Abstract. Proper vertex colorings of a graph are related to its boundary map, also called its signed vertex-edge incidence matrix. The vertex Laplacian of a graph, a natural extension of the boundary map, leads us to introduce nowhere-harmonic colorings and analogues of the chromatic polynomial and Stanley’s theorem relating negative evaluations of the chromatic polynomial to acyclic orientatio...

the term degradation is used to specify the status of the environment. it is often associated with ‘improper use’. ‘use’ also implies environmental aspects other than physical ones and implies that the more intensive the use, the more susceptible the environment is to degradation, particularly if proper care for the environment is lacking. the question is, and has always been, how to map someth...

Two proper polynomial maps f1, f2 : C 2 −→ C are said to be equivalent if there exist Φ1, Φ2 ∈ Aut(C) such that f2 = Φ2 ◦ f1 ◦ Φ1. We investigate proper polynomial maps of topological degree d ≥ 2 up to equivalence. Under the further assumption that the maps are Galois coverings we also provide the complete description of equivalence classes. This widely extends previous results obtained by Lam...

in this paper, we first present a new important property for bouligand tangent cone (contingent cone) of a star-shaped set. we then establish optimality conditions for pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

The coordinate system has been proposed as a fundamental and cross-culturally used spatial representation, through which people code location and direction information in the environment. Here we provided direct evidence demonstrating that daily experience with the cardinal coordinate system (i.e., east, west, north, and south) contributed to the representation of cognitive maps. Behaviorally, ...