– PCP theorem. The classic PCP theorem is most useful for proving that optimization problems have no PTAS. – E3LIN2. The 1− 2 vs 1/2− 2 hardness of this problem is most useful for proving that problems have no approximation beyond a fixed constant factor; i.e., for statements like “such-and-such maximization problem has no 77 78 -approximation unless P = NP”. – Raz’s Label Cover. The hardness o...

We have developed a method for prediction of the hardest crystal structures in a given chemical system. It is based on the evolutionary algorithm USPEX (Universal Structure Prediction: Evolutionary Xtallography) and electronegativity-based hardness model that we have augmented with bond-valence model and graph theory. These extensions enable correct description of the hardness of layered, molec...

Various “hardness” measures have been studied for resolution, providing theoretical insight into the proof complexity of resolution and its fragments, as well as explanations for the hardness of instances in SAT solving. In this paper we aim at a unified view of a number of hardness measures, including different measures of width, space and size of resolution proofs. Our main contribution is a ...

THE HARDNESS of human dentin has been reported by a number of investigators using a variety of methods. Wright and Fenske' used an abrasion method which gave macroscopic results and reported that there was no relationship between hardness and anatomic position in dentin. They also reported that dentin in the teeth of females was significantly harder than in males and that the hardness of dentin...

.\ hardness tester, especially adapted for grain, was cor~structecl by modifying a commercial portable soft metal tester known as the Barcol Impressor. h preloaded stylus is forced into grain sections preparetl by rneans ot a microtome. The displacement of the stylus, nleasured by a dial micrometer, is used as a hardness index. This has been related to tlie l'ickers tlianlontl pyramid hardness ...

MC-nets constitute a natural compact representation scheme for cooperative games in multiagent systems. In this paper, we study the complexity of several natural computational problems that concern solution concepts such as the core, the least core and the nucleolus. We characterize the complexity of these problems for a variety of subclasses of MC-nets, also considering constraints on the game...

The measurement of micro-hardness with loads between 0.09807 N and 0.9807 N has been carried out in direct mode (appraiser measured the dimensions of indentations with a measuring device fitted to the micro-hardness tester, a part of microscope) and in modified remote modes. The reference block – certified reference material with defined specified hardness and its uncertainty was used as a spec...

The nanoindentation experiment was carried out to estimate nanomechanical characteristics of polycarbonate polymer films. Hardness, effective elastic modulus and contact stress–strain rate curve were obtained. The results showed that the effective elastic modulus and the hardness decreased as the applied load was increased. As the hold time was increased, the effective elastic modulus and the h...

A new concept, the strength of bond, and a new form expressing the hardness of covalent and ionic crystals are presented. Hardness is expressed by means of quantities inherently coupled to the atomistic structure of matter, and, therefore, hardness can be determined by first-principles calculations. Good agreement between theory and experiment is observed in the range of 2 orders of magnitude. ...

We conducted the measurement of the hardness-depth relationship of NiTi shape memory alloy with a sharp Berkovich indenter. Different from most ductile metals, NiTi reacts to the mechanical load of indentation through phase transition underneath the indentation tip. We found that the hardness decreases rapidly with the increase of the indentation depth and eventually approaches a constant. To u...