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  essential
On the notion of essential dimension for algebraic groups
      
We introduce and study the notion of essential dimension for linear algebraic groups defined over an algebraically closed fields of characteristic zero.
      
The essential dimension is a numerical invariant of the group; it is often equal to the minimal number of independent parameters required to describe all algebraic objects of a certain type.
      
We develop a general theory, then compute or estimate the essential dimension for a number of specific groups, including all of the above-mentioned examples.
      
Serre, relating essential dimension to Galois cohomology.
      
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The essential oil of the chinese drug, Hu-Io-po-tze, the seeds of Daucus carota L., was found to contain the following constituents: (1)a small amount of tiglic acid,(2) asarone, and(3) bisabolene which forms a trihydrochloride, melting point 77-78℃ and a hexabromide, melting point 155-157℃. From the non-volatile residue obtained by extracting the drug with benzene there have been isolated, an asaraldehyde, its semicarbazone melts at 205-207℃ and an unknown sterol having a molecule formula C_(27)H_(52)O...

The essential oil of the chinese drug, Hu-Io-po-tze, the seeds of Daucus carota L., was found to contain the following constituents: (1)a small amount of tiglic acid,(2) asarone, and(3) bisabolene which forms a trihydrochloride, melting point 77-78℃ and a hexabromide, melting point 155-157℃. From the non-volatile residue obtained by extracting the drug with benzene there have been isolated, an asaraldehyde, its semicarbazone melts at 205-207℃ and an unknown sterol having a molecule formula C_(27)H_(52)O and a melting point 87℃.

国产胡萝卜子经化学分析後,除证实共挥发油中含有细辛酮及毕纱倍半萜革外,并发现其中亦含有顺芷酸,细辛醛及一种未知固醇C_(27)H_(52)O,熔点87℃。

In connection with experiments on the control of the rice stem borer, aseries of observations were conducted in 1949 to 1952 in Canton to determinethe form of the distribution of the moth, the egg-mass and the larval popula-tions of this species. It was found that the moth and egg-mass populations inrice seed-beds are in essential agreement with the random distribution of thePoisson series. The larval population in spring-crop fields apparently conformsto the contagious and the negative binomial distributions....

In connection with experiments on the control of the rice stem borer, aseries of observations were conducted in 1949 to 1952 in Canton to determinethe form of the distribution of the moth, the egg-mass and the larval popula-tions of this species. It was found that the moth and egg-mass populations inrice seed-beds are in essential agreement with the random distribution of thePoisson series. The larval population in spring-crop fields apparently conformsto the contagious and the negative binomial distributions. The larval population during hibernation period appears to be neither of the random distribution norof the contagious type but agrees with the negative binomial distribution. The population distribution of the injured stems, characterized by the ap-pearance of "dead-hearts" and "white ears" was also studied. The "dead-hearts"popolation in autumn-crop fields conforms with the contagious and the negativebinomial distribution. The distribution of the "white ears" is not at random. It iseither in essential agreement with the contagious or with the negative binomialdistribution, depending on the size of the sampling unit. Based on the form of population distribution the questions of sampling tech-nique, the design of field experiments, the transformation of data for statisticalanalysis, as well as the habits and control of insects have been discussed inrelation to the rice stem borer. Since the populations of larvae and "whiteears" differ significantly from the random distribution, a new technique forsampling has been proposed. It is hoped that this may be useful in the investi-gations on the relative effectiveness of control operations and for census purposes.

(一)本文就昆虫常见的数种集团分布:潘松分布、核心分布和负二项式分布的公式、性质和例子等略加讨论介绍。 (二)我们在广州附近对三化螟各时期和白穗、枯心苗的田间分布型式作了初步的调查,所得结果如下: 1.螟蛾和卵块在秧田上是随机分布的。 2.幼虫在本田分布不随机,符合核心分布和负二项式分布。 3.白穗在田间的分布不随机,1×1丛、2×2丛、……6×6丛各种取样单位型样本均符合负二项式分布,4×4丛、5×5丛和6×6丛三种取样单位型样本则更符合核心分布。 4.稻遗株内越冬幼虫分布不随机,亦不符合核心分布,但符合负二项式分布。 5.晚造本田枯心苗田间分布不随机,符合核心分布和负二项式分布。 (三)本文就昆虫集团分布型式的调查在实用上的意义,联系到三化螟来讨论,我们论及与虫害调查取样技术、田间试验设计、统计代换方法、昆虫生活习性和害虫防治等各方面的关系;其中取样技术方面,我们举出针对三化螟幼虫在本田和白穗不随机分布的取样新方法的尝试,希望对今后螟害调查工作有所帮助。 (四)最后,我们就一些昆虫分布的特殊问题加以论列,像密度对分布型式的影响,混合集团和环境因素的影响于昆虫集团分布类型等,就中说明了密度过大过 小时了解分...

