We prove that the first-order theory of the Medvedev degrees, the first-order theory of the Muchnik degrees, and the third-order theory of true arithmetic are pairwise recursively isomorphic (obtained independently by Lewis, Nies, and Sorbi [7]). We then restrict our attention to the degrees of closed sets and prove that the following theories are pairwise recursively isomorphic: the first-orde...

In this paper, we introduce and characterize the concept of fuzzy almost generalized $e$-continuous mappings. Several interesting properties of these mappings are also given. Examples and counter examples are also given to illustrate the concepts introduced in the paper. We also introduce the concept of fuzzy $f T_{frac{1}{2}}e$-space, fuzzy $ge$-space, fuzzy regular $ge$-space and  fuzzy gener...

We propose a two-stage optimization approach for protein folding simulation in the FCC lattice, inspired from the phenomenon of hydrophobic collapse. Given a protein sequence, the first stage of the approach produces compact protein structures with the maximal number of contacts among hydrophobic monomers, using the CPSP tools for optimal structure prediction in the HP model. The second stage u...

A surprising consequence of non-linear flavor evolution is the spontaneous breaking initial symmetries neutrino gas propagating in a dense astrophysical environment. We explore conversion physics by taking into account polar and azimuthal angular distributions neutrinos present very first example symmetry context fast mixing nonlinear regime. Intriguingly, we find that does not always develop p...

In this paper we provide the derivation of a super compact pairwise model with only 4 equations in the context of describing susceptible-infected-susceptible (SIS) epidemic dynamics on heterogenous networks. The super compact model is based on a new closure relation that involves not only the average degree but also the second and third moments of the degree distribution. Its derivation uses an...