A construction of integer-valued polynomials with prescribed sets of lengths of factorizations

For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a product of n irreducibles in Int(Z)={g in Q[x] | g(Z) contained in Z}.Comment: To appear in Monatshefte f\"ur Mathematik; 11 page

Rotordynamic coefficients and leakage flow of parallel grooved seals and smooth seals

Based on Childs finite length solution for annular plain seals an extension of the bulk flow theory is derived to calculate the rotordynamic coefficients and the leakage flow of seals with parallel grooves in the stator. Hirs turbulent lubricant equations are modified to account for the different friction factors in circumferential and axial direction. Furthermore an average groove depth is introduced to consider the additional circumferential flow in the grooves. Theoretical and experimental results are compared for the smooth constant clearance seal and the corresponding seal with parallel grooves. Compared to the smooth seal the direct and cross-coupled stiffness coefficients as well as the direct damping coefficients are lower in the grooved seal configuration. Leakage is reduced by the grooving pattern

Pollen dispersal and gene flow within and into a population of the alpine monocarpic plant Campanula thyrsoides

Background and Aims Gene flow by seed and pollen largely shapes the genetic structure within and among plant populations. Seed dispersal is often strongly spatially restricted, making gene flow primarily dependent on pollen dispersal within and into populations. To understand distance-dependent pollination success, pollen dispersal and gene flow were studied within and into a population of the alpine monocarpic perennial Campanula thyrsoides. Methods A paternity analysis was performed on sampled seed families using microsatellites, genotyping 22 flowering adults and 331 germinated offspring to estimate gene flow, and pollen analogues were used to estimate pollen dispersal. The focal population was situated among 23 genetically differentiated populations on a subalpine mountain plateau (<10 km2) in central Switzerland. Key Results Paternity analysis assigned 110 offspring (33·2 %) to a specific pollen donor (i.e. ‘father') in the focal population. Mean pollination distance was 17·4 m for these offspring, and the pollen dispersal curve based on positive LOD scores of all 331 offspring was strongly decreasing with distance. The paternal contribution from 20-35 offspring (6·0-10·5 %) originated outside the population, probably from nearby populations on the plateau. Multiple potential fathers were assigned to each of 186 offspring (56·2 %). The pollination distance to ‘mother' plants was negatively affected by the mothers' degree of spatial isolation in the population. Variability in male mating success was not related to the degree of isolation of father plants. Conclusions Pollen dispersal patterns within the C. thyrsoides population are affected by spatial positioning of flowering individuals and pollen dispersal may therefore contribute to the course of evolution of populations of this species. Pollen dispersal into the population was high but apparently not strong enough to prevent the previously described substantial among-population differentiation on the plateau, which may be due to the monocarpic perenniality of this specie

IS THE END-TIDAL PARTIAL PRESSURE OF ISOFLURANE A GOOD PREDICTOR OF ITS ARTERIAL PARTIAL PRESSURE?

End-tidal partial pressure of isoflurane (PE′iso) may be used as a measure of anaesthetic depth. During uptake, an arterial partial pressure (Paiso) which is considerably less than PE′iso(Paiso/PE′iso<<1) leads to underestimation of depth of anaesthesia and, during elimination, PE′iso/Paiso<<1 will lead to an overestimation of anaesthetic depth. We measured Paiso/PE′iso during a 60-min uptake period of 1% isoflurane and PE′iso/Paiso during the subsequent 60-min elimination period in 26 patients (age 13-88 yr, ASA I-III) undergoing various surgical procedures. After 15 min of isoflurane uptake, Paiso/PE′iso of 26 patients was mean 0.78 (SD 0.10) and this increased only marginally at 60 min (0.79 (0.09)), whereas during elimination, PE′iso/Paiso was in the range 0.79 (0.14)-0.83 (0.11). Predictability of Paiso in a given patient is hindered by the high SD of Paiso/PE′iso and PE′iso/Paiso, but it may be improved by taking into account age, ASA physical status category, vital capacity, inspired minus end-tidal isoflurane partial pressure and arterial minus end-tidal carbon dioxide partial pressure during uptake; and obesity, end-tidal isoflurane partial pressure and arterial minus end-tidal carbon dioxide partial pressure during elimination. However, even with multiple regression analysis (to account for the various possible variables), clinically useful prediction of Paiso/PE′iso and PE′iso/Paiso in a particular patient is not possible (residual SD 0.084 and 0.113, respectively

