Structure and electrochemical behaviour of 4,7-diazaheptyl-trimethoxy-silane and vinyl-trialkoxy-silane adsorbed at silver surface

Novel self-assembled monolayers were obtained on silver using 4,7-diazaheptyl-trimethoxy-silane (SiN) and vinyl-trialkoxy-silane (SiVA, where the alkyl group is 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60-eicozaoxa- hexaheptaconan). It was shown that thus modified metal surface was protected against electrooxidation. A densely packed monolayer remained stable and did not desorb from the Ag electrode on the potential cycling. The structure of SiN and SiVA as well as their complexes with Li⁺ cations were calculated and visualised by the AM1d and PM5 semi-empirical methods.     

On the diameter and radius of randon subgraphs of the cube

The n-dimensional cube Qⁿ is the graph whose vertices are the subsets of {1,…n}, with two vertices adjacent if and only if their symmetric difference is a singleton. Clearly Qⁿ has diameter and radious n. Write M = n2^n-1 = e(Qⁿ) for the size of Qⁿ. Let Q = (Q_t)_o^M be a random Qⁿ-process. Thus Q^t is a spanning subgraph of Qⁿ of size t, and Q_t is obtained from Q_t–1 by the random addition of an edge of Qⁿ not in Q_t–1, Let t^(k) = τ(Q;δ?k) be the hitting time of the property of having minimal degree at least k. We show that the diameter d_t = diam (Q_t) of Q_t in almost every Q? behaves as follows: d_t starts infinite and is first finite at time t⁽¹⁾, it equals n + 1 for t⁽¹⁾ ? t⁽²⁾ and d_t, = n for t ? t⁽²⁾. We also show that the radius of Q_t, is first finite for t = t⁽¹⁾, when it assumes the value n. These results are deduced from detailed theorems concerning the diameter and radius of the almost surely unique largest component of Q_t, for t = Ω(M). © 1994 John Wiley & Sons, Inc.     

Characterization and TG-MS studies of lactato and bipyridine-lactato complexes of Co(II) and Ni(II)

Two lactates and four new mixed ligand complexes with formulae Co(lact)₂·2H₂O, Ni(lact)₂·3H₂O, Co(4-bpy)(lact)₂, Co(2,4'-bpy)₂(lact)₂, Ni(4-bpy)(lact)₂·2H₂O and Ni(2,4'-bpy)₂(lact)₂ (where 4-bpy=4,4'-bipyridine, 2,4'-bpy=2,4'-bipyridine, lact=CH₃CH(OH)COO^-) were isolated and investigated. The thermal behaviour of compounds was studied by thermal analysis (TG, DTG, DTA). In the case of hydrated complexes thermal decomposition starts with the release of water molecules. The compounds decompose at high temperature to metal(II) oxides in air. A coupled TG-MS system was used to analyse the principal volatile products of thermolysis and fragmentation processes of obtained complexes. This revised version was published online in July 2006 with corrections to the Cover Date.     

1,4‐Michael Addition – The Analytical Way for Quantitative Sensing of Neurotransmitter at Bare Gold Electrode in Physiological Solution in the Presence of Interfering Biogenic Compounds

Electrooxidation of norepinephrine in the presence a nucleophile was investigated on a bare gold electrode. Electrochemically produced norepinephrinequinone undergoes an attack by morpholine as nucleophile via 1,4‐Michael addition. The reaction products were identified by electrospray ionization mass spectrometry. The procedure used was suitable for quantitative norepinephrine determination in the concentration range from 1×10^?9 M to 8×10^?4 M with a detection limit of 8.7×10^?10 M in a samples containing an excess of ascorbic and uric acids. The proposed method is simple, green which means that it does not require the use of toxic compounds and solvents and thus is promising for detection of norepinephrine in physiological environment.     

Colorful flowers

For a set A let k[A] denote the family of all k-element subsets of A. A function f:k[A]→C is a local coloring if it maps disjoint sets of A into different elements of C. A family F⊆k[A] is called a flower if there exists E∈[A]^k−1 so that |F∩F^′|=E for all F,F^′∈F, F≠F^′. A flower is said to be colorful if f(F)≠f(F^′) for any two F,F^′∈F. In the paper we find the smallest cardinal γ such that there exists a local coloring of k[A] containing no colorful flower of size γ. As a consequence we answer a question raised by Pelant, Holický and Kalenda. We also discuss a few results and conjectures concerning a generalization of this problem.     

Claw‐free 3‐connected P11‐free graphs are hamiltonian

We show that every 3‐connected claw‐free graph which contains no induced copy of P₁₁ is hamiltonian. Since there exist non‐hamiltonian 3‐connected claw‐free graphs without induced copies of P₁₂ this result is, in a way, best possible. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 111–121, 2004     

Asymmetry and structural information in preferential attachment graphs

Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd?s‐Rényi graphs are typically asymmetric, real networks are highly symmetric. So a natural question is whether preferential attachment graphs, where in each step a new node with m edges is added, exhibit any symmetry. In recent work it was proved that preferential attachment graphs are symmetric for m = 1, and there is some nonnegligible probability of symmetry for m = 2. It was conjectured that these graphs are asymmetric when m ≥ 3. We settle this conjecture in the affirmative, then use it to estimate the structural entropy of the model. To do this, we also give bounds on the number of ways that the given graph structure could have arisen by preferential attachment. These results have further implications for information theoretic problems of interest on preferential attachment graphs.     

Adsorption of methylamine at a polycrystalline gold/solution interface

Adsorptive behaviour of the methylamine molecules has been investigated by measuring changes in the differential capacitance of the double layer at the gold/solution interface by the tensammetric method. The differences in adsorption parameters at Θ < 0.8 and >0.8 have been explained by changes in arrangement of the adsorbate.