Proof of a conjecture on irredundance perfect graphs

Let ir(G) and γ(G) be the irredundance number and the domination number of a graph G, respectively. A graph G is called irredundance perfect if ir(H)=γ(H), for every induced subgraph H of G. In this article we present a result which immediately implies three known conjectures on irredundance perfect graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 292–306, 2002     

Ab initio calculations on H transfer in the HF trimer

Systematic ab initio LCAO MO calculations with basis sets of increasing size have been performed to analyze the changes in relative stabilization energies of the two cyclic (D_3h and C_3h symmetry) and the noncyclic HF trimers. The results form the basis for a discussion of cyclic H-transfer reactions.     

Nitrido-Sodalithe. II. Synthese,Struktur und Eigenschaften von M(6+(y/2)–x)H2x[P12N24]Zy mit M = Fe,Co, Ni,Mn; Z = Cl,Br, I; 0 ≤ x ≤ 4; y ≤ 2

Nitrido-Sodalites. II. Synthesis, Crystal Structure, and Properties of M_{(6+(y/2)–x)}H_2x[P₁₂N₂₄]Z_y with M = Fe, Co, Ni, Mn; Z = Cl, Br, I; 0 ≤ x ≤ 4; y ≤ 2 The nitrido sodalites M_{(6+(y/2)–x)}H_2x[P₁₂N₂₄]Z_y with M = Fe, Co, Ni, Mn; Z = Cl, Br, I; 0 ≤ x ≤ 4; y ≤ 2 are obtained by the reaction of HPN₂ or [PN(NH₂)₂]₃ with the metal halogenide MZ₂ (T = 700°C). The compounds are isotypic to Zn_(7–x)H_2x[P₁₂N₂₄]Cl₂. An increase of the ionic radii of the cations or anions results in an expansion of the lattice which is caused by an increase of the P? N? P angle. The influence of the cation is more dominant than that of the anion. By reacting [PN(NH₂)₂]₃ with metal halogenide (MZ₂) hydrogen free, X-ray amorphous products are obtained. The formation of the chloride-containing P? N-sodalite in this reaction begins at temperatures below 450°C.     

On functions having Cauchy differences in some prescribed sets

Summary AssumeE is a real topological vector space,F is a real Banach space,K is a discrete subgroup ofF andC is a symmetric, convex and compact subset ofF such thatK (6C) = {0}. If a functionh:E F is continuous at at least one point andh(x + y) – h(x) – h(y) K + C for allx, y E, then there exists a continuous linear functiona:E F such thath(x) – a(x) K + C for everyx E.     

On Strassen's law of the iterated logarithm

Summary Kolmogorov's law of the iterated logarithm has been sharpened by Strassen who proved a more refined theorem by using tools from functional analysis. The present paper gives a classical proof of Strassen's theorem, using a method along the lines of Kolmogorov's original approach. At the same time the result proved here is more general since a) the random variables involved need not have the same distributions, b) the condition of independence is weakened and c) instead of Kolmogorov's growth condition on the random variables, only a mild restriction on their moments of order l3 is needed.     

All 2-connected in-tournaments that are cycle complementary

An in-tournament is an oriented graph such that the negative neighborhood of every vertex induces a tournament. A digraph D is cycle complementary if there exist two vertex-disjoint directed cycles spanning the vertex set of D. Let D be a 2-connected in-tournament of order at least 8. In this paper we show that D is not cycle complementary if and only if it is 2-regular and has odd order.