background: enzymatic hydrolysis of lactose is one of the most important biotechnological processes in the food industry, which is accomplished by enzyme β-galactosidase (β-gal, β-d-galactoside galactohydrolase, ec 3.2.1.23), trivial called lactase. orthogonal arrays design is an appropriate option for the optimization of biotechnological processes for the production of microbial enzymes. metho...

Taguchi's catalog of orthogonal arrays is based on the mathematical theory of factorial designs and difference sets developed by R. C. Bose and his associates. These arrays evolved as extensions of factorial designs and latin squares. This paper (1) describes the structure and constructions of Taguchi's orthogonal arrays, (2) illustrates their fractional factorial nature, and (3) points out tha...

In an earlier paper 9], we studied a generalized Rao bound for ordered orthogonal arrays and (T; M; S)-nets. In this paper, we extend this to a coding-theoretic approach to ordered orthogonal arrays. Using a certain association scheme, we prove a MacWilliams-type theorem for linear ordered orthogonal arrays and linear ordered codes as well as a linear programming bound for the general case. We ...

An important question in the construction of orthogonal arrays is what the minimal size of an array is when all other parameters are fixed. In this paper, we will provide a generalization of an inequality developed by Bierbrauer for symmetric orthogonal arrays. We will utilize his algebraic approach to provide an analogous inequality for orthogonal arrays having mixed levels and show that the b...

Generalizing orthogonal arrays, a new class of arrays called quasiorthogonal arrays, are introduced and it is shown that fractional factorial plans represented by these arrays are universally optimal under a wide class of models. Some methods of construction of quasi-orthogonal arrays are also described.

with u0 = 0, where the dot indicates differentiation with respect to t. In this note, we shall show how solutions to this equation can be formulated in the context of exponential Riordan arrays. The Riordan arrays we shall consider may be considered as parameterised (or “time”-dependent) Riordan arrays. We have already considered parameterized Riordan arrays [1], exploring the links between the...

We introduce methods for enumerating mixed orthogonal arrays of strength 3. We determine almost all mixed orthogonal arrays of strength 3 with run size up to 100.

Taking inspiration from eukaryotic cilia, we report a method for growing dense arrays of magnetically actuated microscopic filaments. Fabricated from the bottom-up assembly of polymer-coated cobalt nanoparticles, each segmented filament measures approximately 5–15 mm in length and 23.5 nm in diameter, which was commensurate with the width of a single nanoparticle. A custom microscope stage actu...