The exact hardness of computing a Nash equilibrium is a fundamental open question in algorithmic game theory. This problem is complete for the complexity class PPAD. It is well known that problems in PPAD cannot be NP-complete unless NP = coNP. Therefore, a natural direction is to reduce the hardness of PPAD to the hardness of problems used in cryptography. Bitansky, Paneth, and Rosen [FOCS 201...

The Brinell, Vickers, Meyer, Rockwell, Shore, IHRD, Knoop, Buchholz, and nanoindentation methods used to measure the indentation hardness of materials at different scales are compared, and main issues and misconceptions in the understanding of these methods are comprehensively reviewed and discussed. Basic equations and parameters employed to calculate hardness are clearly explained, and the di...

BACKGROUND Aim of the study was to verify the efficiency of Martens hardness measurements in detecting the degradation of composite resin cements during artificial aging. METHODS Four cements were used: Variolink II (VL2), RelyX Unicem 2 Automix (RUN), PermaFlo DC (PDC), and DuoCem (DCM). Specimens for Martens hardness measurements were light-cured and stored in water at 37 °C for 1 day to al...

The ability of hardness discrimination in 11 implant denture wearers was compared with those in 10 bridge wearers and 11 normal dentate subjects. The hardness discrimination was tested using silicone rubber blocks having rubber hardness that ranged at intervals of 10 degrees from 30 degrees to 70 degrees. Using a rubber block with rubber hardness of 50 degrees as a standard, the ability of disc...

The main efficiency metrics for a cryptographic primitive are its speed, its code size and its memory complexity. For a variety of reasons, many algorithms have been proposed that, instead of optimizing, try to increase one of these hardness forms. We present for the first time a unified framework for describing the hardness of a primitive along any of these three axes: code-hardness, timehardn...

Laser-Induced Breakdown Spectroscopy (LIBS) was applied to the analysis of bioceramic samples. The relationship between sample hardness and LIBS plasma properties was investigated, with comparison to conventional Vickers hardness measurements. The plasma excitation temperature Te was determined using the lineto-continuum ratio for the Si (I) 288.16 nm emission line; we have demonstrated a linea...

We evaluate Vickers hardness and true instrumented indentation test (IIT) hardness of 24 metals over a wide range of mechanical properties using just IIT parameters by taking into account the real contact morphology beneath the Vickers indenter. Correlating the conventional Vickers hardness, indentation contact morphology, and IIT parameters for the 24 metals reveals relationships between conta...

An approximated hardness kernel, which includes the second derivative with respect to the density of the kinetic energy, the electron-electron coulomb repulsion, and the exchange density functionals, has been tested for the calculation of the global hardness. The results obtained for a series of 40 cations and neutral systems and 16 anions represent in most cases an improvement of the results o...

INTRODUCTION The hardness of denture base materials may undergo changes due to continued polymerization reaction and water uptake. However, the extent to which these processes affect the hardness of materials is still unclear. OBJECTIVE In this study, the degree of conversion of two hard chair-side reline resins (Duraliner II-D and Kooliner-K) and one heat-cured acrylic resin (Lucitone 550-L)...