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We study the composition of the functor from the category of modules over the Lie algebra $\mathfrak{gl}_m$ to the category of modules over the degenerate affine Hecke algebra of GLN introduced by I.


We also establish a connection between the composition of the functors, and the "centralizer construction" of the Yangian ${\rm Y}(\mathfrak{gl}_n)$ discovered by G.


We also determine all the composition factors of the symmetric tensors of the natural osp(22n)module.


For Fourierbandlimited symbols, we derive the expected formulae for composition and commutators and construct an orthonormal basis of common approximate eigenvectors that could be used to study spectral theory.


For Fourierbandlimited symbols, we derive the expected formulae for composition and commutators and construct an orthonormal basis of common approximate eigenvectors that could be used to study spectral theory.

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 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... 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。  The thermodynamic functions of an ideal subetance represented by van der Waals equation are obtained with the help of the condition that these functions reduce to those of a perfect gas in the limiting case of vanisning prassure. The volumes of the liquid state and gas state in coexistence as determined by Maxwell's rule of equal areas are expressed in a parametrie form. The nature of the dependence of the constants a and b on the chemical composition of the gas is briefly considered.  任何气体在压力极小时皆变为理想气体。今利用此点以求一凡得瓦尔气体之各种热力学函数。当气体与液体同时存在时,其由等面积法所定各自之体积,今以参数表之。最后约略言及a,b二常数与气体化学组成之关系。  The generalization of the quasichemical method of Fowler and Guggenheim in the statistical theory of superlattices made by one of the authors is extended to a binary alloy of any composition. The formulae are very similar to those for the composition 1:1. The alloy AuCu3 is treated in more detail.  本文推广准化学方法二元合金超格学说中之应用於合金之任何组成成分,所得式与组成在一比一时者极相似。最後对於AuCu_3之合金有较详之讨论。   << 更多相关文摘 
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