Sintered diamond compacts using metallic cobalt binders

Method is developed for sintering diamond powder which uses metallic cobalt as binder. Present samples show maximum microhardness of over 3000 kg/sq mm on Knoop scale. Material may be used as hard surface coating or may compete with cubic boron nitride as abrasive grain

The support of local cohomology modules

We describe the support of F-finite F-modules over polynomial rings R of prime characteristic. Our description yields an algorithm to compute the support of such modules; the complexity of our algorithm is also analysed. To the best of our knowledge, this is the first algorithm to avoid extensive use of Gröbner bases and hence of substantial practical value. We also use the idea behind this algorithm to prove that the support of HjI(S) is Zariski closed for each ideal I of S where R is noetherian commutative ring of prime characteristic with finitely many isolated singular points and S=R/gR (⁠g∈R⁠)

Multiplicity bounds in prime characteristic

We extend a result by Huneke and Watanabe bounding the multiplicity of F-pure local rings of prime characteristic in terms of their dimension and embedding dimensions to the case of F-injective, generalized Cohen–Macaulay rings. We then produce an upper bound for the multiplicity of any local Cohen–Macaulay ring of prime characteristic in terms of their dimensions, embedding dimensions and HSL numbers. Finally, we extend the upper bounds for the multiplicity of generalized Cohen–Macaulay rings in characteristic zero which have dense F-injective type

Lower bounds for the query complexity of equilibria in Lipschitz games

Nearly a decade ago, Azrieli and Shmaya introduced the class of λ-Lipschitz games in which every player's payoff function is λ-Lipschitz with respect to the actions of the other players. They showed that such games admit ϵ-approximate pure Nash equilibria for certain settings of ϵ and λ. They left open, however, the question of how hard it is to find such an equilibrium. In this work, we develop a query-efficient reduction from more general games to Lipschitz games. We use this reduction to show a query lower bound for any randomized algorithm finding ϵ-approximate pure Nash equilibria of n-player, binary-action, λ-Lipschitz games that is exponential in nλ/ϵ. In addition, we introduce “Multi-Lipschitz games,” a generalization involving player-specific Lipschitz values, and provide a reduction from finding equilibria of these games to finding equilibria of Lipschitz games, showing that the value of interest is the average of the individual Lipschitz parameters. Finally, we provide an exponential lower bound on the deterministic query complexity of finding ϵ-approximate Nash equilibria of n-player, m-action, λ-Lipschitz games for strong values of ϵ, motivating the consideration of explicitly randomized algorithms in the above results

Global parameter test ideals

This paper shows the existence of ideals whose localizations and completions at prime ideals are parameter test ideals of the localized and completed rings. We do this for Cohen-Macaulay localizations (resp., completions) of non-local rings, for generalized Cohen-Macaulay rings, and for non-local rings with isolated non Cohen-Macaulay points, each being an isolated non $F$-rational point. The tools used to prove this results are constructive in nature and as a consequence our results yield algorithms for the computation of these global parameter test ideals. Finally, we illustrate the power of our methods by analyzing the HSL numbers of local cohomology modules with support at any prime ideal

An extension of a theorem of Hartshorne

We extend a classical theorem of Hartshorne concerning the connectedness of the punctured spectrum of a local ring by analyzing the homology groups of a simplicial complex associated with the minimal primes of a local ring

A data-driven approach for predicting printability in metal additive manufacturing processes

Metal powder-bed fusion additive manufacturing technologies offer numerous benefits to the manufacturing industry. However, the current approach to printability analysis, determining which components are likely to build unsuccessfully, prior to manufacture, is based on ad-hoc rules and engineering experience. Consequently, to allow full exploitation of the benefits of additive manufacturing, there is a demand for a fully systematic approach to the problem. In this paper we focus on the impact of geometry in printability analysis. For the first time, we detail a machine learning framework for determining the geometric limits of printability in additive manufacturing processes. This framework consists of three main components. First, we detail how to construct strenuous test artefacts capable of pushing an additive manufacturing process to its limits. Secondly, we explain how to measure the printability of an additively manufactured test artefact. Finally, we construct a predictive model capable of estimating the printability of a given artefact before it is additively manufactured. We test all steps of our framework, and show that our predictive model approaches an estimate of the maximum performance obtainable due to inherent stochasticity in the underlying additive manufacturing process. © 2020, The Author(s)