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dual
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     Dual Lasers
     双激光器
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     Dual Images
     双重影像
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     On the Dual Space of W~(m, p))
     关于W~(m,p)(Ω)的对偶空间
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     The dual space of B(Ω,F)
     B(Ω,F)的对偶空间
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  dual
The cohomology algebra of the classifying space of a compact Lie group admits the structure of ann-Hopf algebra, wheren is the order of the Weyl group; the homology with dual structure is also ann-Hopf algebra.
      
In a first step we prove that the Satake compactification of the modular variety of genus 2 and level 3 is the normalization of the dual of the Burkhardt quartic.
      
The second part consists in the normalization of the Burkhardt dual.
      
Finally, we study their reducibility of the action of the Casimirs on the zero-weight spaces of self-dual g-modules and obtain complete classification results for g = sln and g2.
      
This boils down to a Duistermaat-Heckman exact stationary phase calculation, involving a Poisson structure on the dual symmetric space G0/K discovered by Evens and Lu.
      
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Even though in the application of adsorption to industry or research one almost never deals with solutions containing only a single solute, yet the number of investigations on the adsorption from mixed solutions is very limited. Following the lead of Freundlich the generally held opinion is that the effect of one adsorbate on the adsorption of another is simple displacement. While this may be true for some special cases, it is undoubtedly too simple to be of general validity, because the various interactions,...

Even though in the application of adsorption to industry or research one almost never deals with solutions containing only a single solute, yet the number of investigations on the adsorption from mixed solutions is very limited. Following the lead of Freundlich the generally held opinion is that the effect of one adsorbate on the adsorption of another is simple displacement. While this may be true for some special cases, it is undoubtedly too simple to be of general validity, because the various interactions, such as solid-solvent, solute-solute, solute-solvent, have been neglected in this theory. In the theoretical study of chromatography it is necessary to know the equation for the adsorption isotherm when more than one solute are present in the solution. The most widely adopted equation for this purpose is (x/m)_a=k'_aC_a/(1+k_iC_i) (1) This equation can be easily derived from that for a single adsorbate: x/m = k'C/ (1+kC) (2) by assuming that the presence of an additional solute merely reduces the available surface area of the solid. Formally, this equation is analogous to that of Langmuir for the adsorp- tion of gaseous mixtures, replacing pressures by concentrations, but it is actually an empirical equation, because the numerical values of the k's can be obtained only from experimental data and their physical significance is not at all clear. This equation predicts the de-pression of the adsorption of one solute by another. While it is in line with the current idea, there is no experimental proof of its validity. It is the dual purpose of the present investigation to substantiate or disprove the dis- placement theory and to test the applicability of equation (1). We have studied the adsorption from binary solutions of hydrochloric, acetic, and oxalic acids by sugar char. The adsorbates are chosen because of their widely different strength. Sugar char is chosen because it has been shown from previous studies that with this adsorbent the experimental data for single adsorbate follow equation (2). The experimental results are given below: HCl-CH_3COOH and CH_3COOH-H_2C_2O_4 systems: (1) The adsorption of any acid is less than when it is present alone; (2) When the corresponding (x/m)'s are plotted, straight lines with negative slopes are obtained; (3) The slopes of these straight lines vary with the concentration of the acid being displaced; (4) The order of the displacing power, measured by the slope, is HCl> CH_3COOH > H_2C_2O_4, while the order of adsorption is just the reverse; (5) Equation (1) is not valid. HCl-H_2C_2O_4 system: (6) The adsorption of HCl is decreased; (7) When its concentration is higher than about 0.005 N, the adsorption of oxalic acid is increased; at lower concentrations the adsorption is decreased; (8) The higher the concentration of HCl is, the more pronounced will be the increase of adsorption of oxalic acid; (9) Corresponding (x/m)'s give straight lines whose slopes change sign as C_ox increases beyond 0.005 N. From (3) and (4) it is concluded that the observed decrease of adsorption is not due to simple displacement. Based on the hypothesis that it is primarily the solvent which is displaced with the subsequent shift of equilibrium, a mechanism is proposed to account for the effect of one solute on the adsorption of another, which seems to agree with all the observed results. The increase of the adsorption of oxalic acid disproves conclusively the displacement theory. The fact that there is a critical concentration below which the adsorption of oxalic acid is decreased indicates that there are two opposite influences at work. It is suggested that three factors contribute to the increase of adsorption of oxalic acid: (a) the decrease of dissociation; (b) the lowering of solubility; and (c) electrostatic effect. To determine the relative importance of these factors requires further investigation. Finally, an empirical equation involving three constants has been derived to represent the adsorption of oxalic acid in the presence of hydrochloric acid.

