Discussion: Commodity Price Discovery: Problems That Have Solutions or Solutions That Are Problems

An Index Theory for Paths That Are Solutions of a Class of Strongly Indefinite Variational Problems

We generalize the Morse index theorem of [12, 13] and we apply the new result to obtain lower estimates on the number of geodesics joining two fixed non conjugate points in certain classes of semi-Riemannian manifolds. More specifically, we consider semi-Riemannian manifolds (M, g) admitting a smooth distribution spanned by commuting Killing vector fields and containing a maximal negative distr...

Common solutions to pseudomonotone equilibrium problems

‎In this paper‎, ‎we propose two iterative methods for finding a common solution of a finite family of equilibrium problems ‎for pseudomonotone bifunctions‎. ‎The first is a parallel hybrid extragradient-cutting algorithm which is extended from the‎ ‎previously known one for variational inequalities to equilibrium problems‎. ‎The second is a new cyclic hybrid‎ ‎extragradient-cutting algorithm‎....

Solutions to homework problems

1 Homework Assignment # 1 1. Show that the -δ definition of continuity of a map f : X → Y between metric spaces is equivalent to the definition of continuity in terms of open subsets. Proof. Suppose f is -δ-continuous (i.e., continuous in the sense of the -δ definition of continuity) and that U is an open subset of Y . We need to show that f−1(U) is an open subset of X. The definition of an ope...

Creative Solutions to Problems

Math Problems, with Solutions

These are free online notes that I wrote to assist students that wish to test their math skills with some problems that go beyond the usual curriculum. These notes can be used as complimentary to an advanced calculus or algebra course, as training for math competitions or simply as a collection of challenging math problems. Many of these are my own creation, some from when I was a student and s...