An important property with any new material is the band gap. Standard density functional theory methods grossly underestimate band gaps. This is known as the band gap problem. Here, we show that the hybrid B3PW91 density functional returns band gaps with a mean absolute deviation (MAD) from experiment of 0.22 eV over 64 insulators with gaps spanning a factor of 500 from 0.014 to 7 eV. The MAD i...

A proper coloring of the vertices of a graph is called a star coloring if the union of every two color classes induce a star forest. The star chromatic number χs(G) is the smallest number of colors required to obtain a star coloring of G. In this paper, we study the relationship between the star chromatic number χs(G) and the maximum average degree Mad(G) of a graph G. We prove that: 1. If G is...

We answer a question of Gracia-Ferreira and Hrušák by constructing consistently a MAD family maximal in the Katětov order. We also answer several questions of Garcia-Ferreira.

We prove that the incidence chromatic number of every 3-degenerated graph G is at most ∆(G)+ 4. It is known that the incidence chromatic number of every graph G with maximum average degree mad(G) < 3 is at most ∆(G)+3. We show that when ∆(G) ≥ 5, this bound may be decreased to ∆(G) + 2. Moreover, we show that for every graph G with mad(G) < 22/9 (resp. with mad(G) < 16/7 and ∆(G) ≥ 4), this bou...

A proper edge coloring of a graph G is called acyclic if there is no bichromatic cycle in G. The acyclic chromatic index of G, denoted by χa(G), is the least number of colors k such that G has an acyclic edge k-coloring. The maximum average degree of a graph G, denoted by mad(G), is the maximum of the average degree of all subgraphs of G. In this paper, it is proved that if mad(G) < 4, then χa(...

Der folgende Beitrag gibt einen Überblick über den Umgang mit Nullwerten im Molekül-Atom-Datenmodell (MAD-Modell) und dessen Implementierung PRIMA. Zunächst beschreiben wir einige der Lösungen, die im Relationenmodell für die Behandlung von Nullwerten vorgeschlagen wurden, und stellen dann den Umgang mit Nullwerten im MAD-Modell vor, wie wir ihn in PRIMA realisiert haben. Ziel ist es, den Benut...

Recently determined structures of a number of Myc family proteins have provided significant insights into the molecular nature of complex assembly and DNA binding. These structures illuminate the details of specific interactions that govern the assembly of nucleoprotein complexes and, in doing so, raise more questions regarding Myc biology. In this review, we focus on the lessons provided by th...

Recently determined structures of a number of Myc family proteins have provided significant insights into the molecular nature of complex assembly and DNA binding. These structures illuminate the details of specific interactions that govern the assembly of nucleoprotein complexes and, in doing so, raisemore questions regarding Myc biology. In this review, we focus on the lessons provided by the...