Real Second-Order Freeness and the Asymptotic Real Second-Order Freeness of Several Real Matrix Models

Semantic Characterisations of Second-Order Computability over the Real Numbers

$(-1)$-Weak Amenability of Second Dual of Real Banach Algebras

Let $ (A,| cdot |) $ be a real Banach algebra, a complex algebra $ A_mathbb{C} $ be a complexification of $ A $ and $ | | cdot | | $ be an algebra norm on  $ A_mathbb{C}  $  satisfying a simple condition together with the norm $ | cdot | $ on $ A$.  In this paper we first show that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_mathbb{C})^* $ is a complex Banach $ (A_mathbb{C})^{...

Second Order Parallel Tensor in Real and Complex Space Forms

Levy’s theorem "A second order parallel symmetric non-singular tensor in a real space form is proportional to the metric tensor-" has been generalized by showing that it holds even if one assumes the second order tensor to be parallel (not necessarily symmetric and non-singular) in a real space form of dimension greater than two. Analogous result has been established for a complex space form. i...

Irreducible second order SUSY transformations between real and complex potentials

Second order SUSY transformations between real and complex potentials for three important from physical point of view Sturm-Liouville problems, namely, problems with the Dirichlet boundary conditions for a finite interval, for a half axis and for the whole real line are analyzed. For every problem conditions on transformation functions are formulated when transformations are irreducible, i.e. w...

Second-Order Partial Differentiation of Real Binary Functions

For simplicity, we adopt the following convention: x, x0, y, y0, r are real numbers, z, z0 are elements of R2, f , f1, f2 are partial functions from R2 to R, R is a rest, and L is a linear function. Let us note that every rest is total. Let f be a partial function from R2 to R and let z be an element of R2. The functor pdiff1(f, z) yielding a function from R2 into R is defined as follows: (Def....