In this paper, we establish the generalized Hyers-Ulam stability of Jordan homomorphisms and Jordan derivations between ternary algebras via the generalized Jensen equation rf( sx+ty r ) = sf(x) + tf(y).

We prove that a Jordan curve in the 2-sphere is a quasicircle if and only if the closure of its orbit under the action of the conformal group contains only points and Jordan curves.

If F is an algebraically closed field, any element in M n (F) is similar to a sum of a diagonal matrix and a nilpotent matrix whose non-zero entries are all 1, just above the diagonal. Something similar is true for elements of an arbitrary affine algebraic group as well as its Lie algebra. That's what this essay will attempt to explain. I begin with a very elementary account of what happens for...

We investigate the computational complexity of finding the minimum-area circumscribed rectangle of a given two-dimensional domain. We study this problem in the polynomial-time complexity theory of real functions based on the oracle Turing machine model. We show that a bounded domain S with a polynomial-time computable Jordan curve Γ as the boundary may not have a computable minimum-area circums...

Let E be an elementary abelian p-group of rank r and let k be a field of characteristic p. We introduce functors Fi from finitely generated kE-modules of constant Jordan type to vector bundles over projective space Pr−1. The fibers of the functors Fi encode complete information about the Jordan type of the module. We prove that given any vector bundle F of rank s on Pr−1, there is a kE-module M...

Let E ∼= (Z/p)r (r ≥ 2) be an elementary abelian p-group and let k be an algebraically closed field of characteristic p. A finite dimensional kE-module M is said to have constant Jordan type if the restriction of M to every cyclic shifted subgroup of kE has the same Jordan canonical form. I shall begin by discussing theorems and conjectures which restrict the possible Jordan canonical form. The...

In this work we introduce generalized projective geometries which are a natural generalization of projective geometries over a field or ring K but also of other important geometries such as Grassmannian, Lagrangian or conformal geometry (see [3]). We also introduce the corresponding generalized polar geometries and associate to such a geometry a symmetric space over K. In the finite-dimensional...