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1.
《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(5):1337-1371
In this paper we consider minimizers of the functional where is a bounded open set and where are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets have finite perimeter and that their free boundary is composed of a regular part, which is locally the graph of a -regular function, and a singular part, which is empty if , discrete if and of Hausdorff dimension at most if , for some . 相似文献
2.
Abstract
In this note, we consider a Frémond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is
fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining
part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under
the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global
attractor. More precisely, we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence
of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the
non-autonomous case by the limiting global attractor.
* Project supported by the MIUR-COFIN 2004 research program on “Mathematical Modelling and Analysis of Free Boundary Problems”. 相似文献
3.
Fiber-optic reflex sensor for in-line production measurement 总被引:1,自引:0,他引:1
The paper describes experiments concerning distance measurement with fiber-optic sensor and improvement of the measurement principle. The sensor probe was well-designed with a small structure and multi-function. The novel optical fiber probe arrangement as well as the possibilities of use for complex measurement problems are explained using the measurement of an internal screw thread as an example. The experimental results show that the measurement uncertainty of the thread minor diameter can reach ±10 μm, and the stability of the measurement system is better than 0.07%. 相似文献
4.
We investigate some topological properties of a normal functorH introduced earlier by Radul which is some functorial compactification of the Hartman-Mycielski construction HM. We prove
that the pair (H X, HMY) is homeomorphic to the pair (Q, σ) for each nondegenerated metrizable compactumX and each denseσ-compact subsetY. 相似文献
5.
Using spatially modulated illumination (SMI) light microscopy it is possible to measure the sizes of fluorescent structures that have an extension far below the conventional optical resolution limit (“subresolution size”). Presently, the sizes are determined as the object extension along the optical axis of the SMI microscope. For this, however, “a priori” assumptions on the fluorochrome distribution (“shape”) within the examined fluorescent structure have to be made. Usually it is assumed that the fluorochrome follows a Gauss-distribution or a spherical distribution. In this report we overcome the necessity to make an assumption on the shape of the fluorochrome distribution. We introduce two new experimentally obtained parameters which allow the determination of a shape measure to describe the spatial distribution of the fluorescent dye. This becomes possible by independent measurements with different excitation wavelengths. As an example, we present shape parameter measurements on individual fluorescent microspheres with a nominal geometrical diameter (“size”) of 190 nm. In the case investigated, the experimental shape correlated well with a homogeneous fluorochrome distribution (“spherical shape”) but not with a variety of other “shapes”. 相似文献
6.
Calibration of the relationship between height and phase is of uttermost importance to perform accurate 3D measurements in phase measurement profilometry. This work reports a different approach to this problem by first looking at the analytical expression for this relationship and determining the regime spanned by the fringe analysis method. The conclusions thus ascertained, amply justify confronting the analytical expression with a simple normalization procedure of the experimental data, with a remarkable matching between both results. In light of this, a linear calibration procedure with just one plane is proposed and verified experimentally. 相似文献
7.
C~k连续的保形分段2k次多项式插值 总被引:4,自引:0,他引:4
1.引言在每个子区间上,通过插入至多一个内结点,Brodlie和Butt[1]给出了分段三次多项式保形插值算法,Randal[2]等讨论了分段五次多项式插值,作者[31讨论了一般分段奇次多项式的保形插值,并且给1了内结点的位置范围公式.这种插值方法完全解决了一般的分段奇次多项式的保形插值问题.关于分段偶次多项式的保形插值,大多数文献只讨论分段二次保形插值,这里要特别指出的是Shumake[4j导出了二次样条保凸的充要条件,并且给出了一个二次样条保形插值的方法.在每一个子区间上至多插入一个内结点,则一个二次插值样条就可得到.作… 相似文献
8.
The present study is concerned with the determination of the optimal shape for a package containing multiple heating elements.
The optimization tool has been developed based on the inverse heat transfer (IHT) approach, incorporating a direct problem
solver, a numerical grid generator, a direct-differentiation sensitivity analyzer, and the conjugate gradient method. Shape
design that leads to a specified outer surface temperature distribution is predicted by the approach. In this study, the effects
of internal heat generation on optimal shapes of the packagings have also been evaluated. Several practical cases with various
imbedded heating elements and thermal conditions are studied. Results show that the approach provides an efficient computer-aided
design scheme for the shape profile determination. 相似文献
9.
J. Haslinger T. Kozubek K. Kunisch G. Peichl 《Journal of Mathematical Analysis and Applications》2004,290(2):665-685
This contribution combines a shape optimization approach to free boundary value problems of Bernoulli type with an embedding domain technique. A theoretical framework is developed which allows to prove continuous dependence of the primal and dual variables in the resulting saddle point problems with respect to the domain. This ensures the existence of a solution of a related shape optimization problem in a sufficiently large class of admissible domains. 相似文献
10.
通过非球面的零位补偿法,完成了对矩形大口径离轴非球面镜的检测。先用光学设计软件Zemax从理论上分析了在检测中会出现的现象,并结合计算机辅助装调技术,确定在检测过程中相对敏感的自由度,然后控制这些量,使补偿器和非球面的相对关系与理论设计相吻合,在Zygo相位干涉仪上测得最终结果。在λ=632.8nm时,中心圆口径与两个边缘圆口径面形误差RMS分别为0.022λ,0.037λ,0.032λ。检测结果,达到预期目的。 相似文献