Related papers: Two Applications of Desargues' Theorem
The reciprocal Pascal matrix has entries $\binom{i+j}{j}^{-1}$. Explicit formullae for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, $q$-analogues are also presented.
Quark-hadron duality and its potential applications are discussed. We focus on theoretical efforts to model duality.
The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.
In this short note we give counterexamples to several results related to extension theorems published recently.
We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.
We prove two extension theorems for positive maps from operator systems into matrix algebras
A New Trinomial Recombination Tree Algorithm and Its Applications
This expository paper presents some applications of the parameterized Picard-Vessiot theory for ordinary differential equations, mainly related to monodromy.
We observe that successive applications of known results from the theory of positive systems lead to an {\it efficient general algorithm} for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one…
In this note we briefly survey and propose some open problems related to isoparametric theory.
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The…
It gives some new forms of General Neron Desingularization and new applications.
We show analytically and numerically the existence of double vortex solutions in two-Higgs systems. These solutions are generalizations of the \no vortices and exist for all values of the parameters in the Lagrangians considered. We derive…
We prove recursive formulas for sums of squares and sums of triangular numbers in terms of sums of divisors functions and we give a variety of consequences of these formulas. Intermediate applications include statements about positivity of…
The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using…
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…
It is a basic introduction to differential graded Lie algebras, Maurer-Cartan equation and associated deformation functors.
In this paper, we use differential forms to prove a number of theorems of integral vector calculus that are rarely found in textbooks. Two of them, as far as the author knows, have not been published before. Some possible applications to…
In this paper we survey wqo and bqo theory from the reverse mathematics perspective. We consider both elementary results (such as the equivalence of different definitions of the concepts, and basic closure properties) and more advanced…