Related Experiment Video
Updated: Dec 5, 2025

Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging
Published on: November 8, 2012
Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-Rectangular 2-Dimensional Domains
Daniele Mortari1, David Arnas2
1Aerospace Engineering, Texas A&M University, College Station, TX 77845-3141, USA.
None:
This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this manuscript proposes three different mappings techniques: (a) complex mapping, (b) the projection mapping, and (c) polynomial mapping. In that respect, an accurate least-squares approximated inverse mapping is also developed for those mappings with no closed-form inverse. Advantages and disadvantages of using these mappings are highlighted and a few examples are provided. Additionally, the paper shows how to replace boundary constraints expressed in terms of a piece-wise sequence of functions with a single function, which is compatible and required by the Theory of Functional Connections already developed for rectangular domains.
Related Concept Videos
Introduction to One-to-one Functions
Transformations of Functions II
Functional Classification of Joints
The functional classification of joints is determined by the amount of mobility between the adjacent bones. Joints are functionally classified as a synarthrosis or immobile joint, an amphiarthrosis or slightly moveable joint, or as a diarthrosis, a freely moveable joint. Fibrous and cartilaginous joints can be functionally classified as either synarthroses or amphiarthroses, whereas all synovial joints are classified as diarthroses.
Synarthrosis
An...
Transformations of Functions III
Transformations of Functions I
Area Computation by the Alternative Coordinate Method

