We define a pseudo quasi-3 design as a symmetric design with the property that the derived and residual designs with respect to at least one block are quasi-symmetric. Quasi-symmetric designs can be used to construct optimal self complementary codes. In this article we give a construction of an infinite family of pseudo quasi-3 designs whose residual designs allow us to construct a family of co...

The pseudo-perturbative shifted l expansion technique PSLET is shown applicable in the non-Hermitian PT symmetric context. The construction of bound states for several PT symmetric potentials is presented, with special attention paid to V (r) = ir3 − α √ ir oscillators.

We find some properties of Ricci solitons with a semi-symmetric metric connection. When the potential vector field is torse-forming, we obtain characterizations. Applications to submanifolds are also given.

The starting point of this work is the Bochner theorem on harmonics 1-forms stated at 1946. We show that many results on minimal foliations of codimension one and two on compact pseudo-Riemannian manifolds are at the origin of this theorem. We also prove the non existence of minimal Riemannian foliations of codimension one defined by a 1-form with finite global norm on complete non compact Riem...

In this paper, we prove a general maximum principle for the time dependent Lichnerowicz heat equation on symmetric tensors coupled with the Ricci flow on complete Riemannian manifolds. As an application we construct complete manifolds with bounded nonnegative sectional curvature of dimension greater than or equal to four such that the Ricci flow does not preserve the nonnegativity of the sectio...

We describe all almost contact metric, almost hermitian and G 2-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇-parallel spinors. In particular, we obtain solutions of the type II string equations in dimension n = 5, 6 and 7.