A cubic differential system with nine limit cycles

Advances in Computer Algebra software have made calculations possible that were previously intractable. Our particular interest is in the investigation of limit cycles of nonlinear differential equations. We describe some recent developments in handling very large computations involving resultants and present an example of a nonlinear differential system of degree three with nine small amplitude limit cycles surrounding a focus. We know of no examples of cubic systems with more than this number bifurcating from a fine focus, as opposed to a centre. Our example appears to be the first to have been obtained without recourse to some numerical calculation.     

Design of a new electrogenerated polyquinone film substituted with glutathione. Towards direct electrochemical biosensors

We developed a method to graft a tripeptide (glutathione) onto 5-hydroxy-1,4-naphthoquinone, an electropolymerizable molecule. The resulting thin conducting polymer presents a well-defined and stable electroactivity in neutral buffered solution, due to the embedded quinone group, and is able to covalently graft amino-modified DNA probe strands. It is shown that the bioelectrode presents positive current change following DNA hybridization. This makes a “signal-on” direct electrochemical DNA sensor. The results were obtained with low target concentration (50 nM) and the selectivity is excellent as a single-mismatch sequence can be discriminated from the full-complementary target.     

Electroanalytical Study of the Pesticide Asulam

The electrochemical behaviour of the herbicide Asulam was studied by cyclic and square wave voltammetry. Asulam may be irreversibly oxidised at a glassy carbon electrode. Maximum currents were obtained at pH = 1.9 in aqueous electrolyte solution. Based on the electrochemical behaviour of Asulam, two analytical methodologies were developed for its determination in water samples, using square wave voltammetry (SWV) and flow injection analysis (FIA) coupled with an amperometric detector. Limits of detection of 7.1 2 10 m 6 mol L m 1 and 1.2 2 10 m 8 mol L m 1 for SWV and FIA respectively, were achieved. Repeatability was calculated by assessing the relative standard deviation (%) for 10 consecutive determinations of one sample. The found values were 2.1% for SWV and 5.0% for FIA. Validation of the results provided by SWV and FIA methodologies was performed by comparison with results from an HPLC-DAD technique. Good relative deviations were found (< 5%). Recovery trials were performed to assess the accuracy of the results and the obtained values were between 84% and 107% for both methods.     

A new smoothing-regularization approach for a maximum-likelihood estimation problem

We consider the problem min _i=1 ^m (aⁱ,x–b_iloga ⁱ, z) subject tox 0 which occurs as a maximum-likelihood estimation problem in several areas, and particularly in positron emission tomography. After noticing that this problem is equivalent to mind(b, Ax) subject tox 0, whered is the Kullback-Leibler information divergence andA, b are the matrix and vector with rows and entriesa ⁱ,b _i, respectively, we suggest a regularized problem mind(b, Ax) + d(v, Sx), where is the regularization parameter,S is a smoothing matrix, andv is a fixed vector. We present a computationally attractive algorithm for the regularized problem, establish its convergence, and show that the regularized solutions, as goes to 0, converge to the solution of the original problem which minimizes a convex function related tod(v, Sx). We give convergence-rate results both for the regularized solutions and for their functional values.The research of A. N. Iusem was partially supported by CNPq Grant No. 301280/86-MA.     

The prediction of nucleophilic attacking sites via determinants of ‘active’ frontier and near-frontier orbitals

A method for computing the most favourable initial attacking site for a nucleophile on a transition metal complex is described, and applied to the nucleophilic substitution and addition reactions of fluoromethane, and the cationic complexes [BFe(CO)₃]⁺ (B = C₆H₇ and C₇H₉). The reactions considered are classified according to whether they are frontier or non-frontier orbitally or charge controlled. It is found that initial attack on the (polyenyl)M(CO)₃ cations is always predicted to occur at the M(CO)₃ moiety, in agreement with the experimental observation of intermediates in several such reactions and suggesting that the existence of these species is a general phenomenon.     