在此工作中我們研究了三種混合酸的吸附。在鹽酸-酸的體系中,鹽酸增加糖炭對於草酸的吸附量,倘若草酸的濃度超過0.005N。這個事實否定了在混合酸中各溶質間的作用是彼此頂替的說法。在醋酸-草酸及醋酸-鹽酸的混合溶液中,各酸的吸附量皆較其單獨存在時低。根據實驗的數據我們指出了各家說法的可疑之點。我們認為在混合溶液中吸附量之減少主要是因為溶質甲頂替了表面上的溶劑,因而使溶質乙的吸附量降低。若是溶質甲能使溶質乙的電離度或溶度降低,或增加溶質乙的Gegen-ion,則能使乙的吸附量增加。因為Langmuir式的混合吸附公式不能代表吸附之增加,我們提出了一個可以此較滿意的代表實驗結果的三常數經驗公式。各溶質的吸附量皆成直線關係。對此結果我們不能作定量的解釋,雖然此種現象與我們的假設並不矛盾。

Observations made on the cystic arteries of 120 cadavers (62 adults,48children and 10 newborns) showed 85 (70.83±4.1%)to be simple cystic arteryand 35 double (29.07±4.1%).The percentages of the double cystic artery arehigher in children and newborns(20 cases,57.14%,in children and newbornsas compared with 15 cases,42.86%,in adults).In 64 cases,or 53.33±4.5 percent,the simple cystic aretry arises in theCalot's triangle from the typical coeliac right hepatic artery,and in 24 casesor 20.0±3.6 per cent,the superficial...

Observations made on the cystic arteries of 120 cadavers (62 adults,48children and 10 newborns) showed 85 (70.83±4.1%)to be simple cystic arteryand 35 double (29.07±4.1%).The percentages of the double cystic artery arehigher in children and newborns(20 cases,57.14%,in children and newbornsas compared with 15 cases,42.86%,in adults).In 64 cases,or 53.33±4.5 percent,the simple cystic aretry arises in theCalot's triangle from the typical coeliac right hepatic artery,and in 24 casesor 20.0±3.6 per cent,the superficial or deep branches or both have the sameorigin.The single and double cystic arteries,or one branch of the double cysticartery from the replaced right hepatic artery occurs in 12 cases or 10.0±2.7per cent,and from an artery other than the right hepatic,23 cases or 19.7±3.5per cent.In 74 cases,or 61.67±4.2 per cent,the origin of the single and one or twobranches of the double cystic artery is in Calot's triangle;in 49 cases,or 40.83±4.4 per cent,it is from the right hepatic artery or other sources to the leftof the hepatic duct and crossing the hepatic duct or common bile duct posteriorlyor anteriorly.17 cases or 14.17±3.2 per cent are in other locations.The single and dual cystic arteries or one branch of the dual cystic arteryare attached to the gall bladder from the neck in 100 cases,or 83.33±3.3 percent;and from the body in 51 cases,or 42.5±4.5 per cent.The series was classified into 8 types,their relation to the clinical opera-tion was discussed.

