9 citations · 24 across the 19 of their papers we have counts for
20 papers
Infinite-Dimensional Linear Algebra and Solvability of Partial Differential Equations
Todor D. Todorov
We discuss linear algebra of infinite-dimensional vector spaces in terms of algebraic (Hamel) bases. As an application we prove the surjectivity of a large class of linear partial…
Enabling four-dimensional conformal hybrid meshing with cubic pyramids
Miroslav S. Petrov, Todor D. Todorov, Gage S. Walters +2
The main purpose of this article is to develop a novel refinement strategy for four-dimensional hybrid meshes based on cubic pyramids. This optimal refinement strategy subdivides a…
Ordered Fields, the Purge of Infinitesimals from Mathematics and the Rigorousness of Infinitesimal Calculus
James F. Hall, Todor D. Todorov
We present a characterization of the completeness of the field of real numbers in the form of a \emph{collection of several equivalent statements} borrowed from algebra, real analy…
Steady-State Solutions in an Algebra of Generalized Functions
Todor D. Todorov
Formulas for the solutions of initial value problems for ordinary differential equations with singular -like driving terms are derived in the framework of an algebra of ge…
Algebraic Approach to Colombeau Theory
Todor D. Todorov
We present a differential algebra of generalized functions over a field of generalized scalars by means of several axioms in terms of general algebra and topology. Our differential…
Back to Classics: Teaching Limits Through Infinitesimals
Todor D. Todorov
The usual -definition of the limit of a function (whether presented at a rigorous or an intuitive level) requires a "candidate " for the limit value. Thus, we have to start…