DETERMINATION OF THE PARTIAL PRESSURE OF HALOTHANE (OR ISOFLURANE) IN BLOOD

A gas chromatographic method is described for the direct quantitative determination of the partial pressure of halothane {or isoflurane) in blood as well as the blood-gas partition coefficient. A head space technique and a flame ionization detector were used. Standard blood was obtained by equilibrating patients' blood with known gas concentrations in a tonometer. Using an infra-red analyser to measure the halothane gas concentration in the tonometer and within the anaesthetic system allowed for the direct comparison of the partial pressure in blood to the partial pressure in the inspired gas. Technical problems associated with this procedure, and with comparable methods, are discusse

Impact of depth of propofol anaesthesia on functional residual capacity and ventilation distribution in healthy preschool children

Background Propofol is commonly used in children undergoing diagnostic interventions under anaesthesia or deep sedation. Because hypoxaemia is the most common cause of critical deterioration during anaesthesia and sedation, improved understanding of the effects of anaesthetics on pulmonary function is essential. The aim of this study was to determine the effect of different levels of propofol anaesthesia on functional residual capacity (FRC) and ventilation distribution. Methods In 20 children without cardiopulmonary disease mean age (sd) 49.75 (13.3) months and mean weight (sd) 17.5 (3.9)kg, anaesthesia was induced by a bolus of i.v. propofol 2mgkg−1 followed by an infusion of propofol 120µgkg−1min−1 (level I). Then, a bolus of propofol 1mgkg−1 was given followed by a propofol infusion at 240µgkg−1min−1 (level II). FRC and lung clearance index (LCI) were calculated at each level of anaesthesia using multibreath analysis. Results The FRC mean (sd) decreased from 20.7 (3.3)mlkg−1 at anaesthesia level I to 17.7 (3.9)mlkg−1 at level II (P < 0.0001). At the same time, mean (sd) LCI increased from 10.4 (1.1) to 11.9 (2.2) (P = 0.0038), whereas bispectral index score values decreased from mean (sd) 57.5 (7.2) to 35.5 (5.9) (P < 0.0001). Conclusions Propofol elicited a deeper level of anaesthesia that led to a significant decrease of the FRC whereas at the same time the LCI, an index for ventilation distribution, increased indicating an increased vulnerability to hypoxaemi

The Mechanism of CO and CO₂ Hydrogenation to Methanol over Cu-Based Catalysts

Methanol, an important chemical, fuel additive, and precursor for clean fuels, is produced by hydrogenation of carbon oxides over Cu-based catalysts. Despite the technological maturity of this process, the understanding of this apparently simple reaction is still incomplete with regard to the reaction mechanism and the active sites. Regarding the latter, recent progress has shown that stepped and ZnOx-decorated Cu surfaces are crucial for the performance of industrial catalysts. Herein, we integrate this insight with additional experiments into a full microkinetic description of methanol synthesis. In particular, we show how the presence or absence of the Zn promoter dramatically changes not only the activity, but unexpectedly the reaction mechanism itself. The Janus-faced character of Cu with two different sites for methanol synthesis, Zn-promoted and unpromoted, resolves the long-standing controversy regarding the Cu/Zn synergy and adds methanol synthesis to the few major industrial catalytic processes that are described on an atomic level

Cold Strangelets Formation with Finite Size Effects in High Energy Heavy-Ion Collisions

We have studied the phase diagram and evolution of a strangelet in equilibrium with a finite hadronic gas. Significant finite size modifications of the phase diagram are found and their parameter dependences are studied. With the inclusion of finite size effects we have also been able to obtain the detailed properties of the cold strangelet emerging in the final stage of the isentropic expansion of a finite strange fireball in high energy heavy-ion collisions.Comment: 19 pages(RevTex), 11 Postscript figures; To appear in Phys. Rev.