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 为了更好的帮助您理解掌握查询词或其译词在地道英语中的实际用法，我们为您准备了出自英文原文的大量英语例句，供您参考。 
An example shows that the differentiable structures can indeed be different, even though they are isomorphic.


the volume computations involve several different methods according to the parity of dimension, subgroup relations and arithmeticity properties.


Our proof is based on a different approach and is much more rigorous.


In the process we study the properties of different homogeneous models for ${\mathbb H}H(n).$


The constants obtained are independent of the dimension n and depend only on k,p, and the number of different eigenvalues of the matrix B.

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 The effects of copper and zinc ionsupon the precipitation of barium sulphate have been noted for a long time.However,the results published wereeither not systematic(3,4b,5,6)or obtained under conditions apart fromusual analytical practice(7,8).Thus,it seems necessary to investigate thissubject in more detail by the usual methods of determination.The presentcommunication reports(a)the effect of various amounts of cupric and zincions and(b)the influence of different acidities during precipitation in thepresence... The effects of copper and zinc ionsupon the precipitation of barium sulphate have been noted for a long time.However,the results published wereeither not systematic(3,4b,5,6)or obtained under conditions apart fromusual analytical practice(7,8).Thus,it seems necessary to investigate thissubject in more detail by the usual methods of determination.The presentcommunication reports(a)the effect of various amounts of cupric and zincions and(b)the influence of different acidities during precipitation in thepresence and absence of zinc ions.It is found that the interference of copper in the determination of sulphuras barium sulphate up to a ratio of 20:1 for Cu:S is negligible.The deviationsof the results obtained from theoretical values are all within ±2‰(see Table1),and do not show any regularity with the amount of copper added.The presence of zinc ions alone gives satisfactory results(slightly lowerthan theoretical values).As the amount of zinc ions in solution increases,thedeviations become somewhat wider(Table 2).The low results are presumedto be due to(1)the formation of soluble zincsulphate complex,which holdsa part of sulphate in solution,and/or(2)diverse ion effect.In the presenceof zinc ions,introducing hydrochloric acid up to 0.1 N before precipitationcauses essentially the same errors as if hydrochloric acid were absent(cf.Tables2 and 3),while at and beyond 0.2 N positive errors are obtained.A spectrographic examination of the precipitates reveals that zinc doescoprecipitate with barium sulphate,though only to a slight extent.The amountof zinc coprecipitated decreases with the increase of the acidity of the solutionfrom which the precipitate is thrown down.  本文报告铜及锌离子对于硫酸钡定硫的影响,找出了铜的影响几近于零,锌的影响亦微。锌离子能与硫酸钡共同沉淀。  The velocities of reaction of ethyl acetate with sodium hydroxide in dioxane water mixture have been determined in seven different temperatures(5°,10°, 15°,20°,25°,30°and 35°).For each temperature,the compositions of solvent mixture are 0,5,10,15,20,25 and 30% of dioxane.We thus obtain 49 velo city constants as summarized in the following table. At low temperatures,the velocity constant decreases slightly with decrease of dielectric constant of solvent.At higher temperatures,such decreases of k' become... The velocities of reaction of ethyl acetate with sodium hydroxide in dioxane water mixture have been determined in seven different temperatures(5°,10°, 15°,20°,25°,30°and 35°).For each temperature,the compositions of solvent mixture are 0,5,10,15,20,25 and 30% of dioxane.We thus obtain 49 velo city constants as summarized in the following table. At low temperatures,the velocity constant decreases slightly with decrease of dielectric constant of solvent.At higher temperatures,such decreases of k' become more pronounced. The“isocomposition”energy of activation decreases slightly with increase of percentage of dioxane in the solvent mixture. The“isodielectric”energy of activation shows practically no change,when the dielectric constant changes from 80 to 50.Its value is 11300 calories. The experimental data are compared with the three modern theories of ion molecule reaction,namely,by(1)MoelwynHughes,(2)Laidler and Eyring and (3)Amis and Jaffe.From the viewpoint of influence of dielectric constant on the rate of the present reaction,the first two theories disagree qualitatively with our experimental data,while the last one,though qualitatively successful,fails quantitatively.(The “enhanced moment” and index of refraction as calculated from the last theory with the use of our data are unreasonably large.)  作者在7具不同温度(5°,10°,15°,20°,25°,30°,35°)下,研究了乙酸乙酯和氢氧化钠在二氧六圜和水的混合溶剂中的反应速度。每个温度有7个不同的二氧六圜和水的成分(0%,5%,10%,15%,20%,25%,30%的二氧六圜),因此得到49个速度常数。在每个温度里,反应速度常数随溶剂介电常数的减小而略为下降:温度愈高,下降趋势愈为显著。同溶剂成分的活化能随着溶剂里二氧六圜成分的增加而略为下降。同介电常数的活化能,在80至50的介电常数范围中,却和介电常数的变化无关。它的平均值是11300卡。我们用实验结果检验最近三个溶液里离子和分子反应速度理论:(1)MoelwynHughes 的、(2)LaidlerEyring 的和(3)AmisJaffe 的理论。就介电常数对反应速度的影响来说,理论(1)和(2)在质上就不和实验相符。理论(3)在质上似和实验相符,但在量上却相差太远。因此就乙酸乙酯对氢氧化钠的反应来说,三个理论都是不合的。  In this article it is pointed out that the semiempirical van der Waals' equation of state for gases is particularly unsatisfactory in the neighborhood of the critical point, as indicated by the fact that the experimental values of the critical ratio (?) seldom agree with the theoretical constant value 8/3. It is also noted that this τ value may serve as a satisfactory measure (at least to a first approximation) of the deviation of the law of corresponding states when applied to gases at high densities. We have... In this article it is pointed out that the semiempirical van der Waals' equation of state for gases is particularly unsatisfactory in the neighborhood of the critical point, as indicated by the fact that the experimental values of the critical ratio (?) seldom agree with the theoretical constant value 8/3. It is also noted that this τ value may serve as a satisfactory measure (at least to a first approximation) of the deviation of the law of corresponding states when applied to gases at high densities. We have therefore proposed in this communication a rather straightforward modification of the van der Waals' equation which leads to an empirical threeconstant equation of state for gases involving this τ value as an adjustable parameter and thus requiring only critical data for the determination of the three constants. This equation is made to fit the pVT data at the critical point, but reduces itself to the simpler forms of the van der Waals' equation and the ideal gas equation for lower values of gas densities. Numerical calculations made for gases of widely different τ values show that this rather simple equation of state is fairly satisfactory even at high densities. The plausibility of using the τ value as an adjustable parameter both for the equation of state and for the law of corresponding states is also briefly discussed.  本文指出任何僅含兩個常數的氣態方程,在臨界點附近的缺點是特別顯著的。同時也指出,對應態定律應用到高密度氣體的偏差,可以相當滿意地用臨界係數(?)來衡量。因此我們建議將van der Waals方程,修改爲三常數的經驗方程,它的優點是這三個常數可以直接從氣體的臨界點數據計算出來;而且實例計算(包括極性很強和τ值很大的甲醇)說明它在相當大的温度和密度範圍內可以適用。將這個經驗式,寫成對比方程顯然含有臨界係數τ,就離開臨界點不太遠的氣體來說,這個函數關係可以相當满意地用本文方程總結出來。   << 更多相关文摘 
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