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We also show how to distinguish examples of open subsets with a good quotient coming from Mumford's theory and give examples of open subsets with nonquasiprojective quotients.


Morse Theory and Euler Characteristic of Sections of Spherical Varieties


There are reverse inequalities for square functions of differences arising in ergodic theory and differentiation of functions.


The shortcomings of the existing algorithms are thus overcome both in theory and in application.


autgH/*)) is investigated by using bundle map theory and transformation group theory.

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 Magnetization curves of the polycrystalline FeCo and NiCo alloys of the cubic system and also of the pure cobalt were determined by means of a ballistic method. Gans' theory of the magnetic properties of isotropic ferromagnetics was applied. The agreement between his theory and the experimental results is quite good for the strong fields but not so for the weak fields, just as in the ease of the pure ferromagnetics. The discrepancy for the weak fields may be explained by his neglect of the free energy... Magnetization curves of the polycrystalline FeCo and NiCo alloys of the cubic system and also of the pure cobalt were determined by means of a ballistic method. Gans' theory of the magnetic properties of isotropic ferromagnetics was applied. The agreement between his theory and the experimental results is quite good for the strong fields but not so for the weak fields, just as in the ease of the pure ferromagnetics. The discrepancy for the weak fields may be explained by his neglect of the free energy which is required to magnetize the elementary crystals isothermally to the saturation intensities in the easy direction of magnetization. After including this part of the energy the agreement between theory and experiment is improved in general and in some cases, it is remarkably good. For pure cobalt the magnetization intensities for a given field are smaller than those obtained by previous investigators, but in better agreement with the theory than those previously obtained. Since the disagreement cannot be accounted for by the experimental error in the present investigation, the comparatively less studied cobalt needs further investigation.  用冲击法量属於正方晶系之铁钴及镍钴合金并纯钴之多结晶体之磁化曲线与Gans氏各向同性铁磁物质磁性之理论相较知在强磁场时理论与实验之契合甚佳在弱磁场时则较差,弱磁场时之差异,可以Gans氏计算时略去磁化各元晶体於其易磁化方向至饱和度所需之自由能一点解释之改正此点后理论与实验之契合大体改善在数种合金且极佳。纯钴之磁化强度在各磁场下较之前人所得者均小,惟与理论之契合则较佳:此与前人不同之点既不能归诸本实验之误差,则此较少被注意之钴实需要更进一步之研究  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... 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。  A new approximation method is proposed in this article for the discussion of molecular structures,and this new method includes the two wellknown theories,molecular orbital theory and electronpair bond theory as two special cases.Let a molecule have n bonds and let the ith bond be described by the antisymmetrical twoelectron bond function ψ_i(v_(2i1),v_(2i)).(If there exist one electron,threeelectron or manyelectron bonds,they can be similarly described by the corresponding oneelectron,threeelectron... A new approximation method is proposed in this article for the discussion of molecular structures,and this new method includes the two wellknown theories,molecular orbital theory and electronpair bond theory as two special cases.Let a molecule have n bonds and let the ith bond be described by the antisymmetrical twoelectron bond function ψ_i(v_(2i1),v_(2i)).(If there exist one electron,threeelectron or manyelectron bonds,they can be similarly described by the corresponding oneelectron,threeelectron or manyelectron bond func tions.) Then the stationary state of the molecule is represented by the follow ing wave function Ψ, where the summation is over all permutations of 1,2,……,2n except those within the interior of the functions,since each ψ_i is already antisymmetrical.Obviously (2~n/((2n)/!))~(1/2) is the normalization factor. By quantum mechanics the energy of the molecule equals (1) here H_i,T_(ij) and S_(11)' are respectively the following three kinds of operators, (2) (3) (4) The third term of equation (1) is the exchange integral of electrons 1 and 1', while (1,2') is that of electrons 1 and 2'.According to the definition of bond functions,ψ_i may be written as (5) Substituting equation (5) into equation (1) and carrying out the integration over spin coordinates,we obtain (6) It can be easily seen from equation (6) that the combining energy of a mole cule consists of two parts,one being the binding energy of the bonds represent ed by the first term of equation (6),and the other being the interaction energy of the bonds denoted by the second term of that equation. If we choose certain functions φ_i~('s) involving several parameters and substi tute them into equation (6),we may determine the values of those parameters by means of the variation principle. For the discussion of bond interaction energies,we develop a new method for the evaluation of certain types of threecenter and fourcenter integrals.The interaction energy of a unit positive charge and an electron cloud of cylindrical symmetry distribution may be written as (7) where (8) and R_0~2=a~2+b~2+c~2 The interaction energy of two electron clouds both of cylindricalsymmetry distributions with respect to their own respective axes is evaluated to be (9) (10) where is to sum over j from zero to the lesser value of n2i and m, is to sum over i from zero to the integral one of n/2 and (n1)/2,and is to sum over all cases satisfying the relation =mj,while b_(n,n2i) represents the coefficient of x~(n2i) in the n th Legendre polynomial.  本文在分子结构理论方面,作了下列两点贡献:首先建议了用双电子或多电子键函数作为近似基础,来计算分子的近似能量和近似电子云分布。这样计算得来的结果,一定会比用分子轨道理论或电子配对理论好,因为它更真实的反映了分子的化学性质,同时它也包括了后两者,而以它们为特例。我们得到了分子结合能的表示式,用表示式证明了分子结合能由两部分组成:一部分是键的结合能,另一部分是键与键间的作用能。其次是建议了一种新方法,把在计算化学键相互间的作用能中遇到的一些三中心和四中心积分,还原为容易计算的二中心积分。这方法比以往所用的好,因为它计算比较简单,同时限制性也小。   << 更多相关文摘 
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