Dilatation structures I. Fundamentals

Dilatation structures I. Fundamentals

A dilatation structure is a concept in between a group and a differential structure. In this article we study fundamental properties of dilatation structures on metric spaces. This is a part of a series of papers which show that such a structure allows to do non-commutative analysis, in the sense of differential calculus, on a large class of metric spaces, some of them fractals. We also describ...

Stable Banach Spaces and Banach Space Structures, I: Fundamentals

We study model theoretical stability for Banach spaces and structures based on Banach spaces, e.g., Banach lattices or C∗-algebras. We prove that a theory is stable if and only if the following condition is true in every model E of the theory: If (ām ) and (b̄n) are bounded sequences in Ek and El (respectively) and R : Ek × El → R is definable, then there exist subsequences (āmi ) and (b̄n j ) su...

Part I Fundamentals

FUNDAMENTALS Part I of our book lays the physical and conceptual foundations of hydrologic optics, the quantitative study of the interactions of light with the earth's oceans, estuaries, lakes, rivers and other water bodies. Radiative transfer theory is the physical and mathematical framework for hydrologic optics. Chapter 1 begins with a few comments upon the nature of light itself and upon th...

Part I Fundamentals and Concepts

Fundamentals of Electrical Engineering I