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1.
Let N be a minor of a 3-connected matroid M such that no proper 3-connected minor of M has N as a minor. This paper proves a bound on |E(M)−E(N)| that is sharp when N is connected. 相似文献
2.
Carolyn Chun 《Journal of Combinatorial Theory, Series B》2011,101(3):141-189
Let M be a matroid. When M is 3-connected, Tutte's Wheels-and-Whirls Theorem proves that M has a 3-connected proper minor N with |E(M)−E(N)|=1 unless M is a wheel or a whirl. This paper establishes a corresponding result for internally 4-connected binary matroids. In particular, we prove that if M is such a matroid, then M has an internally 4-connected proper minor N with |E(M)−E(N)|?3 unless M or its dual is the cycle matroid of a planar or Möbius quartic ladder, or a 16-element variant of such a planar ladder. 相似文献
3.
Ludomir Newelski 《Israel Journal of Mathematics》1989,65(1):59-78
We prove that the following statement is independent of ZFC+┐CH: IFT is a superstable theory of power <2ℵ
0,M≰N are models ofT withQ(M)=Q(N), then there isN′≱N withQ(N)=Q(N′). This generalizes Lachlan’s (1972) result. 相似文献
4.
Aristide Sanini 《Rendiconti del Circolo Matematico di Palermo》1992,41(2):165-184
Letf: (M,g)→(N,g′) be a differentiable map between the riemannian manifoldsM andN, M being compact.K. Uhlenbeck pointed out a functionalE
m(f), related to the energy density off, that depends only on the conformal structure ofM.
In this paper we prove thatE
m(f) is stationary with respect to deformations of the riemannian metric ofM if and only iff is weakly conformal; in this casef provides a local minimum ofE
m. 相似文献
5.
Homogeneous graded metrics over split ℤ2-graded manifolds whose Levi-Civita connection is adapted to a given splitting, in the sense recently introduced by Koszul,
are completely described. A subclass of such is singled out by the vanishing of certain components of the graded curvature
tensor, a condition that plays a role similar to the closedness of a graded symplectic form in graded symplectic geometry:
It amounts to determining a graded metric by the data {g, ω, Δ′}, whereg is a metric tensor onM, ω 0 is a fibered nondegenerate skewsymmetric bilinear form on the
Batchelor bundleE → M, and Δ′ is a connection onE satisfying Δ′ω = 0. Odd metrics are also studied under the same criterion and they are specified by the data {κ, Δ′}, with
κ ∈ Hom (TM, E) invertible, and Δ′κ = 0. It is shown in general that even graded metrics of constant graded curvature can be supported only
over a Riemannian manifold of constant curvature, and the curvature of Δ′ onE satisfiesR
Δ′ (X,Y)2 = 0. It is shown that graded Ricci flat even metrics are supported over Ricci flat manifolds and the curvature of the connection
Δ′ satisfies a specific set of equations. 0 Finally,
graded Einstein even metrics can be supported only over Ricci flat Riemannian manifolds. Related results for graded metrics
on Ω(M) are also discussed.
Partially supported by DGICYT grants #PB94-0972, and SAB94-0311; IVEI grant 95-031; CONACyT grant #3189-E9307. 相似文献
6.
Joseph Weier 《Annali dell'Universita di Ferrara》1958,8(1):39-42
Résumé étant donnés une variétéM, un ensemble compactN enM, des entiersr, n avec 1≤r≤n, un espace euclidienE àn dimensions, uner-variétéA enE et une transformation continuef: N→E−A, alors c'est un problème bien connu s'il existe une extensionf′ def satisfaisantf′(M)∈E−A. Ce problème est discuté.
Riassunto SianoM una varietà,N un insieme compatto inM, 1≤r≤n degli interi,E uno spazio euclideo adn dimensioni,A unar-varietà inE edf:N→E−A una trasformazione continua. Allora è trattato il problema ben noto dell'esistenza di una estensionef′ dif conf′ (M)∈E−A.相似文献
7.
It is proved that ifE is a separable Banach lattice withE′ weakly sequentially complete,F is a Banach space andT:E→F is a bounded linear operator withT′F′ non-separable, then there is a subspaceG ofE, isomorphic toC(Δ), such thatT
G is an isomorphism, whereC(Δ) denotes the space of continuous real valued functions on the Cantor discontinuum. This generalizes an earlier result of
the second-named author. A number of conditions are proved equivalent for a Banach latticeE to contain a subspace order isomorphic toC(Δ). Among them are the following:L
1 is lattice isomorphic to a sublattice ofE′;C(Δ)′ is lattice isomorphic to a sublattice ofE′; E contains an order bounded sequence with no weak Cauchy subsequence;E has a separable closed sublatticeF such thatF′ does not have a weak order unit.
