A Howell design of side s and order 2n, or more briefly an H(s, 2n), is an s x s array in which each cell is either empty or contains an unordered pair of elements from some (2n)-set V such that (1) every element of V occurs in precisely one cell of each row and each column, and (2) every unordered pair of elements from V is in at most one cell of the array. It follows immediately from the defi...

This report proposes adaptable boundary sets as a new version-space representation. It is shown that adaptable boundary sets can be adjusted to a version-space representation between boundary sets [5, 6, 7] and instance-based boundary sets [11, 12, 13]. This allows the choice of proper version-space representations to be realised dynamically during the learning phase.

Error estimation is a crucial part of classification methodology and it becomes problematic with small samples. We demonstrate here that the complexity of the decision boundary plays a key role on the performance of error estimation methods. First, a model is developed which quantifies the complexity of a classification problem purely in terms of the geometry of the decision boundary, without r...

Microcompression testing is used to probe the uniaxial stress–strain response of a nanocrystalline alloy, with an emphasis on exploring how grain size and grain boundary relaxation state impact the complete flow curve and failure behavior. The yield strength, strain hardening, strain-to-failure and failure mode of nanocrystalline Ni–W films with mean grain sizes of 5, 15 and 90 nm are studied u...

The exceptional properties of nanocrystalline materials lend themselves to a wide range of structural and functional applications. There is recent evidence to suggest that grain boundary impurities may have a dramatic effect on the stability, strength and ductility of nanocrystalline metals and alloys. In this study, transmission electron microscopy and atom probe tomography were used to charac...

We investigate the pinning and driven dynamics of vortices interacting with twin boundaries using large scale molecular-dynamics simulations on samples with near one million pinning sites. For low applied driving forces, the vortex lattice orients itself parallel to the twin boundary and we observe the creation of a flux gradient and vortex-free region near the edges of the twin boundary. For i...

We study the boundary between the vortex-solid and the vortex-liquid phases in the Hc–Hab plane, for irradiated Bi2Sr2CaCu2O8+δ single crystals, by measuring the ac-local magnetic permeability in tilted magnetic fields. For high temperatures and at the phase boundary, we find that the c-axis magnetic field component H trans c decreases linearly when increasing the in-plane magnetic field Hab, s...

in this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....