Theory of 2-structures, part I: Clans, basic subclasses, and morphisms

Morphisms Into Chains . Part I

Let X be a set. Note that there exists a subset of X which is trivial. Let X be a trivial set. Observe that every subset of X is trivial. Let L be a 1-sorted structure. Note that there exists a subset of L which is trivial. Let L be a relational structure. Note that there exists a subset of L which is trivial. Let L be a non empty 1-sorted structure. Note that there exists a subset of L which i...

PART I Basic Deterministic Theory of LQ and Predictive Control

Canonical Community Ordination. Part I: Basic Theory and Linear Methods

Canonical community ordination comprises a collection of methods that relate species assemblages to their environment, in both observational studies and designed experiments. Canonical ordination differs from ordination sensu stricto in that species and environment data are analyzed simultaneously. Part I reviews the theory in a non-mathematical way with emphasis on new insights for the interpr...

Basic formulas and languages Part I. The theory

Magnetotelluric tensor decomposition: Part I, Theory for a basic procedure

The problem of expressing a general 3-D magnetotelluric (MT) impedance tensor in the form of a 2-D tensor that has been distorted in some way is addressed first in terms of a general theorem. This theorem shows that when the real and quadrature parts of a tensor are analyzed separately as distinct matrices, all that is necessary to make a matrix with 2-D characteristics from one with 3-D charac...