(一)本文就昆虫常见的数种集团分布:潘松分布、核心分布和负二项式分布的公式、性质和例子等略加讨论介绍。 (二)我们在广州附近对三化螟各时期和白穗、枯心苗的田间分布型式作了初步的调查,所得结果如下: 1.螟蛾和卵块在秧田上是随机分布的。 2.幼虫在本田分布不随机,符合核心分布和负二项式分布。 3.白穗在田间的分布不随机,1×1丛、2×2丛、……6×6丛各种取样单位型样本均符合负二项式分布,4×4丛、5×5丛和6×6丛三种取样单位型样本则更符合核心分布。 4.稻遗株内越冬幼虫分布不随机,亦不符合核心分布,但符合负二项式分布。 5.晚造本田枯心苗田间分布不随机,符合核心分布和负二项式分布。 (三)本文就昆虫集团分布型式的调查在实用上的意义,联系到三化螟来讨论,我们论及与虫害调查取样技术、田间试验设计、统计代换方法、昆虫生活习性和害虫防治等各方面的关系;其中取样技术方面,我们举出针对三化螟幼虫在本田和白穗不随机分布的取样新方法的尝试,希望对今后螟害调查工作有所帮助。 (四)最后,我们就一些昆虫分布的特殊问题加以论列,像密度对分布型式的影响,混合集团和环境因素的影响于昆虫集团分布类型等,就中说明了密度过大过 小时了解分布型式成为不必要的,因为极度的不均衡会回复为均衡状态的。

Coilia mystus (L.) is a small fish of economic importance, belonging to the Family Engraulidae. It occurs abundantly along the coast of Amoy and vicinity. The present investigation was undertaken with the chief object of finding out the compostion of food and its seasonal variation. A total of 612 stomachs were examined; of these, only 22 stomachs were found to be empty. The following are the results of the investigation:(1) Coilia mystus feeds chiefly upon planktonic Crustacea, of which Copepoda is, by far,...

Coilia mystus (L.) is a small fish of economic importance, belonging to the Family Engraulidae. It occurs abundantly along the coast of Amoy and vicinity. The present investigation was undertaken with the chief object of finding out the compostion of food and its seasonal variation. A total of 612 stomachs were examined; of these, only 22 stomachs were found to be empty. The following are the results of the investigation:(1) Coilia mystus feeds chiefly upon planktonic Crustacea, of which Copepoda is, by far, the most important, constituting no less than 75.9% of total food. Of the 15 species of Copepoda identified, Paracalanus pqrvus, Pseudodiaptomus marinus and Tortanus forcipata are relatively more important than the others. Among other Crustacea, the relative importance of various groups Is of the following order: Decapoda (including Lucifer and Brachyuran larvae) > Mysidae > Euphau-siacea > Amphipoda > Ostracoda > Cumacea > Stomatopoda. Next to Crustacea in the order of importance of food conic Chaetognatha and fish ova, the former being the more important of the two. Judging from the composition of food, Coilia mystus is a plankton-feeder.(2) The composition of food is more or less subject to seasonal variation. The order of numerical importance of various groups* in the four seasons is as follows: SPRING (Mar.-May): Copepoda > fish ova > Decapoda > Amphipoda > Mysidae> Euphausiacea > Cumacea> Stomatopoda, young fish. SUMMER (Junc-Aug.): Copcpoda> fish ova> Decapoda >Mysidae> Amphipoda> Euphausiacea > Cumacea > young fish.AUTUMN (Scpt.-Nov.): Copepoda > Decapoda > Mysidae > Ostracoda > Euphausiacea > Amphipoda > Stomatopoda > young fish.WINTER (Dec.-Feb.): Copepoda > Decapoda > Euphausiacea > Cumacea > fishova > Mysidae > Amphipoda > young fish > Stomatopoda. (3) The composition of food varies with age or length (from the tip of snout to the end of body, exclusive of caudal fin) of fish which appears to he related to the density of gill-rakers. The younger fishes (less than 15 cm. in length) with denser gill-rakers (2.0-2.7 rakers per 1 mm.) feed largely upon smaller crustaceans (Cope-poda); whilst the older fishes (over 15 cm. in length) with sparser gill-rakers (1.4 1.9 rakers per 1 mm.) feed largely upon larger crustaceans (Mysidae, Euphausiacea, Stomatopdda, Decapoda). It shows that increase in the size of fish is associated with increrase in the size of food animals eaten.(4) There exists a fairly close agreement between the composition of food and the composition of plankton in the surrounding waters. During the months of March and November when both fish and plankton were collected at the same time off Hai-Chen near Amoy, Copepoda was found to be the most dominant group in both food and plankton. It shows that the fish fed heavily upon those crustaceans occurring most abundantly in the plankton. In this respect, Coilia mystus exercises no selectivity of food. The writers are of the opinion that abundance and availability rather than selection by the fish determine the species of animal eaten.(5) A comparison of the food of Coilia mystus with that of other Clupeoids in Amoy waters reveals the predominance of Copepoda in the diet of most of these fishes. For the sake of increasing the yield of these economic fishes, it is essential to enhance the production of Copepoda in nature by artificial means such as to fertilize the water with nutrient salts, especially phosphates and nitrates, to increase the production of phytoplankton which will, in turn, lead to the higher production of Copepoda.

