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91.
Julia Hartmann Anne V. Shepler 《Transactions of the American Mathematical Society》2008,360(1):123-133
Steinberg showed that when a finite reflection group acts on a real or complex vector space of finite dimension, the Jacobian determinant of a set of basic invariants factors into linear forms which define the reflecting hyperplanes. This result generalizes verbatim to fields whose characteristic is prime to the order of the group. Our main theorem gives a generalization of Steinberg's result for groups with a polynomial ring of invariants over arbitrary fields using a ramification formula of Benson and Crawley-Boevey.
92.
Peter Vadovič 《Mathematica Slovaca》2008,58(4):509-520
We consider a special space of set-valued functions (multifunctions), the space of densely continuous forms D(X, Y) between Hausdorff spaces X and Y, defined in [HAMMER, S. T.—McCOY, R. A.: Spaces of densely continuous forms, Set-Valued Anal. 5 (1997), 247–266] and investigated also in [HOLá, L’.: Spaces of densely continuous forms, USCO and minimal USCO maps, Set-Valued Anal. 11 (2003), 133–151]. We show some of its properties, completing the results from the papers [HOLY, D.—VADOVIČ, P.: Densely continuous forms, pointwise topology and cardinal functions, Czechoslovak Math. J. 58(133) (2008), 79–92] and [HOLY, D.—VADOVIČ, P.: Hausdorff graph topology, proximal graph topology and the uniform topology for densely continuous forms and minimal USCO maps, Acta Math. Hungar. 116 (2007), 133–144], in particular concerning the structure of the space of real-valued locally bounded densely continuous forms
D
p
*(X) equipped with the topology of pointwise convergence in the product space of all nonempty-compact-valued multifunctions.
The paper also contains a comparison of cardinal functions on D
p
*(X) and on real-valued continuous functions C
p
(X) and a generalization of a sufficient condition for the countable cellularity of D
p
*(X).
This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-006904 and by the Eco-Net
(EGIDE) programme of the Laboratoire de Mathématiques de l’Université de Saint-Etienne (LaMUSE), France. 相似文献
93.
A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions
is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential
links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to
a uniform convergence structure so that the convergence space is complete. The important issue of the denseness of the subset
of all continuous functions is also addressed.
相似文献
94.
Alan Demlow. 《Mathematics of Computation》2007,76(257):19-42
We prove local a posteriori error estimates for pointwise gradient errors in finite element methods for a second-order linear elliptic model problem. First we split the local gradient error into a computable local residual term and a weaker global norm of the finite element error (the ``pollution term'). Using a mesh-dependent weight, the residual term is bounded in a sharply localized fashion. In specific situations the pollution term may also be bounded by computable residual estimators. On nonconvex polygonal and polyhedral domains in two and three space dimensions, we may choose estimators for the pollution term which do not employ specific knowledge of corner singularities and which are valid on domains with cracks. The finite element mesh is only required to be simplicial and shape-regular, so that highly graded and unstructured meshes are allowed.
95.
We study manifolds where the natural skew-symmetric curvature operator has pointwise constant eigenvalues. We give a local classification (up to isometry) of such manifolds in dimension 4. In dimension 3, we describe such manifolds up to a classification of three - dimensional Riemannian manifolds with principal Ricci curvatures r1 = r2 = 0, r3- arbitrary. We give examples of such manifolds in all dimensions which do not have constant sectional curvature; these manifolds are not pointwise Osserman manifolds in general. 相似文献
96.
Alejandro Allendes Gilberto Campaa Erwin Hernndez 《Mathematical Methods in the Applied Sciences》2019,42(10):3549-3567
We derive pointwise error estimates for a generalized Oseen when it is approximated by a low order Taylor‐Hood finite element scheme in two dimensions. The analysis is based on estimates for regularized Green's functions associated with a generalized Oseen problem on weighted Sobolev spaces and weighted interpolation results. We apply the maximum norm results to obtain convergence in an optimal control problem governed by a generalized Oseen equation and present a numerical example that allows us to show the behavior of the error. 相似文献
97.
98.
Numerical analysis for the approximation of optimal control problems with pointwise observations 下载免费PDF全文
Lili Chang Wei Gong Ningning Yan 《Mathematical Methods in the Applied Sciences》2015,38(18):4502-4520
In this paper, we study the numerical methods for optimal control problems governed by elliptic PDEs with pointwise observations of the state. The first order optimality conditions as well as regularities of the solutions are derived. The optimal control and adjoint state have low regularities due to the pointwise observations. For the finite dimensional approximation, we use the standard conforming piecewise linear finite elements to approximate the state and adjoint state variables, whereas variational discretization is applied to the discretization of the control. A priori and a posteriori error estimates for the optimal control, the state and adjoint state are obtained. Numerical experiments are also provided to confirm our theoretical results. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
99.
We offer an approach by means of Clifford algebra to convergence of Fourier series on unit spheres of even-dimensional Euclidean
spaces. It is based on generalizations of Fueter’s Theorem inducing quaternionic regular functions from holomorphic functions
in the complex plane. We, especially, do not rely on the heavy use of special functions. Analogous Riemann-Lebesgue theorem,
localization principle and a Dini’s type pointwise convergence theorem are proved.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
100.
具有内部点耗散的Timoshenko梁的能量衰减估计 总被引:1,自引:0,他引:1
研究具有反馈控制力的Timoshenko梁的能量衰减.证明了梁的能量不是一致衰减的.当梁的能量不是一致衰减时,利用初始值的正则性和无阻尼问题的最佳正则性结果,给出了多项式衰减估计. 相似文献