Some applications of metric currents to complex analysis

The aim of this paper is to extend the theory of metric currents, developed by Ambrosio and Kirchheim, to complex spaces. We define the bidimension of a metric current on a complex space and we discuss the Cauchy–Riemann equation on a particular class of singular spaces. As another application, we investigate the Cauchy–Riemann equation on complex Banach spaces, by means of a homotopy formula.     

To exist or not to exist: example generation in Real Analysis

This article deals with the activity of example generation as a special case of problem solving. We asked university students in the scientific-technological area to produce examples (which may exist or not) of mathematical objects fulfilling given requirements. For the analysis of students’ performances, we have developed a model that attempts to grasp the nature of the different stages in the solving process. The discussion of the findings allows us to outline specificities and educational potentialities of example generation activities.     

Efficient synthesis and environmentally friendly reactions of PEG-supported 1,2-diaza-1,3-butadiene

[reaction: see text] Here, we report the protocol for the preparation of new poly(ethylene glycol)-supported 1,2-diaza-1,3-butadiene. In addition, we discuss an application of this supported reagent in an efficient and environmentally friendly one-pot synthesis of 2-thiazol-4-one derivatives by reaction with thioamides.     

Retrieval of the vertical column of an atmospheric constituent from data fusion of remote sensing measurements

Techniques of data fusion are presently being considered with increasing interest for application to atmospheric observations from space because of their capability to optimally exploit the complementary information provided by different instruments operating aboard on-going and future satellite missions. The task of combining measurements of the same target, when carried out at the level of the retrieved state vectors, faces with two major problems: the need to interpolate the products represented on different retrieval grids which determines a loss of information and the presence of a priori information in the products that can determine a bias in the product of the data fusion. The measurement space solution method avoids these problems. Based on this method we present a novel approach to retrieve the vertical column of an atmospheric constituent from data fusion of remote sensing measurements. We apply the method to retrieve the ozone column from the fusion of simulated measurements of the IASI nadir-viewing spectrometer onboard the METOP-A platform and of the MIPAS limb sounder onboard the ENVISAT satellite. The performance of the method is evaluated in terms of retrieval errors and averaging kernels of the products. The results show the evidence of improved retrieval quality when comparing the outcome of data fusion with that of the inversion process applied to spectra from either of the two instruments.     

Proton and metal binding by cyclen-based highly rigid cryptands

The basicity properties of the two cryptands L1 and L2, featuring, respectively, a dibenzofuran or a diphenyl ether moiety bridging the 1,7 positions of a 1,4,7,10-tetraazacyclododecane macrocycle (cyclen) have been studied by means of potentiometric, UV-vis and fluorescence emission measurements. Both ligands show a high basicity in the first protonation step, the first basicity constant of L1 being too high to be measured in aqueous solution. The crystal structure of {[HL1]L1}(+) shows that the NH(2)(+) group is involved in an intramolecular hydrogen bonding network, which justifies the observed high basicity in solution. (1)H, (13)C NMR, UV-vis and fluorescence emission measurements show that, among first row divalent metal cations, both L1 and L2 selectively bind in acetonitrile Cu(II) and Zn(II), which are encapsulated within the ligand cavities. Zn(II) coordination is accompanied by a remarkable increase of the fluorescence emission of the ligands, pointing out that the molecular architecture displayed by L1 and L2 can be used to develop new OFF/ON chemosensors for this metal cation.     

On examples in mathematical thinking and learning

The importance of examples and exemplification in mathematical thinking, learning and teaching, is well recognized by mathematicians, epistemologists and mathematics educators. In the collection of papers on these topics presented in this issue, we aim to contribute to the debate on this theme, proposing original studies carried out from different approaches and perspectives, and linked to other relevant topics within mathematics education.     