The research of both authors was partially supported by the National Science Foundation, NSF Grant No MPS 71-02839 A04. 相似文献
8.
Michael Talagrand 《Israel Journal of Mathematics》1981,40(3-4):324-330
Letτ be a cardinal with cf(τ)>ℵ0. Then a Banach spaceE contains a subspace isomorphic tol
l(τ) if and only if [0,1]
r
is a continuous image of the unit ballE′1 ofE′, provided with the w*-topology. It follows that, for each cardinalκ, ifE′1 contains a copy ofβκ, thenE has a quotient isomorphic tol
∞(κ). In this situation we show thatE has even a quotientisometric tol
∞(κ).
相似文献
9.
In this paper we introduce some modular forms of half-integral weight on congruence group Гo(4N) withN an odd positive integer which can be viewed as a natural generalization of Cohen-Eisenstein series. Using these series, we
can prove that the restriction of Shimura lifting on Eisenstein spaceE
k+1/2
+
(4N,χl) gives an isomorphism fromE
k+1/2
+
(4N,χl) toE
2k(N). We consider some congruence relationships between modular forms in use of Shimura lifting. 相似文献
10.
Let F′,F be any two closed orientable surfaces of genus g′ > g≥ 1, and f:F→ F be any pseudo-Anosov map. Then we can “extend” f to be a pseudo- Anosov map f′:F′→ F′ so that there is a fiber preserving degree one map M(F′,f′)→ M(F,f) between the hyperbolic surface bundles. Moreover the extension f′ can be chosen so that the surface bundles M(F′,f′) and M(F,f) have the same first Betti numbers.
Y. Ni is partially supported by a Centennial fellowship of the Graduate School at Princeton University. S.C. Wang is partially
supported by MSTC 相似文献
11.
Harmonic maps with potential 总被引:8,自引:0,他引:8
Ali Fardoun Andrea Ratto 《Calculus of Variations and Partial Differential Equations》1997,5(2):183-197
Let (M,g) and (N,h) be two Riemannian manifolds, and G:N →ℝ a given function. If f:M → N is a smooth map, we set E
G
(f)=12 ∫M [∣df∣2− 2G(f)]dv
g. We establish some variational properties and some existence results for the functional E
G
(f): in particular, we analyse the case of maps into a sphere.
Received April 29, 1996 / Accepted May 28, 1996 相似文献
12.
Michel Talagrand 《Probability Theory and Related Fields》2001,121(2):237-268
We study the Hopfield model at temperature 1, when thenumber M(N) of patterns grows a bit slower than N. We reach a goodunderstanding of the model whenever M(N)≤N/(log N)11. For example, we show that if M(N)→∞, for two typical configurations σ
1, σ
2, (∑
i
≤
N
σ1
i
σ2
i
)2 is close to NM(N).
Received: 15 December 1999 / Revised version: 8 December 2000 / Published online: 23 August 2001 相似文献
13.
Jipu Ma 《Frontiers of Mathematics in China》2008,3(2):305-316
Let E and F be Banach spaces, f: U ⊂ E → F be a map of C
r
(r ⩾ 1), x
0 ∈ U, and ft (x
0) denote the FréLechet differential of f at x
0. Suppose that f′(x
0) is double split, Rank(f′(x
0)) = ∞, dimN(f′(x
0)) > 0 and codimR(f′(x
0)) s> 0. The rank theorem in advanced calculus asks to answer what properties of f ensure that f(x) is conjugate to f′(x
0) near x
0. We have proved that the conclusion of the theorem is equivalent to one kind of singularities for bounded linear operators,
i.e., x
0 is a locally fine point for f′(x) or generalized regular point of f(x); so, a complete rank theorem in advanced calculus is established, i.e., a sufficient and necessary condition such that the
conclusion of the theorem to be held is given.
相似文献
14.
This note studies the Chern-Simons invariant of a closed oriented Riemannian 3-manifold M. The first achievement is to establish the formula CS(e) - CS(e) = degA, where e and e are two (global) frames of M, and A : M → SO(3) is the "difference" map. An interesting phenomenon is that the "jumps" of the Chern-Simons integrals for various frames of many 3-manifolds are at least two, instead of one. The second purpose is to give an explicit representation of CS(e+) and CS(e_), where e+ and e_ are the "left" and "right" quaternionic frames on M3 induced from an immersion M^3 → E^4, respectively. Consequently we find many metrics on S^3 (Berger spheres) so that they can not be conformally embedded in E^4. 相似文献
15.
