Israel Journal of MathematicsH. Gillet and C. Soul´e. Erratum for: "On the number of lattice points in convex symmetric bodies and their duals", Israel Journal of Mathematics 74 (1991), 347-357. Israel J. Math., 171:443-444, 2009....
We investigate the fluctuations in N(alpha)(R), the number of lattice points n is-an-element-of Z2 inside a circle of radius R centered at a fixed point alpha is-an-element-of [0, 1)2 . Assuming that R is smoothly (e.g., uniformly) distributed on a segment 0 less-than-or-equ...
The crystal structure of [Fe(bt)2(NCS)2] (A) was determined by X-ray diffraction at 293 and at 150 K in order to analyze the structural changes associated ... A Galet,AB Gaspar,MC Muñoz,... - 《Inorganic Chemistry》 被引量: 84发表: 2006年 Theta functions, quantum tori and Heis...
Problem 20. Find the number of triangles whose vertices are lattice points in the xy-plane satisfying 1≤x≤5 and 1≤y≤5.(A)1650(B)2200(C)2270(D)2160(E)2016 相关知识点: 试题来源: 解析 Dy x x 25 There are =2300 ways to select 3 points. 3 However, not any 3 points will ...
To determine the number of atoms in a unit cell of a face-centered cubic (FCC) crystal, we can follow these steps:1. Identify the positions of the atoms in the FCC unit cell: - In a face-centered cubic unit cell, atoms are l
3- For the graph shown: a- Calculate the number of lattice points on the plane (111) for an fcc crystal with a=3.1A˚ b- In GaAs, the crystal is shown in the figure where a=3.75A˚. There are two elements consisting its basi...
We investigate the fluctuations in the number of integral lattice points on the Heisenberg groups which lie inside a Cygan–Korányi ball of large radius. Let $$ \mathcal{E}_{q}(x)=\big|\mathbb{Z}^{2q 1}\cap\delta_{x}\mathcal{B}\big|-extit{vol}\big(\mathcal{B}\big)x^{2q...
Show that the reciprocal lattice of the direct FCC lattice is a BCC lattice. Determine the number of lattice points per unit cell there are in face-centered and body-centered unit cells. If the number of divisions on the circular scale is 50, calculate the leas...
- 《Mathematics of Computation》 被引量: 163发表: 2003年 Constructing Good Lattice Rules with Millions of Points We develop an algorithm for the construction of randomly shifted rank-1 lattice rules in d -dimensional weighted Sobolev spaces with a significantly reduced construction cost. The results...
We present a formula for the degree of the discriminant of a smooth projective toric variety associated to a lattice polytope P, in terms of the number of integral points in the interior of dilates of faces of dimension greater or equal than dimP2....