共查询到18条相似文献,搜索用时 281 毫秒
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在计算机辅助几何设计中, B\''ezier曲面是一类重要的参数曲面.在微分几何中,坐标曲线网也是重要的研究内容.本文中,我们对具有特殊坐标曲线网(如正交曲线网、曲率曲线网、共轭曲线网等)的B\''ezier曲面进行研究.此外,我们还构造了满足能量约束的特殊B\''ezier曲面,给出了基于控制结构的充分条件并给出具体实例. 相似文献
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本文基于Pythagorean-hodograph (PH)曲线和代数双曲线的良好几何特性,构造了Pythagorean-Hodograph Hyperbolic (PH-H)曲线,并给出了PH-H曲线的定义以及相应性质.同时,分别利用Hyperbolic基函数和Algebraic Hyperbolic (AH) B\''ezier基函数,得到了平面三次AH B\''ezier曲线为PH曲线的两个不同的充要条件.此外,三次PH-H曲线也被用于求解具有确定解的$G^1$ Hermite插值问题.文中给出了具体实例来说明我们的方法. 相似文献
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本文提出了一种全新复合$(\frac{G''}{G})$展开方法,运用这种新方法并借助符号计算软件构造了非线性耦合Klein-Gordon方程组和耦合Schr\"{o}dinger-Boussinesq方程组的多种双行波解,包括双双曲正切函数解,双正切函数解,双有理函数解以及它们的混合解. 复合$(\frac{G''}{G})$展开方法不但直接有效地求出了两类非线性偏微分方程的双行波解,而且扩大了解的范围.这种新方法对于研究非线性偏微分方程具有广泛的应用意义. 相似文献
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本文研究了在股本稀释效应下认股权证的定价问题.假设随机利率服从Vasicek模型,利用Δ-对冲方法建立了权证价格所满足的偏微分方程.然后,通过计价单位变换,将偏微分方程降维,求得了权证价格的显式解,并给出了一种较好的数值计算方法,可运用市场的可观测变量来计算权证价值. 相似文献
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B\'{e}zier曲面有两种不同的形式:三角B\'{e}zier曲面和四边B\'{e}zier曲面,它们有着不同的基底和不同的几何拓扑结构, 但是它们也有很多共同的性质,因此三角B\'{e}zier曲面和四边B\'{e}zier曲面之间的相互转化就成为CAGD 里一个重要研究课题.在本文中, 我们用函数复合的方法实现两者之间的相互转化.被复合的两个函数, 一个用Polar形式表示,另一个用常见的Bernstein基形式表示. 相似文献
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Yongxia Hao & Ting Li 《计算数学(英文版)》2023,41(4):551-568
In this paper, we present a method for generating Bézier surfaces from the boundary information based on a general second order functional and a third order functional associated with the triharmonic equation. By solving simple linear equations, the internal control points of the resulting Bézier surface can be obtained as linear combinations of the given boundary control points. This is a generalization of previous works on Plateau-Bézier problem, harmonic, biharmonic and quasi-harmonic Bézier surfaces. Some representative examples show the effectiveness of the presented method. 相似文献
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We establish a global limiting case of nonlinear Calderon-Zygmund theory to quasilinear elliptic equations div A(x,Du) = div(|F|~(p-2)F) under the BMO smallness of the nonlinearity,that is |F|~(p-2)F∈BMO implies that Du ∈BMO. 相似文献
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Poincar{\''e} Bifurcation from an Elliptic Hamiltonian of Degree Four with Two-saddle Cycle 下载免费PDF全文
In this paper, we consider Poincar{\''e} bifurcation from an elliptic Hamiltonian of degree four with two-saddle cycle. Based on the Chebyshev criterion, not only one case in the Li{\''e}nard equations of type $(3, 2)$ is discussed again in a different way from the previous ones, but also its two extended cases are investigated, where the perturbations are given respectively by adding $\varepsilon y(d_0 + d_2 v^{2n})\frac{\partial }{{\partial y}}$ with $ n\in \mathbb{N^+}$ and $\varepsilon y(d_0 + d_4 {v^4}+ d_2 v^{2n+4})\frac{\partial }{{\partial y}}$ with $n=-1$ or $ n\in \mathbb{N^+}$, for small $\varepsilon > 0$. For the above cases, we obtain all the sharp upper bound of the number of zeros for Abelian integrals, from which the existence of limit cycles at most via the first-order Melnikov functions is determined. Finally, one example of double limit cycles for the latter case is given. 相似文献
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Asymptotic Behavior of a Stochastic Predator-prey Model with Beddington-DeAngelis Functional Response and L\''{e}vy Jumps 下载免费PDF全文
A stochastic two-prey-one-predator model with Beddington-DeAngelis functional response and L\''{e}vy jumps is proposed and investigated in this paper. First of all, we prove the existence and uniqueness of the global positive solution, and stochastic ultimate boundedness of the solution. Next, under a simple assumption, by using It\^{o} formula and other important inequalities, some sufficient conditions are established to ensure the extinction and persistence in the mean of the system. The results show that neither strong white noise nor L\''{e}vy noise is conducive to the persistence of the population. Finally, the theoretical results are verified by numerical simulations. 相似文献
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Huashui ZHAN 《数学年刊B辑(英文版)》2016,37(3):465-482
Consider the initial boundary value problem of the strong degenerate parabolic equation ?_(xx)u + u?_yu-?_tu = f(x, y, t, u),(x, y, t) ∈ Q_T = Ω×(0, T)with a homogeneous boundary condition. By introducing a new kind of entropy solution, according to Oleinik rules, the partial boundary condition is given to assure the well-posedness of the problem. By the parabolic regularization method, the uniform estimate of the gradient is obtained, and by using Kolmogoroff 's theorem, the solvability of the equation is obtained in BV(Q_T) sense. The stability of the solutions is obtained by Kruzkov's double variables method. 相似文献
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The Hopf cyclicities of some smooth polynomial, rational polynomial and piecewise smooth Li\''{e}nard systems are studied. For two Li\''{e}nard systems with the same damping term and different restoring (or potential) terms, we provide sufficient conditions that the two systems have the same Hopf cyclicity. Then, some examples are given to illustrate the efficiency and applicability of our results. 相似文献