含参集值向量均衡问题有效解下半连续的最优条件

在实Hausdorff拓扑向量空间中, 讨论含参集值向量均衡问题有效解下半连续的最优条件. 首先, 给出含参集值向量均衡问题的弱有效解、 Henig有效解、Global有效解、 超有效解和f-有效解的概念. 其次, 在近似锥-次类凸的基础上, 借助f-有效解的形式, 用凸集分离定理给出弱有效解、 Henig有效解、 Global有效解和超有效解的标量化结果. 最后, 在集值映射弱f-性的条件下, 建立含参集值向量均衡问题有效解下半连续的最优性定理.     

广义凸向量优化的Benson真有效性

在拟锥次类凸假设下,研究了局部凸Hausdorff拓扑向量空间中拟锥次类凸映射的向量优化问题。建立了向量优化的Benson真有效解和相应的标量化问题的最优解之间的关系,以及和相应的无约束向量极小化问题的Benson真有效解之间的关系。结果表明:第一,在一定条件下,向量优化的Benson真有效解与其相应的标量化问题的最优解等价;第二,在一定条件下,向量优化的Benson真有效解是其相应的无约束向量极小化问题的Benson真有效解。     

Benson真有效性的对偶特征

本简报指出：若是部凸空间中存在一个凸锥它既具紧基，又具非空内部，则该局部凸空间必为有限维的．利用局部凸空间的对偶理论，在不对序锥附近加其他条件的前提下，我们获得了Benson真有效点的对偶特征．由此，我们给出了几乎锥次凸状集值映照的向量优化问题的Benson真极小元的标量化定理．     

多域自然应力边界积分方程

文章通过对常规应力边界积分方程反复的分部积分,将应力表示成位移ui、面力ti及自然变量wi的积分形式,并推广到多域系统,建立了多域自然应力边界积分方程;该积分方程仅含几乎强奇异积分,同常规应力边界积分方程所含的几乎超奇异积分相比,奇异性降低了一阶;再利用正则化技术解析处理多域自然应力边界积分方程中的几乎强奇异积分,从而可以准确计算多域系统近边界内点的应力。     

几乎次亚可膨胀空间的逆极限性质

该文主要证明如下结果:设X=lim←{χα,παβ},λ=｜∧｜并且每个投射πα是开满映射.如果X是λ-仿紧的且每个Xα是几乎次亚可膨胀的,则X是几乎次亚可膨胀的.     

Experimental earth tidal models in considering nearly diurnal free wobble of the Earth''''s liquid core

Based on the 28 series of the high precision and high minute sampling tidal gravity observations at 20 stations in Global Geodynamics Project (GGP) network, the resonant parameters of the Earth's nearly diurnal free wobble (including the eigenperiods, resonant strengths and quality factots) are precisely determined. The discrepancy of the eigenperiod between observed and theoretical values is studied, the important conclusion that the real dynamic ellipticity of the liquid core is about 5% larger than the one under the static equilibrium assumption is approved by using our gravity technique. The experimental Earth's tidal gravity models with considering the nearly diurnal free wobble of the Earth's liquid core are constructed in this study. The numerical results show that the difference among three experimental models is less than 0.1%, and the largest discrepancy compared to those widely used nowdays given by Dehant (1999) and Mathews (2001) is only about 0.4%. It can provide with the most recent real     

Sparse representation of global features of visual images in human primary visual cortex: Evidence from fMRI

In fMRI experiments on object representation in visual cortex, we designed two types of stimuli： one is the gray face image and its line drawing, and the other is the illusion and its corresponding completed illusion. Both of them have the same global features with different minute details so that the results of fMRI experiments can be compared with each other. The first kind of visual stimuli was used in a block design fMRI experiment, and the second was used in an event-related fMRI experiment. Comparing and analyzing interesting visual cortex activity patterns and blood oxygenation level dependent （BOLD）- fMRI signal, we obtained results to show some invariance of global features of visual images. A plausible explanation about the invariant mechanism is related with the cooperation of synchronized response to the global features of the visual image with a feedback of shape perception from higher cortex to cortex V1, namely the integration of global features and embodiment of sparse representation and distributed population code.     

近拟常曲率空间中双重卷积子流形的不等式

利用代数引理和基本方程得到关于近拟常曲率流形双重卷积子流形的几何不等式,建立关于Ricci曲率和平均曲率的不等式,并讨论不等式中等号成立的条件.     

非线性变换在计算接近奇异积分中的应用

执行边界元方法的一个关键问题是接近奇异积分的快速精确计算.一般来说,经典的数值积分方法在执行边界元方法时是不能满足要求的.基于一类非线性变换,通过选择最优参数,提出了一种高效计算接近奇异积分的方法,数值试验证明这种算法是高效精确的.     

深埋超大断面局部近水平岩层结构垮塌失稳机理

针对深埋超大断面隧道穿越近水平岩层的围岩稳定性问题,建立了局部近水平岩层结构力学模型。认为局部岩层的垮塌失稳为掌子面后方应力重分布形成的均布竖向荷载,及水平荷载作用下结构力学模型的弯拉脆性破坏和剪切塑性屈服过程。通过针对依托工程验证了深埋超大断面隧道,建立局部近水平岩层结构力学模型,分析围岩垮塌失稳的合理性和可靠性;并提出了超大断面深埋隧道近水平围岩失稳后的合理处理措施。研究成果可为深埋超大断面隧道局部近水平岩层结构垮塌失稳及其治理提供理论支持。