Note on the application of the reduced graph model in conjunction with search trees to the enumeration ofKekulé structures

The reduced graph model, when used in conjunction with the search trees method, provides a novel combinatorial procedure for the enumeration and generation ofKekulé structures. The procedure is suited for large benzenoid hydrocarbons consisting of cata- and thin peri-condensed parts.

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Zur Anwendung des Reduced Graph Model im Zusammenhang mit Search Trees zur Ermittlung der Anzahl möglicherKekulé-Strukturen

Zusammenfassung Das Modell erlaubt mit der im Titel genannten Kombination eine neuartige Methode zur Ermittlung und Generierung vonKekulé-Strukturen. Das Verfahren ist für große benzoide Kohlenwasserstoffe geeignet, die aus cata- und (dünnen) peri-kondensierten Teilstrukturen bestehen.

     

Mathematical studies of Kekulé structures

The perfect matching vector and forcing and the Kekulé-vector of cata-benzenoids are defined. Two theorems are given which set the sufficient and necessary conditions for HKZ-vector (Harary et al. J Math Chem 6:295, 1991) and Kekulé-vector in cata-benzenoids. Additional two theorems are obtained which give sharp bounds for the modules of HKZ- and Kekulé vectors. Dedicated to Professor Tadeusz Marek Krygowski on the happy occasion of his 70th birthday.     

Protein secondary structure conformations and associated hydrophobicity scales

We have developed conformational preference functions and a hierarchy of algorithms that can evaluate the success of each hydrophobicity scale in predicting protein secondary conformation. The results of such evaluation are shown for fiftyfive different scales with respect to their ability to predict -helix, -sheet and coil structure in three testing sets of proteins: five integral membrane proteins, twelve -class and sixteen -class soluble proteins. Our scale of conformational parameters is the best predictor of secondary structure segments in membrane proteins and -class proteins. The success rate and correlation coefficient for -helix conformation in membrane proteins are 76% and 0.46 respectively, which is superior to the performance measures attained with other prediction schemes. Evaluation of solution hydrophobicity scales, often used to predict transmembrane segments in membrane proteins, indicated absence of correlation in prediction of helix segments and experimental results for the conformation of membrane proteins. Such scales have better performance (correlation coefficient around 0.30) in predicting sheet conformation in the -class proteins.     

On the z-counting polynomial for edge-weighted graphs

The construction of the Z-counting polynomial for edge-weighted graphs is discussed.Dedicated to Professor Haruo Hosoya (Tokyo) on the occasion of his 55th birthday for enriching chemical graph theory with the elegant concept of the Z-counting polynomial.     

A simple and efficient one-step, regioselective, enzymatic glucosylation of arbutin by α-glucosidase

4-Hydroxyphenyl-β-isomaltoside has been synthesized by α-glucosidase assisted transglycosylation between arbutin as acceptor and sucrose as donor molecules, respectively. Optimum conditions for the transglucosylation reaction were 40 °C for 20 h with 10 mM arbutin and 1.5 M sucrose in a 100 mM sodium citrate/phosphate buffer at pH 5.0. The new glucoside was obtained in a 50% molar yield with respect to arbutin.     

Atomic walk counts of negative order

Atomic walk counts (awc's) of order k (k > or = 1) are the number of all possible walks of length k which start at a specified vertex (atom) i and end at any vertex j separated by m (0 < or = m < or = k) edges from vertex i. The sum of atomic walk counts of order k is the molecular walk count (mwc) of order k. The concept of atomic and molecular walk counts was extended to zero and negative orders by using a backward algorithm based on the usual procedure used to obtain the values of mwc's. The procedure can also be used in cases in which the adjacency matrix A related to the actual structure is singular and therefore A(-1) does not exist. awc's and mwc's of negative order may assume noninteger and even negative values. If matrix A is singular, atomic walk counts of zero order may not be equal to one.     

A study of electronic structures of Pt3M (M=Ti,V,Cr,Fe,Co,Ni) polycrystalline alloys with valence-band photoemission spectroscopy

The surface valence-band densities of states (DOS) of Pt(3)M (M=Ti,V,Cr,Fe,Co,Ni) polycrystalline alloys were investigated with ultraviolet photoemission spectroscopy. Upon annealing the ion-sputter-cleaned alloys at high temperatures, the observed valence-band DOS spectra clearly show the modified electronic structures on the surfaces suggesting the surface segregation of Pt as predicted in thermodynamic models. The measured d-band centers and widths for the annealed alloy surfaces show qualitatively the same trend as predicted by density-functional-theory calculations based on the model of a Pt "skin" on the topmost surface layer and a subsurface layer enriched in the 3d transition metal.