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the volume computations involve several different methods according to the parity of dimension, subgroup relations and arithmeticity properties.


We express the vanishing conditions satisfied by the correlation functions of Drinfeld currents of quantum affine algebras, imposed by the quantum Serre relations.


In this paper we give a full set of simple moves and relations which turnM(Σ) into a connected and simplyconnected 2complex.


We also present recursion relations satisfied by the characters and the monomial bases.


Included is a complete and explicit list of the generators and relations for the left coideal subalgebras of the quantized enveloping algebra used to form quantum symmetric pairs.

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 The gravitational field and the motion of matter in the universe are investigated according to Einstein's field equations and his dynamical equations of motion. In a spatially isotropic and homogeneous spacetime continuum it can be shown that up to about 2x10~8 l.y. the following relation holds between spectrum displacement δλ from distant spiral nebulae and their observationally defined distance d,where A is Einstein's cosmological constant. The first term on the right hand side is essentially Hubble... The gravitational field and the motion of matter in the universe are investigated according to Einstein's field equations and his dynamical equations of motion. In a spatially isotropic and homogeneous spacetime continuum it can be shown that up to about 2x10~8 l.y. the following relation holds between spectrum displacement δλ from distant spiral nebulae and their observationally defined distance d,where A is Einstein's cosmological constant. The first term on the right hand side is essentially Hubble and Humason's velocitydistance relation. The second part is a correction which amounts to 11.5% for d2x10~8 l.y. and hence lies within observational error of the present Mt. Wilson 100inch telescope. The theory shows that both Milne's recent Newtonian theory of the expanding universe and Lemaitre's interpretation of tha velocitydistance are first order approximations and are valid only within 2xl08 l,y. from our galaxy. The calculation for the phenomsna of nebular recession beyond 2xl08 l.y. to be observed by the 200inch telescope now under construction according to the present scheme will be presented in the near future.  本文用安因斯坦力学及引力论解释宇宙之膨胀现象。从本文方程式中可证明雷猛德及米恒诸氏之学说皆为本文之近似值,而本文理论之能成立与否须恃200英寸反光镜完成后之观测云。  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。  Weiss's theory on the change of Schrodinger wave functional on a surface as the surface changes is given in a complete form, allowing the Lagrangian of the field to contain all derivatives of the field quantities. The integrability of the resulting equation is proved by making use of the fact that the corresponding HamiltonJacobi equation is integrable. This gives at the same time a proof of the Lorentz invariancy of the commutation relations between the various conjugate variables, which so far remained... Weiss's theory on the change of Schrodinger wave functional on a surface as the surface changes is given in a complete form, allowing the Lagrangian of the field to contain all derivatives of the field quantities. The integrability of the resulting equation is proved by making use of the fact that the corresponding HamiltonJacobi equation is integrable. This gives at the same time a proof of the Lorentz invariancy of the commutation relations between the various conjugate variables, which so far remained obscure as soon as we allow derivatives higher than the second of the field quantities to appear in the Lagrangian.  对於一曲面上之施落亭格波函数在曲面变化时所发生之变化,威士氏有一理论。今将其理论补充,使其完整,使此理论,在场之兰格伦日包含场量之各种微分时,依然可用。所获得之方程式之可积分性,用与其相当之哈密尔顿—雅科俾方程式之可积分性证明之。此种讨论,同时证明各种变数中之对换关系在罗兰丝变化下之不变性。   << 更多相关文摘 
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