Emergent topological fields and relativistic phonons within the thermoelectricity in topological insulators

Topological edge states are predicted to be responsible for the high efficient thermoelectric response of topological insulators, currently the best thermoelectric materials. However, to explain their figure of merit the coexistence of topological electrons, entropy and phonons can not be considered independently. In a background that puts together electrodynamics and topology, through an expression for the topological intrinsic field, we treat relativistic phonons within the topological surface showing their ability to modulate the Berry curvature of the bands and then playing a fundamental role in the thermoelectric effect. Finally, we show how the topological insulators under such relativistic thermal excitations keep time reversal symmetry allowing the observation of high figures of merit at high temperatures. The emergence of this new intrinsic topological field and other constraints are suitable to have experimental consequences opening new possibilities of improving the efficiency of this topological effect for their based technology.

Soft Structures of Monoids and Fields

The ultimate purpose of this article is to introduce and examine some new kind of algebraic structures such as Soft topological fields, Soft topological groups and Soft monoids with illustrating counter examples. Also we established that every Soft field over a topological field is a Soft topological field and we have given an example GF(16), the finite field of 16 elements which is a soft topological field

Word order variation in Khoekhoe

Khoekhoe, a Central Khoisan language, has been claimed to have a clause-second position and topological fields similar to German and Dutch. The position in front of the clause-second position can be occupied by either the matrix verb or a dependent. We argue that monomoraic words are exempt from the general head-final order of Khoekhoe and suggest that this can give rise to discontinuous constituents, where second-position clitics intervene within the VP. We show that this idea provides a simple account of Khoekhoe word order variation and formalize it within a linearization-based HPSG analysis that has a wider scope than the previous Minimalist analyses of Khoekhoe and that is compatible with evidence from tonology.