Motivated by the well-known Paley graphs over finite fields and their generalizations, in this paper we explore a natural multiplicative-additive analogue of such arising from vector spaces fields. Namely, if n≥2 U⊊Fqn is an Fq-vector space, GU (undirected) graph with vertex set V(GU)=Fqn edge E(GU)={(a,b)∈Fqn2|a≠b,ab∈U}. We describe structure arbitrary maximal clique provide bounds on number ω...

We study renormalizable extensions of the standard model that contain vector-like fermions in a (single) complex representation of the standard model gauge group. There are 11 models where the vector-like fermions Yukawa couple to the standard model fermions via the Higgs field. These models do not introduce additional finetunings. They can lead to, and are constrained by, a number of different...

As shown by Bursztyn et al. (2019), germs of tubular neighborhood embeddings for submanifolds N?M are in one–one correspondence with Euler-like vector fields near N. In many contexts, this reduces the proof ‘normal forms results’ geometric structures to construction an field compatible given structure. We illustrate principle a variety examples, including Morse–Bott lemma, Weinstein’s Lagrangia...