Let Aut$_∗(X)$ denote the group of homotopy classes of self-homotopy
equivalences of $X$, which induce identity automorphisms of homology group. We
describe a decomposition of Aut$_∗(X_1∨· · ·∨X_n)$ as a product of its simpler subgroups.
We consider the subgroup Aut$_Σ(X)$ of all self homotopy classes α of $X$ such that $Σα = 1_{ΣX} : ΣX → ΣX$, and also give some properties of Aut$_Σ(X)$. 相似文献
A simple model is developed to study the laser cooling of solids.The condition of laser cooling of a solid is developed.By using some parameters of the Yb 3+ ion,which is most widely used in laser cooling,we then calculate the cooling power and the cooling efficiency.In order to make a more precise analysis, the effect of fluorescent reabsorption,which is unavoidable in the cooling process,is discussed using the random walk model.Taking Tm 3+ ion as an example,we derive the average number of absorption events and determine the change in quantum efficiency due to reabsorption.Finally,we obtain the red-shift of the fluorescent wavelength and the requirement of sample dimension. 相似文献
Nitrite and nitrate are main stable products of nitric oxide, a pivotal cellular signaling molecule, in biological fluids. Therefore, accurate measurement of the two ions is profoundly important. Nitrite is difficult to be determined for a larger number of interferences and unstable in the presence of oxygen. In this paper, a simple, cost-effective and accurate HPLC method for the determination of nitrite and nitrate was developed. On the basis of the reaction that nitrite is oxidized rapidly to nitrate with the addition of acidic potassium permanganate, the determination of nitrite and nitrate was achieved by the following strategy: each sample was injected twice for HPLC analysis, i.e. the first injection was to measure nitrate, and the second injection was to measure total nitrate including initial nitrate and the nitrate from the conversion of nitrite with the addition of acid potassium permanganate in the sample. The amount of nitrite can be calculated as difference between injections 2 and 1. The HPLC separation was performed on a reversed phase C18 column for 15 min. The mobile phase consisted of methanol–water (2:98 by volume); the water in the mobile phase contained 0.60 mM phosphate salt (potassium dihydrogen and disodium hydrogen phosphate) and 2.5 mM tetrabutylammonium perchlorate (TBAP). The UV wavelength was set at 210 nm. Additionally, we systemically investigated the effects of the concentration of phosphate salt and TBAP in the mobile phase, the pH of the mobile phase, and the amount of acidic potassium permanganate added to the sample on the separation efficacy. The results showed that the limits of detection (LOD) and the limit of quantitation (LOQ) were 0.075 and 0.25 μM for nitrate (containing the oxidized nitrite), respectively. The linear range was 1–800 μM. This developed approach was successfully applied to assay nitrite/nitrate levels in cell culture medium, cell lysate, rat plasma and urine.