We separate many of the basic fragments of classical logic which are used in reverse constructive mathematics. A group of related Kripke and topological models is used to show that various fragments of the Weak Law of the Excluded Middle, the Limited Principle of Omniscience, and Markov’s Principle, including Weak Markov’s Principle, do not imply each other. §

In the present paper, we define regularity and normality like strong S1 regularity, S1 regularity, weak S1 regularity, strong S1 normality, S1 normality as well as weak S1 normality on L-topological spaces. Also we investigate some of their properties and the relations between them. 2010 Mathematics Subject Classification: 54A40, 54D10, 54D15, 54D65, 03E72.

We separate many of the basic fragments of classical logic which are used in constructive reverse mathematics. A group of related Kripke and topological models is used to show that various fragments of the Weak Law of the Excluded Middle, the Limited Principle of Omniscience, and Markov’s Principle, including Weak Markov’s Principle, do not imply each other.

It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more univer...

Transport due to spin-helical massless Dirac fermion surface state is of paramount importance to realize various new physical phenomena in topological insulators, ranging from quantum anomalous Hall effect to Majorana fermions. However, one of the most important hallmarks of topological surface states, the Dirac linear band dispersion, has been difficult to reveal directly in transport measurem...

We investigate Josephson currents in mesoscopic rings with a weak link which are in or near a topological superconducting phase. As a paradigmatic example, we consider the Kitaev model of a spinless p-wave superconductor in one dimension, emphasizing how this model emerges frommore realistic settings based on semiconductor nanowires. We show that the flux periodicity of the Josephson current pr...

Holographic aspects of 2D Fresnel type memory patterns with 3D couplings and mutual diffractions are considered. Encoding topological charges and spin, the nonlinear interaction potentials are assigned to a shared holographic memory phase space with limited information storage density. Neutral intermediate structures arise in the overlap region. The neutralizing process is regarded as a generat...

*Correspondence: [email protected] 1Department of Mathematics, Hunan Shaoyang University, Shaoyang, Hunan 422000, P.R. China Full list of author information is available at the end of the article Abstract This paper is devoted to study a center problem and a weak center problem for cubic systems in Z4-equivariant vector fields. By computing the Lyapunov constants and periodic constants ca...