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Singular Value Estimates for Certain ConvolutionProduct Operators


We present twosided singular value estimates for a class of convolutionproduct operators related to timefrequency localization.


Singular Value Estimates for Certain ConvolutionProduct Operators


The sampling theorem is a Kramertype sampling theorem, but unlike Kramer's theorem the sampling points are not necessarily eigenvalues of some boundary value problems.


We study boundary value problems for the timeharmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the threedimensional Euclidean space.

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 Utilization of sewage to cultivate green algae has high economic value, and also produces high purification effect on sewage, thus reducing the cost of construction of sewage greatment works. This paper gives the results of a series of tests on the cultivation of algae in settled sanitary sewage and textile wastes, covering the concentration of algae in sewage, the condition of growth, the quantity and composition of algae, the methods of separation, and the effect of purification on sewage.  采用污水培养绿藻，一方面可以利用绿藻的经济价值，同时对污水的处理效果很高，可以节 省污水处理建筑物的建筑费用。本文就沉淀后的生活污水及毛纺织厂的工业污水培养绿藻，在污 水与藻液的配合比，绿藻的生长情况，产量与养分，绿藻从水中分离的方法以及培养绿藻对污水 处理的效果等方面，进行了试验，并得到一些初步成果。  Using acetic, sulfuric, hydrochloric, phosphoric and perchloric acid as acidifying agent, gelation time of monostlicic acid of different concentration at various pH was determined. All the log tpH curves were of NShape. The pH value at the minimum point of each curve shifted upward and to ward the left as concentration of silicic acid decreased. With acetic acid as acidifying agent, the gelation curve had the same tendency when concentra tion of silicic acid changed, but with a strong acid, as hydrochloric... Using acetic, sulfuric, hydrochloric, phosphoric and perchloric acid as acidifying agent, gelation time of monostlicic acid of different concentration at various pH was determined. All the log tpH curves were of NShape. The pH value at the minimum point of each curve shifted upward and to ward the left as concentration of silicic acid decreased. With acetic acid as acidifying agent, the gelation curve had the same tendency when concentra tion of silicic acid changed, but with a strong acid, as hydrochloric or sulfuric, no such shift was observed at the maximum point. When log t of the minimum points of each set of gelation time curves were plotted against the corresponding log T_(?), straight lines were always obtained. However, the slope of the lines was about 3 instead of 2 as required by the theoretical equation. This is found to be due to the effect of the salt formed in the process of acidification of sodium monosilicate. When the concentration of sodium monosilicate used was kept constant and different amounts of a salt corresponding to the acid used as acidifying agent were added, the gelation curves obtained indicated that, in case when either hydrochloric acid or sulfuric acid was used as acidifying agent, the added salt had a little pro motion effect at the maximum point but did not change the pH value. However, with the minimum points of all the curves and the maximum of that of acetic acid as acidifying agent, they all shifted downward and rightward. When log t was plotted against log T_s, straight line was also obtained, with a slope of about 1, indicating that getlation time of monosi licic acid is inversely proportional to the first power of the concentration of salt. When the concentration of salt was kept constant and that of silicic acid varied, pH of the maximum points of all gelation curves no matter which acid was used as acidifying agent remained constant, while that of the minimum points changed but a little. And in all cases, when log t was plotted against log T_(?), a straight line was always obtained, the slope of which was 2, indicating experimental results were in complete accord with our theoretical expression. When the effect of added salt is included, the expression should be modified slightly and takes the following form: log t=log C'(2+n')log T_Alog (1+β_1[H~+]+β_2[H~+]~2+β_3[H~+]~3)~2/β_2β_3 [H~+]~3 log(β_1/β_2+[H~+]~2).  以乙酸、硫酸、盐酸、磷酸及高氯酸为胶凝剂,测定了不同浓度单硅酸在不同pH的胶凝时间,得到了一系列硅酸浓度与胶凝时间的曲线。曲线皆为N形。所有曲线的最低点和乙酸曲线的最高点的pH值,皆随硅酸浓度的减少而向左上方移动,但盐酸和硫酸曲线最高点pH值无明显变化。各组曲线最低点的log t和相应的log T_A昔为直綫关系,但直线斜率昔等于3,而不是表达式中的2。这是由於酸化过程所产生的盐的效应。在单硅酸浓度恒定时,加入不同量与所用胶凝剂相当的盐,从所得的胶凝曲綫表明,盐对发盐酸及硫酸为胶凝剂的曲线最高点略有促进作用,而不改变pH值。但所有曲线最低点及乙酸曲线最高点,昔随各种盐浓度的增加而向右下方移动。每组曲线最低点的log t和log T_s皆为直线关系,直线斜率在1左右,表示盐浓度与胶凝时间的一次方成反此。在固定盐浓度,改变单硅酸浓度的实验中,所有盐酸、硫酸、硝酸、乙酸及磷酸的各套胶凝曲线的最高点pH值皆不改变,而最低点的pH值只微有不同,每组曲线的不论最低点或最高点,它们的log t和log T_A皆有直线关系,其直綫的斜率都在2左右,和表达式的要求完全符合。故包括盐效应的硅酸聚合而成凝胶的表达式改进为:  Pulverizedcoalfired precombustion chamber is a kind of new coal burning equipment.By using two precombustion chambers in the boiler SHF20/13 made by the peking Boiler works,the volumetric heat releasing rate of the furnace has attained the value of 240×103 kcal/m3h,the dimensions of the boiler are greatly reduced,the weight of the steel used is reduced about 35 percent. :After careful observations in a series of experiments,the following improvements are made: modification of the construction of the... Pulverizedcoalfired precombustion chamber is a kind of new coal burning equipment.By using two precombustion chambers in the boiler SHF20/13 made by the peking Boiler works,the volumetric heat releasing rate of the furnace has attained the value of 240×103 kcal/m3h,the dimensions of the boiler are greatly reduced,the weight of the steel used is reduced about 35 percent. :After careful observations in a series of experiments,the following improvements are made: modification of the construction of the chamber using II and III type chambers;using a new swirler of smaller attack angle;adding a mixing plate in the duct to make the fuel air mixture more uniform.When some of bituminous coal is used,these improvements make the operation of the precombustion chamber rather reliable.The duration of trouble free operation has attained more than 15 days,without the trouble encountered in the experiment,the duration of operation might be still longer.The experiments show that this kind of precombustion chamer is very prospective.  煤粉予燃室是一种新型的煤粉燃烧方式。北京锅炉厂制造的SHF—20(?)13型锅炉在采用煤粉予燃室后,锅炉炉膛体积热负荷高达240×10~3[大卡/米~3时],锅炉外形尺寸大为缩小,约可节省钢材35％。 煤粉予燃室经过改进,采用了Ⅱ、Ⅲ型予燃筒,35°平面叶片旋流器并加装风粉均匀板,在燃烧灰熔点高的烟煤时,已可连续运行15天以上。试验研究说明煤粉予燃室是可能很有前途的。   << 更多相关文摘 
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