Graph augmentation problems are motivated by network design, and have been studied extensively in optimization. We consider augmentation problems over plane geometric graphs, that is, graphs given with a crossing-free straight-line embedding in the plane. The geometric constraints on the possible new edges render some of the simplest augmentation problems intractable, and in many cases only ext...

Cutting plane methods are exact algorithms for integer programming problems. They have proven to be very useful computationally in the last few years, especially when combined with a branch and bound algorithm in a branch and cut framework. These methods work by solving a sequence of linear programming relax-ations of the integer programming problem. The relaxations are gradually improved to gi...

objectives to compare an out-of-plane interscalene catheter technique to the in-plane technique in a randomized clinical trial. patients and methods eighty-four patients undergoing open shoulder surgery were randomized to either the in-plane or out-of-plane ultrasound-guided continuous interscalene technique. the primary outcome was vas pain rating at 24 hours. secondary outcomes included pain ...

The Finite Formulation is an alternative to the widely used Finite Elements or Edge Elements methods and adopts the global variables as a starting point. The Finite Formulation allows one to straightforwardly deduce the set of algebraic equations. This method has been applied to the solution of plane electrostatic problems on the basis of two different topologies of the primal mesh elements: tr...

Abstract. This investigation studies nonemptiness problems of plane square tiling. In the edge coloring (or Wang tiles) of a plane, unit squares with colored edges of p colors are arranged side by side such that adjacent tiles have the same colors. Given a set of Wang tiles B, the nonemptiness problem is to determine whether or not Σ(B) = ∅, where Σ(B) is the set of all global patterns on Z2 th...

In Beardwood et al. [3], the authors prove that for any bounded uniform i.i.d. random variables {X i : 1 < i < oo} with values in R 2, the length of the shortest tour through {X~ ..... X,} is asymptotic to a constant times ~ with probability one (the same being true in expectation). In fact, this result is valid for any uniform i.i.d. random variables with compact support of measure one in R a,...

We consider a mixed boundary value problem for a quarter-plane with a Robin condition on one edge. We have developed two procedures, one based on the advanced theory of dual integral equations and the other, in our opinion simpler technique, relying on conformal mapping. Both of the procedures are of interest, because the former may be easier to adapt to other boundary value problems.