The fact that certain non-linear W2,s algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize W2,s algebras from linear W1,2,s algebras. In this paper, we first construct the explicit field realizations of linear W1,2,s algebras with double-scalar and doublespinor,respectively. Then, after a change of basis, the realizations of W2,s algebras are presented.The results show that all these realizations are Romans-type realizations.

An asymmetric thick domain wall solution with de Sitter (dS) expansion in five dimensions can be constructed from a symmetric one by using a same scalar (kink) with different potentials. In this paper, by presenting the mass-independent potentials of Kaluza–Klein (KK) modes in the corresponding Schröodinger equations, we investigate the localization and mass spectra of various bulk matter fields on the symmetric and asymmetric dS thick branes. For spin 0 scalars and spin 1 vectors, the potentials of KK modes in the corresponding Schrodinger equations are the modified P¨oschl-Teller potentials, and there exist a mass gap and a series of continuous spectrum. It is shown that the spectrum of scalar KK modes on the symmetric dS brane contains only one bound mode (the massless mode). However, for the asymmetric dS brane with a large asymmetric factor, there are two bound scalar KK modes: a zero mode and a massive mode. For spin 1 vectors, the spectra of KK modes on both dS branes consist of a bound massless mode and a set of continuous ones, i.e., the asymmetric factor does not change the number of the bound vector KK modes. For spin 1/2 fermions, two types of kink-fermion couplings are investigated in detail. For the usual Yukawa coupling, there exists no mass gap but a continuous gapless spectrum of KK states. For the scalar-fermion couplingsin(0) cos−(0) with a positive coupling constant, there exist some discrete bound KK modes and a series of continuous ones. The total number of bound states increases with the coupling constant. For the case of the symmetric dS brane and positive, there are NL(NL1) left chiral fermion bound states (including zero mode and massive KK modes) and NL −1 right chiral fermion bound states (including only massive KK modes).For the asymmetric dS brane scenario, the asymmetric factor a reduces the number of the bound fermion KK modes. For large enough a, there would not be any right chiral fermion bound mode, but at least one left chiral fermion zero mode.

Considering gravitational and gauge anomalies at the horizon, a new method that to derive Hawking radiations from black holes has been developed by Wilczek et al. In this paper, we apply this method to non-rotating and rotating Kaluza-Klein black holes with squashed horizon, respectively. For the rotating case, we found that, after the dimensional reduction, an effective U(1) gauge field is generated by an angular isometry. The results show that the gauge current and energy-momentum tensor fluxes are exactly equivalent to Hawking radiation from the event horizon.