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991.
992.
《Mathematical Methods in the Applied Sciences》2018,41(5):1855-1869
In this paper, the problem of a nonlinear beam equation involving an integral term of the deformation energy, which is unknown before the solution, under different boundary conditions with simply supported, 2‐end fixed, and cantilevered is investigated. We transform the governing equation into an integral equation and then solve it by using the sinusoidal functions, which are chosen both as the test functions and the bases of numerical solution. Because of the orthogonality of the sinusoidal functions, we can find the expansion coefficients of the numerical solution that are given in closed form by using the Drazin inversion formula. Furthermore, we introduce the concept of fourth‐order and fifth‐order boundary functions in the solution bases, which can greatly raise the accuracy over 4 orders than that using the partial boundary functions. The iterative algorithms converge very fast to find the highly accurate numerical solutions of the nonlinear beam equation, which are confirmed by 6 numerical examples. 相似文献
993.
In this paper, the comprehensive national power model with time delays is studied. The condition that there is only one trivial equilibrium in the model is given. Based on the analysis of the distribution of the eigenvalues at the trivial equilibrium, it is found that the trivial equilibrium is a Bogdanov-Takens singularity. Using the center manifold theory and the normal form method, the normal form with delay and ratio parameters of the model is obtained. Furthermore, the topological structures of the model near the bifurcation point with the variation of these two parameters are given. The associated development situations of the comprehensive national power for some topological structures are discussed. Finally, some numerical simulations are performed to support the analytic results. 相似文献
994.
一类非线性波动方程的势对称分类 总被引:1,自引:0,他引:1
先给出了含有一个任意函数的线性波动方程的古典和势对称的完全分类.然后,在此基础上给出了含有两个任意函数的一类非线性波动方程的两种情形势对称分类,得到了该方程的新势对称.在处理对称群分类问题的难点-求解确定方程组时我们提出了微分形式吴方法算法,克服了以往难于处理的困难.在整个计算过程中反复使用了吴方法,吴方法起到了关键的作用. 相似文献
995.
The linear barycentric rational collocation method for solving heat conduction equation is presented. The matrix form of discrete heat conduction equation by collocation method is also obtained. With the help of convergence rate of the barycentric interpolation, the convergence rate of linear barycentric rational collocation method for solving heat conduction equation is proved. At last, several numerical examples are provided to validate the theoretical analysis. 相似文献
996.
Convex quadratically constrained quadratic problems are considered. It is shown that such problems can be transformed to aconic form. The feasible set of the conic form is the intersection of a direct product of standard quadratic cones intersected with
a hyperplane (the analogue of a simplex), and a linear subspace. For a problem of such form, the analogue of Karmarkar's projective
transformation and logarithmic barrier function are built. This allows us to extend “word by word” the method of Karmarkar
for LP to QCQP and allows us to obtain a similar polynomial worst-case bound for the number of iterations. 相似文献
997.
SUN He-jun WU Bao-qiang.Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China .Department of Mathematics Xuzhou Normal University Xuzhou China 《数学季刊》2004,19(1):6-15
We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds Np(n+p). Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel second fundamental form in Np(n+p) and some other ambient spaces. We obtain some distribution theorems for the square norm of the second fundamental form. 相似文献
998.
This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form. 相似文献
999.
In this short note, we determine all balanced bilinear forms for a matrix coalgebra and for one type of matrix-like coalgebra. 相似文献
1000.
在理论上详细分析了利用非线性光学环形镜(NOLM)来减小输出脉冲幅度波动,消除噪声并对脉冲进行压缩整形的物理机制。在主动锁模掺铒光纤环形激光器中(AHML-EDFL)接入一个非线性光学环形镜,形成结构新颖的主被动锁模掺铒光纤激光器(APHML-EDFL),利用非线性光学环形镜所具有的饱和吸收体功能,成功地制抑了4阶有理数谐波锁模(RHML)中较大的幅度噪声,在1GHz量级的调制频率下,由主被动锁模掺铒光纤激光器获产生重复频率为5.1GHz,幅度相当稳定的4阶有理数谐波锁模脉冲序列。 相似文献