1.本文检查了120例尸体的胆囊动脉,其中62例成年尸体,48例童尸和10例胎儿。2.在此120例中有85例单胆囊动脉,占70.83±4.1%;35例双胆囊动脉,占29.17±4.1%,百分率较高,其原因也曾讨论。3.胆囊动脉的起始。(见表1)(1)起始于典型肝右动脉的:单胆囊动脉64例;双胆囊动脉的两支起于此者22例,1支起于此者7例;共93例,占77.50±3.8%。(2)起于变异肝右动脉的:(包括肠系膜肝右动脉、肠系膜肝总肝右动脉、腹腔肝右动脉及腹主肝右动脉等)单胆囊动脉7例;双胆囊动脉两支起于此者4例,1支起于此者1例。共12例,占10.00±2.7%。(3)起于肝左或肝中动脉的:单胆囊动脉7例;双胆囊动脉两支起于此者1例,1支起于此者7例。共15例,占12.50±3.0%。 (4)起于其它动脉的:(包括肝总、肝固有及胃十二指肠动脉等)单胆囊动脉7例;双胆囊动脉1支起於此者1例,2支起於此者无。共8例,占6.67±2.3%。4.胆囊动脉起始的位置(见表2)(1)位在Calot氏三角内者:单胆囊勤脉48例,双胆囊动脉两支位于此者9例,1支位于此者17例,共74例。占61.67±4.4%。(2)位于肝总管...

1.本文检查了120例尸体的胆囊动脉,其中62例成年尸体,48例童尸和10例胎儿。2.在此120例中有85例单胆囊动脉,占70.83±4.1%;35例双胆囊动脉,占29.17±4.1%,百分率较高,其原因也曾讨论。3.胆囊动脉的起始。(见表1)(1)起始于典型肝右动脉的:单胆囊动脉64例;双胆囊动脉的两支起于此者22例,1支起于此者7例;共93例,占77.50±3.8%。(2)起于变异肝右动脉的:(包括肠系膜肝右动脉、肠系膜肝总肝右动脉、腹腔肝右动脉及腹主肝右动脉等)单胆囊动脉7例;双胆囊动脉两支起于此者4例,1支起于此者1例。共12例,占10.00±2.7%。(3)起于肝左或肝中动脉的:单胆囊动脉7例;双胆囊动脉两支起于此者1例,1支起于此者7例。共15例,占12.50±3.0%。 (4)起于其它动脉的:(包括肝总、肝固有及胃十二指肠动脉等)单胆囊动脉7例;双胆囊动脉1支起於此者1例,2支起於此者无。共8例,占6.67±2.3%。4.胆囊动脉起始的位置(见表2)(1)位在Calot氏三角内者:单胆囊勤脉48例,双胆囊动脉两支位于此者9例,1支位于此者17例,共74例。占61.67±4.4%。(2)位于肝总管左侧,且越其前面或后面者:单胆囊动脉25例;双胆囊动脉1支位于此者13例,两支位于此者无。共38例,占31.67±4.2%。(3)位输胆总管左侧,且越其前面或后面者:单胆囊动脉6例,双胆囊动脉的1支位于此者5例,共11例。占9.17±2.6%。(4)位于其它位置的:单胆囊动脉5例;双胆囊动脉两支位于其它位置的6例,1支位于其它位置的5例,共16例,占13.33±2.9%。5.胆囊动脉进入胆囊的部位(见表3)(1)从胆囊颈入胆囊的:单胆囊动脉62例,双胆囊动脉两支从颈进入者4例,1支从颈进入者34例。共100例,占83.33±3.30%。(2)从胆囊体进入者:单胆囊动脉23例,双胆囊动脉的1支从体进入胆囊的28例;共51例,占42.50±4.5%。6.胆囊动脉的类型(见表4)正常的第Ⅰ型占57.60±4.5%;第Ⅱ型估25.00±3.9%;第Ⅲ型占8.33±2.5%;第Ⅳ型占12.50±3.0%;第Ⅴ型占3.33±1.6%;第Ⅵ型占3.33±1.6%;第Ⅷ型占1.67±1.2%;第Ⅶ、Ⅸ、Ⅹ、Ⅺ、Ⅻ型作者未曾见到。双胆囊动脉深支的配布类型:浅深支同一起始动脉的为第Ⅰ型有27例;不同起始的为第Ⅱ型有8例。7.进行胆囊手术时应注意下列几点:(1)双胆囊动脉占29.17±4.1%,分离胆囊管和动脉时应充分注意。(2)正常典型的胆囊动脉仅占57.50±4.5%,馀均异常。在胆囊颈分离时,应注意常有肝右动脉的分枝位其下面;胆囊动脉有时很短,几与其所起始的肝动脉在一处。在胆囊管和动脉未分离清楚以前,勿结紮切断,以免误损肝动脉。(3)胆囊动脉位于肝总管左侧,越肝总管和输胆总管前面的占36.66±4.4%,位其后面者占4.17±1.8%,在分离胆囊管和动脉时应注意之。(4)胆囊动脉从胆囊颈左缘进入是正常的,占65.83±4.2%,另有异常的为从颈右缘或后方进入胆囊的有21例,从体进入胆囊的有51例,共占60.00±4.2%。在分离胆囊时也应注意胆囊颈的右下缘及胆囊体。

