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We use the theory of tilting modules for algebraic groups to propose a characteristic free approach to "Howe duality" in the exterior algebra.


This study was continued in the paper [FKRW] in the framework of vertex algebra theory.


As in the case of Mumford's geometric invariant theory (which concerns projective good quotients) the problem can be reduced to the case of an action of a torus.


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.


The theory is applied to the case of cubic hypersurfaces, which is the one most relevant to special geometry, obtaining the solution of the two classification problems and the description of the corresponding homogeneous special K?hler manifolds.

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 Measurement of the intensity of total scattering of xrays by a number of polyatomic gases was made for scattering angles between 15° and 130 ° using an ionization method of recording the scattered intensity. Balanced filters of ZrO2, and SrO were used to separate the MoKa rays and Soller slits were placed in front of the ionization chamber to obtain a definite scattering angle. The gases studied are CL2, CO2, N2O, H2S, CC14 and CHCl3. In each case the absolute values of the scattered intensity were determined... Measurement of the intensity of total scattering of xrays by a number of polyatomic gases was made for scattering angles between 15° and 130 ° using an ionization method of recording the scattered intensity. Balanced filters of ZrO2, and SrO were used to separate the MoKa rays and Soller slits were placed in front of the ionization chamber to obtain a definite scattering angle. The gases studied are CL2, CO2, N2O, H2S, CC14 and CHCl3. In each case the absolute values of the scattered intensity were determined by comparison with the scattering from oxygen, the results of Wollan for the latter gas being taken as correct. The experimental results are actually compared with Woo's theory of the scattering of xrays by polyatomic gases and the agreement seems to be satisfactory.  吴有训氏最近对于多原子气体散射线之理论,曾作详尽的探讨。吴氏得到一个公式,表示由多原子气体所散射之强度,其中一部为相干的散射,另一部为不相干的散射。 以前关于多原子气体散射X线之实验,为数甚少,且为定性的结果。最近美人Wollan,对于由O_2及N_2(双原子气体)所散射钼的K_3α线之强度,曾作绝对的度量。Wollan的结果,与吴有训氏的理论,甚属相符。本篇目的,在测定由 Cl_2,CO_2,N_2O,H_2S,CCl_4及 CHCl六种气体所散射X线之强度,每一实验,均与由0_2者互相比较,根据Wollan的结果,每种气体所散射之绝对强度,皆一一量得。所用之入射X线为钼之Kα线,系藉Ross的平衡过滤法分出。强度之测量,系用一游离方法。散射角度的范围,自15度至130度。每种气体的实验结果,均与吴氏的理论,互相比较,证明理论与实验,甚属相符。在计算时,原子的“构造因数”,系由Hartree的方法算得,一分子中两原子的相隔距离,则由带光谱的结果推得。  In this paper the writer employs complex Riemannian Geometry and defines the absolute interval between two points as consisting of a real part and an imaginary part. Two postulates (I) and (II) are used: the first may be called law of gravitation and electromagnetism; the second equation of motion. In the absence of electromagnetic phenomena the theory reduces practically to Einstein's theory.  在此文内,作者利用复变来曼几何以宇宙间两点之距离为一实数及一虚数部分相构而成,於此并用假说:一可称为吸力及电磁定律,一为物体行动定律,解释吸力及电磁力之各种现象。在无电磁现象时,此文与爱因斯坦之吸力理论多相符合至於详细情形,容诸续篇。  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... 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。   << 更多相关文摘 
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