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981.
Y. Kaya 《Siberian Mathematical Journal》2006,47(3):452-458
Let f: M m → ? m+1 be an immersion of an orientable m-dimensional connected smooth manifold M without boundary and assume that ξ is a unit normal field for f. For a real number t the map f tξ: M m → ? m+1 is defined as f tξ(p) = f(p) + tξ(p). It is known that if f tξ is an immersion, then for each p ∈ M the number of the focal points on the line segment joining f(p) to f tξ(p) is a constant integer. This constant integer is called the index of the parallel immersion f tξ and clearly the index lies between 0 and m. In case f: $\mathbb{S}^m \to \mathbb{R}^{m + 1} $ is an immersion, we study the presence of a component of index μ in the push-out space Ω(f). If there exists a component with index μ = m in Ω(f) then f is known to be a strictly convex embedding of $\mathbb{S}^m $ . We reveal the structure of Ω(f) when $f(\mathbb{S}^m )$ is convex and nonconvex. We also show that the presence of a component of index μ in Ω(f) enables us to construct a continuous field of tangent planes of dimension μ on $\mathbb{S}^m $ and so we see that for certain values of μ there does not exist a component of index μ in Ω(f). 相似文献
982.
For an arbitrary n-dimensional Riemannian manifold N and an integer m ∈ {1,…,n−1} a covariant derivative
on the Grassmann bundle ^ := Gm(T N) is introduced which has the property that an m-dimensional submanifold M ⊂ N has parallel second fundamental form if and only if its Gauss map M → ^ is affine. (For N Rn this result was already obtained by J. Vilms in 1972.) By means of this relation a generalization of Cartan's theorem on
the total geodesy of a geodesic umbrella can be derived: Suppose, initial data (p,W,b) prescribing a tangent space W ∈ Gm(TpN) and a second fundamental form b at p ∈ N are given; for these data we construct an m-dimensional ‘umbrella’ M = M(p,W,b) ⊂ N the rays of which are helical arcs of N; moreover, we present tensorial conditions (not involving
) which guarantee that the umbrella M has parallel second fundamental form. These conditions are as well necessary, and locally every submanifold with parallel
second fundamental form can be obtained in this way.
Mathematics Subject Classifications (2000): 53B25, 53B20, 53B21. 相似文献
983.
Hans De Sterck Stephanie Friedhoff Alexander J. M. Howse Scott P. MacLachlan 《Numerical Linear Algebra with Applications》2020,27(1)
Parallel‐in‐time algorithms have been successfully employed for reducing time‐to‐solution of a variety of partial differential equations, especially for diffusive (parabolic‐type) equations. A major failing of parallel‐in‐time approaches to date, however, is that most methods show instabilities or poor convergence for hyperbolic problems. This paper focuses on the analysis of the convergence behavior of multigrid methods for the parallel‐in‐time solution of hyperbolic problems. Three analysis tools are considered that differ, in particular, in the treatment of the time dimension: (a) space–time local Fourier analysis, using a Fourier ansatz in space and time; (b) semi‐algebraic mode analysis, coupling standard local Fourier analysis approaches in space with algebraic computation in time; and (c) a two‐level reduction analysis, considering error propagation only on the coarse time grid. In this paper, we show how insights from reduction analysis can be used to improve feasibility of the semi‐algebraic mode analysis, resulting in a tool that offers the best features of both analysis techniques. Following validating numerical results, we investigate what insights the combined analysis framework can offer for two model hyperbolic problems, the linear advection equation in one space dimension and linear elasticity in two space dimensions. 相似文献
984.
LQP交替方向法是求解可分离结构型单调变分不等式问题的一种非常有效的方法.它不仅可以充分地利用目标函数的可分结构,将原问题分解为多个更易求解的子问题,还更适合求解大规模问题.对于带有三个可分离算子的单调变分不等式问题,结合增广拉格朗日算法和LQP交替方向法提出了一种部分并行分裂LQP交替方向法,构造了新算法的两个下降方向,结合这两个下降方向得到了一个新的下降方向,沿着这个新的下降方向给出了最优步长.并在较弱的假设条件下,证明了新算法的全局收敛性. 相似文献
985.
986.
讨论了广义周期七对角矩阵的求逆问题,利用七对角矩阵的特殊结构,通过矩阵的广义LU分解,给出了一种求解广义周期七对角逆矩阵的新型算法,该算法不需要对矩阵的各阶顺序主子式做任何限制并且适用于多种计算机代数系统,如:Mathematics,Macsyma,Matlab和Maple等.最后通过算例来说明了算法的有效性。 相似文献
987.
988.
989.
Joohee Mun Yong‐Hak Kim Jonghan Yu Jinhee Bae Dong‐Young Noh Myeong‐Hee Yu Cheolju Lee 《Electrophoresis》2010,31(20):3428-3436
Autoantibodies obtained from cancer patients have been identified as useful tools for cancer diagnostics, prognostics, and as potential targets for immunotherapy. Serological proteome analysis in combination with 2‐DE is a classic strategy for identification of tumor‐associated antigens in the serum of cancer patients. However, serological proteome analysis cannot always indicate the true antigen out of a complex proteome identified from a single protein spot because the most abundant protein is not always the most antigenic. To address this problem, we utilized multiple parallel separation (MPS) for proteome separation. The common identities present in the fractions obtained using different separation methods were regarded as the true antigens. The merit of our MPS technique was validated using anti‐ARPC2 and anti‐PTEN antibodies. Next, we applied the MPS technique for the identification of glycyl‐tRNA synthetase as the cognate antigen for an autoantibody that was overexpressed in the plasma of breast cancer patients. These results reveal that MPS can unambiguously identify an antibody cognate antigen by reducing false‐positives. Therefore, MPS could be used for the characterization of diagnostic antibodies raised in laboratory animals as well as autoantibodies isolated from diseased patients. 相似文献
990.