1.六丝鲚的食料差不多完全是浮游动物,以甲壳类为主,其中以桡足类为最重要、十足类(包括莹虾)次之,糠虾类,端足类,磷虾类更次之。除甲壳类以外,它还捕食很多毛头类和鱼卵,所以六丝鲚应属蜉食性的鱼类。 2.六丝鲚的食料成份有季节变化,不过不很显著:春夏两季以桡足类为主,鱼卵次之,十足类(包括短尾类幼虫)更次之。秋季以桡足类为主,十足类(包括莹虾和短尾类幼虫)次之,糠虾更次之。冬季以桡足类为主,十足类次之,磷虾类更次之。总的来看,桡足类在四季食料中都占了绝对优势。六丝的次要食料则随季节而异;春夏两季是鱼卵,秋冬两季都是十足类。值得注意的是:糠虾类和介壳类在秋季食料中的比率增加,磷虾类在冬季食料中占相当重要位置。食料的季节变化是和浮游生物的季节变化分不开的。 3.食料种类大小和体长有关:体长在15厘米以上的捕食较大的甲壳类(如磷虾类,口脚类和十足类等),而体长在15厘米以下的则捕食较小的甲壳类(如桡足类)。这和鳃耙密度有关:前者的鳃耙较稀(1毫米长中有1.4—1.9鳃耙)而后者的鳃耙较密(1毫米中有2.0—2.7鳃耙)。 4.食料和浮游生物存在着一定关系;在浮游生物中占优势的种类也同样地在食料中占优势。桡足类便是一个...

1.六丝鲚的食料差不多完全是浮游动物,以甲壳类为主,其中以桡足类为最重要、十足类(包括莹虾)次之,糠虾类,端足类,磷虾类更次之。除甲壳类以外,它还捕食很多毛头类和鱼卵,所以六丝鲚应属蜉食性的鱼类。 2.六丝鲚的食料成份有季节变化,不过不很显著:春夏两季以桡足类为主,鱼卵次之,十足类(包括短尾类幼虫)更次之。秋季以桡足类为主,十足类(包括莹虾和短尾类幼虫)次之,糠虾更次之。冬季以桡足类为主,十足类次之,磷虾类更次之。总的来看,桡足类在四季食料中都占了绝对优势。六丝的次要食料则随季节而异;春夏两季是鱼卵,秋冬两季都是十足类。值得注意的是:糠虾类和介壳类在秋季食料中的比率增加,磷虾类在冬季食料中占相当重要位置。食料的季节变化是和浮游生物的季节变化分不开的。 3.食料种类大小和体长有关:体长在15厘米以上的捕食较大的甲壳类(如磷虾类,口脚类和十足类等),而体长在15厘米以下的则捕食较小的甲壳类(如桡足类)。这和鳃耙密度有关:前者的鳃耙较稀(1毫米长中有1.4—1.9鳃耙)而后者的鳃耙较密(1毫米中有2.0—2.7鳃耙)。 4.食料和浮游生物存在着一定关系;在浮游生物中占优势的种类也同样地在食料中占优势。桡足类便是一个很显著例子。其他甲壳类也有相似情况。可是水母则不然,它在浮游生物中很

 
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