Semicontinuity of betweenness functions

Approximation of Quasiconvex Functions, and Lower Semicontinuity of Multiple Integrals

We study semicontinuity of multiple integrals ~ f~,u,Du)dx~ where the vector-valued function u is defined for xE ~C N with values in ~ . The function f(x,s,~) is assumed to be Carath@odory and quasiconvex in Morrey's sense. We give conditions on the growth of f that guarantee the sequential lower semicontinuity of the given integral in the weak topology 1 N of the Sobolev space H 'P(~;~ ). The ...

Triangle path transit functions, betweenness and pseudo-modular graphs

The geodesic and induced path transit functions are the two well-studied interval functions in graphs. Two important transit functions related to the geodesic and induced path functions are the triangle path transit functions which consist of all vertices on all u, v-shortest (induced) paths or all vertices adjacent to two adjacent vertices on all u, v-shortest (induced) paths, for any two vert...

Semicontinuity of Convex-valued Multifunctions

We introduce semicontinuity concepts for functions f with values in the space C(Y ) of closed convex subsets of a finite dimensional normed vector space Y by appropriate notions of upper and lower limits. We characterize the upper semicontinuity of f : X → C(Y ) by the upper semicontinuity of the scalarizations σf( · )(y∗) : X → R by the support function. Furthermore, we compare our semicontinu...

Lower semicontinuity of surface energies

Further Results on Betweenness Centrality of Graphs

Betweenness centrality is a distance-based invariant of graphs. In this paper, we use lexicographic product to compute betweenness centrality of some important classes of graphs. Finally, we pose some open problems related to this topic.