Electron paramagnetic resonance and density-functional theory studies of Cu(II)-bis(oxamato) complexes

In this work we present the investigation of the influence of electronic and structural variations induced by varying the N,N'-bridge on the magnetic properties of Cu(II)- bis(oxamato) complexes. For this study the complexes [Cu(opba)] (2-) ( 1, opba = o-phenylene- bis(oxamato)), [Cu(nabo)] (2-) ( 2, nabo = 2,3-naphthalene- bis(oxamato)), [Cu(acbo)] (2-) ( 3, acbo = 2,3-anthrachinone- bis(oxamato)), [Cu(pba)] (2-) ( 4, pba = propylene- bis(oxamato)), [Cu(obbo)] (2-) ( 5, obbo = o-benzyl- bis(oxamato)), and [Cu(npbo)] (2-) ( 6, npbo = 1,8-naphthalene- bis(oxamato)), and the respective structurally isomorphic Ni(II) complexes ( 8- 13) have been prepared as ( (n)Bu 4N) (+) salts. The new complex ( (n)Bu 4N) 2[Cu(R-bnbo)].2H 2O ( 7, R-bnbo = (R)-1,1'-binaphthalene-2,2'- bis(oxamato)) was synthesized and is the first chiral complex in the series of Cu(II)-bis(oxamato) complexes. The molecular structure of 7 has been determined by single crystal X-ray analysis. The Cu(II) ions of the complexes 1- 7 are eta (4)(kappa (2) N, kappa (2) O) coordinated with a more or less distorted square planar geometry for 1- 6 and a distorted tetrahedral geometry for 7. Using pulsed Electron Nuclear Double Resonance on complex 6, detailed information about the relative orientation of the hyperfine ( A) and nuclear quadrupole tensors ( Q) of the coordinating nitrogens with respect to the g tensor were obtained. Electron Paramagnetic Resonance studies in the X, Q, and W-band at variable temperatures were carried out to extract g and A values of N ligands and Cu ion for 1- 7. The hyperfine values were interpreted in terms of spin population on the corresponding atoms. The obtained trends of the spin population for the monomeric building blocks were shown to correlate to the trends obtained in the dependence of the exchange interaction of the corresponding trinuclear complexes on their geometry.     

Coordination features of a terpyridine-containing polyamine receptor. Effect of protonation on the photophysical properties of the complexes

The synthesis of the new terpyridine-containing macrocycle 2,6,10,14-tetraaza[15](6,6')cyclo(2,2':6',2')terpyridinophane (L) is reported. The ligand contains a tetraamine chain linking the 6,6' positions of a terpyridine unit. A potentiometric, (1)H NMR, UV-vis spectrophotometric and fluorescence emission study on the basicity properties of in aqueous solutions shows that the first four protonation steps occur on the polyamine chain, while the terpyridine nitrogens are involved in proton binding only in the last protonation step at strongly acidic pH values. Cu(II), Zn(II), Cd(II) and Pb(II) complexation was studied in aqueous solution by means of potentiometric, spectrophotometric and spectrofluorimetric measurements. Cu(II) and Zn(II) can form both mono- and dinuclear complexes in solution, while the larger Cd(II) and Pb(II) give only mononuclear complexes. In the [ML](2+) complexes (M = Zn(II) or Cd(II)) the metal is unequivocally bound to the terpyridine unit. Some amine groups are not coordinated and can quench the fluorescence emission of the terpyridine unit thanks to an electron transfer process. Protonation of the unbound amine groups inhibits the eT process, affording fluorescent [MLH(x)]((2+x)+) complexes.     

A new platinum vapor-derived highly efficient hydrosilylation catalyst: NMR structural investigation

The structural features of a highly efficient hydrosilylation catalyst generated by reaction of Pt vapor and a mixture of mesitylene and 1,3-divinyltetramethyldisiloxane (DVS) were investigated by mono- and bidimensional NMR analyses. The structure around the Pt atoms was highlighted and compared with a commercial sample (Karstedt catalyst) and previously reported Pt vapor-derived system.