1.The principal reactions of methylcyclohexane,methylcyclopentane and heptane on platinum-fluorine-alumina catalyst of various platinum and hydrogen fluoride contents(Pt,0~1%;HF,0~5%)have been investigated under fixed reaction conditions:temperature,472℃,pressure,20 atm.,LHSV,3,H_2:feed (mol.ratio),6:1.The main results of present investigation are found to be in good agreement with the reaction machanism and the dual function of“houdri- forming” catalyst suggested by Mills and Heinemann.Platinum-fluorine-...

1.The principal reactions of methylcyclohexane,methylcyclopentane and heptane on platinum-fluorine-alumina catalyst of various platinum and hydrogen fluoride contents(Pt,0~1%;HF,0~5%)have been investigated under fixed reaction conditions:temperature,472℃,pressure,20 atm.,LHSV,3,H_2:feed (mol.ratio),6:1.The main results of present investigation are found to be in good agreement with the reaction machanism and the dual function of“houdri- forming” catalyst suggested by Mills and Heinemann.Platinum-fluorine- alumina catalyst consists of two important kinds of active sites,i.e.the dehy- drogenation(or metal)site and the isomerization(or acid)site;the former is derived from platinum and the latter from hydrogen fluoride.Dehydroisomeri- zation of methylcyclopentane and isomerization of n-heptane can proceed effec- tively only upon the dual site catalyst. 2.With platinum content fixed at 0.3%,the following results for the effect of hydrogen fluoride on the reactions of methylcyclopentane and n-heptane are obtained:for HF content below 1%,benzene yield of methylcyclopentane increases by increasing hydrogen fluoride content,for HF content greater than 1%,no further appreciable influence is observed.Isomerization of n-heptane is easier than dehydroisomerization of methylcyclopentane,so that catalyst of 0.2% HF is very efficient for isomerization of n-heptane.The major effect of hydrogen fluoride in excess of 0.2% is to accelerate hydrocracking reaction and thereby decrease liquid yield remarkably.A short discussion for these experimental re- sults is presented with the use of the recent information published by Wēbb, which shows how the surface acid strength of alumina is influenced by vary- ing the content of hydrogen fluoride.

铂-氟氢酸-氧化铝催化剂具有两种主要的活性中心;一种是由铂产生的脱氢中心,一种是由氟氢酸产生的异构化中心.甲基环己烷、甲基环戊烷、正庚烷在铂-氟氢酸-氧化铝催化剂上的主要反应结果符合于 Mills-Heinemann 提出的反应机理.催化剂的平均孔径随氟氢酸的含量增加而变大,孔径变大可能是正庚烷的加氢裂化反应随氟氢酸含量增加而显著加速的原因.

 
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