This article describes a formal strategy of geometric complexity theory (GCT) to resolve the self referential paradox in the P vs. NP and related problems. The strategy, called the flip, is to go for explicit proofs of these problems. By an explicit proof we mean a proof that constructs proof certificates of hardness that are easy to verify, construct and decode. The main result in this paper s...

The paper demonstrates the correlation between the chemical composition of steel grades and the hardness as well as the formability of laser welds generated with modern automotive high strength steel grades. At the very low heat input of industrial laser welding and the resulting extremely high cooling rate, the weld hardness is fully controlled by the carbon content of the base materials and n...

Significant measurement differences occur in Rockwell B hardness (HRB) tests when using 1.588 mm diameter ball indenters made of steel and tungsten carbide (WC). In this paper, finite element analysis (FEA) is used to simulate the HRB indentation process using steel, tungsten carbide and rigid ball indenters on the same tested materials under the same testing conditions. The influence of the de...

Objective This study investigated the wear resistance of injection-molded thermoplastic denture base resins using nanoindentation instrument. Materials and methods Six injection-molded thermoplastic denture base resins (two polyamides, two polyesters, one polycarbonate, one polymethylmethacrylate [PMMA]) and a PMMA conventional heat-polymerized denture-based polymer control were tested. Elastic...

Cellulose fibers, cell wall fragments and cellulose microfibrils can be used as reinforced materials for biocomposite manufacture. Understanding nano-mechanical properties of those materials will be very useful to show their full theoretical potential. Nanoindentation testing is a technique that determines the mechanical properties of a material in the sub-micron/nano scale. The test involves p...

In the late 80’s Blum, Luby, Rubinfeld, Kannan et al. pioneered the theory of self–testing as an alternative way of dealing with the problem of software reliability. Over the last decade this theory played a crucial role in the construction of probabilistically checkable proofs and the derivation of hardness of approximation results. Applications in areas like computer vision, machine learning,...

Whereas common Vickers indentation segmentation algorithms are precise with high quality images, low quality images often cannot be segmented appropriately. We investigate an approach, where unfocused images are segmented. On the one hand, the segmentation accuracy of low quality images can be improved. On the other hand we aim in reducing the overall runtime of the hardness testing method. We ...

The security of the most popular asymmetric cryptographic scheme RSA depends on the hardness of factoring large numbers. The best known method for factorization large integers is the General Number Field Sieve (GNFS). One important step within the GNFS is the factorization of midsize numbers for smoothness testing, an efficient algorithm for which is the Elliptic Curve Method (ECM). We present ...

This paper describes the fabrication and mechanical testing of Al-Mg-boron carbide particulate composites using stir casting technique. The size of the boron carbide particulates is ranging between 30 to 100 μm. The boron carbide contents are varied from 3 and 7% by weight and are dispersed in the alloy matrix. The mechanical properties of the castings, particularly their tensile properties and...