Transforming light: illustration of how an arbitrary linear transform can be achieved in an all-optical system using diffractive surfaces (Courtesy: Ozcan Lab/UCLA) Researchers in the US have shown ...

In this review article, we discuss the synthesis and dynamic nature of macromolecular systems that have mechanically linked polymer chains capable of undergoing a topology transformation driven by a ...

In this paper we obtain a linear transformation theorem in which the Radon-Nikodym derivative is very closely related to the transformation. We also obtain a vector-valued conditional version of this ...

Let F be an algebraically closed field and $T : M_{n}(F) \longrightarrow M_{n}(F)$ be a linear transformation. In this paper we show that if T preserves at least one ...

Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Prereq., APPM 1360 ...