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Duality theorems, atomic decompositions, and factorization of functions are treated.


We show that if(X,Σ, μ) is not purely atomic, then the unconditional basis constant of our basis is (max(p, q) 1).


The main tool in our investigations consists of an adapted atomic decomposition.


We provide a general method to derive Banach frames and atomic decompositions for these Banach spaces by sampling the continuous frame.


We also describe natural ways of discretizing those wavelet transforms, or equivalently to obtain atomic decompositions and Banach frames for the corresponding coorbit spaces.

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 The magnetooptical dispersion of acetyl acetone was measured in a magnetic field of about 6000 gausses in intensity and 4 cms in length. Absolute values of Verdet constant for the substance were obtained. Account for the discrepancies of the values of e/m and the atomic specific rotations calculated from the data was given.  吾人曾用各种单色光,测定Acetyl acetone之磁偏极化。  The origin of the system of bands around 2482 A.U. observed in a mercury lamp has been given evidence as due to mercury molecular ion. Quantitative determination of the intensity variations as a function of pressure and current of the 2482 bands and other band of neutral molecules, shows marked difference between 2482 bands and other bands. All the differences can only be explained on the basis of an ionic origin of the 2482 bands. The excited state of the molecular ion that emits 2482 bands is given evidence... The origin of the system of bands around 2482 A.U. observed in a mercury lamp has been given evidence as due to mercury molecular ion. Quantitative determination of the intensity variations as a function of pressure and current of the 2482 bands and other band of neutral molecules, shows marked difference between 2482 bands and other bands. All the differences can only be explained on the basis of an ionic origin of the 2482 bands. The excited state of the molecular ion that emits 2482 bands is given evidence as that state resulted from a combination of a normal atomic ion and a neutral atom at the 3P1 excited state.  水银分子在2482A.U.左右有组光带,是水银分子伊洪的还是水银分子的这问题,我们用光谱强度的测量法解决了。将供作光源的通电管内的电流或水银气压依次的改变,我们发现2482A.U.光带的强度的改变和旁的已知的分子光带绝然不同。那些不同之点,只要引用“分子伊洪是2482光带的原主”这说法,就都明白了我们更进一步问放出2482光带的是那个高能力阶位理论和实验的结果指示出一个在最低能力阶位的原子伊洪(Hg~+)和一个在3P_1能力阶位的原子所结合成的分子伊洪是能放2482光带的高能力阶位。  In the statistical theory of superlattices in binary alloys, the dependence of the interaction energy upon atomic arrangements is taken into account by regarding the interaction energy in Bethe's theory as an average quantity depending on the degree of order and the composition of the alloy. Two simple assumptions concerning the functional relationship of the interaction energy with order and composition are made. The first is a linear function of order and composition. The second is a linear function... In the statistical theory of superlattices in binary alloys, the dependence of the interaction energy upon atomic arrangements is taken into account by regarding the interaction energy in Bethe's theory as an average quantity depending on the degree of order and the composition of the alloy. Two simple assumptions concerning the functional relationship of the interaction energy with order and composition are made. The first is a linear function of order and composition. The second is a linear function of the average numbers of pairs of atoms. The result of applying these assumptions to superlattices of the type AB is that the critical temperature as a function of the composition is a maximum for equal sumber of A and B atoms only when a certain relation between the coefficients in the assumed function is satisfied. In the cass of superlattices of type AB3 the theory of Bragg and Williams is used for simplicity. It is shown that when the composition varies, the maximum of the critical temperature may occur at any desired composition by a suitables adjustment of the coefficients in the assumed functions. There is thus a hope of removing the discrepancy between theory and experiment on this line. The anomalous specific heat at the critical temperature is also calculated for different compositions. In the case of the AB type of superlattices, Bethe's formula for the energy is no longer valid, and in order to calculate the specific heat, an approximate formula for the energy is obtained by analogy with the theory of Bragg and Williams. Finally, the problem of separation into more than one phase is briefly discussed.  在二元合金超格之统计力学理论中,原子间互作用能量,因原子之排列不同而异,其所生之影响,吾人擬於此篇中讨论之。吾人认为有Bethe氏理论中之相互作用能量,实为一平均值,其值因合金之秩序程度及其成分而异。吾人作二简单假设:一设相互作用能量为秩序及成分之线性函数,另一设其与原子对偶之数成线性函数。将此等假设应用於AB类之合金,则必须在所设函数中之系数间,有适当关系,合金之临界温度,始在成分为1:1时,有极大值。在AB_3类之合金,吾人乃应用Bragg及Williams二氏之理论以求简便。於此可证明若所设函数中之系数,可任意调整则所计算出之临界温度之极大值可在任何成分发生。故关於此点理论与实验不合之处,可望解决。又合金之反常比热,亦经算出。在AB类之合金,Bethe氏原来之能量公式不復可用,故另用与Bragg及Williams理论比较而得之公式计算。又关於合金可分为二相或多相之问题,此篇亦大略论及。   << 更多相关文摘 
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