On path lengths modulo three

We show that between any two nodes of a cubic, planar, three-connected graph there are three paths whose lengths are 0, 1, and 2 modulo 3, respectively. The proof is by a rather extensive case analysis. Counterexamples show that all three hypotheses (i.e., planarity, degree-three, and three-connectivity) are necessary.     

Copper(II) complexes of tetrapeptides containing cysteinyl and histidinyl residues

It is becoming increasingly apparent that the coordination chemistry of oligopeptides with Cys-X-Y-Cys and His-X-Y-Cys sequences (X, Y = variable amino acid residues) is an important theme in transition metal and bioinorganic chemistry(1,2). The Cys-X-Y-Cys sequence is often encountered in the metal binding site of several metalloproteins, such as iron–sulfur proteins, e.g. rubredoxins(3) and ferrodoxins(4), high potential iron–sulfur proteins(5), metallothioneins(6), zinc proteins(7) etc. The amino acid sequence His-X-Y-Cys is also of bioinorganic importance since it has been found in the active site of copper(8), iron–sulfur(9) and zinc(10) proteins. We are currently seeking to develop the area of transition metal/Cys-X-Y-Cys and His-X-Y-Cys peptide interactions(11,12); our goals are: (i) to elucidate the role of these sequences in the biological activity and mechanism of action of the above metallobiomolecules, and (ii) to find possible new and more effective agents for the elimination of heavy metals from the human organism or from contaminated waste waters. Here we report the preparation and preliminary characterization of copper(II) complexes of tetrapeptide ligands containing the Cys-X-Y-Cys and His-X-Y-Cys sequences. This revised version was published online in June 2006 with corrections to the Cover Date.     

Investigation for the determination of ultra trace amounts of Co2+ complexed with 1,10-phenanthroline by adsorptive voltammetry

Summary The spontaneous adsorption of the Co²⁺ complex with 1,10-phenanthroline on HMDE was utilized for the development of a voltammetric analytical method employing phase selective alternating current, with first harmonic AC₁ in phase, =0°, voltammetry. The dependence of the analytical voltammetric response on physical and chemical parameters in various supporting electrolytes was investigated in detail. Optimum conditions for Co²⁺ determination were established. The method is very sensitive and selective. The determination limit is 205 ng/l Co²⁺ (adsorption time, t_ads=20 min). The precision and accuracy were evaluated: 1.84 g/l Co²⁺, RSD=3.24%, RE=–0.54%; for 205 ng/l Co²⁺, RSD=4.85%, RE=–3.90%. The results showed good reproducibility and reliabiality. The method was applied to natural waters, wines, mussel tissue and aquatic algae certified reference material.     

Third‐order sensitivity analysis for robust aerodynamic design using continuous adjoint

Robust design problems in aerodynamics are associated with the design variables, which control the shape of an aerodynamic body, and also with the so‐called environmental variables, which account for uncertainties. In this kind of problems, the set of design variables, which leads to optimal performance, taking into account possible variations in the environmental variables, is sought. One of the possible ways to solve this problem is by means of the second‐order second‐moment approach, which requires first‐order and second‐order derivatives of the objective function with respect to the environmental variables. Should the minimization problem be solved using a gradient‐based method, algorithms for the computation of up to third‐order sensitivity derivatives (twice with respect to the environmental variables and once with respect to the shape controlling design variables) must be devised. In this paper, a combination of the continuous adjoint variable method and direct differentiation to compute the third‐order sensitivities is proposed. This is shown to be the most efficient among all alternative methods provided that the environmental variables are much less than the design ones. Apart from presenting the method formulation, this paper focuses on the assessment of the so‐computed up‐to third‐order mixed derivatives through comparison with costly finite‐difference schemes. To this end, the robust design of a two‐dimensional duct is performed. Then, using the validated method, the robust design of a two‐dimensional cascade airfoil is demonstrated. Although both cases are handled as inverse design problems, the method can be extended to other objective functions or three‐dimensional problems in a straightforward manner. Copyright © 2012 John Wiley & Sons, Ltd.     

A remark on the negative activation volume for defects in solids

The evolution of the aging process of glassy materials quenched from temperatures above their glass transition temperature T_g, when plotting the relaxed enthalpy versus the decrease in volume, leads to a slope comparable to the isothermal compressibility close to T_g. This empirical result was explained in an earlier publication (V. Katsika-Tsigourakou, G. E. Zardas J. Non-Cryst. Solids 356 (2010) 179–180) by means of a thermodynamical model. Here, we show that the same model enables the explanation of the rare cases of negative defect activation in solids.     

Hidden Markov models revealing the stress field underlying the earthquake generation

The application of the hidden Markov models (HMMs) is attempted for revealing key features for the earthquake generation which are not accessible to direct observation. Considering that the states of the HMM correspond to levels of the stress field, our objective is to identify these states. The observations are considered after grouping earthquake magnitudes and the cases of different number of states are examined. The problems of HMMs theory are solved and the ensuing HMMs are compared on the basis of Akaike and Bayesian information criteria. A new insight on the evaluation of future seismic hazard is given by calculating the mean number of steps for the first visit to a particular state, along with the respective variance. We further calculate an estimator of the mean number of steps for the first visit to a particular state and we construct its confidence interval. Additionally, a second approach to the problem is followed by assuming a different determination of observations. The HMMs applied to both approaches, contribute significantly to seismic hazard assessment via revealing the number of the stress levels as well as the way in which these levels are associated with certain earthquake occurrence.