Triple Positive Solutions of BVP for Second Order ODE with One Dimensional Laplacian on the Half Line Yuji Liu and Patricia J. Y. Wong Department of Mathematics, Guangdong University of Business Studies, Guangzhou 510320, P.R.China. e-mail: [email protected] School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore. e-mai...

[1] Nemirovski and Yudin. Problems Complexity and Method Efficiency in Optimization. Wiley-Interscience series in discrete mathematics. Wiley, 1983. [2] W. Krichene, A. Bayen and P. Bartlett. Accelerated Mirror Descent in Continuous and Discrete Time. NIPS 2015. [3] W. Su, S. Boyd and E. Candes. A differential equation for modeling Nesterov's accelerated gradient method: theory and insights. NI...

In this paper, we study the minimum size 2-edge connected spanning subgraph problem (henceforth 2EC) and show that every 3-edge connected cubic graphG = (V,E), with n = |V | allows a 2EC solution for G of size at most 7n 6 , which improves upon Boyd, Iwata and Takazawa’s guarantee of 6n 5 .

This paper is devoted to the smooth and stationary Wong-Zakai approximations for a class of rough differential equations driven by geometric fractional Brownian path $\boldsymbol{\omega}$ with Hurst index $H\in(\frac{1}{3},\frac{1}{2}]$. We first construct approximation $\boldsymbol{\omega}_{\delta}$ probabilistic arguments, then using theory obtain solution on any finite interval. Finally, bot...

Amputation is one of the oldest procedures in surgery; this is shown on the wall of the Temple of Rameses III near Luxor. In the foot, amputation between the tarsometatarsal level and the level of the Syme procedure results in an equinus deformity due to imbalance between tendons acting at the ankle. Syme’s amputation is simple and produces a stump with end-bearing properties and good proprioce...