共查询到20条相似文献,搜索用时 109 毫秒
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蔡志杰 《数学建模及其应用》2019,(1)
建立了热防护服系统的偏微分方程模型,给出了适当的初始条件、边界条件及交界面条件,采用隐式差分格式进行计算.在此基础上,建立了热防护服最优参数设计的优化模型,采用二分法求解.最后对2018年"高教社杯"全国大学生数学建模竞赛A题的参赛论文予以评述. 相似文献
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把人体对酒精的吸收、排放简化为一般的房室模型,提出了吸收因子、消除因子的概念.针对短时间饮酒、长时间饮酒以及间断饮酒等情况,分别建立了关于人体体液中酒精浓度的微分方程模型,并且给出了显式解.对于特殊的周期性间断饮酒的模型,给出了更便于计算的叠加公式,并通过分析酒精浓度函数的极限过程,证明了其有界性.对短时间饮酒和长时间饮酒的情况分别计算了酒精浓度的最大值、取得最大值的时间和禁止驾车的时间范围,而且进行了比较,所得结论与实际吻合. 相似文献
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研究有界区域上的n维拟线性椭圆方程组的挠射问题,其中方程的系数在交界面上允许间断,而且交界面允许与区域外边界相交.通过构造一个交界面与外边界不相交的近似挠射问题,利用估计和逼近方法,并讨论弱解的正则性,得到了问题解的存在性,并将这些结果应用到两种群Lotka-Volterra互惠模型. 相似文献
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《数学物理学报(A辑)》2018,(6)
研究一类具广义非线性源的非线性波动方程的初边值问题在高初始能级状态下解的有限时间爆破.利用经典的凹函数方法找到了导致该问题具任意正初始能级的解有限时间爆破的初值. 相似文献
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将单层Kidder自相似解推广到双层,使得两层壳体的交界面两侧存在密度跳跃,使得轻流体向重流体加速产生Rayleigh-Taylor不稳定性;通过采用Lagrange坐标下的Godunov方法进行一维直接数值模拟,将模拟解与双层Kidder自相似基本解进行比较,验证了双层Kidder自相似解的可靠性;最后,通过编制球形内爆的三维扰动的线性稳定性分析程序,对双层Kidder自相似解的Rayleigh-Taylor不稳定性进行了分析计算.计算结果表明:初始扰动越集中于交界面,会造成后期扰动增长得越快,越不稳定;扰动波数越大,扰动增长得越快,越不稳定;从扰动在空间上的发展来看,可压缩性研究表明内外壳体的可压缩性对扰动增长起着相反的作用,外层壳体的可压缩性对Rayleigh-Taylor不稳定起失稳作用,而内层壳体的可压缩性对Rayleigh-Taylor不稳定起致稳作用. 相似文献
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近日参加无锡市组织的教研活动,听取了七位青年教师的课堂教学情况,课题是苏科版八(上)"6.3一次函数的图像(1)",其中有五位教师(以下称A)选择课本上面的生活情境引出初始问题(注:导致数学知识产生的问题),有二位教师(以下称B)选择前面已学的函数图像引出初始问题,都取得了较好的教学效果,达成了预设的课堂教学目标.但他们的课堂引入初始问题,引发了笔者的一些思考和看法,觉得数学的课堂引入:既要选 相似文献
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Complicated Asymptotic Behavior of Solutions for the Cauchy Problem of Doubly Nonlinear Diffusion Equation
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In this paper, we analyze the large time behavior of nonnegative solutions to the doubly nonlinear diffusion equation $$u_t−{\rm div}(|∇u^m|^{p−2}∇u^m)=0$$ in $\mathbb{R}^N$ with $p>1,$ $m>0$ and $m(p−1)−1>0.$ By using the finite propagation property and the $L^1-L^∞$ smoothing effect, we find that the complicated asymptotic behavior of the rescaled solutions $t^{\mu/2}u(t^{β_·},t)$ for $0<\mu<2N/(N[m(p−1)−1]+p)$ and $β>(2−\mu[m(p−1)−1])/(2p)$ can take place. 相似文献
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《复变函数与椭圆型方程》2012,57(2):131-141
We find sharp upper bounds for $ \vert \,f^{\prime \prime }(z)/f^{\prime }(z) \vert $ such that the function f be starlike or strongly-starlike of a given order, where f is holomorphic in the unit disc U , with $ f(0)=f^{\prime }(0)-1=0 $ . These bounds are obtained by using the differential subordination technique. As a useful ingredient we obtain the radius of convexity for the function $ F(z)= z /(\exp (z)-1) $ 相似文献
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Yijing Sun & Xing Liu 《偏微分方程(英文版)》2012,25(2):187-198
In this paper,we consider the following Kirchhoff type problemwith critical exponent $-(a+b∫_Ω|∇u|^2dx)Δu=λu^q+u^5, in\ Ω, u=0, on\ ∂Ω$, where $Ω⊂R^3$ is a bounded smooth domain, $0< q < 1$ and the parameters $a,b,λ > 0$. We show that there exists a positive constant $T_4(a)$ depending only on a, such that for each $a > 0$ and $0 < λ < T_4(a)$, the above problem has at least one positive solution. The method we used here is based on the Nehari manifold, Ekeland's variational principle and the concentration compactness principle. 相似文献
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A Relaxed Approximate Proximal Point Algorithm 总被引:1,自引:0,他引:1
For a maximal monotone operator T, a well-known overrelaxed point algorithm is often used to find the zeros of T. In this paper, we enhance the algorithm to find a point in
