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It is known that the nonlinear system of equations of plane steady isentropic potential gas flow can be linearized and transformed to a single equivalent linear differential equation of second order.


A boundary value problem for a differential equation of second order


Sturmliouville problem for a differential equation of second order with discontinuous coefficients


Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described.


A particular model where these equations reduce to a single differential equation of second order is studied.

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 In this paper, the problem of the antisymctrical small deflection of isotropic sandwich plates (in the theory of E. Reissner[1]) is reduced to the solution of two displacementfunctions w and f, where to satisfies a differential equation of fourth order, and f satisfies a differential equation of second order. For a simply supported polygonal sandwich plates, it is proved that / vanishes identically, and the relation between w and the deflection w0 of a similar singlelayered thin plates is established. By this... In this paper, the problem of the antisymctrical small deflection of isotropic sandwich plates (in the theory of E. Reissner[1]) is reduced to the solution of two displacementfunctions w and f, where to satisfies a differential equation of fourth order, and f satisfies a differential equation of second order. For a simply supported polygonal sandwich plates, it is proved that / vanishes identically, and the relation between w and the deflection w0 of a similar singlelayered thin plates is established. By this relation, the solutions of a class of problems of sandwich plates may be derived from the corresponding solutions of singlelayered thin plates.  本文首先把各向同性夹层板的反对称小挠度問題(E.Reissner的理論)归結为求解两个位移函数ω和f。这里ω满足一个四阶微分方程,而f滿足一个两阶微分方程。接着証明,对于周边簡支的多角形夹层板,f恆等于零,并进一步指出ω与同样形状的单层薄板的挠度w_0的关系。利用这个关系使人有可能从許多单层薄板的已知解答导出相应的夹层板問題的解答。  A simplified method, Laplace transformation, is used to discuss the radial Schrdinger equation with the weakest bound electron potential model (WBEPM). Through using such method, the secondorder differential equation is reduced to a firstorder differential equation and the exact bound state solutions including energy spectrum and normalized wave functions are obtained by making use of the integral. The results agree with those obtained by Zheng. It is most important that the two kinds of new recursion relations... A simplified method, Laplace transformation, is used to discuss the radial Schrdinger equation with the weakest bound electron potential model (WBEPM). Through using such method, the secondorder differential equation is reduced to a firstorder differential equation and the exact bound state solutions including energy spectrum and normalized wave functions are obtained by making use of the integral. The results agree with those obtained by Zheng. It is most important that the two kinds of new recursion relations of radial wave functions are derived by the same method. These new recursion relations are the relations between the effective principal and angularmomentum quantum numbers, and are comprehensive in application to the calculations of transition probabilities in atomic and molecular physics.  应用简单的方法———Laplace变换法来求最弱受约束电子势模型(WBEPM势)的径向Schrdinger方程.通过这种方法使得两阶微分方程变为一阶微分方程,这样可以直接运用积分得到WBEPM势束缚态能量方程和归一化的波函数,所得结果与文献一致.更重要的是用Laplace变换得到径向波函数的两类新的递推关系.这种递推关系是有效主量子数和角量子数之间关系,在计算原子和分子跃迁几率时有着广泛的应用.  
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