Homogenization Fundamentals

Biotic Homogenization

Humanity’s migrations across, and subsequent modification of, the landscape have had innumerable effects on the many organisms in which we share this world. Mounting evidence suggests that the dual processes of humanmediated extirpation of native species and the introduction of nonnative species have resulted in significant changes in biological diversity at different spatial scales. Global spe...

Discrete Geometric Structures in Homogenization and Inverse Homogenization

We introduce a new geometric approach for the homogenization and inverse homogenization of the divergence form elliptic operator with rough conductivity coefficients σ(x) in dimension two. We show that conductivity coefficients are in one-to-one correspondence with divergence-free matrices and convex functions s(x) over the domain Ω. Although homogenization is a non-linear and non-injective ope...

Fundamentals of Supply Chain Management Fundamentals of Supply Chain Management Fundamentals of Supply Chain Management

2 Fundamentals

In this chapter we discuss basic terminology and notation for graphs, some fundamental algorithms, and a few other mathematical preliminaries. We denote the set of integers by , the set of real numbers by , the set of complex numbers by , and the set of rationals by . For a set X of numbers, X denotes the subset of positive numbers in X , and X 0 the subset of nonnegative numbers. The set of po...

Homogenization versus homogenization-free method to measure muscle glycogen fractions.

OBJECTIVE The glycogen is extracted from animal tissues with or without homogenization using cold perchloric acid. Three methods were compared for determination of glycogen in rat muscle at different physiological states. MATERIALS AND METHODS Two groups of five rats were kept at rest or 45 minutes muscular activity. The glycogen fractions were extracted and measured by using three methods. ...