This is a pioneering work, introducing novel class of optimization objective functions over subsets primeonly integer points. We show rich variety Prime Optimization and mixed problems.

We introduce M -tensors. This concept extends the concept ofM -matrices. We denote Z-tensors as the tensors with nonpositive off-diagonal entries. We show that M -tensors must be Ztensors and the maximal diagonal entry must be nonnegative. The diagonal elements of a symmetric M -tensor must be nonnegative. A symmetric M -tensor is copositive. Based on the spectral theory of nonnegative tensors,...

We investigate the reverse mathematical strength of Turing determinacy up to Σ5 which is itself not provable in second order arithmetic.

We consider the question of strong cosmic censorship in spatially compact, spatially locally homogeneous vacuum models. We show in particular that strong cosmic censorship holds in Bianchi IX vacuum space–times with spherical spatial topology.

We investigate the properties of Yablo sentences and formulas in theories of truth. Questions concerning provability of Yablo sentences in various truth systems, their provable equivalence, and their equivalence to the statements of their own untruth are discussed and answered.

The article introduces cyclic dilation groups and finite affine groups for prime integers, and  as an application of this theory it presents a unified group theoretical approach for the  cyclic wavelet transform (CWT) of prime dimensional periodic signals.

The paper uses a new approach to investigate prime submodules and minimal prime submodules of certain modules such as Artinian and torsion modules. In particular, we introduce a concrete formula for the radical of submodules of Artinian modules.