In this study, turning operation of Monel K500 copper-nickel super-alloy was evaluated. Ceramic cutting tools with two different cutting noses (conventional and wiper) were utilized. At first, the experimental tests were designed by using central composite design method. After implementation of the tests, the statistical models for output data (surface roughness, cutting force, and flank wear) ...

We introduce the (j, k)-Kemeny rule – a generalization of Kemeny’s voting rule that aggregates j-chotomous weak orders into a k-chotomous weak order. Special cases of (j, k)Kemeny include approval voting, the mean rule and Borda mean rule, as well as the Borda count and plurality voting. Why, then, is the winner problem computationally tractable for each of these other rules, but intractable fo...

We present an application of the MaxCut problem in statistical physics. We design a branch-and-bound algorithm for MaxCut and use it to nd all ground states in three dimensional 5 5 5 Ising spin glass systems.

Let C be a family of n compact connected sets in the plane, whose intersection graph G(C) has no complete bipartite subgraph with k vertices in each of its classes. Then G(C) has at most n times a polylogarithmic number of edges, where the exponent of the logarithmic factor depends on k. In the case where C consists of convex sets, we improve this bound to O(n log n). If in addition k = 2, the ...

Let G be a graph with vertex set V(G) and edge set E(G), respectively. The set of vertices adjacent to an x e V(G) is denoted by F(x), and the degree of x is d(x) = I F(x)l . For any subset V 'g V(G), let G[ V] denote the subgraph of G induced by the vertices of V' . Further, let K n stand for the complete graph on n vertices. It is easily seen (e.g ., Erdös [7]) that every graph G with n verti...

This is a summary of the proof by G.E. Coxson [1] that P-matrix recognition is co-NP-complete. The result follows by a reduction from the MAX CUT problem using results of S. Poljak and J. Rohn [5].

The problem of finding a maximum cut of an arbitrary graph is one of a list of 21 com-binatorial problems (Karp-Cook list). It is unknown whether or not there exist algorithms operating in polynomial bounded time for any of these problems. It has been shown that existence for one implies existence for all. In this paper we deal with a special case of the maximum cut problem. By requiring the gr...

Two results dealing with the relation between the smallest eigenvalue of a graph and its bipartite subgraphs are obtained. The first result is that the smallest eigenvalue μ of any non-bipartite graph on n vertices with diameter D and maximum degree ∆ satisfies μ > −∆ + 1 (D+1)n . This improves previous estimates and is tight up to a constant factor. The second result is the determination of th...

These notes have quite uneven levels of depth. They were prepared for a course to talented undergraduates at the Nangyang University of Technology for May 2006. The idea is that several different courses could be made from the notes. For example, the flow material could be covered quickly, only pointing at the main ideas, such as max-flow/min cut and applications, for really advanced students. ...