By constructing a Gray map, constacyclic codes of arbitrary lengths over ring \(R = Z_{p^m } + vZ_{p^m }\) are studied, where v 2 = v The structure of constacyclic codes over R and their dual codes are obtained. A necessary and sufficient condition for a linear code to be self-dual constacyclic is given. In particular, (1+(v+1)αp)-constacyclic codes over R are classified in terms of generator polynomial, where α is a unit of \(Z_{p^m }\).
A set of viscoplastic constitutive equations is presented in this study to predict hot compressive deformation behaviour and densification levels of powder metallurgy (P/M) FGH96 nickel-base superalloy during direct powder forging (DPF) process. The constitutive equations make use of the elliptic equivalent stress proposed in porous material models, and unify the evolution of relative density, normalised dislocation density, isotropic hardening and flow softening of the powder compact. A gradient-based optimisation technique is adopted to determine the material constants using the experimental data obtained from Gleeble isothermal uniaxial compression tests of HIPed FGH96 at different temperatures and strain rates. The developed constitutive equations are incorporated into finite element code DEFORM via user-defined subroutine for coupled thermo-mechanical DPF process modelling. The constitutive equations benefiting from the viscoplastic densification model of the calibrated Abouaf, among the six studied porous material models, compare favourably with the experimental data, while the equations integrating the porous material model of Shima and Oyane provide excellent agreement with experiments in the low density outer region of the powder compact. (C) 2018 Elsevier Ltd. All rights reserved.
The intention of this paper is to give an overview of selected R&D trends in the cemented carbide field, focusing on work performed in recent years. Due to the large activity in the field, it is not feasible to give a comprehensive review of all research activities in the hard metal industry and academia. Therefore, focus has been given to areas with a large number of publications in journals on the field of cemented carbides, cermets and powder metallurgy of hard materials, which indicates interesting emerging areas, techniques and trends. Such areas include fine grained materials, interfaces, alternative binders, alternative sintering techniques, and gradients; high resolution microscopy and electron backscatter diffraction. Amongst emerging trends, coupling between experiments and modelling at different scales is growing, as well as three dimensional modelling of microstructure evolution. Trends are discussed and an outlook for future development in the respective fields is given. (C) 2014 Elsevier Ltd. All rights reserved.
While studying the existence of closed geodesies and minimal hypersurfaces in compact manifolds, the concept of width was introduced in different contexts. Generally, the width is realized by the energy of the closed geodesies or the volume of minimal hypersurfaces, which are found by the Min- imax argument. Recently, Marques and Neves used the p-width to prove the existence of infinitely many minimal hypersurfaces in compact manifolds with positive Ricci curvature. However, whether the p-width can be realized as the volume of minimal hypersurfaces is not known yet. We introduce the concept of the (p, m)-width which can be viewed as the stratification of the p-width, and prove that the (p, m)-width can be realized as the volume of minimal hypersurfaces with multiplicities.
We study dynamics of (m, n)-string in (p, q)-five-brane and (p, q)-string background. We determine world-volume stress energy tensor and we analyze the dependence of the string's dynamics on the values of the charges (m, n) and the value of the angular momentum.
Let \(Q(\mathbf{{x}}) = Q(x_1 ,x_2 ,\dots ,x_n )\) be a nonsingular quadratic form over \(\mathbb {Z}\), and \(p\) be an odd prime. A solution of the congruence \(Q({\mathbf {x}}) \equiv {\mathbf {0}}\,(\mathrm{mod}\, p^m )\) is said to be a primitive solution if \(p\not \mid x_i \) for some \(i\). We prove that if \(p > A,\) where \( A = 2^{2(n + 1)/(n - 2)} 3^{2/(n - 2)}\), then this congruence has a primitive solution, with \( \left\| \mathbf{{x}} \right\| \le 6^{1/n} p^{(m/2) + (m/n)}\) whenever \(n>m\) and \(m\ge 2,\) for every even \(n\).