Let C be an n-dimensional sphere with diameter 1 and center at the origin in E<sup>n</sup>. The view-obstruction problem for n-dimensional spheres is to determine a constant v（n） to be the lower bound of...Let C be an n-dimensional sphere with diameter 1 and center at the origin in E<sup>n</sup>. The view-obstruction problem for n-dimensional spheres is to determine a constant v（n） to be the lower bound of those α for which any half-line L, given by x<sub>i</sub>=a<sub>i</sub>t（i=1, 2,...,n） where parameter t≥0 and a<sub>i</sub>（i=1, 2,...,n） are positive real numbers, intersects Δ（C, α）={αC+（m<sub>1</sub>+（1/2）, m<sub>2</sub>+（1/2）,…,m<sub>n</sub>+（1/2））:m<sub>1</sub>, m<sub>2</sub>,…m<sub>n</sub> nonnegative integers}. In this paper, for n=3, the following result is proved. For α】1/5<sup>1/2</sup> we have that any half-line L, given by x<sub>i</sub>=a<sub>i</sub>t（i=1,2,3）, intersects Δ（C, α）, where parameter t≥0 and a<sub>i</sub>（i=1,2,3） are positive real numbers such that |a|+|b|+|c|≠3 whenever aa<sub>1</sub>+ba<sub>2</sub>+ca<sub>3</sub>=0 for three integers a, b, c.展开更多
文摘Let C be an n-dimensional sphere with diameter 1 and center at the origin in E<sup>n</sup>. The view-obstruction problem for n-dimensional spheres is to determine a constant v（n） to be the lower bound of those α for which any half-line L, given by x<sub>i</sub>=a<sub>i</sub>t（i=1, 2,...,n） where parameter t≥0 and a<sub>i</sub>（i=1, 2,...,n） are positive real numbers, intersects Δ（C, α）={αC+（m<sub>1</sub>+（1/2）, m<sub>2</sub>+（1/2）,…,m<sub>n</sub>+（1/2））:m<sub>1</sub>, m<sub>2</sub>,…m<sub>n</sub> nonnegative integers}. In this paper, for n=3, the following result is proved. For α】1/5<sup>1/2</sup> we have that any half-line L, given by x<sub>i</sub>=a<sub>i</sub>t（i=1,2,3）, intersects Δ（C, α）, where parameter t≥0 and a<sub>i</sub>（i=1,2,3） are positive real numbers such that |a|+|b|+|c|≠3 whenever aa<sub>1</sub>+ba<sub>2</sub>+ca<sub>3</sub>=0 for three integers a, b, c.
