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In this paper, we establish maximal LpLq estimates for nonautonomous parabolic equations of the type u'(t)+A(t)u(t)=f(t), u(0)=0 under suitable conditions on the kernels of the semigroups generated by the operators A(t), t∈[0,T].


In this paper we consider the Dirichlet problems of a nonuniformly degenerate elliptic equations of the form div


Elliptic H2volterra projection and the H1galerkin methods for the integrodifferential equations of evolution


This paper studiesH1Galerkin methods for the integrodifferential equations of evolution.


In this paper, the two and threepoint boundary problems (with nonlinear boundary conditions) for the general nonlinear differential equations of fourth order are discussed.

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 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... 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。  This paper deals with a method of treating problems of Turbulence from a kinetic point of view. Turbulence "temperature", "pressure", and "entropy" are first defined as state functions, and then the pressure and temperature are incorporated into the equations of motion. Turbulent flows through a circular pipe and between parallel planes are considered in some detail, while the problems of turbulence decay, turbulence structure, and correlation characteristics are briefly discussed. Practically in all cases,... This paper deals with a method of treating problems of Turbulence from a kinetic point of view. Turbulence "temperature", "pressure", and "entropy" are first defined as state functions, and then the pressure and temperature are incorporated into the equations of motion. Turbulent flows through a circular pipe and between parallel planes are considered in some detail, while the problems of turbulence decay, turbulence structure, and correlation characteristics are briefly discussed. Practically in all cases, the constancy of the turbulence temperature is found to play an important role.  本文系用热性论之观点研讨激流之各项问题。先规定激流之情态函数,如温度压力,熵等,然後将激流温度纳入运行公式内,以求得流速之分布,激流之构造与消灭等情形。自各方面观之,本文之理论结果,大都与事实相符。   << 更多相关文摘 
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