Symmetric linear operator identities in quasigroups

Totally anti - symmetric quasigroups for all

A quasigroup (Q, ∗) is called totally anti-symmetric if (c ∗ x) ∗ y = (c ∗ y) ∗ x⇒ x = y and x∗y = y∗x⇒ x = y. A totally anti-symmetric quasigroup can be used for the definition of a check digit system. Ecker and Poch [9] conjectured that there are no totally anti-symmetric quasigroups of order 4k + 2. This article will completely disprove their conjecture (except for n = 2, 6) as we will give ...

More on embedding partial totally symmetric quasigroups

Parastrophically equivalent identities characterizing quasigroups isotopic to abelian groups

We study parastrophic equivalence of identities in primitive quasigroups and parastrophically equivalent balanced and near-balanced identities characterizing quasigroups isotopic to groups (to abelian groups). Some identities in quasigroups with 0-ary operation characterizing quasigroups isotopic to abelian groups are given.

Nonlinear Picone identities to Pseudo $p$-Laplace operator and applications

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

Symmetric Identities for Euler Polynomials

In this paper we establish two symmetric identities on sums of products of Euler polynomials.