faster than log N if and only if for every eigenvalue λ which is not a root of unity, the sum of the dimensions of the eigenspaces relative
to eigenvalues which are multiplicatively dependent with λ and are not roots of unity, plus the dimensions of the eigenspaces
relative to eigenvalues which are roots of unity, does not exceed d − r − 1. This result will be applied to recover a recent theorem of Luca and Shparlinski [6] which states that the group of rational
points of an ordinary elliptic curve E over a finite field with q
n
elements is almost cyclic, in a sense to be defined, when n goes to infinity. We will also extend this result to the product of two elliptic curves over a finite field and show that
the orders of the groups of
\Bbb Fqn-{\Bbb F}_{q^n}-
rational points of two non isogenous elliptic curves are almost coprime when n approaches infinity. 相似文献
11.
Xiaodong Wang 《Journal of Geometric Analysis》2008,18(1):272-284
Let (M
n
,g) be a compact Riemannian manifold with Ric ≥−(n−1). It is well known that the bottom of spectrum λ
0 of its universal covering satisfies λ
0≤(n−1)2/4. We prove that equality holds iff M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy.
The author was partially supported by NSF Grant 0505645. 相似文献
12.
André Meireles Fernando Xavier Jacqueline Rojas 《Bulletin of the Brazilian Mathematical Society》2010,41(4):531-550
Here we construct an explicit parameter space for cones in ℙ
n
for 4 ≤ n ≤ 6 with vertices of codimension 4 and 5, respectively (when this makes sense), over a reducible cubic scroll of codimension
2 in a hyperplane (in ℙ
n
) and use it to compute the numbers of them that are incident to the appropriate number of linear spaces. 相似文献
13.
Edoardo Ballico Francesco Malaspina Paolo Valabrega Mario Valenzano 《Central European Journal of Mathematics》2012,10(4):1361-1379
Let E be an indecomposable rank two vector bundle on the projective space ℙ
n
, n ≥ 3, over an algebraically closed field of characteristic zero. It is well known that E is arithmetically Buchsbaum if and only if n = 3 and E is a null-correlation bundle. In the present paper we establish an analogous result for rank two indecomposable arithmetically
Buchsbaum vector bundles on the smooth quadric hypersurface Q
n
⊂ ℙ
n+1, n ≥ 3. We give in fact a full classification and prove that n must be at most 5. As to k-Buchsbaum rank two vector bundles on Q
3, k ≥ 2, we prove two boundedness results. 相似文献
14.
Let D, D′ ⊂ ℂn be bounded domains with smooth real analytic boundaries and ƒ: D → D′ be a proper holomorphic map. Our main result implies
that if the graph of ƒ extends as an analytic set to a neighborhood of a poìnt (a, a′) ∈ ∂D × 3D′ with a′ ∈ clƒ(a), then ƒ extends holomorphically to a neighborhood of a. 相似文献
15.
We say that a subset of Cn is hypoconvex if its complement is the union of complex hyperplanes. We say it is strictly hypoconvex if it is smoothly bounded
hypoconvex and at every point of the boundary the real Hessian of its defining function is positive definite on the complex
tangent space at that point. Let Bn be the open unit ball in Cn.Suppose K is a C∞ compact manifold in ∂B1 × Cn, n > 1, diffeomorphic to ∂B1 × ∂Bn, each of whose fibers Kz over ∂B1 bounds a strictly hypoconvex connected open set. Let K be the polynomialhull of K. Then we show that K∖K is the union of
graphs of analytic vector valued functions on B1. This result shows that an unnatural assumption regarding the deformability of K in an earlier version of this result is
unnecessary. Next, we study an H∞ optimization problem. If pis a C∞ real-valued function on ∂B1× Cn, we show that the infimum γρ = infƒ∈H
∞ (B1)n ‖ρ(z, ƒ (z))‖∞ is attained by a unique bounded ƒ provided that the set (z, w) ∈ ∂B1 × C n|ρ(z, w) ≤ γρ has bounded connected strictly hypoconvex fibers over the circle. 相似文献
16.
Yosef Stein 《Israel Journal of Mathematics》1989,68(1):109-122
LetK be an algebraically closed field of characteristic zero. ForA ∈K[x, y] let σ(A) = {λ ∈K:A − λ is reducible}. For λ ∈ σ(A) letA − λ = ∏
i=1
n(λ)
A
iλ
k
μ whereA
iλ are distinct primes. Let ϱλ(A) =n(λ) − 1 and let ρ(A) = Σλɛσ(A)ϱλ(A). The main result is the following:
Theorem.If A ∈ K[x, y] is not a composite polynomial, then ρ(A) < degA. 相似文献
17.
Vladimir A. Kozlov 《Arkiv f?r Matematik》1999,37(2):305-322
The equationx
(n)(t)=(−1)
n
│x(t)│
k
withk>1 is considered. In the casen≦4 it is proved that solutions defined in a neighbourhood of infinity coincide withC(t−t0)−n/(k−1), whereC is a constant depending only onn andk. In the general case such solutions are Kneser solutions and can be estimated from above and below by a constant times (t−t
0)−n/(k−1). It is shown that they do not necessarily coincide withC(t−t0)−n/(k−1). This gives a negative answer to two conjectures posed by Kiguradze that Kneser solutions are determined by their value in
a point and that blow-up solutions have prescribed asymptotics.
Dedicated to Professor Vladimir Maz'ya on the occasion of his 60th birthday.
The author was supported by the Swedish Natural Science Research Council (NFR) grant M-AA/MA 10879-304. 相似文献
18.
W. G. Bridges 《Israel Journal of Mathematics》1972,12(4):369-372
Bounds on the number of row sums in ann×n, non-singular (0,1)-matrixA sarisfyingA
tA=diag (k
1-λ1,…,k
n-λn),k
j>λj>0,λ1=…=λe,λe+1=…=λn are obtained which extend previous results for such matrices. 相似文献
19.
Dave Anderson 《Journal of Algebraic Combinatorics》2007,25(3):349-356
Given two Schubert classes σλ and σμ in the quantum cohomology of a Grassmannian, we construct a partition ν, depending on λ and μ, such that σν appears with coefficient 1 in the lowest (or highest) degree part of the quantum product σλ⋆σμ. To do this, we show that for any two partitions λ and μ, contained in a k × (n − k) rectangle and such that the 180∘-rotation of one does not overlap the other, there is a third partition ν, also contained in the rectangle, such that the
Littlewood-Richardson number c
λμ
ν is 1. 相似文献
20.
N. A. Bushueva 《Siberian Mathematical Journal》2010,51(5):776-788
In ℂn we consider an algebraic surface Y and a finite collection of hypersurfaces Si. Froissart’s theorem states that if Y and Si are in general position in the projective compactification of ℂn together with the hyperplane at infinity then for the homologies of Y \∪ Si we have a special decomposition in terms of the homology of Y and all possible intersections of Si in Y. We prove the validity of this homological decomposition on assuming a weaker condition: there exists a smooth toric
compactification of ℂn in which Y and Si are in general position with all divisors at infinity. One of the key steps of the proof is the construction of an isotopy
in Y leaving invariant all hypersurfaces Y ∩ Sk with the exception of one Y ∩ Si, which is shifted away from a given compact set. Moreover, we consider a purely toric version of the decomposition theorem,
taking instead of an affine surface Y the complement of a surface in a compact toric variety to a collection of hypersurfaces
in it. 相似文献