New results and open problems on Toeplitz operators in Bergman spaces

We discuss some of the recent progress in the field of Toeplitz operators acting on Bergman spaces of the unit disk, formulate some new results, and describe a list of open problems -- concerning boundedness, compactness and Fredholm properties -- which was presented at the conference "Recent Advances in Function Related Operator Theory'' in Puerto Rico in March 2010.

Measuring productivity growth when technological change is biased - a new index and an application to UK agriculture

Productivity growth is conventionally measured by indices representing discreet approximations of the Divisia TFP index under the assumption that technological change is Hicks-neutral. When this assumption is violated, these indices are no longer meaningful because they conflate the effects of factor accumulation and technological change. We propose a way of adjusting the conventional TFP index that solves this problem. The method adopts a latent variable approach to the measurement of technical change biases that provides a simple means of correcting product and factor shares in the standard Tornqvist-Theil TFP index. An application to UK agriculture over the period 1953-2000 demonstrates that technical progress is strongly biased. The implications of that bias for productivity measurement are shown to be very large, with the conventional TFP index severely underestimating productivity growth. The result is explained primarily by the fact that technological change has favoured the rapidly accumulating factors against labour, the factor leaving the sector. (C) 2004 Elsevier B.V. All rights reserved.

Crops and cultures in the Pacific: new data and new techniques for the investigation of old questions

Fifty years ago Carl Sauer suggested, controversially and on the basis of theory rather than evidence, that Southeast Asia was the source area for agriculture throughout the Old World, including the Pacific. Since then, the archaeobotanical record (macroscopic and microscopic) from the Pacific islands has increased, leading to suggestions, also still controversial, that Melanesia was a center of origin of agriculture independent of South-east Asia, based on tree fruits and nuts and vegetatively propagated starchy staples. Such crops generally lack morphological markers of domestication, so exploitation, cultivation and domestication cannot easily be distinguished in the archaeological record. Molecular studies involving techniques such as chromosome painting, DNA fingerprinting and DNA sequencing, can potentially complement the archaeological record by suggesting where species which were spread through the Pacific by man originated and by what routes they attained their present distributions. A combination of archaeobotanical and molecular studies should therefore eventually enable the rival claims of Melanesia versus South-east Asia as independent centers of invention of agriculture to be assessed.

Syntheses of two new 1D and 3D networks of Cu(II) and Co(II) using malonate and urotropine as bridging ligands: Crystal structures and magnetic studies

Two new metal-organic based polymeric complexes, [Cu-4(O2CCH2CO2)(4)(L)].7H(2)O (1) and [CO2(O2CCH2CO2)(2)(L)].2H(2)O (2) [L = hexamethylenetetramine (urotropine)], have been synthesized and characterized by X-ray crystal structure determination and magnetic studies. Complex 1 is a 1D coordination polymer comprising a carboxylato, bridged Cu-4 moiety linked by a tetradentate bridging urotropine. Complex 2 is a 3D coordination polymer made of pseudo-two-dimensional layers of Co(II) ions linked by malonate anions in syn-anticonformation which are bridged by bidentate urotropine in trans fashion, Complex 1 crystallizes in the orthothombic system, space group Pmmn, with a = 14,80(2) Angstrom, b = 14.54(2) Angstrom, c = 7.325(10) Angstrom, beta = 90degrees, and Z = 4. Complex 2 crystallizes in the orthorhombic system, space group Imm2, a = 7.584(11) Angstrom, b = 15.80(2) Angstrom, c = 6.939(13) Angstrom, beta = 90.10degrees(1), and Z = 4. Variable temperature (300-2 K) magnetic behavior reveals the existence of ferro- and antiferromagnetic interactions in 1 and only antiferromagnetic interactions in 2. The best fitted parameters for complex 1 are J = 13.5 cm(-1), J = -18.1 cm(-1), and g = 2.14 considering only intra-Cu-4 interactions through carboxylate and urotropine pathways. In case of complex 2, the fit of the magnetic data considering intralayer interaction through carboxylate pathway as well as interlayer interaction via urotropine pathway gave no satisfactory result at this moment using any model known due to considerable orbital contribution of Co(II) ions to the magnetic moment and its complicated structure. Assuming isolated Co(II) ions (without any coupling, J = 0) the shape of the chi(M)T curve fits well with experimental data except at very low temperatures.