The use of BF(-)(4) as the supporting electrolyte anion in voltammetric studies on carbon electrodes-a cautionary note

BF(-)(4), a supporting electrolyte anion commonly employed in aprotic as well as protic solvents, is found to give an anodic peak at around +0.8 V vs. SCE on glassy carbon electrodes in dimethylformamide media. The voltammetric peak is influenced by the sweep-rate as well as the concentration of BF(-)(4). The electrode, when anodically polarized under these conditions, is also found to retard the charge-transfer rate of the ferricyanide/ferrocyanide redox system. Possible mechanisms for formation of a film on the electrode are discussed; possibilities are fluorination of carbon atoms on the electrode surface by reactions such as C(lattice) + BF(-)(4) --> (CF ... BF(3))(lattice) + e(-) or CH(lattice) + BF(-)(4) --> (CF ... BF(3))(lattice) + H(+) + 2e-. The analytical importance of considering the influence of BF(-)(4) and other fluoride species on carbon electrodes in the anodic region is emphasized.     

An investigation into the role of chloro-substituents in hydrogen-bonded crystals: The crystal structures of the dichlorophenols

A graphical analysis has been made of hydrogen-bonding patterns and non-bonded interactions in the crystal structures of the six dichlorophenols. This shows that hydrogen bonding is the primary interaction in stabilising all the isomers, and that C?C and Cl?Cl non-bonded interactions are also important in stabilising structures characterised by a short (≈ 4 Ã) axis.     

Electronic energy self-exchange with macrocyclic chromium(III) complexes

The luminescence lifetimes of N-deuterated Cr(III) complexes of macrocyclic tetraamine ligands, trans-CrN(4)X(2)(n)()(+), are substantially longer than those of their undeuterated counterparts in room temperature solution. Thus, excited-state emission quenching of the longer lived species by the shorter lived species may be studied by analyzing the decay profile following pulsed excitation. Flash photolysis experiments were carried out for three deuterated/undeuterated pairs of trans-CrN(4)X(2)(n)()(+) complexes (where X = CN-, NH(3), and F-). For the trans-Cr(cyclam)(CN)(2)(+) system in H(2)O, it was determined that energy transfer was occurring between the deuterated and undeuterated species. Although the rate constant of energy transfer was too fast to measure explicitly, it could be bracketed as k(et) >7 x 10(6) M(-1) s(-1). For this reaction it was possible to measure an equilibrium constant which was very near 1.0. For trans-Cr(cyclam)(NH(3))(2)(3+) in DMSO, it was also established that energy transfer was occurring and rate constants of 2.4 x 10(6) M(-1) s(-1) (mu = 0.1) and 9.7 x 10(6) M(-1) s(-1) (mu = 1.0) were determined by a Stern-Volmer analysis. For trans-Cr(tet a)F(2+) in H(2)O, no energy transfer was observed, which implies that the rate constant is <3 x 10(5) M(-1) s(-1). Because these energy-transfer reactions represent self-exchange energy transfer and are thus thermoneutral, we are able to analyze the results using Marcus theory and draw some conclusions about the relative importance of nuclear reorganization and electronic factors in the overall rate.     

The vibrational spectrum of 1,3-dithiole-2-thione

Infrared and Raman spectra of 1,3-dithiole-2-thione have been analysed partially through a normal coordinate calculation to give a vibrational assignment for the molecule.     

Toward templated metal-organic frameworks: synthesis, structures, thermal properties, and luminescence of three novel lanthanide-adipate frameworks

Three novel praseodymium-adipate frameworks were synthesized hydrothermally. GWMOF-3 ([Pr(2)(adipic acid)(3)(H(2)O)(4)].adipic acid.4H(2)O) and GWMOF-6 ([Pr(2)(adipic acid)(3)(H(2)O)(2)].4,4'-dipyridyl) formed three-dimensional structures, whereas GWMOF-4 ([Pr(2)(adipic acid)(3)(H(2)O)(2)].H(2)O) produced a more dense, two-dimensional topology. Single-crystal X-ray and powder diffraction, IR spectroscopy, fluorescence spectroscopy, thermogravimetric analysis, and elemental analysis were employed to characterize all samples. GWMOF-6 represents an innovative step forward in metal-organic framework synthesis where a neutral molecular species not used in the construction of the framework is utilized as a structure-directing agent, or template. Furthermore, this template molecule (4,4'-dipyridyl) is shown to sensitize the fluorescence of lanthanide metal centers in a europium analogue of GWMOF-6.