Đề tài "On Fr´echet differentiability of Lipschitz maps between Banach spaces " docx

... subset G of X into is Γ-almost everywhere Fr´echet differentiable if and only if every σ porous set in X is Γ-null. Annals of Mathematics On Fr´echet differentiability of Lipschitz maps between ... closed convex hull of ˜ R u is equal to the closed convex hull of R u (see e.g. [5, Lemma 2.12]). The proofs in [12] and [8] of existence of points of Fr´echet d...

Ngày tải lên: 05/03/2014, 23:20

... yields the claim in (2.80). This completes the proof of Lemma 6. This completes the proof of Proposition 4 and hence of Theorem 1. 3. Proof of Theorem 2 In this section we indicate how the arguments ... side of the analogue of (2.86). The integral on the right-hand side of (3.9) is of order  1/2 log(1/). Hence we get C 5/6 log(1/) for the second term on the right-hand side...

Ngày tải lên: 14/02/2014, 17:20

... bijection between the irreducible components of |C n | and of |C ∞ | respecting the genera. Proof. By the definition of the cycle topology, for n  0 each component of C ∞ deforms to parts of some ... Cyc pshol (M) as a closed subset of the space of currents on M, or of the space of measures on M. We will not use this point of view here. Next we turn to a semi-continuity...

Ngày tải lên: 16/02/2014, 05:20

... cardinality of E, i.e. the number of irreducible components of double curves in X; • f n : the number of n-faces of G, i.e. the number of E n -points of X, for n  3; • f :=  n  3 f n , the number of ... of G, i.e. the total number of E n -points of X, for all n  3; • r n : the number of open n-faces of G, i.e. the number of R n -points of X, for n  3; • r:=...

Ngày tải lên: 16/02/2014, 06:20

... to decide whether every element of Q(β) ∩(0, 1) has an eventually periodic β-expansion. 5. Proofs of Theorems 1 to 4 We begin by a short proof of Theorem 2. Proof of Theorem 2. Let a =(a k ) k≥1 be ... sense that one bounds explicitly the number of exceptional subspaces). We now turn to the proof of Theorem 5. Keep the notation and the assumptions of this theorem. Assume that th...

Ngày tải lên: 16/02/2014, 06:20

... in N,B ([ILP]). Proof. (i) and (ii) are trivial consequences of 1.4.1 and of the definitions. The first part of (iii) is trivial by (i), (ii). Thus, e P is the supremum of all projections p ∈ ... x 0 ∈B  ∩J(N ). If we now denote by p the orthogonal projection of L 2 (N , Tr)ontothe space of fixed points of the representation of U(B) on it given by ξ → uξu ∗ , then x 0 coincid...

Ngày tải lên: 06/03/2014, 08:21

... vấn đề ôn tập cho học sinh bậc THCS tuy nhiên những vấn đề đó còn rất chung chung chưa đi vào vấn đề cụ thể để giúp cho giáo viên có phương pháp cụ thể . Vậy nên tôi quyết định lựa chọn đề tài ... GD&ĐT huyện Võ Nhai tổ chức. -Tham gia các hội nghị chuyên đề cấp huyện và cụm tổ chức. -Tham khảo các tài liệu có liên quan đến đề tài nghiên cứu. -Dự giờ đồng nghiệp tro...

Ngày tải lên: 05/11/2013, 10:11

Ngày tải lên: 26/01/2014, 15:20

... H(µ) < ∞, but the entropy of the random walk h(µ) > 0. Proof . For the proof of the corollary it is sufficient to show that the group satisfies the assumption of Theorem 1. This is done in ... sequence satisfying the assumption of Theorem 3). Then exp  n ln 2+ε (n)  ≤ v G w ,S (n) ≤ exp  n ln 1−ε (n)  for any ε>0 and any sufficient large n. Proof of Theorem 3. The idea of...

Ngày tải lên: 14/02/2014, 17:20

... coefficients of the expansion of the operator A(z,uz) in powers of z: A(z,uz)=  k∈ Z A k z k .(2.24) As observed in the proof of Proposition 7, the operator A k for k = −1 involves only terms of energy ... directions. Hence, for general values of µ i , the matrix element on the right side of (2.17) is not a priori well-defined. By expansion of the definition of A(µ i ,uµ i ),...

Ngày tải lên: 16/02/2014, 06:20