共查询到20条相似文献,搜索用时 31 毫秒
1.
Pierre Bousquet 《Journal d'Analyse Mathématique》2007,102(1):311-346
We are interested in the location of the singularities of maps u ∈ W
s,p
(S
N
, S
1) when 1 ≤ sp and 1 < sp < 2. To this end, we consider the distributional Jacobian. We show that the range of this operator on W
s,p
(S
N
, S
1) is the closure in W
s−2,p
⋂ W
−1,sp
of the set of N − 2-currents defined as the integration on smooth oriented N − 2-dimensional boundaryless submanifolds. 相似文献
2.
Piotr Haj?asz 《Mathematische Annalen》2009,343(4):801-823
We prove that Lipschitz mappings are dense in the Newtonian–Sobolev classes N
1,p
(X, Y) of mappings from spaces X supporting p-Poincaré inequalities into a finite Lipschitz polyhedron Y if and only if Y is [p]-connected, π
1(Y) = π
2(Y) = · · · = π
[p](Y) = 0, where [p] is the largest integer less than or equal to p.
This work was supported by the NSF grant DMS-0500966. 相似文献
3.
Julio Delgado 《Integral Equations and Operator Theory》2010,68(1):61-74
Let Ω be a second countable topological space and μ be a σ−finite measure on the Borel sets M{\mathcal{M}}. Let T be a nuclear operator on Lp(W,M,m){L^p({\Omega},{\mathcal{M}},\mu) }, 1 < p < ∞, in this work we establish a formula for the trace of T. A preliminary trace formula is established applying the general theory of traces on operator ideals introduced by Pietsch
and a characterization of nuclear operators for σ−finite measures. We also use the Doob’s maximal theorem for martingales with the purpose of studying the kernel k(x, y) of T on the diagonal. 相似文献
4.
For an arbitrary n-dimensional Riemannian manifold N and an integer m ∈ {1,…,n−1} a covariant derivative
on the Grassmann bundle ^ := Gm(T N) is introduced which has the property that an m-dimensional submanifold M ⊂ N has parallel second fundamental form if and only if its Gauss map M → ^ is affine. (For N Rn this result was already obtained by J. Vilms in 1972.) By means of this relation a generalization of Cartan's theorem on
the total geodesy of a geodesic umbrella can be derived: Suppose, initial data (p,W,b) prescribing a tangent space W ∈ Gm(TpN) and a second fundamental form b at p ∈ N are given; for these data we construct an m-dimensional ‘umbrella’ M = M(p,W,b) ⊂ N the rays of which are helical arcs of N; moreover, we present tensorial conditions (not involving
) which guarantee that the umbrella M has parallel second fundamental form. These conditions are as well necessary, and locally every submanifold with parallel
second fundamental form can be obtained in this way.
Mathematics Subject Classifications (2000): 53B25, 53B20, 53B21. 相似文献
5.
S. Yu. Antonov 《Russian Mathematics (Iz VUZ)》2012,56(5):9-22
We estimate the least degree of identities of subspaces M
1(m,k) (F) of the matrix superalgebra M
(m,k)(F) over the field F for arbitrary m and k. For subspaces M
1(m,1) (F) (m≥1) and M
1(2,2) (F) we obtain concrete minimal identities. 相似文献
6.
Marshall Ash 《Journal of Fourier Analysis and Applications》2010,16(6):1053-1069
Let P be a polygon in ℤ2 and consider the mapping of an
L1(\mathbbT2)L^{1}(\mathbb{T}^{2})
function into the partial sum of its Fourier series determined by the dilate of P by the integer N. If the image space is endowed with the L
p
norm, 1<p<∞, then the operator norm will be given by the L
p
norm of ∑(m,n)∈NP
e
2π
i(mx+ny). The size of this operator norm is shown to be O(N
2(1−1/p)) when the polygon is a triangle. The estimate is independent of the shape of the triangle. For a k sided polygon the corresponding estimate is O(kN
2(1−1/p)). 相似文献
7.
In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W
1,P
(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W
1,n
, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W
1,P
(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S
4. 相似文献
8.
Assume that G is a 3-colourable connected graph with e(G) = 2v(G) −k, where k≥ 4. It has been shown that s
3(G) ≥ 2
k
−3, where s
r
(G) = P(G,r)/r! for any positive integer r and P(G, λ) is the chromatic polynomial of G. In this paper, we prove that if G is 2-connected and s
3(G) < 2
k
−2, then G contains at most v(G) −k triangles; and the upper bound is attained only if G is a graph obtained by replacing each edge in the k-cycle C
k
by a 2-tree. By using this result, we settle the problem of determining if W(n, s) is χ-unique, where W(n, s) is the graph obtained from the wheel W
n
by deleting all but s consecutive spokes.
