When considering optimal design problems involving diffraction gratings, it is useful to have some a priori characterization of the range of possible reflectances one can achieve for given material parameters. We consider here the limiting case of a rapidly oscillating dielectric grating and show that such gratings can have reflectance no greater than that of a flat interface, regardless of the...

In this paper, a novel approach involving the concepts from mathematical programming and number theory is proposed to find the D-optimal designs. In specific, we will propose a mathematical formulation for the D-optimal design. In addition to that, we will present the use of cyclotomic cosets in the mathematical formulation, in order to reduce the total number of binary variables. We will illus...

A solution to get the problem off, have you found it? Really? What kind of solution do you resolve the problem? From what sources? Well, there are so many questions that we utter every day. No matter how you will get the solution, it will mean better. You can take the reference from some books. And the the optimal design of blocked and split plot experiments 1st edition is one book that we real...

(2) min {F(u,E) : u = u0 on ∂Ω, |E| = d} , where u0 ∈W (Ω) is a given boundary datum and 0 < d < |Ω| is prescribed. Energies with surface terms competing with a volume term often appear in materials science as a model for optimal design [1], phase transiction [5], liquid crystals [6] or continuum mechanics [4]. A similar functional was studied by L.Ambrosio and G.Buttazzo in [1] where they cons...

We study how the introduction of a central bank-issued digital currency affects interest rates, the level of economic activity, and welfare in a model where both central bank money and private bank deposits are used in exchange. Banks in our model are financially constrained and the liquidity premium on bank deposits affects the level of aggregate investment. We study the optimal design of a di...

The design of drives for high accelerating loads becomes very simple and clear with the fact that the torque– acceleration product is transmitted unchanged by an ideal gear, just like in the case of the torque–speed product (i.e., mechanical power). With this knowledge, it is easy to determine the required rated power and power rate a motor must possess for driving a given load with the specifi...