How to prove whether a set is a closed set? Prove that if f_n \rightarrow f uniformly on a set S, and if g_n \rightarrow g uniformly on S, then f_n + g_n \rightarrow f+g uniformly on S. How can you prove two sets are equal?
With this it should be easy enough to prove that a set is not convex: just find a counterexample. But how do you prove that itisconvex? How do I do it forthis setΩ={(x,y):x2+y2≤1}Ω={(x,y):x2+y2≤1}the unit disk? Ω={(x,y)∈R2∣x2+y2≤1}Ω={(x,y)∈R2∣...
We investigate the regularity of the marginals onto hyperplanes for sets of\nfinite perimeter. We prove, in particular, that if a set of finite perimeter\nhas log-concave marginals onto a.e. hyperplane then the set is convex.Alessio FigalliDavid Jerison...
Prove that a set S of metric space (X,d) is compact? What is the difference between closed, bounded and compact sets? Why sum of convex functions are convex? How to calculate the minkowski sum? How to prove if a polytope is bounded?
Can one use Pick's theorm to prove that area size 5 covers at least 6 grid points? 0 How do you prove the arithmetic mean of vertices of a polygon lies in itself? 1 Area enclosed by a polygon 5 Determine whether a polygon is convex based on its vertices. ...
convex functionslinear matrix inequalitiesThere has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal matrices. Here, we go ...
If someone knows of a prove it would be awesome! Also an answer that contains a proof, even if its for some special case, say "convex function" or in the case of linear regression or whatever the case is, but that provides some insight (or a proof) why this ...
[] = { // How to set this up?? // The compiler wants constant expressions here, // and the extern is not considered a constant expression // This is what I tried: { data1, data1_size, data1_version}, { data2, data2_size, data2_version}, }; int main(void) { return 0; ...
alocal minimizer convex function 地方minimizer凸函数[translate] aThese sisters are my friend 这些姐妹是我的朋友[translate] ago to the newer item. 去更新的项目。[translate] aCode:0 An error occurred while attempting to initialize the Borland Database Engine (error $210D) 正在翻译,请等待... ...
Prove Property 6 of Theorem 11, that is, a times (b times c) = (a cdot c)b - (a cdot b)c Let vec{a} is not equal to vec{0}. If vec{a} times vec{b} = vec{a} times vec{c} and vec{a} cdot vec{b} = vec{a} cdot vec...