For integers n>2 and k>0, an (n×n)?k semi-Latin square is n×n array of k-subsets (called blocks) nk-set (of treatments), such that each treatment occurs once in row column the array. A uniform if every pair blocks, not same or column, intersect positive number treatments. It known a Schur optimal class all squares, here we show when exists, squares are precisely ones. We then compare using crit...

This article considers the problem of selecting two-level designs under baseline parameterisation when some two-factor interactions are important. We propose a minimum aberration criterion, which minimises bias caused by non-negligible effects. Using this class optimal can be further distinguished from one another, and we present an algorithm to find among D-optimal designs. Sixteen-run twenty-...

Factorial designs have broad applications in agricultural, engineering and scientific studies. In constructing and studying properties of factorial designs, traditional design theory treats all factors as nominal. However, this is not appropriate for experiments that involve quantitative factors. For designs with quantitative factors, level permutation of one or more factors in a design matrix ...

Though the human eye generally creates a single image on the retina, the literature contains many examples showing perceptual monocular diplopia. Previously, monocular diplopia resulting from astigmatic defocus has been demonstrated to cause a notch (local minimum) in the contrast sensitivity function (CSF). We examine Verhoeff's (1900) model which explains how monocular diplopia can occur thro...

Two methods of spherical aberration corrections of an electrostatic gridded lens have been studied with ray-tracing simulations. Both methods are based on modifying electrostatic field on the periphery of the lens. In a simplest case such modification is done by extending the part of the grid support on its radial periphery in axial direction. In alternative method the electric field on the rad...

Minimum aberration designs are obtained for two types of mixed-level fractional factorial: (i) (s) × s factorial, and (ii) (s1) × (s2) × s factorial, where s is any prime or prime power, and r, r1, r2 and n are positive integers. Projective geometric tools are employed to find the wordlength pattern of a given design in terms of that of its complementary set. Many useful designs are found