Degree conditions for 2-factors

For any positive integer k, we investigate degree conditions implying that a graph G of order n contains a 2-factor with exactly k components (vertex disjoint cycles). In particular, we prove that for k ≤ (n/4), Ore's classical condition for a graph to be hamiltonian (k = 1) implies that the graph contains a 2-factor with exactly k components. We also obtain a sufficient degree condition for a graph to have k vertex disjoint cycles, at least s of which are 3-cycles and the remaining are 4-cycles for any s ≤ k. © 1997 John Wiley & Sons, Inc.     

Relation between the time and space step-sizes in nonstandard finite-difference schemes for the Fisher equation

A positivity condition is used to obtain functional relations between the time and space step-sizes for nonstandard finite-difference models of the Fisher partial differential equation. An upper bound is also derived for the solutions to the difference equations. © 1997 John Wiley & Sons, Inc.     

Interpolation for Function Spaces Related to Mixed Boundary Value Problems

Interpolation theorems are proved for Sobolev spaces of functions on nonsmooth domains with vanishing trace on a part of the boundary.     

Near-ultraviolet-induced matrix-assisted laser desorption/ionization as a function of wavelength

The matrix-assisted laser desorption/ionization (MALDI) effect for the ablation of polypeptide ions was studied as a function of wavelength in the range 360–450 nm, using a tunable titanium:sapphire laser and the matrices (trans)α-cyano-4-hydroxycinnamic acid, (trans)3,5-dimethoxy-4-hydroxycinnamic acid, and (trans)β-indoleacrylic acid. The results demonstrated that the qualitative aspects of the MALDI effect remained largely unchanged as a function of wavelength until the matrix crystal’s absorption coefficient approached 6 × 10⁴ cm^?1. Wavelengths at which the absorption coefficient was lower than this value did not produce observable polypeptide ions. In the range of wavelengths where polypeptide ions could be observed, the effect was generated only when the average energy absorbed in the 10-nm layer immediately below the crystal surface was >8 kJ/cm³ regardless of the total amount of energy absorbed in the remainder of the crystal. It was demonstrated that on the basis of the other results in this paper and those in the literature that the mechanism that generates polypeptide ions cannot be either photochemically induced or the same mechanism that gives rise to matrix ions. A model for ionization is proposed that decouples matrix and protein ionization in a simple manner that has direct analogy to the behavior of ionic solutes in polar solvents. The model satisfies the currently available experimental evidence and unifies the results obtained by MALDI at all wavelengths.     

Strukturuntersuchungen an Usoviten: Ba2CaMIIV2F14 (MIII = Mn,Fe), Ba2CaMnFe2F14 und Ba2CaCuM2IIIF14 (MIII = Mn,Fe, Ga)

Structural Studies with Usovites: Ba₂CaM^IIV₂F₁₄ (M^III = Mn, Fe), Ba₂CaMnFe₂F₁₄ and Ba₂CaCuM₂^IIIF₁₄ (M^III = Mn, Fe, Ga). Single crystals of six compounds Ba₂CaM^IIM₂^IIIF₁₄ were prepared to refine their usovite type structure (space group C2/c, Z = 4) using X‐ray diffractometer data. The cell parameters of the phases studied with M^IIM₂^III= MnV₂, FeV₂, CuMn₂, MnFe₂, CuFe₂ und CuGa₂ are within the range 1374≤a/pm≤1384, 534≤b/pm≤542, 1474≤c/pm≤1510, 91, 3≤ß/°≤93, 2. The atoms Ca and M^II are incompletely ordered on the 8‐ and 6‐coordinated positions, 4e and 4b, respectively. In the case of Ba₂CaFeV₂F₁₄ and Ba₂CaCuGa₂F₁₄ there is reciprocal substitution (x≈0, 1): (Ca_1‐xM_x^II) (4e) and (M_1‐x^IICa_x) (4b). In the case of the other usovites Ca‐enriched phases Ba₂Ca(M_1‐y^IICa_y)M₂^IIIF₁₄ occured (up to y≈0, 35), exhibiting partial substitution at the octahedral position (4b) only, showing a corresponding increase in M^II‐F distances. The distortion of [M^IIF₆] and [M^IIIF₆] octahedra within the structure is considerably enhanced on replacement by Cu^II and Mn^III. The results of powder magnetic susceptibility measurements of Ba₂CaMnV₂F₁₄ and Ba₂CaFeV₂F₁₄ (T_N≈7K) are reported.