scholarly journals A computational search for the zeta phase in the tantalum carbides

2018 ◽  
Vol 102 (3) ◽  
pp. 1454-1462 ◽  
Author(s):  
Christopher R. Weinberger ◽  
Gregory B. Thompson
Keyword(s):  
Tantalum Carbides ◽  
Computational Search

New optimal covering arrays using an orderly algorithm

2018 ◽  
Vol 10 (01) ◽  
pp. 1850011 ◽  
Author(s):  
Idelfonso Izquierdo-Marquez ◽  
Jose Torres-Jimenez
Keyword(s):  
Small Subset ◽  
Computational Results ◽  
Covering Array ◽  
Covering Arrays ◽  
Computational Search ◽  
Minimum Number ◽  
Orderly Algorithm

A covering array [Formula: see text] is an [Formula: see text] array such that every [Formula: see text] subarray covers at least once each [Formula: see text]-tuple from [Formula: see text] symbols. For given [Formula: see text], [Formula: see text], and [Formula: see text], the minimum number of rows for which exists a CA is denoted by [Formula: see text] (CAN stands for Covering Array Number) and the corresponding CA is optimal. Optimal covering arrays have been determined algebraically for a small subset of cases; but another alternative to find CANs is the use of computational search. The present work introduces a new orderly algorithm to construct non-isomorphic covering arrays; this algorithm is an improvement of a previously reported algorithm for the same purpose. The construction of non-isomorphic covering arrays is used to prove the nonexistence of certain covering arrays whose nonexistence implies the optimality of other covering arrays. From the computational results obtained, the following CANs were established: [Formula: see text] for [Formula: see text], [Formula: see text], and [Formula: see text]. In addition, the new result [Formula: see text], and the already known existence of [Formula: see text], imply [Formula: see text].

scholarly journals Combinatorial Nullstellensatz Modulo Prime Powers and the Parity Argument

10.37236/4124 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
László Varga
Keyword(s):  
Complexity Class ◽  
Combinatorial Nullstellensatz ◽  
Search Problem ◽  
Search Problems ◽  
Computational Search

We present new generalizations of Olson's theorem and of a consequence of Alon's Combinatorial Nullstellensatz. These enable us to extend some of their combinatorial applications with conditions modulo primes to conditions modulo prime powers. We analyze computational search problems corresponding to these kinds of combinatorial questions and we prove that the problem of finding degree-constrained subgraphs modulo $2^d$ such as $2^d$-divisible subgraphs and the search problem corresponding to the Combinatorial Nullstellensatz over $\mathbb{F}_2$ belong to the complexity class Polynomial Parity Argument (PPA).

scholarly journals The Dilatometric Analysis of the High Carbon Alloys from Ni-Ta-Al-M System

2014 ◽  
Vol 59 (3) ◽  
pp. 977-980 ◽  
Author(s):  
P. Bała
Keyword(s):  
Elevated Temperatures ◽  
Volume Fraction ◽  
Intermetallic Phase ◽  
Coarse Grained ◽  
Precipitation Process ◽  
Cast State ◽  
High Carbon ◽  
Chromium Carbides ◽  
Tantalum Carbides ◽  
Co Alloys

Abstract In the following work presents results of high carbon alloys from the Ni-Ta-Al-M system are presented. The alloys have been designed to have a good tribological properties at elevated temperatures. Despite availability of numerous hot work tool materials there is still a growing need for new alloys showing unique properties, which could be used under heavy duty conditions, i.e. at high temperatures, in a chemically aggressive environment and under heavy wear conditions. A characteristic, coarse-grained dendritic microstructure occurs in the investigated alloys in the as-cast condition. Primary dendrites with secondary branches can be observed. Tantalum carbides of MC type and graphite precipitations are distributed in interdendritic spaces in the Ni-Ta-Al-C and Ni-Ta-Al-C-Co alloys, while Tantalum carbides of MC type and Chromium carbides of M7C3 type appeared in the Ni-Ta-Al-C-Co-Cr and Ni-Ta-Al-C-Cr alloys. In all alloys g’ phase is present, however, its volume fraction in the Ni-Ta-Al-C and Ni-Ta-Al-C-Co alloys is small.During heating from as-cast state in Ni-Ta-Al-C and Ni-Ta-Al-C-Co alloys, the beginning of the tantalum carbides precipitation process (MC type) followed (or simultaneous) by the intermetallic phase precipitation (g’ – Ni3(AlTa)) was stated, while in Ni-Ta-Al-C-Co-Cr and Ni-Ta-Al-C-Cr alloys, besides Tantalum carbides also the Chromium carbides precipitation occurred. It means that the investigated alloys were partially supersaturated in as-cast state. Above 1050°C in all investigated alloys the g’ phase is dissolving. In addition, the precipitation of secondary carbides during slow cooling was occured.

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