Đề tài "A sharp form of Whitney’s extension theorem " ppt
Đề tài "A sharp form of Whitney’s extension theorem " ppt
... Cdetermined by A, m, n.(8)Annals of Mathematics A sharp form of Whitney’s extension theorem By Charles L. Fefferman A SHARP FORM OF WHITNEY’S EXTENSION THEOREM 527From (1), ,(5), we ... thatJy(ϕSα)=Pyαfor all α ∈A.(24)The conclusions of the lemma are (19), (20), (22), (23), (24). The proof of Lemma 10.3 is complete.A SHARP FORM OF WHITNEY’S EXTENSION THEOREM 535Lemma 10.4. Suppose k#≥ ... thatany (D + 1) of them have nonempty intersection. Moreover, each Kf(y; S, 1) isA SHARP FORM OF WHITNEY’S EXTENSION THEOREM 531easily seen to be a convex, bounded subset of the D-dimensional...
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Đề tài " A new application of random matrices: Ext(C red(F2)) is not a group " ppt
... proof aswell as Chernoff’s proof is based on an expansion of f in Hermite polynomials(or tensor products of Hermite polynomials in the case N ≥ 2). Chen givesin [Cn] a self-contained proof ... thatϕ(xi)=yi,i=1, 2, ,r.Before the proof of Theorem 2.2, we make a few observations:2.3 Remark. (1) In connection with condition (2.1) above, let V be asubspace of Mm(C) containing the unit 111m. ... 111B(H2)−1=111B(H1)0−z 111B(H2).Proof of Theorem 2.2. By Lemma 2.1, our objective is to prove theexistence of a unital completely positive map u0: E → F , satisfying...
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Đề tài " A quantitative version of the idempotent theorem in harmonic analysis " docx
... ερ))ρ∈[0,4] of Bohr sets, where Γ ⊆G is a set of characters. It turns out not to be muchharder to deal with the join of a pair of Bourgain systems in general.Definition 4.9 (Joining of two Bourgain ... equivalent to the lower bound on the size of S ∧Sthat we claimed.We move on now to one of the more technical aspects of the theory of Bourgain systems, the notion of regularity.Definition 4.11 (Regular ... care to recall the definitions of d(f, Z)and of fZat this point: they are given at the start of Section 3.QUANTITATIVE IDEMPOTENT THEOREM 1037The main result of this section states that if...
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Đề tài " A new construction of the moonshine vertex operator algebra over the real number field " pot
... over Q ), we can rewrite Theorem 4.1 of [Mi5] into the following theorem. Theorem 3.25. Under Hypotheses I,V =α∈SVαhas a structure of (D, S)-framed VOA with a PDIB -form. A framed VOAstructure ... 2-group. LetV = ⊕χ∈Irr(Q)Vχbe the decomposition of V into the direct sum of eigenspaces of Q, whereIrr(Q) is the set of linear characters of Q. Since dim V0= 1 and Vχis anirreducible ... even linear code S of length 2n by Proposition 3.5. It iseasy to see dim(MS)1=n(2n−1) and so S is the set of all even words of length2n. Hence MDhas a PDIB -form. Annals of Mathematics ...
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Tài liệu Đề tài " On the holomorphicity of genus two Lefschetz fibrations " pptx
... irreducible components of |Cn| 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 component of Cn. This sets ... as the virtual num-ber of double points. This is the number of nodes of the image of a small,general, J-holomorphic deformation of the parametrization map from a union of unit disks to M belonging ... locus of a section of OCP1(d) that is unique up to rescaling. The restrictions of sr0sd−r1to any fiber form a basis for the space of global sections of OCP1(d). Hence,after choice of...
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Tài liệu Đề tài " The causal structure of microlocalized rough Einstein metrics " pptx
... Thus,2εABRA43B= −εABRAB43.In view of Corollary 4.6 we can therefore express εABRA43Bin the form curl/π(2)+ E(2).5. Strategy of the proof of the Asymptotics Theorem In this section we describe ... assumption B2).We shall next formulate versions of the Calderon-Zygmund theorem for theabove types of Hodge systems; see also [B-W]. The proof is a straightforwardmodification of the standard approach.Proposition ... this difficulty and prove the following: Theorem 8.1. On any null hypersurface Cu,tu∇R44(H)L2(Sτ,u)dτ λ−1.(110)Proof. The proof of the theorem requires a rather long and tedious...
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Tài liệu Đề tài " The topological classification of minimal surfaces in R3 " pptx
... to isotope Γ so asto reduce the number of points of intersection of that part of the graph in theboundary of the singular disk which is the extension of E.After finitely many steps, we have ... interior of W.Let S denote the collection of ends of planes and catenoids defined abovewhich arises from the collection of nonsimply connected components W of Hi−∪Di. It follows from the proof of ... ordering of ends. The proof of the case where F has two limit ends issimilar.Let W be the set of closures of the components of H1−∪D1and H2−∪D2.Given W ∈W, let P(W ) be the collection of...
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Đề tài " Hypergraph regularity and the multidimensional Szemer´edi theorem " ppt
... triangles of G, and if A = {1, 2, 3}, say, then H∗(A) consists of all triangles in G with one vertex in each of X1, X2and X3, while H(A)consists of all 3-edges of H with one vertex in each of ... bounded number of pieces, almost all of which are quasiran-dom. This generalizes Szemer´edi’s regularity lemma for graphs (which formedpart of his proof of his theorem on arithmetic progressions).Given ... Ui= {x0i,x1i},and B consist of all sets of the form Bε= {xε11, ,xεkk}, with ε =(ε1, ,εk) ∈{0, 1}k. The set Ω was the set of all ways of choosing x0iand x1iin Xi,...
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Đề tài " A proof of Kirillov’s conjecture " potx
... result.Annals of Mathematics A proof of Kirillov’s conjecture By Ehud Moshe Baruch* APROOF OF KIRILLOV’S CONJECTURE 225The proof of Lemma 5.2 is an easy consequence of the description of ... Jacobson-Morosov triple.Set G =GLn(K). The G conjugacy class of X ∈ is the set of elements of of the form OG(X)={gXg−1| g ∈ G}. The G conjugacy class of X ispartitioned into P conjugacy classes OP(˜X)={p˜Xp−1| ... ]byanelement of Y∩X. This is the content of the following theorem which is the main result of this section and is one of thekey results in this paper. It was stated in the introduction as Theorem...
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Tài liệu Báo cáo khoa học: Proteomic analysis of dopamine and a-synuclein interplay in a cellular model of Parkinson’s disease pathogenesis docx
... Department of Structural and Functional Biology, and Centre of Neuroscience, University of Insubria, Busto Arsizio, Italy2 Department of Biotechnology, University of Verona, Italy3 Department of Clinical ... familial forms of PD [6].However, a-synuclein deposition into LB is a generalhallmark of the PD state, suggesting that the accumula-tion of a-synuclein might cause selective degeneration of dopaminergic ... but rather a rearrangement of the isoformpattern. This finding could also reflect a proteomeadaptation as a response to perturbation of proteinlevels caused by stimuli of different origin [20]....
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