Packing Non-Zero A-Paths In Group-Labelled Graphs

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊂V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k −2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem. These results were obtained at a workshop on Structural Graph Theory at the PIMS Institute in Vancouver, Canada. This research was partially conducted during the period the first author served as a Clay Mathematics Institute Long-Term Prize Fellow.     

Automatic continuity and representation of group homomorphisms defined between groups of continuous functions

Let C(X,G) be the group of continuous functions from a topological space X into a topological group G with pointwise multiplication as the composition law, endowed with the uniform convergence topology. To what extent does the group structure of C(X,G) determine the topology of X? More generally, when does the existence of a group homomorphism H between the groups C(X,G) and C(Y,G) implies that there is a continuous map h of Y into X such that H is canonically represented by h? We prove that, for any topological group G and compact spaces X and Y, every non-vanishing C-isomorphism (defined below) H of C(X,G) into C(Y,G) is automatically continuous and can be canonically represented by a continuous map h of Y into X. Some applications to specific groups and examples are given in the paper.     

The Role of a Specific Response of Media in the Vavilov-Cherenkov Effect

It is shown that the condition υ > υ_p (ω), which is necessary in order to trigger the Vavilov-Cherenkov effect, determines the interval of radiated frequencies and it alone cannot establish a strong restriction to the velocity of the particle. It is exhibited that it is possible to define a general lower bound for the velocity of the particle, which does not depend on the frequency when both, a specific response of the medium is taken into account and the mentioned condition is considered. The minimum value of the phase velocity of light in the medium determines the existence of such general lower bound.     

MgO films grown on yttria-stabilized zirconia by molecular beam epitaxy

MgO films were grown on (0 0 1) yttria-stabilized zirconia (YSZ) substrates by molecular beam epitaxy (MBE). The crystalline structures of these films were investigated using X-ray diffraction and transmission electron microscopy. Growth temperature was varied from 350 to 550 °C, with crystalline quality being improved at higher temperatures. The MgO films had a domain structure: (1 1 1)[1 1 2¯]_MgO(0 0 1)[1 0 0]_YSZ with four twin variants related by a 90° in-plane rotation about the [1 1 1]_MgO axis. The observed epitaxial orientation was compared to previous reports of films grown by pulsed laser deposition and sputtering and explained as resulting in the lowest interface energy.     

Synthesis and structural characterisation of [(Ph3P)AuCo(CO)3(PPh3)]

Summary [(Ph₃P)AuCo(CO)₃(PPh₃)] has been synthesised from [(Ph₃P)AuCo(CO)₄], PPh₃v and Me₃NO in acetonitrile. Its molecular structure, determined by single-crystal x-ray crystallography, consists of an almost linear P-Au-Co-P arrangement in which the Co atom is in a slightly distorted trigonalbipyramidal geometry, with the Au and P atoms occupying the apical sites. The Au-Co bond length of 2.450(1) ? is shorter than that reported for [(Ph₃P)AuCo(CO)₄]. The carbonyl ligands are bent towards the Au atom and the mean Au-Co-C angle is 81(1)°.     

Solid sampling Fourier transform infrared determination of Mancozeb in pesticide formulations

A series of approaches have been assayed for FTIR determination of Mancozeb in several solid commercial fungicides using different calibration strategies. The simplest procedure was based on the use of the ratio between the absorbance of a characteristic band of Mancozeb and that of a KSCN internal standard measured in the FTIR spectra obtained from KBr pellets. It was employed the quotient between peak height absorbance values at 1525 cm⁻¹ for Mancozeb and 2070 cm⁻¹ for KSCN. In these conditions a precision as relative standard deviation (RSD) of 0.6% and a relative accuracy error of 0.8% (w/w) were found. For complex formulations, containing other compounds with characteristic absorption bands at different wavenumbers than Mancozeb, one of them was used as internal reference being employed the standard addition approach. In this case, the Mancozeb bands at 1525 cm⁻¹ or at 1289 cm⁻¹ were employed, being used the ferrocyanide band at 2075 cm⁻¹ as internal reference. RSD values between 0.7-1.4% and a relative accuracy error of 3% (w/w) were found. A third strategy was based on the use of partial least squares (PLS) calibration. A reference set was prepared mixing Mancozeb, Kaolin, Cymoxanil and KBr, being predicted the Mancozeb concentration in pesticide formulations by using the quotient between absorbance bands of Mancozeb and those of Cymoxanil. In these conditions a relative accuracy error of 0.6% (w/w) and a relative standard deviation of 1.3% were found.     

Kinetically inert transition metal complexes that reversibly bind to DNA

Transition metal complexes that reversibly bind to DNA have been studied for almost 30 years. In the last few years a variety of new systems have been developed, employing a range of metal ions and ligand architectures. In many cases, high affinity binding and specific selectivities have been observed. These complexes display properties that make them attractive as probes of DNA structure and function, suggesting that they may find a r?le as prototypical tools for a spectrum of applications, from basic molecular biology to medicine. This review presents an overview of some of the structures and properties of such complexes.