Elasticity is a well-established field within mathematical physics, yet new formulations can provide deeper insight and computational advantages. This study explores the geometry of two- and three-dimensional elastic curves using the formalism of geometric algebra, offering a unified and coordinate-free approach. This work systematically derives the Frenet, Darboux, and Bishop frames within the three-dimensional geometric algebra and employs them to integrate the elastica equation. A concise Lagrangian formulation…

Elasticity is a well-established field within mathematical physics, yet new formulations can provide deeper insight and computational advantages. This study explores the geometry of two- and three-dimensional elastic curves using the formalism of Geometric Algebra, offering a unified and coordinate-free approach. The work systematically derives the Frenet, Darboux, and Bishop frames within the three-dimensional Geometric Algebra and employs them to integrate the elastica equation. A concise Lagrangian formulation …

Clifford algebras are an active area of mathematical research having numerous applications in mathematical physics and computer graphics, among many others. This paper demonstrates algorithms for the computation of characteristic polynomials, inverses, and minimal polynomials of general multivectors residing in a non-degenerate Clifford algebra of an arbitrary dimension. The characteristic polynomial and inverse computation are achieved by a translation of the classical Faddeev–LeVerrier–Souriau (FVS) algorithm in…

This article investigates the continuity of derivatives of real-valued functions from a topological perspective. This is achieved by the characterization of their sets of discontinuity. The same principle is applied to Gateaux derivatives and gradients in Euclidean spaces. This article also introduces a generalization of the derivatives from the perspective of the modulus of continuity and characterizes their sets of discontinuities. There is a need for such generalizations when dealing with physical phenomena, su…

The two-parameter Wright special function is an interesting mathematical object that arises in the theory of the space and time-fractional diffusion equations. Moreover, many other special functions are particular instantiations of the Wright function. The article demonstrates finite representations of the Wright function in terms of sums of generalized hypergeometric functions, which in turn provide connections with the theory of the Gaussian, Airy, Bessel, and Error functions, etc. The main application of the pr…