Received: January 29, 1999 Final version received: April 8, 2000 相似文献
9.
Let M be a closed Willmore hypersurface in the sphere S^n+1(1) (n ≥ 2) with the same mean curvature of the Willmore torus Wm,n-m, if SpecP(M) = Spec^P(Wm,n-m ) (p = 0, 1,2), then M is Wm,n-m. 相似文献
10.
Vito Lampret 《Central European Journal of Mathematics》2012,10(2):775-787
An asymptotic approximation of Wallis’ sequence W(n) = Π
k=1
n
4k
2/(4k
2 − 1) obtained on the base of Stirling’s factorial formula is presented. As a consequence, several accurate new estimates
of Wallis’ ratios w(n) = Π
k=1
n
(2k−1)/(2k) are given. Also, an asymptotic approximation of π in terms of Wallis’ sequence W(n) is obtained, together with several double inequalities such as, for example,
W(n) ·(an + bn ) < p < W(n) ·(an + b¢n )W(n) \cdot (a_n + b_n ) < \pi < W(n) \cdot (a_n + b'_n ) 相似文献
11.
Mark Pankov 《Journal of Algebraic Combinatorics》2011,33(4):555-570
Let V be an n-dimensional vector space (4≤n<∞) and let Gk(V){\mathcal{G}}_{k}(V) be the Grassmannian formed by all k-dimensional subspaces of V. The corresponding Grassmann graph will be denoted by Γ
k
(V). We describe all isometric embeddings of Johnson graphs J(l,m), 1<m<l−1 in Γ
k
(V), 1<k<n−1 (Theorem 4). As a consequence, we get the following: the image of every isometric embedding of J(n,k) in Γ
k
(V) is an apartment of Gk(V){\mathcal{G}}_{k}(V) if and only if n=2k. Our second result (Theorem 5) is a classification of rigid isometric embeddings of Johnson graphs in Γ
k
(V), 1<k<n−1. 相似文献
12.
We characterise the space of newforms of weight k + 1/2 on Γ0(4N), N odd and square-free (studied by the second and third authors with Vasudevan) under the Atkin-Lehner W(4) operator. As an application, we show that the (±1)-eigensubspaces of the W(4) operator on the space of modular forms of weight k + 1/2 on Γ0(4N) is mapped to modular forms of weight 2k on Γ0(N), under a class of Shimura maps. The existence of such subspaces having this mapping property was conjectured by Zagier in
a private communication. One of the special features of the (±1)-eigensubspaces is that the (2k + 1)-th power of the classical theta series of weight 1/2 belongs to the + eigensubspace and hence this gives interesting
congruences for r
2k+1(p
2). 相似文献
13.
For Y any space that has the homotopy type of a wedge of finitely many circles, and for g : Y → Y a map, the Nielsen number of g, N(g), is a homotopy invariant lower bound for the size of the fixed point set of any map homotopic to g. Such a map g has k-remnant if, roughly, there is limited cancellation in any product g
♯(u)g
♯(v) where g
♯ is the induced homomorphism and u, v ∈ π1(Y) and |u| = |v| = k. We prove that such maps are (k + 1)-characteristic, meaning that in order to determine the Nielsen classes of fixed points, we need only test whether a
limited, specified, set of elements z ∈ π1(Y) are solutions to the equation z = W
−1
x
f
♯(z)W
y
, with x and y fixed points that are represented in the fundamental group by W
x
and W
y
, respectively. The number of elements to be tested is profoundly decreased by using abelianization as well.
This work is a significant extension of Wagner’s results involving maps with remnant and Wagner’s algorithm. Our proofs involve
new concepts and techniques.
We present an algorithm for N(g) for any map g with k-remnant, and we provide examples for which no algebraic techniques previously known would work. One example shows that for
any k there is a map that does not have (k − 1)-remnant but does have k-remnant.
Dedicated to Edward Fadell for inspirational teaching and guidance as the thesis advisor of the first author 相似文献
14.
Wenguang Zhai 《中国科学A辑(英文版)》1999,42(11):1173-1183
Thek-dimensional Piatetski-Shapiro prime number problem fork⩾3 is studied. Let π(x
1
c
1,⋯,c
k
) denote the number of primesp withp⩽x,
, where 1<c
1<⋯<c
k
are fixed constants. It is proved that π(x;c
1,⋯,c
k
) has an asymptotic formula ifc
1
−1
+⋯+c
k
−1
>k−k/(4k
2+2).
