Geršgorin variations III: On a theme of Brualdi and Varga

Brualdi brought to Geršgorin Theory the concept that the digraph G(A) of a matrix A is important in studying whether A is singular. He proved, for example, that if, for every directed cycle of G(A), the product of the diagonal entries exceeds the product of the row sums of the moduli of the off-diagonal entries, then the matrix is nonsingular. We will show how, in polynomial time, that condition can be tested and (if satisfied) produce a diagonal matrix D, with positive diagonal entries, such that AD (where A is any nonnnegative matrix satisfying the conditions) is strictly diagonally dominant (and so, A is nonsingular). The same D works for all matrices satisfying the conditions. Varga raised the question of whether Brualdi’s conditions are sharp. Improving Varga’s results, we show, if G is scwaltcy (strongly connected with at least two cycles), and if the Brualdi conditions do not hold, how to construct (again in polynomial time) a complex matrix whose moduli satisfy the given specifications, but is singular.     

Network flows and non-guillotine cutting patterns

Up till now there has been no exact and effective algorithm for the problem of finding optimal cutting patterns of rectangles which are not restricted to those with the ‘guillotine’ property. This problem can be interpreted in a resource constrained scheduling context. The contribution of this paper to this topic is a good characterization of the flow functions and graphs corresponding to cutting patterns.     

Über die Änderung des respiratorischen Quotienten von Hefezellen bei der Übertragung aus einem Wachstumsmedium in ein Sporulierungsmedium und die Umkehrbarkeit dieses Effekts

Ohne ZusammenfassungMit 3 Abbildungen     

Exclusive and essential sets of implicates of Boolean functions

In this paper we study relationships between CNF representations of a given Boolean function f and certain sets of implicates of f. We introduce two definitions of sets of implicates which are both based on the properties of resolution. The first type of sets, called exclusive sets of implicates, is shown to have a functional property useful for decompositions. The second type of sets, called essential sets of implicates, is proved to possess an orthogonality property, which implies that every CNF representation and every essential set must intersect. The latter property then leads to an interesting question, to which we give an affirmative answer for some special subclasses of Horn Boolean functions.     

Activation of metal hydride complexes by tri-tert-butylphosphine-platinum and -palladium groups

The compounds HM(CO)4SnPh3, M = Os (10), Ru (11) are activated in the presence of Pt(PBut3)2 and Pd(PBu(t)3)2 toward the insertion of PhC2H into the M-H bond. The compounds PtOs(CO)4(SnPh3)(PBu(t)3)[mu-HCC(H)Ph], 12, and PtOs(CO)4(SnPh3)(PBu(t)3)[mu-H2CCPh], 13, were obtained from the reaction of 10 with PhC2H in the presence of Pt(PBu(t)3)2. Compounds 12 and 13 are isomers containing alkenyl ligands formed by the insertion of the PhC2H molecule into the Os-H bond at both the substituted and unsubstituted carbon atoms of the alkyne. Both compounds contain a Pt(PBu(t)3) group that is bonded to the osmium atom and a bridging alkenyl ligand that is pi-bonded to the osmium atom. The reaction of 11 with PhC2H in the presence of Pt(PBu(t)3)2 yielded the products PtRu(CO)4(SnPh3)(PBu(t)3)[mu-HC2(H)Ph], 14, and PtRu(CO)4(SnPh3)(PBut3)[mu-H2C2Ph], 15, which are also isomers similar to 12 and 13. The reaction of 11 with PhC2H in the presence of Pd(PBu(t)3)2 yielded the product PdRu(CO)4(SnPh3)(PBu(t)3)[mu-H2C2Ph], 16. Compound 16 contains a Pd(PBu(t)3) group bonded to the ruthenium atom and a bridging H2C2Ph ligand that is pi-bonded to the palladium atom. Compound 10 reacted with Pt(PBu(t)3)2 in the absence of PhC2H to yield the compound PtOs(CO)4(SnPh3)(PBu(t)3)(mu-H), 17. Compound 17 is a Pt(PBu(t)3) adduct of 10. It contains a Pt-Os bond with a bridging hydrido ligand. Compound 17 reacted with PhC2H to yield 12. Compound 12 reacted with PhC2H to yield the compound PtOs(CO)3(SnPh3)(PBu(t)3)[mu-HCC(Ph)C(H)C(H)Ph], 18. Compound 18 contains a bridging 2,4-diphenylbutadienyl ligand, HCC(Ph)C(H)C(H)Ph, that is pi-bonded to the osmium atom and sigma-bonded to the platinum atom. Fenkse-Hall molecular orbitals of 17 were calculated. The LUMO of 17 exhibits an empty orbital on the platinum atom that appears to be the most likely site for PhC2H addition prior to its insertion into the Os-H bond.     

