... that
three other points y
i
,y
j
,y
q
lie inside the hemisphere H
+
bounded by Ω
2
. Let Ω
Annals of Mathematics
The kissing number in
four dimensions
By Oleg R. Musin
THE KISSING NUMBER ... method.
1. Introduction
The kissing number k(n) is the highest number of equal nonoverlapping
spheres in R
n
that can touch another sphere of the same size....
... ≥−L
1
|x|<R
Z
5/2
|x|
−5/2
dx − ZNR
−1
.
The estimate in the theorem follows by evaluating the integral and choosing
the optimal value for R.
Remark 3.3. The function N → E
HF
(N,Z)isnonincreasing. This can
be seen ... (γ)=0,hence the minimizer in this case is simply
the projection onto a ground state of the operator −
1
2
∆ −Z|x|
−1
on the space
L
2
(
3
;
2
). The...
... NHỮNG PHÁT HIỆN MỚI CỦA ĐỀ TÀI CŨNG
NHƯ NHỮNG HẠN CHẾ CỦA ĐỀ TÀI NÀY, TỪ ĐÓ ĐỀ XUẤT NHỮNG
ĐỀ TÀI NGHIÊN CỨU MỚI ĐỂ GIẢI QUYẾT NHỮNG HẠN CHẾ NÀY ?
6.1 Những phát hiện mới của đề tài
Nghiên cứu tác ... hạn chế của đề
tài này, từ đó đề xuất những đề tài nghiên cứu mới để giải quyết những hạn
chế này ?
Nhóm 4 –K20 Đêm 6 Trang 1
The “advantage of latecomer” in abating air-polluti...
... 0. On the other hand, the first probability in the
second line of (2.21) is bounded above by the probability of B
t
not hitting
i(D
T
2
(x, ε)) = D(0,ε) during n
ε
excursions, each starting at ... δ
=1(4.1)
since the complementary upper bound on T
n
is contained in [4, Cor. 25, Chap.
7] (see also the references therein). Our approach is to use Theorem 1.2 to-
gether with the...
... 8: The separation w for a multi-valued graph in (II.1.1).
PLANAR DOMAINS
535
The main result of the next two sections is the following theorem (Γ
1
(∂)
is the component of B
1
∩ Γ containing ... For instance, a curve lying in the boundary
of an intrinsic ball is strictly convex. In this section we give similar estimates for
half of normal tubular neighborhoods of curves lyin...
... that it intersects HP
i
in fewer points or we can find a nontrivial cycle of
Γ contained in the singular disk extending E. In the case that we reduce the
number of points, we continue on. Either ... III
Figure 5: The endpoints of the bad arc are near ∂
−
H.
Figure 6: Reducing the number of bad arcs when m = 1. In the figure on the
left, the waist is the curve γ a...
... used in a paper of I.Z. Ruzsa
and the author [9]. In the present context things look rather different however
and, in the absence of anything which might be called a “grain”, we think the
terminology ... result of the form (6.4).
For this we need Theorem 2.1, the restriction theorem for primes.
The idea of constructing a
1
, and the technique for constructing it, has
its...
... bounded in terms of ∆
L
. There are only
finitely many such polynomials, and counting them gives the theorem of [18].
The main idea of Theorem 1.1 is to count r-tuples of integers in L instead
of single ... Substituting these
values of r, c into (2.6) yields the upper bound of Theorem 1.1.
In the language of the beginning of this section, we have taken A to
be Spec R
Σ
and the...
... completely
to the right of the origin (or a point just to the the left of the origin) after
k steps. In Section 11 we give estimates for this probability. In the case
z = 2y, the desired probability ... accounts for
the discrepancy between the upper estimates in Theorem T1 and the bounds
in Theorem 1.
1.6. Some open problems. (i) Strengthen Theorem 1 to an asymptotic...