New dioxadiaza- and trioxadiaza-macrocycles containing one dibenzofuran unit with two amino pendant arms: synthesis, protonation and complexation studies

New dioxadiaza- and trioxadiaza-macrocycles containing one rigid dibenzofuran unit (DBF) and N-(2-aminoethyl) pendant arms were synthesized, N,N'-bis(2-aminoethyl)-[17]( DBF) N2O2 (L-1) and N,N'-bis(2-aminoethyl)-[22](DBF)N2O3 (L-2), respectively. The binding properties of both macrocycles to metal ions and structural studies of their metal complexes were carried out. The protonation constants of both compounds and the stability constants of their complexes with Co2+, Ni2+, Cu2+, Zn2+, Cd2+, and Pb2+ were determined at 298.2 K, in aqueous solutions, and at ionic strength 0.10 mol dm(-3) in KNO3. Mononuclear complexes with both ligands were formed, and dinuclear complexes were only found for L-2. The thermodynamic binding affinities of the metal complexes of L-2 are lower than those of L-1 as expected, but the Pb2+ complexes of both macrocycles exhibit close stability constant values. On the other hand, the binding affinities of Cd2+ and Pb2+ for L-1 are very high, when compared to those of Co2+, Ni2+ and Zn2+. These interesting properties were explained by the presence of the rigid DBF moiety in the backbone of the macrocycle and to the special match between the macrocyclic cavity size and the studied larger metal ions. To elucidate the adopted structures of complexes in solution, the nickel(II) and copper( II) complexes with both ligands were further studied by UV-vis-MR spectroscopy in DMSO-H2O 1 : 1 (v/v) solution. The copper(II) complexes were also studied by EPR spectroscopy in the same mixture of solvents. The crystal structure of the copper complex of L-1 was also determined. The copper(II) displays an octahedral geometry, the four nitrogen atoms forming the equatorial plane and two oxygen atoms, one from the DBF unit and the other one from the ether oxygen, in axial positions. One of the ether oxygens of the macrocycle is out of the coordination sphere. Our results led us to suggest that this geometry is also adopted by the Co2+ to Zn2+ complexes, and only the larger Cd2+ and Pb2+ manage to form complexes with the involvement of all the oxygen atoms of the macrocyclic backbone.

Bioactive peptides from food proteins: new opportunities and challenges

Food proteins such as milk and soy are a rich source of bioactive peptides. In the last decade, research into this area has intensified and new bioactive peptide sequences have been discovered with a range of apparent biological functions; for example, antihypertensive, antioxidant, and antimicrobial effects and opiate-like qualities have been reported. These peptides could therefore lead to the development of important functional food products and ingredients for the prevention and even treatment of chronic diseases such as cardiovascular disease and cancer. Peptides can be produced by fermentation with dairy starters for instance, and by enzymatic hydrolysis with pancreatic and microbial enzymes. Further purification is typically carried out by membrane filtration and/or chromatographic methods. The production of novel bioactive peptides and their incorporation into functional food products poses several technological challenges as well as regulatory and marketing issues. Proof of efficacy is of paramount importance; this should be verified by conducting appropriate tests in vivo in animals and in humans. In addition, tests for cytotoxicity and allergenicity must be conducted. Despite all of these hurdles, scientific evidence is increasingly demonstrating the health benefits of diet-based disease prevention, and therefore new developments in this area are likely to continue both at the research and the commercialisation level.

New alkamide and ent-kaurane diterpenoid derivatives from Senecio erechtitoides (Asteraceae)

Fractionation of a MeOH/CH2Cl2 (1/1) extract of the aerial parts of Senecio erechtitoides led to the isolation of six compounds including the hitherto unknown N-phenethylamide derivative named N-(p-hydroxyphenethyl)pentacosanamide (1), and a kauranoid derivative named derivative named ent-7-oxo-16 alpha,17-dihydroxykauran-19-oic acid (2), as well as four known compounds, ent-Kaur-16-en-19-oic acid (3), ent-7 beta-hydroxykaur-16-en-19-oic acid (4), ent-7-oxokaur-16-en-19-oic acid (5), steppogenin 4′-O-beta-d-glucoside (6). Their structures and relative configurations were elucidated on the basis of spectroscopic methods, chemical reactions, and comparison with previously known analogs. All isolates were evaluated for their antimicrobial activity and only diterpenoids were found to possess a potent inhibitor effect against the range of microorganism.