High-order moments conservation in thermostatted kinetic models

Recently the thermostatted kinetic framework has been proposed as mathematical model for studying nonequilibrium complex systems constrained to keep constant the total energy. The time evolution of the distribution function of the system is described by a nonlinear partial integro-differential equation with quadratic type nonlinearity coupled with the Gaussian isokinetic thermostat. This paper is concerned with further developments of this thermostatted framework. Specifically the term related to the Gaussian thermostat is adjusted in order to ensure the conservation of even high-order moments of the distribution function. The derived framework that constitutes a new paradigm for the derivation of specific models in the applied sciences, is analytically investigated. The global in time existence and uniqueness of the solution to the relative Cauchy problem is proved. Existence and moments conservation of stationary solutions are also performed. Suitable applications and research perspectives are outlined in the last section of the paper.     

Iron-catalyzed hydroxylation of β-ketoesters with hydrogen peroxide as oxidant

The hydroxylation of β-ketoesters was studied using simple iron catalysts and 30 wt % hydrogen peroxide as the terminal oxidant. The highest activity and yield were achieved in the presence of iron(III) chloride. Cyclic β-ketoesters could be smoothly hydroxylated in 75-90% yield. For linear β-ketoester and β-ketoamide, the chloro-substituted products were obtained.     

Influence of one- and two-dimensional gel electrophoresis procedure on metal-protein bindings examined by electrospray ionization mass spectrometry, inductively coupled plasma mass spectrometry, and ultrafiltration

Three independent methods, (i) electrospray ionization mass spectrometry (ESI-MS), (ii) carrying out the complete protein preparation procedure required for protein gel electrophoresis (GE) including extraction, precipitation, washing, and desalting with subsequent microwave digestion of the produced protein fractions for metal content quantification, and (iii) ultrafiltration for separating protein-bound and unbound metal fractions, were employed to elucidate the influences of protein sample preparation and GE running conditions on metal-protein bindings. A treatment of the protein solution with acetone instead of trichloroacetic acid or ammonium sulfate for precipitate formation led to a strongly enhanced metal binding capacity. The desalting step of the resolubilized protein sample caused a metal loss between 10 and 35%. The omission of some extraction buffer additives led to a diminished metal binding capacity of protein fractions obtained from the sample preparation procedure for GE, whereas a tenside addition to the protein solution inhibited metal-protein bindings. The binding stoichiometry of Cu and Zn-protein complexes determined by ESI-MS was influenced by the type of the metal salt which was applied to the protein solution. A higher pH value of the sample solution promoted the metal ion complexation by the proteins. Ultrafiltration experiments revealed a higher Cu- and Zn-binding capacity of the model protein lysozyme in both resolubilization buffers for 1D- and 2D-GE compared to the protein extraction buffer. Strongly diminished metal binding capacities of lysozyme were recorded in the running buffer of 1D-GE and in the gel staining solutions.     

Polyamine-based anion receptors: Extraction and structural studies

In the discussion that follows some of the more recent progress in the area of anion binding by synthetic polyamine receptors is presented, with emphasis given to work undertaken by the authors’ groups. A continuing theme in these studies has been the relationship between receptor structure and its anion extraction properties.Systematic solvent extraction and structural studies for halide and perrhenate complexes with polyamines of tripodal, macrocyclic and macrobicyclic architecture that contain both aromatic moieties and four to eight amine functions have been performed in order to derive relevant structure-binding/extractability relationships. The results demonstrate that the binding and extraction behaviour of the polyamines towards halides and perrhenate is a complex function of their structural features, degree of protonation and lipophilic properties. The extraction is characterized by the preferred formation of mono- and diprotonated amine species in the organic phase. X-ray structure studies of iodide and perrhenate complexes with open-chain tetraamino derivatives and octaamino cryptands in different protonation states lead to the conclusion that in the first case only limited chelation of the anion occurs and in the second only highly protonated species are able to encapsulate the anion. The structural patterns observed are strongly influenced by the presence of water molecules in the crystals.     

A Gallai–Edmonds‐type structure theorem for path‐matchings

As a generalization of matchings, Cunningham and Geelen introduced the notion of path‐matchings. We give a structure theorem for path‐matchings which generalizes the fundamental Gallai–Edmonds structure theorem for matchings. Our proof is purely combinatorial. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 93–102, 2004     

Down syndrome and parity

OBJECTIVE: To investigate the effect of parity on Down syndrome (DS). METHODS: The study was conducted on data from Northeast Italy (NEI) (1981-1996) and Sicily (ISMAC) (1991-1996) Congenital Malformation Registries. In these areas, all DS births are recorded and confirmed by chromosomal analysis; the NEI Registry also registers pregnancy terminations (TOPs) after prenatal diagnosis of DS. In order to estimate the effect of parity independently of the mother's age and to reduce the truncation effect, different age classes and three classes of parity (1, 2-4, >4) were defined. RESULTS: The study sample consisted of 1,088 consecutive newborns and 169 consecutive fetuses affected by DS. In both NEI and ISMAC samples, we found a significantly increased risk of having a DS child for multiparas > or =35 years of age. In the NEI sample, the inclusion of TOP data did not seem to modify this finding. In the ISMAC sample, a significantly reduced risk for primiparas was found at all ages. CONCLUSIONS: Our data confirm a higher risk of having a DS child in women with parity >4. As this effect is evident only in women > or =35 years age, its practical impact is null because these women are usually offered prenatal diagnosis in any case. However, the mechanisms involved, if this association is true, are very intriguing and the observation should stimulate scientific studies allowing a better knowledge of the nondisjunction mechanism.