Regina Rotman 《Mathematische Zeitschrift》2007,257(2):427-437
Let M
n
be a closed 2-connected Riemannian manifold, such that π3(M
n
) ≠ { 0 }. In this paper we prove that either there exists a periodic geodesic on M
n
of length ≤ 6d, where d is the diameter of M
n
, or at each point p ∈ M
n
there exists a geodesic loop of length ≤ 2d. 相似文献
16.
Xu Sheng Liu 《数学学报(英文版)》2010,26(2):361-368
We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M ≠SO0(2, 2)/SO(2) × SO(2). Let π : E →* M be any vector bundle. Then any E-valued L2 harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps from irreducible symmetric spaces of noncompact type. 相似文献
17.
David Helm 《Israel Journal of Mathematics》2007,160(1):61-117
Fix a squarefree integer N, divisible by an even number of primes, and let Γ′ be a congruence subgroup of level M, where M is prime to N. For each D dividing N and divisible by an even number of primes, the Shimura curve X
D
(Γ0(N/D) ∩ Γ′) associated to the indefinite quaternion algebra of discriminant D and Γ0(N/D) ∩ Γ′-level structure is well defined, and we can consider its Jacobian J
D
(Γ0(N/D) ∩ Γ′). Let J
D
denote the N/D-new subvariety of this Jacobian.
By the Jacquet-Langlands correspondence [J-L] and Faltings’ isogeny theorem [Fa], there are Hecke-equivariant isogenies among
the various varieties J
D
defined above. However, since the isomorphism of Jacquet-Langlands is noncanonical, this perspective gives no information
about the isogenies so obtained beyond their existence. In this paper, we study maps between the varieties J
D
in terms of the maps they induce on the character groups of the tori corresponding to the mod p reductions of these varieties for p dividing N. Our characterization of such maps in these terms allows us to classify the possible kernels of maps from J
D
to J
D′, for D dividing D′, up to support on a small finite set of maximal ideals of the Hecke algebra. This allows us to compute the Tate modules
J
D
of J
D
at all non-Eisenstein
of residue characteristic l > 3. These computations have implications for the multiplicities of irreducible Galois representations in the torsion of
Jacobians of Shimura curves; one such consequence is a “multiplicity one” result for Jacobians of Shimura curves. 相似文献
18.
Let {M
r,s
(p,p′)}1≤r≤p−1,1≤s≤p′−1 be the irreducible Virasoro modules in the (p,p′)-minimal series. In our previous paper, we have constructed a monomial basis of ⊕
r=1
p−1
M
r,s
(p,p′) in the case 1<p′/p<2. By ‘monomials’ we mean vectors of the form
, where φ
−n
(r′,r):M
r,s
(p,p′)→M
r′,s
(p,p′) are the Fourier components of the (2,1)-primary field and |r
0,s〉 is the highest weight vector of
. In this article, we introduce for all p<p′ with p≥3 and s=1 a subset of such monomials as a conjectural basis of ⊕
r=1
p−1
M
r,1(p,p′). We prove that the character of the combinatorial set labeling these monomials coincides with the character of the corresponding
Virasoro module. We also verify the conjecture in the case p=3.
相似文献
19.
Gejza Jenča 《Order》2010,27(1):41-61
We prove that every orthocomplete homogeneous effect algebra is sharply dominating. Let us denote the greatest sharp element
below x by x
↓. For every element x of an orthocomplete homogeneous effect algebra and for every block B with x ∈ B, the interval [x
↓,x] is a subset of B. For every meager element (that means, an element x with x
↓ = 0), the interval [0,x] is a complete MV-effect algebra. As a consequence, the set of all meager elements of an orthocomplete homogeneous effect
algebra forms a commutative BCK-algebra with the relative cancellation property. We prove that a complete lattice ordered
effect algebra E is completely determined by the complete orthomodular lattice S(E) of sharp elements, the BCK-algebra M(E) of meager elements and a mapping h:S(E)→2
M(E) given by h(a) = [0,a] ∩ M(E). 相似文献
20.
A standard matrix representation of a matroid M represents M relative to a fixed basis B, where contracting elements of B and deleting elements of E(M)–B correspond to removing rows and columns of the matrix, while retaining standard form. If M is 3-connected and N is a 3-connected minor of M, it is often desirable to perform such a removal while maintaining both 3-connectivity and the presence of an N-minor. We prove that, subject to a mild essential restriction, when M has no 4-element fans with a specific labelling relative to B, there are at least two distinct elements, s 1 and s 2, such that for each i ∈ {1, 2}, si(M/s i ) is 3-connected and has an N-minor when s i ∈ B, and co(M\s i ) is 3-connected and has an N-minor when s i ∈ E(M)–B. We also show that if M has precisely two such elements and P is the set of elements that, when removed in the appropriate way, retain the N-minor, then (P, E(M)–P) is a sequential 3-separation. 相似文献