, where
is a given closed convex set. In the inexact case of our modified relaxed proximal point algorithm, we give a new criterion.
The convergence analysis is quite easy to follow. 相似文献
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Let $\{P_n(x) \}_{n=0}^\infty$ be an orthogonal polynomial system
relative to a compactly supported measure. We find
characterizations for $\{P_n(x) \}_{n=0}^\infty$ to be a
Bochner--Krall orthogonal polynomial system, that is, $\{P_n(x)
\}_{n=0}^\infty$ are polynomial eigenfunctions of a linear
differential operator of finite order. In particular, we show that
$\{P_n(x) \}_{n=0}^\infty$ must be generalized Jacobi polynomials
which are orthogonal relative to a Jacobi weight plus two point
masses. 相似文献
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We concern with fast domain decomposition methods for solving the total
variation minimization problems in image processing. By decomposing the image
domain into non-overlapping subdomains and interfaces, we consider the primal-dual problem on the interfaces such that the subdomain problems become independent problems and can be solved in parallel. Suppose both the interfaces and
subdomain problems are uniformly convex, we can apply the acceleration method
to achieve an $\mathcal{O}(1 / n^2)$ convergent domain decomposition algorithm. The convergence analysis is provided as well. Numerical results on image denoising, inpainting, deblurring, and segmentation are provided and comparison results with existing
methods are discussed, which not only demonstrate the advantages of our method
but also support the theoretical convergence rate. 相似文献
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Nearest polynomial with given properties has many applications in control theory and applied mathematics. Given a complex univariate polynomial f(z) and a zero α, in this paper we explore the problem of computing a complex polynomial f(z) such that f(α) = 0 and the distance ∥f-f ∥ is minimal. Considering most of the existing works focus on either certain polynomial basis or certain vector norm, we propose a common computation framework based on both general polynomial basis and general vector norm, and summarize the computing process into a four-step algorithm. Further, to find the explicit expression of f(z), we focus on two specific norms which generalize the familiar lp-norm and mixed norm studied in the existing works, and then compute f(z) explicitly based on the proposed algorithm. We finally give a numerical example to show the effectiveness of our method. 相似文献
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Ying-Guang Shi 《计算数学(英文版)》1983,1(3):243-246
Let $P,Q \subset L_1(X,\Sigma,\mu)$ and $q(x)>0$ a. e. in $X$ for all $q\in Q$. Define $R=\{p/q:p\in P,q\in Q\}$. In this paper we discuss an $L_1$ minimization problem of a nonnegative function $E(z,x)$, i.e. we wish to find a minimum of the functional $\phi(r)=\int _X qE(r,x)d\mu$ form $r=p/q\in R$. For such a problem we have established the complete characterizations of its minimum and of uniqueness of its minimum, when both $P,Q$ are arbitrary convex subsets. 相似文献
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YoungJu Choie Patrick Solé 《Proceedings of the American Mathematical Society》2002,130(11):3125-3131
In this paper, we find a connection between the weight enumerator of self-dual codes and half-integral weight modular forms. We generalize in that way results of Broué-Enguehard, Hirzebruch, Ozeki, Rains-Sloane, Runge.