where 1 < p < N+2 N−2 , N ≥ 3. It is well-known that this equation has a unique positive radial solution. The existence of sign-changing radial solutions with exactly k nodes is also known. However the uniqueness of such solutions is open. In this paper, we show that such sign-changing radial solution is unique when p is close to N+2 N−2 . Moreover, those solutions are non-degenerate, i.e., the...

We introduce the regularized Newton method (rnm) for unconstrained convex optimization. For any convex function, with a bounded optimal set, the rnm generates a sequence that converges to the optimal set from any starting point. Moreover the rnm requires neither strong convexity nor smoothness properties in the entire space. If the function is strongly convex and smooth enough in the neighborho...

0. Summary. This paper is concerned with the properties of convex cones and their dual cones generated by points randomly distributed on the surface of a d-sphere. For radially symmetric distributions on the points, the expected nGmber of k-faces and natural measure of the set of k-faces will be found. The expected number of vertices, or extreme points, of convex hulls of random points in E~ an...

In this paper, we consider the approximation problem on the volume of a convex body K in Rn by those of its radial mean bodies RpK. Specifically, we establish the identity lim p→∞ p log p (1− 2−n |Rp(K)| |K| ) = n(n+ 1) 2 , when K is an ellipsoid in Rn. c ©2016 All rights reserved.

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex N-fold integer minimization problems and to convex 2-stage stoch...

We consider the focusing \begin{document}$ L^2 $\end{document}-supercritical Schrödinger equation in exterior of a smooth, compact, strictly convex obstacle id="M3">\begin{document}$ \Theta \subset \mathbb{R}^3 $\end{document}. We construct solution behaving asymptotically as s...

For the problem of maximizing a convex quadratic function under convex quadratic constraints, we derive conditions characterizing a globally optimal solution. The method consists in exploiting the global optimality conditions, expressed in terms of ε-subdifferentials of convex functions and ε-normal directions, to convex sets. By specializing the problem of maximizing a convex function over a c...

This paper deals with the Legendre wavelet (LW) collocation method for the numerical solution of the radial Schrodinger equation for hydrogen atom. Energy eigenvalues for the hydrogen bound system is derived -13.6 eV. Numerical results of the ground state modes of wave function for the hydrogen R(r) or the electron probability density function, has been presented. The numerical results ha...

All GL(n) covariant Lp radial valuations on convex polytopes are classified for every p > 0. It is shown that for 0 < p < 1 there is a unique non-trivial such valuation with centrally symmetric images. This establishes a characterization of Lp intersection bodies. 2000 AMS subject classification: 52A20 (52B11, 52B45)