Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all
root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen root number. The condition “f satisfies the Wecken property is known to be equivalent to |deg(f)|≤N R[f]/(1−χ(M2)−χ(M10/(1−χ(M2)) for maps between closed orientable surfaces. In the case of nonorientable surfaces the condition is A(f)≤N R[f]/(1−χ(M2)−χ(M2)/(1−χ(M2)). Also we construct, for each integer n≥3, an example of a map f: Kn→N from an n-dimensionally connected complex of dimension n to an n-dimensional manifold such that we cannot deform f in a way that all the Nielsen root classes reach the minimal number of points at the same time. 相似文献
Summary Crystals of the title compounds are both monoclinic, with unit cell dimensions:a = 9.293(5),b = 10.122(5),c = 16.737(7) Å. = 103.44(3)°,Z = 4, space groupP21/c for the cobalt derivative;a = 13.1ß5(7),b = 17.546(ß),c = 6.871(3) Å, = 107.01(4)°Z = 4, space groupP21/n for the copper derivative. The structures were solved from diffractometer data by the heavy-atom technique for the first compound and by direct methods for the second compound. Refinement by block diagonal least-squares gaveR = 5.9% for 3511 independent reflections andR = 8.8% for 2885 independent reflections for the cobalt and copper compound respectively. In both compounds the biguanide moiety behaves as a bidentate chelating ligand in a symmetrical tautomeric form, but it is deprotonated in the octahedral cobalt compound and neutral in the square planar copper compound. 相似文献
This paper describes the synthesis, characterization and a thermogravimetric (t.g.) study of 11 adducts of general formula MCl2·nL (M = Cu, Co and Sn; n = 1 and 2 for Sn, and 2 for Cu and Co; L = ethyleneurea eu, ethylenethiourea etu, and propyleneurea pu). The i.r. results shows that the eu and pu adducts are coordinated through oxygen, whereas for etu nitrogen is the coordination site. The (C=O) or (C=S) trend is: Cu > Co > Sn. The t.g. curves show that the adducts release ligand molecules in a single mass loss step. As regards considering adducts with the same stoichiometry, the observed thermal stability trend is: etu > pu > eu. 相似文献
Highly dispersed zirconium phosphate was prepared by reacting Cel/ZrO(2) (ZrO(2)=6.7 wt%; 0.56 mmol g(-1) of zirconium atom per gram of the material) with phosphoric acid. High power decoupling magic angle spinning (HPDEC-MAS)(31)P NMR and X-ray photoelectron spectroscopy data indicated that HPO(2-)(4) is the species present on the fiber surface. The X-ray diffraction patterns showed that zirconium hydrogen phosphate particles were amorphous and had an ion-exchange capacity, determined by ammonia gas adsorption, of 0.30 mmol g(-1). The ion-exchange capacities for Li(+), Na(+), and K(+) ions were determined from ion-exchange isotherms at 298 K and showed the following values (in mmol g(-1)): Li(+)=0.01, Na(+)=0.23, and K(+)=0.30. The higher affinity of the surface hydrogen phosphate particles for Na(+) and K(+) is due to its lamelar structure which permits easier diffusion of these two ions whose hydrated radii are smaller than that of Li(+). 相似文献
Rosiglitazone (RSG) is marketed as a racemic mixture although the antidiabetic activity is essentially related to the (S)-enantiomer. The chiral center has an adjacent carbonyl group; therefore, the (R)-enantiomer could be transformed to the (S)-enantiomer or vice versa by keto-enolic tautomerism. The literature indicates that this racemization is slow enough to allow the evaluation of the properties of the isolated enantiomers. However, there is no information about the enantioselective kinetic disposition and metabolism of RSG. Additionally, there are no studies on the racemization of its metabolites. Considering these facts, a chiral HPLC method was developed and used for the first time to study the racemization of RSG and its main metabolites. Different conditions, including those used to evaluate the in vitro enantioselective metabolism, were employed. The simultaneous chiral separation of RSG and metabolites was achieved on a Chiralcel OJ-H column by employing methanol/ethanol (90:10, v/v) as mobile phase. The racemization studies showed that the half-life of RSG decreased more than 30 times when the temperature increased from 4 to 37 °C. It was also observed that the half-life of RSG changed from approximately 20 h at pH 3.5 to approximately 2 h at pH 7.4. The same profile was observed for its metabolites. Organic solvents and UV light did not present influence on the racemization process. In addition, a Complete Factorial Design was conducted to evaluate the influence of some parameters that can be changed during an in vitro metabolism study. The results obtained showed that the racemization occurs under in vitro metabolism conditions.
Recent developments in wastewater treatment have led to a renewed interest to obtain elemental sulphur (S°) as a by-product from bioreactors. However, practical studies are limited by the gap of adequate analytical techniques for its determination. This paper provides a statistical study and matrix effect evaluation of an adapted spectrophotometric method for routine S° analyses in aqueous samples, based on a methodology previously described by Hart (1961). Four complex matrices were tested: domestic sewage and effluent samples from three different bioreactors. Tested performance criteria included linearity, matrix effect, limit of detection and quantification and S° recovery. Results were linear (R2 = 0.99994) in the studied range (5 to 100 mg S° L?1) and no matrix effect was observed. The accuracy was based on recovery values that varied from 100% to 106%. The colloidal S° separation and extraction protocol was also considered suitable for aqueous samples, reaching more than 99.0% of S° recovery. 相似文献