Project supported by the National Natural Science Foundation of China (Grant No. 19801021) and the Natural Science Foundation
of Shandong Province (Grant No.Q98A02110). 相似文献
15.
Given a permutation , construct a graph G
π on the vertex set {1, 2,..., n} by joining i to j if (i) i < j and π(i) < π(j) and (ii) there is no k such that i < k < j and π(i) < π(k) < π(j). We say that π is forest-like if G
π is a forest. We first characterize forest-like permutations in terms of pattern avoidance, and then by a certain linear map
being onto. Thanks to recent results of Woo and Yong, these show that forest-like permutations characterize Schubert varieties
which are locally factorial. Thus forest-like permutations generalize smooth permutations (corresponding to smooth Schubert
varieties).
We compute the generating function of forest-like permutations. As in the smooth case, it turns out to be algebraic. We then
adapt our method to count permutations for which G
π is a tree, or a path, and recover the known generating function of smooth permutations.
Received March 27, 2006 相似文献
16.
The Blow-up Locus of Heat Flows for Harmonic Maps 总被引:5,自引:0,他引:5
Abstract
Let M and N be two compact Riemannian manifolds. Let u
k
(x, t) be a sequence of strong stationary weak heat flows from M×R
+ to N with bounded energies. Assume that u
k→u weakly in H
1, 2(M×R
+, N) and that Σt is the blow-up set for a fixed t > 0. In this paper we first prove Σt is an H
m−2-rectifiable set for almost all t∈R
+. And then we prove two blow-up formulas for the blow-up set and the limiting map. From the formulas, we can see that if the
limiting map u is also a strong stationary weak heat flow, Σt is a distance solution of the (m− 2)-dimensional mean curvature flow [1]. If a smooth heat flow blows-up at a finite time, we derive a tangent map or a weakly
quasi-harmonic sphere and a blow-up set ∪t<0Σt× {t}. We prove the blow-up map is stationary if and only if the blow-up locus is a Brakke motion.
This work is supported by NSF grant 相似文献
17.
Let A be an n×N real-valued matrix with n<N; we count the number of k-faces f
k
(AQ) when Q is either the standard N-dimensional hypercube I
N
or else the positive orthant ℝ+
N
. To state results simply, consider a proportional-growth asymptotic, where for fixed δ,ρ in (0,1), we have a sequence of matrices An,NnA_{n,N_{n}} and of integers k
n
with n/N
n
→δ and k
n
/n→ρ as n→∞. If each matrix An,NnA_{n,N_{n}} has its columns in general position, then f
k
(AI
N
)/f
k
(I
N
) tends to zero or one depending on whether ρ>min (0,2−δ
−1) or ρ<min (0,2−δ
−1). Also, if each An,NnA_{n,N_{n}} is a random draw from a distribution which is invariant under right multiplication by signed permutations, then f
k
(Aℝ+
N
)/f
k
(ℝ+
N
) tends almost surely to zero or one depending on whether ρ>min (0,2−δ
−1) or ρ<min (0,2−δ
−1). We make a variety of contrasts to related work on projections of the simplex and/or cross-polytope.
These geometric face-counting results have implications for signal processing, information theory, inverse problems, and optimization.
Indeed, face counting is related to conditions for uniqueness of solutions of underdetermined systems of linear equations.
Below, let A be a fixed n×N matrix, n<N, with columns in general position.
18.
We investigate Besov spaces and their connection with trigonometric polynomial approximation inL
p[−π,π], algebraic polynomial approximation inL
p[−1,1], algebraic polynomial approximation inL
p(S), and entire function of exponential type approximation inL
p(R), and characterizeK-functionals for certain pairs of function spaces including (L
p[−π,π],B
s
a(L
p[−π,π])), (L
p(R),s
a(Lp(R))),
, and
, where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r.
This project is supported by the National Science Foundation of China. 相似文献
19.
In this paper the structure of subspaces and quotients ofl
p
N
of dimension very close toN is studied, for 1≤p≤∞. In particular, the maximal dimensionk=k(p, m, N) so that an arbitrarym-dimensional subspaceX ofl
p
N
contains a good copy ofl
p
k
, is investigated form=N−o(N). In several cases the obtained results are sharp. 相似文献
20.
The number of self-dual cyclic codes of length p
k
over GR(p
2, m) is determined by the nullity of a certain matrix M(p
k
, i
1). With the aid of Genocchi numbers, we determine the nullity of M(p
k
, i
1) and hence determine completely the number of such codes. 相似文献
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