In this lecture, we first examine several classes of NP-hardness and polynomial time algorithms which arise from differences in how integers are encoded in problem input. We then look at the 3-partition problem, which is very useful for proving the strongest notion of NP-hardness. Finally, we use reduction from 3-partition to prove NP-hardness for a handful of problems, including a set of 4 pac...

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 ...

INTRODUCTION For the construction of any dental prosthesis, accurate impressions are necessary. Hence, we undertook the present study to evaluate and compare the surface hardness of gypsum casts poured from impressions made using conventional alginate and self-disinfecting alginate. MATERIALS AND METHODS A total of 30 impressions of stainless steel die were made, out of which 15 impressions w...

Formulas governing fixed orbital hardnesses and their relation to the hardness kernel are derived. It is shown how the orbital hardness matrix and its inverse matrix, the orbital softness matrix, may thus be directly calculated, and then the total chemical hardness, softness, and electronegativity of a molecular species. These quantities are calculated for the molecule HCN, using Dirac exchange...

In this paper we study the small Na+N (N 12) cationic clusters fragmentation channels, with all electronic calculations performed at the B3LYP/6–311G+(d,p) DFT level of theory. For these cluster sizes, we obtain for all neutral, cationic, bi-cationic and anionic species the optimized geometries, total energies and electronic properties such as the adiabatic ionization potentials, electron affin...

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 ...

AIM The aim of this in vitro study was to evaluate the surface roughness and hardness of both unbleached and bleached (opalescence; 10% carbamide peroxide) human enamel brushed with water (without dentifrice), fluoride abrasive dentifrice (Colgate Total) and whitening dentifrice (Natural White). MATERIALS AND METHODS Human enamel samples were obtained from third molars and randomly divided in...

The present investigation deals with limnobiotic status of the Almatti reservoir from February, 2003 to January, 2005. The study revealed that there exists a fluctuations of the physical factors viz., rainfall, humidity, air and water temperature, pH and electrical conductivity (EC), and chemical factors viz., dissolved oxygen (DO), free carbon dioxide, total alkalinity, total hardness, calcium...