Đề tài " The kissing number in four dimensions " pdf

... 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....

Ngày tải lên: 06/03/2014, 08:21

... ≥−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...

Ngày tải lên: 14/02/2014, 16:20

... 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...

Ngày tải lên: 06/01/2014, 14:53

... 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...

Ngày tải lên: 14/02/2014, 17:20

... 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...

Ngày tải lên: 14/02/2014, 17:20

... 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...

Ngày tải lên: 16/02/2014, 06:20

... 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...

Ngày tải lên: 06/03/2014, 08:21

... 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...

Ngày tải lên: 06/03/2014, 08:21

... 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...

Ngày tải lên: 06/03/2014, 08:21