...
Annals of Mathematics, 157 (2003), 545–556
On a coloring conjecture
about unit fractions
By Ernest S. Croot III
Abstract
We prove an old conjecture of Erd˝os and Graham on sums of unit fractions:
There ... Series Math. 84, Amer. Math. Soc., Prov-
idence, RI, 1994.
(Received May 16, 2001)
Annals of Mathematics
On a coloring conjecture
about unit fracti...
... Hecke functors exact
by passing to a quotient triangulated category.
Recall that if C is a triangulated category, and C
⊂ C is a full triangulated
subcategory, one can form a quotient C/C
. ... have no isomorphic quotients.
ON A VANISHING CONJECTURE
641
Again, by Σ
i+n
-equivariance, we can assume that σ
1
is the unit element,
and σ = σ
2
is such that the permutation that...
... abelian
∗
-subalgebra A of a finite von Neumann factor M is called semiregular if N (A)
generates a factor, equivalently, if N (A)
∩ M = C. Also, while maximal
abelian ∗-subalgebras A with N (A)
= ... pseudogroup
action (N.B.: v ≡ 1 is always a 2-cocycle, ∀R), there exists a type II
1
fac-
tor with a Cartan subalgebra (A ⊂ M ) associated with it, via a group-
measure s...
... has a cycle class in the dual of
a rational homology space of X and the duals of these cycle classes span a
subspace of homology, which might be large. Up to normalisation, the integral
of an ... the abelian integrals that
arise as periods of elliptic curves with complex multiplication (i.e. whose ra-
tional endomorphism ring is an imaginary quadratic field) can be related to
special val...
... details.
Remark 6.2. One may of course replace the Laplacian in (1.4) by a more
general quasilinear operator with variational structure and obtain similar re-
sults.
Acknowledgment. Part of the research ... for general nonlinearities and a local minimality property, Acta Appl.
Math. 65 (2001), 9–33.
[2]
L. Ambrosio and X. Cabre,Entire solutions of semilinear elliptic equations in R
3
and...
... strong Macdonald conjecture and
Hodge theory on the loop Grassmannian
By Susanna Fishel, Ian Grojnowski, and Constantin Teleman
Abstract
We prove the strong Macdonald conjecture of Hanlon and ... more than linear algebra, and, while Nakano’s identity (3.15) effects a
substantial simplification, we have included a brutal computational by-pass in
Appendix A, to avoid reliance on exte...
... and S. Zakeri
To the memory of Michael R. Herman (1942–2000)
Abstract
Let 0 <θ<1 be an irrational number with continued fraction expansion
θ = [a
1
,a
2
,a
3
, ], and consider the quadratic ... 1.
An important corollary of (ii), which exhibits a sharp contrast with the
case of rigid rotations, is that the scaling ratio is bounded from above and
below by an asymptotically universa...
... đúng:
-Giai cấp công nhân Việt Nam:
+Ra đời trước chiến tranh thế giới thứ nhất.
+Ra đời sau chiến tranh thế giới thứ nhất
+Ra đời sau giai cấp tư sản Việt Nam
+Ra đời trước giai cấp tư ... c a 2 giai
đoạn từ đó rút ra sự phát triển vượt bậc c a phong trào công nhân Việt Nam.
-phong trào giải phóng dân tộc 1930-1945 cần chú ý đến đường lối, lực lượng,
diễn biến c a từng giai ... k...
... that____________
A. John had an interesting summer vacation. B. John didn't have an interesting summer vacation.
C. John had the cheapest summer vacation. D. John didn't have a cheap summer vacation.
Last ... stress pattern.
6. A. hardware B. appear C. office D. manage
7 .A. computer B. magical C. lightening D. calculate
8. A. appropriate B. miraculous C. communicate D. accura...
... quan niệm về vật chất c a chủ ngh a duy vật
trước Mác. Quan niệm c a chủ ngh a duy vật biện chứng về vật chất và ý ngh a c a
quan niệm này.
4. Vật chất và vận động:
Quan niệm c a chủ ngh a ... 141
4
Một số quan điểm phi Mácxit về giai cấp. Quan niệm c a chủ ngh a duy vật biện
chứng về giai cấp, nguồn gốc và đặc trưng c a giai cấp, đấu tranh giai cấp với tư cách là
một trong nhữ...