In view of this representation, Crandall asked what integers are of the form of xy + yz + xz with x, y, z ≥ 1 and he made a conjecture that every odd integer greater than one can be written as xy + yz + xz. In this manuscript, we shall show that Crandall’s conjecture is indeed true. In fact, we are able to show Theorem 1.1. There are at most 19 integers which are not in the form of xy + yz + xz...

The peculiar pulsating variable XZ Ceti has a period of 0.8231 day, suggesting that it is a Bailey type ab RR Lyrae star, but it has a light curve shape and amplitude which is like that of the Bailey type c variables. Fourier decomposition analysis verifies that the parameters of its light curve match those of the type c variables, except for its unacceptably long period. We have obtained a new...

Subdirectly irreducible non-idempotent groupoids satisfying x · xy = y and x · yz = xy · xz are studied.

Electronic nematicity is a ubiquitous phenomenon in iron-based superconductors but its origin still debated. Most models consider either spin or orbital degrees of freedom as the driving force typically do not take electronic correlations into account. However, mass enhancements, coherent-incoherent crossovers, and strong differentiation can only be understood using Hund's metal framework. Here...

This section shows that the equilibrium of the action game in section 1 of the main text is unique. It does that by adapting an argument first made Angeletos and Pavan (2007, propositions 1 and 3) to our environment. The idea of the proof is that there is a social planner problem such that every equilibrium of our model is also a solution to this planning problem. The planning problem is strict...

Abstract Multi-orbital physics in quasi-two-dimensional electron gases (q2DEGs) triggers intriguing phenomena not observed bulk materials, such as unconventional superconductivity and magnetism. Here, we investigate the mechanism of orbital selective switching spin-polarization oxide q2DEG formed at (001) interface between LaAlO 3 , EuTiO SrTiO band insulators. By using density functional theor...

The electronic structure of the enigmatic iron-based superconductor FeSe has puzzled researchers since spectroscopic probes failed to observe expected electron pocket at $Y$ point in 1-Fe Brillouin zone. It been speculated that this pocket, essential for an understanding superconducting state, is either absent or incoherent. Here, we perform a theoretical study preferred nematic order originati...

We report the revised crystal structure, static and dynamic magnetic properties of quasi-two dimensional honeycomb-lattice silver delafossite Ag3Co2SbO6. The magnetic susceptibility and specific heat data are consistent with the onset of antiferromagnetic long range order at low temperatures with Néel temperature TN ∼ 21.2 K. In addition, the magnetization curves revealed a field-induced (spin-...