In this research, the feasibility of using mathematical modelling in the ball milling process has been evaluated to verify the hardness changes of an aluminium nanostructure. Considering the model of normal force displacement (NFD), the radius of elastic-plastic and normal displacement of two balls were computed by applying analytical modelling and coding in MATLAB. Properties of balls and alum...

A human can perceive the hardness of an object by tapping its surface. We compared the ranked subjective hardness values and physical properties of objects, including their stiffness, viscosity, density, and Shore hardness, and the frequencies and time constants of the natural vibrations caused by tapping. The stiffness, frequency, and viscosity exhibited a relatively strong positive correlatio...

In a very recent article (Torrent-Sucarrat et al., J Comput Chem 2007, 28, 574), we have shown how to evaluate the global hardness for polyatomic molecules using a hardness kernel approximation. We present here an extension of this previous work by improving the model used to evaluate the hardness kernel and the Fukui function. In addition, the concept of the local hardness is analyzed in detai...

Gustedt, J., On the pathwidth of chordal graphs, Discrete Applied Mathematics 45 (1993) 233-248. In this paper we first show that the pathwidth problem for chordal graphs is NP-hard. Then we give polynomial algorithms for subclasses. One of those classes are the k-starlike graphs a generalization of split graphs. The other class are the primitive starlike graphs a class of graphs where the inte...

The minimum k-enclosing ball problem seeks the ball with smallest radius that contains at least k of m given points in a general n-dimensional Euclidean space. This problem is NP-hard. We present a branch-and-bound algorithm on the tree of the subsets of k points to solve this problem. The nodes on the tree are ordered in a suitable way, which, complemented with a last-in-first-out search strat...

We prove that two pushing-blocks puzzles are intractable in 2D. One of our constructions improves an earlier result that established intractability in 3D [OS99] for a puzzle inspired by the game PushPush. The second construction answers a question we raised in [DDO00] for a variant we call Push-1. Both puzzles consist of unit square blocks on an integer lattice; all blocks are movable. An agent...

PURPOSE Light units used for polymerization of resin composites are subject to deterioration with age, and frequent maintenance is required to maintain optimal efficacy. This study examined the efficacy of quartz-tungsten-halogen light units in private dental offices in Toronto for polymerization of resin composites. MATERIALS AND METHODS One hundred dental offices met all selection criteria ...

Abstra t. We study the minimum kover problem. For a given string x of length n and an integer k, the minimum kover is the minimum set of ksubstrings that overs x. We show that the on-line algorithm that has been proposed by Iliopoulos and Smyth [IS92℄ is not orre t. We prove that the problem is in fa t NP-hard. Furthermore, we propose two greedy algorithms that are implemented and tested on di ...