Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2

We classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 2. In other words we characterize all the global phase portraits of the quadratic polynomial vector fields having all their orbits contained in conics. For such a vector field there are exactly 25 different global phase portraits in the Poincaré disc, up to a reversal of sense.     

The Center Problem for a Linear Center Perturbed by Homogeneous Polynomials

The centers of the polynomial differential systems with homogeneous polynomials have been studied for the degrees s = 2, 3, 4, 5. for s = 2, 3, and partially classified for s = 4, 5. In this paper we recall and we give new centers for s = 6, 7 a linear center perturbed by They are completely classified these results for s = 2, 3, 4, 5,     

Schwinger Formula Revisited

We apply the formal W.K.B. method in the complex plane to the quantum field theory to obtain the Schwinger formula for spin and spinless particles; i.e., we obtain the probability that the vacuum state remains unchanged in presence of a constant electric field. Finally, from Schwinger formula we calculate the probability that n pairs are produced.     

On the relation between protonium level shifts and nucleon-antinucleon scattering amplitudes

We study the Coulomb and threshold corrections to the low-energy scattering parameters for the proton-antiproton system, with numerical examples based on current optical models. Some commonly used expressions are shown to be inconsistent with our results. We check that the Trueman formula is valid for the level shifts of protonium, provided one takes properly into account the Coulomb corrections to the scattering lengths and volumes.     

New synthetic “tricks” using old reagents. A mild method for the conversion of RCONHR′ to RCONHR″

N-Alkyl-N-nitrosoamides, RCON(NO)R′, react with primary aliphatic amines (NH₂R″), in refluxing dichloromethane or at room temperature, to give RCONHR″ in 65–98% yields.     

Interactions of thiophenes and acidophilic,thermophilic bacteria

The growth and oxygen consumption of a variety of thermophilic, acidophilic bacteria in the presence of thiophene-2-carboxylate (T2C) and dibenzothiophene (DBT) have been determined. T2C was extremely toxic to the acidophiles in comparison with neutrophiles, but appeared to be degraded by a heterotrophicSulfolobus- like thermophile. DBT proved to be unstable at high temperatures, even in the absence of bacteria, and was not a substrate for the thermophiles.     

Linked crystallites in the conducting topmost layer of polymer bilayer films controlled by temperature: from micro- to nanocrystallites.

Temperature has great impact on the structure and size of the linked crystallites of the conducting topmost layer formed at the surface of a polycarbonate film via the reaction BEDT-TTF+IBr [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene]. We show that fine temperature control permits formation of a semiconducting topmost layer of alpha'-(BEDT-TTF)(2)(I(x)Br(1-x))(3) crystallites with either micro- or nanometre size, a result that opens a route to miniaturized conducting plastic materials.     

Plutonium Activity Ratios in Plankton: New Evidence of Hold-Up Time in Irish Sea Sediments

The determination of activity ratios for radioisotopes of different half-lives can be used to estimate transit times from a point source to locations further away. For conservative elements, this time is approximately equivalent to the net hydrological transport. However, for non-conservative elements such as plutonium, the additional influence of biogeochemical processes decreases the net transport time. In this study, ²⁴¹Pu and ^239,240Pu concentrations in Irish Sea plankton samples, collected in May 1994, were determined and the ²⁴¹Pu/^239,240Pu ratios calculated. Plutonium-239,240 was measured using a standard method by ion exchange chromatography and alpha counting, and ²⁴¹Pu was determined by liquid scintillation counting using the disk-supported technique. The latter showed some methodological problems, which are briefly discussed. The ²⁴¹Pu/^239,240Pu ratios gave an estimate of the "transit time" from Sellafield to the different sampling points. In fact, this time represents the age of plutonium in plankton, i.e., the time lag between release from Sellafield and detection at the different sampling stations. The mean plutonium age was 17±2 years (n = 10) and 18.6±0.8 years (n = 13) in phytoplankton and zooplankton, respectively. The spatial distribution was reasonably homogeneous over the Irish Sea. The assimilation-elimination processes of plutonium in plankton are rather rapid. Therefore, it may be assumed that, in this time scale, the plutonium concentrations were in equilibrium with surrounding waters. Thus, it is concluded that plutonium was rather old because resuspension-sedimentation processes had occurred that delayed its transport within the Irish Sea. Therefore, the age of plutonium in plankton represented the hold-up time of plutonium in the sediments from the Irish Sea.     

Synthesis of isoxazolo[4,5-d]pyridazin-4(5H)-ones and 4-acyl-5-hydroxy-3(2H)-pyridazinones

The title compounds were prepared from ethyl 5-acyl- or 5-(1-hydroxyethenyl)isoxazole-4-carboxylates which in turn were prepared from ethyl 3-methylamino-2-butenoate or 3(2H)-furanones.