The singular homology groups of compact CW-complexes are finitelygenerated, but the groups of compact metric spaces in generalare very easy to generate infinitely and our understanding ofthese groups is far from complete even for the following compactsubset of the plane, called the Hawaiian earring:
Griffiths [11] gave a presentation of the fundamental groupof H and the proof was completed by Morgan and Morrison [15].The same group is presented as the free -product of integers Z in [4, Appendix]. Hence the firstintegral singular homology group H1(H) is the abelianizationof the group . These results have been generalized to non-metrizable counterparts HI of H(see Section 3). In Section 2 we prove that H1(X) is torsion-free and Hi(X) =0 for each one-dimensional normal space X and for each i 2.The result for i 2 is a slight generalization of [2, Theorem5]. In Section 3 we provide an explicit presentation of H1(H)and also H1(HI) by using results of [4]. Throughout this paper, a continuum means a compact connectedmetric space and all maps are assumed to be continuous. Allhomology groups have the integers Z as the coefficients. Thebouquet with n circles is denoted by Bn. The base point (0, 0) of Bn is denoted by o forsimplicity. 相似文献
Polyvinyl chloride) was treated with triethylaluminum in 1,2-dichloroethane solution. Negligibly small amounts of hydrogen chloride are evolved from the modified polyvinyl chloride) in decomposition at 180°C for 150 min in nitrogen. Quantitative analysis of the rate of dehydrochlorination of the modified polymer gave a calculated activation energy for the alkylation of 8.3 kcal/mole in 1,2-dichloroethane solution; the concentration of the labile chlorines in the original polyvinyl chloride) was less than 0.25 mole % Furthermore, the fact that the average polyene length of the modified polymer for the thermal decomposition was much shorter than that of the starting material suggests that the labile chlorines inherent in the polymer exist not only in the chain end but also in the polymer chain. 相似文献
Endogenous steroids such as dehydroepiandrosterone (DHEA) and dehydroepiandrosterone 3‐sulfate (DHEA?S) have commonly used as doping materials by athletes and to date novel techniques are needed for detection of these molecules. In this study, antibody‐based electrochemical biosensor has developed for testing level of the DHEA?S. For this aim, gold surfaces were initially modified with cysteamine (Cys) and then, DHEA?S antibody was immobilized on the surface via glutaraldehyde (GA) as a crosslinking agent. The stepwise modification of electrode surface was monitored by using various electrochemical techniques such as cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). Linear range was determined as 2.5–100 ng/mL DHEA?S using differential pulse voltammetry (DPV) technique, as well. Moreover, repeatability (±S.D.), coefficient of variation (%) and limit of detection (LOD) values were calculated as 0.033, 1.030 and 3.971, respectively. Also, DHEA?S in synthetic serum and urine samples were successfully determined with standard addition method and confirmation analysis were performed with liquid chromatography quadrupole‐time of flight mass spectrometry (LC‐QTOF/MS) system. The selectivity was studied with the addition of some interfering molecules (testosterone, bovine serum albumin (BSA), cholesterol, uric acid, lactic acid, codein (COD), ascorbic acid, DHEA). Consequently, this work is proposed as practical, innovative and cost‐effective technique that can be easily adapted for the miniaturized form for the analysis of other doping substances as well as DHEA?S for the future works. 相似文献
Diverse furoxans (1,2,5‐oxadiazole 2‐oxides) were synthesized from the corresponding styrenes using nitrosonium tetrafluoroborate as the nitrosation reagent in pyridine (basic media) or dichloromethane (neutral media). Acid‐sensitive functional groups were tolerated under these conditions. The probable reaction mechanism was elucidated. The experimental results support an ionic reaction pathway in contrast to the conventional acidic conditions with a radical mechanism. 相似文献
Regeneration of carboxylic acids from the loaded-organic phase is an essential step to complete the reactive extraction process. A study on the regeneration of levulinic acid from loaded-organic phase (methyl isobutyl ketone + tri-n-octylamine + acid) was carried out using various techniques including NaOH, temperature swing, diluent swing, and tri-methylamine methods. Equilibrium data obtained show that among all the methods, the recovery of acid is the highest for the tri-methylamine method when the molar ratio of tri-methylamine to levulinic acid concentrations is greater than 1. Kinetic studies performed for the tri-methylamine method showed that there are no changes in the specific rate of extraction with changes in stirrer speed rate and phase volume ratio (Vaq/Vorg), and the overall order of reaction is 1.5. Based on the effects of stirrer speed and phase volume ratio on the specific rate of extraction, the reaction was concluded to occur in the fast regime. Also, about 80% of acid was recovered by the evaporation of tri-methylamine phase at 104–140 °C. A detailed economic evaluation for the recovery of levulinic acid using reactive extraction for a feed rate of 2 m3 h?1 shows that the payback period for recovering capital investment is 0.49 years. 相似文献
A reagentless third generation electrochemical glucose biosensor was fabricated based on wiring the template enzyme glucose oxidase (GOx) with graphene nanoribbons (GN) in order to create direct electron transfer between the co-factor (flavin adenine dinucleotide, FAD) and the electrode. The strategy involved: (i) isolation of the apo-enzyme by separating it from its co-enzyme; (ii) preparation of graphene nanoribbons (GN) by oxidative unzipping of multi-walled carbon nanotubes; (iii) adsorptive immobilization of GNs on the surface of a screen printed carbon electrode (SPCE); (iv) covalent attachment of FAD to the nanoribbons; (v) recombination of the apo-enzyme with the covalently bound FAD to the holoenzyme; and (vi) stabilization of the bio-layer with a thin membrane of Nafion. The biosensor (referred to as GN/FAD/apo-GOx/Nafion/SPCE) is operated at a potential of +0.475 V vs Ag/AgCl/{3 M KCl} in flow-injection mode with an oxygen-free phosphate buffer (pH 7.5) acting as a carrier. The signals are linearly proportional to the concentration of glucose in the range from 50 to 2000 mg?L?1 with a detection limit of 20 mg?L?1. The repeatability (10 measurements, at 1000 mg?L?1 glucose) is ±1.4% and the reproducibility (5 sensors, 1000 mg?L?1 glucose) is ±1.8%. The biosensor was applied to the determination of glucose in human serum.
Graphical abstract Wiring of the apo-enzyme of glucose oxidase (apo-GOx) with graphene nanoribbons (GN) bound to FAD at a screen-printed carbon electrode (SPCE). Cyclic voltammetric and amperometric responses to various glucose concentrations.