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     

Studies on pre-hump and main fractions of cellulose-2,5-acetate in acetone

Technical cellulose-2.5-acetates (CA 2.5) were characterized regarding their carbohydrate composition in comparison to the raw material. The association of the CA 2.5 samples in acetone was studied by size exclusion chromatography (SEC) using various acetone grades and styrene divinylbenzene copolymer columns. In HPLC grade acetone with and without addition of 1% water up to three different pre-humps eluted in front of the main fraction of the polymer. The evaluation of the main peak by light scattering measurements resulted in high molar masses indicating that for these technical CA 2.5 samples even the main fraction is not dissolved without association. No pre-humps or association phenomena were observed after addition of 1 ppm LiBr to HPLC grade acetone or with p.a. grade acetone. In addition pre-hump enriched and pre-hump free fractions were isolated by fractionated precipitation. The carbohydrate composition of these fractions was determined and correlated with their association pattern in SEC investigations.     

Zur Berechnung Stekloffscher Eigenwerte

Zusammenfassung Es wird ein neues Verfahren zur numerischen Berechnung des ersten nichttrivialen Stekloffschen Eigenwertes beschrieben. Dieses Verfahren arbeitet nur mit oberen Schranken.

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We describe a new procedure for the numerical evaluation of the first nontrivial Stekloff eigenvalue. This procedure works only with upper bounds.

     

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.