Pseudo equality algebras were initially introduced by Jenei and Kóródi as a possible algebraic semantic for fuzzy type theory, and they have been revised by Dvurečenskij and Zahiri under the name of JK-algebras. The aim of this paper is to investigate the internal states and the state-morphisms on pseudo equality algebras. We define and study new classes of pseudo equality algebras, such as com...

We consider a closed manifold M with a Riemannian metric gij(t) evolving by ∂t gij = −2Sij where Sij(t) is a symmetric two-tensor on (M, g(t)). We prove that if Sij satisfies the tensor inequality D(Sij , X) ≥ 0 for all vector fields X on M , where D(Sij , X) is defined in (1.6), then one can construct a forwards and a backwards reduced volume quantity, the former being non-increasing, the latt...

Multidimensional model describing the cosmological evolution and/ or spherically symmetric configuration with (n+1) Einstein spaces in the theory with several scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, n ”internal” spaces are Ricci-flat, one space M0 has a non-zero curvature, and all p-branes do not ”live” in M0, a class of exact solutions ...