Synthesis, characterization, and electronic structures of a series of two-dimensional trimetallic cluster complexes, Ru3(CO)9(mu-SnPh2)3[Pt(PBu(t)3)]x, x = 0-3

The triruthenium-tritin cluster complex, Ru3(CO)9(mu-SnPh2)3, 13 was obtained from the reaction of Ru3(CO)12 with Ph3SnH. Compound 13 reacts with Pt(PBut3)2 to yield three new Pt(PBut3) adducts of 13 Ru3(CO)9(mu-SnPh2)3[Pt(PBut3)]x, 14-16 x = 1 - 3 formed by the addition of Pt(PBut3) groups to the Ru-Sn bonds. The new complexes form a novel series of trimetallic complexes having planar arrangements of the metal atoms. The UV-vis absorptions of the four complexes shift progressively to longer wavelengths as the number of platinum atoms is added to the cluster. The electronic structures of these complexes have been investigated in the ground and excited states by density functional theory and time-dependent density functional theory, and this has provided a detailed understanding of the metal-metal bonding and electronic transitions that are responsible for their UV-vis absorption properties. The predicted absorption maximum for the model structures for 13, 14, 15, and 16 at 465, 508, 556, and 585 nm differ only 4-18 nm from the experimental values of 474, 490, 552, and 576 nm. The shift of principal UV-vis absorption can be explained by a lowering of the HOMO-LUMO energy gap due to interactions of the platinum atoms with the HOMO and LUMO of the Ru3Sn3 core.     

Quick and sensitive HPLC separations on non-porous reversed-phase packings

Summary The aim of this work was to evaluate reversed-phase chemically bonded non-porous (micropellicular)d _p=1.5 μm stationary phases. On these modern phases the time for analysis of complex mixtures of solutes—whether monomeric or polymeric (e.g. drugs, vitamins, peptides, or protein)—is very short compared with that on porous phases. Different surface chemistries were elaborated for the separation of different types of sample. For the separation of small molecules a long-chain (C₁₄) hydrocarbon-coated phase seems to be optimum; a short chain (C₆) hydrocarbon bonded to the surface of the silica seems better for the separation of polymers. The efficiency, the low analysis times, and sensivities were demonstrated by separation of different proteins, peptides, drugs, alkaloids, and mixtures of water and fat-soluble vitamins.     

Impact of the Oxygen Defects and the Hydrogen Concentration on the Surface of Tetragonal and Monoclinic ZrO2 on the Reduction Rates of Stearic Acid on Ni/ZrO2

The role of the specific physicochemical properties of ZrO₂ phases on Ni/ZrO₂ has been explored with respect to the reduction of stearic acid. Conversion on pure m‐ZrO₂ is 1.3 times more active than on t‐ZrO₂, whereas Ni/m‐ZrO₂ is three times more active than Ni/t‐ZrO₂. Although the hydrodeoxygenation of stearic acid can be catalyzed solely by Ni, the synergistic interaction between Ni and the ZrO₂ support causes the variations in the reaction rates. Adsorption of the carboxylic acid group on an oxygen vacancy of ZrO₂ and the abstraction of the α‐hydrogen atom with the elimination of the oxygen atom to produce a ketene is the key to enhance the overall rate. The hydrogenated intermediate 1‐octadecanol is in turn decarbonylated to heptadecane with identical rates on all catalysts. Decarbonylation of 1‐octadecanol is concluded to be limited by the competitive adsorption of reactants and intermediate. The substantially higher adsorption of propionic acid demonstrated by IR spectroscopy and the higher reactivity to O₂ exchange reactions with the more active catalyst indicate that the higher concentration of active oxygen defects on m‐ZrO₂ compared to t‐ZrO₂ causes the higher activity of Ni/m‐ZrO₂.     

Masked imidazolyl-dipyrromethanes in the synthesis of imidazole-substituted porphyrins

Imidazole-substituted metalloporphyrins are valuable for studies of self-assembly and for applications where water solubility is required. Rational syntheses of porphyrins bearing one or two imidazol-2-yl or imidazol-4-yl groups at the meso positions have been developed. The syntheses employ dipyrromethanes, 1-acyldipyrromethanes, and 1,9-diacyldipyrromethanes bearing an imidazole group at the 5-position. The polar, reactive imidazole unit was successfully masked by use of (1) the 2-(trimethylsilyl)ethoxymethyl (SEM) group at the imidazole pyrrolic nitrogen, and (2) a dialkylboron motif bound to the pyrrole of the dipyrromethane and coordinated to the imidazole imino nitrogen. The nonpolar nature of such doubly masked imidazolyl-dipyrromethanes facilitated handling. Selected masked dipyrromethanes were characterized by 11B and 15N NMR spectroscopy. Five distinct methods were examined to obtain trans-A2B2-, trans-AB2C-, and trans-AB-porphyrins. Each porphyrin contained one or two SEM-protected imidazole units. The SEM group could be removed with TBAF or HCl. Two zinc(II) porphyrins and a palladium(II) porphyrin bearing a single imidazole moiety were prepared and subjected to alkylation (with ethyl iodide, 1,3-propane sultone, or 1,4-butane sultone) to give water-soluble imidazolium- porphyrins. This work establishes the foundation for the rational synthesis of a variety of porphyrins containing imidazole units.